In the order I discovered them:
Peace, Freedom, Focus and Love
1) Peace
In 2003 sat in the chapel of St Serf in Lichfield cathedral I realised the importants of peace. Peace is calm and harmony. It is opposed in every way to conflict and disharmony. In this sense it is not "opposed" to conflict but rather seeks to avoid conflict, agression or disagreement. It is the state of tolerance and acceptance and if characterised by stillness and ease within oneself. This should be sort in every dealing with the world, others and oneself.
2) Freedom
Last year I realised the importants of freedom. Freedom seeks to escape the control of desires and controlling forces. It seeks for a self which interacts with the world in honesty and truth without the demands of controlling desires which corrupt. It seeks especially to deal with others in a way which promotes ease and the opportunity for others to be themselves.
3) Focus
This is the essence of mind. Mind occurs where there is focus upon an object and strength of focus gives one strength of mind to master its objects and see them for what they are. A focused mind should seek to instill focus, sincerity and truth into everything that it allies itself to, and to master distraction which is the source of non-mind and ultimately all wrongs.
4) Love
Love is the appreciation of others and our acceptance that we need others and cannot exist without them. It is not a weakness but the strength to accept our dependence on others and the world. It seeks to promote the well being of others and to make its relations with others fullfilling and joyful.
With these perfected life is good.
Friday, 21 December 2007
Tuesday, 18 December 2007
Theory of everything
http://freeinternetpress.com/story.php?sid=14658
The more I think about tis problem the more I realise (like with so many things I have attempted) that I know nothing and can't even get on the ladder of the problem. Its at least supportive to see scientists beings just as naive as I am :-)
So far in the quest for a proof that "a definite fundamental truth is a contradiction" I've got stuck on self-reference which is the most likely place where a fixed truth is likely to defeat itself.
A self-reference does 2 things.
1) its refers to itself
2) and it refers to something which refers to itself.
Now I can't seem to resolve this issue.
"I have 4 words"
meets condition 1 since it refers to the sentence which is doing the referring. But does it meet condition 2? If it doesn't meet condition 2 then condition 1 must also fail, and if it does meet condition 2 then it must meet condition 1 ... but while 2 implies 1, 1 does not imply 2!
and is there the loop problem here... that it needs to refer not to itself, but to the self-reference itself...
4 some reason this is escaping my grey matter... altho it is Xmas and I'm distracted with presents and stuff...
also distracted by a catrastrophy at work... I lost all the company backup data last week. This is the worst thing I've ever done I think, but I've learned a lot. "What doesn't kill you only makes you stronger" has a corollary... if u want to be strong then nothing must kill you ;-) So I had a few sleepless nights and struggled through and hopefully this will be ok in the end.
Strangely I didn't get that awareness of the universe being a vast wheel with our lives and the events of the world just occuring for short periods of its rotation... like I did when my father died. Instead I began to realise the enormilty of the universe "outside" our sphere of influence. That while I am confident in IT events can transpire against me and I took too many risks with the data and the events did transpire in a very unlikely way. Hubris is what it is called and its the lack of humility at the size of the universe and the way that humans are extremely dependent on good conditions for their well being. There is the growing doom I feel for the human race as a whole... I've always known we were heading for destruction, but the frustration I used to feel and the resignation to our fate seems to have got more ingrained. Hubris.
The more I think about tis problem the more I realise (like with so many things I have attempted) that I know nothing and can't even get on the ladder of the problem. Its at least supportive to see scientists beings just as naive as I am :-)
So far in the quest for a proof that "a definite fundamental truth is a contradiction" I've got stuck on self-reference which is the most likely place where a fixed truth is likely to defeat itself.
A self-reference does 2 things.
1) its refers to itself
2) and it refers to something which refers to itself.
Now I can't seem to resolve this issue.
"I have 4 words"
meets condition 1 since it refers to the sentence which is doing the referring. But does it meet condition 2? If it doesn't meet condition 2 then condition 1 must also fail, and if it does meet condition 2 then it must meet condition 1 ... but while 2 implies 1, 1 does not imply 2!
and is there the loop problem here... that it needs to refer not to itself, but to the self-reference itself...
4 some reason this is escaping my grey matter... altho it is Xmas and I'm distracted with presents and stuff...
also distracted by a catrastrophy at work... I lost all the company backup data last week. This is the worst thing I've ever done I think, but I've learned a lot. "What doesn't kill you only makes you stronger" has a corollary... if u want to be strong then nothing must kill you ;-) So I had a few sleepless nights and struggled through and hopefully this will be ok in the end.
Strangely I didn't get that awareness of the universe being a vast wheel with our lives and the events of the world just occuring for short periods of its rotation... like I did when my father died. Instead I began to realise the enormilty of the universe "outside" our sphere of influence. That while I am confident in IT events can transpire against me and I took too many risks with the data and the events did transpire in a very unlikely way. Hubris is what it is called and its the lack of humility at the size of the universe and the way that humans are extremely dependent on good conditions for their well being. There is the growing doom I feel for the human race as a whole... I've always known we were heading for destruction, but the frustration I used to feel and the resignation to our fate seems to have got more ingrained. Hubris.
Monday, 10 December 2007
Thursday, 6 December 2007
Colour and self-reference
There are 2 ways to get orange. The colour with frequency between 585 – 620 nm and a mixture of red and yellow pigments which averages to that frequency.
The reason that this works is that the eye has a limited resolution. There are 3 types of retina cell: red, green and blue. A mozaic of tiny red and yellow particles activates the red and green cells exactly the same as particles in the orange frequency range above. (Yellow itself lies between the red and green).
We can study a subjects neuron excitement to watch how this occurs. Clearly the red, green and blue neuron pathways must be distinct for were they to cross before colour processing had ocurred the distinction would be lost.
It remains though that there is nothing different between red, green and blue colour pathways other than the frequency at which the end receptor activates. All the brain - so to speak - knows of the end receptors colour preference is whether it has fired or not.
Structuralists have a good way of explaining how the brain comes to "know" what it is looking at. Knowledge is held in language. We learn our language in association with all the brain activity. Naturally then we use the words for red, orange and whatever in the situations in which they are properly used and so it is a circular argument that we "see" red when our "red" neurons fire because that is the situation in which we use the word red.
Given the huge range of neuron states in our colour system this analysis also suggests we could have many more colours were our language and culture to demand it. Indigo i understand is recent colour. To "see" a new colour just find a situation in which is occurs and give that a name. Soon enough there will be a new colour!
That seems to be the brain all wrapped up, and the old issue of "conscious experience" evaporates in a simple explanation of culture and word use. We "see" what is established by our normative environment.
However can we really use this explanation to refer to our "own" experience. It is not a simple matter of taking what is objectivel known and just imagining it applies to us.
At any moment as we try to explain what is happening in our minds we are also changing what is happening in our minds. It is impossible to actually pick out a moment of experience and at the same time, think what that is (objectively) without changing it.
We do an experiment to see what neurons are activated when we look at the colour red. But to see the MRI scan we obviously can't look at the colour red. Maybe we can record the MRI scan and press a button to say when we are looking at the colour. But then we need to record our own experience to compare with the MRI later.
If we focus on red, then we are focused on red and it is no-longer and objective process of knowledge and language, but rather a state of mind called "looking". To be able to look, the actual experience of being a mind, is not like the knowledge we might have of it. The knowledge does not capture the experience of being a mind.
This becomes more obvious if we "think" about the neuron processes behind thinking itself. The familiar hall of mirrors of self-reference open up.
If we are "truely" a collection of activating neurons, then is this the "thought" created by a collection of activating neurons or the "real" collection of activating neurons.
Saying that thoughts are identical with neuron systems, is then both a thought and a neuron system. So that statement is both a thought and a neuron system, and neither!
The reason that this works is that the eye has a limited resolution. There are 3 types of retina cell: red, green and blue. A mozaic of tiny red and yellow particles activates the red and green cells exactly the same as particles in the orange frequency range above. (Yellow itself lies between the red and green).
We can study a subjects neuron excitement to watch how this occurs. Clearly the red, green and blue neuron pathways must be distinct for were they to cross before colour processing had ocurred the distinction would be lost.
It remains though that there is nothing different between red, green and blue colour pathways other than the frequency at which the end receptor activates. All the brain - so to speak - knows of the end receptors colour preference is whether it has fired or not.
Structuralists have a good way of explaining how the brain comes to "know" what it is looking at. Knowledge is held in language. We learn our language in association with all the brain activity. Naturally then we use the words for red, orange and whatever in the situations in which they are properly used and so it is a circular argument that we "see" red when our "red" neurons fire because that is the situation in which we use the word red.
Given the huge range of neuron states in our colour system this analysis also suggests we could have many more colours were our language and culture to demand it. Indigo i understand is recent colour. To "see" a new colour just find a situation in which is occurs and give that a name. Soon enough there will be a new colour!
That seems to be the brain all wrapped up, and the old issue of "conscious experience" evaporates in a simple explanation of culture and word use. We "see" what is established by our normative environment.
However can we really use this explanation to refer to our "own" experience. It is not a simple matter of taking what is objectivel known and just imagining it applies to us.
At any moment as we try to explain what is happening in our minds we are also changing what is happening in our minds. It is impossible to actually pick out a moment of experience and at the same time, think what that is (objectively) without changing it.
We do an experiment to see what neurons are activated when we look at the colour red. But to see the MRI scan we obviously can't look at the colour red. Maybe we can record the MRI scan and press a button to say when we are looking at the colour. But then we need to record our own experience to compare with the MRI later.
If we focus on red, then we are focused on red and it is no-longer and objective process of knowledge and language, but rather a state of mind called "looking". To be able to look, the actual experience of being a mind, is not like the knowledge we might have of it. The knowledge does not capture the experience of being a mind.
This becomes more obvious if we "think" about the neuron processes behind thinking itself. The familiar hall of mirrors of self-reference open up.
If we are "truely" a collection of activating neurons, then is this the "thought" created by a collection of activating neurons or the "real" collection of activating neurons.
Saying that thoughts are identical with neuron systems, is then both a thought and a neuron system. So that statement is both a thought and a neuron system, and neither!
Wednesday, 5 December 2007
The other path
At 2pm 10 years ago i said yes to what I discovered less than an hour later was certain disaster. I fell in profoundly in love with a teenager based upon a look, a joke and a discussion about poetry and the moon. Then she said she had homework to complete and my heart sank... I already knew this was impossible.
If I put down my hopes and dreams for one goddamn minute there is no mystery to any of this. The world is fractured and there is no pure path through it. In her new world there were two things sex and friendship. Frustrated by my lack of physical exertion within only a matter of months I was designated best friend forever... and that was it... forever!
In my world there were 3 designations. Sex - that which prostitutes are smart enough to get paid for, friendship that which ignored sex, and love which was supposed to be a physical-spiritual communion joining both body and mind. Love however means commitment, the end of freedom, a bondage and ultimately children, marriage and family. She knew this, she avoided this until the year before she died.
My project is a myth. The great mistake was to join my spiritual path to my sexual path. I believed until yesterday that both could be completed together. Through physical intimacy a communication and sharing between souls might be possible that would evaporate the self - that two might really become one... a death of the individual and a birth of something new. That orgasm was a tool to trigger release from self-attachment etc etc.
You and me
When we touch:
Where?
My hopes seemed almost to materialise except for one thing... she did not understand. There was only sex and friendship.
That said except for whatever happened between us, she remained loyal to her lover for 2 years, saying that when she was with him she didn't want to be anywhere else. Pretty good at her age! I've never experienced that, except with her. So there was more than sex for her, but it was not love... she always said she didn't believe in love. Quite what that chimera was - may be something substatial or maybe just momentary indulgences - remains a mystery to me.
But for me combining a spiritual and sexual path was a disaster. I lost one and so I lost the other. The spiritual path is not contingent. You do not need to complete something, or have some conditions arise before you can embark upon it, it is always possible and available. That is the beauty of spiritual realisation: it is not conditional, and, thus is flawless and indestructable. Sexual experience on the other hand is fraught with conditions: ones own state of mind, that of the other, physical health, opportunity, morality and good luck. She has died now: if that does not demonstrate the imperfection of physical existence then nothing will.
She was psychic. That was another level of confusion. Being able to see and speak to ghosts is not a spiritual capability, it is psychic. It is quite a different sort of energy. It is a often a by product of spiritual practice, but something to ignore on the spiritual path.
Friday last I dreamt of her father. He told me to behave myself and treat his wife and remaining daughter with respect. The following night, the eve of first ever seeing "my muse", she appeared in a dream and basically told me with little sympathy to get my act together. Strange that I needed her to tell me to move on (rather than the usual telling ghosts to move on) but it has been good and has evaporated remaining sentimentality and attachment to my dreams.
Dreams can come true, but they can also not come true and then what of them? The simple reality is that I should have become physically intimate when I had the chance. Ignored the morality of it, ignored her boyfriends feelings (which I found out much later were trivial anyway), trusted her to take her own path on life and make her own choices, risked inviting her into a fools paradise, and not demanded love or deeper spiritual connections before embarking. What is the worst that could have happened? wasted my most profound desires on a trivial sexual fling? maybe that way I would have got to where i am now much quicker! The realisation that there is nothing profound in worldly communion of any type. It all leads to death. Accepting her friendship, while it seemed to noble thing, was a fools move. If I loved, then it should be love, if i desired then it should be sex, and while friendship was there and I miss her very much, the distractions of the other things were greater.
All that said there is nothing to worry about in Earth bound relationships and life. It is fantastic and often highly beautiful and there to be enjoyed. But that road if you follow it to its end leads no where. The ride stops and we need to get off - always in the hall of earthly things.
Instead i now return (hopefully reinvigorated) 10 years late to the spiritual path. Recent investigations have pushed closer to realising that "self-reference is impossible". For the self this means that the path of trying to discover what it itself is is fundamentally flawed. We can never know ourselves in essence. Instead we can only "be" ourselves.
and that links to dhyana - the essence of mind which is "focus" or more often translated as meditation... but really it is focus. Focus on something and other things go. Focus very deeply on something and that process continues until everything else goes but what you focus on. That way the mind is "concentrated" (pardon the pun) and comes to know itself truely. Mind - the nature of all things - is present in all things - and knowing mind liberates us from all things. That is the spiritual path. I must have been on the path in passed lives, indeed I must have met "my muse" in passed live, but hopefully the latter is now ended and my last words to her "see you in another life" fall upon deaf ears, and instead i continue the fruitful spiritual path into future lives.
At 2pm today I will say "no" and take the most important other path that was available on 5th December 2007.
If I put down my hopes and dreams for one goddamn minute there is no mystery to any of this. The world is fractured and there is no pure path through it. In her new world there were two things sex and friendship. Frustrated by my lack of physical exertion within only a matter of months I was designated best friend forever... and that was it... forever!
In my world there were 3 designations. Sex - that which prostitutes are smart enough to get paid for, friendship that which ignored sex, and love which was supposed to be a physical-spiritual communion joining both body and mind. Love however means commitment, the end of freedom, a bondage and ultimately children, marriage and family. She knew this, she avoided this until the year before she died.
My project is a myth. The great mistake was to join my spiritual path to my sexual path. I believed until yesterday that both could be completed together. Through physical intimacy a communication and sharing between souls might be possible that would evaporate the self - that two might really become one... a death of the individual and a birth of something new. That orgasm was a tool to trigger release from self-attachment etc etc.
You and me
When we touch:
Where?
My hopes seemed almost to materialise except for one thing... she did not understand. There was only sex and friendship.
That said except for whatever happened between us, she remained loyal to her lover for 2 years, saying that when she was with him she didn't want to be anywhere else. Pretty good at her age! I've never experienced that, except with her. So there was more than sex for her, but it was not love... she always said she didn't believe in love. Quite what that chimera was - may be something substatial or maybe just momentary indulgences - remains a mystery to me.
But for me combining a spiritual and sexual path was a disaster. I lost one and so I lost the other. The spiritual path is not contingent. You do not need to complete something, or have some conditions arise before you can embark upon it, it is always possible and available. That is the beauty of spiritual realisation: it is not conditional, and, thus is flawless and indestructable. Sexual experience on the other hand is fraught with conditions: ones own state of mind, that of the other, physical health, opportunity, morality and good luck. She has died now: if that does not demonstrate the imperfection of physical existence then nothing will.
She was psychic. That was another level of confusion. Being able to see and speak to ghosts is not a spiritual capability, it is psychic. It is quite a different sort of energy. It is a often a by product of spiritual practice, but something to ignore on the spiritual path.
Friday last I dreamt of her father. He told me to behave myself and treat his wife and remaining daughter with respect. The following night, the eve of first ever seeing "my muse", she appeared in a dream and basically told me with little sympathy to get my act together. Strange that I needed her to tell me to move on (rather than the usual telling ghosts to move on) but it has been good and has evaporated remaining sentimentality and attachment to my dreams.
Dreams can come true, but they can also not come true and then what of them? The simple reality is that I should have become physically intimate when I had the chance. Ignored the morality of it, ignored her boyfriends feelings (which I found out much later were trivial anyway), trusted her to take her own path on life and make her own choices, risked inviting her into a fools paradise, and not demanded love or deeper spiritual connections before embarking. What is the worst that could have happened? wasted my most profound desires on a trivial sexual fling? maybe that way I would have got to where i am now much quicker! The realisation that there is nothing profound in worldly communion of any type. It all leads to death. Accepting her friendship, while it seemed to noble thing, was a fools move. If I loved, then it should be love, if i desired then it should be sex, and while friendship was there and I miss her very much, the distractions of the other things were greater.
