Proof that you can't have an Emulator (wrong)

This is wrong; you can have an Emulator (update 20/8/2025)

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This is an odd recent result that makes no sense.

(1) List all one argument functions so that each function has a number.

f1(x) is the function on the 1st row where n=1
f2(x) is the function on the 2nd row where n=2
etc

let #f be the notation that gives the row number of the function so that #fn = n

(2) Suppose there is an emulator function E(#f,x) which takes the row number from (1) and provides the result that f(x) would provide so that:

E(#f,x) == f(x)

(3) For each particular value of x, lets call it 'a', in (2) there is a function Ea(n) such that:

Ea(#f) == E(#f,a) == f(a)

In other words for every value of x there is a corresponding function fx(n) which provides the result of the function fn(x) on x.

(4) Each Ea(x) if it exists must have a row number #Ea. Substituting in 3 gives

Ea(#Ea) == E(#Ea, a) == Ea(a)

Therefore:

#Ea = a

This means that the row position of each Emulator of functions on value a is 'a' itself.

This is clearly a problem already. The following is simply looking for a contradiction in this statement:

But f5 is the name we have for the function at row 5, and 'fa' for the function at row 'a'

So:

fa(x) == Ea(x) == fx(a)

The function at row a applied to x gives the same result as the function at row x applied to a.

This is clearly nonsense as the order of function listing at the start was quite arbitrary... but how do we prove it.

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This is correct:

Ea(#Ea) == E(#Ea, a) == Ea(a)

And so:

Ea(#Ea) == Ea(a)

But what does this assure that #Ea = a.

if #Ea = b

Ea(b) == Ea(a)

For b = a there would need to be just one 'b' for which Ea(b) == Ea(a). However we cannot guarantee this. There nay be many numbers 'b' where Ea(b) == Ea(a).

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What we can do however is use this construction to prove Kleene's Fixed Point Theorem. #TODO

Proof of God progress

If a(b(x)) = f(x) and b(a(x)) != f(x) then there is no a(x) nor b(x) such that a(x) = f(x) or b(x) = f(x)

Basically the existence of "meta information" i.e. order of operations is outside either operation a or b. Thus a() and b() cannot be equal to f(x)

This is a concrete example of the SRH which states that self reference is impossible. If self-reference means more than simply self-naming which is trivial, but a computational function e.g. with self-knowledge or self-consciousness, then we are saying that bcos the Total system has components that are structured then the components cannot be both components in a structure and also represent that structure. Structure is a concrete example of the more general "meta" system. Originally it was awareness that text itself is meaningless, it needs a language user.

Equally computer code is meaningless it needs a CPU. Thus the CPU can never be expressed in code. However emulators exist, and emulators of Turing capability can emulate anything. But at root the emulator must run on a CPU that is not itself emulated. You cannot have M.C.Eshers hand drawing a hand drawing itself, it must have basis outside the system. This is because the emulated entities while homomorphic with the "real" CPU can be "necessary components", and thus there must be the possibility of information that is outside the emulations.

Definition: "necessary components" are components whose structure is critical to their compositions of the entity. A grain of sand in a bucket of concrete is not a "necessary component" as the grain of and can be swapped with a pebble and it is still a bucket of concrete. There is no structural information. However a strut in a roof frame is. The roof frame fails if the strut and joist components are swapped.

There is an exception to the opening statement.

While a(b(x)) != b(a(x)) across most values, there may be a Fixed Point value.

Since a(b(fp)) == b(a(fp))

Fixed Points were central to earlier exploration of the SRH. Godel Statements lead to contradictions and so incompleteness which breaks systems and allowed statements to exist "outside" systems, or the boundaries of systems to be broken. This is SRH, in that systems are forced to acknowledge an "outside". A truly self-referential statement would reference itself within itself, that would be a statement that would need no "outside", one that depended only upon itself. "Myself" is synonymous with totality and exclusion of "Other". This is very much the Dark-Tetrad problem discussed in previous post.

The negation of a tautological statement is a contradiction.

Similarly it was theorised that where a fixed point in a system like: x = "x is True" cannot be false without contradition, its negation x = Not("x is True") is a contradiction and Godel uses this structure to break Principia. x = Not(x is in Principia)

This is very loose logic, probably a lot of nonsense, but broadly sweeping out over the mental possibilities.

