What is a Riemannian Manifold?

Mr. Tea

Shub-Niggurath, Please
Staff member
So Deleuze is basically making terms up to suit himself, borrowing words from mathematics as and when he sees fit? If he doesn't care about Riemannian manifolds, and can't be arsed to stick to the agreed definitions of mathematical terms, why doesn't he just invent a Deleuzian manifold that has whatever properties he wants to give it, without bothering to pretend to some kind of mathematical rigour?

Frankly I think it's a bit trite to tell me and Rich we've "missed the point" when we flag up an inaccuracy in some maths that turns out to be some philosopher's pseudo-maths and is merely masquerading as maths. I mean, surely you can see why this style of discourse gets up some people's noses, especially people who actually know a bit of maths?
 
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nomadthethird

more issues than Time mag
So Deleuze is basically making terms up to suit himself, borrowing words from mathematics as and when he sees fit?
I really wouldn't be surprised if he were. Did he actually study mathematics anywhere? I don't think so. This is from wiki:

Similar considerations apply, in Deleuze's view, to his own uses of mathematical and scientific terms, pace critics such as Alan Sokal: "I'm not saying that Resnais and Prigogine, or Godard and Thom, are doing the same thing. I'm pointing out, rather, that there are remarkable similarities between scientific creators of functions and cinematic creators of images. And the same goes for philosophical concepts, since there are distinct concepts of these spaces."

I have more and more sympathy for Sokal and Bricmont all the time, I must say.
 

josef k.

Dangerous Mystagogue
Deleuze did in fact study mathematics.

Robin McKay (who you may know as the editor of Collapse) writes:
From the probably unique position of (a)someone who's (supposed to be) writing a PhD on Deleuze and Mathematics and (b)someone who spent much of their life ignorant of what calculus was and why it might be important:

>1. Does my ignorance of calculus matter?
>For my understanding of Deleuze, for my
>understanding of philosophy, or for
>anything else?

Important for Deleuze: Yes, because from D&R onwards he bases his logic of difference and problems on concepts drawn directly from modern mathematical analysis (whose foundation is calculus). Without an understanding of analysis I think one can only achieve a vague discursive idea of Deleuze's argument (like most secondary texts). Implicitly Deleuze's -somewhat Badiousian- argument is that philosophical thought needs to take account of the conceptual manouevres contained in mathematical analysis, relating to universality, generality, singularity, if it is to escape various classical images - just as modern analysis finally escaped the long reign of aristotelianism, so must philosophy. The new mode of thought Deleuze is proposing bases itself on the historical thought-events of modern analysis. Briefly, to appreciate the mathematical side deepens your historical and philosophical understanding of what Deleuze is doing.

For an understanding of philosophy: Yes, because the more you look into this the more you will see that every major philosopher has something to say about calculus (even Engels!) - Why? (and this is the answer to the final question): because it is the single most important enabling conceptual mechanism for modern science. Put simply, it provides a mathematical handle on the large majority of physical phenomena which are not rectilinear. It constitutes a singular meeting-point of the problems of physics, mathematics and metaphysics (hence the interest in the 'esoteric history' - Whereas for Badiou mathematics eventually sloughs off all philosophical problematics clinging to it, Deleuze is interested in recovering these metaphysical problems and the relation of mathematics to philosophy and physics that they suggest.)

>2. Is Deleuze's use of calculus a Sokalian
>"intellectual imposture"? Is he right about
>the maths? And does that matter?

No, it's not simply a rhetorical misuse. But it is difficult to read and interpret. It's not an 'example' or an 'illustration' or a 'metaphor' either: deleuze's discussion is about the relationship between history, mathematics, physics and philosophy, from a (french philosophy of science) point of view which attempts to fathom the articulation of different orders (historical order, logical order, epistemological order. Obviously this is something Sokal can't understand. But obviously it doesn't matter if a wilfully myopic pigheaded scientist doesn't get it.

>3. What is calculus for or about anyways?
>Is there a good introduction somewhere that
>will explain it even to me?

It's used to give a formal treatment of problems which involve relationships between continuously varying quantities, ie. almost any physical, economical, astronomical, etc. problem you care to mention. (see Kline book, below, for simplest possible examples)

The problem I've found, as other comments suggest, is that pedagogical texts, even high school ones, never give any conceptual explanation that would be satisfying to a philosopher (which is rather shocking given the historical importance of calculus).

