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
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