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Wednesday, November 18, 2009

Bad Analogy or "The Time of the Fractal" (thoughts on symmetry)

First I want to say thanks to Street Dog for helping direct me to the following wiki: renormalization. I must say I am having a hard time following most of it, and am hopeful he will give us a simple translation, but it is where my latest inquiry in understanding fractals has arrived. It has generated the following thoughts on the drive home from work this morning.


Fractals are formed when chaos is broken and symmetry (or cooperation) is created (and/or vice versa)- hat tip SD. Further, this time or moment or space (or whatever you want to call it) of fractal formation- what I will hence forth refer to as "the time of the fractal"- is a very special time/moment/space/event/period/epoc/region/etc...

For if you think about it, this time of the fractal has been called many things by many people in many languages from many viewpoints since language and thought was first introduced.

If you are not following me, a few examples may jog your neurons: phase transition(s), boundary condition(s), time of change(s), moment of transformation(s), point of conversion(s), etc...

Are you getting the idea?

Anyway, as additional background, we know the conservation of energy implies that in a closed system, everything is connected to everything else. For discussion purposes on this post, we will pretend the universe is a closed system... Yes, yes, I can already hear some of you complaining, especially with the universe expanding at an accelerated rate and all. I want you to know I hear your concerns (these are simply thoughts after all), but we need to create some boundary conditions to the discussion in order to even have a discussion so let's keep it to a static universe just to make it simple.

Further, if you think about it, everything connected to everything else also implies a kind of infinite network between everything and everything else. Of course the links in this (infinite?) network are hard for most of us to see...

So anyway, we have an infinite network in a closed system, and we further have smaller boundary conditions within this network, and then a change happens from at least one viewpoint- voila! We have fractals!

And this is where we get back to the theory of renormalization.

For if something changes in a closed system- e.g. symmetry is either broken or created (really can be either and probably the creation of one means the creation of the other), a break in symmetry must be felt everywhere else.

Really another viewpoint on zero-sum so nothing special here, but here is where I am going:

Does this mean the newest element in the periodic table, humanium, is subject to the same laws as every other element in the periodic table?

When humanium moves from one boundary condition (or phase transition) to another, will it display the same wave-particule duality we see with every other element in the periodic table?

Does humanium display quanta properties? e.g. individual properties?

Does humanium display wave like properties? e.g- collective/cooperative properties?

Neuroanatomist Jill Taylor suggests it does

Thoughts appreciated


Thai said...

Just a comment to get your comments

Debra said...

Um, Thai, I have some... questions.
What justification can you give to creating the element "humanium" and putting it right there alongside of the other elements, WITHIN the system ? (I'm not saying you're wrong, but I want to know your reasoning.)
Second methodological comment :
My spy mentor says that... metaphor and analogy are not at all the same thing. Like the difference between analogical and numeric, for example ? I don't know enough about this to comment intelligently. Are you sure that you are not sticking your new element in the closed system through the process of... analogy ? This is... methodologically fraught with danger.
The idea that symmetry is cooperation and vice versa grates on my nerves. In my professional field, symmetry is seen as non movement, and within our monotheistic (human) context, movement is synonymous with LIFE. Symmetry is synonymous with.. death.
What you're saying reminds me of Freud's theoretical exploration of the nature of mind, starting with the idea of an initial, homeostatic condition that he (mistakenly) equated with death/non-being. He posited that matter tended to SEEK to return to a state of non being/death.
So...I could say that your fractal theory is a reformulation of 19th century homeostatis theory.
At that point... what is more interesting is NOT the CONTENT of the theory, but the fact that YOU are coming out with it some 100+ years later, with an entirely different vocabulary and it looks NEW to you. It might LOOK different to you, but to what extent is it REALLY different (and I admit that words count, but...) ?

Thai said...

I think I am using analogy- title changed! Thanks

re: originality

Remember Fractals?!?! e.g. self similar, etc... AKA nothing new under the sun???

