Mathematics as the result of natural selection

[Evgenii Rudnyi]

"In the past decades, recent paradigm shifts in ethology, psychology,
and the social sciences have given rise to various new disciplines like
cognitive ethology and evolutionary psychology. These disciplines use
concepts and theories of evolutionary biology to understand and explain
the design, function and origin of the brain. I shall argue that there
are several good reasons why this approach could also apply to human
mathematical abilities. I will review evidence from various disciplines
(cognitive ethology, cognitive psychology, cognitive archaeology and
neuropsychology) that suggests that the human capacity for mathematics
is a category-specific domain of knowledge, hard-wired in the brain,
which can be explained as the result of natural selection."

Helen De Cruz. Towards a Darwinian approach to mathematics. Foundations
of science 11, no. 1-2 (2006): 157-196.
https://www.researchgate.net/publication/226764172_Towards_a_Darwinian_Approach_to_Mathematics

[Lawrence Crowell]

There are various animals with numerical and geometrical skills. Curiously some birds such as crows and parrots are very skilled. Dogs have considerable social skills and language comprehension, as I know from being a long term dog lover and owning 3, but they have almost no numerical and spatial reasoning. Some animals appear to have had some natural selection for numerical and spatial reasoning. We humans with our frontal vision, hands and motor skill have a well developed ability. Our abilities outstrip the original selection mechanism or need. There seems to be no evolutionary advantage to knowing algebraic topology.

LC

[Russell Standish]

On Sun, Jun 17, 2018 at 03:41:12PM -0700, Lawrence Crowell wrote:
> There are various animals with numerical and geometrical skills. Curiously
> some birds such as crows and parrots are very skilled. Dogs have
> considerable social skills and language comprehension, as I know from
> being a long term dog lover and owning 3, but they have almost no numerical
> and spatial reasoning. Some animals appear to have had some natural
> selection for numerical and spatial reasoning. We humans with our frontal
> vision, hands and motor skill have a well developed ability. Our abilities
> outstrip the original selection mechanism or need. There seems to be no
> evolutionary advantage to knowing algebraic topology.
>

There's considerable evolutionary advantage, just not enough time yet
for evolution to have acted :).

But presumably the argument is about certain cognitive skills which
helped our species be extraordinarily successful, and also gave us the
capability to understand algebraic topology.


--

----------------------------------------------------------------------------
Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow hpc...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au
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[Steven Ridgway]

On Mon, Jun 18, 2018 at 01:25 Dr Russell Standish wrote:
> "But presumably the argument is about certain cognitive skills which helped our species be extraordinarily successful, and also gave us the capability to understand algebraic topology."

I've always found it a bit mysterious that humans are so good at abstract mathematics. I can see that the evolutionary pressures to improve tool making and hunting skills could have given us basic mathematical capabilities - but we are far better at it than seems reasonable. i.e. it seems a stretch to imagine our ability to understand differential equations and prove Fermat's last theorem just fell into place as an accidental by product of something else.

It seems to me that a lot of complex engineering in our brains must exist to support the level of abstract reasoning we are capable of - and I don't see much evolutionary advantage to explain how this evolved.

We are familiar with the idea that a large multiverse could explain the apparent fine tuning of our universe to support conscious observers. I.e. given we are conscious observers it shouldn't be surprising that we find ourselves in a part of the multiverse that allows our existence.

However, right now we aren't just conscious observers, we are conscious observers pondering the unreasonable effectiveness of brains to do mathematics. Maybe similarly to the fine tuning argument we shouldn't be surprised to find ourselves in a part of the multiverse where brains did develop mathematical ability. It would have been extremely unlikely for our brains to have evolved the way they did - but in a sufficiently large multiverse we will inevitably find ourselves in the place where it did - given that we are observer moments that must have exactly that kind of abstract reasoning capability to understand this point!

Is it valid to use this kind of reasoning? To use the details of the type of conscious experience we are having right now to condition the type of universe we expect to find ourselves in? I'm not sure to be honest - but I think there is a mystery to be explained so the idea is appealing.

