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

_{Denyse O'Leary

September 21, 2021

Evolution, Intelligent Design}

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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

Querius -
Bob O’H, Did you forget to answer the questions addressed to you?
No, but it's not worth answering those questions until you've understood the very basics (like how chaotic systems are deterministic).Bob O'H_{October 2, 2021
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SA @ 139 -
If you cannot predict the outcomes, then the system is random according to your perspective and knowledge
But for chaotic systems you can predict the outcomes.
It’s also definitional – if you know the initial state with 100% perfect accuracy, then and only then do you consider it a chaotic system. That’s a tautology.
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.Bob O'H_{October 2, 2021
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Thank you, Silver Asiatic. What's exciting it that a lot of these factors appear in odd corners of the sciences, computer science, and cryptography resulting in rich areas of further research and amazing discoveries! Not to mention that God may be completely comfortable with probabilities, which he created in the first place, Einstein's understanding of God notwithstanding. -QQuerius_{October 1, 2021
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Querius - thanks. You've done a nice job in laying-out the issues clearly and adding details. I think the terms random, predictable, deterministic, chaos, non-random -- all are used differently in different contexts. The fact that we can use mathematics to describe complex aspects of the universe is a point that supports ID. It's something mysterious that did not have to occur. In fact, in a blind, mindless, unintelligent universe, precise mathematical models of nature should not occur at all.Silver Asiatic_{October 1, 2021
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Silver Asiatic, Looks like you've shredded Bob O'H's assertions better than I could. But the subject is fascinating! Mathematicians sometimes claim that they can tell "random number" sequences generated by humans from real ones simply by inspection. True random numbers will have some improbable sequences in them while human-generated ones often do not. But . . . if a sequence of numbers contains a longer string of such numbers, then it becomes more and more likely that it's not. For example, examine PI to find improbable sequences such as double 3's and double 8's. presumably your telephone number is buried somewhere in PI as well. But a string such as 999999 only appears once in the first million digits of PI. Consider how long the string of zeros follows the exponent in the inverse square law? Hanks @128,
@Querius , Bob is just trolling you. The points of view should be reversed to correspond to your own worldviews.
Yeah, no doubt. But I suspect that God, in order to give us True Freewill, limits his absolute power. According to the scriptures, our God who exists simultaneously in the past, present, and future and who describes himself as I AM, provided prophecies that were and will be fulfilled, but might choose not to observe many other things. Pure speculation, but you know how tricky mathematicians can be! (wink) Bornagain77 @130, Yes, it really does seem that God is a mathematician! We seem to be existing in a probability field of some kind with the power to collapse wavefunctions at a tiny scale. Perhaps, God can do this at any scale . . . o.o Bob O'H, Did you forget to answer the questions addressed to you? If so, I can sympathize. They say that one's memory is the second thing that goes with age. I can't remember what the first thing was . . . -QQuerius_{October 1, 2021
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Bob O'H
Oh no, I’m just exempting anyone who is not ignorant of the simple mathematical truism that deterministic systems are deterministic, and the mathematical fact that chaotic systems are by definition deterministic.
If you cannot predict the outcomes, then the system is random according to your perspective and knowledge. "I can perfectly predict the outcome, I just won't demonstrate that for you". It's also definitional - if you know the initial state with 100% perfect accuracy, then and only then do you consider it a chaotic system. That's a tautology. "Any result that I predict with 100% accuracy is non-random". That's begging the question -- but I accept that's part of the game. All of this aligns with the claim "natural selection is non-random" but clearly, that claim needs to be peeled apart and not taken at face value.Silver Asiatic_{October 1, 2021
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SA @ 136 -
You said this: “chaos is perfectly predictable”. Following up, I see you have two choices: 1. I can offer perfect predictions of outputs from chaotic systems. (No explanation necessary – just show us those predictions).
Of course that can be done. e.g. the logistic map is defined as x_t+1 = m x_t(1-x_t) and is chaotic when m=4 (for example). I hope it is not difficult to see that this can be calculated without any randomness, but you don't need to calculate each iteration: there is a solution for any t. So yes, it can be predicted. There is a lot of maths around this, e.g. a proof that if a system oscillates with a period of 3, then for other parameter values it will be chaotic.
