Evolutionists are fond of citing Orgel’s Second Rule: “Evolution is smarter than you are.” I have previously expressed skepticism about this rule (see here and here), but I’ve had no success in persuading people with a naturalistic metaphysical outlook. Yesterday, however, I came across a LiveScience article by Tia Glose titled, The Spooky Secret Behind Artificial Intelligence’s Incredible Power (October 9, 2016), which might prove to be a game-changer. We’ll see.
The article discussed a research team’s startling new findings regarding deep-learning algorithms, a class of algorithms which somehow manage to outperform other AI algorithms – and human beings – at playing games such as chess or go, despite the fact that they start out absolutely “clueless,” while the other algorithms are given the rules of the game in advance. Deep learning algorithms also have a hierarchy, which makes them far superior to shallow networks that may contain as little as one layer:
…[D]eep learning or deep neural network programs, as they’re called, are algorithms that have many layers in which lower-level calculations feed into higher ones. Deep neural networks often perform astonishingly well at solving problems as complex as beating the world’s best player of the strategy board game Go or classifying cat photos, yet no-one fully understood why.
It turns out, one reason may be that they are tapping into the very special properties of the physical world, said Max Tegmark, a physicist at the Massachusetts Institute of Technology (MIT) and a co-author of the new research.
The laws of physics only present this “very special class of problems” — the problems that AI shines at solving, Tegmark told Live Science. “This tiny fraction of the problems that physics makes us care about and the tiny fraction of problems that neural networks can solve are more or less the same,” he said…
It turns out that the math employed by neural networks is simplified thanks to a few special properties of the universe. The first is that the equations that govern many laws of physics, from quantum mechanics to gravity to special relativity, are essentially simple math problems, Tegmark said. The equations involve variables raised to a low power (for instance, 4 or less). [The 11 Most Beautiful Equations]
What’s more, objects in the universe are governed by locality, meaning they are limited by the speed of light. Practically speaking, that means neighboring objects in the universe are more likely to influence each other than things that are far from each other, Tegmark said.
Many things in the universe also obey what’s called a normal or Gaussian distribution. This is the classic “bell curve” that governs everything from traits such as human height to the speed of gas molecules zooming around in the atmosphere.
Finally, symmetry is woven into the fabric of physics. Think of the veiny pattern on a leaf, or the two arms, eyes and ears of the average human. At the galactic scale, if one travels a light-year to the left or right, or waits a year, the laws of physics are the same, Tegmark said…
All of these special traits of the universe mean that the problems facing neural networks are actually special math problems that can be radically simplified.
“If you look at the class of data sets that we actually come across in nature, they’re way simpler than the sort of worst-case scenario you might imagine,” Tegmark said. [Bolding mine – VJT.]
I’d like to summarize my argument:
[UPDATE, in response to comments below: I define an algorithm as smart if it can solve problems that even the most talented humans, working separately or together in a team, are incapable of solving – even when given ample time – VJT.]
1. The deep-learning algorithms, which are so much smarter than we are, excel human beings (and other algorithms) only for a special class of mathematical problems that are capable of being radically simplified, thanks to certain properties they possess.
1a. Deep-learning algorithms are the only ones that could be said to be “smarter” than we are, at solving certain problems. [UPDATE, in response to criticisms below – VJT.]
2. Only if evolution’s “search” (or sampling) problem belongs to this special class of mathematical problems is there good reason to believe that evolution is smarter than we are, and that it is capable of producing “designoid” structures which far exceed in sophistication anything that our best scientists could come up with.
3. The evolutionary “search” (or sampling procedure) doesn’t appear to belong to this special class of mathematical problems, as it fails the first condition: it cannot be exhaustively described by a set of simple equations involving variables raised to a low power (four or less), as the laws of physics can.
4. Hence there is no reason to believe that “evolution is smarter than you are,” when searching for proteins that fold up and are capable of performing a useful biological task – or more generally, creating a biological system which is functionally coherent, such as photosystem I, or the visual system (described in Douglas Axe’s book, Undeniable).
5. If there is no reason to believe that even the best unguided natural processes (deep-learning algorithms) are capable of producing complex biological structures which are more advanced than anything humans could come up with, then the only remaining alternative is to suppose that these structures are the result of an intelligently guided process.
Discuss.
