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Chaos theory and postmodernism

Gregory January 19, 2020 at 18:09 10950 views 63 comments Logic & Philosophy of Mathematics
The word "random" is used in two very related ones. It can mean "spontaneous action" such that world seems to act as if it has free will but no consciousness, and it can mean irregular patterns. I am wondering if the latter is based on anything objective. We all have different tastes in physical appearances. Someone might seem beautiful to someone else, but not to a third person. We all have different tastes in art and music as well. Further, autistic people see patterns within disorder. What is one person's order is another person's mess. Therefore, IQ tests seem to measure how a person scores within an arbitrarily assigned range of what is "smart". If I have a sequence 2,4,8 and ask what comes next, any answer can be right. What if it is the law of the human nature that after two doublings you multiply by 100. The answer would be 800. What if that was the law of just some peoples' genes? They would score low on an IQ test. But the IQ test is not objective then. If beauty is in the eye of the beholder, than so is order.

In conclusion, is chaos theory all bunk?

Comments (63)

RegularGuy January 19, 2020 at 18:15 ¶ #373228
Reply to Gregory People with high IQs in pattern recognition can make a lot of money trading Forex using technical analysis (reading candlestick chart patterns). It may or may not be objective, but it is useful.
Joshs January 19, 2020 at 18:31 ¶ #373234
Reply to Noah Te Stroete Is there evidence that they reliably make money over longer periods of time?
RegularGuy January 19, 2020 at 18:32 ¶ #373235
Reply to Joshs With money management (such as the Kelly criterion and a good reward to risk ratio), yes.
MathematicalPhysicist January 19, 2020 at 18:46 ¶ #373240
Well, if we humans and others exist is there any meaning to the term "disorder"?

I would guess that a true disorder is not possible...
My proof for this is our existence, or at least mine I don't know about you zombies. :-)
RegularGuy January 19, 2020 at 19:01 ¶ #373245
Quoting MathematicalPhysicist
I would guess that a true disorder is not possible...
My proof for this is our existence, or at least mine I don't know about you zombies. :-)


:smile:
fdrake January 19, 2020 at 19:49 ¶ #373256
Quoting Gregory
In conclusion, is chaos theory all bunk?


Made a post describing how "chaos" is actually a property of a system here. Other I made in that discussion talk about the role random variables (which can be deterministically driven anyway) play in them (up to my idiosyncratic interpretation of things).
Gregory January 19, 2020 at 19:56 ¶ #373257
I think Derrida was saying we can never predict the random because true randomness is more random and free than we can imagine. Our concepts of the random and the infinity is an approximation of the substance of those ideas
fdrake January 19, 2020 at 19:58 ¶ #373258
Reply to Gregory

I don't think Derrida actually said anything about randomness? There's a very old reading group on the forum for "Voice and Phenomenon" which goes into a lot of detail, you'll see that he can be quite rigorous.
Gregory January 19, 2020 at 20:08 ¶ #373263
That pattern recognizes works in science can be explained by compatabilism. The free will (the random factor in Bell's theorem and the Quantum eraser experiment) could be parallel to the world and work like Leibniz said about harmony. Newton got his idea of a deterministic world from Descartes, who thought we can in reality know all the workings of the universe (and of all human truth) if we applied ourselves. This rather esoteric, or at least philosophical, opinion doesn't grasp that he world is a lot freer than we may think.

Anything could have happened in the past, and anything may happen in the future. We never see the "laws" themselves, to know them in their nature.

Newton thought God stepped every now and then to correct the disorder that naturally happens in this universe.

Side note: Teilhard believed God let randomness run it's course and help form evolution. The randomness would not be controlled by God, but merely sustained in nature.

