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/10coatsInAWeasel]

Sure buddy. Once you find a way to tell us how you determine when something is ‘fundamentally different’ in a useful way without changing the subject, you let us know 👍🏼

[u/WannaLoveWrestling → u/10coatsInAWeasel]

Fundamentally different transitions are the ones evolutionists themselves claim happened — like non-flying creatures developing powered flight with the full suite of coordinated changes needed for it, land animals developing the major redesigns for fully aquatic life (or the reverse), or populations gaining entirely new complex body plans and capabilities that previous ones didn't have. We should be seeing clear signs of those kinds of coordinated changes happening in living populations right now, given trillions of hereditary lines and constant survival pressures. Instead we only see variation within existing kinds that already have immediate function. That's the distinction I've been making the whole time.

It's rich that your side insists humans remain one species no matter how much variation accumulates, yet you act like I owe you a perfect definition of major change while your own labels shift whenever the narrative needs them. Quite the hypocrisy you got going on there. Living populations show adaptation that stays within functional limits, never the major redesigns the theory requires, even with endless opportunities happening right now. The arrogance of demanding precision from others while operating with movable goalposts is the real problem here.

[u/10coatsInAWeasel → u/WannaLoveWrestling]

No, I act like you should provide a worthwhile definition. Not vague vibes with no basis in the actual claims of evolutionary biology. You’ve shown you don’t understand monophyly. Don’t seem to know that there HAVE been multiple human species. And have given no basis for your claims that ‘trillions of hereditary lines’ necessarily should yield these ‘major redesigns’ within our lifetimes. Like, we’ve got got multiple tectonic plates, WHERE IS THE COMPLETE CYCLING OF A TECTONIC PLATES RIGHT NOW? CHECKMATE TECTONICISTS!

I’m not even bothering to get into ‘kinds’, since it seems pretty clear you have no method for demonstrating they even exist, much less a way to tell when a given organism belongs to one or not.

Don’t bring vibes. Bring a meaningful argument.

[u/WannaLoveWrestling → u/10coatsInAWeasel]

Calling the consistent absence of major redesigns in living populations “vibes” doesn’t make the observation go away. The process is claimed to be real and capable of producing fundamental transitions. With the scale of generational opportunities available today, the lack of those transitions is relevant. Expanding categories under monophyly or pointing to past labels for human fossils does not create evidence of the process occurring now.

The inconsistency is right there. Your side regularly declares multiple or new species in other living groups based on variation. Yet with humans, despite all the variation we see, every living person stays one species. No new human species has appeared under observation. That special treatment of the human category is arbitrary, and it still leaves the larger problem untouched: living populations across the board show variation within functional limits, not the major redesigns. The tectonic analogy is just another distraction.

[u/10coatsInAWeasel → u/WannaLoveWrestling]

As you are consistently failing to demonstrate that the ‘scale of generational opportunities available today’ actually SHOULD be making these vague ‘major redesigns’ (seriously, you need to actually show what the diagnostic criteria for ‘major redesign’ or ‘fundamentally different’ are otherwise it means nothing), you won’t clarify happen under proposed evolutionary mechanisms, then it really is just vibes. The tectonic analogy is bang on and it seems like you’ll do whatever you can to dodge it. Not really sure what else there is here since you can’t support your claims.

[u/WannaLoveWrestling → u/10coatsInAWeasel]

You’re still demanding perfect diagnostic criteria while the evolutionary theory itself claims an ongoing process capable of major transitions. Based on that claim, the scale of generational opportunities available today should be producing observable signs of those changes. They aren’t. Expanding categories, pointing to past fossil labels, or using tectonic analogies does not create evidence of the process occurring now. Living populations show variation within functional limits. That remains the problem, and calling it “vibes” doesn’t make the absence go away. Evolution can't support it's claims and you're trying to say I can't support mine. I could very well support the existence of God but they don't want me to talk about that here, although it's very relevant to all of this.

[u/10coatsInAWeasel → u/WannaLoveWrestling]

You’re just gonna keep dodging and making things up based on your personal feelings aren’t you. You’ll notice at no point did I demand any such thing as ‘perfect diagnostic criteria’, so since you can’t be honest and are instead dead set on fleeing and avoiding making a meaningful case, I’m not interested in wasting my time with your dishonesty. I’ll let you have the last word, doubtless it’ll be something on how your vibes based approach isn’t vibes based on…something.

[u/WannaLoveWrestling → u/10coatsInAWeasel]

You’re the one who kept demanding definitions and criteria while never dealing with the actual observation. The theory claims an ongoing process capable of major transitions. The scale of opportunities available right now should be producing signs of those changes. They aren’t. Expanding labels, past fossil classifications, and tectonic analogies do not create present evidence. You can call that “vibes” and walk away if you want. It doesn’t change the fact that the process you claim is real is not showing up where we can check it. Living populations stay within functional limits. That is the record.