clifford (of whom i only read one fairly popular book from the 1800's i think) is viewed with reimann as anticipating einstein and essentially seeing the universe (or matter) as a geometrical property---matter as curvature .( wheeler's geometrodynamics continued the legacy; i've seen some stuff arguing you actually just need topology (order relations, no metric) to get everything...) i think some people with credentials etc. are using his numbers to try to disprove quantum mechanics now (ie bell's theorem---god dont take no random walk down wall street for nothing). (the issue of 'what is outside the universe' always comes up in relativity---eg if its expanding then what is it expanding into---the standard answer is there is no outside. or maybe, to quote wheeler and topolpgy 'the boundary of a boundary is zero'.)
interestingly, if you look at the 'foundations of math' archives (an e-list where even martin davis sometimes posts) there is a discussion of badieu this month---they basically give him acceptable reviews, saying he knows his math even is he is not a practicioner, though they say his philosophical extrapolations are just that---speculations. there's alot more on that list too. (harvey friedman puts category theory in its place, which i agree with, in a discussion about hilary putnam---i've known some people who take the reverse view, holding that set theory is just pretentious . these 2 vie for being most basic (and category theory is more topological or spatial using graphs. i view it as a tower of babble but no worse than other dialects.)
its hard to know what to make of taking ideas like the platonic solids or forcing or 'relativity' and then extrapolating that to life, eg ontologoes and ethics of a platonic universe of timeless forms (which essentially chomsky does with his cartesian linguistics (his south end press book on mind and language goes through it---i consider it a proof of insanity, but at least its nonviolent (wear your home detention bracelet on the MIT campus or you'll end up like Gates, drinking bud in the paint it balck house...) ---all the words actually live out there, and humans innately pick up on those, just as they do radio stations which also are naturally out there thanks to free market optimization and the FCC (didnt that guy ted kazinski call himself fc? so maybe thats to the fcc what zf is to zfc. 'we are family' (pointer sisters---signifying nothing, like boris rotman (another weird math philosopher) ).
on the FOM list there's also a review from last month of russian math people who believed in a religion of 'naming names'---eg if you name god, then s/he exists, and so on. they even thought the trinity followed from the triangle somehow---luzin is one of them i think (they were measuring infinities..). that is similar to the forcing idea----you just name whatever you need and see what follows (even politically). like forcing, apparently the names are dependent, so once you make one sort of choice you get alot of other relationships fixed (or at least thats what shelah and such claim about large cardinal axioms. i think paul cohen believed that the continuum was aleph 3 so you have 2 uncountable steps before you are there.)
i remember this little kid once saying 'you are nothing'. very disrespectful, but maybe its true.
for some more crazy stuff along this line check out the notorious G (not big G of backyard nor BIG) but G spencer Brown whose stuff is on the web (f/laws of form). i did try to read being and nothingness but playing in the sandbox might be more fun. wikipedia or the new york review and reader's digeest are pretty much my sources for hegel, foucault, spinoza, leibniz etc. the historical devbates with frege, cassierer, bertrand russell etc. are interesting to dip into, like a dose of ezra pound. but nowadays we have progressed to linux and 'you say your a gangsta but you ainst said nohting, you're a wangsta, you aint never done nothing' whcih more or less covers the territory.
or, without neccesarily going back and reading dedekind or principia mathematica or darwin, one could distill those very long disucssions and try to impose some order on the real numbers. (find some x defined recursively or by a function such that you cannot prove that it is greater or less than zero because each approximation hops around the origin. there is one very good result of this form which i unfortunately cannot remember what it is---i think its in a nonstandard logic. )
--- On Wed, 7/29/09, Chuck Grimes <cgrimes at rawbw.com> wrote:
> From: Chuck Grimes <cgrimes at rawbw.com>
> Subject: [lbo-talk] Badiou again
> To: lbo-talk at lbo-talk.org
> Date: Wednesday, July 29, 2009, 9:11 PM
> ``just to throw in the mix, clifford
> is also pretty interesting (eg
> clifford numbers, even popular now in quantum
> theory)..'' Mart
>
> Thanks for these references. I just went on a quick google
> of
> Clifford. Glanced through his textbook on classical
> mechanics (google
> books). He starts off with the concept of a center of mass.
> He looks
> like another of those guys with a great mind.
