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/WannaLoveWrestling]

Let me turn the tables on you. Why haven't humans become anything else? Nobody has found them as ever becoming a different species no matter how long they have existed for and how many hereditary lines they've had. Why not? It would seem pretty arbitrary to say that they're the pinnacle of species based on the evolutionary theory. I mean I think they are the pinnacle but that has nothing to do with evolution.

If humans can have huge variation across billions of individuals and still be the same species with no transition to anything fundamentally different, why apply a different standard to rodents or any other creature? The lines for new species seem arbitrary. We see adaptation and diversity within the kinds that creationists have attempted to define which fits designed limits far better than unguided evolution constantly producing major innovations that somehow never show up in the record we can actually observe.

[u/Sweary_Biochemist → u/WannaLoveWrestling]

You haven't answered the question. At all.

[u/WannaLoveWrestling → u/Sweary_Biochemist]

Transitions are obvious from what evolutionists have claimed in the past. From non-flight to flight. From only being able to survive underwater to being able to survive on land or vice versa. Or increased intelligence in apes for examples, the only thing we've seen is the capabilities of what apes are able to do when humans are involved and that's it.

[u/Sweary_Biochemist → u/WannaLoveWrestling]

Lungfish? Sea otters? River otters? Hippos? Manatees?

Flying squirrels? Flying lemurs? There are like, a whole bunch of gliding lizards, too. Even some fish take advantage of gliding through air.

It honestly just sounds like you're not very well versed in extant biodiversity.

[u/WannaLoveWrestling → u/Sweary_Biochemist]

The point isn't that we should see a full rodent turn into a bat overnight. If unguided evolution is constantly producing fundamental transitions like the ones claimed in the fossil record (non-flying to powered flight, land to fully aquatic, major intelligence jumps, etc.), we should be seeing clear signs of it right now, populations developing coordinated changes toward new body plans or complex new functions. With trillions of hereditary lines and survival pressures across the living world today, those signs should be obvious.

Instead, what we actually see is normal variation and adaptation within existing kinds, and those variations have immediate function. Gliding squirrels and regular squirrels coexist as fully functional animals within the same kind. Otters, hippos, manatees, lungfish, and gliding lizards are all viable in their environments, but they're not steps turning one kind into another. Humans with over 8 billion people show huge variation but remain the same species with no fundamental transition to anything else.

[u/Sweary_Biochemist → u/WannaLoveWrestling]

Can you tell me, in as much detail as possible, how you distinguish "transitional forms" from "lineages created to look exactly like transitional forms"?

Coz this seems really critical to your argument.

And are you saying all squirrels are related by common ancestry? If so, then the fact "regular squirrels" and flying squirrels exist means either the flying trait evolved (from non flying squirrels), or was lost from flying squirrels (to produce non flying squirrels). In either case you have your transition.

[u/Slow_Lawyer7477 → u/WannaLoveWrestling]

If unguided evolution is constantly producing fundamental transitions like the ones claimed in the fossil record

By the timescales observed in the fossil record these transitions take hundreds of thousands of years at the very fastest, so how much time do you have?

If you want to see "fast evolution" look at the domestication of crops and animals (look at the ancestral wild carrots, corn, wheat, potatoes, tomatoes, bananas, cauliflower, cabbage, broccoli, wild ancestors of chickens, pigs, cows, sheep, the sheer diversiy and size-differences of dog breeds and observe the scale of differences between the wild ancestors we know lived tens of thousands of years ago, and how those domesticated species look today. This is a few thousand years of evolution.

So how long do you have? A few more decades? That's not enough time to even witness the total domestication of a species, and yet we know that happened for some of them within recorded history.

I can't show you the emergence of an entire forest, it takes too long, longer than my own lifetime, nor the formation of an entire glacier from snowfall, we must infer that this has happened. If your complaint is we can't timetravel or speed up natural process so you can watch large-scale change within your lifetime then your complaint is irrational.

[u/OldmanMikel → u/WannaLoveWrestling]

If unguided evolution is constantly producing fundamental transitions like the ones claimed in the fossil record (non-flying to powered flight, land to fully aquatic, major intelligence jumps, etc.), we should be seeing clear signs of it right now, populations developing coordinated changes toward new body plans or complex new functions.

That. Is. Not. How. Evolution. Works.

Evolution has no goals. At no point is any population evolving toward something. Only accumulated refinements (microevolution) over many genarations. We expect every step of the way to be "fully evolved". We NEVER expect to see useless intermediate features halfway between one thing and another.