So it is interesting that Fixed Points that were the focus before, and which we thought provided the mechanism to break any system and point "outside" defeating any Totalising project like Russells. Now they are the unique cases that break my proof that meta-data, or structure must exist in the order of operations that cannot therefore be grasped by those operations.

If we rewrite f(x) == a(b(x)) as f(x) == {a,b,ab}(x) meaning that we have a, b and the order ab.

If A(x) == {a, ab}(x) i.e. somehow it was able to contain the structural info so that when combined with b there is "nothing more" and it is then equal to f(x) so that:

f(x) = A(b(x)) = b(A(x))

we would need to show that whatever {a, ab}(x) represents is always a chimera.

Tentative steps forward. It is encouraging that this looks like nonsense. Either it is madness, or it is pushing against something (to me) new.

Note on the madness of Capitlsim

A war is excellent for Capitalism. It causes a lot of destruction and so a lot of jobs in the construction industry, in medicine, in counseling: it is good for the economy. But it is bad for the people. How is this contradiction possible?

When my house is destroyed and I must pay for a new one. Through the lens of economics this is good it increases the circulation of money and provides jobs, income and livelihood for people. But through the lens of common sense it is bad. This is the madness of Capitalism.

Buddhism and the Dark Triad/Tetrad

Have done a bit of reading about the Dark Tetrad. This seems like a very important classification in psychology because it identifies the key qualities surrounding what has been broadly called before Evil.

It is the battle against Evil which is at the centre of Human Life. Enlightenment more than anything is the defeat of Evil. Traditional stories of Evil include the creation of suffering through evil acts and the entering of Hell for those who become controlled by Evil. Both these remain sensible. The nature of Evil (and of the Dark Tetrad) is isolation and this is the opposite of our True Nature which is universal, total and unified. The obvious proof of this lies in examining what barriers really exist between people, and of what those barriers might be made of?

It is fascinating to me that the qualities of the Dark Tetrad include misunderstanding of True Nature.

The Narcissist is actually a paper thin version of a Buddha. It is appealing to our Narcissistic tendencies to feel we are a Buddha - superior, complete, indestructable, perfect, universal. The irony of course is that we are almost perfectly the opposite. When we face their own death and the humiliation and shame of sickness and old age like Buddha we will quickly realise we have only achieved a shell from reality: one that must be broken before even starting on the path to Buddhahood. Shame and humiliation is the key to the Narcissist but also the path to Enlightenment: the totally crushing realisation that we do not stand alone but are made by our parents and the universe around us and we cannot exist without other people and the world.

The Machiavellian which I cannot relate to at all, must be very stupid. For them life and other people is a game to be won. But they measure the winning only upon their own status. Thus a win-win is of less value than a win-lose because the latter enables them to defeat the enemy, while a win-win strengthens the enemy. But when we realise like above that we did not make ourselves, we have arrived mysteriously upon this planet by forces other than ourselves: our parents, the health care workers, teachers, farmers and everyone who has made and supported us and actually there is nothing about us that will survive death the idea of "winning for myself" appears ludicrous. We are the fool, and the irony is that our chosen target in the game like money, or sex, respect or whatever is only ever increased at the expense of everything else we don't measure. Like economics that while the money and wealth may increase the environment is destroyed and we are ultimately the poorer. The devil is very good at using fake goals to tempt us to the pit of destruction.

