Sunday 9 June 2024

Deleuze on Foucault & pretending to know Math.

Because of their Cartesian heritage, French pedants pretended to know Math. More sadly, they also pretended to know French history and literature. More ludicrously, they pretended to have read each other's shite and, on occasion, would pretend to write books about that shite. 

This is the opening of Deleuze's book on Foucault 

A new archivist has been appointed.

In which case he has an appointment letter and the Curator of Archives has received an official notification. 

But has anyone actually appointed him?

Yes. Whoever funds the Archive has appointed him and given him an appointment letter.  

Is he not rather acting on his own instructions?

No. He has been appointed. He is acting on the instructions of those who pay his fucking salary.  

Certain malevolent people say that he is the new representative of a structural technology or technocracy.

They can say what they like. But, if he has an appointment letter and gets paid punctually, there is shit they can do about it.  

Others, mistaking their insults for wit, claim that he is a supporter of Hitler, or at least that he offends the rights of man (they will not forgive him for having proclaimed the 'death of man'). Some say that he is a shammer who cannot back himself up with reference to the sacred texts, and who seldom quotes the great philosophers. Others, though, claim that something radically new has appeared in philosophy, and that this work is as beautiful as those it challenges.

An archivist is not a philosopher though, no doubt, he can do what he likes in his spare time.  

It celebrates the dawn of a new age. In any case, it all begins like a story by Gogol (rather than by Kafka).

Only if you live under Tzarist autocracy.  

The new archivist proclaims that henceforth he will deal only with statements.

In which case he could be sacked for not doing his job which has to do with archiving stuff he is paid to fucking archive.  

He will not concern himself with what previous archivists have treated in a thousand different ways: propositions and phrases. He will ignore both the vertical hierarchy of propositions which are stacked on top of one another, and the horizontal relationship established between phrases in which each seems to respond to another. Instead he will remain mobile, skimming along in a kind of diagonal line that allows him to read what could not be apprehended before, namely statements.

We don't care what the archivist reads providing he archives stuff he is paid to fucking archive.  

Is this perhaps an atonal logic?

No. It is nonsense.  

It is natural for us to have misgivings.

Only if we are naturally nitwits.  

For the archivist deliberately refuses to give examples.

Also he should refuse to give head.  

He believes that he never stopped giving them in the past, even if at the time he was unaware that they were examples. 

Or fellatio.  

Now the only formal example he analyses is intended to be disquieting: a series of letters which I might write down at random, or record in the order in which they appear on the keyboard of a typewriter: 'The keyboard of a typewriter is not a statement; but the same series of letters, A, Z, E, R, T, listed in a typewriting manual, is the statement of the alphabetical order adopted by French typewriters.'

Who will pay an archivist to archive random shite?  

Such multiplicities have no set linguistic construction, yet they are statements.

No. A statement is a fucking linguistic construction though, no doubt, it could have more than one interpretation.  

Azert? Since we are used to the approach of other archivists, we find ourselves wondering how Foucault can possibly produce statements under these conditions.

But Foucault wrote books in the same boring way other such shitheads did.  

This is especially true since Foucault asserts that statements are essentially rare. This is the case de facto and de jure: they are necessarily tied to a law and an effect of rarity.

No. Both de facti and de jure are 'buck-stopped' terms of art drawn from jurisprudence. The law is only concerned with statements. Suppose I file an affidavit which has no 'linguistic structure'. It will be ruled inadmissible. It is not a statement. It is nonsense. On the other hand, if it is known that I am incapable of producing an actual statement, I may be judged legally incompetent.  

Indeed, this is one of the characteristics that make them different from propositions and phrases.

A statement may be a proposition and is generally composed of phrases. It is not different from them.  

For propositions can be thought of in any number of ways,

but not for any useful purpose 

since we can use the differences between types to express any one in terms of the others.

Only if we have access to a ramified type theory which is 'complete' or 'decidable'. Weiner showed we can get rid of 'reducibility' with 'ordered pairs'.  

Such a formalization does not have to distinguish between what is possible and what is real; it generates possible propositions.

As opposed to impossible propositions. Why stop there? Why not say 'the possible generates the possible. The impossible doesn't which is why if cries itself to sleep.'  

As for what is really said,

it is really said.  

its de facto rarity

Guys who are talking are really saying something. You may wish this was de facto very rare indeed.  

comes about because one phrase denies the existence of others,

Like me saying 'I would never call you a stupid bitch, you fucking stupid bitch'  

forbidding, contradicting or repressing them to such an extent that each phrase remains pregnant with everything left unsaid.

Which is why when I said you were a stupid bitch I was leaving you pregnant with everything unsayable about any fetus unfortunate enough to carry any of my DNA.  

This virtual or latent content multiplies meaning and opens itself up to interpretation, creating a 'hidden discourse' that de jure is a source of great richness.

Fuck off! The law decides what is 'de jure'. I may claim to have given George Lucas the idea for Star Wars. This was because when I shouted at him from my bedroom in Delhi, what I left unsaid was the notion that there was this dude named Darth Vader and Luke is actually his son! Sadly, a law court may decide that my 'hidden discourse' does not entitle me to billions of dollars or, at the very least, a T-shirt.  

A dialectic of phrases is always open to contradiction,

No. What is cool about 'dialectics' is that you can pretend 'contradictions' are resolved at a higher level.  

even if the end result merely overcomes or reinforces that contradiction; while a typology of propositions lays itself open to abstraction,

Such a typology is already an abstraction 

and so creates a type for each level that is in fact superior to its constituent elements.