But what if premise 3 of my argument turns out to be wrong? Would that undercut the case for design? No: what it would do is kick it up one level. One could still ask why we happen to live in a universe where not only physics, but also evolution, can be described by a special class of mathematical problems that are capable of being radically simplified. Why, in other words, is the universe – and evolution – governed by processes which are so “mind-friendly”? However, this would be a fine-tuning (or cosmological) design argument, rather than a biological argument for intelligent design.
A final thought: the article also seems to suggest a way of saving the world from being overrun by AI, as many scientists fear it will be. People of my age will remember this humorous cartoon, which appeared in Punch, on August 25, 1981. Robots on wheels proved to be utterly unable to navigate stairs. The cartoon’s caption read: “Well, this certainly buggers our plan to conquer the Universe.” Today’s robots are far more mobile, of course. However, let us suppose that in order to enter a certain neighborhood, they had to pass through a certain gate, where they were required to solve a problem which humans can solve, but which doesn’t fall into the narrow set of problems at which deep-learning algorithms excel. The robots would be stymied at the outset. Communities may have to be redesigned with these kinds of gates guarding vital links in our infrastructure, in order to prevent society from being overrun by rogue AI systems. Thoughts?
I responded at one point:
I don’t think you’ve explained such things using “design.”
Some of the quoted examples were from biology. Biology is physics, and a lot of issues, like arranging neurons in the brain, or the branching of vascular systems, are quite susceptible to rather simple physics. What is more, development often involves sorts of “selection processes” as well. I’m not saying that everything in biology involves simple equations, but some do.
How does this follow? What undergirds the premises, more importantly? GAs are alternatives to deep-learning processes, and they seem to work quite well for many problems. The discussion was of why the deep-learning algorithms work, not why GAs or evolution do not–especially since they do.
Glen Davidson
If I were to claim “Hillary Clinton is smarter than Donald Trump”, then about half of the electorate in the US would agree. And the other half would strongly disagree.
As far as I can tell, “X is smarter than Y” has no actual meaning. We don’t have a way of assessing degrees of smartness.
There is a theoretical advantage to evolution. Suppose we ask the question “Is it smarter to do A or is it smarter to do B”. The advantage for evolution, is that it can do both and see which survives.
Nevertheless, I think it is all an empty argument. Arguing whether evolution is smarter than us is about as important as arguing over how many angels can dance on the head of a pin.
Congratulations. You have just proven that evolution is not a deep-learning algorithm, I think to nobody’s surprise. As an argument against evolution, it would seem convincing only to those who desperately want to accept its conclusion, as you do.
Various other problems and questions: Are we to suppose that humans can solve problems a machine can’t, because we are aided by our possession of souls? Not clear. Is this also not a repetition of “humans can’t do this, which shows that intelligence can do it”? Can the problem of “Who designed the designer” be solved simply by assuming the designer to be undesigned? Why is the mathematical describability of certain aspects of the universe an argument for fine-tuning?
Vincent’s OP point #2: “Only if evolution’s “search” (or sampling) problem belongs to this special class of mathematical problems……”
Nice strawman, Vincent.
Don’t really get it I am afraid. Apart from being a bit of a throwaway joke on Orgel’s part, evolution is only ‘smarter’ in the sense that it actually does what we might sit there cogitating about. It conducts the experiment, which involves actual integration of a whole bunch of variables. So, it’s an empirical thang. If I think about chucking a bunch of organisms onto an island, am I smart enough to know which ones will stick? Probably not. Actually chuck them, and lo and behold, practical demonstration beats me hands down.
I agree with VJT, there’s no good reason to believe that evolution can design even a self-replicating molecule of RNA. Oh, wait, you have to first have replication before you can even have evolution.
Perhaps it was not evolution but rather a deep learning algorithm that gave us the first self-replicating RNA.
And begging of the question of teleology. Is there a name for fallacious substitution of necessity (“only if”) for sufficiency (“if”)?
I understand why Vincent hasn’t a clue about the significance of the paper by Lin and Tegmark (“Why does deep and cheap learning work so well?“). I don’t understand why someone with a doctorate fails to recognize when he’s clueless. And I don’t understand why someone with a doctorate in philosophy fails to detect multiple egregious errors in his own logic.
Can deep-learning algorithms detect errors in their logic?
It’s not about evolution being smarter than anyone. It is more about hindsight being 20/20.
We have all looked at inventions (or recipes, or first lines) and wondered, “that is so obvious, why didn’t I think of that?”
Hi Tom and Mung,
There’s no fallacy in the logic, just an unstated premise:
Deep-learning algorithms are the only ones that could be said to be “smarter” than we are, at solving certain problems.