The randon was a demi-god for Teilhard.
Joshs January 19, 2020 at 20:22 ¶ #373266
Reply to Gregory Derrida deconstucted the modern empirical notion of the random alongside its opposite,determinism, in order to show that this binary presupposes certain underlying metaphysical assumptions about the nature of reality in terms of 'objectivity, physicalism, naturalism, etc.
In Derrida's thinking(not just Derrida but also the phenomenologists, including Heidegger, there is neither randomness or determinism but codependent subjective-objective relationaltiy
Gregory January 19, 2020 at 20:33 ¶ #373269
If the Christian says "why not drink hemlock since you agree with Hume that any law from anywhere in the universe or other dimensions might intervene to stop your death", I can retort that God might interfere to stop your death, or cause your death from eating a prexel. The Christians have a god to rely on ultimately.

To be truly philosophical is to be anti-science and be more Buddhistic. I think Teilhard at heart was a Buddhist (after all he cried when he discovered as a child that iron rusts with a Catholic virus in him.

Become a sage
Gregory January 19, 2020 at 20:35 ¶ #373271
Reply to Joshs Reply to Joshs

If "the other" is predictable for phenomenologists, than there is no random. I thought Derrida thought writing and thinking too random and subjective to be objective
Joshs January 19, 2020 at 20:38 ¶ #373273
Reply to Gregory The phenomenologists argue that the notion of objectivity is constituted via intersubjective relations, which makes objectivity always relative to a social field.The 'other' is not predicable, it affects me as something alien, foreign to my previous experieince. At the same time, it is not utterly independent of my history . There is something familiar or recognizable in even the most surprising experience.This does not make it predictable but neither does it make it random in a mathemtical sense.

Husserl says"
“We do not say that in the unity of the stream of my lived experiences each lived experience is necessary, necessarily conditioned by the lived experiences which precede it and are co-lived. If we say that every lived experience of an act is motivated, that relations of motivation are intertwined in it, this is not to imply that every meaning-intending is one "in consequence of." When I become aware of a thing, the thesis contained in the perception is not always a thesis "in consequence of": e.g., when I see the night sky lit up by a meteor shower or hear quite unexpectedly the crack of a whip.”
Gregory January 19, 2020 at 21:09 ¶ #373295
Reply to Joshs

If any law can suddenly ooze out into reality at any time, then to our subjectivity the world is random. The many dimensions theory gives even more visual support for this argument
Mephist January 20, 2020 at 02:20 ¶ #373365
Reply to Gregory About the randomness of sequences, I think a good definition is the following one: a sequence is random if it cannot be generated by a program shorter than the sequence itself.
In other words, it's all about the quantity of information needed to generate that sequence.
Short sequences are always random.
jgill January 20, 2020 at 05:37 ¶ #373399
Quoting Gregory
In conclusion, is chaos theory all bunk?


You are referring to something other than mathematical chaos theory, which is not bunk IMO.
Gregory January 20, 2020 at 09:46 ¶ #373455
As Heraclitus said, everything may be in flux. I don't see how the human mind can grasp through math the many infinities in which the random can take form
RegularGuy January 20, 2020 at 09:48 ¶ #373458
Quoting Gregory
As Heraclitus said, everything may be in flux. I don't see how the human mind can grasp through math the many infinities in which the random can take form


On the other hand, Fibonacci patterns exist throughout nature, even in stocks charts. Fractals exist in nature, too.
Gregory January 20, 2020 at 09:50 ¶ #373459
Reply to Noah Te Stroete ,

Patterns are in the eye of the beholder. Patterns work in technology perhaps by a preestablished harmony
RegularGuy January 20, 2020 at 09:51 ¶ #373461
Reply to Gregory There is chaos and patterns. You can’t separate the human mind from empirical experience.
Gregory January 20, 2020 at 09:54 ¶ #373464
The distinction between chaos and patterns is in the mind of the beholder. Who is to say what the chaos theory would be for a different species
RegularGuy January 20, 2020 at 10:03 ¶ #373473
Quoting Gregory
The distinction between chaos and patterns is in the mind of the beholder. Who is to say what the chaos theory would be for a different species


I presume any technologically advanced alien species would likewise see these patterns, too, and maybe many more.
Gregory January 20, 2020 at 10:06 ¶ #373475
But patterns are nothing more than what humans perceive is beautiful, regardless if infinite chaos can be contained in a mathematical system
RegularGuy January 20, 2020 at 10:07 ¶ #373477
Gregory January 20, 2020 at 10:13 ¶ #373478
If we were to get ahead of the random and understand it almost like understanding a person, our actions would still be in control all along by this universe
RegularGuy January 20, 2020 at 10:17 ¶ #373481
Reply to Gregory