I would recommend firstly the calculus chapter in Kline's 'mathematics in western culture', which is the simplest account I have read of why calculus matters.

Secondly Boyer's 'The Concepts of the Calculus' is a fascinating book on the history (Deleuze read it).

More technically, Bruce Exner's book 'Inside Calculus' is the only academic maths book I have read which seems thoughtful on a conceptual level, and which gives discursive expositions before introducing massive equations; it describes very clearly the modern (epsilon-delta) form of calculus.
VIA

So Deleuze is basically making terms up to suit himself, borrowing words from mathematics as and when he sees fit?
He must be stopped!
 

vimothy

yurp
Yeah, of course, but it is my understanding that more people learn maths at a higher level in France, and that most French philosophers studied maths (along with other subjects) in the Grandes ecoles system. I may be misremembering this of course.
 

nomadthethird

more issues than Time mag
How can that be a "Badiousian" argument when Badiou had written basically nothing at that point, when Deleuze was writing D&R? I mean, perhaps in an anachronistic sense this is true. It's more correct, however, to say that Badiou's arguments using set theory have a Deleuzian flavor to them, given Deleuze made his 20 years earlier and they were well-known to Badiou.

Edit: Thanks for posting that Josef it's a good find.
 
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Mr. Tea

Shub-Niggurath, Please
Staff member
Which brings me to a wider question I've been meaning to explore for a while, namely: Is there a convincing argument as to why it's a good idea to model theories of social, political or psychoanalytic philosophy on mathematical theorems? Because to me it's very far from obvious that this should be the case.
 

nomadthethird

more issues than Time mag
Yeah, of course, but it is my understanding that more people learn maths at a higher level in France, and that most French philosophers studied maths (along with other subjects) in the Grandes ecoles system. I may be misremembering this of course.
Sounds right...
 

nomadthethird

more issues than Time mag
Which brings me to a wider question I've been meaning to explore for a while, namely: Is there a convincing argument as to why it's a good idea to model theories of social, political or psychoanalytic philosophy on mathematical theorems? Because to me it's very far from obvious that this should be the case.
I'm with you on this.

"But obviously it doesn't matter if a wilfully myopic pigheaded scientist doesn't get it."
How crazy of those pigheaded scientists to demand clarity and rigor of allegedly scientific work!

Sometimes I wouldn't care if "art" went up in smoke tomorrow. It seems so narcissistic and lame, and full of all of those idiotic things that come with narcissism, like nationalism, and homelandcentricity.
 

josef k.

Dangerous Mystagogue
How can that be a "Badiousian" argument when Badiou had written basically nothing at that point, when Deleuze was writing D&R?
You're right - that was an interesting piece of rhetoric. A significant indication of the rise of Badiou, that he is being projected back in time.

How crazy of those pigheaded scientists to demand clarity and rigor of allegedly scientific work!
Granted... But nevertheless: to demand clarity and rigor from philosophical work and philosophical language seems like an imposition. None of the people Sokal and Bricmont argue against in Intellectual Impostures would have considered themselves scientists, or their work scientific.
 

nomadthethird

more issues than Time mag
So Deleuze is basically making terms up to suit himself, borrowing words from mathematics as and when he sees fit? If he doesn't care about Riemannian manifolds, and can't be arsed to stick to the agreed definitions of mathematical terms, why doesn't he just invent a Deleuzian manifold that has whatever properties he wants to give it, without bothering to pretend to some kind of mathematical rigour?

Frankly I think it's a bit trite to tell me and Rich we've "missed the point" when we flag up an inaccuracy in some maths that turns out to be some philosopher's pseudo-maths and is merely masquerading as maths. I mean, surely you can see why this style of discourse gets up some people's noses, especially people who actually know a bit of maths?
No, don't let my statements reflect on Deleuze's math, I was just trying to draw a parallel up there, between different spaces within manifolds and "smooth" versus "striated" ones in the Deleuzo-Guattarian philosophical jargonny sense of the terms. Since I know nothing about manifolds but what has been typed in this thread, and not even really that, it was just a guess. (I mean, isn't there supposed to be Euclidean and non-Euclidean space within Riemannian manifolds? If so, that's what I was talking about...smooth and striated jargon words vaguely equating to those Euclidean and non-Euclidean spaces within RM...I am probably missing something here)

What I meant to say was... I'm not sure "hybrids" of math and philosophy are entirely meaningful at this juncture.
 