Yes, exactly right.
Evolution doesn’t solve specific problems. Rather, we invent the problem that evolution is said to have solved. We invent the problem after evolution has been successful.
And that’s really Acartia’s point about hindsight being 20/20.
We invent the idea that evolution has been successful too, Neil.
Ignorance on parade. If you want to learn about machine intelligence, then invite discussion of the subject, rather than pretend to understand it well enough to formulate a “killer” argument. I’m not giving a free tutorial in response to this pathological behavior of yours.
That’s why I said that he was begging the question of teleology.
What else could Neil have meant?
We also invent the problems that The Designer is said to have solved.
Texas Sherpshooter.
I don’t agree there is any smartness going on at all. its just a function of memory.
nothing here figures anything out. its already in the equation.
Math doesn’t exist without a already finale conclusion.
Then memory takes over.
Board games have nothing to do with intelligence. Anymore then any/every video game.
its just memory and unthinking.
Design in nature is also a settled memory thing.
However the creator had to create the memory.
AI is boring as a subject for creation or human thought.
The segregation of the memory from thought , including the organs in the skull, is not being made still.
Tell you what, Vincent.
We’ll have a third party make an equation, a function mapping A to B, with a minimum of 5 terms and a maximum of 10 terms, (for example B = A^(2A-1)+A!/Cos(A)+32.74 ) and then return 100 records for A and B, with B randomly varied from the exact answer by between +5% and -5%. We can then see who is smarter, you or evolutionary computation?
Richardthughes,
Find the logical problem with Richards task in 3,2,1…
An even easier question is, is a bacteria smarter than Richard.
phoodoo,
The challenge isn’t for you, Phoodoo, its too hard. Here’s yours:
https://www.walmart.com/ip/764680
Why not just let Vincent design a tame fox instead of evolving one?
Should be a piece of cake to determine the exact changes required to the genome, assuming people are smarter than variation and selection.
“Darwinian” evolution would better be characterized as natural variation and selection. Or better yet, natural variation and differential reproductive success.
The article cited contained this interesting point
“What’s more, objects in the universe are governed by locality, meaning they are limited by the speed of light. Practically speaking, that means neighboring objects in the universe are more likely to influence each other than things that are far from each other, Tegmark said.”
That is an argument I have also been using here and at PT, in critiquing Dembski, Ewert, and Marks’s Conservation of Information argument. It is one of the chief reasons why fitness surfaces are not “white noise” landscapes but much smoother than that. And the smoothness helps GAs do well.
… and, I should add, the “locality” property of different parts of organisms has to do not with the speed of light but with much slower processes such as diffusion of chemicals.
Why don’t ID supporters start OP’s on ID and how it solves such problems? What’s the obsession with something they think is bunk?
Hi everyone,
I’d just like to make a few clarifying remarks.
A number of commenters have argued that evolution doesn’t solve problems. On one level that’s true: “evolution” is not an intentional agent, and it has no foresight or conscious goals. But neither do computers – yet we routinely speak of them as solving problems. You might reply that computers solve problems for the people who program them. Fair enough. But evolution solves problems too, for the organisms which flourish as a result of the beneficial mutations it generates. Ask a fleet-footed gazelle if evolution solves problems.
At first blush, the origin of life might not seem to be an exercise in problem-solving. But retrospectively, it can be seen that way. Somehow, proteins were generated which were able to fold and do something biologically useful. And somehow, a genetic code was generated. These innovations enabled living things to flourish. From their perspective, looking backwards, the origin of proteins and the genetic code were biochemical hurdles which needed to be overcome before they could arise.
You might say this is 20/20 hindsight. But there’s more to it than that. The problem of generating a living thing is not like the Texas sharpshooter fallacy, because a living thing is not just any old entity. The abilities it has are, from a causal and informational standpoint, extremely odd, as Sara Walker and Paul Davies point out in their paper at https://arxiv.org/abs/1207.4803 .
Tom English scoffs at my assertion that deep-learning algorithms are the only ones that could be said to be “smarter” than we are, at solving certain problems. I don’t pretend to have anything like his background knowledge of genetic algorithms, but for the record, I’d like to define what I mean by “smart.” I would call an algorithm smart if it can solve problems that even the most talented humans, working separately or together in a team, are incapable of solving – even when given ample time. A program that can merely solve problems faster than I can, or that can solve problems which I can’t but which a team of mathematicians can, isn’t smart. An algorithm that can trounce a world-class team of Go players, even when they are given years or decades to think about their next move, is what I would call smart. If readers don’t like that definition, I’m open to replacing it with a better one.