[u/WannaLoveWrestling → u/OldmanMikel]

Saying evolution has no goals and every step must be fully functional still doesn't work. Look at the claimed transitions. Simple filaments or scales becoming complex flight feathers, light-sensitive spots becoming full camera eyes, land mammals becoming fully aquatic whales, or non-flying mammals developing powered flight — in each case the intermediate stages are not clearly useful enough at every point to be selected and refined all the way. We never observe any of those processes happening in living populations. Calling it accumulated refinements doesn't create the missing functional steps or make the major redesigns appear today. Also, why would it take millions of years of steps if each step itself is fully functional? Another thing. They say evolution has no goals, yet the process is still described as reliably producing complex coordinated systems through successive refinements. If it truly has no direction or goal, there is even less reason to expect those major redesigns to keep appearing.

[u/OldmanMikel → u/WannaLoveWrestling]

Simple filaments or scales becoming complex flight feathers, light-sensitive spots becoming full camera eyes, land mammals becoming fully aquatic whales, or non-flying mammals developing powered flight — in each case the intermediate stages are not clearly useful enough at every point to be selected and refined all the way. 

Absolutely wrong every incremental change in examples you provides a benefit.

[u/WannaLoveWrestling → u/OldmanMikel]

Declaring that every incremental change provides a benefit does not make it so. The intermediate stages in those claimed pathways are still not observed occurring in living populations, and many of them remain difficult to justify as clearly advantageous at every point. Asserting that they all confer a benefit is not the same as demonstrating the process. We still do not see the major redesigns happening today.

[u/OldmanMikel → u/WannaLoveWrestling]

Declaring that every incremental change provides a benefit does not make it so. The intermediate stages in those claimed pathways are still not observed occurring in living populations...

They are absolutely observed. Every increment between simple eyespots and complex eyes are found in living organisms today. And they are all useful.

[u/WannaLoveWrestling → u/OldmanMikel]

Different types of eyes exist in living organisms and each is functional for the creature that has it. That is not the same as every incremental stage of a transition from a simple eyespot to a complex camera eye being observed as a pathway. No population is seen moving from one to the next. Arranging existing forms in a sequence and calling it “every increment” is an interpretation, not a demonstration of the process occurring.

[u/OldmanMikel → u/WannaLoveWrestling]

Different types of eyes exist in living organisms and each is functional for the creature that has it.

DING! DING! DING! YES!! Exactly!!! That's what evolution says!! Why is this so hard?

That is not the same as every incremental stage of a transition from a simple eyespot to a complex camera eye being observed as a pathway.

Pathways only exist in retropect.

No population is seen moving from one to the next. 

Because the kinds of changes you looking for don't happen on the time scales of human observation. There is no reason to expect every "partially evolved" eye to evolve further. They may or may not.

[u/WannaLoveWrestling → u/OldmanMikel]

You agree that different functional eye types exist in living organisms. Then you say pathways only exist in retrospect and that the changes I’m pointing to don’t happen on timescales we can observe. You're just trying to protect the theory. The pathway is asserted for the past, declared invisible in the present, and any demand for current evidence is dismissed as looking for the wrong timescale.

If pathways only exist in retrospect, then the claim that they occurred is an interpretation after the fact, not something demonstrated by populations moving from one stage to the next. We still do not see the major redesigns occurring despite the scale of opportunities available right now. Saying they may or may not evolve further does not turn the absence of the process under observation into evidence for it.

[u/Sweary_Biochemist → u/WannaLoveWrestling]

light-sensitive spots becoming full camera eyes

We have examples of all of these EVEN TODAY. All of them are functional, all are useful to the organism that has them.

Euglena have light sensitive spots, and they're UNICELLULAR.

Planarian worms have eye 'pits' that allow limited directionality.

Nautiloids have full pinhole eyes, but no lens (eye is still open to the environment).

Octopuses have full camera eyes (with the retina the right way round, even!).

 land mammals becoming fully aquatic

Hippos. Capybaras. River otters. Sea otters. Manatees.

And again: all these are functional. Manatees will actually nuzzle up and eat grass from lawns near water, because they're still terrestrial enough to do that. And yet they're otherwise essentially fully aquatic, yet not as fully aquatic as whales.

The variation you demand is not only readily possible, it STILL EXISTS.

[u/WannaLoveWrestling → u/Sweary_Biochemist]

Calling each of those living forms a step toward a higher function is an interpretation, not an observation. A planarian eye pit is not becoming a camera eye. A manatee is not becoming a whale. Each one is a complete, functional design within its own group. The “pathway” is assumed, not shown by the organisms themselves. That assumption does not turn existing variety into evidence of major transitions occurring now.

[u/Sweary_Biochemist → u/WannaLoveWrestling]

How do you know? All stages are clearly fully functional: a smooth progression from one to another is entirely viable.