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nomadthethird

more issues than Time mag
Granted... But nevertheless, to demand clarity and rigor from philosophical work and philosophical language seems like an imposition.
Agreed, but aren't halfassed, sloppy "hybrids" exactly what's wrong with 'postmodern' thought? Why add to this travesty?
 

josef k.

Dangerous Mystagogue
Which brings me to a wider question I've been meaning to explore for a while, namely: Is there a convincing argument as to why it's a good idea to model theories of social, political or psychoanalytic philosophy on mathematical theorems? Because to me it's very far from obvious that this should be the case.
I think scientific and mathematical models can be applied to social, political, psychoanalytic philosophy, as, precisely, models. In the same way that scientists invoke metaphors in order to present their own findings. To base social theories on scientific or mathematical models (held-up as the highest of all methods) seems more problematic, and has previously produced monsters.

Agreed, but aren't halfassed, sloppy "hybrids" exactly what's wrong with 'postmodern' thought? Why add to this travesty?
I support Hybrid Rights. I think the point for Serres is that rigor (non-sloppiness) comes with the subordination to a discipline, which is what he wants to avoid... he is the philosopher of the crossroads, which is to say, the half-ass.
 

Mr. Tea

Shub-Niggurath, Please
Staff member
He must be stopped!
Well personally I couldn't care less if some philosophy professor gets a hard-on for writing about Riemannian manifolds, but it would seem to call into question his credibility if he does so in a sloppy, capricious way.

Obviously this is something Sokal can't understand. But obviously it doesn't matter if a wilfully myopic pigheaded scientist doesn't get it.
Zing!

The problem I've found, as other comments suggest, is that pedagogical texts, even high school ones, never give any conceptual explanation that would be satisfying to a philosopher (which is rather shocking given the historical importance of calculus).
Oh, the horror. Could it be that maths teachers are using maths lessons primarily to teach maths - or, at the very least, the ability to pass a maths exam - rather than philosophy?

I'm sure there are plenty of things that are not "satisfying to a philosopher" but which 99.99% of people don't lose sleep over, if they're even aware of them.
 

vimothy

yurp
Oh, the horror. Could it be that maths teachers are using maths lessons primarily to teach maths - or, at the very least, the ability to pass a maths exam - rather than philosophy?
This is almost certainly true, and probably a bad thing.
 

nomadthethird

more issues than Time mag
I'm sure there are plenty of things that are not "satisfying to a philosopher" but which 99.99% of people don't lose sleep over, if they're even aware of them.
As far as I'm concerned, the most interesting philosophy is already going on in cosmology. Not that I can understand it, because I can't. But it's there.

I'm a neo-Aristotelian.
 

Mr. Tea

Shub-Niggurath, Please
Staff member
This is almost certainly true, and probably a bad thing.
You mean the bit about passing exams? Well yes, it's kind of missing the point rather. But this has been discussed at length in other threads.

Obviously I'm not against teachers/lecturers encouraging their students to think about what things mean, as opposed to merely how things are. That said, an exhaustive analysis of Newtonian vs. Leibnitzian conceptions of infinitesimal quantities is probably not a prerequisite for a class of 16-year-olds to get to grips with the basics of calculus.
 

josef k.

Dangerous Mystagogue
Oh, the horror. Could it be that maths teachers are using maths lessons primarily to teach maths - or, at the very least, the ability to pass a maths exam - rather than philosophy?
I don't think Deleuze (and/or Serres) is demanding the destruction of maths and gulagization of maths teachers... I think he (they) is trying to find a way of thinking about maths philosophically... exploring its connections to other disciplines... Which will naturally involve stepping-outside of mathematical norms and deforming mathematical concepts a little... he (and G.) says in "What in Philosophy" that philosophy is about inventing concepts, science is about inventing functions, and art is about inventing something or another.

I'm sure there are plenty of things that are not "satisfying to a philosopher" but which 99.99% of people don't lose sleep over, if they're even aware of them.
Perhaps nothing* is satisfying to a "true" philosopher... philosophy being, after all, a really stupid thing to want to do.

*EDIT: Beyond normal run of the mill things like dressing up like a women, and plotting the terms of Aroundball...

*EDIT2: And stapling pieces of paper together...
 
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