http://math.ucr.edu/home/baez/week203.html
ebook
http://ebook30.com/science/mathematics/305483/introduction-to-the-perturbation-theory-of-hamiltonian-systems.html
Back to more my type of analysis of stock markets ...
http://finance.martinsewell.com/stylized-facts/distribution/Gabaix-etal2003.pdf
esp. "Such a theory
where large individual participants move the market is consistent
with the evidence that stock market movements are dif®cult to
explain with changes in fundamental values." [Cutler,D., Poterba, J. M.& Summers, L. H.What moves stock prices? J. Portfolio Management 15, 4±12 (1989).]
Excellent something workable really seems to be building here.
Friday, 21 January 2011
It gets deeper...
This Phi thing is extra-ordinary. Self-relationship at the heart of the universe... I still maintain the SRH but there is a lot more to Self!!!
http://icanseefar.tripod.com/phitheoryweb.htm
and just as I accept Caitin's argument I'm beginning to see Wolfram's and this is before I've even read the book! Amazing, and probably stupid, that I assume so much about things I've never read... but I guess if you hear someone calling from over the hill you go over there even before they've come to fetch you!
===
ok this guy might be talking a load of rubbish the sqrt(10) thing is a tautology... shall examine later
http://icanseefar.tripod.com/phitheoryweb.htm
and just as I accept Caitin's argument I'm beginning to see Wolfram's and this is before I've even read the book! Amazing, and probably stupid, that I assume so much about things I've never read... but I guess if you hear someone calling from over the hill you go over there even before they've come to fetch you!
===
ok this guy might be talking a load of rubbish the sqrt(10) thing is a tautology... shall examine later
Now we're talking...
Brilliant discussion of this feature here...
http://scienceforums.com/topic/13548-do-a-spiral-galaxy-and-a-hurricane-share-a-similar-formation-mechanism/
Virtually every aspect of fractal geometry and type of dynamical system can be expressed by variations upon the simple quadratic iterator: X = X**2 + c which expresses the particular type of feedback being examined, Phi can be expressed by a related but more archetypal variation to derive the Fibonacci series: X[n+1] = X[n] + X[n-1] which incrementally gravitates towards a particular ratio which possesses unique qualities. Numerically, it can be derived from the relation: (1 + sqrt(5))/2. For example, if one diminishes Phi by Unity you derive its reciprocal. Additionally, Phi is the unique ratio that fulfils: 1/Ø + 1/Ø**2 = 1 in other words, Phi is also the only possible geometric and arithmetic, expansion and partitioning of One.This leads us to the other cardinal feature of Phi. There is only one proportional division of One possible using two terms, with the third being One itself. From Euclid's ELEMENTS Book Five, Theorem Three (Alexandria, 3rd century B.C.):"A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less."The Golden Mean then, is an archetypal fractal in that it preserves its relationship with itself (its inherent similarities under scaling are conformal symmetries - with topological consequences, that are invariant about themselves), in the most mathematically robust, economical but also elegant, way. It is analogia exemplified.As we shall see, this reciprocal, squaring behaviour about One, or Unity, as it is more properly termed, is far from being mathematically trivial.All feedback loops deterministically involve the passage of time. The quadratic iterator is derived from Newton's differential calculus, and from a period when nature was seen as a mechanistic and time-reversible automaton. Recent science demonstrates that in fact it consists of both the above and irreversible processes, known as the entropy barrier, or the arrow of time. The Golden Mean can also be seen as mathematically (because of the above) the simplest and most stable way of communing or mediating between the two, as we shall see.Nigel Reading
Quote
You may assume.But it is never safe
Quote
According to the Nobel laureate Ilya Prigogine, these far from equilibrium dissipative systems locally minimise their entropy production by being open to their environments --- they export it in fact, back into their environments, whilst importing low entropy. Globally, overall entropy increase is nevertheless preserved, with the important caveat that the dissipative system concerned often experiences a transient increase (or optimisation) of its own complexity, or internal sophistication, before it eventually subsides back into the flux.This is known as the region of alternatively, Emergence, Maximum Complexity, Self-organised Criticality, Autopoiesis, or the Edge of Chaos. (Nascent science debates nomenclature routinely - and appropriately, in this case, the crucial point being that they are all different terms for essentially the same phenomena.)Lifeforms, ecosystems, global climate, plate tectonics, celestial mechanics, human economies, history and societies, even consciousness itself - all manifest this feedback-led, reflexive behaviour; they maximise their adaptive capacities by entering this region of (maximum) complexity on the edge of Chaos, whenever they are pushed far from their equilibrium states, thereby incrementally increasing their internal complexity, between occasional catastrophes.Remarkably, this transition zone is mathematically occupied by The Golden Mean. This ratio acts as an optimised probability operator, (a differential equation like an oscillating binary switch), whenever we observe the quasi-periodic evolution of a dynamical system. It appears in fact, to be the optimal, energy-minimising route to the region of maximum algorithmic complexity, and to be a basin of attraction for the edge of Chaos.
