At Quanta: Mathematical Analysis of Fruit Fly Wings Hints at Evolution’s Limits

_{Denyse O'Leary

September 21, 2021

Evolution, Intelligent Design}

Share: Facebook; Twitter; LinkedIn; Flipboard; Print; Email

On one hand, despite dramatic mutations in individuals’ genes and diverse environments in which they grow, members of a species develop into strikingly similar creatures. This robustness ensures that almost all individuals are functional. On the other hand, for evolution to occur, members of a species need diverse traits that natural selection can act upon. Those two forces — robustness and evolvability — tug in opposite directions. One wants less variation, and one wants more.
Around 20 years ago, biologists expected genetics and environmental factors to produce substantial heterogeneity, giving natural selection plenty of choice, said Alex Lancaster, an evolutionary biologist at the Ronin Institute in New Jersey who wasn’t involved in the new study. But, he said, more recent observations have attested to unexpected similarity across populations…
The photos of fly wings offered no clues as to the mechanisms that restrict the possible morphologies that can develop. Rather, the results substantiated the extensive power of these guardrails. Natural selection must mostly act on the significant diversity exhibited in the small number of linked, variable traits, while robustness tightly constrains the rest. Elena Renken, “Mathematical Analysis of Fruit Fly Wings Hints at Evolution’s Limits” at Quanta

Evolution has LIMITS? Isn’t it supposed to account for everything? Put another way, consider the Darwinian claim:

It may be said that natural selection is daily and hourly scrutinizing, throughout the world, every variation, even the slightest; rejecting that which is bad, preserving and adding up all that is good; silently and insensibly working, wherever and whenever opportunity offers, at the improvement of each organic being in relation to its organic and inorganic conditions of life.

The claim is doubtful, given the huge constraints on the system.

The paper is open access.

Comments

Thank you, Kairosfocus. Well put. What amazes me is how fast the noise amplifies. What also intrigues me is the application or discovery of chaotic effects everywhere. For example, I'm not sure whether anyone has considered chaotic noise in genetic mutations that amplify quickly, either succeeding or becoming extinct. This might be a possible factor for those researchers pursuing a mechanism for the theory of punctuated equilibrium. -QQuerius_{October 11, 2021
October
10
Oct
11
11
2021
10:03 AM
10
10
03
AM
PDT}

PS: A summary https://news.mit.edu/2008/obit-lorenz-0416 >>A professor at MIT, Lorenz was the first to recognize what is now called chaotic behavior in the mathematical modeling of weather systems. In the early 1960s, Lorenz realized that small differences in a dynamic system such as the atmosphere--or a model of the atmosphere--could trigger vast and often unsuspected results. These observations ultimately led him to formulate what became known as the butterfly effect--a term that grew out of an academic paper he presented in 1972 entitled: "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" Lorenz's early insights marked the beginning of a new field of study that impacted not just the field of mathematics but virtually every branch of science--biological, physical and social. In meteorology, it led to the conclusion that it may be fundamentally impossible to predict weather beyond two or three weeks with a reasonable degree of accuracy. Some scientists have since asserted that the 20th century will be remembered for three scientific revolutions--relativity, quantum mechanics and chaos. "By showing that certain deterministic systems have formal predictability limits, Ed put the last nail in the coffin of the Cartesian universe and fomented what some have called the third scientific revolution of the 20th century, following on the heels of relativity and quantum physics," said Kerry Emanuel professor of atmospheric science at MIT.>>kairosfocus_{October 11, 2021
October
10
Oct
11
11
2021
04:16 AM
4
04
16
AM
PDT}

BO'H, yes hypersensitivity to initial conditions tied to nonlinearity in in principle deterministic systems that were expected to behave closely similarly on different runs led to distinct runs of seemingly simple weather models in the case of Lorenz diverging rapidly and the why had to be figured out. The noise from rounding or resolution more broadly -- analogue cases -- is associated with the heart of the effect as we observe it. That is how the hypersensitivity expresses itself in many cases. KFkairosfocus_{October 11, 2021
October
10
Oct
11
11
2021
04:09 AM
4
04
09
AM
PDT}

Err, I am well aware that computers have finite precision, but so what?
So what? So, it’s only the entire basis of Chaos Theory.
This is flat out wrong. Poincaré and Hadamard certainly didn't use computers, did they? And Lorenz doesn't discuss chaos as coming from rounding in his seminar paper.
So what? We’re not discussing the difference between an exact calculation and a computer approximation.
Anyone familiar with Chaos Theory knows that those tiny differences are exactly what defines chaos.
No,. anyone familiar with chaos theory know that it is not defined by the differences between exact and simulated trajectories. Those differences are just an annoying consequence of them. Lorenz discusses chaos as "determinsitic nonperiodic flow", and defines them mathematically, not computationally. He even points out that simulations on a computer are, strictly, not aperiodic. It's amazing what you learn if you actually do the research and read stuff.Bob O'H_{October 11, 2021
October
10
Oct
11
11
2021
12:33 AM
12
12
33
AM
PDT}