The Psychopath I can identify with because for my whole life I have seen feeling as useless. It is a primitive part of the brain and a vestige of our animal past. It makes us weak because people can emotionally blackmail us, and we are vulnerable to animal instincts. Like the little mermaid accepting feelings also means we have to accept pain so is it worth it? (This is all a wrong view btw). I neither want to feel in myself nor feel in others. The rational by contrast is the pure, it is universal, it is the correct. the Vulcans of Star Trek embody this view. Indeed Buddha as desireless and indifferent seems like a cool Psychopath at first look. But there is a problem with the real Psychopath actually they are not entirely honest with themselves. They do have feelings but "only for themselves". So the psychopath will get angry, and they will want love, and they will get hurt so they are firstly dishonest - feelings are centre in their life. Now they say that there are genes that make people into psychopaths so that they have no mirror neurons and they actually cannot feel what other people feel. They end up faking interactions with other people their whole lives so they can fit in, and they know its a fake. They are like blind people but it is others feelings they cannot see rather than their faces. But does this make them Evil? Like a blind person it means that life is different, and living with sighted people is difficult because sighted people themselves tend to not understand blind people. But inside they are not Evil. A psychopath will want to help themselves when they suffer. Thus a psychopath once they discover suffering in another (harder because of their blindness) will want to help another. Suffering is after all something we seek to tackle. Compassion is not affected by psychopathy. I read that empathy is something we learn and get better at as we get older. Looking at children there is a huge range in the development of empathy but at the start kids have none. Obviously developing empathy is a much bigger mountain for a psychopath with their partial/total blindness. The brain is plastic and changes as we learn. Can a psychopath learn to grow mirror neurons, and is the lack of mirror neurons simply a result of them not exercising empathy? And genetics can only give us the tools, it doesn't dictate whether or how we use them. My genes give me hands, they don't dictate whether I use them for good or evil. Evidence of epigenetics exists also so that "we" can even turn genes on and off! Genes are not the point. So what is the psychopath's real problem? I suspect they are more likely to end up as criminals because they are not encouraged by their peers to think about other people. They need to do this a lot to overcome their weakness. A physically weak person may want to visit the gym to develop their muscles, so it is with the Psychopath but it is the much more useful feelings they are need to develop, experience and understand rather than just the physical (for which we can hire body guards and machines). Any negativity, shyness, sensitivity to pain, hatred is going to send a person with psychopathic tendency in the same protective shell as the narcissist. Being cut off from the world around once again is the Hell to be avoided. When this shut in Hell gets out, that is when other people around suffer also.

Finally the Sadistic. I had an experience of Schadenfreude for the first time recently. It is a very strange occurrence because rationally you know there is simply no reason for this. How can someone else's misfortune possibly achieve anything good in the Real World. But if I look more deeply I had a grievance against the person so their misfortune was like payback and I realised I had harboured a dislike and hatred of them for ages. But the misfortune was way in excess of any negative feelings I had, it was nasty. So where does the pleasure or satisfaction in being nasty come from? The projection of negativity? Lets try the universal test of goodness: Would I be nasty to myself and enjoy it? Most likely I would end up hating myself as I do people who are nasty to me, so I would both hate myself and enjoy it. Perhaps hating myself is itself a form of nastiness so I could get caught in a loop or hating myself, enjoying that, but then hating myself more for being so nasty to myself. Normally we do this via projection to hide ourself (as being both the victim and the perpetrator contradicts the belief there is only one of us and spoils the fun of the perpetrator and the anguish of the victim) so we find the outside world nasty and hate that instead, even while all the badness is actually our own choices. So actually sadism to the self causes a contradiction that splits the self. The key to this is that with Sadism the belief is that the victim and the perpetrator are separate. Here we go again, the apparent pleasure is at the expense of being alone and in isolation. Like all the above. And why would we give away the negativity if we liked the negativity? We push negativity and hatred onto others precisely because we don't like it. I saw Slavoj Zizek recently trying to argue that people like suffering. Worth noting that man himself is overrun with suffering. I think perhaps when we cannot overcome our suffering we try and save face and pretend we like it. To suffer appears like failure, so better to say like it. But we lie to ourselves: our every thoughts and action is ultimately to be free from displeasure, discomfort and dis-ease. We can give positivity to others and see them flourish. But when we give negativity they whither. When we have negativity we whither. Negativity is suffering, we don't want it, but we take command of it by giving it to others which gives us apparent relief from our own suffering. But it is a fake, cos we haven't mastered the horrible negativity at all and in fact make it worse by becoming isolated. Our victim is actually the winner because while they may suffer at our inflicted negativity we must give them it for them to suffer. It is ours, and we cannot escape that. We are the loser. Any Machiavellian instinct should fight the sadistic instinct to win over our negativity! The devil once again gives us a fake goal to lead us into the pit of isolation and desolation.

So all this points directly at Buddha's teachings which are much simpler and less infected with materialism and empirical evidence than the psychological world, which is flailing around thousands of years after the subcontinent clearly wrote it all down. The key point is Anatta and the illusion of self. All things are non-self : that includes other people, but also everything is in our own heads! It is ALL not-self. The mistake in the Dark Tetrad is that we can attach to things like feelings and thought and believe they "belong" to a mythical self which we have never even seen! As greater fantasy even than Father Christmas but one propagated unquestioningly by Western culture. Actually there is nothing to separate people, or things - there is just One World with everything side by side. The One World is both composed of individual (Democritus) and the complex interaction and unity from which those individuals emerge (Parmenides) "we are all individuals" - where there are individuals there is also necessarily a group! The ultimately irony of that is usually missed by much of the Monty Python community who uses it only as a criticism of group thinking. So the Dark Tetrad are the collection of mental processes that have deep effects on our body and brains that lead us into isolation - which is the diametric opposite of the truth and the darkest of the Hells. It is the new word for what was called the Devil. The cure is to reject the Devil which is the same as to reject these thought process - tho we may not realise how dangerous they are until damage is done. The goal is to seek integration with the world and other people, and to challenge our negativity when we find it and ultimately to turn energy that is negativity around into positive.

