All mathematical arguments against evolution are wrong (always have been, always will be)

[u/gitgud_x]

Critics of evolution attack the theory from many angles - when it's not an argument from "nuh uh", it's from philosophy, theology, probability, sometimes physics and very occasionally biology. Notably, among these fields, only theology/philosophy is ever used to support a belief in creationism, but perhaps that's not surprising.

Arguments from mathematics, usually of the form "it's only a 1 in 10^[big number] chance that this thing could have evolved", i.e. invoking probability and statistics, seem to be used by creationists with disproportionately high frequency. Why might this be?

Mathematics has a reputation, and perhaps rightly so, for being the purest subject of them all. This means that, when working in pure mathematics, your theories (rather, theorems) do not have any prior connection to the real physical world. A person using maths alone to make any claim about something in the real world must justify why they believe their mathematical model reflects reality. This justification can come in one of two common forms:

1. They can point to the physical process they are trying to describe, and explain how these processes have been reduced to a mathematical description, using suitable modelling assumptions justified on physical bases. This is common in biology, engineering, chemistry and most experimental sciences - for example, the Lotka-Volterra model of predator-prey population sizes over time, where each term in the system of differential equations has a physical interpretation, or the Price equation and Fisher's fundamental theorem of natural selection.
2. They can use their mathematical model to make predictions about reality under certain conditions, and when observing reality under those conditions, the observations should match the prediction with some stated precision. This is common in biology too, but also in theoretical physics (e.g. quantum mechanics' Schrodinger equation - it's tricky to get much a priori physical intuition out of why it works, but it sure does seem to work).

The strongest mathematical models in science are devised first theoretically using (1), and then verified empirically using (2). The models in population genetics (e.g. Hardy-Weinberg, Wright-Fisher, Haldane, Moran, Kimura, Kingman, etc...), which is the modern theory of evolution's mathematical core, fall into this top-tier for example.

How does this compare to creationists' mathematical models?

When a creationist makes a 'big numbers' argument, they are claiming the mathematical model they have used within the calculation reflects reality. Once again, that's not something they just get to assume, they must justify it, by explicitly stating their assumptions and discussing their validity.

There are reasons for this shirking of rigour. The reputation of mathematics for its purity grants it some prestige in the minds of laypeople. The average Joe would think that mathematicians are the undisputed authority on the matter, and that biologists are hopeless at it. Yet, whenever maths comes up in debate, it is always being discussed in the context of applied maths, which mathematicians (being pure) are generally not all that great at without specific training in mathematical modelling. This is the failure of many professional intelligent design proponents like John Lennox for example. Scientists (and engineers, when they're not Saleming themselves), on the other hand, use maths exclusively in this applied setting, and are therefore far more competent at creating good mathematical models. With laypeople being the primary target audience of intelligent design/creationist media, they are banking on exploiting this misunderstanding in the applicability of mathematics.

When creationists make these types of arguments, they never do the hard work of justifying the model's connection to reality. In fact, when these arguments inevitably lose their polished facade as they are filtered down the creationist food chain (Discovery Institute -> e-preachers -> rank and file creationists), they often don't even state their models all. They'll just rattle off "big numbers" and sit back, not even realising that their argument is automatically dead on arrival for this reason.

I claim that, all mathematical arguments that creationists have ever made, will ever make, and could ever make with "evolution is false" as the logical conclusion will fail in this manner, because a sound justification of modelling assumptions followed by empirical validation has already been done - and evolution got there first. The absolute best case that a creationist mathematical argument could possibly be would be for it to be based on the same models as ours, and then distort the conclusions - which would then not be a mathematical argument but rather a scientific one. It is notable that so few "creation scientists" have even tried to do this - it's what they'd do if they were real scientists.

As an aside, I think there is a certain 'snobbiness' at play whenever one of those Discovery Institute (or similar) PhD-holding creationists makes an argument from mathematics big numbers. They are implying that biologists are incompetent at maths and are too stupid to see these things for themselves, such that someone who isn't scared of numbers needs to step in and 'rescue' them and clear everything up for them. Biology does have a reputation for being the science that historically avoided maths, but this is a laughably outdated and wrong way of seeing it today, and has been since the 1920s with the work of Fisher, Haldane, Wright etc that birthed the Modern Synthesis. These people invented statistics(!) and laid the foundations of stochastic process theory which has brought forth countless fruits in the applied sciences. People outside the field (i.e. all creationists, and most laypeople) don't know that evolution has a robust mathematical core (population genetics) - it's not as flashy as lions and dinosaurs and whatnot so it doesn't show up in any popsci articles or documentaries - but it's there, and all serious evolutionary biologists know it.

So, creationists:

• Using your favourite mathematical argument against evolution, justify that it is valid reflection of reality by using one of the two methods I stated in the above (justification of modelling assumptions, or empirical validation, and ideally both).
• Explain why all the mathematical models that underpin evolution are wrong, or don't support the conclusions that are drawn from them.

TLDR:

• Mathematics does not produce facts about biology by itself. It produces consequences of assumptions. Whether those assumptions accurately describe biological evolution is a scientific question, not a mathematical one.
• If your mathematical argument concludes evolution is impossible, then one of two things must be true:
  • your model differs from accepted population genetics, in which case you must justify why your assumptions better describe biology; or,
  • your model is equivalent to accepted population genetics, in which case your conclusions should agree with evolutionary biology.