Bob O'H,
Err, I am well aware that computers have finite precision, but so what?
So what? So, it’s only the entire basis of Chaos Theory. It’s those tiny differences such as a butterfly makes in Brazil that can be the direct cause of a tornado in Texas! Rounding them off is exactly the wrong thing to do.
I’m sorry, I have no idea what you’re trying to say. This is gibberish.
You either are clueless about Chaos Theory or hiding behind feigned ignorance. Chaos emerges out of the tiniest differences in phenomena that result in profound consequences.
So what? We’re not discussing the difference between an exact calculation and a computer approximation.
Anyone familiar with Chaos Theory knows that those tiny differences are exactly what defines chaos. That’s how Ed Lorenz discovered chaos in his meteorological simulation on a computer!
I’m ignoring your other questions until we get these issues sorted out.
No, you’re ignoring the questions because you either don’t want to answer them or you don’t know the answer to “Assuming you’re a statistician, what is the probability for any measurement to be a number that ends with an infinite number of zeros?” -QQuerius_{October 10, 2021
October
10
Oct
10
10
2021
09:54 PM
9
09
54
PM
PDT}

Oh my. You don’t understand that computers don’t have infinite precision?
Err, I am well aware that computers have finite precision, but so what?
What happens if your initial conditions require only 16 decimal places (i.e. not infinite) to be identical? You’ll get radically different results each time!
I'm sorry, I have no idea what you're trying to say. This is gibberish.
Round PI to 4 decimal places and divide by 2. Is that identical with PI/2? You need an infinite number of decimal places and that’s not possible with computers.
So what? We're not discussing the difference between an exact calculation and a computer approximation. I'm ignoring your other questions until we get these issues sorted out.Bob O'H_{October 10, 2021
October
10
Oct
10
10
2021
01:24 PM
1
01
24
PM
PDT}

Bob O'H, Oh my. You don't understand that computers don't have infinite precision? What happens if your initial conditions require only 16 decimal places (i.e. not infinite) to be identical? You'll get radically different results each time! Round PI to 4 decimal places and divide by 2. Is that identical with PI/2? You need an infinite number of decimal places and that's not possible with computers. But there's a way out. Assuming you're a statistician, what is the probability for any measurement to be a number that ends with an infinite number of zeros? And while you're at it
The Japanese theoretical population geneticist Motoo Kimura emphasized the role of indeterminism in evolution. Do you agree or disagree with his conclusion? Are you familiar with Haldane’s Dilemma?
-QQuerius_{October 10, 2021
October
10
Oct
10
10
2021
12:53 PM
12
12
53
PM
PDT}

And what about this?
and if you’re not infinitely accurate, you’re just going to get different results.
You can never start from the identical starting point with infinite accuracy. The universe doesn’t work that way.
Except it does. At least the bit of the universe that has computers in it. See my comment @ 161 for an example. FWIW, I think you are confusing two things: the process and the initial conditions. If initial conditions are different, then so will be the outcome of the (totally deterministic) chaotic dynamics. But if they are the same, then the outcome will be the same. The same is, of course, true for other deterministic processes, such as halving a number.Bob O'H_{October 10, 2021
October
10
Oct
10
10
2021
01:26 AM
1
01
26
AM
PDT}

Bob O'H @165, What is it about
Chaos is somewhere between random and predictable.
that you don't understand? And what about this?
and if you’re not infinitely accurate, you’re just going to get different results.
You can never start from the identical starting point with infinite accuracy. The universe doesn't work that way. The information I provided you is sufficient.
Simple deterministic laws can generate very complicated and even random motion
Again, MIT Professor Michael Berry is a leader in researching quantum chaos. So starting with "simple deterministic laws," you wind up with . . . only deterministic results? Nope. And your response to ". . . which is why I’m trying to tell you that applying diehard tests over time will have different results that reveal the trend toward randomness."
Yes, for some chaotic systems that will be true
FINALLY! And you once again avoided the questions asked of you:
The Japanese theoretical population geneticist Motoo Kimura emphasized the role of indeterminism in evolution. Do you agree or disagree with his conclusion? Are you familiar with Haldane’s Dilemma?
-QQuerius_{October 9, 2021
October
10
Oct
9
09
2021
12:32 PM
12
12
32
PM
PDT}

Ok, here are some specific quotes on the subject of chaos, quantum chaos, and what’s not determinate from credible sources.
aka one quote that says nothing about quantum chaos, from an article where the word "quantum" does not appear.
Regarding the applicability of using diehard tests over time, I think you’re stumbling over a misconception that the systems producing chaotic results are static. They’re not. The results are dynamic over time and trending toward pseudo-random and random, which is why I’m trying to tell you that applying diehard tests over time will have different results that reveal the trend toward randomness
Yes, for some chaotic systems that will be true, e.g. a chaotic logistic map with a starting value far enough away from attractor. But for other systems, e.g. the Mersenne twister or any other decent random number generator, this is not true. Also - stochastic systems can also show the same behaviour, starting off with relatively determinsitic paths as they approach their equilibrium distribution. So I've still got no idea how this will help. You might as well throw darts at a board. So we still haven't discovered in what way chaotic systems are not deterministic. I think my question at the end of 161 probably gets to the point best: if chaotic systems are not deterministic, how can I run them multiple times from the same starting point, and get exactly the same results?Bob O'H_{October 9, 2021
October
10
Oct
9
09
2021
02:27 AM
2
02
27
AM
PDT}

