Mathematics is human thinking, we are smart to have mastered SOME of it (not all, as the progression of math shows).
John M John one question that comes to mind then is: if math is the cultural accumulated product of human thought over the arc of the history of recorded culture, then what about all the mathematical and geometric patterns that appear and reappear in nature quite apart from any human cultural input. For example how ratios such as the golden ratio (e.g. 1·618034 approximately), or the Fibonacci series manifest in things as diverse as conch shells to the spiral arms of [spiral] galaxies. And in geometry the ratio of a radius to a circumference has been very closely approximated by human cultural achievement, but this ratio certainly is not a human cultural invention… is it? There exists a large number of such ratios in geometry, math and in nature itself. Certainly these precisely defined relationships existed before there were hominids on this planet… in fact can you even conceive of a time or universe where these basic mathematical ratios do not hold true? Perhaps you can, but it would be a bizarre universe utterly unlike the one in which we inhabit. Even the most basic stuff… say the concept of the set. Is this just a human cultural invention? Certainly on one level it is, we have developed a theory of sets and incorporate and manipulate sets at so many levels of human activity, but does this fact of our cultural discovery of set theory and wide employ of the techniques and structures it provides us with translate into the much more fundamental claim that set theory itself only exists in so far as humans have invented it. Would not some alien culture (biological or with some artificial substrate) come discover the same set theory as we have? If not… then why? I am arguing that there is something fundamental about an abstract something such as a set… even an empty set. The kinds of operations the manner in which it selectively includes “likes” while excluding “unlikes”. What about fractals? Purely a human artifact? Then explain how fractals show up all over nature from ferns to snowflakes? And… the infinite set of countable natural numbers [e.g. 1, 2, 3… N]? Is this purely a human cultural invention with no independent existence outside of human culture? As you can see from my questions… If that is I understood your position of course <grin>… I think that there is strong evidence for many kinds of mathematically precise relationships in nature, that many quite clear patterns exist and repeat across many scales and domains in the natural universe (outside of human culture). It seems to me that math is better defined as our accumulated human cultural achievement in understanding basic fundamental laws and patterns of the universe we inhabit. It is our human cultural discovery of something a lot deeper and vaster than what can possibly be contained in the meager store of our species accumulated musings over the last handful of millennia. Cheers, Chris -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