I don’t know. Logically that conclusion is inescapable if you only consider us as matter and energy. I even wrote a now unpublished book which I have since rebuffed saying just that.
Gregory January 20, 2020 at 10:23 ¶ #373484
I don't think we can get ahead of the ball with the universe since its always ahead of us! What does the universe rest on, if it's matter. Does a force keep it in place? If the force is from an object we have an infinite regress. So I think meta nothing is like what people call spiritual or Plotinus "pure potency". Like a thought without a thinker, it acts without an actor
jgill January 21, 2020 at 05:31 ¶ #373883
Quoting Gregory
But patterns are nothing more than what humans perceive is beautiful, regardless if infinite chaos can be contained in a mathematical system


It might be best to avoid referring to mathematics in this regard. Mathematical chaos theory is a fairly well-defined, logical and coherent area of inquiry. It has to do with iterative systems in the complex plane initially. What does "infinite chaos contained in a mathematical system" really mean? I can generate chaotic behavior in a mathematical context by formulating a complex function and iterating it over regions of the plane. I suppose that's what you're getting at.
Gregory January 22, 2020 at 01:10 ¶ #374198
Reply to jgill

But how do we know the pattern is not controlling us? We think that we discover patterns, like Descartes thought he discovered innate ideas. It could come from a different source
Gregory January 22, 2020 at 01:47 ¶ #374205
Does not compatibilism completely explain the Quantum Eraser experiment and Bell's theorem away? If there is no random factor with regard to the subject observing, how can it ever be proved that there is randomness out there? I guess on this thread I am trying to argue that you can't prove there is order either. Neither one nor the other
jgill January 22, 2020 at 05:12 ¶ #374272
Quoting Gregory
But patterns are nothing more than what humans perceive is beautiful,


There are patterns that are not beautiful. For instance, an aerial view of a battlefield having a symmetric array of exploded mines. Or a pattern of murders by a serial killer.

Quoting Gregory
But how do we know the pattern is not controlling us?


Do you mean that by simply contemplating a pattern it might somehow control us? Or at least influence our thinking? Like mandalas?

Wiki: "In various spiritual traditions, mandalas may be employed for focusing attention of practitioners and adepts, as a spiritual guidance tool, for establishing a sacred space and as an aid to meditation and trance induction."

TheMadFool January 22, 2020 at 08:16 ¶ #374305
Quoting Gregory
The word "random" is used in two very related ones. It can mean "spontaneous action" such that world seems to act as if it has free will but no consciousness, and it can mean irregular patterns. I am wondering if the latter is based on anything objective. We all have different tastes in physical appearances. Someone might seem beautiful to someone else, but not to a third person. We all have different tastes in art and music as well. Further, autistic people see patterns within disorder. What is one person's order is another person's mess. Therefore, IQ tests seem to measure how a person scores within an arbitrarily assigned range of what is "smart". If I have a sequence 2,4,8 and ask what comes next, any answer can be right. What if it is the law of the human nature that after two doublings you multiply by 100. The answer would be 800. What if that was the law of just some peoples' genes? They would score low on an IQ test. But the IQ test is not objective then. If beauty is in the eye of the beholder, than so is order.

In conclusion, is chaos theory all bunk?


The word "random", to me, indicates a systems state where every possible outcome is equi-probable. For instance a die is random if every outcome: 1, 2, 3, 4, 5, and 6, is equally likely.

Once, given a system of outcomes, some outcomes become more probable then that system isn't random. That said, consider a pair of die and you'll notice certain sums of outcomes in throwing them together, despite each individual outcome actually being totally random, have a greater probability of occurring. Does this mean that the 2-dice system isn't random? No, because we have an explanation for why some outcomes are more likely even in a completely random system. In the case of the 2-dice system we need only look at how many ways a particular outcome can occur and if there are more ways to get outcome x then x will occur with that frequency.