With respect to chaotic systems, we know (by definition) they are deterministic, and thus 100% predictable, so what you describe as randomness is in fact wholly due to your own ignorance.
That kind of ignorance is a chronic condition of the human race – unless you’re going to exempt yourself from it.
Oh no, I'm just exempting anyone who is not ignorant of the simple mathematical truism that deterministic systems are deterministic, and the mathematical fact that chaotic systems are by definition deterministic. Of course, whether a system is chaotic is a more difficult question, but one mathematicians have worked on. the nice thing is that if they prove a system is chaotic, then we can be certain about that.Bob O'H_{October 1, 2021
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Bob O'H
The problem is that even if you can’t predict it, that doesn’t mean that nobody else can.
Again, you just have to show someone who can do it. Failing that, it's not predictable. Just claiming, "someone might be able to predict it" really doesn't work.
With respect to chaotic systems, we know (by definition) they are deterministic, and thus 100% predictable, so what you describe as randomness is in fact wholly due to your own ignorance.
That kind of ignorance is a chronic condition of the human race - unless you're going to exempt yourself from it. We don't know what conditions God placed into the physical laws of the universe when He created it. Perhaps you know them, but if not - then this is the ignorance that you suffer with. But again, you're not alone. We have ignorance of how the laws of the universe were created and how consistent they are now, or will be in the future. Thus, claiming "I could predict everything if only I wasn't so ignorant" is not saying much. If you can't predict it, within a high degree of accuracy - then it's not "perfectly predictable". "You" here - is "anybody on earth ever".Silver Asiatic_{October 1, 2021
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Bob O'H
I don’t see anyone saying that, at least with respect to chaos.
You said this: “chaos is perfectly predictable”. Following up, I see you have two choices: 1. I can offer perfect predictions of outputs from chaotic systems. (No explanation necessary - just show us those predictions). Or 2. Chaos is perfectly predictable, but I cannot predict the outputs because ... [fill in the blank] I filled in the blank with , "because I don’t have enough information". But you can choose your own reason why you can't predict a perfectly predictable output.Silver Asiatic_{October 1, 2021
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If I cannot predict where the darts will fall with a certain (there’s a fuzzy boundary) degree of accuracy – then it not only “seems random” but it is a random output.
That's a very Bayesian approach. The problem is that even if you can't predict it, that doesn't mean that nobody else can. With respect to chaotic systems, we know (by definition) they are deterministic, and thus 100% predictable, so what you describe as randomness is in fact wholly due to your own ignorance.Bob O'H_{October 1, 2021
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Hanks
The points of view should be reversed to correspond to your own worldviews.
It's a good point. This is weird because I'm arguing for the materialist world-view trying to indicate that there's no basis to claim that "it's all deterministic" -- so I argue in favor of the existence of randomness. But in a theistic worldview, we would accept God's order in the universe - in fact, that's the basis of science - and therefore the idea that "all is determined (planned, designed, directed) by God makes sense. We can say "nothing is random" because God has the knowledge. Materialism would have to object to this and claim randomness as the source of everything. So, to hear a materialist proclaim determinism as the source of all thingss is a contradiction, ultimately. That worldview cannot sustain that assumption. But it's one way for materialism to escape the problems of a supposed blind, unintelligent, random universe.Silver Asiatic_{October 1, 2021
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Saying, “it’s perfectly predictable, but I just can’t predict it because I don’t have enough information” is the cleverness of it.
I don't see anyone saying that, at least with respect to chaos.Bob O'H_{October 1, 2021
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Querius
I think you’re on the right track. From 50 feet the darts seem to land randomly, from 7 feet, the results seem deterministic. And there’s a gradient between the extremes.