By the way, the problems I’m interested in are applied, real-world problems.
Petrushka asks: “Why not just let Vincent design a tame fox instead of evolving one?” It’s been done already: see https://en.wikipedia.org/wiki/Russian_Domesticated_Red_Fox
Take a look:
https://upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Georgian_white_Russian_domesticated_Red_Fox.jpg/450px-Georgian_white_Russian_domesticated_Red_Fox.jpg
Finally, I agree with Professor Felsenstein’s remarks on locality. Within our own universe, the smoothness of fitness landscapes is no big mystery. If Earth-based life were transported to Mars, I’m sure it would start evolving there, too.
Let me quickly dismiss one point of Vincent’s. He says:
For people whose basic motivation is to argue Yes/No/God this may be relevant. But for a biologist who is arguing that the processes of evolutionary biology explain the adaptations we see, it is completely irrelevant. The questions are whether in our universe evolution works. Arguing that it does work, but only because some deity designed the laws of physics, leaves us with an admission that yes, it does work. Most evolutionary biologists who feel unprepared to argue about cosmology or where the laws of physics come from will be happy to set aside the issue of what would happen in some other universe, even the average other universe. Ours may be special, but it is the one that contains the phenomena that we are arguing about.
Why are you even discussing this? This isn’t UD where “an evolutionist” says something and that counts as an “admission against interest” or some such thing and so is absolute truth for UDites. This is TSZ, and no one here really cares about fallacies like argument from authority. Orgel metaphorically made a point. Address the point, rather than writing as if it’s really a “law” or to be taken as true in every way.
In some sense, sure, it could be said to be true in that by no means could anyone invent a human de novo, while evolution apparently can, given the evidence for evolution in comparing humans with other organisms. But would Orgel say that evolution is smarter than us in that it can’t transfer powered flight “knowledge” from pterosaurs or birds into bats, yet somehow the “knowledge” embodied in fish appears in all of these organisms? No, that’s where evolution is just plain stupid, it doesn’t know anything, it just tinkers with what it gets from its ancestors.
It is especially where evolution isn’t by any means smarter than us, but is much more stupid than us, that it is unlike deep-learning algorithms. Why not deal with these matters in their wholes, rather than cherry-picking an Orgel claim and comparing it to something else that is said to be “smarter than you are” as if there were any reason to pretend that evolution has to be like that? We here who actually care about science know very well that evolution isn’t “smarter than us” like a deep-learning algorithm might be, or it wouldn’t do the very stupid things that it does.
Are GAs (EAs, whatever) “smarter than us”? Yes, they are, in that they can certainly come up with solutions that,. basically, no one (including the very bright) would ever do in a reasonable period of time. I’m not interested in whether or not teams thinking for unreasonable periods of time ever could come up with the same thing (probably not in many cases, but ruling things out is hard to do). Was that what Orgel was claiming? As pathetic as it is for you to be pulling the UD trick of pretending that Orgel’s words are an absolute claim across the board and that evolution thereby should be held to that standard, you don’t seem to even care about what Orgel’s something of a joke really meant, which almost certainly was not about teams of experts managing to do something or other. He said evolution’s smarter than you, presumably meaning that it comes up with solutions that you wouldn’t expect. An adage, a proverb, as in, don’t expect evolution to be limited by your imagination.
Are GAs dumber than us? Yes, like evolution they don’t see very far beyond inherited knowledge. It’s well-understood that human smarts are usually better at coming up with the more fundamental ideas in design, while GAs and/or EAs can fiddle with complex details. That’s evolution, which fails to come up with steel and other metals (can take heat, notably), with radio communication, or with the simple transfers of knowledge from one unrelated thing to another. Stephen Gould was actually quite wrong to compare evolution to a tinkerer, for a tinkerer readily jams unrelated stuff together to make a kludge. Evolution produces kludges, but primarily according to inherited material (including whatever is laterally transferred), not like a tinkerer at all, except that some of the results are rather sub-par (panda’s “thumb” actually being a poor example of that, since it’s very good for its specialized task).