> I just did a google books on Badiou and google came up with
> page 34:
>
> ``It is here that Dedekind's `ordinal' orientation comes
> into effect:
> function f, via the mediation of the concept of the chain,
> is that
> which defines N as the space of a total order. The first
> `point' of
> this order is obviously 1. For philosophical reasons
> (compare 1.17)
> Dedekind prefers a denotation beginning with 1 to one
> beginning with
> 0; `1' denotes the first link of a chain, whereas zero is
> `cardinal'
> in its very being; it marks lack, the class of all empty
> extensions''
>
> [BTW Dedekind, Essays on the Theory of Numbers, is in the
> Dover
> collection. It's very accessible and at once
> mathematical...]
>
> Now isn't that above quote interesting? Halmos argued 0 was
> essential
> to all ordered sets and built his axiom of infinity on the
> idea of 0.
>
> So then, looking up sec 1.17 listen to this:
>
> ``On the infinite. Dedekind with admirable profunity,
> _begiins with the
> infinite_ , which he determines with a celebrated postive
> property; `A
> system S is said to be infinite when it is similar to a
> proper part of
> itself.' And he undertakes immediately to `prove' that such
> an
> infinite system exists. The finite will be determined only
> subsequently, and it will be the finite that is the
> negation of the
> infinite (in which regard Dedekind's numberical dialectic
> has
> something of the Hegelian about it). Frege, on the other
> hand, begins
> with finite, with natural whole numbers, of which the
> infinite will be
> the `prolongation' or recollection in the concept.
>
> On zero. Dedekind abbors the void and its mark, and says so
> quite
> explicity: `[We] intend here for certain reasons wholly to
> exclude the
> empty system which contains no elements at all.' Whereas
> Frege makes
> the statement `zero is a number' the rock of his whole
> ediface.''
>
> Whatever else Badiou is, he is a serious philosopher in my
> book. [And
> like everybody on my shelves, I don't have to own him all
> the way
> down. I can steal what I want and leave what I don't.]
>
> I hope people see some of the issues at stake in the above.
>
> The first one that popped into my mind is the interesting
> ordinal
> series (Null, 0, 1, ..., Inf). You see that Null functions
> like a
> bracket with Infinity at the other end. This problematic
> idea crops up
> over and over in number theory analysis because there is
> something
> wrong with the basic theorems on limits, the summation of
> an infinite
> series, convergence, etc.
> The other interesting issue that popped next was that
> Dedekind and
> Frege seem like the progenator-followers of the whole
> constructionist
> v. formalist, started by Kronecker v. Cantor.
>
> Then the last and most interesting to me, problem is the
> relationship
> between this set-number theory discussion and the
> philosophical
> problem with the Big Bang hypothesis.
> If you follow the (1) school, there was never a (0) or
> Nothing, before
> we get to Everything (1). So we have to start with
> something
> (1). However, if we start with Everyhting, how can there be
> any
> Beginning?
>
> On the other hand if we start with (0) and Nothing, then we
> get to
> Everything (1), but we are stuck with beginning and an end.
>
> So how can there be non-being? Nothing sounds like
> some meaningless
> statement. Doesn't meaninglessness have to exist, just to
> understand
> what a meaningful statement is?
>
> See this is very ontic stuff. Hegel begins his
> Phenomenology of Mind,
> hashing out this dilemma of Being and Nothing. It was
> difficult to
> follow and so tedious that I just skipped after awhile and
> moved
> on. He basically says Nothing and Being need each and going
> around in
> circles, getting nowhere. So we are forced to procede.
> This
> duality and the need to procede further is the logical
> outcome
> that joins nothing and being to produce the synthesis of
> becoming,
> which is also the essence of Time
>
> Personally, I am with the Nothing (0) crowd. There is a
> religious and
> exitential angle involved. I came from nothing. I am not
> nothing
> now. I will return to nothing. (Something from Adorno's
> probably) So
> then I am also a Heideggerian in some sense. I mean also
> to
> acknowledge that it was partly Heidegger who turned me on
> to the idea
> of doing philosophy as if we knew nothing about it...the
> whole idea of
> going back to before Socrates.
>
> Cassirer starts his Substance and Function, with a
> discussion on set
> theory and its problems.
> He begins with the identities Concept <-> Substance,
> and Substance <->
> Space. He historizes these ideas as an Aristotlian view of
> the world
> that must be gotten around in order to understand the new
> discoveries
> in physics and math.
>
> What he argues is that we have been acculturated into our
> most basic
> ideas that date back at least to Aristotle, such as the
> idea the world
> or space is made up of a substance and needs a container.
> And, that
> for each object of thought there corresponds an object in
> the
> world... These ideas need to be re-examined if we are to
> have an
> understanding of our emerging and different looking
> physical
> world... I forget how it goes from there...
>
> CG
>
>
>
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