Thanks. Yes, I'd only object to the term "seems random". If I cannot predict where the darts will fall with a certain (there's a fuzzy boundary) degree of accuracy - then it not only "seems random" but it is a random output. If I can predict, perhaps 1 in 100 - that's random. If I predict 99 of 100 - that's deterministic. As stated - every deterministic process has some randomness at a certain scale. We can say "life is deterministic because all living beings come into existence and all die". But there's quite a lot of randomness (from our perspective) within that time-frame between birth and death. Also - there is no purely random occurence. Everything has some determination built in. I cannot accept Dr. O'Hara's statement "Chaos is perfectly predictable" until he can demonstrate that level of "perfect prediction". Saying "well, if we had all possible information, then it would be predictable" is an assumption and in the end, it ignores what we mean by the term random. If you can't predict it, it's random. "The lottery is perfectly predictable. If we knew exactly which numbers would be picked - then I could tell you every time what the winners are. It's perfectly deterministic." That doesn't work for me. You can't predict the lottery because it's a random sort. Yes, there is some determination - the lottery will only pick numbers between a defined range. A probability can be assigned to the selection. But that's not enough to say "the lottery is non-random". In the same way, the phrase "natural selection is non-random" has the same problems.Silver Asiatic_{October 1, 2021
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Well, it's a clever game - even more clever than darts. Saying, "it's perfectly predictable, but I just can't predict it because I don't have enough information" is the cleverness of it. If you can't predict it - then it not only "seems random" but it is random. As Hanks points out above - it's predictable from God's point of view. But from your point of view, it's random until you can predict it. Again, claiming a perspective from God's point of view is taking on a very big assumption - starting from the creation of the universe, claiming to know with certainty that all effects we observe now are perfectly determined by physical causes (and will remain as such forever). We don't know that. We can believe it by faith - and accept that God has created a natural order that is constant and predictable. But materialism gives us no such basis for faith. But certainly, if a materialist wants to claim that all evolutionary effects are deterministic that just raises not only the question "how do you know that?" but "what caused initial conditions in the big bang to be fine-tuned and amazingly determined to produce all of life on earth?" The universe itself cannot create its own deterministic powers. Knowing that, most atheists prefer to say that there is randomness in the universe - thus they don't have to explain where determinism came from. Randomness reflects blind, mindless, unintelligent effects - of the sorts that Richard Dawkins was famous for claiming as the essence of the universe. Saying "there's no randomness, it's all deterministic" -- is pointing directly to God as the cause. Nothingness and blind, lawless, unguided unintelligence cannot be deterministic sources.Silver Asiatic_{October 1, 2021
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Bob: "mathematicians are not God" Yet God is. apparently, a mathematician
As the British physicist James Jeans (1877-1946) once put it: "The universe appears to have been designed by a pure mathematician." https://www.washingtonpost.com/wp-srv/style/longterm/books/chap1/godmath.htm “Mind-boggling, isn't it? Centuries before the question of why mathematics was so effective in explaining nature was even asked, Galileo thought he already knew the answer! To him, mathematics was simply the language of the universe. To understand the universe, he argued, one must speak this language. God is indeed a mathematician.” - Mario Livio, Is God a Mathematician? - 2009 - page 77 https://books.google.com/books?id=gwr4-n2ZnB0C&pg=PA77 Why God Appears To Be A Mathematician (Freeman Dyson) - 2020 https://uncommondescent.com/philosophy/why-god-appears-to-be-a-mathematician/
bornagain77_{October 1, 2021
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Hanks - despite what you may think, mathematicians are not God. Except possibly the head of my department.Bob O'H_{October 1, 2021
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“Chaos is perfectly predictable” from the point of view of God not from the point of view of a troll. @Querius , Bob is just trolling you. The points of view should be reversed to correspond to your own worldviews.Hanks_{October 1, 2021
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Querius @ 125 -
From 50 feet the darts seem to land randomly, from 7 feet, the results seem deterministic.
You've obviously never seen me play darts.Bob O'H_{October 1, 2021
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So then, do you disagree with Vertiasium when he states the following in the video you haven’t watched:
It seems like a paradox, but this system is both deterministic and unpredictable.
