Comments on: A Brief History of Nothing http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/ refracting theory: politics, cybernetics, philosophy Thu, 07 Jan 2010 13:04:27 +0000 http://wordpress.com/ hourly 1 By: Burhan http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2294 Burhan Fri, 30 May 2008 08:43:01 +0000 http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2294 This is a very interesting topic, and I don't think there has been any direct research - at least on the side of theoretical mathematics - on the position of the event in mathematical research. What's for sure is that axiomatics is pretty much dead. Mathematics no longer just about reduction, derivations and deductions. Gian-Carlo Rota, in 'Indiscrete Thoughts', wrote something about what he called 'mathematicial enlightenment'. And I remember that Alain Connes, in 'Triangle of Thoughts', said something about what he called 'primordial mathematicial reality', which might be close to Deleuze's transcendental field. Perhaps the theory of computation, complexity or heuristics might have something important to say. It is a popular opionion by some computer scientist that the mathematical event can be understood by looking into the gap between P and NP complexity classes. This is a very interesting topic, and I don’t think there has been any direct research – at least on the side of theoretical mathematics – on the position of the event in mathematical research.

What’s for sure is that axiomatics is pretty much dead. Mathematics no longer just about reduction, derivations and deductions. Gian-Carlo Rota, in ‘Indiscrete Thoughts’, wrote something about what he called ‘mathematicial enlightenment’. And I remember that Alain Connes, in ‘Triangle of Thoughts’, said something about what he called ‘primordial mathematicial reality’, which might be close to Deleuze’s transcendental field. Perhaps the theory of computation, complexity or heuristics might have something important to say. It is a popular opionion by some computer scientist that the mathematical event can be understood by looking into the gap between P and NP complexity classes.

]]> By: Joseph Weissman http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2292 Joseph Weissman Fri, 30 May 2008 03:17:56 +0000 http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2292 Thank you so much for this comment. Remember that a lot of Badiou's work is about chance too -- this is, strangely enough, where Badiou reaches out to poetry and discourse as well. There is an uncanny kind of eloquence about the axioms of probability, isn't there? I think it's because they "decide" an undecidable -- they emerge late (relatively speaking, of course) and as the discovery of a certain kind of "internal" limitation on the extent of the validity of deduction. A transcendental limitation by which we are made free -- precisely by limiting the scope of our axioms, we open up completely new generative fields, radical sources of creative exploration and experimentation. Imaginary machines are quite real: I am reminded of Deleuze and Guattari's description of modern society, oscillating between a capitalistic "internal" limit and a schizophrenic "external" limit. Does the inventor-discoverer of a novel system of mathematics always run a double risk -- that of over-extending an axiomatic, over-generalizing and hence discounting the role of human ingenuity; as well as that of becoming totally absorbed in details and thus becoming completely oblivious to the power of imagination? Perhaps the constitutive "break" within mathematics itself -- Badiou's "meaningless" primacy of truth -- is no more real than the rupture between the human and natural sciences, or even science and literature. Thank you so much for this comment. Remember that a lot of Badiou’s work is about chance too — this is, strangely enough, where Badiou reaches out to poetry and discourse as well. There is an uncanny kind of eloquence about the axioms of probability, isn’t there? I think it’s because they “decide” an undecidable — they emerge late (relatively speaking, of course) and as the discovery of a certain kind of “internal” limitation on the extent of the validity of deduction. A transcendental limitation by which we are made free — precisely by limiting the scope of our axioms, we open up completely new generative fields, radical sources of creative exploration and experimentation. Imaginary machines are quite real: I am reminded of Deleuze and Guattari’s description of modern society, oscillating between a capitalistic “internal” limit and a schizophrenic “external” limit. Does the inventor-discoverer of a novel system of mathematics always run a double risk — that of over-extending an axiomatic, over-generalizing and hence discounting the role of human ingenuity; as well as that of becoming totally absorbed in details and thus becoming completely oblivious to the power of imagination? Perhaps the constitutive “break” within mathematics itself — Badiou’s “meaningless” primacy of truth — is no more real than the rupture between the human and natural sciences, or even science and literature.

]]> By: Burhan http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2291 Burhan Thu, 29 May 2008 22:51:06 +0000 http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2291 I met Brian a few weeks ago at a conference and his opinion of 'Being and Event' wasn't favorable. The mathematics was out-of-date and influenced too much by the Bourbaki school -- which was in vogue back when Badiou was still an active mathematician -- and less by Grothendieckian category theory. As you probably know, category theory is exactly what Badiou used with his later work, although Brian wasn't aware of that. And I wonder if Brian's ideas can be attributed to the fact that he did a lot of research in combinatorics. I forget the details but i think Badiou, in some essay, said something to the effect that his philosophy in 'Being and Event' goes against the Hilbertian understanding mathematics as a game of formal languages. I met Brian a few weeks ago at a conference and his opinion of ‘Being and Event’ wasn’t favorable. The mathematics was out-of-date and influenced too much by the Bourbaki school — which was in vogue back when Badiou was still an active mathematician — and less by Grothendieckian category theory. As you probably know, category theory is exactly what Badiou used with his later work, although Brian wasn’t aware of that.

And I wonder if Brian’s ideas can be attributed to the fact that he did a lot of research in combinatorics. I forget the details but i think Badiou, in some essay, said something to the effect that his philosophy in ‘Being and Event’ goes against the Hilbertian understanding mathematics as a game of formal languages.

]]> By: Joseph Weissman http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2289 Joseph Weissman Thu, 29 May 2008 21:57:33 +0000 http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2289 Haven't, but it sounds pretty interesting -- math as experimental science. I wonder how it fits in with Badiou's conception of math as fundamental ontology. Are our ontologies imaginary, and if so, what does that mean about possible worlds...? If mathematics is a kind of imagination-machine, ultimately at the service of writers... but then math would lose its status as revealing something essential about our knowledge, unless we recognize that truth is not an impersonal ontology, but already a language -- or, at least, theoretically expressible in an imaginary language. :) Haven’t, but it sounds pretty interesting — math as experimental science. I wonder how it fits in with Badiou’s conception of math as fundamental ontology. Are our ontologies imaginary, and if so, what does that mean about possible worlds…? If mathematics is a kind of imagination-machine, ultimately at the service of writers… but then math would lose its status as revealing something essential about our knowledge, unless we recognize that truth is not an impersonal ontology, but already a language — or, at least, theoretically expressible in an imaginary language. :)

]]> By: Burhan http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2288 Burhan Thu, 29 May 2008 21:49:00 +0000 http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2288 hi, love this site. have you read brian rotman's 'signifying nothing'? hi, love this site. have you read brian rotman’s ’signifying nothing’?

]]> By: History http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2127 History Sat, 02 Feb 2008 23:15:57 +0000 http://fractalontology.wordpress.com/2008/02/02/a-brief-history-of-nothing/#comment-2127 [...] A Brief History of Nothing [...] [...] A Brief History of Nothing [...]

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