Thanks, Silver Asiatic. You're right. He wrote in 29
For example Haldane’s dilemma (which reduces down to whether evolution can counter-act the effects of a degrading environment), and (as I had previously mentioned) trade-offs have all been discussed for a long time. The notion that evolution has limits was a long way from being new when Behe published his book.
But his mischaracterizes Haldane's Dilemma--obviously Darwinists will affirm that, yes, evolution is indeed able to more than counteract the effects of a degrading (actually changing) environment, otherwise nothing would have evolved or survived to the present! My next questions will be Why then is/was Haldane's Dilemma considered a dilemma? If Michael Behe's book addresses the thoroughly ho-hum question of whether evolution has limits, why all the fuss then? Of course, he hasn't answered any of the previous questions asked of him, but hope never dies. -QQuerius_{October 8, 2021
October
10
Oct
8
08
2021
05:06 PM
5
05
06
PM
PDT}

Querius - Bob's comment @29 references Haldane's DilemmaSilver Asiatic_{October 8, 2021
October
10
Oct
8
08
2021
02:02 PM
2
02
02
PM
PDT}

Bob O'H, Ok, here are some specific quotes on the subject of chaos, quantum chaos, and what's not determinate from credible sources.
Randomness, like cards or dice, is unpredictable because we just don't have the right information. Chaos is somewhere between random and predictable. A hallmark of chaotic systems is predictability in the short term that breaks down quickly over time, as in river rapids or ecosystems. Scientists define chaos as the amplified effects of tiny changes in the present moment that lead to long-term unpredictability. https://phys.org/news/2021-10-chaos-complex-scientist.html
Emphasis added. Regarding the applicability of using diehard tests over time, I think you're stumbling over a misconception that the systems producing chaotic results are static. They're not. The results are dynamic over time and trending toward pseudo-random and random, which is why I'm trying to tell you that applying diehard tests over time will have different results that reveal the trend toward randomness. But, I have no idea about what shape the curve of diehard test results over time will actually look like. I previously used the word, endemic, because chaotic behavior is observed in weather, orbital mechanics (Pluto will likely be ejected from the solar system in a matter of millions of years), electrical circuits, solving for mathematical roots, population models, and almost everything else in science.
Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. These phenomena are often described by fractal mathematics, which captures the infinite complexity of nature. Many natural objects exhibit fractal properties, including landscapes, clouds, trees, organs, rivers etc., and many of the systems in which we live exhibit complex, chaotic behavior. Recognizing the chaotic, fractal nature of our world can give us new insight, power, and wisdom. - https://fractalfoundation.org/resources/what-is-chaos-theory/
Emphasis added. What do these systems fundamentally have in common and why should the same chaotic behaviors emerge from these disparate sources?
“It was appreciated around 1900 by the great French theorist Henri Poincaré, who discovered that there are some systems, which are unpredictable. You cannot solve them mathematically. If you try to predict the future mathematically, you find that the system behaves wildly. Behaving wildly means that if you change the initial conditions of the system infinitesimally, you get a totally different answer. For well-behaved systems, if you change the initial conditions a little bit, the motion will be a little different.” “. . . until the 1970s when a climatologist-mathematician here at MIT by the name of Ed Lorenz discovered that there are numerical equations which describes the atmosphere for which you cannot make predictions. He discovered this in a most interesting fashion. These were the early days of computers and he was using a rather simple computer to integrate a rather simple equation, and then he tried just doing it again and he found he got a different answer. And the reason was the computer itself had changed the initial conditions infinitesimally—I mean, computers are not infinitely accurate, and if you’re not infinitely accurate, you’re just going to get different results.” MIT Physics Prof. Daniel Kleppner on quantum mechanics and chaos
Emphasis added. Prof. Kleppner is describing the rounding done by older, single-precision computer programs. Let that last phrase sink in. Without infinite precision/accuracy (I prefer using the word precision in this case), determinate results are impossible. That's my point. You cannot perfectly repeat a chaotic process, so the results diverge.
Simple deterministic laws can generate very complicated and even random motion, because some systems are so unstable that the course of their trajectories depends sensitively on how they are started off. Quantum physics has its own randomness, to be sharply distinguished from any irregularity that Newtonian trajectories might possess. We cannot, for example, predict when a radioactive nucleus will decay, or where the next photon in a laser beam will strike a screen. But from the equations of quantum mechanics we can calculate with great accuracy the probabilities of these events from the intensities of the quantum waves. So quantum randomness lies not in the waves but in the processes the waves describe. – Prof. Michael Berry, a mathematical physicist at the University of Bristol, a leader in the research on quantum physics and chaos (aka quantum chaos)
Now perhaps you will answer the questions:
The Japanese theoretical population geneticist Motoo Kimura emphasized the role of indeterminism in evolution. Do you agree or disagree with his conclusion? Are you familiar with Haldane’s Dilemma?
-QQuerius_{October 8, 2021
October
10
Oct
8
08
2021
01:55 PM
1
01
55
PM
PDT}

