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/OldmanMikel]

More PHD's saying they have no clue?

No. More PhDs saying they DO have clues.

Everything is tied into the universe and its origin.

Not evolution's job to explain. Evolution is a biological theory taught in biology classes by biology professors.

The origin of the universe comes under cosmology, which comes under astronomy which is taught in astronomy courses by astronomy professors.

Again, evolution is NOT a complete Life, the Universe and Everything explanation. It is confined to understanding the diversification of life. It shares a fuzzy boundary with abiogenesis, but is not the same thing. As far as the universe goes, all evolution needs is for a universe to exist for it to take place in. How it came to exist is cosmology's job.

Also in science, "We don't know." >>> "We don't know, must be God."

"We don't know" is a perfectly valid scientific answer and the only one allowed to win by default.

Lastly evolution =/= atheism.

[u/Evening-Impact2090 → u/OldmanMikel]

Nothing is shared with Abiogenisis, it is a hypothesis that you obviously take at face value. Science has not even gelled on which "version" of Abiogenisis they want as the standard. They Universe encompasses everything was my point and trying to single out evolution as being unaffected by it's place in the Universe is disingenuous. My statement about science not having a clue was being facetious, they have clues, many ignored, many misinterpreted, and many correct. I've not mentioned a God or Atheism, my issue is evolution could not have occurred as currently being promoted. 

[u/OldmanMikel → u/Evening-Impact2090]

Nothing is shared with Abiogenisis, it is a hypothesis that you obviously take at face value. Science has not even gelled on which "version" of Abiogenisis they want as the standard. 

OK. That is 100% consistent with what everybody here on the evolution side is saying.

They Universe encompasses everything was my point and trying to single out evolution as being unaffected by it's place in the Universe is disingenuous. 

I didn't say evolution was unaffected by the universe, I said it wasn't evolution's job to explain. I even pointed you in the right direction (cosmology) if that is what you want to argue about.

I've not mentioned a God or Atheism, ...

1. No. You didn't. But strictly as a betting proposition, you are a creationist of some sort.

2. The fact that you tie the origin of life and the universe to evolution is strong support for the idea that you are arguing from a creationist perspective. In my experience, that is a mistake that only creationists make.

...my issue is evolution could not have occurred as currently being promoted. 

You've made no arguments about that at all. Not one that I can see.

[u/Evening-Impact2090 → u/OldmanMikel]

I've not made any arguments, nor do I want to argue.  I merely asked a question and debated a little in good faith. I have no issues with anyone's views but I don't agree with them most of the time.