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I am trying to convince a friend that human beings evolved from primates, and he challenged me that advanced mathematical ability couldn't have been the product of mutation and natural selection because this ability wouldn't have conferred any reproductive advantage until the last few hundred years, and the process of mutation and natural selection would have taken much longer than this to produce the extensive genetic basis of advanced mathematical ability. How do we refute this?

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  • $\begingroup$ What is his definition of advanced mathematical ability? $\endgroup$
    – have fun
    Commented Sep 21, 2017 at 9:37
  • $\begingroup$ I think, advanced mathematical ability is more an effect of the social evolution, that is a consequence of the brain evolution anyway. $\endgroup$
    – alec_djinn
    Commented Sep 21, 2017 at 10:17
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    $\begingroup$ Your friend is incorrectly assuming that all evolutionary developments directly contribute to the organisms success. Also, the burden of proof should [initially] be on your friend, and not you, for him/her to establish that "advanced mathematical ability" is even a relevant criteria to determine the plausibility of evolutionary behaviors to begin with. Lastly, as your friend mentioned, and which argues against their own case, is that mathematics is new, which could then very easily suggest that it's a recent emergent property of logic & reasoning, of which primates do [seem to] have. $\endgroup$
    – user22020
    Commented Sep 21, 2017 at 13:40
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    $\begingroup$ Your question may be valid, but give up on thinking that you will convince your friend of anything. Believe me, it's a waste of time. In cases like this people believe what they want to believe — rationality or logic doesn't come in to it. $\endgroup$
    – David
    Commented Sep 21, 2017 at 17:03
  • $\begingroup$ @David How come you voted to close if you think the question is valid? $\endgroup$
    – Remi.b
    Commented Sep 22, 2017 at 22:16

4 Answers 4

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Just to avoid misunderstandings

Just to avoid potential misunderstandings on your side, I wanted to talk about the saying that

human [are] evolved from primates

  • Humans are primates, so did our common ancestor with other primates.
  • Our ancestors are different from modern day primates. Chimps for example (which are great apes, like us) are not our ancestor more than we are their ancestors. We just share a common ancestor (who lived about 13 millions years ago).

Spandrel, exaptation and panselectionist arguments

Your are doing two mistakes. 1) The mistake of the spandrel (named after the title of the famous and old paper Gould and Lewontin (1979)) and the exaptation and 2) a panselectionist mistake.

1. Spandrel and exaptation

Spandrel

In evolutionary biology, a spandrel is a phenotypic characteristic that is a byproduct of the evolution of some other characteristic, rather than a direct product of adaptive selection

See also What is the “Spandrels” debate about?.

Exaptation

Exaptation [..] describe[s] a shift in the function of a trait during evolution.

While the existence of a spandrel in an evolutionary process does not necessarily cause the existence of an exaptation, but I will not go into these semantics details for simplicity.

Consider for example the two following wrong statements.

  • Birds have feathers to fly. It is impossible that birds evolved feather to fly because early feathers would have served no purpose to flight.

Bird feather actually probably first evolved for temperature regulation. Once this was done feathers were an exaptation for early flying tools.

  • Humans have nose to wear glasses. It is impossible that nose would have evolved because there was no glasses before

Noses evolved for another purpose and happen to be an exaptation for wearing glasses.

  • Humans have a big brain for advanced mathematical skills. It is impossible that humans evolved such big brains as such mathematical skills were useless in a time where we did not invent/discover much of the most basic math concept yet.

Humans evolved a big brain, mainly for social reasons incl. social hunting and social communication and probably because it was/is under sexual selection (see wikipedia > evolution of human intelligence). It just happen that logical reasoning, abstract thinking and other cognitive skills are an exaptation for advanced math skills.

2. Panselectionist view of evolution

I just want to highlight that there is much more to evolution than just mutations and natural selection. Not every trait has been selected for (otherwise we would not have any genetic disease).