Querius - I've been trying to get you to explain the evidence for your claim that chaos is intrinsic to quantum indeterminism. I think it is reasonable to expect that you would already have some evidence to hand, and wouldn't have to google it yourself! Anyway, it's great that you've finally presented some evidence:
Now, you switch back to quantum chaos. Ok, here’s a paper called “Quantum Chaos, Classical Randomness, and Bohmian Mechanics” https://www.academia.edu/54098955/Quantum_Chaos_Classical_Randomness_and_Bohmian_Mechanics
But doesn't the first paragraph demolish your claim, that chaos is intrinsic to quantum indeterminism? The nearest the paper gets is to not rule out quantum chaos (bottom of p266). So I'm still waiting to see something that backs up your specific claim that chaos is intrinsic to quantum indeterminism. TBH, I don't think you have anything.
And how would this help distinguish a random number from a pseudo-random number? I can’t see how it would help.
As I said before, we can see how the outcomes of a chaotic system over time changes from nearly deterministic to asymptotically approaching randomness.
Yes, but irrelevant. If we know we have a sequence of numbers that we know were produced by a chaotic process, then we know they are not random, so we know a priori that they were produced by a pseudo-random process.
I tried to explain to you that the diehard tests are statistical tests for measuring the quality of a random number generator.
Right, but as pseudo-random number generators are designed to pass these tests, they're not very good at helping you to distinguish pseudo-random numbers from random numbers. Unless hte PRNG isn't very good, of course.
As I repeatedly said, the rules of any chaotic system are deterministic, but the result and output of the system is indeterminate and likely asymptotic to random over time. You, on the other hand insist that both the rules and outcomes are deterministic.
Well, yes, because if the system starts at the same point each time, then the deterministic rules mean it has to follow exactly the same path. This is true with finite precision, because rounding is also deterministic. A simple example, using the R package. I set the seed (i.e. the starting value) to 1, and generate 10 million ransom numbers (from a standard uniform distribution). Then I set the seed again, and repeat. If, as you say, the process becomes random, I should get different values. But I don't. Both times, the 10 millionth value is exactly the same. > set.seed(1) > runif(1e7)[1e7] [1] 0.6015152 > set.seed(1) > runif(1e7)[1e7] [1] 0.6015152 Now explain how his can be if the process is random.Bob O'H_{October 8, 2021
October
10
Oct
8
08
2021
06:57 AM
6
06
57
AM
PDT}

Bob O'H,
Predictably? When I search for “quantum chaos”, like you said, I get a bunch of links to pages about quantum chaos, but this page isn’t in the first 5 Google pages.
No, you said in 157 that
I did do a google search. I couldn’t find anything on quantum indeterminism.
So, as apparently I’m now your obedient servant, I performed a search for you on “quantum indeterminism,“ and found this link as the first result (your search results may vary): https://en.wikipedia.org/wiki/Quantum_indeterminacy Now, you switch back to quantum chaos. Ok, here’s a paper called “Quantum Chaos, Classical Randomness, and Bohmian Mechanics” https://www.academia.edu/54098955/Quantum_Chaos_Classical_Randomness_and_Bohmian_Mechanics Regarding the discovery of chaos, Poincaré is now given indirect credit and Ed Lorenz is usually given direct credit.
And how would this help distinguish a random number from a pseudo-random number? I can’t see how it would help.
As I said before, we can see how the outcomes of a chaotic system over time changes from nearly deterministic to asymptotically approaching randomness. That was the point of my apparently futile attempt to explain it through throwing darts at a colorized Mandelbrot set as a target at increasing distances. The double-pendulum video I also provided you demonstrates this same process over time as did the video of the three-body problem.
That quantum effects have something to do with waves, and the effects are modelled with probabilities is certainly not in dispute. I’ll let a physicist decide if what you wrote is accurate.
Ok. Physicists Bruce Rosenblum and Fred Kuttner expressed it this way:
The waviness in a region is the probability of finding the object in a particular place. But we must be careful: the waviness is not the probability of the object being in a particular place. There’s a crucial difference here! The object did not exist before you found it there.
Emphasis added. The key insight here is realizing that when we simply observe light, electrons, even small molecules or viruses in the famous double-slit experiment, our conscious choice of what to observe determines whether the probabilities, termed the wavefunction collapse into matter or energy.
Taking the output of parallel chaotic systems such as two double pendulums, one can apply the diehard tests to these numbers at the beginning, middle, and end of a run. The quality of the results as a “random number generator” over several points in time can then be measured and compared.
And how would this help distinguish a random number from a pseudo-random number? I can’t see how it would help.
I tried to explain to you that the diehard tests are statistical tests for measuring the quality of a random number generator. As such, one can use
. . . the diehard tests to track the rate of change in chaotic systems over time toward stochasticity?
The key here is the rate of change over time within any chaotic system toward stochasticity.
Unless you’re going to give up on trying to argue that chaos is not deterministic, I don’t see the point of getting side-tracked onto another topic.
As I repeatedly said, the rules of any chaotic system are deterministic, but the result and output of the system is indeterminate and likely asymptotic to random over time. You, on the other hand insist that both the rules and outcomes are deterministic. I objected to this conclusion on the grounds that infinite precision would be needed to make chaotic behaviors predictable. Neither we nor computers are capable of infinite precision, obviating your conclusion, so I suggested tracking the results or output of a chaotic system over time to show the trend as we do for limits. But you don't get it. Ok. I’m now trying to drag you back to the subject of the OP, which is not a side track. The Japanese theoretical population geneticist Motoo Kimura emphasized the role of indeterminism in evolution. Do you agree or disagree with his conclusion? Are you familiar with Haldane’s Dilemma? -QQuerius_{October 7, 2021
October
10
Oct
7
07
2021
01:01 PM
1
01
01
PM
PDT}