Note if it's true that evolving mathematical capability was a long shot, then a consequence of it would be that it would be very unlikely that we find technologically advanced aliens in the observable universe. There are a lot of stars out there - but the small probability of brains evolving abstract reasoning would overwhelm that I suspect.

- Steven Ridgway

--

----------------------------------------------------------------------------
Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow hpc...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au
----------------------------------------------------------------------------

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[Jason Resch]

I think a lot of our abstract reasoning ability results from our being social creatures, and having to create mental models of other people/groups/tribes, etc. to predict their behaviors under different scenarios. To guess what they want, what they will do, what is likely to happen if this happens or if that happens.  In our evolutionary environment, nothing was more complex than other humans or groups of humans, and the smarter we became, the smarter we had to get to maintain some ability to model and predict the behavior of others.

It is then, perhaps not too major of a leap to turn this "abstract modeling of a systems behavior" ability from analyzing people or groups, to analyzing other systems, be they games, puzzles, engineering, mathematical objects, contemplating physical laws, etc.

A question might arise, why don't other social animals have similar abstract reasoning abilities?  Perhaps they do and cannot communicate it, or perhaps communication itself adds so many additional layers of complexity to the analyzing of social systems and people that it required the evolution of special purpose structures in the brain which enhanced abstract reasoning abilities.  Still a third option, is that human analytical capability largely relies on the high level of language processing capacity of the brain as a necessary ingredient in performing some forms of abstract reasoning. -- I think there are exceptions and counter examples in many of these cases, for example Tesla could visually manipulate designs in his mind, and high level Chess players can see and manipulate board states in their minds without relying on language to represent those states.

Jason

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[Brent Meeker]

On 6/18/2018 4:44 AM, Steven Ridgway wrote:
> On Mon, Jun 18, 2018 at 01:25 Dr Russell Standish wrote:
> > "But presumably the argument is about certain cognitive skills which helped our species be extraordinarily successful, and also gave us the capability to understand algebraic topology."
>
> I've always found it a bit mysterious that humans are so good at abstract mathematics. I can see that the evolutionary pressures to improve tool making and hunting skills could have given us basic mathematical capabilities - but we are far better at it than seems reasonable. i.e. it seems a stretch to imagine our ability to understand differential equations and prove Fermat's last theorem just fell into place as an accidental by product of something else.
>
> It seems to me that a lot of complex engineering in our brains must exist to support the level of abstract reasoning we are capable of - and I don't see much evolutionary advantage to explain how this evolved.

It's not that abstract mathematics provides an evolutionary advantage
(just look at the reproduction rate of mathematicians). But making
persuasive arguments very much does, and logical inference is important
in persuasive argument.

Brent

[scerir]

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[scerir]

> Il 18 giugno 2018 alle 2.24 Russell Standish <li...@hpcoders.com.au> ha scritto:

> There's considerable evolutionary advantage, just not enough time yet
> for evolution to have acted :).

For some reason this reminds me of a quote: "It is because we have blindly excluded the lessons of these regular bodies from the domain of human knowledge that we are still in doubt about the great doctrine that the only laws of matter are those which our minds must fabricate, and the only laws of mind are fabricated for it by matter". -James Clerck Maxwell, "Analogies in Nature", Feb. 1856, (The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862).

I'm inclined to think there is something deeper at work here, deeper than the evolution based on the survival of the fittest (are mathematicians fittest?). I'm inclined to think there is a smooth transition from matter to form or - to say it better - to information (and mathematics may be a sort of *objective* *testable* information theory about possible worlds, relations, laws of nature, objects). Hylo-morphism.

[Bruno Marchal]

I will take a look (I have to go.). Looks interesting. Note that with mechanism, all of math and physics arises from arithmetic in a sort of Darwinian way.

I doubt you could explain arithmetic itself “Darwinianly", as Darwin has to assume at least the very elementary arithmetic, and it can be proved not to be derivable by anything simpler.