All that said there is nothing to worry about in Earth bound relationships and life. It is fantastic and often highly beautiful and there to be enjoyed. But that road if you follow it to its end leads no where. The ride stops and we need to get off - always in the hall of earthly things.
Instead i now return (hopefully reinvigorated) 10 years late to the spiritual path. Recent investigations have pushed closer to realising that "self-reference is impossible". For the self this means that the path of trying to discover what it itself is is fundamentally flawed. We can never know ourselves in essence. Instead we can only "be" ourselves.
and that links to dhyana - the essence of mind which is "focus" or more often translated as meditation... but really it is focus. Focus on something and other things go. Focus very deeply on something and that process continues until everything else goes but what you focus on. That way the mind is "concentrated" (pardon the pun) and comes to know itself truely. Mind - the nature of all things - is present in all things - and knowing mind liberates us from all things. That is the spiritual path. I must have been on the path in passed lives, indeed I must have met "my muse" in passed live, but hopefully the latter is now ended and my last words to her "see you in another life" fall upon deaf ears, and instead i continue the fruitful spiritual path into future lives.
At 2pm today I will say "no" and take the most important other path that was available on 5th December 2007.
Tuesday, 4 December 2007
Home
I have returned finally to an enquiry that "my muse" in many ways upset, the search for Home. Love is extremely tempting for it offers us the sense of being profoundly found. I have felt profoundly lost since losing her: unsettled, unstable, chaotic, insecure, panic attacks etc - I imagine this is the most unpleasant experience. Finding ones destiny in employment, or in life's application, can also be profound I am sure. The sense of peace that comes when the soul knows its place in the world and can rest upon the life it has found is the goal. This has always eluded me. If there was one destiny I knew I had it was to meet this girl. But that is done and the story told. There is no peace, or so it would seem.
But I persist in this knowledge of maybe something deeper. The problem with "getting what you want" is that you will fear forever losing it, unless that is you can satisfy that desire and be free from it... and there's the rub... its the being free from it that counts... that is why we want it. Not having what we want is suffering. The soul hurts. The more we need it the more our soul hurts. "My muse" was to play the deepest role in my souls life... through her I would unravel the mysteries of my relations with the outer world, the mysteries of sexual desire, the mysteries of birth and life - through her I would be able to live. Without her I would die, which is how it feels. Ironically her death in many ways seems the easier path; for i am the walking dead, the souless.
But not to despair for this is the other side of the same coin. If I cannot walk this path, I am not worthy to walk the other path of having what I most desire. Do I suffer because lacked the courage to take what i wanted most dearly, or do I suffer because I had the courage to face what I feared most. I have been unable to decide on that. Certainly what i have done has been madness and reckless by any imagination, but i knew i would only know if this was true love through the loss... too quickly familarity would have bred contempt had I walked the other road and that I had to protect love from.
If we are truely to belong then surely we must be able to belong anywhere and not be condemned to run the gauntlet of loss. In many ways I am too proud to live in fear of loss. If I fear loss then i will take loss head on and defeat it in the open, rather than have waged a guerilla war in the shadows. Loss it what I have fashioned my life upon now, that is the battle. But the paradox is that how can we not fear losing what we hold so deeply? If we do not fear losing it, one has to question how important it is to us. In this paradox there can never be happiness. We either have loss, or joy tainted with fear of loss. Naive lovers who believe that it will last forever will undoubtably have a shock.
I am running between work and this... risking being caught by the boss... this very text is written in the shadows... where is truth and honesty in this fractured world.
I wish to add a slightly adjacent point before continuing. 10 years ago I made my choice. She had a boyfriend I over heard. How was I to know that he was cheating on her, maybe that is what she wanted. That maybe she measured me up, and stayed with him in the background, that is the weakness that my love would never have shown. If you see before you what you truely desire do you not drop everything and risk everything for that? Surely the outcome can only be glory or destruction? She did not play such a bold game, she did not love like i did. How was I to know that she was not happy with him and I would be just a fools paradise; he was rich, she chose that; I was poor she did not know that. She was young, i felt I had to protect her and make the choices that I knew would be best for her, is that not what you do to those you love? So i chose what proved to be the path of destruction for I was not strong enough to love without gain, and jealousy consumed and hate for the world replaced what had been satisfaction with existence. In that maybe lies the errors, but documentation will never change what was done.
Returning... there is life in loss. It is extradordinary how resilient this life is. Infact life in loss is the same as life in gain simply without the emotional landscape and the feelings of being found and blessed and peace. An analysis of that might begin with the awareness that to be in loss or in gain is just a point of view. It is not a reality. But we need to go really deep to play these games because the suggestion for me is that my life could only be complete with her, that "this point of view" is actually my own life. That is how deep i need to search now to unravel this, much deeper than I ever thought possible. Is that the quest that I have been curious about?
I had a very deep mediatation experience as a kid.. even a jhana I believe. The feeling that followed that was I remember beyond description... maybe even greater than love. That was "being found". I could not communicate it, find any sympathy amongst my friends, thought it odd and it was forgotten.
But that is being found. That is our true home. It is when the mind is focused. If "my muse" gave me love it was not sexual it was because my whole soul was focused upon her, I become a disparate disorganised rabble become one under one leader. They say that the greatest man commands not an army but himself. "my muse" requires a replacement... myself.
A friend said that while playing darts recently he forgot all about his opponent and the people in the room as he focused on his shots. That is self mastery. Focus. That is what brings the rabble of the mind together under one leader. My object had been "my muse" but with her came a million other thoughts and desires, and pains and distractions. Under the master of oneself we are secure and found.
So I have become meditation again with a single goal to come home. Come home to my true home that no-one can take away, that I can only lose by leaving home, that depends upon nothing but an ability to remain undistracted and command the ship through the oceans to the port that it left before memory began. That is the true "being found" and now finally the journey Home has become. May "my muse" always be remembered exactly how she was, and the love remain exactly as it was, and my desire remain exactly as it was, and the fear of loss remain exactly as it was, but may i and she, daughter of the moon to me, and everyone in all directions now complete the true journey home.
But I persist in this knowledge of maybe something deeper. The problem with "getting what you want" is that you will fear forever losing it, unless that is you can satisfy that desire and be free from it... and there's the rub... its the being free from it that counts... that is why we want it. Not having what we want is suffering. The soul hurts. The more we need it the more our soul hurts. "My muse" was to play the deepest role in my souls life... through her I would unravel the mysteries of my relations with the outer world, the mysteries of sexual desire, the mysteries of birth and life - through her I would be able to live. Without her I would die, which is how it feels. Ironically her death in many ways seems the easier path; for i am the walking dead, the souless.
But not to despair for this is the other side of the same coin. If I cannot walk this path, I am not worthy to walk the other path of having what I most desire. Do I suffer because lacked the courage to take what i wanted most dearly, or do I suffer because I had the courage to face what I feared most. I have been unable to decide on that. Certainly what i have done has been madness and reckless by any imagination, but i knew i would only know if this was true love through the loss... too quickly familarity would have bred contempt had I walked the other road and that I had to protect love from.
If we are truely to belong then surely we must be able to belong anywhere and not be condemned to run the gauntlet of loss. In many ways I am too proud to live in fear of loss. If I fear loss then i will take loss head on and defeat it in the open, rather than have waged a guerilla war in the shadows. Loss it what I have fashioned my life upon now, that is the battle. But the paradox is that how can we not fear losing what we hold so deeply? If we do not fear losing it, one has to question how important it is to us. In this paradox there can never be happiness. We either have loss, or joy tainted with fear of loss. Naive lovers who believe that it will last forever will undoubtably have a shock.
I am running between work and this... risking being caught by the boss... this very text is written in the shadows... where is truth and honesty in this fractured world.
I wish to add a slightly adjacent point before continuing. 10 years ago I made my choice. She had a boyfriend I over heard. How was I to know that he was cheating on her, maybe that is what she wanted. That maybe she measured me up, and stayed with him in the background, that is the weakness that my love would never have shown. If you see before you what you truely desire do you not drop everything and risk everything for that? Surely the outcome can only be glory or destruction? She did not play such a bold game, she did not love like i did. How was I to know that she was not happy with him and I would be just a fools paradise; he was rich, she chose that; I was poor she did not know that. She was young, i felt I had to protect her and make the choices that I knew would be best for her, is that not what you do to those you love? So i chose what proved to be the path of destruction for I was not strong enough to love without gain, and jealousy consumed and hate for the world replaced what had been satisfaction with existence. In that maybe lies the errors, but documentation will never change what was done.
Returning... there is life in loss. It is extradordinary how resilient this life is. Infact life in loss is the same as life in gain simply without the emotional landscape and the feelings of being found and blessed and peace. An analysis of that might begin with the awareness that to be in loss or in gain is just a point of view. It is not a reality. But we need to go really deep to play these games because the suggestion for me is that my life could only be complete with her, that "this point of view" is actually my own life. That is how deep i need to search now to unravel this, much deeper than I ever thought possible. Is that the quest that I have been curious about?
I had a very deep mediatation experience as a kid.. even a jhana I believe. The feeling that followed that was I remember beyond description... maybe even greater than love. That was "being found". I could not communicate it, find any sympathy amongst my friends, thought it odd and it was forgotten.
But that is being found. That is our true home. It is when the mind is focused. If "my muse" gave me love it was not sexual it was because my whole soul was focused upon her, I become a disparate disorganised rabble become one under one leader. They say that the greatest man commands not an army but himself. "my muse" requires a replacement... myself.
A friend said that while playing darts recently he forgot all about his opponent and the people in the room as he focused on his shots. That is self mastery. Focus. That is what brings the rabble of the mind together under one leader. My object had been "my muse" but with her came a million other thoughts and desires, and pains and distractions. Under the master of oneself we are secure and found.
So I have become meditation again with a single goal to come home. Come home to my true home that no-one can take away, that I can only lose by leaving home, that depends upon nothing but an ability to remain undistracted and command the ship through the oceans to the port that it left before memory began. That is the true "being found" and now finally the journey Home has become. May "my muse" always be remembered exactly how she was, and the love remain exactly as it was, and my desire remain exactly as it was, and the fear of loss remain exactly as it was, but may i and she, daughter of the moon to me, and everyone in all directions now complete the true journey home.
10 years on ....
Tomorrow at 2pm, the 5th, it is 10 years since I first spoke to my muse. The 1st was 10 years since the evening I stood in Clapham common gazing at the alignment of 9 planets across the sky to the cresent moon (which I read recently was followed by another on 3-5th May 2000 and the last 9 planet aligment for 600+ years) and the 2nd was 10 years since I first saw the golden light of her form float past me in the shop. This week I have had ample time to relive and remember what has become a defining moment in my life. There is no doubt we were in profound love, and no doubt that I simply let it slip. I knew in January that she was confused and frustrated with me, she never let it show but I knew, and could feel it slipping. We had different ways of dealing with it, she simply continued in her relationship and the many that followed I came to study this event in minute detail to understand.
What is true love? I believed at the time that if we were destined to be together then no word need ever be uttered between us on the subject. It would just happen. The same way the the greater world had brought us together, and set our stories so perfectly that we were in love. That is something we can never manufacture. So why do we need to manufacture the rest? Not if it true love I argued, and argue still.
So no it cannot have been true love because we never were together. On her side I did not provide the physical romance that she longed for, and on my side I knew I had nothing material to offer her. I can write a million letters, and give her a cosmos of gifts, but as she said to me many times, an imagination is no substitue for reality... and she I was always reminded was a realist.
So I blew it, but in that it was never meant to be. I still love her that is the problem, and I knew she appreciated the friendship I cannot believe she kept that painted egg so dear to her. Why would anyone do that? It was just a painted egg from a frustrating friend. Maybe I don't appreciate the love of friendship?
Anyway! Love is flawed. Indeed the world is flawed I can safely say. Love is something that must be built and nurtured like a plant. The seeds may fall but without care and attention it will die. And, in that I am dissappointed in love. What good is that which we have made with our own hands? If i can make something, then at journeys end I have what i started with... except the potential has become the real. Maybe it can be argued that without making something we'll never know what potenial we had, but is knowledge all this is about?
This morning I think otherwise. What is this path of destruction and pain that i am on? I was inspired by Kierkegaard at college and how inexplicably he turned scorned his fiancee and lived the rest of his life anguishing about that choice. The was something perculiar and heroic about chosing against ones wishes. For, those who chose according to their wishes i have always suspected become slaves to those wishes.
The very fact that we can enter futures where what we want either does or does not happen shows us that the world is greater than our desires. It is true that the potential is always there to not have even the greatest desire of one life. I have been fascinated I suppose by the prospect of losing what I hold most dear. Indeed I have done just that. It has happened. It is real and I despite enormous suffering am still here. The world keeps turning. Existence is greater than desire. Not that desire is not important... what world is there without desire. But that "my" desire is but one of countless desires in this world and while everything to me, it just a small part of an unlimited universe.
I always knew that she would enlighten me. Maybe I got it wrong that the enlightenment would come through bearing the loss, than the luxury of gain. Time will tell.
What is true love? I believed at the time that if we were destined to be together then no word need ever be uttered between us on the subject. It would just happen. The same way the the greater world had brought us together, and set our stories so perfectly that we were in love. That is something we can never manufacture. So why do we need to manufacture the rest? Not if it true love I argued, and argue still.
So no it cannot have been true love because we never were together. On her side I did not provide the physical romance that she longed for, and on my side I knew I had nothing material to offer her. I can write a million letters, and give her a cosmos of gifts, but as she said to me many times, an imagination is no substitue for reality... and she I was always reminded was a realist.
So I blew it, but in that it was never meant to be. I still love her that is the problem, and I knew she appreciated the friendship I cannot believe she kept that painted egg so dear to her. Why would anyone do that? It was just a painted egg from a frustrating friend. Maybe I don't appreciate the love of friendship?
Anyway! Love is flawed. Indeed the world is flawed I can safely say. Love is something that must be built and nurtured like a plant. The seeds may fall but without care and attention it will die. And, in that I am dissappointed in love. What good is that which we have made with our own hands? If i can make something, then at journeys end I have what i started with... except the potential has become the real. Maybe it can be argued that without making something we'll never know what potenial we had, but is knowledge all this is about?
This morning I think otherwise. What is this path of destruction and pain that i am on? I was inspired by Kierkegaard at college and how inexplicably he turned scorned his fiancee and lived the rest of his life anguishing about that choice. The was something perculiar and heroic about chosing against ones wishes. For, those who chose according to their wishes i have always suspected become slaves to those wishes.
The very fact that we can enter futures where what we want either does or does not happen shows us that the world is greater than our desires. It is true that the potential is always there to not have even the greatest desire of one life. I have been fascinated I suppose by the prospect of losing what I hold most dear. Indeed I have done just that. It has happened. It is real and I despite enormous suffering am still here. The world keeps turning. Existence is greater than desire. Not that desire is not important... what world is there without desire. But that "my" desire is but one of countless desires in this world and while everything to me, it just a small part of an unlimited universe.
I always knew that she would enlighten me. Maybe I got it wrong that the enlightenment would come through bearing the loss, than the luxury of gain. Time will tell.
Friday, 23 November 2007
The bliss of a final resting place
The goal in life is to have those experiences where we want for nothing more.
Baby you'll all that I have
when I'm lying here in your arms
I'm finding it hard to believe
We're in Heaven.
As Brian Adams would say. But that is it, the experience of being found, or of finding what we are looking for, of being at home, and the journey complete, with no need anymore to search and no sense at all that we have to journey more. We have arrived at ourselves, in peace and there is nothing else to say.
Words are the currency of desires, just as money is the currency of getting. We talk of those things we have not got, and think of how we might get them. But when we finally arrive at ourselves, at home with ourselves then we have no need of thought we have no need of currency.
The problem of course is that these earthly experiences no matter how "found" and "home" they may feel are illusions because the outsider can see it is doomed to a short term.
The goal is that experience of being found, of being at peace with oneself, but after having found nothing and after having gone no-where.
It is odd however that within the realm of Earthly experiences, the experience of finding a resting place (especially in someones arms) is so completely satisfying. To people in such a state it is very hard to argue that this is just a stop on the journey, because it is not over yet.
Being over (the Enlightenment) is quite extraordinary then for it is being home but the final unshakeable one, no doubt anymore that the morning will rise on lovers bliss and carry their beloved away.
Baby you'll all that I have
when I'm lying here in your arms
I'm finding it hard to believe
We're in Heaven.
As Brian Adams would say. But that is it, the experience of being found, or of finding what we are looking for, of being at home, and the journey complete, with no need anymore to search and no sense at all that we have to journey more. We have arrived at ourselves, in peace and there is nothing else to say.
Words are the currency of desires, just as money is the currency of getting. We talk of those things we have not got, and think of how we might get them. But when we finally arrive at ourselves, at home with ourselves then we have no need of thought we have no need of currency.
The problem of course is that these earthly experiences no matter how "found" and "home" they may feel are illusions because the outsider can see it is doomed to a short term.
The goal is that experience of being found, of being at peace with oneself, but after having found nothing and after having gone no-where.
It is odd however that within the realm of Earthly experiences, the experience of finding a resting place (especially in someones arms) is so completely satisfying. To people in such a state it is very hard to argue that this is just a stop on the journey, because it is not over yet.
Being over (the Enlightenment) is quite extraordinary then for it is being home but the final unshakeable one, no doubt anymore that the morning will rise on lovers bliss and carry their beloved away.