In fact, here is a rather funny fractal. ;-)

Re: "Symmetry is synonymous with.. death."

Depends on the viewpoint ;-)
I think this is just one of those linguistic associations we do not share resulting from different backgrounds.

And I suspect it is one of those mental associative negative photographic things. We each have the others opposite symbolism on this akin to Chinese-white-death, etc...

I tend to think of chaos as death as I can't possibly see how the symmetric conditions necessary for life can exist in chaos.

Remember the conversation I had with SD? He see fractals as symmetry breaking while I see them as symmetry forming- e.g. the reverse.

Debra said...

I share SD's comments on symmetry breaking. (I try, at least...)
I suspect that you will find, Thai, that ANY definition of chaos is basically... a metaphysical one. (Just what IS it, by the way ? And, please, spare me the wikipedia entries, I'm not buying...)
Boundary conditions bring to mind the situation of the... crisis. It would be interesting to reflect on the situation of crisis, and different theories of crisis.
Another methodological comment : it is my impression that all (?) of our theories are torn between two temptations : the binary and ternary one. Our western culture "sees" the world in terms of... the dualism good/bad, and if you are congratulating yourself that YOU don't fall into this trap, think again, and start observing yourself because... how can YOU not do it, when your surrounding social body is devoted to doing it, and it is.. DONE in your language ???

Debra said...

Kitty just ran over to open Salon and dug her long sharp claws into a blog writer !!!
OOOH it feels SO good.
Specially when it's done well.
You guys are really SO fortunate that I don't unsheathe those claws on you...

Thai said...

Good for you! ;-)

... My eyelid is twitch having not unsheathed my claws in a wile myself.

Why would you want to unsheathe your claws here? Is there an issue you want to push back against/explore?

If so which one?

And I have no idea what chaos is (though I do intellectually understand that it must be symmetry looked at from simply another viewpoint).

Your comment on the metaphysical is fair.

But understand I am not a mystic not would not have considered myself a metaphysicalist before I explored these ideas; again I am not religious.

I think the best I can say is I think I understand religious/metaphysical viewpoints (I know they are different) and might often agree with these views. Yet I do not think of myself as either and taking them too seriously is likely to have me running for the hills.

I see the legitimacy of Dr Taylor's TED lecture, I also see the legitimacy of the views which would refute it. Indeed some people with Dr Taylor's exact views would see my claws if other things were different! ;-)

Agreement on one thing usually requires some degree of agreement on other things since we can never get away from that issue of aspect in language.

Re: phase transition and the crisis


That is the whole point of this post. Let's have fun with the fractals of phase transitions is as a starting point to discuss the crisis- e.g. start at either 30,000 feet or the subatomic level, and ultimately come back to where we are today.

The fact you linked the terms "phase transition" to the current crisis implies we are getting cognitively closer!

Wonderful :-)

As I have been saying all along, the fractal broke at a micro level and now it is breaking at a macro level as it must.

Re: binary vs. ternary


I absolutely see I fall into this trap as I agree we all do. Every time we find a way to merge binary/ternary, analog/digital theories, we always kick the problem upstairs and downstairs, where we are forced to see a new point where phase transitions will occur.

Again, it reminds me of SDs comment on Godel's theorem which I have always seen as the inherent problem/meaning of the second law of thermodynamics/conservation of energy.

"This statement is false"

Indeed, listen to any respected modern physicist go on for any length of time, and you will recognize they keep reconciling their latest duality/ternary issues by kicking the problem upstairs and down.

Be well

Debra said...

Thai, sweetie, please don't be offended, I'm not unsheathing my claws but, in your last comment I definitely found some indications of the... rabbit, and may I suggest that you warp up into vorpal mode a little bit ?? I DIDN'T say that I wanted to unsheathe my claws HERE, why should I since I can unsheathe them elsewhere (over in the jungle, for example...)
I am an aggressive kitty, Thai. And I love arguing. It is too bad that too many people take arguing SO SERIOUSLY these days... like they are going to fall into little teeny tiny pieces if you don't agree with them on everything.
Totalitarianism in action... Domestic tyranny.
Crisis means... well, it doesn't necessarily refer to the.. um, ah, financial crisis. There are lots of other crises going on around us. As a matter of fact, living beings seem to traverse life, moving from one... crisis to the next, right ?