[credit Nigel Reading]
http://scienceforums.com/topic/13548-do-a-spiral-galaxy-and-a-hurricane-share-a-similar-formation-mechanism/
Virtually every aspect of fractal geometry and type of dynamical system can be expressed by variations upon the simple quadratic iterator: X = X**2 + c which expresses the particular type of feedback being examined, Phi can be expressed by a related but more archetypal variation to derive the Fibonacci series: X[n+1] = X[n] + X[n-1] which incrementally gravitates towards a particular ratio which possesses unique qualities. Numerically, it can be derived from the relation: (1 + sqrt(5))/2. For example, if one diminishes Phi by Unity you derive its reciprocal. Additionally, Phi is the unique ratio that fulfils: 1/Ø + 1/Ø**2 = 1 in other words, Phi is also the only possible geometric and arithmetic, expansion and partitioning of One.This leads us to the other cardinal feature of Phi. There is only one proportional division of One possible using two terms, with the third being One itself. From Euclid's ELEMENTS Book Five, Theorem Three (Alexandria, 3rd century B.C.):"A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less."The Golden Mean then, is an archetypal fractal in that it preserves its relationship with itself (its inherent similarities under scaling are conformal symmetries - with topological consequences, that are invariant about themselves), in the most mathematically robust, economical but also elegant, way. It is analogia exemplified.As we shall see, this reciprocal, squaring behaviour about One, or Unity, as it is more properly termed, is far from being mathematically trivial.All feedback loops deterministically involve the passage of time. The quadratic iterator is derived from Newton's differential calculus, and from a period when nature was seen as a mechanistic and time-reversible automaton. Recent science demonstrates that in fact it consists of both the above and irreversible processes, known as the entropy barrier, or the arrow of time. The Golden Mean can also be seen as mathematically (because of the above) the simplest and most stable way of communing or mediating between the two, as we shall see.Nigel Reading
Quote
You may assume.But it is never safe
Quote
According to the Nobel laureate Ilya Prigogine, these far from equilibrium dissipative systems locally minimise their entropy production by being open to their environments --- they export it in fact, back into their environments, whilst importing low entropy. Globally, overall entropy increase is nevertheless preserved, with the important caveat that the dissipative system concerned often experiences a transient increase (or optimisation) of its own complexity, or internal sophistication, before it eventually subsides back into the flux.This is known as the region of alternatively, Emergence, Maximum Complexity, Self-organised Criticality, Autopoiesis, or the Edge of Chaos. (Nascent science debates nomenclature routinely - and appropriately, in this case, the crucial point being that they are all different terms for essentially the same phenomena.)Lifeforms, ecosystems, global climate, plate tectonics, celestial mechanics, human economies, history and societies, even consciousness itself - all manifest this feedback-led, reflexive behaviour; they maximise their adaptive capacities by entering this region of (maximum) complexity on the edge of Chaos, whenever they are pushed far from their equilibrium states, thereby incrementally increasing their internal complexity, between occasional catastrophes.Remarkably, this transition zone is mathematically occupied by The Golden Mean. This ratio acts as an optimised probability operator, (a differential equation like an oscillating binary switch), whenever we observe the quasi-periodic evolution of a dynamical system. It appears in fact, to be the optimal, energy-minimising route to the region of maximum algorithmic complexity, and to be a basin of attraction for the edge of Chaos.
[credit Nigel Reading]
Monday, 17 January 2011
Name
How do we know our own name?
We know someone else's based on some character. This is most evident with identical twins where physical characteristics are so similar that it is hard to tell them apart. What we may need to do is talk to them to see their personality. If this is also the same we can check for information they remember which links them to a place and a time. For example if they can't remember what they ate when you last had a meal together.