I'm not in a position to say whether I'm right or wrong!
Well if I could determine if I was right or wrong, then how do I know that this itself is right or wrong? ad infinitum!
So what are the conditions that allow right and wrong?
So what are the conditions that allow right and wrong?
Thursday, 22 November 2007
Wednesday, 14 November 2007
Self-Reference is impossible!!
There is a problem with T= {T} but not under that disguise.
Consider the universal set U = {A,B,C} where
A = {10}
B = {1,2}
C = {3,4}
Now construct the set D = {x : x = 2} i.e. the set of all set with 2 members.
D = {B,C}
But D has 2 members so,
D = {B,C,D}
but now it has 3!
Either way D is an exception to it own rule. There is something wrong with the set construction.
There was no problem up to defining D = {B,C} but then we noticed that D was a new set which was an exception to its rule. Exactly! D is a "new" set and not a member of the Universal U = {A,B,C}. D is created from the universal U and creates a new universal in the process U* = {A,B,C,D}. So correctly its like this...
U = {A,B,C}
A={10}
B={1,2}
C={3,4}
D = {x : x e U & x = 2} (where e means "a member of")
Which also creates a new universal U* = {A,B,C,D}
Thus T = {T} is a trick of language because it should be written T = {x : x e U & ... } and T is not a member of the universal U.
The only way around this is to leave an unbound floating symbol in the universal definition...
i.e. U = {A,B,C,D} where D = nothing i.e. it is unbound and we reference it later ... but that is the point: a system requires an empty symbol to refer to itself - which doesn't become bound to the system until AFTER it picks up its reference. Self reference is indeed impossible.
This also solves a similar problem...
U = {A,B} where
A = {1,2,3}
B = {4,5,6}
now construct
C = {x : x = 3}
there are 2 answers
C = {A,B}
or
C = {A,B,C}
Now C refers to the same set i.e. {x : x = 3} but the axioms of set theory state that 2 sets are only the same when they have the same members and clearly
{A,B} /= {A,B,C}
However
C = {x : x e U & x = 3} solves it neatly.
Hypothesis: Self reference is only apparently possible if the symbol space/solution space/universe/etc is not properly defined.
===
Just a start but if self reference is impossible then that opens up the whole world. The limit cannot be expressed within the limit. Thus returning to the start the ideas of "materialism" cannot account or refer to itself (obvious really since ideas are not material). And, 2 sided positions fail because such dualistic argument works on the basis that "I am correct" and "you are wrong" but if no system can refer to itself without expansion then no such self-assured "I am x" is possible. War for one can never be justified since ultimately a "self" consistent argument would have to expand indefinitely to include the enemy at least! (And, G-d is out of the picture 4 sure - originally there was no symbol for Him)
Consider the universal set U = {A,B,C} where
A = {10}
B = {1,2}
C = {3,4}
Now construct the set D = {x : x = 2} i.e. the set of all set with 2 members.
D = {B,C}
But D has 2 members so,
D = {B,C,D}
but now it has 3!
Either way D is an exception to it own rule. There is something wrong with the set construction.
There was no problem up to defining D = {B,C} but then we noticed that D was a new set which was an exception to its rule. Exactly! D is a "new" set and not a member of the Universal U = {A,B,C}. D is created from the universal U and creates a new universal in the process U* = {A,B,C,D}. So correctly its like this...
U = {A,B,C}
A={10}
B={1,2}
C={3,4}
D = {x : x e U & x = 2} (where e means "a member of")
Which also creates a new universal U* = {A,B,C,D}
Thus T = {T} is a trick of language because it should be written T = {x : x e U & ... } and T is not a member of the universal U.
The only way around this is to leave an unbound floating symbol in the universal definition...
i.e. U = {A,B,C,D} where D = nothing i.e. it is unbound and we reference it later ... but that is the point: a system requires an empty symbol to refer to itself - which doesn't become bound to the system until AFTER it picks up its reference. Self reference is indeed impossible.
This also solves a similar problem...
U = {A,B} where
A = {1,2,3}
B = {4,5,6}
now construct
C = {x : x = 3}
there are 2 answers
C = {A,B}
or
C = {A,B,C}
Now C refers to the same set i.e. {x : x = 3} but the axioms of set theory state that 2 sets are only the same when they have the same members and clearly
{A,B} /= {A,B,C}
However
C = {x : x e U & x = 3} solves it neatly.
Hypothesis: Self reference is only apparently possible if the symbol space/solution space/universe/etc is not properly defined.
===
Just a start but if self reference is impossible then that opens up the whole world. The limit cannot be expressed within the limit. Thus returning to the start the ideas of "materialism" cannot account or refer to itself (obvious really since ideas are not material). And, 2 sided positions fail because such dualistic argument works on the basis that "I am correct" and "you are wrong" but if no system can refer to itself without expansion then no such self-assured "I am x" is possible. War for one can never be justified since ultimately a "self" consistent argument would have to expand indefinitely to include the enemy at least! (And, G-d is out of the picture 4 sure - originally there was no symbol for Him)
Firstly note that a set construction involves the assigning of a reference
A = {1,2} = {x : 0 < x <3}
The character A, the set name, is not usually part of the symbols that build the set. If however we did used the symbols {1,2} as a name then the statement
{1,2} = {1,2}
does not mean that the set {x : 0 < x <3} contains the number 1 and 2, but rather that {1,2} is a name that - meaningless in itself - will now refer to the set {x : 0 < x <3}. It could be expressed like this for clarity:
"{1,2}" = {1,2}
1.0) Now consider a universal set containing three sets U = {A,B,C} where,
A = {10}
B = {1,2}
C = {3,4}
2.0) Now construct the set D = {x : x = 2} i.e. a set whose members are sets with 2 members, and call it D
2.1) D = {B,C}
But D has two members. If D is not included in itself then D is not the set of "all" sets with 2 members because it is the exception. We are thus inclined to include D to give the set
2.2) D = {B,C,D}
However now D has 3 members and so should not be included. How ever we try to build D we end up with a contradiction. Where is the problem?
Up until step 2.1 everything was good. It was only "after" constructing D that we noticed it became an exception to its own rule.
Step 2.1 suggests statement 2.2 but something goes wrong in building it. Let us recreate the process without assigning any names or references (beyond the basic elements i.e. 10,1,2,3,4}
supposing we write statement 2.1 as {{1,2},{3,4}}
We notice that it contains 2 members and so should be a member of itself so we try to write the self-referential statement without using reference:
{{1,2},{3,4}, itself} = {{1,2},{3,4}, {{1,2},{3,4}, {{1,2},{3,4}, {{1,2},{3,4}, itself}}}}
it cannot be done. This expression cannot be resolved into "definite" sets. The process of attributing a reference D to the unresolved set in 2.2 hides the fact that we don't yet know for sure what the set is. Writing D looks like a definite answer but actually it is an "unbound" reference. By "unbound" I mean we is unsure what it refers to.
The statement D = {B,C,D} is a formula for the answer. B and C are bound references because we know clearly what they are, but exactly what D refers to is uncertain. When we ask what D refers to we get another formula containing D. It resolves to nothing, a trick of language without reference, meaningless. Creating formulas is easy. g = 4*Hg¬K but until we know what these refer to it is meaningless.
"The unicorn in my garden is eating grass" is meaningless because "the unicorn" is an unbound reference, it is a formula we might use in the event of a unicorn being in the garden. When asked "which unicorn?" we cannot simply answer the unicorn eating grass (q.v. what is D it is {B,C,D}).
Predicate logic resolved this issue with: Ex: x = unicorn & x = eating grass. It is false because there is no unicorn (and it certainly then can't be eating grass) but the issue of reference is implicit.
Quick addition on reference. Reference is not the linking of "physical reality" to symbols and words, because objects in the world can only be referred to with symbols i.e. what do we mean by "physical reality" since that itself is a reference! mystery!
So we are stuck with D = {B,C} but it is unsatisfactory because it becomes an exception to its own rule.
The solution might be that D = {x : x = 2} creates a new Universal. Remember that U = {A,B,C} so the construction of D creates a universal U* = {A,B,C,D}
D = {x : x e U & x = 2}
And that is the point about self-reference. The reference to oneself cannot be in the same universe as onself.
It is the +1 conjecture again that a system needs to expand by 1 to take a useless entity and use it to reference the self.
===
Can we get from this position to the general situation that the self cannot contain itself.
And is this the same as the situation where the rules of a game (like war) can only occur because they try to reference themselves within themselves i.e. we Allies without understanding the requirement to see the Enemy and the Allies are part of the same game.
A = {1,2} = {x : 0 < x <3}
The character A, the set name, is not usually part of the symbols that build the set. If however we did used the symbols {1,2} as a name then the statement
{1,2} = {1,2}
does not mean that the set {x : 0 < x <3} contains the number 1 and 2, but rather that {1,2} is a name that - meaningless in itself - will now refer to the set {x : 0 < x <3}. It could be expressed like this for clarity:
"{1,2}" = {1,2}
1.0) Now consider a universal set containing three sets U = {A,B,C} where,
A = {10}
B = {1,2}
C = {3,4}
2.0) Now construct the set D = {x : x = 2} i.e. a set whose members are sets with 2 members, and call it D
2.1) D = {B,C}
But D has two members. If D is not included in itself then D is not the set of "all" sets with 2 members because it is the exception. We are thus inclined to include D to give the set
2.2) D = {B,C,D}
However now D has 3 members and so should not be included. How ever we try to build D we end up with a contradiction. Where is the problem?
Up until step 2.1 everything was good. It was only "after" constructing D that we noticed it became an exception to its own rule.
Step 2.1 suggests statement 2.2 but something goes wrong in building it. Let us recreate the process without assigning any names or references (beyond the basic elements i.e. 10,1,2,3,4}
supposing we write statement 2.1 as {{1,2},{3,4}}
We notice that it contains 2 members and so should be a member of itself so we try to write the self-referential statement without using reference:
{{1,2},{3,4}, itself} = {{1,2},{3,4}, {{1,2},{3,4}, {{1,2},{3,4}, {{1,2},{3,4}, itself}}}}
it cannot be done. This expression cannot be resolved into "definite" sets. The process of attributing a reference D to the unresolved set in 2.2 hides the fact that we don't yet know for sure what the set is. Writing D looks like a definite answer but actually it is an "unbound" reference. By "unbound" I mean we is unsure what it refers to.
The statement D = {B,C,D} is a formula for the answer. B and C are bound references because we know clearly what they are, but exactly what D refers to is uncertain. When we ask what D refers to we get another formula containing D. It resolves to nothing, a trick of language without reference, meaningless. Creating formulas is easy. g = 4*Hg¬K but until we know what these refer to it is meaningless.
"The unicorn in my garden is eating grass" is meaningless because "the unicorn" is an unbound reference, it is a formula we might use in the event of a unicorn being in the garden. When asked "which unicorn?" we cannot simply answer the unicorn eating grass (q.v. what is D it is {B,C,D}).
Predicate logic resolved this issue with: Ex: x = unicorn & x = eating grass. It is false because there is no unicorn (and it certainly then can't be eating grass) but the issue of reference is implicit.
Quick addition on reference. Reference is not the linking of "physical reality" to symbols and words, because objects in the world can only be referred to with symbols i.e. what do we mean by "physical reality" since that itself is a reference! mystery!
So we are stuck with D = {B,C} but it is unsatisfactory because it becomes an exception to its own rule.
The solution might be that D = {x : x = 2} creates a new Universal. Remember that U = {A,B,C} so the construction of D creates a universal U* = {A,B,C,D}
D = {x : x e U & x = 2}
And that is the point about self-reference. The reference to oneself cannot be in the same universe as onself.
It is the +1 conjecture again that a system needs to expand by 1 to take a useless entity and use it to reference the self.
===
Can we get from this position to the general situation that the self cannot contain itself.
And is this the same as the situation where the rules of a game (like war) can only occur because they try to reference themselves within themselves i.e. we Allies without understanding the requirement to see the Enemy and the Allies are part of the same game.
Monday, 12 November 2007
Reference & Existence
OK it seems that all that explosion of reading and ideas boils down to the issue of reference and existence.
The issue is what is "a thing"? If for example we refer to a box A we are "referring" but we are not handling the real thing, only a reference or name to the real thing. If on another case we say that we are holding box A, on one hand we are reffering to the act of holding this box (as written in fact in this blog) but on the other hand we are actually holding the box, and event that we can refer to but which is in existence. It is through the act of refering that we can lie and play all those games of reference, like telling a story like just done here without ever actually handling the box A. The symbols have a life of their own regardless of the actual events.
Now with set theory it is a similar situation. Let us take a set {1,2,3}. What we are saying is that we have a collection of numbers 1,2,3. Now consider what the set of arabic symbols for 1,2,3 looks like... {1,2,3}. But the first case is a collection of counting numbers while the second is a collection of symbols. Thus {I,II,III} are the counting numbers 1,2,3 expressed in roman numerals, so it is identical with the first case, but different from the second case. Each symbol has several uses:
1- the level of its actual existence as a mark on the page (in which case A and A are different examples)
2- the level of its place in a symbol set (where "A" = "A")
3- its level as a reference (where if A=5 then A=A because 5=5)
This is explicitly found in computers where referencing is common place.
A variable has 3 meanings. the symbol as understood by the compiler within a namespace (1) so that variables with the same name in different namespaces are different, the memory location linked to that name (2) and the value at that location (3)
In computers the human programing interface often uses symbols from the ASC set to code for variables. At run time these are converted into actual memory locations and the name becomes linked to an address. Into each address data can be stored.
While all data in a computer is simply binary numbers the destination of code is of two fundamental types. If the data in loaded into the instruction register of the CPU then it is used to control the CPU at the next clock cycle, if it is loaded into the data registers of the CPU then it is processed. Thus for every symbol that we may type in at a key board its fundamental meaning is augmented by where that will go. If the symbol "A" with a binary value of 65 or 01000001 is directed through the data part of the CPU as this has just been then it is processed, in this case to appear as a symbol on the screen and data for a file to be sent over the internet to update the blog program. If on the other hand I could direct that code into the instruction register (which I can't through this blog program) then it would instruct the CPU to perform some operation (I don't know Intel assembly language so don't know which operation 01000001 is).
So we have 3 flavours to symbols and then another 2 types of symbols on top of that. An example...
"=" is well known as the symbol for equality in maths. It is an operator so in computing terms it would go to the instruction register to tell the CPU to compare the values in its data registers.
However "=" can also be data as it is in this file since its simply a word processor and = is just a symbol in fact symbol #61.
In some esoteric language you might be able to write "= ? 5" where = is a variable and ? is understood as the equality operator i.e. it translates to "A = 5". Its just numbers at the end of the day and what we are conditioned to understand from the symbols need not apply.
So in set theory the statement A = {1,2,3} is a complex system. Firstly A,1,2,3 are references to things, but are not to be taken as what they are, otherwise we would thing that the letter A was the set of symbols 1,2,3 when in fact we are supposed to be saying that A stands for a set of numbers. The equality operator is a reference to the idea of an assignment operator telling us to take A as a reference to this set from now on.
Now there are a lot of complications possible here. How might be assign a reference to the assigment operator "= = what" ? Can a set really hold an actual thing?
A = {1} could hold this symbol 1, in which case A = {1} is a new assigment rather than a repeat of the same assigment. Or if we take A and 1 to be in the same name space, then is A = the symbol 1 (i.e. the set containing the symbol 1) which is also false since A is the symbol A! unless we mean that A refers to the set containing the symbol 1 which is a mix up of contexts. Or finally we take the whole thing as a reference to the set idea of containing a number.
Now with that in mind when we talk of self-reference we are very much in the world of thoughts where lying and many other unrealities are true. The set T = {T} is a system of self-reference where while T is an existent in its own right it can occur in multiple places and each refers to the same things namely a set which contains another set by the same name, i.e. itself. This is not a real event, but a thought made possible by multiple entities referring to the same thing. Obviously such a state of affairs cannot be done in reality, you have an infinite regress.
This issue of reference and object/existence, and also operators and data are the two dualisms which i need to resolve to bring this flurry of exploration to a close.
The issue is what is "a thing"? If for example we refer to a box A we are "referring" but we are not handling the real thing, only a reference or name to the real thing. If on another case we say that we are holding box A, on one hand we are reffering to the act of holding this box (as written in fact in this blog) but on the other hand we are actually holding the box, and event that we can refer to but which is in existence. It is through the act of refering that we can lie and play all those games of reference, like telling a story like just done here without ever actually handling the box A. The symbols have a life of their own regardless of the actual events.
Now with set theory it is a similar situation. Let us take a set {1,2,3}. What we are saying is that we have a collection of numbers 1,2,3. Now consider what the set of arabic symbols for 1,2,3 looks like... {1,2,3}. But the first case is a collection of counting numbers while the second is a collection of symbols. Thus {I,II,III} are the counting numbers 1,2,3 expressed in roman numerals, so it is identical with the first case, but different from the second case. Each symbol has several uses:
1- the level of its actual existence as a mark on the page (in which case A and A are different examples)
2- the level of its place in a symbol set (where "A" = "A")
3- its level as a reference (where if A=5 then A=A because 5=5)
This is explicitly found in computers where referencing is common place.
A variable has 3 meanings. the symbol as understood by the compiler within a namespace (1) so that variables with the same name in different namespaces are different, the memory location linked to that name (2) and the value at that location (3)
In computers the human programing interface often uses symbols from the ASC set to code for variables. At run time these are converted into actual memory locations and the name becomes linked to an address. Into each address data can be stored.
