Chaos theory and postmodernism
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?
In conclusion, is chaos theory all bunk?
Comments (63)
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:
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).
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.
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.
In Derrida's thinking(not just Derrida but also the phenomenologists, including Heidegger, there is neither randomness or determinism but codependent subjective-objective relationaltiy
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
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
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.”
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
In other words, it's all about the quantity of information needed to generate that sequence.
Short sequences are always random.
You are referring to something other than mathematical chaos theory, which is not bunk IMO.
On the other hand, Fibonacci patterns exist throughout nature, even in stocks charts. Fractals exist in nature, too.
Patterns are in the eye of the beholder. Patterns work in technology perhaps by a preestablished harmony
I presume any technologically advanced alien species would likewise see these patterns, too, and maybe many more.
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.
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.
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
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
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."
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.
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:
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.
https://www.maa.org/press/periodicals/convergence/mathematics-as-the-science-of-patterns-mathematics-as-the-science-of-patterns :cool:
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)
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:
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:
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)?
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
Yes, I've done lots of unpredictable images. Look at my icon on TPF. Here's another I call Reproductive Universe:
Lots of notes/articles as a hobby. Here's an example: Woven Contours
I've written all my computer programs in BASIC.
But the maths is beyond my keen.
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.
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...
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
Like Pac-Men. My friend, you need to get out of the house more often. :wink:
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...
Wolfram is physicist also. Interesting stuff! I don't agree with it all, luckily!
Have you seen his other works? Out of this world! Seems he had an encounter with the gods, high up those mountains he bouldered!
:smile:
Sadly that's the strongest part of my body now. :worry:
Quoting Agent Smith
Hidden within those intricate folds are the secrets of the universe.
Well, maybe not. :sad:
Well, you climbed the 6 meter rope in 3.4 seconds once... with arms only! Did you succeed with that Victorian cross (no offense!)?
Not more than a fraction of a second. It awaited a smaller, stronger body.
Quoting jgill
: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).