Dink said...

"Re: phase transition and the crisis


These are my two favorite words for the concept. Critical mass, etc.

It was a nice post! The renormalization stuff is terrifying, but I'll try to keep up. I read the TED speaker's book A Stroke Of Insight so I wasn't expecting any surprises. But she has added some detail and her delivery was very moving. I hope my pets are always in right-sided la-la land.

I was going to add something else, but I'll do it to the newest post for organization's sake.

Street Dog said...

No laughing at my latest post! ;-)

Hahahaha. What mad pursuit this fractal? What struggle to escape? Perhaps it's time for an intervention. At the very least you should consider Fractals Anonymous (1-800-QUIT-NOW). I will support you all 12 steps of the way.*

renormalization. I must say I am having a hard time following most of it, and am hopeful he will give us a simple translation

Thai, you are taking me back to my undergraduate days in Pasadena. Broheim, I would love to have a beer with you and discuss this topic. It's seems too much to discuss within the limitations of blog comments. A leisurely conversation would be more satisying. This is a good example of Street Dog Blog Comment Axiom #1. I could talk for hours about this stuff, sadly, my typing fingers are poor substitutes.

I'm not sure how renormalization applies to your thesis below. Renormalization is simply a mathematical tool to deal with divergent integrals (calculus) in perturbative calculations. In quantum theory, Feynman diagrams with closed loops of virtual particles, under naive calculations, can make infinitely large contributions. With renormalization you impose a cutoff in order to get finite answers.

Anyway, as additional background, we know the conservation of energy implies that in a closed system, everything is connected to everything else...For if something changes in a closed system...a break in symmetry must be felt everywhere else.

This is your thesis. We would have to have a conversation about the Fluctuation Theorem and how quantum mechanics may violate causality.

Does humanium display wave like properties? e.g-collective/cooperative properties?

Again, there is much to discuss. This is a holistic approach with reductionist concepts within boundaries, the Tao of Thai, if you will. Much of what the neuroanatomist says makes sense, she does, however, verge on the mystical a few times. I have come to similar conclusions myself. Our individual brains ARE connected by linguistics and vision among other things. Memes or conscious versions of Jung's Collective Unconscious and Archetypes (I'm not a Jungian) are examples of this. One reason we love the internet so much is that it augments this interconnectivity. The human brain is not a pure tabula rasa. It is a template, however, that has evolving heritable predispositions and capabilities. I once had an interest (Surely You're Joking, Mr. Feynman!) in sensory deprivation and I actually spent some time in an isolation tank. The effects of extreme sensory deprivation support Donne's passage No man is an island...for whom the bell tolls, it tolls for thee. So, fellow grasshopper, different aspects see the same truth. Beauty is truth, truth beauty, that is all Ye know on earth, and all ye need to know (I almost included this couplet in my earlier pastiche, Keats saw the Greek urn carvings/paintings of people the same way Thai sees fractals, depictions of frozen immortal permanence, glimpses of the actual dynamic flux of humanity/nature).

* Well maybe not, but I am confident you can get this monkey off your back. My biggest fear is that you will relapse if I partake of a Julia or Cantor in your presence. Don't worry, what happens in Street Rat Crazy Saloon, stays in Street Rat Crazy Saloon.

Street Dog said...

symmetry is seen as non movement, and within our monotheistic (human) context, movement is synonymous with LIFE. Symmetry is synonymous with.. death.

Remember the conversation I had with SD? He see fractals as symmetry breaking while I see them as symmetry forming- e.g. the reverse.