While all data in a computer is simply binary numbers the destination of code is of two fundamental types. If the data in loaded into the instruction register of the CPU then it is used to control the CPU at the next clock cycle, if it is loaded into the data registers of the CPU then it is processed. Thus for every symbol that we may type in at a key board its fundamental meaning is augmented by where that will go. If the symbol "A" with a binary value of 65 or 01000001 is directed through the data part of the CPU as this has just been then it is processed, in this case to appear as a symbol on the screen and data for a file to be sent over the internet to update the blog program. If on the other hand I could direct that code into the instruction register (which I can't through this blog program) then it would instruct the CPU to perform some operation (I don't know Intel assembly language so don't know which operation 01000001 is).
So we have 3 flavours to symbols and then another 2 types of symbols on top of that. An example...
"=" is well known as the symbol for equality in maths. It is an operator so in computing terms it would go to the instruction register to tell the CPU to compare the values in its data registers.
However "=" can also be data as it is in this file since its simply a word processor and = is just a symbol in fact symbol #61.
In some esoteric language you might be able to write "= ? 5" where = is a variable and ? is understood as the equality operator i.e. it translates to "A = 5". Its just numbers at the end of the day and what we are conditioned to understand from the symbols need not apply.
So in set theory the statement A = {1,2,3} is a complex system. Firstly A,1,2,3 are references to things, but are not to be taken as what they are, otherwise we would thing that the letter A was the set of symbols 1,2,3 when in fact we are supposed to be saying that A stands for a set of numbers. The equality operator is a reference to the idea of an assignment operator telling us to take A as a reference to this set from now on.
Now there are a lot of complications possible here. How might be assign a reference to the assigment operator "= = what" ? Can a set really hold an actual thing?
A = {1} could hold this symbol 1, in which case A = {1} is a new assigment rather than a repeat of the same assigment. Or if we take A and 1 to be in the same name space, then is A = the symbol 1 (i.e. the set containing the symbol 1) which is also false since A is the symbol A! unless we mean that A refers to the set containing the symbol 1 which is a mix up of contexts. Or finally we take the whole thing as a reference to the set idea of containing a number.
Now with that in mind when we talk of self-reference we are very much in the world of thoughts where lying and many other unrealities are true. The set T = {T} is a system of self-reference where while T is an existent in its own right it can occur in multiple places and each refers to the same things namely a set which contains another set by the same name, i.e. itself. This is not a real event, but a thought made possible by multiple entities referring to the same thing. Obviously such a state of affairs cannot be done in reality, you have an infinite regress.
This issue of reference and object/existence, and also operators and data are the two dualisms which i need to resolve to bring this flurry of exploration to a close.
Thursday, 8 November 2007
clarification of ideas
Let us take a set of symbols where S is {A, B, =}
Now take the set of all combinations of any number of these symbols, which is the inifinite set of all possible sentences containing these symbols where S* is
{A, B, =, AA, BB, ==, AB, A=,B=, AAA, BBB, ===, AAB, AA=, ABA, ABB, AB=, ..., A=B, ..., B=A, ... }
Now a logical system will adopt certain of these sentences and ignore the rest.
We might for example have a system with only two sentences
A=B
B=A
or we might have a Lindenmayer system
A=AB
B=A
A=AB=ABA=ABAAB=ABAABABA (http://en.wikipedia.org/wiki/L-system)
where = means "goes to" and the symbols A and B get replaced according to the two rules.
In the Lindenmayer system if A=AB and B=A is the general rule then an infinite subset of S* can be included in the system. So that the sentence:
A=ABAABABA could be considered a member of the L-system because it could be considered a short hand of the sentence above.
Another version of the L-system might be freedom to apply any of the rules, more like logic:
A=AB
B=A
A=AB=ABB=ABBB=ABBA
In such an odd system ABBA,ABAB,AABB could all be derived by applying rule 1 three times and then rule 2 on any of the B symbols.
The point here is to avoid "thinking" outside the system of symbols and simply to see them as sentences.
Now when we say that the sentences "A=AB=ABA=ABAAB=ABAABABA" and "A=ABAABABA" are in the L-system clearly our inclusion of them is quite arbitrary according to the set of sentences. The meaning and use we ascrive to these sentences is not present within the sentence, any more than the game of rugby can be deduced from the rugby ball.
Two sketched point to work on...
If a sentence A is included in a system and two sentence B and C which are not included in the system are derived from changing two different symbols, can we express non inclusion within the system itself?
A is a member of the system if conforms to some rules say (not not present in the system itself for how else would we decide if those rules were present in the system ad infinitum). B and C are not members if they do not conform to rules, if they cannot be derived from the axioms, i.e. proven. However if they cannot be proven then they are outside the system and yet we know that they were derived by changing two symbols.
Explore this firstly by creating a system in which arbitrary symbols can be changed at will.
Point 2... Godel theorem in short...
If a function was present in a system which could determine if a sentence was provable, i.e. could be derived from the axioms and rules, i.e. was in the system then would sentences containing that function themselves be part of the system. i.e. could they be derived from axioms? there is a problem here but I need a bit more brain power to get over the hurdle...
Now take the set of all combinations of any number of these symbols, which is the inifinite set of all possible sentences containing these symbols where S* is
{A, B, =, AA, BB, ==, AB, A=,B=, AAA, BBB, ===, AAB, AA=, ABA, ABB, AB=, ..., A=B, ..., B=A, ... }
Now a logical system will adopt certain of these sentences and ignore the rest.
We might for example have a system with only two sentences
A=B
B=A
or we might have a Lindenmayer system
A=AB
B=A
A=AB=ABA=ABAAB=ABAABABA (http://en.wikipedia.org/wiki/L-system)
where = means "goes to" and the symbols A and B get replaced according to the two rules.
In the Lindenmayer system if A=AB and B=A is the general rule then an infinite subset of S* can be included in the system. So that the sentence:
A=ABAABABA could be considered a member of the L-system because it could be considered a short hand of the sentence above.
Another version of the L-system might be freedom to apply any of the rules, more like logic:
A=AB
B=A
A=AB=ABB=ABBB=ABBA
In such an odd system ABBA,ABAB,AABB could all be derived by applying rule 1 three times and then rule 2 on any of the B symbols.
The point here is to avoid "thinking" outside the system of symbols and simply to see them as sentences.
Now when we say that the sentences "A=AB=ABA=ABAAB=ABAABABA" and "A=ABAABABA" are in the L-system clearly our inclusion of them is quite arbitrary according to the set of sentences. The meaning and use we ascrive to these sentences is not present within the sentence, any more than the game of rugby can be deduced from the rugby ball.
Two sketched point to work on...
If a sentence A is included in a system and two sentence B and C which are not included in the system are derived from changing two different symbols, can we express non inclusion within the system itself?
A is a member of the system if conforms to some rules say (not not present in the system itself for how else would we decide if those rules were present in the system ad infinitum). B and C are not members if they do not conform to rules, if they cannot be derived from the axioms, i.e. proven. However if they cannot be proven then they are outside the system and yet we know that they were derived by changing two symbols.
Explore this firstly by creating a system in which arbitrary symbols can be changed at will.
Point 2... Godel theorem in short...
If a function was present in a system which could determine if a sentence was provable, i.e. could be derived from the axioms and rules, i.e. was in the system then would sentences containing that function themselves be part of the system. i.e. could they be derived from axioms? there is a problem here but I need a bit more brain power to get over the hurdle...
Sunday, 4 November 2007
What does a set contain?
Let us take the set of colours again...
{red, orange, yellow, green, blue, indigo, violet}
This clearly does not contain actual colours. "green" is not actually green.
It contains instead symbols that refer to colours.
If we have the set A = {1,2,3} and B = {4,5,6} we can easily see the process of setting symbols the mean things. A can be used instead of {1,2,3}.
1,2,3,4,5,6 are symbols that refer to numbers, they are not numbers themselves. In roman numerals we would write A = {I, II, III} and B = {IV, V, VI} to mean exactly the same.
So we make a distinction between the symbols that we see and the things they refer to.
So what of the rest of the symbols that we use to construct a set: { } , = what do they represent?
The basic idea in set theory is "containing" and we express containing in symbols by understanding that the brackets enclose the objects to be contained { } and each object is separated by a comma , and the whole set can be called something by using the = sign.
Obviously { } does not by itself "contain" anything without us knowing what the symbols mean, or how they are used. It would appear impossible then to construct the axiom within symbols and the question is raised how do we come by the concept of "containing"? This is running very close to what Wittgenstein was looking at and which he knowingly said he would never complete saying in his lifetime.
Returning to sets. On paper they are sequences of references, or symbols with specific uses. Thus { } we understand in the context to evoke the notion of containing, and the names that follow separated by spaces and commas we understand to evoke the things they are naming. The whole symbol system isolated and by itself is meaningless, but connected with the greater world of maths takes on the usual meanings and use. There is no containing at all within the symbols, indeed no meaning.
So let us turn to the reality of symbols and see if we can create a kind of existential self reference.
{x: x is a symbol for a counting number y & 0 < y < 4}
certainly gives us the set {1,2,3} but the context is different. This is a set of symbols, while A above is a set of numbers.
Furthermore there is a trickly problem... the entire expression is a sequence of symbols {, }, 1, 2, 3 so { and } are being used to articulate the notion of "containment" while 1, 2, 3 are not articulating anything ... they are just themselves... now sets contain references while this set is containing "real things". is that possible?
consider the following (none of this is new from recent posts I'm just seeking a clear expression of it)
The set of all symbols used in the expression for A
{A, =, {, ,, }, 1, 2, 3}
Clearly the symbols have become inadequate because in one place they are performing their function to construct the set, and in other places they are being operated upon.
Now this requirement of a system to be both subject and object is the question... does this have to be so? and why?
{red, orange, yellow, green, blue, indigo, violet}
This clearly does not contain actual colours. "green" is not actually green.
It contains instead symbols that refer to colours.
If we have the set A = {1,2,3} and B = {4,5,6} we can easily see the process of setting symbols the mean things. A can be used instead of {1,2,3}.
1,2,3,4,5,6 are symbols that refer to numbers, they are not numbers themselves. In roman numerals we would write A = {I, II, III} and B = {IV, V, VI} to mean exactly the same.
So we make a distinction between the symbols that we see and the things they refer to.
So what of the rest of the symbols that we use to construct a set: { } , = what do they represent?
The basic idea in set theory is "containing" and we express containing in symbols by understanding that the brackets enclose the objects to be contained { } and each object is separated by a comma , and the whole set can be called something by using the = sign.
Obviously { } does not by itself "contain" anything without us knowing what the symbols mean, or how they are used. It would appear impossible then to construct the axiom within symbols and the question is raised how do we come by the concept of "containing"? This is running very close to what Wittgenstein was looking at and which he knowingly said he would never complete saying in his lifetime.
Returning to sets. On paper they are sequences of references, or symbols with specific uses. Thus { } we understand in the context to evoke the notion of containing, and the names that follow separated by spaces and commas we understand to evoke the things they are naming. The whole symbol system isolated and by itself is meaningless, but connected with the greater world of maths takes on the usual meanings and use. There is no containing at all within the symbols, indeed no meaning.
So let us turn to the reality of symbols and see if we can create a kind of existential self reference.
{x: x is a symbol for a counting number y & 0 < y < 4}
certainly gives us the set {1,2,3} but the context is different. This is a set of symbols, while A above is a set of numbers.
Furthermore there is a trickly problem... the entire expression is a sequence of symbols {, }, 1, 2, 3 so { and } are being used to articulate the notion of "containment" while 1, 2, 3 are not articulating anything ... they are just themselves... now sets contain references while this set is containing "real things". is that possible?
consider the following (none of this is new from recent posts I'm just seeking a clear expression of it)
The set of all symbols used in the expression for A
{A, =, {, ,, }, 1, 2, 3}
Clearly the symbols have become inadequate because in one place they are performing their function to construct the set, and in other places they are being operated upon.
Now this requirement of a system to be both subject and object is the question... does this have to be so? and why?
Friday, 2 November 2007
Self - containing systems again
Have made some progress...
the general argument from Godel to Logical Positivist school goes like this...
Some statement about the world... what if that statement apply to itself? and it always leads to "paradoxes".
So with the LP principle of verification, one asks what empirical evidence leads to the VP?
Especially this is true of truth itself. If a system can encode truth then you can get the absurdities of true statements that say they are false.
Godel showed that in numerical systems a wff can be formed which is unprovable. Provability is thus not the same a truth, and truth lies outside the system of provability. Systems are either incomplete - where unprovable statement exist or are inconsistent.
This is more obvious when one considers the "truth" of axioms. Clearly they are true "outside" a system since the system relies upon their truth. Such Judgement one must assume as a condition for the system.
Other fundamental conditions also exist like the education of users of a system, reason, existence, thought etc a pro pos Kant. There is a hermeneutic circle of given conditions which must be present before any system can be constructed. To construct that hermeneutic circle would require a position outside itself, and presumably another hermeneutic circle. The question formally that these speculations are true.
The implications are that there is no "fundamental" system with which to construct the world. That indeed the world is at root indefinable, and that is a construction of a notion of absolute Liberty.
So can this process be generally shown?
From Wittgenstein let us assume that the "meaning" of a statement is its "use".
To know the use of something we can simply create a set of all the possible uses of that statement.
A system of axioms and logic is thus a "compression" of the set of all possible statements but extracting the information to simply show that it can be reconstructed.
Thus in a logical system we could have a number refering to the sequence of rules applied to generate a statement, which would be identical with all the statements, and that set of numbers would constitute the meaning of the system.
The difference between that set and the normal expression of axioms however would be that the axioms no longer have a meaning outside the system from which the set of possible statements can be constructed, instead the set of possible statements becomes its meaning.
consider further....
the general argument from Godel to Logical Positivist school goes like this...
Some statement about the world... what if that statement apply to itself? and it always leads to "paradoxes".
So with the LP principle of verification, one asks what empirical evidence leads to the VP?
Especially this is true of truth itself. If a system can encode truth then you can get the absurdities of true statements that say they are false.
Godel showed that in numerical systems a wff can be formed which is unprovable. Provability is thus not the same a truth, and truth lies outside the system of provability. Systems are either incomplete - where unprovable statement exist or are inconsistent.
This is more obvious when one considers the "truth" of axioms. Clearly they are true "outside" a system since the system relies upon their truth. Such Judgement one must assume as a condition for the system.
Other fundamental conditions also exist like the education of users of a system, reason, existence, thought etc a pro pos Kant. There is a hermeneutic circle of given conditions which must be present before any system can be constructed. To construct that hermeneutic circle would require a position outside itself, and presumably another hermeneutic circle. The question formally that these speculations are true.
The implications are that there is no "fundamental" system with which to construct the world. That indeed the world is at root indefinable, and that is a construction of a notion of absolute Liberty.
So can this process be generally shown?
From Wittgenstein let us assume that the "meaning" of a statement is its "use".
To know the use of something we can simply create a set of all the possible uses of that statement.
A system of axioms and logic is thus a "compression" of the set of all possible statements but extracting the information to simply show that it can be reconstructed.
Thus in a logical system we could have a number refering to the sequence of rules applied to generate a statement, which would be identical with all the statements, and that set of numbers would constitute the meaning of the system.
The difference between that set and the normal expression of axioms however would be that the axioms no longer have a meaning outside the system from which the set of possible statements can be constructed, instead the set of possible statements becomes its meaning.
consider further....
Thursday, 25 October 2007
Wednesday, 24 October 2007
The +1 conjecture = ambiguity problem
Firstly there is the issue of a system "actually" containing itself ... a box containing itself.
A box is a simple system with a single relevant function namely to contain things (like a set). Suppose a box could contain its real self. When would it perform this function?
Usually we put something in a box and it there by performs the containing function on that object. But if it can contain itself it forms a closed system, with self-containing an intrinsic feature. Suppose there is a condition which determines whether it performs the containing function on itself or not.
This is very abstract (since boxes don't contain themselves) but when that condition is present the box would contain itself. It would not however be able to contain that condition as well.
If however the self-containing function was triggered by some condition and then operated to contain both the box and the condition the two would always be present together and inseparable within the system.
Whichever way this gets looked at self containing creates an odd man out.
===
This is the ambiguity problem in symbol systems.
A symbol system has two types of symbol: the entities and the operators. For example
1+1=2
Now the system cannot operate on itself because + and = only operate on numbers, and the list of symbols above is an expression.
In computing for example we can express this expression as a string using a new operator the quote marks so
"1+1=2"
is an expression. Now quote marks operate on expressions so we can quote itself
""1+1=2""
However now there is ambiguity. Does this mean "" expression and 1+1=2 expression and "" expression written side by side or does it mean the string containing "1+1=2". It is not explicitly decidable.
This is not self-referential as only a copy is contained, and an inferior copy to lacking the outer most strings quotes.
To really contain itself it needs to contain a reference to itself, say:
S = "S"
But there is ambiguity again because both the S things are symbols. Is this saying that S is the string containing the symbol S (character 83cin ASCII) or the string containing the string called S. Is S a character or a reference to a string?
if we were to PRINT S in a programming language we would just get an output of S.
Another possible output is the recursive """"""..."""""" where S keeps being replace by "S"
But the real thing we wanted to express was self membership which can't be expressed in this language.
The ambiguity problem like the self-operation problem above requires an external switch to decide whether to treat the entity as a reference to the system self, or as the entity itself.
