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Wednesday, August 31, 2016

Evolution of mathematics traced using unusually comprehensive genealogy database


Most of the world’s mathematicians fall into just 24 scientific 'families', one of which dates back to the fifteenth century. The insight comes from an analysis of the Mathematics Genealogy Project (MGP), which aims to connect all mathematicians, living and dead, into family trees on the basis of teacher–pupil lineages, in particular who an individual's doctoral adviser was.
“You can see how mathematics has evolved in time,” says Floriana Gargiulo, who studies networks dynamics at the University of Namur, Belgium and who led the analysis.
This result just tickles our fancy a bit.
Our belief here is that 'the mathematical sense" is primary in our brain's functioning (prior to logic and language and indeed, as a key component of what we now know as the Salience Newtork and its operation...without which the Salience Network would be inept and/or inadequate.
And, of course, in tandem with that belief we consider that evolution must show that this particular aspect of our brains has emerged as a key factor in the rest of our culture and society's taking shape.
The fundamental area of the brain in which we now have considerable interest is the Intra Parietal Sulcus...and it is that area where all "numerical sense" is centered, not only numbers, but geometry and space and all comparisons of relative magnitude, whether greater or less, brighter or dimmer, louder or more quiet, sooner or later, faster or slower, friendlier or less friendly...and so on...more or less in every way, incluiding how simnilar or not to a past experience to merit a "novelty" response or a danger response or to simply ignore.... is centered there.
http://www.jneurosci.org/content/28/46/11819.short
We can speak about these matters in ordinary language, and say that what we encounter may be somewhere 'along a spectrum", or in a "dimension" or part of a "space" but that is only possible because the sense of number allows us to take experiences and consolidate them within our brains along such a dimension, spectrum or space.
We now recognize the incredible importance of the Salience Network. Organisms must have a way of distinguishing situations in such a manner that what is 'salient" is noticed and attended to and dealt with. But how does an organism realize which moment of experience presents it with salience. Of course, absolute danger is salient and that is recognizable.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2899886/
But the key in most life situations that result in adaptation and learning and intelligent responses that develop is to understand "novelty' as it is called nowadays...but which tells us when two experiences are different enough to be salient and thus to warrant adjustment and action on our part.
Without the role played by the Intra Parietal Sulcus the immediately surrounding areas..how would "comparisons" be made. Does an organism actually bring to awareness two experiences, two representations or one of each and then do some sort of inventory of features side by side and then make decisions after such a stepwise item by item comparison.
There must be some better way to achieve those "comparisons". That better way evolves to become "measuring" and to conceiving of things experience along spectra of comparison.
https://www.edge.org/…/stanislas_dehaene-what-are-numbers-r…
And thus the Salience Network would not be able to function without this IPS being a kernel aspect of its function and all the resultant connectivity in the brain.
This particular genealogical study revealed 84 distinct family trees with two-thirds of the world’s mathematicians concentrated in just 24 of them. The high degree of clustering arises in part because the algorithms assigned each mathematician just one academic parent: when an individual had more than one adviser, they were assigned the one with the bigger network.
But the phenomenon chimes with anecdotal reports from those who research their own mathematical ancestry, says MGP director Mitchel Keller, a mathematician at Washington and Lee University in Lexington, Virginia. “Most of them run into Euler, or Gauss or some other big name,” he says
http://www.nature.com/…/majority-of-mathematicians-hail-fro…