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Re: Who is the greatest published mathematician in history? If you were asked..
Posted:
Apr 7, 2012 11:00 AM


On Fri, Apr 6, 2012 at 6:50 PM, Joe Niederberger <niederberger@comcast.net> wrote: > The hippo story was first quoted (via Wikipedia) by Haim  I was just rerereiterating. It took me awhile but I then realized it was a clever play on youstwos Neocon showdown. > > I would need a course to understand Wittgenstein. He probably has many interesting things to say about language. >
We know the idiom "elephant in the room no one talks about". One could see Wittgenstein asking his students "is there an elephant in the room?" The answer might be ambiguous, given the number of taboo subjects one'd rather not raise.
> As far as math goes, my sense is not many mathematicians take him seriously, at this point. Maybe in the future that will change. Some of his ideas I've read about seem interesting, like homeless numbers. Search for
You are correct about that, including about the level of seriousness being a variable.
This book in my library, '(Over)interpreting Wittgenstein' (yes the title has parens in it like that), goes over like five waves of interpretation we've had by now, with a whole separate chapter on the mathfocused interpretations. There was a period of some decades where it was fashionable to knock Wittgenstein's math stuff, whereas today there's more interest in a more seamless approach wherein the "math stuff" is not dealt with so separately.
Probably most Wittgensteinians would agree with me that "definitions" may *appear* to get all the definitional work out of the way up front, such that from then on its just a matter of applying those definitions, but that *in actuality* a definition is one use among many that's going to give the rules for some term.
"Definitions don't nail anything down" might be one way of putting it, or "definitions are ongoing and continue to perturb one another". Put that way, I think many who consider themselves mathematicians would go along. Consider the concept of "dimension" for example. It's always jostling around (e.g. "fractional dimensions"), and that has ripple effects in many areas.
> the paper by Daesuk Han about Wittgenstein the Real Numbers (abstract here: http://philpapers.org/rec/HANWAT3)  if you find a full text version for free please post if you can. It addresses the "existence" of The Reals  and I don't think along the lines you are talking about here, but I could be wrong. > (Also see http://plato.stanford.edu/entries/wittgensteinmathematics/#WitIntCriSetThe) > > Joe N >
One of my main applications of Wittgenstein's stuff is to the writings of New England transcendentalist R. Buckminster Fuller, a humanist writer of many popular titles whom it's popular to dismiss as a kind of benign nut who mostly piggybacked on smarter peoples' good ideas. His reputation for "genius" at the time was less about earning that title and more about schmoozing and to some extent boozing his way through life, taking credit where none (or at least far less) was due.
Countering this view is a hard core of humanities types who believe there was something there, based on the hard core of original writings that seem to maintain sufficient coherence to meet that bar. James Joyce scholar Hugh Kenner included quite a bit about Fuller in 'The Pound Era' (about Ezra Pound and contemporaries), wrote a bio ('Bucky') and even heeded Fuller's call for humanities people to cross the C.P. Snow chasm and pitch a tent in STEM. He wrote 'Geodesic Math and How to Use It' in that spirit (I'm talking about Hugh Kenner, who also wrote a column for BYTE magazine).
The hard core diehards on the humanities side keep trying to bring Fuller back into the limelight, most recently with this exhibit that just opened in San Francisco. They're also remodeling the exhibit on his Dymaxion House at the Henry Ford Museum in Dearborn. The Whitney in New York and Museum of Contemporary Art in Chicago have had major exhibits in the last five years (Fuller died in 1983 having been born in the 1800s), as has the Isamu Noguchi museum in Queens, NY.
This "hard core" set of writings, his collaborations with E.J. Applewhite in particular, includes a revised view of what 3rd powering might mean, making everything come back to the tetrahedron as the topologically minimal enclosure with lots of other interesting properties, such as that slicing parallel to a face creates a smaller similar tetrahedron (not true of cubes for example).
If you imagine a mixing board (like in a recording studio) with all these levels that can be set, Fuller has his tetrahedron pushed way way high compared to any other writer.
Finding any kind of rant against right angles, cubes, rectilinear thinking, is really quite rare, certainly to his level. Polyhedron volumes are given in "tetravolumes" (tetrahedrons comprise his modular units of measure). And yet the tilt or bias does much to distill what actually happened in the course of the 1900s, as the secrets of the very small, down to the nano level, increasingly came to light. Lots of hexagons and pentagons, not many squares. Graphene might be the core symbol, with buckyballs and nanotubes its avatars. http://en.wikipedia.org/wiki/Graphene This hexagonal grid has replaced anything XY as the paradigm "high technology" look and feel. Fuller counterposed XYZ and its prominence in our thinking with another skeleton, which turned out to have immediate applications in architecture (where Lloyd Kahn picked it up in his derivative works).
My response, as a philosophy guy, is to wade in with my background in Wittgenstein (Princeton etc.) and treat Fuller's alternative universe (semantic space) as a kind of sandbox wherein to demonstrate what Wittgenstein was talking about. Meanings get defined / refined operationally over the course of an opus, not once in some numbered section near the beginning, although such a section may appear. What we mean by "3rd powering" is still amenable to "revectoring", even at this late date (one might not have suspected that).
Kirby
Message was edited by: kirby urner