You seem to need to learn to leave behind much of the bad thinking at UD. They don’t do philosophy right, they don’t tackle issues properly, they’re using fallacies all over the place. And you’re following them, first using Orgel’s claim as if it were some fact about evolution, then not really considering what he really meant by it. Then you compare evolution to something else said to be “smarter than humans” as if that were a fair and just comparison because Orgel said something. It’s sloppy thinking all of the way through, and it’s really not good for you to persist in the types of poor thinking that go on at UD.
Glen Davidson
I tried, but it ran away.
Not by design, though. By natural selection, or possibly by pleiotropy. Nobody was trying to create a tame fox.
This is an example of why I am not a fan of Tegmark. I see that statement as jumping to a conclusion not warranted by the evidence.
The problems facing the neural network are not math problems at all. They are practical problems of survival within the environment.
We humans, particularly scientists, create mathematical models of the world. That decomposes science into two parts:
Part 1: Coming up with an effective model of the world. (I call this “geometry”).
Part 2: Solving formal problems within that model (I call that logic).
Tegmark, Theologians, philosophers, AI people, and perhaps most people, concentrate on Part 2. They jump to the conclusion that the neural system is solving the mathematical/logical problems of part 2. Part 1 seems invisible to them. But part 1 is the most important part of science. That’s where the intelligence goes.
A neural system is likely doing mainly a modified part 1. That is to say, it is coming up with effective neural models. But they are not mathematical models, so there isn’t any actual part 2 in what the neural system does.
The mathematical structure of the universe comes from humans, not from God. “Fine tuning” is nonsense.
The willful misinterpreters will ignore the substance of your remarks, and turn your language into an admission that evolution works at something, i.e., serves a purposive.
Uh, I think they were. And the selection was “artificial”.
I fail to see any important distinction between natural and artificial selection. Darwin made the distinction because people knew that selective breeding could produce dramatic plumage in birds, and useful characteristics in plants and animals.
He extended this observation by claiming it happened in nature without planning by man or god.
Which is why I said it would be interesting to characterize evolution as natural variation plus selection or differential reproductive success. The differential success could be due to selection or it could be due to drift. But variation is not managed by any person or entity. New variants arrive without regard to their phenotypic effect or survival value.
I assumed that Petrushka was referring to the long-term experiment in evolution by artificial selection (selective breeding) conducted by Russian geneticists. Pleiotropy actually is a point of interest in the experiment. Some of the distinctive morphological traits of domesticated wolves have emerged also in domesticated foxes. (If I recall correctly — a big if — some of the tame foxes have curly tails and floppy ears.)
[ETA: I was composing when Petrushka posted.]
I’m not the best to respond here, but I think that it’s by definition only the former.
I stand corrected. I was thinking about the accidental domestication that has happened in several attempts to breed animals for fur. I thought foxes were one of those. Sables definitely are.
Nope. Differential success caused by differences in genotype is selection; differential success caused by chance is drift. But differential success in both cases.
I tried, but it had been eaten by dogs that had collectively solved the problem of killing a gazelle.
I did, but, you know, I’d already shot it and it was dead or close to it.
I don’t think they’ve solved the talking problem anyway.
I’m not just joking, though, since this does sort of get to the point that while gazelles may be selected for running fast and long (longer than most predators, anyway), nothing’s been done for their threat against bullets or their lack of ability to communicate very well. Naturally the problem of staying live for a while is going to impact gazelles, but there’s no grand strategy for problem solving going on at all.
Once again, this is the problem of glib answers that are all too typical at UD. It’s a serious matter of what selection is about, and the mere fact that it handles certain “problems” doesn’t mean that it’s a process for solving problems, like deep-learning algorithms are. Again, pointing out evolution’s lack of deep-learning algorithms doesn’t have anything to do with its success.
By the way, “evolution is cleverer than you are” is what seems to be attributed to Orgel, which sort of gets to the point of evolution’s “innovations” better than does your “smarter than you” paraphrase. It’s not about evolution being smart, considering that it’s clueless in so many ways, it’s just that its “solutions” may indeed be viewed as “clever” in our anthropocentric thinking, even as “cleverer” than we are.
Glen Davidson
LoL. Everyone here is an expert so they only commit the fallacy of arguing from their own authority.
Next up, expert witnesses will no long be allowed to testify.
Who says that citing or quoting authorities, or having an authority testify, is a fallacy? Some guy named glen, who is no authority on arguments from authority, therefore we should listen to him?
Thanks for the laughs.
Did you count the functional ovaries? Surely land animals cold run faster with fewer ovaries, John. Don’t you think?
Count the non-functioning ovaries on those dogs! We may be on to something here.