Semantic issue here. Fractals have "symmetry" in the generic sense. Symmetry breaking uses "symmetry" with different semantics. Symmetry breaking is a concept in physics with a rigorous background to support it. It is NOT an inverse or vice-versa concept. Symmetry breaking --> fractaloid shapes or "symmetries" in nature. Two different concepts with the same name. Symmetry breaking is synonymous with life. Life, the universe, and everything can't exist without it.

You guys are really SO fortunate that I don't unsheathe those claws on you...

Now you are really scaring me. Catnip time.

Thai said...

"Symmetry breaking is synonymous with life. Life, the universe, and everything can't exist without it."

And no fair!!! You can't stop with just this statement!

Stopping now is like finally getting that chronic pain management appointment you have been waiting months for only to be told by the anesthesiologist he doesn't prescribe narcotics.

I am not ready for a cold turkey 12 step approach yet. Can't I get a little Methadone, at least for a little while? ;-)

And I am confuse with the following paradox you have created:

"I'm not sure how renormalization applies to your thesis below"

contrasted with

"With renormalization you impose a cutoff in order to get finite answers."

Doesn't this give us the boundary condition for the fractal????

But if this helps, I came across renormalization while reading about a slightly different fractal pattern: network theory.

Q: How does order emerge from disorder?

A: The ordered and the disordered states of matter (humanium, etc...) correspond to thermodynamically distinct phases.

At this critical point, individuals stop acting as individuals and start acting as cooperative communities where power laws and fractals apply.

From what I found, the theory on why order emerges in complex systems around a critical point/phase transition apparently centers on renormalization.

As I understand the theory, in the vicinity of the critical points, the laws of physics apply in an identical manner in all scales.

Nature hates power laws, and prefers gaussian, but in the vicinity of critical points/phase transitions/the time of the fractal/ power laws take over.

This theory apparently won a Cornell physicist by the name of Kenneth Wilson the 1982 Nobel Prize. His theory is known as renormalization.

You probably learned about it from a slightly different viewpoint which is why this is a little unfamiliar.

And as I see it, it is the critical point/or critical band, in which the life network resides.

Life is truly special indeed as it can only exist in a phase transition.

... I guess this is what you mean when you say "Symmetry breaking is synonymous with life" and why Deb has the inverse association that I have.

... Hummm

Debra said...

I'm going to throw out a few associations here. This is not, strictly speaking, scientific thought as you know it, but I think that it will help.
My reading on symmetry is that it is an analogy to a state of "matter" at rest, known as static vs dynamic.
But our senses are designed to perceive difference, and one of the most important ways of perceiving difference is through (dynamic) movement.
I am saying that this phenomenon is a limitation imposed on our perception of whatever it is out there that we come into contact with, and I'M NOT CALLING THAT REALITY. (I will stay away from the expression "reality"...)
I have already said on this blog that I have epistemological axioms. Number 1 : the act of thinking is synonymous with the perception of difference, or the breakdown of a global construct into differentiated parts. This involves... making judgments (careful, a judgment is not necessarily to determine good/bad...).
Nobody has commented on the homeostasis theory. Aren't you guys familiar with homeostasis ?
Finally... some reflections on metaphor, as I see this as being one of our major problems.
Lacan spent mucho time trying to understand just exactly HOW metaphors work.
When Hell creates the metaphor "bankstie", INITIALLY, when it first appears, it "combines" the associations/definitions produced by "banks" AND those produced by "pigstye/stie".
Just... WHAT is the statute of the... AND ???
How do the two go together ?
It is not a... superposition.
It is not a... juxtaposition.
So.... what is it, exactly ?
My research in psychoanalysis brought me back to this question of what is called the... copula.
Two basic ones... AND, and... OR.
Inclusion and exclusion...
Pretty interesting, I think.
Inclusion is not all that easy to understand...
And remember that at all times the human mind has an incredible necessity to localize... Another axiom, I think.
Street Dog, I never had to go into a tank to live sensory deprivation. I did it in an apartment in 5 square meters. It was... not fun...
I'm impressed by your curiosity.

Thai said...