===
In case self-reference seems void as it appears to be in these sterile examples. Consider a robot which like the ones in Japan can play football. When it picks its team it needs to be able to model itself as a member of the team, otherwise it will pick 11 players and try to play along side them making 12!
However it is not good enough just to model a team of 11 robots in its system... it needs to operate on the situation of just one of those robots (itself).
ok phone call...
A box is a simple system with a single relevant function namely to contain things (like a set). Suppose a box could contain its real self. When would it perform this function?
Usually we put something in a box and it there by performs the containing function on that object. But if it can contain itself it forms a closed system, with self-containing an intrinsic feature. Suppose there is a condition which determines whether it performs the containing function on itself or not.
This is very abstract (since boxes don't contain themselves) but when that condition is present the box would contain itself. It would not however be able to contain that condition as well.
If however the self-containing function was triggered by some condition and then operated to contain both the box and the condition the two would always be present together and inseparable within the system.
Whichever way this gets looked at self containing creates an odd man out.
===
This is the ambiguity problem in symbol systems.
A symbol system has two types of symbol: the entities and the operators. For example
1+1=2
Now the system cannot operate on itself because + and = only operate on numbers, and the list of symbols above is an expression.
In computing for example we can express this expression as a string using a new operator the quote marks so
"1+1=2"
is an expression. Now quote marks operate on expressions so we can quote itself
""1+1=2""
However now there is ambiguity. Does this mean "" expression and 1+1=2 expression and "" expression written side by side or does it mean the string containing "1+1=2". It is not explicitly decidable.
This is not self-referential as only a copy is contained, and an inferior copy to lacking the outer most strings quotes.
To really contain itself it needs to contain a reference to itself, say:
S = "S"
But there is ambiguity again because both the S things are symbols. Is this saying that S is the string containing the symbol S (character 83cin ASCII) or the string containing the string called S. Is S a character or a reference to a string?
if we were to PRINT S in a programming language we would just get an output of S.
Another possible output is the recursive """"""..."""""" where S keeps being replace by "S"
But the real thing we wanted to express was self membership which can't be expressed in this language.
The ambiguity problem like the self-operation problem above requires an external switch to decide whether to treat the entity as a reference to the system self, or as the entity itself.
===
In case self-reference seems void as it appears to be in these sterile examples. Consider a robot which like the ones in Japan can play football. When it picks its team it needs to be able to model itself as a member of the team, otherwise it will pick 11 players and try to play along side them making 12!
However it is not good enough just to model a team of 11 robots in its system... it needs to operate on the situation of just one of those robots (itself).
ok phone call...
Simplest Universal Turing Machine
One might think that computational ability would be a more gradual phenomenon: that as one increased the complexity of the rules for a system, the system would gradually show greater computational ability.
But PCE says that's not how it works. It says that above a very low threshold, all systems will be exactly equivalent in their computational capabilities.
http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html?lid=title
i.e. the old argument that if we could just juice up machines a bit more we would get more out of them may be even consciousness is not true.
But PCE says that's not how it works. It says that above a very low threshold, all systems will be exactly equivalent in their computational capabilities.
http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html?lid=title
i.e. the old argument that if we could just juice up machines a bit more we would get more out of them may be even consciousness is not true.
The +1 conjecture
A self-operating system cannot complete operation in its domain.
If a system could operate on itself, for example a hand grasping itself, then the system would be able to complete the operation intrinsically.
The question then is under what circumstances would it simply complete under itself and under what circumstances would it complete under external circumstances.
If it is a truely intrinsic system then it negates its own operation because it would always complete under itself.
If there is an extrinsic factor that triggers self completion then it can operate on all factors except that extrinsic factor where the result is self-operation.
Thus there must always be one element within the domain of the input which it cannot operate upon, if it is to have self operation.
A set cannot essentially contain itself, because if it could complete under itself it would negate its containing function.
This is why a hand cannot grasp itself, for if it could then to be able to grasp anything else there would need to be an external trigger, which it could not itself grasp. Evidentally in the realm of things there are not rules enough to distinguish that special thing which would cause self-grasping. It is worth exploring this to find the rules...
On References....
The same argument then applies to references. A box can contain other boxes but it cannot contain itself. It contains instead a reference to itself.
However then it cannot then contain also that thing without breaking the reference rule. Thus to have self-membership you need a symbol which has a special meaning i.e. self. and not its obvious meaning.
Now it might seem absurd. If we can model 14 rugby players there is nothing to modelling a 15th and calling it myself. However this is not the system of self modelling. This is simply treating the self as another entity and there is no notion of selfhood.
Formally... and this is where I need to push ahead...
A universal set {A,B,C}
Now the powerset requires no new symbols. Within the rules we can construct subsets at liberty. e.g. {A,B},{A,B,C}
Now if the set {B,C} was to have self membership we would need to create a new symbol with which to reference it. T = {T,B,C} and the system increases by 1
The set of all symbols {A,B,C} and itself has a problem then because it requires a new symbol T, but that creates a new set and so on...Recursively this creates a problem...
Now let us start with a special symbol T for self reference
{A,B,C,T}
I guess the problem might be that T has no definition, and doesn't really belong to the same set as the other symbols so it can't be a member at this stage... to explore
If a system could operate on itself, for example a hand grasping itself, then the system would be able to complete the operation intrinsically.
The question then is under what circumstances would it simply complete under itself and under what circumstances would it complete under external circumstances.
If it is a truely intrinsic system then it negates its own operation because it would always complete under itself.
If there is an extrinsic factor that triggers self completion then it can operate on all factors except that extrinsic factor where the result is self-operation.
Thus there must always be one element within the domain of the input which it cannot operate upon, if it is to have self operation.
A set cannot essentially contain itself, because if it could complete under itself it would negate its containing function.
This is why a hand cannot grasp itself, for if it could then to be able to grasp anything else there would need to be an external trigger, which it could not itself grasp. Evidentally in the realm of things there are not rules enough to distinguish that special thing which would cause self-grasping. It is worth exploring this to find the rules...
On References....
The same argument then applies to references. A box can contain other boxes but it cannot contain itself. It contains instead a reference to itself.
However then it cannot then contain also that thing without breaking the reference rule. Thus to have self-membership you need a symbol which has a special meaning i.e. self. and not its obvious meaning.
Now it might seem absurd. If we can model 14 rugby players there is nothing to modelling a 15th and calling it myself. However this is not the system of self modelling. This is simply treating the self as another entity and there is no notion of selfhood.
Formally... and this is where I need to push ahead...
A universal set {A,B,C}
Now the powerset requires no new symbols. Within the rules we can construct subsets at liberty. e.g. {A,B},{A,B,C}
Now if the set {B,C} was to have self membership we would need to create a new symbol with which to reference it. T = {T,B,C} and the system increases by 1
The set of all symbols {A,B,C} and itself has a problem then because it requires a new symbol T, but that creates a new set and so on...Recursively this creates a problem...
Now let us start with a special symbol T for self reference
{A,B,C,T}
I guess the problem might be that T has no definition, and doesn't really belong to the same set as the other symbols so it can't be a member at this stage... to explore
Tuesday, 23 October 2007
Containing Oneself - 3 approaches
The problem then is that a theory seems to always be about something else. Systems must be extrinsic, you cannot have a system which is intrinsic.
The Existential/Essential Approach
=========================
In essential terms, if we take a materialist point of view, then a system embodies itself already... it "is" itself. To contain itself again would require there to be a copy of the system within it, in which case it would have a "similar" system inside but not the "same" system. A box cannot thus contain itself as to contain something being the "nature" (or essence) of the box requires something else to be contained... at best a copy of the box. Likewise a hand can only grasp for something else as to grasp for itself. You cannot for example shake hands with yourself.
It is the chicken and egg situation. To have a chicken you must have an egg etc. To grasp you must already have a hand, so you cannot then grasp that hand... still unconvinced of the apparent "necessity" of this. Why can't these things be true?
The Referencing Approach
===================
Anyway when we say that we must grasp, or box, a copy of the hand or box then we are "referencing" a copy to mean the object.
An entity can thus contain a "reference" to itself. This by itself is not very useful. We would need rules to govern how to model this reference and its relationship with references to other entities.
Also we can try to include the system within itself by referencing its own components. So how many components does a system have? It depends how many components are determined. This is a function of the simplicity of emergent properties and the level of detail. We could reference each atom of a car or we could model its engine parts. The rules that govern these references are very different.
I will explore later a very simple Lindenmayer System
variables : A B
constants : none
start : A
rules : (A -> AB), (B -> A)
This system is already a reference system, it will be interesting to see if it can reference itself.
Ofcourse what does that mean? Because at the end there is only input, interations and output. It still requires a user to see the "similarities" but it is a start at self-identity.
Black Box approach
==============
Finally if we say that two systems that produce the same output from the same input, regardless of their mechanics are identical then we can rephrase the problem as a system which models its own output.
But this is ridiculous! If all the system does is model its own output then it has an undefined output, so what is there to model? How could it be correct or incorrect? If it can't model its own output then it certainly can't model itself.
Now if the system did something useful say model some extrinsic data, and then we ask it to model itself then it would produce the same output and so again cannot succeed.
If we say that it models some extrinsic data, and also reports on its processing, then we are simply adding to the data that it outputs. This is no difference from the first case.
Still however the hand grasping itself says it best. That issue applied to data processing leads to a requirement for all systems to have extrinsic qualities.
If this is true then we cannot have any system which exists independent of its objects, and no system can explain itself.
Now Dave's idea of 2 systems modelling each other. However this closed system is really just one system.
Then we are into Strawson because it seems that the universe is just a single intrinsic system, with no extrinsic source of meaning. That is where people turn to God.
This is a bleak view arising maybe from the replacing of all "things" with references in models. Reality is not a model it is reality, and a model is not reality because it is a model.
However then we begin the very hard work of ontology and epistomology asking how is it that we have referencing at all, and are there really "things" independent of our knowing of them.
The problem is that the idea of "references" suggests that there is things which are linked by a meaning. Crudely this suggests that the link is a new thing and we are in the third man falacy. If it is a new things and we reference it then we have an eternal heirachy of references supporting the last link we made.
References are "implicit" within the process of knowledge, they only exist when we reference and do not exist independent of the things within the reference. They are "meaning" itself, the dialectic between things which are not one another, but at the same time are one another as they are used interchangeably.
If we cannot speak of references without their things, as they themselves are not things, then likewise we cannot speak of things without their references because how would we call them?
The dualism is thus only for teaching purposes. In its organic in-vitro environment there is no problem, they are sides of the same coin... that of Mind.
Still very whooly but getting there...
The Existential/Essential Approach
=========================
In essential terms, if we take a materialist point of view, then a system embodies itself already... it "is" itself. To contain itself again would require there to be a copy of the system within it, in which case it would have a "similar" system inside but not the "same" system. A box cannot thus contain itself as to contain something being the "nature" (or essence) of the box requires something else to be contained... at best a copy of the box. Likewise a hand can only grasp for something else as to grasp for itself. You cannot for example shake hands with yourself.
It is the chicken and egg situation. To have a chicken you must have an egg etc. To grasp you must already have a hand, so you cannot then grasp that hand... still unconvinced of the apparent "necessity" of this. Why can't these things be true?
The Referencing Approach
===================
Anyway when we say that we must grasp, or box, a copy of the hand or box then we are "referencing" a copy to mean the object.
An entity can thus contain a "reference" to itself. This by itself is not very useful. We would need rules to govern how to model this reference and its relationship with references to other entities.
Also we can try to include the system within itself by referencing its own components. So how many components does a system have? It depends how many components are determined. This is a function of the simplicity of emergent properties and the level of detail. We could reference each atom of a car or we could model its engine parts. The rules that govern these references are very different.
I will explore later a very simple Lindenmayer System
variables : A B
constants : none
start : A
rules : (A -> AB), (B -> A)
This system is already a reference system, it will be interesting to see if it can reference itself.
Ofcourse what does that mean? Because at the end there is only input, interations and output. It still requires a user to see the "similarities" but it is a start at self-identity.
Black Box approach
==============
Finally if we say that two systems that produce the same output from the same input, regardless of their mechanics are identical then we can rephrase the problem as a system which models its own output.
But this is ridiculous! If all the system does is model its own output then it has an undefined output, so what is there to model? How could it be correct or incorrect? If it can't model its own output then it certainly can't model itself.
Now if the system did something useful say model some extrinsic data, and then we ask it to model itself then it would produce the same output and so again cannot succeed.
If we say that it models some extrinsic data, and also reports on its processing, then we are simply adding to the data that it outputs. This is no difference from the first case.
Still however the hand grasping itself says it best. That issue applied to data processing leads to a requirement for all systems to have extrinsic qualities.
If this is true then we cannot have any system which exists independent of its objects, and no system can explain itself.
Now Dave's idea of 2 systems modelling each other. However this closed system is really just one system.
Then we are into Strawson because it seems that the universe is just a single intrinsic system, with no extrinsic source of meaning. That is where people turn to God.
This is a bleak view arising maybe from the replacing of all "things" with references in models. Reality is not a model it is reality, and a model is not reality because it is a model.
However then we begin the very hard work of ontology and epistomology asking how is it that we have referencing at all, and are there really "things" independent of our knowing of them.
The problem is that the idea of "references" suggests that there is things which are linked by a meaning. Crudely this suggests that the link is a new thing and we are in the third man falacy. If it is a new things and we reference it then we have an eternal heirachy of references supporting the last link we made.
References are "implicit" within the process of knowledge, they only exist when we reference and do not exist independent of the things within the reference. They are "meaning" itself, the dialectic between things which are not one another, but at the same time are one another as they are used interchangeably.
If we cannot speak of references without their things, as they themselves are not things, then likewise we cannot speak of things without their references because how would we call them?
The dualism is thus only for teaching purposes. In its organic in-vitro environment there is no problem, they are sides of the same coin... that of Mind.
Still very whooly but getting there...
Monday, 22 October 2007
Referencing, things and reality
Having looked at it there is nothing wrong with T={T}. But try and do this in reality and there is a problem.
Take 2 boxes. Now make a box of all boxes called C. In common sense we'd just put them in a third box, but strickly it is true that third box should be in itself. This cannot be done in "reality" so we would put a third box in and call it C. That is we would "reference" C with something else. Pretty obvious.
Take T = {T}
Actually there are 5 symbols (existing things). There is not one T symbol but two. When we say they are the same thing they cannot be the same thing else there would be only one symbol. In the example they are different things but they reference the same thing, belong to a finite symbol set so we can quantise them the same, and they are constructed in a way that our visual cortex picks out well (especially being made of lines). Nevertheless in "reality" they are different things and all the similarity occurs off the page in what I have been calling "mind". If similarity occurs in the mind then so does difference.
Another example to illustrate would be an orchestra. If the conductor asks the strings to form one group, and everyone else to form another. He might then ask I want a "group of all groups over here" i'll call the "orchestra". In common sense reality this simply means a group with the strings and everyone else. In the context no one thinks the groups are "real" they are in the "mind".
Now it's a trivial point. No one thinks that what I am writing is itself "real". The writing is just marks on a page, we assume I am talking "about" something "real" and the connection, the understanding and thinking, is "the mind".
What is "in the mind" is not real. So I was wrong "sets" are neither things nor real. They require "action" to become real. Action like things can be referenced but it has its own unique existence. Two actions are not the same thing, even when they look the same. This enters the vast realm of ethics.
Now apply that to materialism, and especially theories of mind. Materialism holds the belief that everything is founded upon a physical reality which is knowable. Clearly referencing cannot be founded upon the things it references that in other words is "mind" cannot be ignored in our account of "reality". Problems then for brain sciences because "the mind" cannot then be the same as "the brain".
Take 2 boxes. Now make a box of all boxes called C. In common sense we'd just put them in a third box, but strickly it is true that third box should be in itself. This cannot be done in "reality" so we would put a third box in and call it C. That is we would "reference" C with something else. Pretty obvious.
Take T = {T}
Actually there are 5 symbols (existing things). There is not one T symbol but two. When we say they are the same thing they cannot be the same thing else there would be only one symbol. In the example they are different things but they reference the same thing, belong to a finite symbol set so we can quantise them the same, and they are constructed in a way that our visual cortex picks out well (especially being made of lines). Nevertheless in "reality" they are different things and all the similarity occurs off the page in what I have been calling "mind". If similarity occurs in the mind then so does difference.
Another example to illustrate would be an orchestra. If the conductor asks the strings to form one group, and everyone else to form another. He might then ask I want a "group of all groups over here" i'll call the "orchestra". In common sense reality this simply means a group with the strings and everyone else. In the context no one thinks the groups are "real" they are in the "mind".
Now it's a trivial point. No one thinks that what I am writing is itself "real". The writing is just marks on a page, we assume I am talking "about" something "real" and the connection, the understanding and thinking, is "the mind".
What is "in the mind" is not real. So I was wrong "sets" are neither things nor real. They require "action" to become real. Action like things can be referenced but it has its own unique existence. Two actions are not the same thing, even when they look the same. This enters the vast realm of ethics.
Now apply that to materialism, and especially theories of mind. Materialism holds the belief that everything is founded upon a physical reality which is knowable. Clearly referencing cannot be founded upon the things it references that in other words is "mind" cannot be ignored in our account of "reality". Problems then for brain sciences because "the mind" cannot then be the same as "the brain".
Sunday, 14 October 2007
Look this argument is so simple...
Why have I spent so long trying to get this argument out... (like about 25 years on and off!!!) its nothing special, but it's implication are I think?