I did do a google search. I couldn’t find anything on quantum indeterminism.
So did I. Here’s (predictably) the first result: https://en.wikipedia.org/wiki/Quantum_indeterminacy
Predictably? When I search for "quantum chaos", like you said, I get a bunch of links to pages about quantum chaos, but this page isn't in the first 5 Google pages. Also - there is no mention of chaos on that page. You're really not doing a good job of showing that chaos is intrinsic to quantum indeterminism. So far you've given us nothing.
You’re grasping at straws. Yes, the polymath, Poincaré, is given indirect credit for finding what’s now known as chaotic behavior in his iterative computations for the three-body problem
Right. So we agree that he is given credit for first discovering it.
Ed Lorenz is usually given direct credit when he found to his astonishment that repeated computer-based meteorological simulations rapidly diverged in deterministic computations due to rounding (which I don’t know why you’ve denied).
I'm not sure what I'm meant to have denied here.
Taking the output of parallel chaotic systems such as two double pendulums, one can apply the diehard tests to these numbers at the beginning, middle, and end of a run. The quality of the results as a “random number generator” over several points in time can then be measured and compared.
And how would this help distinguish a random number from a pseudo-random number? I can't see how it would help.
That quantum effects in reality are the result of the interaction of probability waves should not be in dispute.
That quantum effects have something to do with waves, and the effects are modelled with probabilities is certainly not in dispute. I'll let a physicist decide if what you wrote is accurate.
That chaos is also endemic to reality should also not be in dispute,
I'm not sure I'd say endemic, but I wouldn't dispute that there are systems that have processes that lead to chaotic dynamics.
and neither should be the observed fact that to make two chaotic systems maintain coincident behavior (output) requires infinite precision, without which they increasingly diverge.
I don't disagree with this either.
I don’t understand why you’re arguing against these.
I'm not. I don't know where you get the idea that I am. Unless you're going to give up on trying to argue that chaos is not deterministic, I don't see the point of getting side-tracked onto another topic. Especially one which is going to start off with a discussion of semantics.Bob O'H_{October 7, 2021
October
10
Oct
7
07
2021
03:51 AM
3
03
51
AM
PDT}

Bob O'H,
I did do a google search. I couldn’t find anything on quantum indeterminism.
So did I. Here’s (predictably) the first result: https://en.wikipedia.org/wiki/Quantum_indeterminacy Although, I wouldn’t use Wikipedia (or Quora) as a reliable source. And yes, I read your link.
It has been known since the time of Poincare that simple deterministic systems can give rise to unpredictable behaviour.
You’ve just quoted a book that says that chaos was known since Poincaré. He died in 1912. Lorenz was born in 1917. You’re struggling with linear time now.
You’re grasping at straws. Yes, the polymath, Poincaré, is given indirect credit for finding what’s now known as chaotic behavior in his iterative computations for the three-body problem. Ed Lorenz is usually given direct credit when he found to his astonishment that repeated computer-based meteorological simulations rapidly diverged in deterministic computations due to rounding (which I don't know why you’ve denied). And that was one of my original points about the results of a chaotic system trending toward randomness over time. I then suggested
Have you thought of using the diehard tests to track the rate of change in chaotic systems over time toward stochasticity?
I have not idea what you’re on about. But that seems fair – you have no idea what you are on about either.
Nice. Ok, let me help you understand with the Wikipedia definition:
The diehard tests are a battery (get the joke? -Q) of statistical tests for measuring the quality of a random number generator. They were developed by George Marsaglia over several years and first published in 1995 on a CD-ROM of random numbers.
Taking the output of parallel chaotic systems such as two double pendulums, one can apply the diehard tests to these numbers at the beginning, middle, and end of a run. The quality of the results as a “random number generator” over several points in time can then be measured and compared. That quantum effects in reality are the result of the interaction of probability waves should not be in dispute. That chaos is also endemic to reality should also not be in dispute, and neither should be the observed fact that to make two chaotic systems maintain coincident behavior (output) requires infinite precision, without which they increasingly diverge. I don’t understand why you’re arguing against these. Back to the OP. The Japanese theoretical population geneticist Motoo Kimura emphasized the role of indeterminism in evolution. Do you agree or disagree with his conclusion? Are you familiar with Haldane's Dilemma? -QQuerius_{October 6, 2021
October
10
Oct
6
06
2021
11:58 AM
11
11
58
AM
PDT}