"My reading on symmetry is that it is an analogy to a state of "matter" at rest, known as static vs dynamic."


Re: and/or


re: copula

And I have to point out this particular passage in the linguistic definition of copula:

"Most languages have one main copula verb, but some languages, like Spanish or Thai, have two, and some have none."

For you had to know I would get more of it than everyone else. ;-)

And somehow I missed the following: "Number 1 : the act of thinking is synonymous with the perception of difference, or the breakdown of a global construct into differentiated parts."


Indeed it is the iterative combining or clumping of the broken parts into larger global structures and the still further iterative combing of these larger global structures into a still larger things that IS the fractal I see everywhere.

It is true with everything (and I mean everything), not just knowledge/thought/information structures.

We don't disagree

I am Sorry I missed your statement earlier

Thai said...

And Deb re: symmetry

Scroll midway down the page and you will see a section that describes symmetry. Your "at rest" association is not correct, symmetry can be moving even in chaotic fashion.

A fluid, which is composed of atoms arranged in a disordered but homogeneous manner, possesses continuous translational symmetry: each point inside the fluid has the same properties as any other point. A crystalline solid, on the other hand, is made up of atoms arranged in a regular lattice. Each point in the solid is not similar to other points, unless those points are displaced by an amount equal to some lattice spacing.

Generally, we may speak of one phase in a phase transition as being more symmetrical than the other. The transition from the more symmetrical phase to the less symmetrical one is a symmetry-breaking process. In the fluid-solid transition, for example, we say that continuous translation symmetry is broken.

You do not need the topic to be a fluid or material. Substitute the word "energy" for fluid" or "information structure" or etc...

You come up with the same concepts re: symmetry and from this the fractal(s) should not be hard to see.

By the way, I say "see" as I tend to process things visually/geometrically but I recognize this is simply unique to my own visual method of processing information. The fractal exists in all information they could exist in any other information systems so you could "hear" the fractal or "feel " the fractal, etc...

As a psychologist, I am sure you are aware that different people process different types of information differently- e.g. there are: kinesthetic learners, visual learners, olfactory learners, auditory learners, etc...

... One of the (many) things biodiversity punks seem to endlessly forget when they apply their value systems to engineer humanium social solutions.

And re: homeostasis

What point are you trying to make?

Thai said...

SD, I can be SOOOOOO dense at times, though I guess I did not see the symmetry issue you mentioned earlier... it can take me a while to think about fractals.

Here is my question:

Does the breaking of symmetry (again from whatever manifold/viewpoint the symmetry exists in) release energy into that manifold/viewpoint?

If so it all makes sense and would explain why life (a scale free network) can ONLY exist at phase transition boundary conditions.

Deb, I ran a quick Google search when I realized this must be the case and I found the following link for you in case you have more interest in the linguistic definition of symmetry- which I suspect will be a rabbit hole like everything else.

Personally I think the best way to think of symmetry is first chose your manifold (or energy structure/information structure, etc...) and then think relative to that same manifold/viewpoint.

... I have a hard time thinking thoughts on symmetry would not incorporate the theory of relativity or relative viewpoints.

So if you want to discuss the breaking of symmetry where the manifold is the sound of a galloping horse and the viewpoint is you listening to this sound, I suspect that would work fine... Though I suspect we would have to develop an awful lot of new engineering tools to acquire the energy released from this fractal ;-)

Debra said...

I'm going to LIMIT my axioms now...
I am not sure, but I think that my axiom about thinking being about the capacity to recognize differences is... directly related to the monotheistic/Judaic mindset.
Cultures that we have labeled "primitive" may NOT think this way...
For symmetry, Thai... somewhere I read a while ago that... geneticists have determined some kind of logic in the... choice that the egg performs when uniting with a sperm cell. The egg "chooses" the sperm cell with which it shares the least possible genetic material.
Interesting, huh ?

Thai said...

re: "Cultures that we have labeled "primitive" may NOT think this way..."

Do you have a link to support this?

re: "The egg "chooses" the sperm cell with which it shares the least possible genetic material."

