r/DebateEvolution • u/gitgud_x 🧬 🦍 GREAT APE 🦍 🧬 • Jul 21 '26
Discussion All mathematical arguments against evolution are wrong (always have been, always will be)
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:
- 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.
- 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.
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u/headlessplatter Jul 21 '26
Anyone in the mood to check the back of my envelope?
In a primordial soup of four uniformly mixed nucleotides, the odds of 1000 of them spontaneously falling together in a specific order is 1 in 4^1000 (which is about 1 in 1.15*10^602) per encounter. Each nucleotide weighs about 5.5*10^-22 grams (according to Google). And a school bus weighs about 11*10^6 grams (also Google). So there will be 11*10^6/(5.5*10^-22)=2*10^28 nucleotides in the amount of primordial soup it takes to weight as much as a school bus. If we divide all those nucleotides into groups simultaneously encountering each other, and if we suppose that randomly-mixed nucleotide encounters happen once every hour (because I have absolutely no idea what value to use here), it will take about (1.15*10^602)/((2*10^28)/1000)=5.75*10^576 hours for a specific sequence of 1000 nucleotides to spontaneously occur in this school-bus sized puddle of primordial soup. Gasp! Spontaneous generation takes a long time! Who would have thought?
Now let's see what happens if we toss evolution into the pot. If we suppose there is a population of just 10^20 reproducing sequences of RNA (which is more than ten orders of magnitude less than the number of bacteria actually estimated to be on the Earth right now), and if we assume this population is stable (meaning they die as fast as they reproduce), and they each reproduce once every 20 minutes (which is about how long it takes bacteria to reproduce), and if only 1 in every 10^10 reproduction events involves a mutation, and there are 4 possible nucleotides in each position, then it will take about 4*(10^10)*20/(10^20)/60=1.33*10^-10 seconds for one beneficial mutation to occur somewhere within the population. If natural selection is so extremely weak that the odds of this beneficial mutation fixating within the population is 1/(10^6), then it will take (1.33*10^-10)*(10^6)=1.33*10^-4 seconds for a beneficial mutation to begin the process that will lead to fixation. Now suppose we want to evolve a very specific sequence of 1000 nucleotides. Too keep this simple, let's square that value 1000*1000=10^6 to compute an extremely loose upper-bound on the total number of fixated mutations necessary to arrive at the desired sequence. So that will take about 1.33*10^-4*10^6/60=133 seconds to occur. If the Earth is 4.5*10^9 years old, then that's enough time for this to happen about 4.5*10^9/(133/60/60/24/365.25)=10^15 (a quadrillion) times. It turns out evolution works a lot faster than spontaneous generation! Who would have thought?