If the twins were never apart however then this is hard. It would be like a Turing test where we had a fixed period of time to determine who was who and if we couldn't then we could conclude, not that they were "a conscious person", but rather there was no difference between these two persons. We would then have to rely on what each of then told us, in other words what they called themselves. No good one saying "i'm me and not them" and the other saying exactly the same. We need them to uniquely identify themselves.
Now how can we tell whether they are telling the truth? We have to be able to mark them with a constant characteristic and compare what they say relative to that mark - measure them so to speak. Suppose we could put them in different cells then ask them their name, write it on the door and ask them each day. They need to always say the same thing AFTER isolation. What was said before is not important!
But what if they are called the same name? Lots of people have the same name. What we tend to do in that situation is give them a nick name. Two Marks renovating my cousins place gained the names Mark-the-floor and Mark-the-plasterer for obvious reasons just as people gained the names Margaret Thatcher or Adam Smith in days of yore. And usually people come t accept their monikers. But it is not satisfying if our two twins keep calling themselves say John. It is as though 'inside' they still don't accept their difference. Outside however we can test their memories and gradually their different histories will show up; for example if we give them different meals and then ask them to remember their meals. This is what Buddhism calls streams of consciousness which I believe is the way that we pass through time for Buddhist theory (but i am unsatisfied by this explanation: it doesn't really get to the heart of the illusion of "self" because we can just replace the idea of self with "my stream of consciousness").
Now is this how we know our own name? Do we look for a character in order to know that it is us? That is the problem for a speculative philosophical moment. In reality however we don't think like like this. Our name is a part of our learned behaviour. From a young age we know what to do when addressed. Almost like a dog who can tell when he is being called because his master is looking at him and saying this word in that high pitched way. Our name becomes part of the language game that surrounds us and in which we have grown up. In this way our name is unique to the social context in which each of us finds ourselves. It is not about naming some object but rather 'being' part of a team and social reality. So how do we know our name? It is because we are part of a social reality in which our name gets used. What is my name? Is a question we are a fool if we can't answer just as I felt very childish not to be able to spell my middle name when I was 11. In the same way we learn to address other people in this culture for a variety of purposes. So it is not so much a case of directly refering to a 'self' when we use a name - a thing called 'Alva' that is naming that thing (any self-reference) - but rather being part of a society that uses this word in particular situations and "Alva" becomes just a social context rather than an object . . Just as a "goal keeper" is a context in a game of football so "Alva" is a context in the game of English Western society. So our twins above are perplexing because they seem to be able to cheat at something that is so fundamental to this society. Just as a man the size of a goal mouth would 'cheat' at goal keeping!
We know someone else's based on some character. This is most evident with identical twins where physical characteristics are so similar that it is hard to tell them apart. What we may need to do is talk to them to see their personality. If this is also the same we can check for information they remember which links them to a place and a time. For example if they can't remember what they ate when you last had a meal together.
If the twins were never apart however then this is hard. It would be like a Turing test where we had a fixed period of time to determine who was who and if we couldn't then we could conclude, not that they were "a conscious person", but rather there was no difference between these two persons. We would then have to rely on what each of then told us, in other words what they called themselves. No good one saying "i'm me and not them" and the other saying exactly the same. We need them to uniquely identify themselves.
Now how can we tell whether they are telling the truth? We have to be able to mark them with a constant characteristic and compare what they say relative to that mark - measure them so to speak. Suppose we could put them in different cells then ask them their name, write it on the door and ask them each day. They need to always say the same thing AFTER isolation. What was said before is not important!
But what if they are called the same name? Lots of people have the same name. What we tend to do in that situation is give them a nick name. Two Marks renovating my cousins place gained the names Mark-the-floor and Mark-the-plasterer for obvious reasons just as people gained the names Margaret Thatcher or Adam Smith in days of yore. And usually people come t accept their monikers. But it is not satisfying if our two twins keep calling themselves say John. It is as though 'inside' they still don't accept their difference. Outside however we can test their memories and gradually their different histories will show up; for example if we give them different meals and then ask them to remember their meals. This is what Buddhism calls streams of consciousness which I believe is the way that we pass through time for Buddhist theory (but i am unsatisfied by this explanation: it doesn't really get to the heart of the illusion of "self" because we can just replace the idea of self with "my stream of consciousness").
