To be fair, it looks like Buium's drawing is only a crown assemblage, while the quanta map (sold as "absurdly ambitious") does seem to have a problem with omissions near the root node. Penrose's road to reality is not a map per se, but does have something geographic about it. Chapter three discusses numbers, sets, and functions on equal footing. I agree that a Last Universal Common Ancestor to our scientific ideas (if such a thing could even exist) would need to have some mixture of these three concepts in its makeup. Wikipedia claims that functions were not invented until the XII or XVII century; however, this is nonsense. Evolution itself is a recursive function, as is the human thought process, and even antiquity's geometric tools are essentially functional. So the following article gets my nomination for "worst of Wikipedia": https://en.wikipedia.org/wiki/History_of_the_function_concept Cheers, Brad On Fri, Feb 14, 2020 at 6:58 PM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Neither attempt makes any mention of Logic & Foundations, which are arguably more fundamental than (say) Numbers: it is difficult to imagine how any activity justifying the label `Mathematics' can take place lacking the prerequisite of some capacity for logical inference. WFL
On 2/14/20, Brad Klee <bradklee@gmail.com> wrote:
See: https://www.quantamagazine.org/the-map-of-mathematics-20200213/
It's no surprise that scientists would eventually get to the idea of making a map of scientific ideas. Such a task could be useful for orienteering, and possibly an opportunity to explore Hofstadter-esque quine-making.
Such creations can eventually be seen as most indicative of the psychology particular to the cartographer or cartographers. Often times you will get some sort of phylogenetic tree structure, which needs to be amended with extra connections. The necessity of amendments seems to be the only common feature between the various tree models, and this underscores the empirical fact that mathematical ideas tend to converge as often as they diverge (ideas are not ultimately constrained by sexual or genetic reproduction).
Alexandru Buium did not make the same mistake with definite / indefinite articles when producing "a map of mathematics", see also:
https://math.unm.edu/~buium/mapp.pdf
These are both interesting takes, but not entirely similar to the map that I would probably prefer, because time is not included as a variable of the branching process.
Is there any reason for "Function Phylogeny"? And what is the best way to limit subjectivity? Any thoughts in general?
--Brad
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