Consilience and Cognitive Science

In a recent essay, the polymath philosopher Ian Hacking, as the first and most fundamental of his list of “applications” of mathematics, puts “App 0:  Math Applied to Math”.

Why should there be so much ultimate connectedness …?  If we follow the cognitive scientists who think that there are distinct mental modules for arithmetical reasoning and for spacial reasoning, Descartes’ Geometry of 1637 is all the more astonishing.  This question needs a lot of philosophical work, right now.

-- Ian Hacking, “Why is there Philosophy of Mathematics at All?”, repr. in Mircea Pitici, ed., The Best Writing on Mathematics 2012, p. 248

Well, here’s a tidbit towards that.

Hacking is right, that the Idols of the Neuroscientists make the success of Descartes’ breakthrough the more astonishing, as indeed they do any of the insights of mathematicians.  But that simply redounds to the discredit of the Neuroscientists.

Hacking happens to have chosen an instance of Consilience that neatly matches two pre-posited “modules” of the CogSci crowd.  (Such “modules” can be had for the asking, according to fancy;  there is no net, in that tennis-game.  -- Table-tennis, rather.  -- Right now, my “Stuff and Nonsense!” module is blinking red.)   But they would be rather more hard-pressed to come up with a separate “point-set topology module”, “abelian group theory module”, “number-theory module”, “operator theory modules”, “ring theory module”,  ET cetera ET cetera, to attempt to account all the sundry other intersubdisciplinary interilluminations which keep arising within mathematical practice -- deep connections among concepts that never fell within human ken, back when our geometry module, in collaboration with the arithmetical module, was calculating the angle and distance to the rampaging mastodon, yet which now yield such fruits as the beans Jack received in barter for a cow.

Perhaps the explanation lies well apart from the contingent biochemicalisms of the grey-matter blancmange in our brainpan, modular or otherwise.   Mayhap there is an actual unity -- a unity in variety, which we do but discover --

in bits and glimpses,

in pieces and snatches,

by dint of much study,

and by grace of Grace.

~

We are making a New Year’s Resolution, not to be so darned snarky.  (Having successfully shed nearly twenty pounds this past calendar year, we are ready to take on even greater challenges.)

Accordingly, so as to redeem our good standing among our Cognitive Scientist brethren (with whom we used to rub elbow-patches daily, back at UC Berkeley, in the permanent “temporary building” T-2), we herewith offer an extra-virgin olive branch:   preliminary results from a massive structural-neuro-longitudinal study undertaking by the Pataphysical Department of the World of Dr Justice (headquarters:  Geneva), abundantly funded by the grateful taxpayer.  With this we obtain direct insights into the child’s developing mind.   As our investigations prove, this comes pre-compartmented into the following empirically buttressed cubby-holes:

(1)  The “Everything is What it is and Not  Another Thing” foodstuff module.

The vegetables are bad enough, but when they touch the mashed potatoes -- Eeewwww.

(2)  The “Mine and Thine” module.

Though discernable in outline already in the early embryo, this module does not become activated until much later in development;  and in some specimens (B. Madoff, D. Trump) never.

Prior to activation -- much like the notocord that serves the embryo until the spinal column takes its place -- behavior is governed by the following, non-modular (“opportunist”) pragmatic maxim:

     “My bear.  My toy.  Mine.”

(3)  The “Girls Have Cooties” module.

For reasons not yet well understood, this module is activated only in immature males;  some genetic link to the Y chromosome is suspeced.  In any event, it is normally de-activated at puberty.