So, randomness isn't simply a matter of equi-probability; although if the presence of some favored/some disfavored outcomes can be explained by an underlying random process it is.

Chaos theory, as I understand it, seems to be about small changes in a system resulting in large deviations in outcomes. The classic example is that of the small air disturbances caused by a butterfly leading to storms in far off, distant places. I believe Lorenz, who coined the term the butterfly effect, had entered data that differed only in the hundredth or thousandth decimal place and the outcomes for these inputs that differed in such small degrees produced large variations in the output, whatever that was. Data was fed into a system, probably a set of deterministic functions, but the functions spat out numbers that differed by massive amounts. It's this effect of small changes causing large differences in outcome that chaos theory is all about (in my opinion).Chaos theory isn't about randomness per se but is, in essence, a difficulty we face in making predictions about chaotic systems.



jgill January 23, 2020 at 00:27 ¶ #374493
Wiki: "Chaos theory is a branch of mathematics focusing on the study of chaos—states of dynamical systems whose apparently-random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions."

The article goes on to state that it is an interdisciplinary area, however. "Chaotic behavior" might be more accurate outside the mathematical umbrella. Using "theory" makes the concept more formal and technical. Just my two bits. :smile:
Gregory January 23, 2020 at 04:29 ¶ #374580
Reply to TheMadFool

Chaos behavior is about "patterns" in randomness. How could "some outcomes are more likely even in a completely random system".? I think we sense patterns based on beauty only. If I cut a square into four triangles, can you prove it has more "pattern" than a white sheet of paper with one dot in the corner? Is it more patterned if the dot is in the middle? If beauty is in the soul of the beholder, then even pattern might not inherently out there.
Gregory January 23, 2020 at 06:35 ¶ #374601
Spinoza and Leibniz thought everything was controlled by one principle. Infinity in substance, which far outstrips when you count to infinity and call it infinity. Occasionalism is a much better option. Did Einstein believe in compatabism. Spinoza was a determinalist. Either way the subjective and objective don't interact. When you say the first principle is impersonal or even nothingness personified, patterns cease
TheMadFool January 23, 2020 at 08:01 ¶ #374608
Quoting Gregory
Chaos behavior is about "patterns" in randomness. How could "some outcomes are more likely even in a completely random system".? I think we sense patterns based on beauty only. If I cut a square into four triangles, can you prove it has more "pattern" than a white sheet of paper with one dot in the corner? Is it more patterned if the dot is in the middle? If beauty is in the soul of the beholder, then even pattern might not inherently out there.


I'm not quite sure about that. To begin with I don't think chaos, as conventionally understood, is about patterns; quite to the contrary, when a system exhibits no discernible pattern it is said to be in chaos. However, I'm willing to entertain the possibility that chaos may be construed as a completely random system.

Secondly, the only subject that studies patterns seriously is math and I don't know if there's a subfield devoted to just the study of patterns or not.
Gregory January 23, 2020 at 16:35 ¶ #374706
If I roll a dice a zillion times, each roll is one and six that I will come up with a 6. So the same applies the zillion (one to one correspondence). Strict logic seems to say the world does work by determinism and Einstein was right therefore. If the laws suddenly "changed" because we didn't really understand them, the scientists would say a new force has enter our universe. Hume would say "what's the difference, what is force", and he might be right
jgill January 23, 2020 at 18:38 ¶ #374730
Quoting TheMadFool
Secondly, the only subject that studies patterns seriously is math and I don't know if there's a subfield devoted to just the study of patterns or not.


https://www.maa.org/press/periodicals/convergence/mathematics-as-the-science-of-patterns-mathematics-as-the-science-of-patterns :cool:
Gregory January 24, 2020 at 04:25 ¶ #374906
Einstein's position was self refuting. If things are all determined you can't even do science because the law might be that the after an age a new age with the opposite laws appear. You can never catch the universe red handed. Can the determined become random or the random become determinef. Nobody knows.
Agent Smith April 17, 2022 at 08:44 ¶ #682521
To Mathematicians

Is Chaos Theory (math) an admission that the calculations involved are too complex for humans and current top-of-the-line supercomputers (extremely difficult to predict) or is the claim that there's true randomness (unpredictability).

