I must apologize...Whenever I'm engaged in preparing a manuscript I become completely absorbed in it and tend to become "over-empassioned." So I'd like to put forth a more sober analysis here. The question of why did we develop math is as principal a question as why do we know we exist in the first place. So I think it's an important one. These neuroscience questions of the hard problem and the easy problem of consciousness I think are splitting hairs. You can't separate the qualitative experience of being conscious from the "contents" of consciousness such as looking at the world through a mathematical lens. I think the OP makes a good point about this. You have to do a little reading through the lines in his posts, but what I distill from his argument is that there is this mysterious "thing" called mathematical cognition that is deeply infused in our perception of the world and how we interact and survive in it. Where did this come from and why does this seem to be a (mostly) distinctive human trait?
That's a legitimate question. And we do have some clues that can lead us to answer this question. The principal clue is that it can be instructive
not to look as mathematical ability as a separate "module" of brain function distinct from all the other putatively distinct human capacities. The curious thing about distinctly human abilities is that they pretty much, across the board, are distinguished by the model that they are hierarchically organized sequential structures. This is as true for math, spoken language, and musical ability, three principle features that seem to distinguish humans from the rest of the animal kingdom.
In W.W. Sawyer's popular book, "Mathemetician's Delight," he starts off every chapter with a quote. In one of the chapters later in the book, the quote is "Mathematics is a language." And so it is.
Karen Schrock wrote a nice article called "Why music moves us" which compellingly argues for an organic link between music and language. I think it's behind a paywall though, sorry..
http://www.scientificamerican.com/article/why-music-moves-us/
There are, of course many more staid scholarly articles and book chapters devoted to this connection, but, the conclusion I think we may be able to glean here is that there may be some general language-related mechanism that somehow was birthed into the human brain, and perhaps this is what defines humanity and can answer these deep existential questions such as why can we differentiate a function, why can we play a pentatonic scale, and why
can't we talk to the animals?
Hornbein said:
Noam Chomsky observes that all peoples can learn math, whether or not their ancestors used it. So this ability is not he result of evolution. He thinks that it is simply a variation on the innate ability to learn a language.
Yes, I think he famously coined this the uniquely human "language acquisition device."
https://en.wikipedia.org/wiki/Language_acquisition_device
I first came across this idea, I think, in his
precis of his book "Rules and representations" in the Journal Brain and Behavioral Sciences in the 80's.
http://journals.cambridge.org/actio...e=online&aid=6468760&fileId=S0140525X00001515
I completely agree with his argument other than the perhaps not so explicitly stated subtext that the language acquisition device is some sort of modular addition to the human brain, perhaps the equivalent of upgrading your computer's graphics card from the Geforce 8600gts to the new 970GTX with the 1664 CUDA cores? Sounds like a good first approximation, but it doesn't hold up under more detailed analysis. So these are a few of the things that keep me up at night as I'm preparing this new manuscript.
To make a short story, long, then, the model I have developed is essentially in the spirit of Chomsky's, BUT, I envision a radical reordering of the brain on essentially every level. In the isocortex, though, subcortical systems essentially remain conserved with the partial exception of "top-down" (cortex to subcortex) modifications.
As I said in an earlier post in this thread, What I'm using to defend my hypothesis in this recent paper is largely the wide spate of recent genetic data that has accumulated over the part decade related most specifically to the human genome project. Also, I'm using a good deal of archaeological evidence that also seems to be progressing nicely lately.
The crux of the argument is that the adaptive evolution of genes such as ASPM created what we might call a language acquisition device in humans, but not in the same way Chomsky envisioned it. This was a "graduated continuum" process that occurred over millions of years of hominin evolution. It occurred in stages. Nothing "continuous" is going on here. These discrete "jumps" in the evolution of human somatic traits again occurred through the adaptive evolution of microcephlay related genes such as ASPM. There's implications all along the line, from the production of hand-axes to the taming of fire to the descent of the larynx and others. But the most recent significant jump occurred about 6000 years ago, which is what gave us the ability to do math and talk. I'm thinking it was a modification of the ASPM gene:
From:
http://www.ncbi.nlm.nih.gov/pubmed/16151010
"Here, we show that one genetic variant of ASPM in humans arose merely about 5800 years ago and has since swept to high frequency under strong positive selection."
But again, I'm just giving my opinion here to address the OP's question, not trying to advance any personal model