Then there’s a technical distinction between neutral mutations and drift that I’ve not understood. (I have no problem thinking of the number of offspring as a random function F(g) of the genotype g, with variation due to non-genetic factors.) I’ll work on getting that straight. I regret having added to the sound and the fury, even though I hedged.
No, no,no. Tom. If it is doing work it is violating the second law.
Tom,
The distinction is that drift can affect mutations of all types — beneficial, neutral, and deleterious. Beneficial mutations can be lost via drift, and deleterious mutations can be fixed by it.
I’d be interested to hear how drift overcomes the effect of selection with beneficial alleles…
…and in hearing how drift fixes deleterious alleles.
Deleterious alleles can’t be seriously detrimental. Unless, as in humans, medicine finds a way to correct the malfunction. But a mutation having a fractional effect can become fixed by chance. That is the point of Muller’s ratchet.
I posted a link in Sandbox addressing a possible way that bacteria escape from the ratchet.
I have always thought it rather odd that creationists haven’t notices that bacteria don’t go extinct due to genetic meltdown. Something is going on to prevent this, and the problem is being studied.
Just not by creationists.
There is indeed a distinction between neutral mutations and drift. Mutation creates a new allele at a frequency of 1/2N (in a diploid population); drift changes that frequency. There is also a distinction between neutral evolution and drift, which you may have meant. Drift can occur even when there are differences in selection coefficient among alleles, as long as the ratio between selection and population size is small. See “nearly neutral evolution”. Drift can result in the extinction of advantageous alleles and the fixation of deleterious ones.
Perhaps a scenario would help. Say Fred is born with a clearly advantageous immunity to cancer. But before Fred can reproduce, a 16-ton weight drops on his head out of the sky, purely at random. Or, closer to the math, suppose Fred manages to have 3 kids, but none of them inherits the good allele. In either case, drift has just eliminated a beneficial mutation. There’s a lot of population genetics math relating to such things. But drift can overcome selection, and it depends on the relationship between selection coefficient and population size. A small enough advantage (or disadvantage) can be eliminated (or fixed) in a small enough population.
Can you give us some selection coefficients and associated (effective) population sizes at which drift ought to dominate selection?
Say an effective population size of 100, to begin with.
No reputable scholar clings needlessly to terminology that has promoted misunderstanding. Indeed, when the misunderstanding serves his ends, he goes out of his way to prevent it. Ethical codes for professions like mine prescribe that one avoid the appearance of misconduct. You’re presently doing an execrable job of that.
Your “fair enough” is altogether too cute. You’ve just insinuated an analogy that is essential to crypto-creationist “evolutionary informatics.” Will you go the next step, and claim that nature probably would not solve problems with evolution unless information had been added by the
Great ProgrammerDesigner of the Great Program? “Darwinian evolution is incomplete,” isn’t it, because the theory does not account for the Universe being the way it is? (Joe Felsenstein went straight to the crux with his comment above.)I see nothing here but an attempt to save the rhetoric. Scientists who identify an event after the fact, and attempt to account for the process by which it occurred, do something radically different from what engineers do when they target an event in advance, and initiate a process in hope that the event will occur. The crypto-creationist “conservation of information” theorem (Winston Ewert acknowledged that the “information” is bias, but continued to call it information) applies to the latter scenario. I have quantified the error in misapplying the theorem to the former, using a theorem that does apply. Winston Ewert, representing the Evolutionary Informatics Lab, had no sensible response, but executed his duties as an activist in a religio-political movement, and reassured the faithful [ETA: donors] that everything was copacetic in the Land of Id. George Montanez is in the process of changing the Math of Id, evidently in response to the criticism of Joe Felsenstein, D. Eben, and me.
In short, I have a very hard time believing that you would insist on referring to the “problem” if you were not intent on introducing a problem solver. My objection to that is grounded in solid mathematical analysis: “The Law of Conservation of Information Is Defunct.” I never doubted that crypto-creationists would find something different to call “conservation of information.” George Montanez has already done so. And you perhaps knew that already.
Well of course there’s no firm line, just a gradient along which selection becomes less and less important. The probability of fixation for a beneficial mutation depends on both s (bigger=more likely) and N-sub-e (bigger=more likely); and for deleterious mutations, the other way around. If you want the actual math, you should talk to Joe Felsenstein or some other population geneticist.
Been there, done that. iirc, Joe appealed to an infinite selection coefficient to support the claim that selection could overcome drift in small population sizes.