This is not my understanding of the issue at all. Again, do you have a link?

Debra said...

No link for number 2, Thai, I read it somewhere. Do you have a link that suggests the contrary ?
For point 1, Thai, I am going to take you through it without a link because... if you can understand something WITHOUT a link, why do you need SOMEBODY ELSE to tell you what to believe ???
The capacity to recognize difference and put things together by comparison, thereby assigning hierarchical positions of value is the very basis of.. analytic thought. And... Western Civilization takes analytic thought to be the be all, end all of.. THOUGHT itself. But...just because Western Civilization takes analytic thought for the be all, end all of thought, does that mean that it... IS ?
Back to Genesis, Thai. First part. Find yourself the King James Bible, one of the.. BEST translations still available.
And take some time to study HOW the creation is pictured. The peculiar status of language, the WORD (Christian) in the creation story. And then notice that... the successive acts of God in the first part of the creation story are all acts of.... separation.
Judaïsm posits creation by... separation. Creation by separation = differentiation.
But.... is ALL creation, creation by.. SEPARATION ?
Why ?
And... is all THOUGHT that is worthy of being called thought a result of... differentiation/separation ?
Why ?
And for a look into just HOW steeped we are in this mindset, look at what we are doing with your famous... LHC, or whatever the acronym is. The principle behind it is... to separate further and further, to differentiate particles further and further in a quintessential application of analytic thought UNTIL we get to what ??? GOD ? The God particle ??? (love that one, Thai...) This is... disguised religion, Thai, as I hope you know...
When I play my piano, and bring my entire mind to bear on my physical sensations in producing music, is that... THOUGHT ?
Why ? Why not ?
Lots of questions, Thai...

Debra said...

Street Dog... just my personal preference, but.. I liked the video of "what really happens to cats on catnip" starring Quincy better than yours... in spite of the title...

Thai said...

I guess I am a little confused why you see religion as an explanation for why we think the way we think and why you see primitive cultures as thinking different.

I can certainly see how the authors of modern western religions thought the same we we do and that it would therefore be possible to see the DNA of our thinking today in the DNA of the thinking that went into producing the bible. I am even will entertain the notion that there were certain templates that were created with the emergence of modern western religions that can been seen in most western thought processes today as a kind of unrecognized standard that we in the west use for convenience sake- this is where I thought you were going and was curious if you had an example to back your thesis.

I am a little more skeptical in believing that Christianity/Judaism are responsible for major features of modern thought structure, etc... which would not exist amongst pre-Columbians.

And re: "When I play my piano, and bring my entire mind to bear on my physical sensations in producing music, is that... THOUGHT ?"

The answer is YES but it gets into linguistic definitions of what the word thought means so I do see one could create a rabbit hole on this issue if you wanted.

Take any issue in the world and you can split it into is sub-components and ultimately you will find differences in the way we all think on things- I get it. Remember, I too found nihilism from a different angle.

And yet we all must have faith ;-)

And faith require common values.

Hence the forever war between the simpletons and the complexitrons.

Debra said...

NO THAI, faith does NOT require common values.
That is not at all what faith is about.
Faith transcends common values, because if it didn't it would not be faith.
Now, belief, that requires commmon, thus... shared values. Faith... is essentially an extremely individual, personal experience. One that.. can not be transmitted, but must be recreated from one generation to the next.
You do not understand because you are still thinking of religion in terms of particular content, and not in terms of general structure.
Religion is what... imparts meaning to our world.
That is why... materialistic science is... religious.
That is why... fractals are a.. religious belief for you, Thai. You... DID know that, didn't you ?

Thai said...

re: "Faith transcends common values, because if it didn't it would not be faith."

Ah, I think I now see what you are saying- we are coming at the word religion from different angles and I needed to shift my viewpoint.

Fair enough.

And concerning faith- agreed. I was careless with my wording and mist spoke.

By your definition I agree science is a religion

AI can see what you are saying, I had to shift my

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