I do. Because these systems are determinstic, they are predictable. Of course, you need to know what the system is, and also the initial conditions, but once you have those, their dynamics can be predicted.Bob O'H_{October 1, 2021
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Silver Asiatic, I think you're on the right track. From 50 feet the darts seem to land randomly, from 7 feet, the results seem deterministic. And there's a gradient between the extremes. Or let's say you pick a random point in 3D space using an arbitrary coordinate system. What do you know about the coordinates? They're likely to be irrational numbers, right? That means even a double-precision floating point operation in a computer, for example, will round off the value at (arguably) 15 decimal digits (12-14 is more practical). The point of chaos theory is that any tiny round-off accumulates far more rapidly than we intuitively expect. And that's why covering the earth with weather stations at the corners of every square meter and then successively larger spheres of weather stations at one-meter increments out to the extremes of the atmosphere only would increase our weather forecasting ability to maybe two weeks. At what point does a chaotic system produce random results? I don't know. It's likely asymptotic and subject to running statistical tests on the data for at least pseudo-randomness. -QQuerius_{September 30, 2021
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Querius Maybe I'm missing it but I wouldn't call the process a deterministic one. First of all, I'm firing a dart - and the reason why a game of darts is fun and the reason why people put little bets on the game is that it is not deterministic. Even some with a lot of skill cannot perfectly hit every target where they want to. So, depending on the skill of the player, or the composition of the dart - there's a random aspect. Taking the dart and sticking it directly into the board wherever you want - that would be deterministic. Or, making the bullseye 10 feet in circumference and standing 5 feet away, that's deterministic. But making the bullseye 1/100th of an inch and standing 50 feet away - that's going to be a random distance from the target - and the number of direct hits will be unpredictable. That's a random output - not deterministic. We can model all of that with mathematics and physics - so we would say it's determined, and non-random. But in fact, it's unpredictable - and thus the definition of random in that sense. I think that's the same with chaos - we can't predict it. Bob O'H is saying “Chaos is perfectly predictable”. I didn't question him on that - but we could think about your fractal experiment or even something like predicting the weather. I wouldn't call that perfectly predictable - and therefore I wouldn't call the outputs non-random. It's like saying the pattern of raindrops on the ground is "non-random" because they all come from deterministic physical sources. That's confusing what is meant by random - we can't predict where or when the raindrops will fall just by standing in the rain. That's why we call it a random pattern. (Please append "I think" or "Is it true that" - to my assertions. I'm not saying I know - I'm just offering what I think and I'm open to correction on this).Silver Asiatic_{September 30, 2021
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Silver Asiatic, In the Veritasium video (and you can confirm this in Gleich's book, Chaos if you have the time), you can see that chaotic systems do not repeat themselves. The rules or equations of any chaotic system are deterministic, but the outcomes become less and less predictable over time. That makes chaotic systems unique. This is true even in examples of chaotic systems in mathematics. Try this thought experiment: 1. Print out a large colorized copy of a portion of the Mandelbrot set such as this one: http://www.joachim-reichel.de/software/fraktal/mandelbrot_large.png 2. Pin it to your dart board so that the large area in the center covers most of the board. At 7 feet, 9.25 inches, your throws will likely all land in the center dark area and you can claim the operation is deterministic. 3. Now try it at 14, 21, 28 feet or more and your dart will start landing on different colors that you won't be able to predict. The colors in the image are not random but your results will appear more and more random as your distance from the dart board increases. The problem with the experiment is that you'd need a dart with an infinitely thin point and a target with infinite detail to be absolutely certain of the color. -QQuerius_{September 30, 2021
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Querius You quoted:
It seems like a paradox, but this system is both deterministic and unpredictable.
My concern is the phrasing. "It seems like a paradox". That's like what I was concerned with before "it seems unpredictable but it's deterministic". In that case, it should be "chaos seems unpredictable but it is perfectly predictable". That's easy to prove - just show the chaotic system and give your predictions. It either works or it doesn't. In the above "it seems like a paradox" - should then follow "but it's not a paradox because it's deterministic or its random - one or the other". But to say something is both random and deterministic - is simply a paradox, not that it seems like a paradox. It is one.