The rules of a system cannot be built within that system.
This is all it is!
Consider. How do you construct a system unless you know the rules? You can only construct a system once you know the rules. Now once you know a game, you can then use that game to write axioms (in a hermeneutic way) but you cannot escape the system now.
Like the anthropic principle, the very presence within a system is a "given". This has been argued to mean that there are many different systems and only some of which can support our presence. This seems like a circularity based upon the rules that have been worked out within this 1 system... that needs some thought. The alternative is that this universe had a special creation to be suitable for life... its interesting how the two ideas are so similar... that "specialness" in general seems to reflect an aspect of the ego.
There is no escape from the system... well within terms of that system. And since a kid I have realised that no theory we can construct has any real value unless it an build things from the start, and since we can't do that it seems and we have to start with a "given" universe we have to just accept the system of rules we call existence and live with it. God given or whatever we want to call it.
So the project (before I forget completely where I'm heading) is simply to create a game and try to build that game within itself to prove one way or another tat it can't be done fromally.
Quine's are a good game where rules are simple PRINT and "{string}". However there is a lot of stuff happening behind the scenes including creating memory which is hidden from the system.
So to propose: a system of characters on a grid (like chess) which have meaning in building characters, so that they can build themselves.
Things to note...
>that the meaning the "user" ascribes is not the same as the meaning the system ascribes (like with Aime)
>that some rules cannot be constructed within the system
>that given the rules a pretty good version of the rules can be built within the system using those rules ... but how good?
What is the constraint on a system that stops it building itself? Formalise that!!!
The rules of a system cannot be built within that system.
This is all it is!
Consider. How do you construct a system unless you know the rules? You can only construct a system once you know the rules. Now once you know a game, you can then use that game to write axioms (in a hermeneutic way) but you cannot escape the system now.
Like the anthropic principle, the very presence within a system is a "given". This has been argued to mean that there are many different systems and only some of which can support our presence. This seems like a circularity based upon the rules that have been worked out within this 1 system... that needs some thought. The alternative is that this universe had a special creation to be suitable for life... its interesting how the two ideas are so similar... that "specialness" in general seems to reflect an aspect of the ego.
There is no escape from the system... well within terms of that system. And since a kid I have realised that no theory we can construct has any real value unless it an build things from the start, and since we can't do that it seems and we have to start with a "given" universe we have to just accept the system of rules we call existence and live with it. God given or whatever we want to call it.
So the project (before I forget completely where I'm heading) is simply to create a game and try to build that game within itself to prove one way or another tat it can't be done fromally.
Quine's are a good game where rules are simple PRINT and "{string}". However there is a lot of stuff happening behind the scenes including creating memory which is hidden from the system.
So to propose: a system of characters on a grid (like chess) which have meaning in building characters, so that they can build themselves.
Things to note...
>that the meaning the "user" ascribes is not the same as the meaning the system ascribes (like with Aime)
>that some rules cannot be constructed within the system
>that given the rules a pretty good version of the rules can be built within the system using those rules ... but how good?
What is the constraint on a system that stops it building itself? Formalise that!!!
Friday, 12 October 2007
Consciousness, experiments, systems
What is consciousness?
Brain function correlates well with the "experiences", in that what we become conscious of corresponds with both physical entities and the discrete events caused within the brain.
Clearly naive realism is not true since phsyical objects by themselves do not create experiences, and idealism is not true because brains by themselves do not create experiences "of things".
However quite arbitrary causes like touching the brain and chemicals can create experiences which do not seem to correspond with either the cause.
Cause and experience are not clearly related.
That we do have a correlation under "usual" circumstances, for example when a volunteer sees a chair there is an organised pattern of predictable responses, is probably because the investigator has a similar effect in their brain. So the statement that the brain is corresponding in a orderly fashion to the stimulation, is simply a statement that the patients brain is corresponding in the same way as the investigors. Looking at the chair and then the patient, the investigator having established for themselves that there is a chair there, and then looked for correspondence in the brain of the patient, is really finding correspondence in the brain of the patient which corresponds to their own brain function. Afterall the investigator cannot see what the patient sees by definition, and only make sense of what they say because they come from the same linguistic world in which "seeing chairs" carries a certain language.
If the investigator was blind for example, no matter what instruments existed, they would not be able to make sense of "seeing a chair". It would simply be a pattern of brain activity, and associated words, which corresponded with a chair and its position before the eyes, and also certain predictive elements like being able to tell when a chair was present in a room without touching it. Factually the blind person can establish all this. But to understand from all this what having your own experience of "seeing" is like is beyond the experiment.
So these experiments in neuro-science are unable to shed light upon the nature of "personal" experience precisely because it is personal.
To do that we must go deeper into the nature of existence and personal identity it seems.
===
On the subject of systems suppose we had a 2D phase diagram of a system with 2 independent variables. That system can establish nothing greater than its own state. To model that phase diagram (without being that system) it must have more state variables than the system it is modelling. Is this true?
Also... philosophers and scientists are not looking to model the brain. They are looking to explain the brain. That means to provide a high level model of the elements of the brain.
So the suggestion then is that higher level state variables are available for systems which approximate the behaviour, which is actually produced by much more intricate lower level workings.
For example we might reduce the function f(x) = x ^ 10 to a binary description which states whether the function is high or low, since it appears to go along slowly before rising very fast through the (1,1) co-ordinate and away.
So a general theory of "scales" in theories is required to look at what might be considered a good enough explanation of th brain? afterall how good do we need to explain it before we might say we understand ourselves?
Add to this the fact that consciousness is not a low level phenomena either. We are conscious only of very high level entities, not the vast amounts of minute data available in any situation.
Brain function correlates well with the "experiences", in that what we become conscious of corresponds with both physical entities and the discrete events caused within the brain.
Clearly naive realism is not true since phsyical objects by themselves do not create experiences, and idealism is not true because brains by themselves do not create experiences "of things".
However quite arbitrary causes like touching the brain and chemicals can create experiences which do not seem to correspond with either the cause.
Cause and experience are not clearly related.
That we do have a correlation under "usual" circumstances, for example when a volunteer sees a chair there is an organised pattern of predictable responses, is probably because the investigator has a similar effect in their brain. So the statement that the brain is corresponding in a orderly fashion to the stimulation, is simply a statement that the patients brain is corresponding in the same way as the investigors. Looking at the chair and then the patient, the investigator having established for themselves that there is a chair there, and then looked for correspondence in the brain of the patient, is really finding correspondence in the brain of the patient which corresponds to their own brain function. Afterall the investigator cannot see what the patient sees by definition, and only make sense of what they say because they come from the same linguistic world in which "seeing chairs" carries a certain language.
If the investigator was blind for example, no matter what instruments existed, they would not be able to make sense of "seeing a chair". It would simply be a pattern of brain activity, and associated words, which corresponded with a chair and its position before the eyes, and also certain predictive elements like being able to tell when a chair was present in a room without touching it. Factually the blind person can establish all this. But to understand from all this what having your own experience of "seeing" is like is beyond the experiment.
So these experiments in neuro-science are unable to shed light upon the nature of "personal" experience precisely because it is personal.
To do that we must go deeper into the nature of existence and personal identity it seems.
===
On the subject of systems suppose we had a 2D phase diagram of a system with 2 independent variables. That system can establish nothing greater than its own state. To model that phase diagram (without being that system) it must have more state variables than the system it is modelling. Is this true?
Also... philosophers and scientists are not looking to model the brain. They are looking to explain the brain. That means to provide a high level model of the elements of the brain.
So the suggestion then is that higher level state variables are available for systems which approximate the behaviour, which is actually produced by much more intricate lower level workings.
For example we might reduce the function f(x) = x ^ 10 to a binary description which states whether the function is high or low, since it appears to go along slowly before rising very fast through the (1,1) co-ordinate and away.
So a general theory of "scales" in theories is required to look at what might be considered a good enough explanation of th brain? afterall how good do we need to explain it before we might say we understand ourselves?
Add to this the fact that consciousness is not a low level phenomena either. We are conscious only of very high level entities, not the vast amounts of minute data available in any situation.
Wednesday, 10 October 2007
Free, Bound variable + misc
A notion I was thinking of using before is already defined in maths...
A free variable is a symbol which has an external use. A bound variable has a particular use within the expression and so has no external meaning. Bound variables have closure of meaning while free variables must link to the outside.
A closed expression (a black box) can only replicate "all" the output of a open expression, it cannot determine "which" value a free variable takes.
This is the concise way of expressing the problem I had with "Aime" my 1996 AI experiment. Aime was written in a hermetic box seeking whether "feedback" could explain consciousness. It became apparent very quickly that anything that operates within a closed box has no meaning to the outside world.
Arguing further now, an AI machine must be able to link with its environment in order to mix with other agents ... i.e. as required by the Turing test.
Now any computer program, being just a collection of bits, is a number. There are a finite number of programs (given that no-one is ever going to write for ever, and no machine could ever write for ever).
One of those programs is the Mind Machine (MM) and we assume that humans have found it. Now the MM takes some input. There must be a finite amount of input for the MM to discover itself ... given that humans have done so. So that input is also a finite number. So the MM and the input data together form another single finite number.
Now we have to give the MM a machine on which to run else we would need to code how to build it, another number. And another number to build that machine and so on forever. So we give it a machine. Maybe like in Hitchhikers Guide to the galaxy it needs to build a new machine * x before it can get started
OK some problems here since maybe working out the start data is non-computable... anyway that is a start on a method of proof...
Miscellaneous ...
Vertical/lateral thinking - step by step proof/deduction forward and leaps followed by working back.
Could there ever be "artificial life". That is a question very closely related to this blog and one that will become more central after this initial work is done. Can the mind be artificial is the current project since we can use self-reference more easily to test ideas.
Hermeneutics seems more relevant as time is progressing to. I just need to find a nail for the coffin of deductive/logical/mechanical process thinking to show that fixed within rules we cannot escape to investigate those rules.
Rules btw might be the foundation to work with. Even set theory has rules that define what is a good and a bad formulation and process.
So the question is what rules define the rules? or if we define a rule how do we know that the rule is being followed? or if we define the word "rule" how do we know that it is being used correctly?
All these questions come down to the old point that the question "what is reason?" can't be answered without reason so it presupposes the answer.
Or the famous Anthropic principle http://en.wikipedia.org/wiki/Anthropic_principle which I would want to expand to the mind. We need a mind before we can even do the investigations into Life (carbon or anything else) and existence.
btw the issue of can things be their own foundations didn't get anywhere in set theory. I wanted to show that T <> {T} but the following suggests its quite consistent...
Consider a U = {T, A} where T = {T}
so T' = A
Now P(U) = { {}, {T}, {A}, {T, A} }
and consider a new universe of the elements of P(U) = U1
Given the definitions above this universe has 3 members U1 = {T, {A}, U}
so now T' = { {A}, U}
I was hoping for a contradiction. But actually if T' = A = { {A}, U} then
A = { {A}, U }
So A u T = { T, {A}, U } which is a perfectly consistent universe! I think...
anyway my brain hurts now so off to pub :-)
A free variable is a symbol which has an external use. A bound variable has a particular use within the expression and so has no external meaning. Bound variables have closure of meaning while free variables must link to the outside.
A closed expression (a black box) can only replicate "all" the output of a open expression, it cannot determine "which" value a free variable takes.
This is the concise way of expressing the problem I had with "Aime" my 1996 AI experiment. Aime was written in a hermetic box seeking whether "feedback" could explain consciousness. It became apparent very quickly that anything that operates within a closed box has no meaning to the outside world.
Arguing further now, an AI machine must be able to link with its environment in order to mix with other agents ... i.e. as required by the Turing test.
Now any computer program, being just a collection of bits, is a number. There are a finite number of programs (given that no-one is ever going to write for ever, and no machine could ever write for ever).
One of those programs is the Mind Machine (MM) and we assume that humans have found it. Now the MM takes some input. There must be a finite amount of input for the MM to discover itself ... given that humans have done so. So that input is also a finite number. So the MM and the input data together form another single finite number.
Now we have to give the MM a machine on which to run else we would need to code how to build it, another number. And another number to build that machine and so on forever. So we give it a machine. Maybe like in Hitchhikers Guide to the galaxy it needs to build a new machine * x before it can get started
OK some problems here since maybe working out the start data is non-computable... anyway that is a start on a method of proof...
Miscellaneous ...
Vertical/lateral thinking - step by step proof/deduction forward and leaps followed by working back.
Could there ever be "artificial life". That is a question very closely related to this blog and one that will become more central after this initial work is done. Can the mind be artificial is the current project since we can use self-reference more easily to test ideas.
Hermeneutics seems more relevant as time is progressing to. I just need to find a nail for the coffin of deductive/logical/mechanical process thinking to show that fixed within rules we cannot escape to investigate those rules.
Rules btw might be the foundation to work with. Even set theory has rules that define what is a good and a bad formulation and process.
So the question is what rules define the rules? or if we define a rule how do we know that the rule is being followed? or if we define the word "rule" how do we know that it is being used correctly?
All these questions come down to the old point that the question "what is reason?" can't be answered without reason so it presupposes the answer.
Or the famous Anthropic principle http://en.wikipedia.org/wiki/Anthropic_principle which I would want to expand to the mind. We need a mind before we can even do the investigations into Life (carbon or anything else) and existence.
btw the issue of can things be their own foundations didn't get anywhere in set theory. I wanted to show that T <> {T} but the following suggests its quite consistent...
Consider a U = {T, A} where T = {T}
so T' = A
Now P(U) = { {}, {T}, {A}, {T, A} }
and consider a new universe of the elements of P(U) = U1
Given the definitions above this universe has 3 members U1 = {T, {A}, U}
so now T' = { {A}, U}
I was hoping for a contradiction. But actually if T' = A = { {A}, U} then
A = { {A}, U }
So A u T = { T, {A}, U } which is a perfectly consistent universe! I think...
anyway my brain hurts now so off to pub :-)
Monday, 8 October 2007
Not, Truth and the Universe
When we create any proposition we are at the same time eliminating other "similar" propositions.
This process of elimination is called "negating". Without negation all propositions would have the same standing.
The negation process occurs under a universal, or a context. This is most clearly seen in set theory where A n A' = U gives the set of all things under discussion. U is not "All things" simply the limit of the discussion.
Given any proposition we have a relationship to the limit of the discussion through the "not" operator.
Truth and Falsehood lie outside the Universal as shown by Godel since statements can be true but cannot be proven within the Universal.
However a proposition which is deemed true gives rise to false propositions through negation.
When we define a proposition then it follows that this is being done under a larger context that allows for the propositions negation.
The negation of the Universal, i.e. the set of things we are not in discourse about, is not defined and creates a limit for "existence" within set theory. Thus existence is assumed for the elements of a universal (may even be the same thing).
The "God paradox" arises then when we use the elements of a set A to build the Universal, because the Universal contains both A and A' and so A cannot construct U.
Take the example of brains. The set of things to do with cognition are limited to "Brain". Then if we make an identity between brain and our experience, and we acknowledge that we know nothing outside our experience, then we know nothing outside our brain, the brain becomes the Universal. But our brain was originally defined as a subset of our knowledge. A creates U and so A' has no existence! We are simply eliminating elements to force U to A rather than explaining U.
U cannot be explained in terms of a subset since U = A & A'
A set such as T = {T} assumes an ontology: T, T', {T}, {T'} and a greater U. work this out...
In Hegelian logic a proposition A, entails its counter proposition A' and the possibility of a new set {A, A'} forces the U to expand to encompass it.
Hermeneutics may b of interest. This would say that we must take all the elements together to explain the whole system. It cannot be done heirachically bottom up, or top down.
This process of elimination is called "negating". Without negation all propositions would have the same standing.
The negation process occurs under a universal, or a context. This is most clearly seen in set theory where A n A' = U gives the set of all things under discussion. U is not "All things" simply the limit of the discussion.
Given any proposition we have a relationship to the limit of the discussion through the "not" operator.
Truth and Falsehood lie outside the Universal as shown by Godel since statements can be true but cannot be proven within the Universal.
However a proposition which is deemed true gives rise to false propositions through negation.
When we define a proposition then it follows that this is being done under a larger context that allows for the propositions negation.
The negation of the Universal, i.e. the set of things we are not in discourse about, is not defined and creates a limit for "existence" within set theory. Thus existence is assumed for the elements of a universal (may even be the same thing).
The "God paradox" arises then when we use the elements of a set A to build the Universal, because the Universal contains both A and A' and so A cannot construct U.
Take the example of brains. The set of things to do with cognition are limited to "Brain". Then if we make an identity between brain and our experience, and we acknowledge that we know nothing outside our experience, then we know nothing outside our brain, the brain becomes the Universal. But our brain was originally defined as a subset of our knowledge. A creates U and so A' has no existence! We are simply eliminating elements to force U to A rather than explaining U.
U cannot be explained in terms of a subset since U = A & A'
A set such as T = {T} assumes an ontology: T, T', {T}, {T'} and a greater U. work this out...
In Hegelian logic a proposition A, entails its counter proposition A' and the possibility of a new set {A, A'} forces the U to expand to encompass it.
Hermeneutics may b of interest. This would say that we must take all the elements together to explain the whole system. It cannot be done heirachically bottom up, or top down.
Saturday, 6 October 2007
Hermeneutic systems and their elements
OK the problem "the God paradox" occur when we try to found the elements of our universal upon themselves. What we have in fact is a hermeeutic circle where the collection of elements taken as a whole defines the world in which we can justify - as consistent - our elements. God is both the elements of our word and the collection of our world. You cannot reduce to the elements and throw away the aggregates and you cannot take the whole and ignore the elements that come together to make that whole.