For the Narcissistic tendency we accept shame, and those who humiliate us and show us as mundane we can thank for breaking the shell. Even Superman loses his power when he falls in love - and love and the abandoning of the cold isolation of the Fortress of Solitude makes us ultimately stronger and more truthful! For the Machiavellian tendency we replace loss with giving, and thank those takers for breaking the shell. For the Psychopath tendency we allow the full experience of painful feelings and gradually seek to observe that everyone must have them equally - they don't belong to us. For those who hurt us we can thank for breaking the shell. For the Sadistic tendency we take all the negativity in ourselves and the world and we seek to make it good - however doing this gently, as we will exhaust ourselves if we do more than a step at a time. We don't need to die on a cross, we may even accept Him who did that, if it is our path. For all those we have negative feelings toward and who inspire nastiness we can thank for making us aware of the things we must make positive. When we fail we can use that shame and humiliation to check our Narcissism.

Ok I didn't think this through too well, I'm no expert, and as with everything else on this blog its just a regurgitation of current thought processes.

Meditation, Heart, Fear and Morality

Disclosure: I have been meditating on average 15 minutes a day for a year and a half. This has included increasing my sitting skills to include 2 hour meditations which have been very useful. I started to learn it 17 years ago, and while developing a good knowledge of its many techniques from a variety of teachers of different school, have never stuck to it until now. I have learned it within a Buddhist context and see Buddhism as really the manual for Meditation - the two are inseparable. Everything in Buddhism has been discovered via meditation. I was born Christian and have never seen a conflict between Jesus and Buddha. There is however an obvious conflict between Christianity and Buddhism as both groups wish to lock in their congregations and are quite jealous of each other. There are jealousies even between sects of each. These are just human frailties and I shall ignore here. But this initial disclosure digresses from the point of the post.

Meditation simply practices and strengthens concentration and mindfulness. These are distinct. Concentration is focus, as when we read a book in a quiet library or seek solitude to get on with a job. Mindfulness is awareness of what is going on in our senses. What we can hear, see, smell, taste, feel and also what thoughts we are having. When we break out of concentration and become aware of the world around and within us we will find our mindfulness extremely acute. We will Notice a lot of things. The two are intimately linked.

In the past I have focused exclusively on Concentration seeking the insights of Jhana that I once gained by Christian practice as a child. But this time I have included more Mindfulness and Compassion meditation.

Along with Mindfulness practice there is Contemplation meditation. I would classify Compassion meditation as a kind of Contemplation meditation. Here we ignore the senses of mindfulness and use our imagination to contemplate specific things. For compassion we are seeking to discover and strengthen our wish to help people in suffering. Linked to this is Loving Kindness meditation (Metta) where we seek to discover and enhance are feelings of Friendship, Support and Warmth toward all people. We begin with those we naturally love (if any, if we have become particularly hurt, withdrawn, cynical and hateful) and as we get stronger can can expand this toward neutral people and finally the people we dislike and hate (if any).