What this means is that this system is not exclusively random AND it’s not exclusively deterministic, but it’s BOTH, which is something different: a chaotic system.
We can add the terms that Bob added "predictable or unpredictable". Those are some measures that can be used. If the system is not-predictable, then it's random. If the system is predictable, then it is deterministic. If I can predict with great precision, the exact output of the system - then call it random is a paradox. If I fail to predict the outputs of the system but then call it deterministic is also a paradox. If I say that I cannot predict the outcomes of a chaotic system, but that it's deterministic anyway - that's not different than just calling the outcomes random, because I can't predict them.Silver Asiatic_{September 30, 2021
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Bob O'H, Statistics is such a fascinating subject! So then, do you disagree with Vertiasium when he states the following in the video you haven't watched:
It seems like a paradox, but this system is both deterministic and unpredictable.
Notice the critical word, "and." Question: In statistics, do you have any examples of non-chaotic systems that are both deterministic and unpredictable (even from a probabilistic solution)? Question: What aspects of chaos theory do you teach or use in statistics? What about the previous questions you haven't answered yet? -QQuerius_{September 30, 2021
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Querius @ 118 -
Don’t let Bob O’H confuse you. There are many people who are ideologically committed to determinism and try to jam chaos into a deterministic mold, but this doesn’t work.
I'm quite literally a professor of statistics. That means I am quite literally considered an expert in analysing non-deterministic systems. The reason I am trying to "jam chaos into a deterministic mold" is because, quite literally, it is deterministic. There is no random component in the way the values change from one iteration to the next.Bob O'H_{September 30, 2021
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Querius - I don't see the point in discussing further questions about chaos until we've established that you understand that chaos is deterministic. Because if you don't understand that, we're not going to make any headway with anything else.Bob O'H_{September 30, 2021
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Silver Asiatic @117, Don't let Bob O'H confuse you. There are many people who are ideologically committed to determinism and try to jam chaos into a deterministic mold, but this doesn't work. You can see what I mean from reviewing this video starting here: https://youtu.be/fDek6cYijxI?t=422 You'll get to the place where Veritasium states the following at 7:31:
It seems like a paradox, but this system is both deterministic and unpredictable.
What this means is that this system is not exclusively random AND it's not exclusively deterministic, but it's BOTH, which is something different: a chaotic system. -QQuerius_{September 29, 2021
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Bob O'H
What should follow from that is something like “but, it’s not random because it is predictable”. But that’s what I did do, when I quote “Chaos is seemingly random because the patterns look like they are not predictable, but if you look under the hood they are perfectly deterministic.”
Ok, I didn't see that as saying "Chaos is perfectly predictable", but apparently that's what you were trying to say there.Silver Asiatic_{September 29, 2021
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Bob O'H, You still have refused or been unable to answer any of the questions posed to you in 109 and before, and you haven't bothered to look at the explanatory videos that might give you a clue to what you're arguing. Next you'll be telling us that rounding random numbers makes them deterministic. You assert that the double pendulum system behaves in such a bizarre way without repeating itself because (drumroll) . . .
Because it’s chaotic. But the finite representation will repeat, thanks to discretisation (and thus a finite state space), and hence be in a limit cycle.
"Finite representation" of the infinite number of points in the set of its positions? But we just have to wait an infinite amount of time? Random numbers then are also deterministic if you wait an infinite amount of time. So is evolution. But the determinism ascribed to chaos depends entirely on infinite precision in matching the initial conditions. As I said, this is not possible in our universe. Now, about the questions you're still refusing to answer . . . Chaotic systems have been discovered even in mathematics. Question: Can you give us an example? -QQuerius_{September 29, 2021
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SA @ 113 -
What should follow from that is something like “but, it’s not random because it is predictable”.
But that's what I did do, when I quote "Chaos is seemingly random because the patterns look like they are not predictable, but if you look under the hood they are perfectly deterministic." *sigh*Bob O'H_{September 29, 2021
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