Bruno

[Brent Meeker]

But do they represent them realistically, or schematically?  I think
language had a lot to do with the evolution of abstract thinking. It's
very hard to think of something like a battle plan either in full 4d
realism or in language, but it is possible visualizing things
schematically and the first abstract mathematics, geometry was a matter
of graphic abstraction plus reasoning in words.

Brent

[Brent Meeker]

On 6/18/2018 11:51 PM, 'scerir' via Everything List wrote:
>> Il 18 giugno 2018 alle 2.24 Russell Standish <li...@hpcoders.com.au> ha scritto:
>> There's considerable evolutionary advantage, just not enough time yet
>> for evolution to have acted :).
> For some reason this reminds me of a quote: "It is because we have blindly excluded the lessons of these regular bodies from the domain of human knowledge that we are still in doubt about the great doctrine that the only laws of matter are those which our minds must fabricate, and the only laws of mind are fabricated for it by matter". -James Clerck Maxwell, "Analogies in Nature", Feb. 1856, (The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862).
>
> I'm inclined to think there is something deeper at work here, deeper than the evolution based on the survival of the fittest (are mathematicians fittest?).

Not survival of the fittest, but survival of those who reproduce (which
leaves out a lot of mathematicians).  Reasoning and what used to be
taught at rhetoric, is part of the art of persuasion.  Master it and be
a leader of men and a seducer of women.

Brent

[Russell Standish]

There was a slight misinterpretation of my original statement, not
deliberate I'm sure.

I was alluding to a group selection effect - that a society or species
that includes practising mathematicians will outcompete one that
doesn't. It's not to say that the mathematicians themselves are
evolutionarily fit individuals - as has been pointed out, the evidence
weighs against this.

A similar argument is made for the continuing presence of
homosexuality - there is a group selection effect (probably kin
selection) that helps maintain homosexuality as a small percentage of
the population, even if the individuals are much less likely to reproduce.

[Brent Meeker]

On 6/19/2018 6:11 PM, Russell Standish wrote:
> On Mon, Jun 18, 2018 at 10:50:05PM -0700, Brent Meeker wrote:
>>
>> On 6/18/2018 4:44 AM, Steven Ridgway wrote:
>>> On Mon, Jun 18, 2018 at 01:25 Dr Russell Standish wrote:
>>> > "But presumably the argument is about certain cognitive skills which helped our species be extraordinarily successful, and also gave us the capability to understand algebraic topology."
>>>
>>> I've always found it a bit mysterious that humans are so good at abstract mathematics. I can see that the evolutionary pressures to improve tool making and hunting skills could have given us basic mathematical capabilities - but we are far better at it than seems reasonable. i.e. it seems a stretch to imagine our ability to understand differential equations and prove Fermat's last theorem just fell into place as an accidental by product of something else.
>>>
>>> It seems to me that a lot of complex engineering in our brains must exist to support the level of abstract reasoning we are capable of - and I don't see much evolutionary advantage to explain how this evolved.
>> It's not that abstract mathematics provides an evolutionary advantage (just
>> look at the reproduction rate of mathematicians). But making persuasive
>> arguments very much does, and logical inference is important in persuasive
>> argument.
>
> There was a slight misinterpretation of my original statement, not
> deliberate I'm sure.
>
> I was alluding to a group selection effect - that a society or species
> that includes practising mathematicians will outcompete one that
> doesn't. It's not to say that the mathematicians themselves are
> evolutionarily fit individuals - as has been pointed out, the evidence
> weighs against this.

But that seems as hard to make specific as the personal advantage to the
neolithic caveman.  How would this work exactly?  I think the answer is
in cultural evolution.  A society with practising mathematicians might
have had little or no advantage in 600BC...did the Greeks defeat the
Romans?  But by the time of sailing ships and navigation it might have
made a significant difference.  I think the ability of social
circumstances to drive biological evolution is underestimated.  Look at
what we did to dogs in only a thousand generations or so.

Brent