Buddhism Theory is particularly important in understanding and guiding what these meditations are doing. The theory is that we are Ignorant of our True Nature. This means we have Wrong View. Bold words for something very simple. The point is that we tend to learn how to see the world, and tend to inherit opinions about it from other people. We very rarely actually check whether we can see these things for ourself. This is especially and uniquely important when speaking about ourself. How can we learn about ourself from someone else? The obvious irony is that Buddha appears to Tell us about ourselves. But of central importance he never actually says anything exactly, he only guides us to look for ourself and that is the key point of Meditation. It is a looking at ourselves and the world properly, deeply and accurately to ensure that we see it as it is for us, not for someone else and not via some improperly understood theory from a book. Meditation is Me Time where we take good time to look at the world and ourselves carefully to just see how it Really is. When we do Compassion meditation and Metta meditation we are taking it on faith that we have these qualities in our True Nature and we are looking for them and focusing on them. The reason we cannot see them very well is that they are covered in mental dust and dirt - the analogy for ignorance. We often think and do things knowing they are not quite right but we never actually sat down and sorted it out. For example we may have always washed our clothes at setting 4 on the machine but one day we get the manual out and do a proper investigation and we see we are a bit right but there is more to know. Meditation is like being an Archaeologist digging through layers of dirt and time to uncover what we Really Are. The story doesn't end until Enlightenment however: "I" is an ongoing process of investigation and discovery. The Buddhist belief is that Siddhartha discovered his True Nature which it turns out is just One and the same as for All Beings. So Buddhist believe they are looking for their own buddha just as Siddhartha did. But how we get there is as diverse as there are beings in search so Siddhartha never built a single motorway but only highlighted a few of the bigger tributaries of a universal river. If Buddhism has one criticism of Religion it is that it is often sold to new comers as a single motor way. It doesn't take long for the new comer to realise however they are not quite like other people, don't have quite the same ideas, and even don't have quite the same God or goal. Is God a kind person, a strict person, a punishing person, a unknowable person, a person who visits the world for common people or only saints etc. And the new comer will realise their relationship with God and the Religion changes all the time also. They may go through Dark Nights of the Soul filled with doubt, and then periods of strong conviction and security. Everything is change. There is no single Motor Way but a largely unmapped journey through a single track in the mountains never before walked. Even if that path takes us away from Religion and God we are still walking the path. Buddhism recognises perhaps better than any other religion that our journey to salvation is ours not someone elses. We must walk it, and in Meditation we are taking steps on a path never before walked.

So where to begin? Concentration is the key and this is typically built by Anapanasati or Breathing Meditation. We have been breathing from the moment we were born but despite so many breaths we are almost never aware of it. Focus on the breathing, noting each in breath and then out breath and being sure that we are aware that these are happening. Usually we start by counting breaths in groups of 10 going back to 1 if we find we missed a breath when the mind wanders. Each time we bring the mind back we are growing stronger. Even now it can take 30 minutes for the mind to calm down and for me to be able to watch the stream of breathing quietly and for the most part undistracted. Locked On is the mental state of mind where we feel very calm and are inside the bubble of concentration that contains the breath. We don't feel like responding to distractions, we can go out and listen to a sound, or even change our body posture if we feel pain, but we want to come back inside the bubble and sit with our breathing. There is no suffering in this state of mind. THIS IS THE CRITICAL FIRST MIND STAGE OF CONCENTRATION. Get here often.

Once we have concentration then we can do Mindfulness to examine deeply the world and our feelings and thoughts. Or we can do Metta to clean our Hearts and enhance our feelings and relationships with people and the world. As one meditation teacher said Metta is probably the most important meditation because it includes all the others. It requires concentration to focus on the feelings of love, kindness and helpfulness but it also cleans the Heart. We can do Mindfulness and Metta at any moment in our lives, sitting meditation is just to get this process onto a strong start.

Heart has a special meaning in Buddhism. In English we force Heart into two quite separate thoughts. There is mind which is intellectual and there is heart which is emotional. But what do we call an intelligent heart? Someone who gives alcohol to an alcoholic may feel generous but they lack a deeper reflection on the situation. An Intelligent Heart is both kind and perceptive rolled into one. Enlightenment does not occur to the mind and the brain nor does it occur to the emotions and the body it occurs to the Intelligent Heart. In Meditation we removing the dirt that hides the intelligent heart so we need to both clear our Views of incorrect things and we need to clear our emotions of negativity and obstructive feelings. Metta meditation does both.

Intelligent Heart as we start to discover it has strength. It is the thing in Christianity which fights the Devil. When we stand there and we deep down know that something is wrong and we resist it, investigate it and try to throw it off. That is Intelligent Heart. The key to Intelligent Heart is the presence of wise force. When we are angry or fearful we have lots of energy but we use it very unwisely saying hurtful things to people or getting into a panic. These things achieve nothing and often make the situation worse. If we look closely they are also suffering and so are actually telling us that this is not the correct path and also pointing out which issues to examine and solve next. When we have the strength of Intelligent Heart we can see with resilience and clarity the path and we can walk through the storm that has blown up. It takes some force but it is kind and intelligent force that leads us in the right direction. I have certainly been confused out the use of force. I used to be a tutor and was always reluctant to force the children to study as I thought this would create resentment and dislike of the subjects. I wanted to encourage them and bring out their good qualities. This is half intelligent. After years I discovered there is a right time to push and I regret not pushing much more than I did. One very difficult student even said to me once when he realised that he could have done better in his exams, why didn't I push him more! Intelligent Heart uses kind force to get through struggles. Before in meditation I have called it "firmtle". When our mind is being a badly behaved child and will not focus we need to be firm with it, but we must not punish it and make it feel bad at not "meditating well". The generating of negative feelings in meditation can build up toward hating and avoiding it. Obviously if we are strong we can just meditate on those negative feelings but for beginners (like me!) they can upset the process of meditation.