On this subject, you might want to have a look at the paragraph Did you say Natural Selection? of this answer to Why don't mammals have more than 4 limbs? and to Why do some bad traits evolve, and good ones don't?

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There is no such thing as "advanced mathematical ability" as a separate ability of the human brain. Advanced mathematical ability is formed by aspects of the general human intelligence. Given that not everyone is able to do advanced maths, it's a moniker for the high end of these aspects of human intelligence.

I can't give you a perfect description of all the aspects of human intelligence that are important for "advanced mathematical ability", but maybe a few examples will suffice:

  • The ability to abstract.
  • Reasoning by analogy.
  • Logical reasoning.
  • Spatial or geometric imagination.

All these abilities are pretty obviously useful, even in our far evolutionary past. Especially the first two abilities underly pretty much all our thinking.

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Why did humans become increasingly intelligent long past what they needed to hunt prey? A large part of it is the intelligence needed to outfox other humans without being manipulated themselves. After language developed, we were our own greatest selective pressure. Indeed, no matter how smart we became because of this mechanism, it would continue to select for greater intelligence still to out-think the brains of the present. Going back to the spandrel point, the reasoning in mathematics may be a side-effect of this.

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Thanks to B for posting this question -- I asked him to post it to biology.stackexchange, so that our interaction might be useful to others. My answer is a quickly-typed email but might be useful anyway.

My answer follows:

Hi B -- briefly, advanced mathematical ability WASN'T the product of mutation and natural selection. Neither was writing, poetry, symphonic music, representative democracy, genius comedy, etc. etc. yadda yadda.

All of these cultural achievements are the product of a very long line of causes, very roughly,

A. general human physical and mental traits

B. hundreds of thousands of years of co-evolution of human brains, societies, and fundamental human technologies like the making of spearpoints, fishing hooks, clothes, rock art, etc. in stone-age, hunter-gatherer societies

C. farming and subsequent large, high-densities human societies

D. writing

E. well-organized governments, nation-states, and subsequent "space" for "high arts" (science, math, opera, whatever)

F. substantial economic and technological progress (better ship-building, international trade, the Mediterranean mercantile revolution before/during the Renaissance)

G. A long history of cultural development within each of the specialities in (E). Each of these began seriously building and expanding, generation on generation. E.g. for math specifically, we only really got going seriously with the introduction of Arabic numerals, the idea of the numeral "0", etc., into the context of the European economic and academic structure, and their linkage to the general Scientific Revolution (e.g. the massive success of Kepler, Galileo, Newton etc. in applying math to physics and astronomy)

H. A concurrent massive expansion of organized, formalized educational system, ranging from childhood education through to university and postgraduate education

I. Massive growth in the human population, and generation of a huge leisure class, creating a relatively large number of people that can do advanced math. Most of us still can't!

I suspect that advanced mathematical ability is roughly on a bell-curve. Most of us have the aptitude/ability/focus to do things like counting, which would have been useful even in stone-age times, and which clearly exist even in animals. It is relevant to know that you have better odds getting by 1 lion, instead of 10 lions.

The rest of the explanation of math ability is mostly due to the cultural factors above, which, through massive training (20 years plus for advanced math), take human's general counting abilities, language ability, good memory, etc., and produce mathematicians ranging from OK (like me) through to amazing (Einstein or someone).

Natural selection only has a role in explaining A and B. The rest is culture, which (very slowly) built on humans' general intelligence, language ability, sociality, etc.

Repeat this explanation for any other remarkable cultural achievement.

And, anyone else wondering about evolution and some major cultural achievement, should ask themselves the following:

  1. Can I myself produce a similar cultural achievement in the same area? Is everyone as good as Mozart and Einstein were in their specialties? If not, why not?

  2. For humans, language is easy, but any non-trivial math is hard. But for computers, math is easy and language is hard. Why is that? Hmm, which one was useful back in the Stone Age?

  3. Similar question: Why is math hard for most people? Why is producing new advances in math basically always hard, even for extreme experts?

Cheers! Nick Matzke nick.matzkeATanu.edu.au

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