Democritus and Paremenides I understand put forward 2 hypotheses in ancient Greece... that the world was built up from atoms in the first ase and that the world was divided down from the universal. They are both parts of the hermeneutic circle. The whole system and its parts must be taken together as a dialectic.
In the system T = {T} we have an interesting system where the aggregate {T} is also the only element. This is the simplest hermeneutic system.
I am undecided whether it is to be shown that you cannot create such a system and it be hermeneutically part of another system, or to how that such a system is internally consistent.
In 1994 I had a thesis called "harmonic structuralism". The idea was that given competing systems, the system with the least contradictions and conflicts that was the largest also (i.e. the system which accounted for the most harmony) was the ethically better system. So while the Nazi system may have been internally consistent to some existent it had a huge fracture in it that maybe the democratic system does not.
Democritus and Paremenides I understand put forward 2 hypotheses in ancient Greece... that the world was built up from atoms in the first ase and that the world was divided down from the universal. They are both parts of the hermeneutic circle. The whole system and its parts must be taken together as a dialectic.
In the system T = {T} we have an interesting system where the aggregate {T} is also the only element. This is the simplest hermeneutic system.
I am undecided whether it is to be shown that you cannot create such a system and it be hermeneutically part of another system, or to how that such a system is internally consistent.
In 1994 I had a thesis called "harmonic structuralism". The idea was that given competing systems, the system with the least contradictions and conflicts that was the largest also (i.e. the system which accounted for the most harmony) was the ethically better system. So while the Nazi system may have been internally consistent to some existent it had a huge fracture in it that maybe the democratic system does not.
Thursday, 4 October 2007
Axioms n beyond
OK so axioms and logic do seem to have some value in this. The consciousness conundrum can be formulated very simply ... this is informal I'll spend some time to make it precise later...
If we postulate that there are things, and then use those things to explain how we came to postulate that there are things then we have a theory in terms of the thing we were trying to explain. It would be impossible to have a theory not in terms of things so we can't replace that original postulate.
More generally a theory must be in terms of what it is not, otherwise we are taking it as an starting assumption... an axiom. We can't prove an axiom we can only show that it is consistent with other axioms.
The question then of how we arrive at axioms is beyond axioms then. It must be accepted by reason that we can generate propositions as a fact. That cannot be the work of the brain!
===
Set theory again. On a table let us take some red beads and put them in a box and some yellow beads and put them in a box we have 2 boxes which might be described as the red box and the yellow box. The red box is not actually red, and the yellow box is not actually yellow. Our table universe (U1) has only 2 entities, namely the two boxes.
Now if we were to think about the box of boxes; in the analogy, we would create a big box for the two boxes and then we would have a new universe (U2) with 1 box (namely the box of boxes of universe U1). What we obviously can't do in the physical world is to put the big box in itself.
Now in set theory it is assumed that all subsets of a set already exist, so set theory says that in universe U1 the set of boxes {red box, yellow box} exists automatically which is the same as U1. However it is not an actual box.
When we actually build that box we get a new universe with 1 member. Only once that set is constructed does is actually exist, but to make it a member of its own construction is a problem.
If it didn't exist then it would bring its own constrcution down. If it does exist then it makes itself exist. The existence of the set depends upon itself. e.g. if T = {T} then T needs to exist to create T (so it doesn't really exist). If T does not exist then T = {} which exists.
Now we can create sets simply by chosing our ontology, and we can change subject to make sets disappear. Now with T = {T} what ontology do we have? or what universe is that a member of? To create T we must already have T.
The set of all Universes which have "blue" as a member. Which universe is T in?
===
Having shown to myself today (almost like Descartes) that there is a "just is" feature of experience that at the root our experiences just are, I'm now ledt thinking how far does "just is" go. Obviously the arrangement of things in my room can be changed, it is not "just is". So what rule divides that which "just is" and that which can be investigated, understood and changed?
If we postulate that there are things, and then use those things to explain how we came to postulate that there are things then we have a theory in terms of the thing we were trying to explain. It would be impossible to have a theory not in terms of things so we can't replace that original postulate.
More generally a theory must be in terms of what it is not, otherwise we are taking it as an starting assumption... an axiom. We can't prove an axiom we can only show that it is consistent with other axioms.
The question then of how we arrive at axioms is beyond axioms then. It must be accepted by reason that we can generate propositions as a fact. That cannot be the work of the brain!
===
Set theory again. On a table let us take some red beads and put them in a box and some yellow beads and put them in a box we have 2 boxes which might be described as the red box and the yellow box. The red box is not actually red, and the yellow box is not actually yellow. Our table universe (U1) has only 2 entities, namely the two boxes.
Now if we were to think about the box of boxes; in the analogy, we would create a big box for the two boxes and then we would have a new universe (U2) with 1 box (namely the box of boxes of universe U1). What we obviously can't do in the physical world is to put the big box in itself.
Now in set theory it is assumed that all subsets of a set already exist, so set theory says that in universe U1 the set of boxes {red box, yellow box} exists automatically which is the same as U1. However it is not an actual box.
When we actually build that box we get a new universe with 1 member. Only once that set is constructed does is actually exist, but to make it a member of its own construction is a problem.
If it didn't exist then it would bring its own constrcution down. If it does exist then it makes itself exist. The existence of the set depends upon itself. e.g. if T = {T} then T needs to exist to create T (so it doesn't really exist). If T does not exist then T = {} which exists.
Now we can create sets simply by chosing our ontology, and we can change subject to make sets disappear. Now with T = {T} what ontology do we have? or what universe is that a member of? To create T we must already have T.
The set of all Universes which have "blue" as a member. Which universe is T in?
===
Having shown to myself today (almost like Descartes) that there is a "just is" feature of experience that at the root our experiences just are, I'm now ledt thinking how far does "just is" go. Obviously the arrangement of things in my room can be changed, it is not "just is". So what rule divides that which "just is" and that which can be investigated, understood and changed?
Sunday, 30 September 2007
A full outline of the suggestion. Minds, Things and Universes
The argument is a form of John Searles famous Chinese Room argument. Here he argues that humans following rule books blindly (like machines do) do not understand the rules so how can computers be said to?
The argument proposed here is: the output of human minds, (i.e. in the form of symbols (like this email), or in the form of computing machines, or even paintings or music) cannot be understood in isolation from the mind.
Consider: if something could be understood "as independent from the mind", then you would not need a mind to understand it. Conversely if we need a mind to understand things, then things cannot be considered independent from the mind.
This has wide implications as has already been discovered and I expand below.
In advance: by "mind" I am not referring to a "thing", it is simply undefined so far. The form of the argument is natural language. The issue is one of processes.
What I was trying to show previously was the processes of the mathematician processing symbols. The symbols cannot process themselves so I was hoping to find evidence of the "mathematician" in the symbols. In particular the evidence that systems are incomplete and that this implies work outside the system. That has been done by Godel.
I'll reconstruct a similar argument.
If we define a set A = {x : x <= 3, x in N} = {1,2,3}
Now it is true that A is a subset of itself. But that doesn't mean that the definition of A can "write" itself. Clearly the mathematician has done work to understand the set constructor notation and ensure the equality. For example I've had to learn how to do this.
So let us define B = {x: x is in set constructor notation} this is like a set of all sets that can be constructed.
Unlike the precise x<=3 above, there is no formal set constructor notation that I know to define set constructor notation, I'm relying upon the reader to understand that informal set definition.
What Godel would do here in essence is to give each set-constructor a number so that he could refer to it within itself. That way you can construct the set constructor {x : x is this constructor, x is not in constructor notation}.
That is a member of the set which is a member by virtue of saying it is not a member. Thus the member can be seen to be a member (because of its form), but you try and prove within the system you get a contradiction. This shows for my purposes (and has been identified elsewhere) that "truth" cannot always be proven within the system and relies on something else.
This is the liar paradox which is expressed well like this:
The Liar Paradox. "Truth" for English sentences is not definable in English.
Proof. Suppose it is. Then so is its complement "False". Let s be the sentence "This sentence is false" . Since the phrase "This sentence" refers to s, we have s iff "This sentence is false" iff "s is false" iff not s. A contradiction.
There are many oddities all very similar: consider Richard's Paradox which I quite like.
It all points to systems not being self-sufficient and I am taking that to point to the fact that if they were then why are minds needed to work on them?
Turing machines again find limitations in the halting problem (same link as Liar Paradox is good). I am trying to write a Turing machine on a Turing machine, its proving hard - any one know if it is possible? Obviously Turing machines carry the name Turing because of the work "He" did not the machines themselves.
Another paradox comes about like this:
Take a simple set system, we must define 2 things.
The Universal set (U), e.g. the colours = {red, white, blue, green}
A subset of U obeying some rule, A = {x: x is in the Union Jack, x in U}
So A = {red, white, blue}
The Universal is a special type of set which allows the complement: A' = U - A = {green}
Now the Universal set is "the universe of discourse", or "all the things we are talking about", or the "context". A new Universal set arises whenever we change subject, clearly that is the choice and work of the operator (mind).
Let me change subject to U1 = {x: x is four letter words} and define the set B = {x: x words beginning with "b", x in U1}
So we can see that "blue" is now a member of B. What has become of "green" in this universe? it doesn't exist. This is well documented in some philosophy esp. Buddhism that the mind creates existence, or that things have no existence outside the "field of discource".
Now if we can refer to the elements under discourse U, can we also refer to the "elements not-under discourse" for example {green} in this example. Well if we did then it would be under discourse and therefore part of U which contradicts U's definition, and if we don't then what is the meaning of "changing subject". Clearly the person using the set theory must be free from the field of discourse in order to define the U from the many elements which are not in U.
That is the more general paradox that we know that there are things outside our field of "view" or discussion, but if we try to refer to them they come under our field of view or discussion. So it is impossible to refer to things outside the field of view, or discussion, even while knowing they are there. How is that possible? i.e. there are things in the room next door that I can't see, but I know they are there... so what do they look like? we sort of imagine ghostly things that are both what they would look like if they were here, but which aren't here. Well I suspect in general that is called God to some, and I call it mind. Its the unbounded limits beyond the discourse which can't be in the discourse, but we know are there anyway.
The implications:
Materialist theories posit existence as a fundamental starting point. As seen above, existence is a product of mind or at least the field of discourse. Thus any theory trying to explain mind in terms of existences is flawed. I just had a "discussion" with a American neuro-scientist on the web and the unquestionable faith he put in existence was extraordinary. On one hand he says that the brain creates our world-view, on the other hand he says that world creates our brain. Well I pointed out if the world exists already what is the brain doing? He says it is creating a "representation" of the world. I said then what you call "the world" is only a "representation" since you are your brain, a representation of what? He didn't understand. Daniel Dennett is in the same camp, as is Dawkins and their hard materialist ilk.
AI etc runs into the same problems. Clearly we could make a human, women make humans every day. Its that this would not give us insight into mind. Mind is not brain because brain is only a field of discourse of mind.
Physics. There are a lot of quantum theories to explain mind and world. Again minds must be used ultimately to operate these theories and so these theories only posit a field of discourse. If machines could be made to operate these theories (like Deep Thought of Hitch Hikers fame) they would fall foul of the same problems surely?
The argument proposed here is: the output of human minds, (i.e. in the form of symbols (like this email), or in the form of computing machines, or even paintings or music) cannot be understood in isolation from the mind.
Consider: if something could be understood "as independent from the mind", then you would not need a mind to understand it. Conversely if we need a mind to understand things, then things cannot be considered independent from the mind.
This has wide implications as has already been discovered and I expand below.
In advance: by "mind" I am not referring to a "thing", it is simply undefined so far. The form of the argument is natural language. The issue is one of processes.
What I was trying to show previously was the processes of the mathematician processing symbols. The symbols cannot process themselves so I was hoping to find evidence of the "mathematician" in the symbols. In particular the evidence that systems are incomplete and that this implies work outside the system. That has been done by Godel.
I'll reconstruct a similar argument.
If we define a set A = {x : x <= 3, x in N} = {1,2,3}
Now it is true that A is a subset of itself. But that doesn't mean that the definition of A can "write" itself. Clearly the mathematician has done work to understand the set constructor notation and ensure the equality. For example I've had to learn how to do this.
So let us define B = {x: x is in set constructor notation} this is like a set of all sets that can be constructed.
Unlike the precise x<=3 above, there is no formal set constructor notation that I know to define set constructor notation, I'm relying upon the reader to understand that informal set definition.
What Godel would do here in essence is to give each set-constructor a number so that he could refer to it within itself. That way you can construct the set constructor {x : x is this constructor, x is not in constructor notation}.
That is a member of the set which is a member by virtue of saying it is not a member. Thus the member can be seen to be a member (because of its form), but you try and prove within the system you get a contradiction. This shows for my purposes (and has been identified elsewhere) that "truth" cannot always be proven within the system and relies on something else.
This is the liar paradox which is expressed well like this:
The Liar Paradox. "Truth" for English sentences is not definable in English.
Proof. Suppose it is. Then so is its complement "False". Let s be the sentence "This sentence is false" . Since the phrase "This sentence" refers to s, we have s iff "This sentence is false" iff "s is false" iff not s. A contradiction.
There are many oddities all very similar: consider Richard's Paradox which I quite like.
It all points to systems not being self-sufficient and I am taking that to point to the fact that if they were then why are minds needed to work on them?
Turing machines again find limitations in the halting problem (same link as Liar Paradox is good). I am trying to write a Turing machine on a Turing machine, its proving hard - any one know if it is possible? Obviously Turing machines carry the name Turing because of the work "He" did not the machines themselves.
Another paradox comes about like this:
Take a simple set system, we must define 2 things.
The Universal set (U), e.g. the colours = {red, white, blue, green}
A subset of U obeying some rule, A = {x: x is in the Union Jack, x in U}
So A = {red, white, blue}
The Universal is a special type of set which allows the complement: A' = U - A = {green}
Now the Universal set is "the universe of discourse", or "all the things we are talking about", or the "context". A new Universal set arises whenever we change subject, clearly that is the choice and work of the operator (mind).
Let me change subject to U1 = {x: x is four letter words} and define the set B = {x: x words beginning with "b", x in U1}
So we can see that "blue" is now a member of B. What has become of "green" in this universe? it doesn't exist. This is well documented in some philosophy esp. Buddhism that the mind creates existence, or that things have no existence outside the "field of discource".
Now if we can refer to the elements under discourse U, can we also refer to the "elements not-under discourse" for example {green} in this example. Well if we did then it would be under discourse and therefore part of U which contradicts U's definition, and if we don't then what is the meaning of "changing subject". Clearly the person using the set theory must be free from the field of discourse in order to define the U from the many elements which are not in U.
That is the more general paradox that we know that there are things outside our field of "view" or discussion, but if we try to refer to them they come under our field of view or discussion. So it is impossible to refer to things outside the field of view, or discussion, even while knowing they are there. How is that possible? i.e. there are things in the room next door that I can't see, but I know they are there... so what do they look like? we sort of imagine ghostly things that are both what they would look like if they were here, but which aren't here. Well I suspect in general that is called God to some, and I call it mind. Its the unbounded limits beyond the discourse which can't be in the discourse, but we know are there anyway.
The implications:
Materialist theories posit existence as a fundamental starting point. As seen above, existence is a product of mind or at least the field of discourse. Thus any theory trying to explain mind in terms of existences is flawed. I just had a "discussion" with a American neuro-scientist on the web and the unquestionable faith he put in existence was extraordinary. On one hand he says that the brain creates our world-view, on the other hand he says that world creates our brain. Well I pointed out if the world exists already what is the brain doing? He says it is creating a "representation" of the world. I said then what you call "the world" is only a "representation" since you are your brain, a representation of what? He didn't understand. Daniel Dennett is in the same camp, as is Dawkins and their hard materialist ilk.
AI etc runs into the same problems. Clearly we could make a human, women make humans every day. Its that this would not give us insight into mind. Mind is not brain because brain is only a field of discourse of mind.
Physics. There are a lot of quantum theories to explain mind and world. Again minds must be used ultimately to operate these theories and so these theories only posit a field of discourse. If machines could be made to operate these theories (like Deep Thought of Hitch Hikers fame) they would fall foul of the same problems surely?
Thursday, 27 September 2007
Self-organising systems
Self-organising systems are dynamic systems which show stable emergent properties. i questioned already whether the emergent properties are really part of the under-lying dynamics - that is a question from Buddha!
In humans there are self-organising systems (basically the series that form societies structures, and also a large part of the processes that underlie all group formation). People may believe that they can create political parties and societies but unless the dynamics are already there it won't happen. Plus it is maybe rather egotistical that one person believes that by their own power they can influence so many people!
But as seem with the Nazis such self organising groups can put the individuals who are part of the self organisation in bizarre circumstances and make them behave in ways which alone they might disagree with.
It is precisely because social self-organisation can be so dangerous that it is something we should shy from, and remain personally conscious and responsible for everything we do. That is a repeat of the arguments against society and for Anarchy before.
In humans there are self-organising systems (basically the series that form societies structures, and also a large part of the processes that underlie all group formation). People may believe that they can create political parties and societies but unless the dynamics are already there it won't happen. Plus it is maybe rather egotistical that one person believes that by their own power they can influence so many people!
But as seem with the Nazis such self organising groups can put the individuals who are part of the self organisation in bizarre circumstances and make them behave in ways which alone they might disagree with.