There is no devil in Buddhism, or the one that is, is actually the form of our most important teacher. How else to do learn without tests? Wrong views about the world, dislikes, quarrels, hatreds, hurdles, obstacles, struggles, depressions, loss, anxiety, fears are all the tests thrown at us by the devil. Usually we will fail, but the tests are always exactly what we need to point us down the path. As we get stronger the tests often get more fierce. So being faced by what seems an unsurmountable obstacle is testament to our ambition and the strength our as yet undiscovered True Self believes we can gain.

Once we have Locked In meditation we will feel secure and we will have the mental strength to investigate deeply the tests that we have been set. There is no test that we cannot succeed at. However some may take large parts of our life to solve. But in solving them we become cleaner, purer and closer to our True Nature. What is the point of taking a test that will waste our whole life? This is thought is actually just a test. Remember "thoughts" and "questions" are also the objects of meditation just as sights, sounds, tastes, touches and feelings. It is actually Wrong View but to undo it will take a long time. Buddhism believes in reincarnation. It is a helpful thought because it points us toward understanding that we do not just get born, live and die pointlessly but are more like leaves on a river flowing with no beginning and no end, or a leaf stuck on a wheel turning round again and again. The world keeps flowing forever and without beginning (people might think Big Bang was the start, but then we think what caused Big Bang there is no initial thought or beginning). But while the world keeps flowing we come and go like leaves in this bigger picture of which we are a part. No trees no leaves, no leaves no trees. Correct View involves the slow breaking down of lots of wrong views about ourselves and our relationship with the world and gradually integrating ourselves again to see the whole process. My Intelligent Heart as I become more aware of it and it shines brighter will see clearly the Correct View. Cleaning it up is a long but fascinating path.

And finally morality. How to behave and what to do we usually copy from other people. But lots of times in life we must make our own choices from our sexual orientation to who to marry to what job to do, to where to live, what styles to wear and what pass-time we like. Much is chosen for us: our parents may push us into a particular career or way of feeling about ourselves. At some stage we need to look closely and decide. I became vegetarian, stopped smoking and am tackling recurrent anxiety are three personal choices that required and require a lot of personal investigation. Meditation obviously is the perfect method to achieve personalised moral choices. By looking closely at what is going on within ourselves, seeing suffering as the guide and with the strength of Intelligent Heart we can see a better path and a better life for our bodies and our minds.

The Illuminati & Conspiracy

Illuminati are an 18th Century European club whose goal was to improve the world. The European Enlightenment movement was in full swing then too with similar aims.

“It was not my intention to doubt that, the doctrines of the Illuminati, and principles of Jacobinism had not spread in the United States. On the contrary, no one is more truly satisfied of this fact than I am." [G.W.]

It's interesting that George Washington decided that the Illuminati were a threat to American independence and freedom. He also saw other groups as threats to US like the Jacobians. Since its violent break from the controlling force of Britain the US has always been suspicious of private groups from Europe trying to take over the US. Even as late at 1815 Britain was fighting American Independence. The split between Commonwealth Canada and aggressively independent USA is the result of that war. The Star Spangled Banner is an old British tune with the words of a poem penned as the US withstood a British onslaught. Even as late as 1974 the US was prepared for a British attack through Canada to continue that 150 year old war. It was code named War Plan Red. This history of independence and opposing the Old World very much lives on in Conspiracy Theory and these days the principle is symolised by the Illuminati.

Ironically the New World Order can be seen as either a New "World Order" or a "New World" Order. As someone from the Old World with a Queen still in place and long traditions I see it as the "New World" Order with the US seeking to control the world. New American Century clearly had this aim. With the fall of the USSR the US saw the opportunity to take over the world and spread its values and control. Thus began the push for military supremacy (Joint Vision 2020) and expansion into regions that had previously resisted US control Afghanistan, Iran, Syria. Iraq was a stepping stone with Hussein only recently fallen out of favour. As the drive expanded Gadaffi mysteriously fell out of favour along with others. Russia remains the US main opponent. This is all "New World" Order to me.