Querius @ 156 -
As I said, to educate yourself on quantum chaos, simply do a Google search on “quantum chaos.”
I did do a google search. I couldn't find anything on quantum indeterminism.
I already gave you a book reference on the subject, and you won’t read or watch any of the previous links I provided.
A book which, as I have already pointed out, does not have quantum indeterminism (or similar) in the index. You don't seem capable of backing up your own claim. Oh, I did find that someone on Quora had asked Is chaos theory related in any way to quantum indeterminacy?. And the answers were (you can see the link for the full answers, with fuller explanations):
No. Not without really stretching. They are different things.
and
That’s actually a great question that made some of the greatest minds of the 20th century busy, but now has been settled and the answer is No.
(emphasis in original) and
It may turn out that in some future universal theory of dynamical systems they turn out to be somehow related but for now they are unrelated in their origins.
and
No, not really.
and
No.
and
I would say - while you can describe how the two relate to each other (should both actually exist) one does not need to exist for the other to also exist,
You did get one "yes", from a Finn who says that quantum chaotic systems amplify quantum fluctuations. Which may well be true, but doesn't show - as you claimed - that chaos is intrinsic to quantum indeterminism.
You’ve claimed that, but you still haven’t shown how a chaotic system is anything but deterministic. In what way is the logistic map (x_{t-1}= r x_t(1-x_t)) not 100% deterministic?
Simply do my dartboard experiment described previously to convince yourself.
Eh? How does the dartboard relate to the logistic map? That's like asking "what does 2 + 2 equal" and being told "go for a swim".
But you won’t do that, so here’s another quote from a book on Chaos Theory:
It has been known since the time of Poincare that simple deterministic systems can give rise to unpredictable behaviour.
How does that help you? It refers to deterministic systems, and you're trying to argue that chaotic systems aren't deterministic.
There are also examples of chaotic behaviors in iterative computational methods in mathematics,
Yes, I know. Like the logistic map - the very thing I was asking you about. I doubt many of them involve darts games.
What has rounding got to do with this?
That’s how Chaos Theory was first identified in a meteorological simulation by Ed Lorenz.
You've just quoted a book that says that chaos was known since Poincaré. He died in 1912. Lorenz was born in 1917. You're struggling with linear time now.
And how would you distinguish a random number from a pseudo-random number?
Have you thought of using the diehard tests to track the rate of change in chaotic systems over time toward stochasticity?
I have not idea what you're on about. But that seems fair - you have no idea what you are on about either.Bob O'H_{October 6, 2021
October
10
Oct
6
06
2021
06:55 AM
6
06
55
AM
PDT}

Bob O’H,
Well, that’s a total non-answer. I’m pretty sure a lot won’t deal with quantum indeterminism, so can you be more specific, and point to a specific paper that explains how chaos is intrinsic to quantum indeterminism?
You haven’t answered any of the questions posed to me, yet you judge my response and a non-answer? As I said, to educate yourself on quantum chaos, simply do a Google search on “quantum chaos.” I already gave you a book reference on the subject, and you won’t read or watch any of the previous links I provided.
You’ve claimed that, but you still haven’t shown how a chaotic system is anything but deterministic. In what way is the logistic map (x_{t-1}= r x_t(1-x_t)) not 100% deterministic?
Simply do my dartboard experiment described previously to convince yourself. But you won’t do that, so here’s another quote from a book on Chaos Theory:
It has been known since the time of Poincare that simple deterministic systems can give rise to unpredictable behaviour.
There are also examples of chaotic behaviors in iterative computational methods in mathematics, which I’ve posed as another question that you also haven’t answered.
No, I’m making the weaker claim that chaotic systems can be used to generate pseudo-random numbers.
Finally, you’re getting closer. Kicking and screaming.
What has rounding got to do with this?
That’s how Chaos Theory was first identified in a meteorological simulation by Ed Lorenz.
Of course the determinism it will decrease and then increase. And then, so what?
Of course? So, how would you define “a decrease in determinism” in context with “how a chaotic system is anything but deterministic” as you claimed? How would determinism “then increase” again?
And how would you distinguish a random number from a pseudo-random number?
Have you thought of using the diehard tests to track the rate of change in chaotic systems over time toward stochasticity? -QQuerius_{October 5, 2021
October
10
Oct
5
05
2021
01:24 PM
1
01
24
PM
PDT}

So I think you’ll have to be more explicit and explain how the two are related: how is chaos intrinsic to quantum indeterminism?
If you do a search on “quantum chaos,” you’ll find numerous papers that will explain the concept to you.
Well, that's a total non-answer. I'm pretty sure a lot won't deal with quantum indeterminism, so can you be more specific, and point to a specific paper that explains how chaos is intrinsic to quantum indeterminism? Because even if is it, a lot of those papers won't explain it, as they will be building on that result. Assuming your claim is based on some actual knowledge, and isn't just BS, you'll have a better grasp of the literature, and should be able to point to something that thinks that quantum indeterminism is more relevant than non-Euclidean billiards. If you can't point to anything specific, will you concede that you might be wrong?
I explained that the results of a chaotic system can range between determinism and randomness (likely asymptotic at both ends) depending on scale and precision. A simple double pendulum can demonstrate this transformation over t.
You've claimed that, but you still haven't shown how a chaotic system is anything but deterministic. In what way is the logistic map (x_{t-1}= r x_t(1-x_t)) not 100% deterministic?
So, you’re asserting that the output data of a chaotic system is, by definition, a pseudo-random number data that only approximates randomness?
No, I'm making the weaker claim that chaotic systems can be used to generate pseudo-random numbers.
I would suggest to you that this is indeed the case when using a computer, because as you should know, computers round off numbers even with DPFP calculations.
What has rounding got to do with this? If anything, it makes the numbers less random, because the period will be less. In practice, this shouldn't be a problem because the period is so long (e.g. the Mersenne twister has a period of 2^19937 ? 1).
So, you might be able to get your physics department to rig up a couple of double pendulums for you with very low friction. Then, take your data periodically from the differences in distances between the ends of the double pendulums using a timed camera, let’s say once per second, and see how determinism decays to randomness over time. You could then use the randomness tests of your choice to record this decay and prove whether such a chaotic system decays to either random numbers or pseudo random numbers.
Of course the determinism it will decrease and then increase. And then, so what? The mathematical model of a double pendulum exhibits chaos, but real one will also have stochasticity (especially when measurement error is added). And how would you distinguish a random number from a pseudo-random number? (well, a good pseuso-random number, not the ones Excel used to produce, for example).Bob O'H_{October 5, 2021
October
10
Oct
5
05
2021
01:43 AM
1
01
43
AM
PDT}