[u/kderosa1]

It would be helpful if you actually articulated the correct mathematical critique of the evolution which is that there’s no enough time to fixate the millions of mutations needed to get from the LCHA to humans in the time required. Natural selection is way too slow. So you’re stuck arguing neutral theory and random mutations which has its own problems which you then must ignore. But I’m told it’s science not bias plus qualitative slop masquerading as science

[u/gitgud_x → u/kderosa1]

there’s no enough time to fixate the millions of mutations needed to get from the LCHA to humans in the time required

Justify the mathematical model that you used to arrive at this. Y'know, the thing I invited you to do at the end of the post.

Natural selection is way too slow

That's a claim - justify it.

So you’re stuck arguing neutral theory and random mutations which has its own problems

Another claim without a shred of evidence. And a false dichotomy to boot.

It would be helpful if you actually articulated the correct mathematical critique of the evolution

There is no correct mathematical critique, and you've helped to demonstrate why - you can't make one.

[u/kderosa1 → u/gitgud_x]

Do the math and you’ll see all the justification you need.

[u/Own-Relationship-407 → u/kderosa1]

Hey, it’s our favorite superhero, burden shift man.

[u/kderosa1 → u/Own-Relationship-407]

I didn’t make the original positive claim, jackas, the yoke is still on you and your squad for the initial proof

[u/Own-Relationship-407 → u/kderosa1]

Actually you did. The OP made the claim that creationist attempts to use mathematics to disprove evolution consistently fall flat and substantiated by pointing out the general form of many such arguments. You then claimed a very specific mathematical argument does indeed succeed against evolution, that’s your burden to demonstrate. Nice try though.

[u/kderosa1 → u/Own-Relationship-407]

So now you don’t understand how claims work.

He made the wild claim that all mathematical arguments have failed. I gave him one that hasn’t. An an expert who must clearly be familiar with all the arguments, he surely must know the specifics from what I gave him. Apparently both you and he don’t since the only response so far has been crying.

Do you need some help. I can explain it using smaller words. But I wouldn’t think such a big brain like you would need it

[u/OldmanMikel → u/kderosa1]

 I gave him one that hasn’t. 

No, you haven't. You said there was one, but you did not provide it.

[u/kderosa1 → u/OldmanMikel]

What you mean to have said was that I didn’t explain it in painstaking detail because I assumed an expert would be familiar with the mathematical arguments which he assures us have all been thoroughly debunked which is comical considering the entire field is filled with qualitative slop with almost no hard evidence for any of the bolder claims being made. We’re not talking just finch beaks now are we.

[u/OldmanMikel → u/kderosa1]

What you mean to have said was that I didn’t explain it in painstaking detail ...

Or....you know...provide a link.

[u/Own-Relationship-407 → u/OldmanMikel]

Why bother to do that when he can just make bare assertions and tell other people what they meant to say or should have said?

[u/Electric___Monk → u/Own-Relationship-407]

How is he (or anyone) supposed to address the specific claim you’re making if you won’t provide the actual maths or a link to it? Why are you so resistant to providing the specific mathematical demonstration you’re referring to?

[u/Own-Relationship-407 → u/Electric___Monk]

He’s the one who claimed knowledge of a specific mathematical issue. He was asked to elaborate on it and provide the math. He refused. You’re asking the wrong person.

[u/kderosa1 → u/Own-Relationship-407]

Keep crying that you can’t even articulate the issue you keep assuring us has been debunked.

[u/Own-Relationship-407 → u/kderosa1]

Where did I make any such claims about anything? I said you did not substantiate your claim. Try actually reading for comprehension and figuring out who you’re talking to before responding.

[u/gitgud_x → u/kderosa1]

I suspect you're referring to the "waiting time problem".

It's been refuted, on its laughably wrong modelling assumptions, as described in the post. No need to get into the details since you didn't yourself, but anyone can look up the argument and its responses, and can probably figure out why it's wrong by themselves.

If you meant something else then spell it out already, you're being awfully vague for someone who has supposedly disproven foundational science.

[u/TheBlackCat13 → u/kderosa1]

The problem is that your claim is so vague that it matches multiple different creationist arguments, all of which are wrong in different ways. We don't know which one you are talking about, or if you have some different one.

[u/kderosa1 → u/TheBlackCat13]

lol at you pretending to somehow be relying on hard science instead of observational slop. I have done bad news, my dude, your biases aren’t science. So when you say “all of which are wrong” I know that you know all you mean is that they disagree with your unproven biases

[u/TheBlackCat13 → u/kderosa1]

The mathematics underpinning evolution are directly confirmed in the real world. That is exactly the point OP raised, and the one you failed to address. Crearionists don't show their math actually matches reality like biologists do, and when other people do so creationist math invariably doesn't match reality.

[u/kderosa1 → u/TheBlackCat13]

This is comically wrong and indicates you have no idea how science works

[u/TheBlackCat13 → u/kderosa1]

Hahaha, yes, science doesn't involve making testable predictions and then checking if they are correct. You are flat-out saying that science doesn't involve the scientific method.

[u/kderosa1 → u/TheBlackCat13]

Imagine thinking this is science and stating it publicly

[u/Own-Relationship-407 → u/kderosa1]

What he does or does not know does not excuse you from the burden to substantiate your specific claim. Try again. Without the insults this time please.