But the recent win by Trump flying the banner of US control by Elites suggests that even in the US they are not benefiting from the "New World" Order. Perhaps indeed it is a New "World Order" that benefits neither Old World nor New World but rather an international elite class. Certainly Capitalism has generated this, and globalisations has meant that with money people now have the ability to influence all regions of the world. Obviously Russia and China are more controlling and close their borders to this Global Elite which would be why the Western News, which one can assume is owned by these Elites, hates these countries. To be powerful the first thing to do is control the media! Then you have the support of the people. Then control the banks!

 I said in a previous post that there is a mystic and religious dimension to this type of thinking. In the absence, or rejection of mass religions, the suspicious have formed their own religions. Aliens is prominent as a "other worldly" source of influence on Earth. I have clearly seen a flying saucer with friends who confirm it so I am not speculating on alien craft and aliens. I am speculating on the beliefs that surround them which are all unfounded and chosen because people like the beliefs. "Other worldly" forces then spiral up and down into angels and demons respectively and masonic and other esoteric occult rituals. Certainly all this happens. The only question is how significant it is and whether it makes any difference to our daily lives.

What is without question is that people have varying levels of power. As much in the "free" West as anywhere else in space and time. Once there were Kings and Dictators now there are Capitalists and Bankers who have more influence on our lives than even the worst dictators. But we are also always free as while people can influence us they can never tell us what to do. So in many ways all talk of Illuminatis and Conspiracy even by George Washington is rather irrelevant. The sun rises and falls regardless who is in power. Some say this is the work of God but actually even that doesn't matter. One day the sun won't rise any more and there is nothing we can do about it. Power is just a perspective on the way the world already is.

Mandelbrot fixed systems… Some questions.

Within the set functions of the form Z=Z^2+C decay to a limited number of repeating values. The starting value for these interations was Z0 = 0+0i and the system was run for 1E5 iterations before testing for repetition.

Here Fixed-Points are white (a single value). Binary systems with each value mapped to the other value by the function in Red. Triple systems in Blue and Quaternary systems in Green.

Are there any values of C forming systems that never repeat?

Looking at the arrangement of “dusts” there is a definite pattern. It appears to involve some level of reflection and rotation. The sense I formed is like walking into a hallof mirrors with the object image being broken up and distorted by the function. Is this pattern fractal and exist at lower scales?

Regarding fixed points. So the repetative use of the function gradually removes information from the system until the path collapses into a repeating system. Reversing the function now cannot retrace the path. The information is lost.

Given a fixed point how many points in the set collapse to this point? Is there a method to reverse it?

The existence of dynamic systems with more than 1 state suggests that the SRH should not be concerned with the point itself, but rather the system of values/terms which provide something like a “hermaneutic circle”. Given 1 point we can travel to all the others, but we cannot leave the system. In Russel’s Principia rather than just a single statement which maps to itself via Godel Numbering we can have any number of closed loops. A contradiction can be sort in any of these loops by creating a mirror image of the loop using negation. Because the system is defined by the logic of the loop, the negative mirror image can be easily constructed to contradict the logic. I am provable/I am not provable.

 

Julia Sets

For the function Z = Z^2+(0.4 + 0.6i) the fixed point Zf occurs where Zn+1 == Zn. There are always 2 solutions for every function.

Zf1 = 0.983976  - 0.619865 i

Zf2 = 0.0160238 +0.619865 i

Plotted on the Julia set:

Interestingly the symetrical points in the other 2 quadrants iterate immediately to these 2 fixed points.

Clearly fixed points are integral to the set, marking here the centre of the cross and the end of the long branch. However unclear what special position they hold in the structure.

The original guess was that fixed points are strange attractors. They determine the anchors for the structures. Perhaps this is still partly true.

Logistic Equation

This is much simpler to explore. The question is why does repeated application of a function decay it. The suggestion is decrease of entropy and loss of information when we apply a function. To process of mapping increases the order but uses energy. And under what conditions does it decay to a fixed, binary etc system. Is a chaotic system “really” chaotic does it not increase order at all, or is it just very slow.

Remember the system bouncing between the Quadratic and the y=x line as a way to visualise the process. Why do only certain curves create bifurcation.