Note: There's a difference between computational complexity (difficult to prognosticate) and randomness (impossible to prognosticate)
Haglund April 17, 2022 at 09:46 ¶ #682552
Reply to Agent Smith

Chaos theory is about sensitivity to initial conditions. Vary them a tiny bit and you might end up in Bakerstreet instead of Trafalgar Square.
Agent Smith April 17, 2022 at 09:49 ¶ #682556
Quoting Haglund
Chaos theory is about sensitivity to initial conditions. Vary them a tiny bit and you might end up in Bakerstreet instead of Trafalgar Square


You say it better than the mathematicians! :up:
jgill April 19, 2022 at 00:10 ¶ #683181
Quoting Agent Smith
To Mathematicians

Is Chaos Theory (math) an admission that the calculations involved are too complex for humans and current top-of-the-line supercomputers (extremely difficult to predict) or is the claim that there's true randomness (unpredictability).


The computer calculations define the dynamical system in C (complex plane). Iteration of a function carries an initial point in C to a new position - usually not the same position unless the original point is a fixed point of the function. When there is a condition in which two points very close to one another diverge dramatically and relatively unpredictably under iteration the system may be chaotic (under other circumstances fractals might appear). This might occur everywhere on a set S in C, or on a part of S. This is the simplest version of chaos theory. Draw your own conclusions. :cool:
Agent Smith April 19, 2022 at 05:13 ¶ #683247
Reply to jgill Is the unpredictability absolute i.e. is it impossible to predict or is it just that we don't have powerful enough supercomputers i.e. unpredictability is relative, possible but not with current tech?
jgill April 19, 2022 at 20:52 ¶ #683497
Here is a non-chaotic image arising from an iteration process that involves differing functions rather than a single function. Its' beautiful intricacies might possibly be predictable were an attempt made to do so, but it would take a significant effort. This is a dynamical system in C that rewards its inventor. I call it Dream of Gold.

User image
Haglund April 19, 2022 at 21:12 ¶ #683502
Reply to jgill

Wow! Incredible and beautiful! Anyone claiming that math is dull, arid, and ugly is asked to kindly STFU! Can you zoom in like in those colored fractal zoomings (where the colors represent a rate of convergence, if Im not mistaken)?
Banno April 19, 2022 at 21:27 ¶ #683505
Reply to jgill Impressive. This is yours?
jgill April 19, 2022 at 23:15 ¶ #683548
Quoting Haglund
Can you zoom in like in those colored fractal zoomings (where the colors represent a rate of convergence, if Im not mistaken)?


It's not a fractal, but sometimes one can focus on a spot and enlarge it and find additional intricacies. Iterations are done at pixel levels with light shades when the modulus is great and dark shades when it is small. Very simple.

Quoting Banno
?jgill
Impressive. This is yours?


Yes, I've done lots of unpredictable images. Look at my icon on TPF. Here's another I call Reproductive Universe:
User image
Banno April 19, 2022 at 23:22 ¶ #683550
Reply to jgill It's a topic I sometimes think of getting in to - I programmed a mac plus to draw the Mandelbrot set once; a run would take days. But what you are doing is quite novel. Have you a gallery? Have you written some background on the maths involved?
jgill April 19, 2022 at 23:39 ¶ #683560
Quoting Banno
Have you written some background on the maths involved?


Lots of notes/articles as a hobby. Here's an example: Woven Contours

I've written all my computer programs in BASIC.
Banno April 19, 2022 at 23:51 ¶ #683566
Reply to jgill Very cool. They look to me like stills from some animation, "2001" or "Dr Who"...

But the maths is beyond my keen.
Cuthbert April 20, 2022 at 04:17 ¶ #683604
@jgill Amazing images, thank you!

For non-programmers with basic skills (me), there is a way to explore chaos with a simple iterative function on a calculator or in Excel.

Begin with a number between 0 and 1 in the first cell. Next cell = previous cell x (1 - previous cell) x some constant between 2 and 4. Copy down a few hundred times. Graph the outputs.

