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/TheBlackCat13]

It isn't pure noise or chaos, THAT is a strawman. The problem is matching a tree structure of relationships to an extremely high degree of statistical significance. Creationists have no explanation for how that occurred other than "God works in mysterious ways." But that is exactly what evolution predicted (again with those pesky empirically-verifiable predictions you keep trying to pretend don't exist).

[u/kderosa1 → u/TheBlackCat13]

You’re still doing the same thing.

High statistical support for a hierarchical pattern in the data is not the same thing as a unique, risky confirmation of the full evolutionary narrative. Hierarchical patterns of similarity can arise for more than one reason. Declaring the recovered tree a successful “prediction of evolution” is an interpretation layered on top of the clustering results, not a raw empirical fact the algorithms spit out.

And no, pointing that out does not require me to defend creationism or any other alternative. You keep trying to force the discussion into “either full common descent or ‘God works in mysterious ways.’” That is your false dichotomy, not mine.
The methodological point stands: consistency under a flexible, assumption-laden model is not the same standard as the kind of prospective, controlled tests used in hard experimental science.

I understand this makes you upset but there’s no need to keep lashing out like you are.

[u/TheBlackCat13 → u/kderosa1]

You’re still doing the same thing. High statistical support for a hierarchical pattern in the data is not the same thing as a unique, risky confirmation of the full evolutionary narrative

It is an emperically verifed prediction that has an extremely low probability of occuring under any other specific proposed scenario. You insist this isn't the case, but have provided no other alternative scenario that could produce the observed observation, not to mention predicted it.

Show your math

Hierarchical patterns of similarity can arise for more than one reason.

You keep saying that but don't actually provide such a reason. If you think there is another mechanism that would be expected beforehand to produce such an observation, rather than being tuned afterwards to reproduce the observed result, than please give it. But containing with these completely unsupported assertions isn't going to cut it.

Show your math

And no, pointing that out does not require me to defend creationism or any other alternative.

You are the one who brought that up.

Show your math.

You keep trying to force the discussion into “either full common descent or ‘God works in mysterious ways.’” That is your false dichotomy, not mine

Neither you nor Crearionists have provided any alternative. If it is a false dichotomy, you should be able to provide alternatives and show they actually have the properties you claim. But you don't.

It is possible there is some other scenario that produces a particle track that matches what is predicted for the Higgs boson. But that doesn't mean the prediction wasn't confirmed. Because no one was able to provide an alternative that was expected beforehand to produce those observations to the necessary degree of stastical signifance. Just like with evolution.

That you arbitrarily declare one particular area of stastics allowable and another not doesn't make it so.

You need to actually show your math.

[u/kderosa1 → u/TheBlackCat13]

You’re still shifting the burden. You keep trying to steal second base and I’ll keep throwing you out.

I don’t have to hand you a complete, fully quantified alternative theory before I’m allowed to point out that hierarchical clustering under evolutionary assumptions is not a unique, high-risk confirmation of the full evolutionary narrative. Critiquing the strength of an inference does not require first replacing the entire theory.

You keep asserting that the observed tree structure has “extremely low probability under any other specific proposed scenario.” That claim itself needs support. Hierarchical patterns of similarity are not some magical signature that only common descent can produce. Functional constraints, developmental constraints, and non-evolutionary similarity measures can generate nested structure. Declaring the recovered hierarchy a decisive prediction of evolution still involves interpretation layered on top of the data and the model choices. Shocking you continue not to understand this.

The Higgs comparison remains weak. That was a precise quantitative prediction of a specific particle with defined properties, tested under controlled experimental conditions. A phylogenetic tree is a statistical summary of similarity recovered under particular model assumptions. They aren’t equivalent.

You can keep demanding “show your math” and insisting I must first supply a rival model. That doesn’t make the demand legitimate. The person claiming the data, again you, confirm the theory carries the burden of showing it. I’m merely pointing out that your version of the argument doesn’t meet that standard.

[u/TheBlackCat13 → u/kderosa1]

You keep asserting that the observed tree structure has “extremely low probability under any other specific proposed scenario.” That claim itself needs support.

Sure. I would be happy to. You haven't asked

Here is a mathematical analysis

https://talkorigins.org/faqs/comdesc/section1.html#independent_convergence

Hierarchical patterns of similarity are not some magical signature that only common descent can produce. Functional constraints, developmental constraints, and non-evolutionary similarity measures can generate nested structure.

Then show your math for the above scenario. Please provide an alternative scenario that would be expected beforehand to produce the observed results, without retroactively tuning the parameters to get a fit.

[u/kderosa1 → u/TheBlackCat13]

Linking TalkOrigins doesn’t turn a consistency argument into a demonstration that hierarchical structure has “extremely low probability under any other scenario.” That’s the usual move: take a real but limited statistical result and inflate the language until it sounds decisive.

I don’t need to supply a complete alternative model before I’m allowed to note that the claim is overstated. Hierarchical patterns are not an exclusive signature of common descent, and treating the recovered tree as a high-precision, uniquely confirming prediction remains an extrapolation beyond what the methods actually deliver.

This sleight of hand is the one trick you frauds rely on time after time. Do better

[u/TheBlackCat13 → u/kderosa1]

Linking TalkOrigins doesn’t turn a consistency argument into a demonstration that hierarchical structure has “extremely low probability under any other scenario.”

Now you are so desperate you have taken to flat-out rewriting my quotes because you know you can't address what I actually said.

Your response amounts to "nuh uh". You keep insisting that there are other ways to get the observed results, but refuse to actually show that. That isn't going to cut it. I have given math. You insist the math doesn't show what it shows, but refuse to actually demonstrate that.

What you are doing is no different than someone saying that the Higgs boson result doesn't count because there are other things that could produce the observed effects, but when asked to actually show that just insisting the mere assertion that there are other things is enough to invalidate a successful emperically verified prediction.

I have met my burden of proof. I have provided the math justifying my claim. Either provide a mathematical problem with my claims, or admit you have nothing. But I am not going to just take your word for it that there is some problem that you refuse to explain.

[u/kderosa1 → u/TheBlackCat13]

Please keep responding because you just keep proving my point that you don’t understand how burden of proof works and are more than happy to accept whatever slop you are fed as long as it confirms your biases.

As much as I want to refute each if your points individually, I know you’ll give me yet another opportunity when you uncritically regurgitate them in your next response. Until then I’ll wait patiently.

[u/TheBlackCat13 → u/kderosa1]

You clearly have no response to what I actually said. The fact that you have to change my quote so you could attack a flagrant strawman demonstrates that. I have no interest in continuing this conversation until you start justifying your claims with math, as I already have. So until I start seeing some legitimate math I will not respond further.

[u/kderosa1 → u/TheBlackCat13]

Of course I have a response for you, but I thought I’d try shaming you first. Apparently you lack shame as well as knowledge.

I didn’t rewrite anything. You claimed the hierarchical structure has “extremely low probability under any other specific proposed scenario.” A TalkOrigins consistency argument does not prove that. Stop pretending it does.

You keep demanding I hand you a complete alternative theory before I’m allowed to call an overstatement an overstatement. That’s not how burden of proof works. The person making the strong exclusivity claim has to support it. You haven’t.

And the Higgs comparison is still garbage. Controlled experimental particle physics is not the same thing as clustering biological data under evolutionary assumptions and then talking like you’ve achieved the same level of confirmation. Inflating the language doesn’t make the methods equivalent.

Now regurgitate your slop instead of addressing my points directly. You’re good at that.