Bob O'H, You're sure stuck on the duality of determinism and randomness. You're reminding me of Goodman's green/blue/grue paradox in logic.
So I think you’ll have to be more explicit and explain how the two are related: how is chaos intrinsic to quantum indeterminism?
If you do a search on "quantum chaos," you'll find numerous papers that will explain the concept to you. I explained that the results of a chaotic system can range between determinism and randomness (likely asymptotic at both ends) depending on scale and precision. A simple double pendulum can demonstrate this transformation over t.
Chaotic dynamics are a good choice here, because they are an obvious place to look for something that looks random, even if it is actually deterministic.
So, you're asserting that the output data of a chaotic system is, by definition, a pseudo-random number data that only approximates randomness? I would suggest to you that this is indeed the case when using a computer, because as you should know, computers round off numbers even with DPFP calculations. So, you might be able to get your physics department to rig up a couple of double pendulums for you with very low friction. Then, take your data periodically from the differences in distances between the ends of the double pendulums using a timed camera, let's say once per second, and see how determinism decays to randomness over time. Normalize the distance data to between 0 and 1. You could then use the randomness tests of your choice to record this decay and prove whether such a chaotic system decays to either random numbers or pseudo random numbers. That would be interesting and perhaps even a fun lab! -QQuerius_{October 4, 2021
October
10
Oct
4
04
2021
05:21 PM
5
05
21
PM
PDT}

Then, please explain how a deterministic rather than a chaotic process can be used to generate random numbers.
As chaotic processes are deterministic, that's obviously a nonsensically phrased question, although the underlying issue is an important one. All random numbers generated by your computer are deterministic: they're actually pseudo-random numbers. There is a battery of tests that can be applied to see if a sequence of numbers looks random: Excel used to fail dismally (and perhaps still does). Amongst other things, the ideal pseudo-random number generator generates numbers that follow a uniform distribution, and look statistically independent. Chaotic dynamics are a good choice here, because they are an obvious place to look for something that looks random, even if it is actually deterministic.
Oh come on, the issue of quantum indeterminism has nothing to do with chaos.
Of course it does. It’s termed quantum chaos.
Hm, the book doesn't have indeterminism (or anything similar) in its index, which suggests that the author thinks it is less important than non-Euclidean billiards. So I think you'll have to be more explicit and explain how the two are related: how is chaos intrinsic to quantum indeterminism?Bob O'H_{October 4, 2021
October
10
Oct
4
04
2021
01:34 PM
1
01
34
PM
PDT}

Bob O'H, Reading the link you referenced, you'll notice the following:
It is relatively easy to show that the logistic map is chaotic on an invariant Cantor set for r>2+sqrt(5) approx 4.236 (Devaney 1989, pp. 31-50; Gulik 1992, pp. 112-126; Holmgren 1996, pp. 69-85), but in fact, it is also chaotic for all r>4 (Robinson 1995, pp. 33-37; Kraft 1999).The logistic map has correlation exponent 0.500+/-0.005 (Grassberger and Procaccia 1983), capacity dimension 0.538 (Grassberger 1981), and information dimension 0.5170976 (Grassberger and Procaccia 1983). The logistic map can be used to generate random numbers (Umeno 1998; Andrecut 1998; Gonzáles and Pino 1999, 2000; Gonzáles et al. 2001ab; Wong et al. 2001, Trott 2004, p. 105).
Then, please explain how a deterministic rather than a chaotic process can be used to generate random numbers.
Oh come on, the issue of quantum indeterminism has nothing to do with chaos.
Of course it does. It's termed quantum chaos. Quantum Chaos An Introduction. Hans-Juergen Stoeckmann https://www.amazon.com/Quantum-Chaos-Introduction-Hans-J%C2%BFrgen-St%C2%BFckmann/dp/0521027152
This volume provides a comprehensive and highly accessible introduction to quantum chaos. It emphasizes both the experimental and theoretical aspects of quantum chaos, and includes a discussion of supersymmetry techniques. Theoretical concepts are developed clearly and illustrated by numerous experimental or numerical examples. The author also shares the first-hand insights that he gleaned from his initiation of the microwave billiard experiments. Additional topics covered include the random matrix theory, systems with periodic time dependencies, the analogy between the dynamics of a one-dimensional gas with a repulsive interaction and spectral level dynamics where an external parameter takes the role of time, scattering theory distributions and fluctuation, properties of scattering matrix elements, semiclassical quantum mechanics, periodic orbit theory, and the Gutzwiller trace formula. This book is an invaluable resource for graduate students and researchers working in quantum chaos.
-QQuerius_{October 4, 2021
October
10
Oct
4
04
2021
10:57 AM
10
10
57
AM
PDT}

