The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » Education » math-teach

Topic: Re: Who is the greatest published mathematician in history? If you
were asked..

Replies: 1   Last Post: Apr 7, 2012 7:55 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
kirby urner

Posts: 3,678
Registered: 11/29/05
Re: Who is the greatest published mathematician in history? If you were asked..
Posted: Apr 7, 2012 11:00 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 re-re-reiterating. It took me awhile but I then realized it was a clever play on yous-twos 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
math-focused 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/HANWAT-3) - 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/wittgenstein-mathematics/#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 piggy-backed 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 die-hards 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 counter-posed 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 "re-vectoring", even at
this late date (one might not have suspected that).

Kirby


Message was edited by: kirby urner



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.