Then play with the constant, say starting at 2.5 and raising it 0.01 at a time. The graph will begin as a flat line, then split into peaks and troughs, repeating every second output, period 2, then every fourth, eighth etc output - then it will become non-repeating apparent disorder with bursts of order, e.g. period 3 or 5.

This reproduces one of the ways Feigenbaum used to investigate chaos. I think he started with a calculator, not even a graphed spreadsheet. https://www.youtube.com/watch?v=ETrYE4MdoLQ

No randomness is involved here. It's sometimes confusing because the concept 'chaos' suggests randomness but 'chaos theory' is about sensitivity to initial conditions in a deterministic system.
Haglund April 20, 2022 at 05:43 ¶ #683613
Reply to jgill

Interesting! You make two contours in the complex plane dependent on each other? The z(n) and ksi(n) seem to have a part of the previous ksi(n--1) and z(n-1)? Somehow they seem to eat each other. Raw sex in the complex plane...

jgill April 21, 2022 at 00:37 ¶ #683865
Quoting Cuthbert
Begin with a number between 0 and 1 in the first cell. Next cell = previous cell x (1 - previous cell) x some constant between 2 and 4.


Sound like elementary cellular automata, championed by Wolfram some time ago. I've written programs that show a constant sort of development, then a jump to a weird line or something. Wolfram thought he had come upon a hugely important concept, writing a book with over a thousand pages. I, like most other readers, gave up after a few hundred pages.

Quoting Haglund
Somehow they seem to eat each other. Raw sex in the complex plane...


Like Pac-Men. My friend, you need to get out of the house more often. :wink:
Haglund April 21, 2022 at 06:40 ¶ #683999
Reply to jgill

The dog pulled my arm. Luckily she didn't take puppy course. She is always eager to go to the park. Pulling me along (which I'm fine with, it shows life!). Knowing I'm gonna swing away the biggest treetrunks! With that same right arm she's pulling... Something in my shoulder is stretched too long, I guess... Time heals everything, I hope! :wink:

I guess it pales in the face of your accident about 35 years ago...
Haglund April 21, 2022 at 07:00 ¶ #684005
Reply to jgill

Wolfram is physicist also. Interesting stuff! I don't agree with it all, luckily!

Agent Smith April 21, 2022 at 07:14 ¶ #684010
Reply to jgill Looks very Mayan! Perhaps its just the combination of color and the swirling motif.
Haglund April 21, 2022 at 07:24 ¶ #684015
Reply to Agent Smith

Have you seen his other works? Out of this world! Seems he had an encounter with the gods, high up those mountains he bouldered!
Agent Smith April 21, 2022 at 07:27 ¶ #684016
Quoting Haglund
Seems he had an encounter with the gods


:smile:
jgill April 22, 2022 at 04:23 ¶ #684511
Quoting Haglund
I guess it pales in the face of your accident about 35 years ago...


Sadly that's the strongest part of my body now. :worry:

Quoting Agent Smith
?jgill
Looks very Mayan! Perhaps its just the combination of color and the swirling motif.


Hidden within those intricate folds are the secrets of the universe.

Well, maybe not. :sad:

Haglund April 22, 2022 at 04:45 ¶ #684532
Quoting jgill
Sadly that's the strongest part of my body now. :worry:


Well, you climbed the 6 meter rope in 3.4 seconds once... with arms only! Did you succeed with that Victorian cross (no offense!)?
jgill April 22, 2022 at 04:47 ¶ #684533
Quoting Haglund
Did you succeed with that Victorian cross (no offense!)?


Not more than a fraction of a second. It awaited a smaller, stronger body.
Agent Smith April 22, 2022 at 05:19 ¶ #684545
Quoting jgill
Hidden within those intricate folds are the secrets of the universe.


Quoting jgill
Well, maybe not. :sad:


:chin:

Whac-A-Mole?

Truth pops up randomly in an epistemic, to borrow a mathematical term, field...sometimes at an opportune moment (an example) and at other times at very inconvenient times (in flagrante delicto).