Now is this how we know our own name? Do we look for a character in order to know that it is us? That is the problem for a speculative philosophical moment. In reality however we don't think like like this. Our name is a part of our learned behaviour. From a young age we know what to do when addressed. Almost like a dog who can tell when he is being called because his master is looking at him and saying this word in that high pitched way. Our name becomes part of the language game that surrounds us and in which we have grown up. In this way our name is unique to the social context in which each of us finds ourselves. It is not about naming some object but rather 'being' part of a team and social reality. So how do we know our name? It is because we are part of a social reality in which our name gets used. What is my name? Is a question we are a fool if we can't answer just as I felt very childish not to be able to spell my middle name when I was 11. In the same way we learn to address other people in this culture for a variety of purposes. So it is not so much a case of directly refering to a 'self' when we use a name - a thing called 'Alva' that is naming that thing (any self-reference) - but rather being part of a society that uses this word in particular situations and "Alva" becomes just a social context rather than an object . . Just as a "goal keeper" is a context in a game of football so "Alva" is a context in the game of English Western society. So our twins above are perplexing because they seem to be able to cheat at something that is so fundamental to this society. Just as a man the size of a goal mouth would 'cheat' at goal keeping!
On reference & Custom
When someone is called "John" in human culture it means that the word "John" is taken by speakers to replace the actual person John (who may be short and dark haired with a light hearted attitude) in verbal structures. When John hears his name he knows that he is involved in the conversation.
But this is only convention. John could just as easily refer to the person who is also called Mike. Now we enter the problem of identity loved by Elizabethan playwrites. Quite when we use the name John and Mike can only be determined by custom, context and circumstance. In an alien culture there may be complex formal rules governing when to use particular names that will seem random and of no sense to a human guest. Imagine explaining the old use of you and thou to an alien who doesn't have a concept of intimacy or informality!
Now isn't the same true of sentence themselves. It is customary to interpret a sentence that described the previous sentence as having eight words as meaning the sentence before this one. Were the customs of English different it might mean this sentence itself. Likewise a sentence that says that it has nineteen words might be customarily interpreted to mean the previous sentence.
What is true however is that to create a current point of reference we need some level of identifying the here and now. A sentence which says "the first sentence of this blog entry" must still make reference to the here and now even while not envoking itself. This shows however that "this sentence" is actually referring to itself only by use of an external here and now reference which is customarily accepted for the English language. It is certainly external self reference and so of little interest.
I need also be careful here of use/mention. A sentence can't actually refer to itself so easily because "this sentence" is just a quote and marks on a page. While this sentence is an actual sentence. Or is it because it doesn't quote itself so it is actually non gramatical within the rules of English.
But this is only convention. John could just as easily refer to the person who is also called Mike. Now we enter the problem of identity loved by Elizabethan playwrites. Quite when we use the name John and Mike can only be determined by custom, context and circumstance. In an alien culture there may be complex formal rules governing when to use particular names that will seem random and of no sense to a human guest. Imagine explaining the old use of you and thou to an alien who doesn't have a concept of intimacy or informality!
Now isn't the same true of sentence themselves. It is customary to interpret a sentence that described the previous sentence as having eight words as meaning the sentence before this one. Were the customs of English different it might mean this sentence itself. Likewise a sentence that says that it has nineteen words might be customarily interpreted to mean the previous sentence.
What is true however is that to create a current point of reference we need some level of identifying the here and now. A sentence which says "the first sentence of this blog entry" must still make reference to the here and now even while not envoking itself. This shows however that "this sentence" is actually referring to itself only by use of an external here and now reference which is customarily accepted for the English language. It is certainly external self reference and so of little interest.
I need also be careful here of use/mention. A sentence can't actually refer to itself so easily because "this sentence" is just a quote and marks on a page. While this sentence is an actual sentence. Or is it because it doesn't quote itself so it is actually non gramatical within the rules of English.
Friday, 14 January 2011
Intrinsic/Extrinsic Self-Reference
Almost certainly blogged this before but its clear at the moment:
One type of self reference (extrinsic self-reference) involves a system being able to select itself from amongst others. This sentence has five words. The previous sentence has selected itself from the rest of the text and in particular distinguishes itself from the next sentence. This sentence has five words. It is as though the system looks out into the world, identifies itself and then looks back in again. In reality it is using us, the reader, to do the looking and the thinking and we lie outside the system - or at least we are not the sentence. However I am unimpressed with external self reference because what is the real difference between the second and third sentences of this paragraph, or even this sentence here. The second sentence refers to itself and the third also refers to it. Both sentences are selecting one of the sentences on this page, in that they are the same. So the fact that the second sentence "happens" to select the sentence that is also itself is quite unmiraculous and is just a trivial feature. There is no "self" here other than that which a reader may infer when (or if) they realise that the sentence is referring to the same sentence they are reading.