Querius @ 150 -
And as I mentioned in one of the questions you haven’t answered, chaotic systems emerge even in purely mathematical systems.
Errm I guess you haven't noticed that I've been discussing chaos as a mathematical phenomenon all this time.
As I said before, the rules or computations of chaotic systems are deterministic, but the outcomes are not, precisely due to the requirement for infinite precision, without which those systems rapidly approach statistical randomness.
This sort of comment is why it's not worth going further. Yes, the outcomes of chaos are deterministic. What you're discussing here (I think. I hope) are iterative calculations, where errors will propagate. But as I pointed out @138, there are mathematical solutions to the (chaotic) logistic map, so for any i we can calculate it without needing i-1, i-2 etc. And, as I pointed out earlier, iterative calculation is also deterministic: rounding is a deterministic operation.
Furthermore, this indeterminism is intrinsic to quantum mechanics where locations of subatomic particles exist as only probability waves until they are observed or measured, collapsing the wavefunction and they do not have deterministic locations.
Oh come on, the issue of quantum indeterminism has nothing to do with chaos.Bob O'H_{October 3, 2021
October
10
Oct
3
03
2021
11:54 PM
11
11
54
PM
PDT}

Bob O'H,
Do you mean that we don’t get perfect predictions? Because if so, the primary reason is that we don’t have all of the initial conditions, and also the models we use are approximations. Climate may or may not be chaotic, but there are plenty of other reasons for the lack of perfect predictability.
Yes, weather prediction would indeed have “perfect predictability” . . . except for that pesky little detail of never having infinite precision and finite computing power. Haha. As I explained to Silver Asiatic, filling the earth and its atmosphere with a concentric matrix of weather stations at about one-meter intervals has been calculated to improve weather prediction only to maybe two weeks--kinda far from "perfect." Climate is not the same thing as weather, but weather, along with many other systems have indeed been shown to be chaotic, as you would know if you bothered watching any of the video links I provided. And as I mentioned in one of the questions you haven’t answered, chaotic systems emerge even in purely mathematical systems.
. . . the questions are probably feeling relieved that they aren’t being dragged into this mess.
Not to mention your repeated inability or unwillingness to answer any of them.
As I’ve already stated, I don’t see the point in dealing with other questions until we’ve established that you understand that chaos is a deterministic phenomenon.
Oh, but you now have the *Golden Opportunity* to Impress and Enlighten the others here with your grasp of Chaos Theory. As I said before, the rules or computations of chaotic systems are deterministic, but the outcomes are not, precisely due to the requirement for infinite precision, without which those systems rapidly approach statistical randomness. Thus, chaotic systems exhibit both determinism and randomness at the extremes. Furthermore, this indeterminism is intrinsic to quantum mechanics where locations of subatomic particles exist as only probability waves until they are observed or measured, collapsing the wavefunction and they do not have deterministic locations. The “noise” (as Kairosfocus terms it) or fuzziness is intrinsic to and permeates our existence, enabling the fusion that powers or sun, the photosynthesis that powers plant life, effects that limit the miniaturization of microprocessors and result in errors in memory, and might even explain consciousness. -QQuerius_{October 3, 2021
October
10
Oct
3
03
2021
02:57 PM
2
02
57
PM
PDT}

BO'H, chaos, nonlinear dynamics sense is deterministic. However real systems all exhibit noise, which feeds into the chaos via butterfly effects. Further, there is a non technical sense of chaos, disorder opposite to cosmos. KFkairosfocus_{October 3, 2021
October
10
Oct
3
03
2021
02:27 AM
2
02
27
AM
PDT}

Querius - the questions are probably feeling relieved that they aren't being dragged into this mess. As I've already stated, I don't see the point in dealing with other questions until we've established that you understand that chaos is a deterministic phenomenon. Because any further questions along those lines are going to be hampered by your not understanding the absolute basics.Bob O'H_{October 3, 2021
October
10
Oct
3
03
2021
02:23 AM
2
02
23
AM
PDT}

If the system possesses non-linear dynamics and is extremely sensitive to initial conditions, then we call it chaotic since it fits our model.
The definition is actually more complex that that, otherwise there would be linear stochastic models that would fit this definition.
If it fits the model, then we conclude that it fits the model.
I don't know what you mean here: the chaotic system is a model (well, it is if it is being used to model the real world), so either "it"
Climate is, in this sense, not chaotic because we can’t model it from initial conditions.
Err, we do model it from initial conditions: that's what weather forecasts are. Do you mean that we don't get perfect predictions? Because if so, the primary reason is that we don't have all of the initial conditions, and also the models we use are approximations. Climate may or may not be chaotic, but there are plenty of other reasons for the lack of perfect predictability.Bob O'H_{October 3, 2021
October
10
Oct
3
03
2021
02:07 AM
2
02
07
AM
PDT}

Bob O'H @144, The poor, forlorn questions are sitting there earlier in the comments still waiting for you. Go ahead. Impress everyone here with your knowledge. -QQuerius_{October 2, 2021
October
10
Oct
2
02
2021
10:48 AM
10
10
48
AM
PDT}

Bob O'H
No it isn’t, because not all deterministic systems are chaotic. The logistic map, for example, is only chaotic for some values of its parameter.
As you said previously, deterministic systems are deterministic. This is a proof by definition. If the system possesses non-linear dynamics and is extremely sensitive to initial conditions, then we call it chaotic since it fits our model. If it fits the model, then we conclude that it fits the model. If it doesn't fit, then we exclude it. Climate is, in this sense, not chaotic because we can't model it from initial conditions. So, there's no expectation of predictions for climate change. If the system is predictable, then it's deterministic. This is just a matter of definitions and what gets included within the scope and what excluded.Silver Asiatic_{October 2, 2021
October
10
Oct
2
02
2021
09:16 AM
9
09
16
AM
PDT}

1 2 3 … 6 Next

You must be logged in to post a comment.

Leave a Reply