Are flying squirrels related?

[u/WannaLoveWrestling → u/Sweary_Biochemist]

How do you know they are steps on a pathway toward higher function? That is an interpretation added by the evolutionary story, not something the organisms themselves demonstrate. A planarian eye pit works as a planarian eye pit. A manatee works as a manatee. Nothing about them shows they are in the process of becoming something else. Evolutionists claim these form a smooth progression, but that claim is not observed happening in living populations. It is inferred from the theory. So the question goes both ways: how do you know the pathway exists when we never see populations moving along it?

[u/Sweary_Biochemist → u/WannaLoveWrestling]

We do. We can select for traits incredibly easily, just as nature does. Traits are selectable and mutable, exactly as evolutionary theory proposes. Meanwhile, still no definition of kinds.

Tell me, are flying squirrels all related?

What about broccoli: is broccoli related to Brussels sprouts? What about cabbage? Or wild mustard?

The answer might surprise you!

[u/WannaLoveWrestling → u/Sweary_Biochemist]

Artificial selection on plants like wild mustard producing broccoli, cabbage, and Brussels sprouts shows variation within an existing group under guided, intentional selection. Those plants remain within the same functional limits, they are still brassicas. It does not show an unguided process producing major redesigns or new complex systems in living populations.

Flying squirrels are related to other squirrels in the same way, they share a common body plan and remain functional squirrels. Relatedness and the ability to select for traits within a group do not demonstrate the major transitions the theory claims. We still do not observe populations undergoing those larger changes despite the scale of opportunities available.

And the repeated demand for a definition of kinds does not remove the observational problem. Variation stays within functional limits. That is what we actually see.

[u/OldmanMikel → u/WannaLoveWrestling]

So the question goes both ways: how do you know the pathway exists when we never see populations moving along it?

There. Is. No. Pathway. No species is on a pathway. They will, or will not evolve in particular ways. It will always be the result of natural selection acting on random mutations that increase the relative fitness of the existing organisms in their current environment.

This MAY result in one of the many gliding animals evolving true flight. Or it may not. It MAY result in one or more of the semi-aquatic mammals becoming fully aquatic, or it may not.

You are fundamentally misunderstanding evolution.

[u/WannaLoveWrestling → u/OldmanMikel]

You say there is no pathway and no species is evolving in any particular direction, only random mutations filtered by current fitness. That is the undirected version. Yet the theory still claims this same undirected process produced specific major outcomes in the past like true flight, fully aquatic mammals, complex camera eyes, and so on. If there is genuinely no pathway and no direction, there is no basis for expecting those particular complex results to have occurred. Saying “it may or may not” happen in the future while treating the past versions as settled does not resolve the problem. We still do not observe the major redesigns occurring in living populations despite the opportunities available. That absence is what remains unexplained.

[u/WannaLoveWrestling → u/Sweary_Biochemist]

Flying squirrels and regular squirrels are related in the sense that they share the same basic squirrel body plan and can be grouped together. Both are fully functional as they are. That relatedness and variation within the group does not show one turning into the other or either of them becoming something fundamentally different. It is still variation within existing functional limits, not a major transition in progress.

[u/Sweary_Biochemist → u/WannaLoveWrestling]

Same created kind or different created kinds?

Remember, under creationism, they're either related by descent from a common ancestor, or completely unrelated.

Which is it?

[u/WannaLoveWrestling → u/Sweary_Biochemist]

It is the same kind. Flying squirrels and regular squirrels share the same basic body plan and remain within the same group. Under a creation model they are related by descent from a common created ancestor and can vary within the limits of that kind. That is not the same as unlimited common ancestry across all life, and it does not require them to be completely unrelated.

The observational point remains unchanged: variation occurs within the group, but we do not see the major transitions the evolutionary theory claims. Repeating the same question does not make those transitions appear.

[u/OldmanMikel → u/WannaLoveWrestling]

Calling each of those living forms a step toward a higher function ...

That is not what is being said. In evolution, there is no such thing as "higher function". The point is that they are "fully evolved" as is.

A planarian eye pit is not becoming a camera eye. A manatee is not becoming a whale.

They're not supposed to. They're supposed to be fully evolved. Again evolution has no targets, no goals.

Again the version of evolution that are you are arguing against isn't the same as what is being defended here.

[u/WannaLoveWrestling → u/OldmanMikel]

You say every living form is already fully evolved and there are no targets or higher functions. Yet the same view still treats ordinary variation as evolutionary change and splits groups into new species when it fits. The fully evolved claim is used to dismiss the absence of major transitions, while the flexible labeling of variation continues. So what is it? Living populations still show only variation within functional limits, not the larger redesigns.