The other type of self-reference, and the one which I'm saying is logically impossible in the SRH, is intrinsic self-reference where the entity refers to itself within itself. Now this is non trivial and quite miraculous if it exists. It is the situation monists believe is true within humans where somehow we have a secret mirror in which we can see ourselves, and know our own thoughts and wishes. This they believe would be true even on a desert island or in a world where nothing else existed but them. I used to hold this view and it is through failure to actually find consciousness or a self and after being given a push by Buddha that I changed view.
The idea that somehow self-refernece and recursive feedback in the brain causes consciousness just doesn't go anywhere. Recursion does indeed creates a many leveled intersecting fractal structure (which is Hoffstadter's brilliant view) but that anything would be mysteriously "created" is untenable. What "I" am would be just be phantoms in the swirling mix of data (the hall of mirrors as it is called in this blog). What I am careful to avoid however is the suggestion that the "world" is any less a phantom. The belief in material entities like brains that somehow mysteriously underly the "self" or consciousness implies some special knowledge of "reality" which I am yet to see myself! After all if it was so easy to escape the hall of mirrors why hasn't everyone other than Hoffstadter and Dennett!
Intrinsic self-reference involves not having to identify oneself from other things by "external" features but involves having an almost tautologically connection to oneself - and inner bond to oneself. The "I think: I am" bound into ones existence. I'm not taking sides and saying that outside is better than inside (though the Western Materialists side totally with the outside while Buddha said that inside/outside is just part of the illusion) , just looking for an immanent problem with holding the inside view.
One type of self reference (extrinsic self-reference) involves a system being able to select itself from amongst others. This sentence has five words. The previous sentence has selected itself from the rest of the text and in particular distinguishes itself from the next sentence. This sentence has five words. It is as though the system looks out into the world, identifies itself and then looks back in again. In reality it is using us, the reader, to do the looking and the thinking and we lie outside the system - or at least we are not the sentence. However I am unimpressed with external self reference because what is the real difference between the second and third sentences of this paragraph, or even this sentence here. The second sentence refers to itself and the third also refers to it. Both sentences are selecting one of the sentences on this page, in that they are the same. So the fact that the second sentence "happens" to select the sentence that is also itself is quite unmiraculous and is just a trivial feature. There is no "self" here other than that which a reader may infer when (or if) they realise that the sentence is referring to the same sentence they are reading.
The other type of self-reference, and the one which I'm saying is logically impossible in the SRH, is intrinsic self-reference where the entity refers to itself within itself. Now this is non trivial and quite miraculous if it exists. It is the situation monists believe is true within humans where somehow we have a secret mirror in which we can see ourselves, and know our own thoughts and wishes. This they believe would be true even on a desert island or in a world where nothing else existed but them. I used to hold this view and it is through failure to actually find consciousness or a self and after being given a push by Buddha that I changed view.
The idea that somehow self-refernece and recursive feedback in the brain causes consciousness just doesn't go anywhere. Recursion does indeed creates a many leveled intersecting fractal structure (which is Hoffstadter's brilliant view) but that anything would be mysteriously "created" is untenable. What "I" am would be just be phantoms in the swirling mix of data (the hall of mirrors as it is called in this blog). What I am careful to avoid however is the suggestion that the "world" is any less a phantom. The belief in material entities like brains that somehow mysteriously underly the "self" or consciousness implies some special knowledge of "reality" which I am yet to see myself! After all if it was so easy to escape the hall of mirrors why hasn't everyone other than Hoffstadter and Dennett!
Intrinsic self-reference involves not having to identify oneself from other things by "external" features but involves having an almost tautologically connection to oneself - and inner bond to oneself. The "I think: I am" bound into ones existence. I'm not taking sides and saying that outside is better than inside (though the Western Materialists side totally with the outside while Buddha said that inside/outside is just part of the illusion) , just looking for an immanent problem with holding the inside view.
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The classic antimony is between : (1) action that is chosen freely and (2) action that comes about through physical causation. To date no ...
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Following from the last blog on animal/human a beautiful male Oedemera nobilis resting in a flower after presumably a good meal of po...
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Same current territory (and raft) but a bit more polished. Or perhaps not! That will be be explained. With Deepseek: https://chat.deepseek.c...