It is precisely because social self-organisation can be so dangerous that it is something we should shy from, and remain personally conscious and responsible for everything we do. That is a repeat of the arguments against society and for Anarchy before.
Some problems from Physics
I don't have a formal understanding of this yet but as much as I understand: firstly Godel's incompleteness theorum states that in systems that correspond with maths it can be shown that some theorums cannot be proven from axioms. But we may be able to show they are true by computer process. Turing non-computability theorum indicates that some problems cannot be computed.
Disregarding those problems, the issue of where did all the data (information) in the universe come from? Now we might be able to determine equalities and equations, and we might be able to write comptable processes but upon what data can we work?
The possibility from the Quine investigation is that we could work on those theories themselves. If a theory could be created which produced which working on itself created itself this is a good step forward.
Disregarding those problems, the issue of where did all the data (information) in the universe come from? Now we might be able to determine equalities and equations, and we might be able to write comptable processes but upon what data can we work?
The possibility from the Quine investigation is that we could work on those theories themselves. If a theory could be created which produced which working on itself created itself this is a good step forward.
Constructing a Quine
I'm a bit annoyed with myself that I gave up too quick and had a glimpse of a quine which gave me the way forward. But I can construct the argument, and the sticking point, since I only gleened a small part of the problem.
A quine is a program which outputs (prints) itself. I'll use QBasic which is free and simple. It uses " for quotations and can't print " direct u need to use CHR$(34). I'm going to use ' for simplicity, so to use the program this will need be corrected.
We know then that it must include an output function that is 'PRINT' which sends whatever follows to the output screen. So our starting program is:
PRINT
it does nothing. So we know we need to print itself so we get
PRINT 'PRINT'
which produces an output of: PRINT. But putting new PRINTs in the code while it does produce a new PRINT in the output, also puts a new PRINT in the code so we never solve the problem.
What we need to do is add a PRINT to the output without typing it directly in the program. The easiest way to do this is to put the PRINT in memory (like a second screen) and then copy that twice to the output. That way you have 2 prints in the program (like the example above) and two in the output. Thus the problem has been solved and the backbone of the quine is done.
convert PRINT 'PRINT' to
a$ = 'PRINT': PRINT a$ a$
This was the sticking point for me last night, I was stuck on the approach of thinking that the a$ must include the program so I was starting like this:
a$ = 'a$ = ': PRINT a$ a$ -- This creates another problem of the type above. You need to mix data/code between the two parts of the equation ... it will be explained.
So given the basic structure above all we need to do is fill in the syntactic details. Firstly let us get the PRINT statement right so that it outputs as close as we possible to the above. In other words lets take the program elements of the first part and feed them into the data element of the PRINT statement in th second part.
: PRINT 'a$ = '' + a$ + '':' + a$
This outputs: a$ = 'PRINT': PRINT
So now take the program code of the second part (after the :) and feed that into the a$ data of the first part.
a$ = "PRINT 'a$ = '' + a$ + '':' + a$' :
Stick those together and you got a quine
a$ = "PRINT 'a$ = '' + a$ + '':' + a$' : PRINT 'a$ = '' + a$ + '':' + a$
However this does not work because on each line the data is enclosed by " marks, while the representation of " as data is '. If they were the same the program does not know whether to treat them as string delimiters or just parts of a string. If you then start filling out CHR$(34) then the code just keeps expanding endlessly.
This method does not work.
Trying to code delimiters and then enclode them within other delimiters is bound to fail because you will always have that problem we started with of a highest level delimiter which cannot be encoded.
A brute force method to solve this is to not use delimiters at all. The CHR$(34) method suggested above is the only way in QBasic to PRINT a " symbol since the " symbol is recognised by the language so we PRINT CHR$(34). We will have to use this method anyway somewhere.
So convert the whole string into ASC codes. There is a standard method in the language using READ to assign a variable with data from a DATA list.
Simply write the READ, DATA block with a line to print the CHR$ of each number, and another line to collect the list of data. Then once the data has all been read it prints the collection of data.
So the quine program reads its own data. Turns this into character output and then prints the data that it constructed itself from.
What the program could do is find its own place in memory and read itself into another memory location. Not that amazing really.
In the Quine though I've done that work already creating the data list. Using a recursive algorithm to write the program block, then encode it, then see how big it is and adjust the program and the code parameters until they match.
To note then: obviously the program gets written first. Without the engine nothing happens. This is a general solution to the problem of outputting data. Then just get it to print the data again to produce the data block at the end of the program. Then put in the data specific to itself and voila.
Its not as neat or intriguing as the first approach and I write endlessly here trying to find a way into the problem of "encoding itself". This second solution simply avoids the problem completely ... but how?
===
blurb from the first draft of this entry...
Now I'm interested in this process analogously because what I am having difficulty with, and the basis of my proof if such exists, is the implication of dualisms. For example where someone presents a limit to knowledge then this limit must be different from the knowledge itself. This is analogous to the data / program distinction. Other examples are subject / object. However if arguments of the Quine type can be constructed we have a way of expressing the "back breaking" job that dualisms create and find a way of overcoming the division.
Maybe then this investigation does not lead to a disproof of limits, but rather an personal understanding of how to construct limits within themselves, so that we can have something which full represents itself.
It is interesting that to do this we need to construct 2 copies of the partial structure, and that partial structure "represents" that dual creation. This if we were a "quine" only processing data we would know that our theorum on which we worked had two copies.
Q: how could a quine ever know that it was a quine? The process of comparing program and output is done by the user?
Q2: Next task a binary quine.
Q3: Is there a self-organising automaton version of the quine using recursive processes like above? Thesis/Anti-thesis -> Synthesis.
A quine is a program which outputs (prints) itself. I'll use QBasic which is free and simple. It uses " for quotations and can't print " direct u need to use CHR$(34). I'm going to use ' for simplicity, so to use the program this will need be corrected.
We know then that it must include an output function that is 'PRINT' which sends whatever follows to the output screen. So our starting program is:
it does nothing. So we know we need to print itself so we get
PRINT 'PRINT'
which produces an output of: PRINT. But putting new PRINTs in the code while it does produce a new PRINT in the output, also puts a new PRINT in the code so we never solve the problem.
What we need to do is add a PRINT to the output without typing it directly in the program. The easiest way to do this is to put the PRINT in memory (like a second screen) and then copy that twice to the output. That way you have 2 prints in the program (like the example above) and two in the output. Thus the problem has been solved and the backbone of the quine is done.
convert PRINT 'PRINT' to
a$ = 'PRINT': PRINT a$ a$
This was the sticking point for me last night, I was stuck on the approach of thinking that the a$ must include the program so I was starting like this:
a$ = 'a$ = ': PRINT a$ a$ -- This creates another problem of the type above. You need to mix data/code between the two parts of the equation ... it will be explained.
So given the basic structure above all we need to do is fill in the syntactic details. Firstly let us get the PRINT statement right so that it outputs as close as we possible to the above. In other words lets take the program elements of the first part and feed them into the data element of the PRINT statement in th second part.
: PRINT 'a$ = '' + a$ + '':' + a$
This outputs: a$ = 'PRINT': PRINT
So now take the program code of the second part (after the :) and feed that into the a$ data of the first part.
a$ = "PRINT 'a$ = '' + a$ + '':' + a$' :
Stick those together and you got a quine
a$ = "PRINT 'a$ = '' + a$ + '':' + a$' : PRINT 'a$ = '' + a$ + '':' + a$
However this does not work because on each line the data is enclosed by " marks, while the representation of " as data is '. If they were the same the program does not know whether to treat them as string delimiters or just parts of a string. If you then start filling out CHR$(34) then the code just keeps expanding endlessly.
This method does not work.
Trying to code delimiters and then enclode them within other delimiters is bound to fail because you will always have that problem we started with of a highest level delimiter which cannot be encoded.
A brute force method to solve this is to not use delimiters at all. The CHR$(34) method suggested above is the only way in QBasic to PRINT a " symbol since the " symbol is recognised by the language so we PRINT CHR$(34). We will have to use this method anyway somewhere.
So convert the whole string into ASC codes. There is a standard method in the language using READ to assign a variable with data from a DATA list.
Simply write the READ, DATA block with a line to print the CHR$ of each number, and another line to collect the list of data. Then once the data has all been read it prints the collection of data.
So the quine program reads its own data. Turns this into character output and then prints the data that it constructed itself from.
What the program could do is find its own place in memory and read itself into another memory location. Not that amazing really.
In the Quine though I've done that work already creating the data list. Using a recursive algorithm to write the program block, then encode it, then see how big it is and adjust the program and the code parameters until they match.
To note then: obviously the program gets written first. Without the engine nothing happens. This is a general solution to the problem of outputting data. Then just get it to print the data again to produce the data block at the end of the program. Then put in the data specific to itself and voila.
Its not as neat or intriguing as the first approach and I write endlessly here trying to find a way into the problem of "encoding itself". This second solution simply avoids the problem completely ... but how?
===
blurb from the first draft of this entry...
Now I'm interested in this process analogously because what I am having difficulty with, and the basis of my proof if such exists, is the implication of dualisms. For example where someone presents a limit to knowledge then this limit must be different from the knowledge itself. This is analogous to the data / program distinction. Other examples are subject / object. However if arguments of the Quine type can be constructed we have a way of expressing the "back breaking" job that dualisms create and find a way of overcoming the division.
Maybe then this investigation does not lead to a disproof of limits, but rather an personal understanding of how to construct limits within themselves, so that we can have something which full represents itself.
It is interesting that to do this we need to construct 2 copies of the partial structure, and that partial structure "represents" that dual creation. This if we were a "quine" only processing data we would know that our theorum on which we worked had two copies.
Q: how could a quine ever know that it was a quine? The process of comparing program and output is done by the user?
Q2: Next task a binary quine.
Q3: Is there a self-organising automaton version of the quine using recursive processes like above? Thesis/Anti-thesis -> Synthesis.
Tuesday, 25 September 2007
random jot about consciousness
remember that a flat worm trained to do a maze and fed to another flat worm somehow passes on the knowledge. Examine that because information must be encodeable in flatworm matter!!
Don't forget music and consciousness. Frequences seem important, n music has been taken as a higher state of reality than text by quite a few!
Don't forget music and consciousness. Frequences seem important, n music has been taken as a higher state of reality than text by quite a few!
Notes as I read...
In other words true autopoesis is impossible.
Ok an autopoetic system supports itself, like butter is needed to make more butter. But you get chicken and egg because the first system must have been formed by other means. So it can't really "create" itself, only "support" itself
Alternatively its simply emergent property (almost epi-phenomalism), whereby an underlying dynamic system produces a stable property. But such a property is not involved in the system! Its a higher order.
An interesting possibility then is a system which creates an emergent property which is involved in the autopoesis. i suspect category mistake, but very interesting if this exists. i think immediately of group fitness versus individual fitness in behavioural ecology... however while these 2 levels can be studied i don't see yet how they interact.. if at all. Interesting way forward...
V. INTERSETING actually because this would test absolutely whether structure or "scale" was a product of perception or a reality. The world can be described in the level of atoms. It can also be described on the level of humans. But can it be described on both levels at the same time! This collection of atoms "died" thus leading to rapid dissipation. Does that make sense?
Just to state at this time, I've failed to see any "substance" in ideas of emergent properties. It seems to me to be simply a feature of "classification". Shall determine that belief for sure in this on going...
Just adding... regarding the old question about how remarkable it is that the world makes sense to humans... i wonder what the logical implications of it not making sense would be? What does this sentence really mean? Are we imagining a world that does not make sense? How about a world that makes more sense and in what sense. Obviously predicting the future is the test, and science does well. So in a world where we could not predict the future, or a world where the future was always known what are the logical implications? Well if the future was always known then it wouldn't be th future, and there would be no time (i suspect) and in a world where we simply could not predict the future and every moment was a complete suprise ther would be no memory or past (cos everything would be new). So time itself entails being slap bang in between the two!!! So why maths? That's the other big question... no thoughts yet...
self-organising -> basically decreasing entropy at one level, increasing at another.
Quines. Linked to compression. but first...
Compression a simple proof. If every binary sequence encodes a number, then there are as many binary sequences as N (natural numbers).
Now in compression we are saying that a number can be mapped to a smaller number and back again. In other words it is a 1 to 1 mapping within N. (btw The set of such mappings is the same size as N.) So given a number and a compression algorithm we need a bit of information to know whether the number is meant to be decompressed or not. ok that is not the proof just following a tangent, the proof was that each number by itself might or might-not be useful so compression is not an elimination of useless numbers, but rather a mapping and so it requires an algorithm to compress/decompress and that algorithm effectively generalises the information lost by compression. To develop an algorithm we extract the general information from the code, so that the code is smaller and the algorithm bigger. (We don't usually include the algorithm in the size of the result, but we should to be honest ... something need to just test with zip).
anyway the point and the relationship with Quines is that the code while producing itself is a cheat, because the binary exection code is not reproduced. A machine language Quine would be cute!! i.e. one that truely reproduced itself. And that is in Turing territory cos I need to write a Turning machine which first of all runs a set of Turing tables, and then writes itself. That would be exceptionally cute!!!
Same logic as the Turing machine on a Turing machine, consider a self interpreter... i.e. a compiler compiled by itself. Chicken and egg.
probably useless but tuppers self ref formula : http://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula
note: an argument I used against Dawkins Memes thus: has a weakness. He says that ideas evolve like genes (I had the idea of viruses). The problem tho is that Memes is an idea so if follows that it has evolved like a gene. Now the fitness of the Meme meme is not what Dawkins is meaning by its truth. I can't see the idea catching on, while it might be true. So we return to truth as a measure of fitness rather than population. Its not a strong argument against it, but it shows up the fact it can't be taken to totality, cos if the Meme meme was floated and then went extinct it loses any notability. This argument needs to be strengthened cos I suspect its a form of a general argument that could be applied to all formualtions including itself!
End. brain ache! off to eat.
Ok an autopoetic system supports itself, like butter is needed to make more butter. But you get chicken and egg because the first system must have been formed by other means. So it can't really "create" itself, only "support" itself
Alternatively its simply emergent property (almost epi-phenomalism), whereby an underlying dynamic system produces a stable property. But such a property is not involved in the system! Its a higher order.
An interesting possibility then is a system which creates an emergent property which is involved in the autopoesis. i suspect category mistake, but very interesting if this exists. i think immediately of group fitness versus individual fitness in behavioural ecology... however while these 2 levels can be studied i don't see yet how they interact.. if at all. Interesting way forward...
V. INTERSETING actually because this would test absolutely whether structure or "scale" was a product of perception or a reality. The world can be described in the level of atoms. It can also be described on the level of humans. But can it be described on both levels at the same time! This collection of atoms "died" thus leading to rapid dissipation. Does that make sense?
Just to state at this time, I've failed to see any "substance" in ideas of emergent properties. It seems to me to be simply a feature of "classification". Shall determine that belief for sure in this on going...
Just adding... regarding the old question about how remarkable it is that the world makes sense to humans... i wonder what the logical implications of it not making sense would be? What does this sentence really mean? Are we imagining a world that does not make sense? How about a world that makes more sense and in what sense. Obviously predicting the future is the test, and science does well. So in a world where we could not predict the future, or a world where the future was always known what are the logical implications? Well if the future was always known then it wouldn't be th future, and there would be no time (i suspect) and in a world where we simply could not predict the future and every moment was a complete suprise ther would be no memory or past (cos everything would be new). So time itself entails being slap bang in between the two!!! So why maths? That's the other big question... no thoughts yet...
self-organising -> basically decreasing entropy at one level, increasing at another.
Quines. Linked to compression. but first...
Compression a simple proof. If every binary sequence encodes a number, then there are as many binary sequences as N (natural numbers).
Now in compression we are saying that a number can be mapped to a smaller number and back again. In other words it is a 1 to 1 mapping within N. (btw The set of such mappings is the same size as N.) So given a number and a compression algorithm we need a bit of information to know whether the number is meant to be decompressed or not. ok that is not the proof just following a tangent, the proof was that each number by itself might or might-not be useful so compression is not an elimination of useless numbers, but rather a mapping and so it requires an algorithm to compress/decompress and that algorithm effectively generalises the information lost by compression. To develop an algorithm we extract the general information from the code, so that the code is smaller and the algorithm bigger. (We don't usually include the algorithm in the size of the result, but we should to be honest ... something need to just test with zip).
anyway the point and the relationship with Quines is that the code while producing itself is a cheat, because the binary exection code is not reproduced. A machine language Quine would be cute!! i.e. one that truely reproduced itself. And that is in Turing territory cos I need to write a Turning machine which first of all runs a set of Turing tables, and then writes itself. That would be exceptionally cute!!!
Same logic as the Turing machine on a Turing machine, consider a self interpreter... i.e. a compiler compiled by itself. Chicken and egg.
probably useless but tuppers self ref formula : http://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula
note: an argument I used against Dawkins Memes thus: has a weakness. He says that ideas evolve like genes (I had the idea of viruses). The problem tho is that Memes is an idea so if follows that it has evolved like a gene. Now the fitness of the Meme meme is not what Dawkins is meaning by its truth. I can't see the idea catching on, while it might be true. So we return to truth as a measure of fitness rather than population. Its not a strong argument against it, but it shows up the fact it can't be taken to totality, cos if the Meme meme was floated and then went extinct it loses any notability. This argument needs to be strengthened cos I suspect its a form of a general argument that could be applied to all formualtions including itself!
End. brain ache! off to eat.
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