Nonsense! My typology of Pizzas is inferior to actual Pizzas which is why I'm not eating one right now.  

But contradiction and abstraction are the means by which phrases and propositions are multiplied,

to no useless purpose. Any kid can say 'sez you' and then making a farting noise.  

since one phrase can always be opposed to another, or one proposition formed on the basis of another.

but we still have to eat and this means we need to get around to doing useful stuff.  

Statements, on the other hand, inhabit a general realm of rarity

meaningful statements are rare in Deleuze.  

within which they are distributed begrudgingly and even inadequately.

Not by this nutter. He could talk the hindlegs off a donkey.  

No sense of possibility or potentiality exists in the realm of statements.

Stupid ones- sure.  

Everything in them is real and all reality is manifestly present.

Nope. Nothing in them is real unless they are useful- e.g. a statement about a Pizza which is backed up by the action of handing me a fucking pizza.  

All that counts is what has been formulated at a given moment, including any blanks and gaps.

No. What counts is useful stuff- e.g. Pizzas as opposed to claims that the ramified theory of Pizza types sodomized the subaltern in Singur while Spivak stood by laughing maniacally.  

It is none the less certain that statements can be opposed to one another, and placed in hierarchical order.

No. It is certain that only a God could do this but wouldn't because the thing is pointless.  

But in the space of two chapters

in the Archaeology of Knowledge 

Foucault rigorously demonstrates that contradictions between statements can be measured only by calculating the concrete distance between them within this space of rarity.

Fuck off! There is no 'concrete distance' between things which aren't themselves concrete. True, one could arbitrarily say 'the Gettysburg Address in two meters away from the Bill of Rights' and this may be true of certain books on your bookshelf. But it isn't true of the statements represented by either. 

Comparisons between statements are therefore linked to a mobile diagonal line that allows us, within this space, to make a direct study of the same set at different levels,

only if the set is compact. But statements have no point set topology save by arbitrary stipulation.  

as well as to choose some sets on the same level while disregarding others (which in their turn might presuppose another diagonal line).

'Diagonal arguments' require the explicit meeting of all applicable requirements.  You can't pick and choose. A canonical measure- e.g. Lebesgue for the real number line- arises from compactness and total ordering. What Deleuze has written is nonsense. 

It is precisely the rarefied nature of this space which creates these unusual movements and bursts of passion that cut space up into new dimensions.

Deleuze is thinking of Cartan connectors of locally Euclidean spaces into a Reimannian manifold. But, ininitesmally, local Euclideanism is ubiquitous. It isn't rare at all. Moreover, it is our assumptions about global curvature which dictate our choice of connectors. It may be that our universe is a 3-torus and there may already be some evidence available of this. But this has nothing to do with 'hidden dimensions'. The motivation there is symmetry or super-symmetry. 

To our amazement, this 'incomplete, fragmented form' shows, when it comes to statements, how not only few things are said, but 'few things can be said'.

Too much nonsense is spoken. That isn't amazing at all.  

What consequences from this transportation of logic will find their way into that element of rarity or dispersion which has nothing to do with negativity, but which on the contrary forms that 'positivity' which is unique to statements?

Nothing. Logic hasn't been 'transported'. Deleuze may have tried to rape it but it was located far away from him and so he ended up fucking the drapes.  

Foucault also tries to reassure us, though: if it is true that statements are essentially rare, no originality is needed in order to produce them.

Why then should they be rare? Most people have no originality whatsoever- more particularly if they teach stupid shite.  

A statement always represents a transmission of particular elements distributed in a corresponding space.

It never does so unless it is a mathematical statement restricted in scope to a particular axiom system. This is because to, qualify as a space, certain topological- and therefore set theoretic- criteria must be fulfilled. The most important one is that it should always be possible to fully specify the 'extension' of a term- i.e. decide what is an element and what isn't an element of the set. The law can have a buck-stopped way of doing this for certain matters. But many issues will be non-justiciable.  

As we shall see, the formations and transformations of these spaces themselves pose topological problems that cannot adequately be described in terms of creation, beginning or foundation.

This nutter is pretending to be a mathematician. Why not a go-go dancer?  

When studying a particular space, it matters even less whether a statement has taken place for the first time, or whether it involves repetition or reproduction.

No. Guys who study particular mathematical spaces do want to know who first invented them. There was renewed interest in Grete Hermann when Bell rediscovered her disproof of Von Neumann's no hidden variable theorem. The fact is the originator of an idea later found to be useful may have had unique insights or motivations which need to be uncovered so that the subject can make more rapid progress.  

What counts is the regularity of the statement: it represents not the average, but rather the whole statistical curve.

It can't do so. Imagine a police detective who starts reading witness statements. He does not know how many witnesses will confirm the account given by the first statement. The only way you get to a 'statistical curve' is by surveying or sampling the entire field. 

In effect the statement is to be associated not with the transmission of particular elements presupposed by it but with the shape of the whole curve to which they are related,

A statistician may relate one thing to other similar things. But things are not related to each other. I am not related to other fat bastards of my age who have a similarly low IQ.  

and more generally with the rules governing the particular field in which they are distributed and reproduced.

There are rules 'governing' driving a car. This does not change the fact that I am shit at driving.  

This is what characterizes the regularity of statements: The originality/banality opposition is therefore not relevant: between an initial formulation and the sentence, which, years, centuries later, repeats it more or less exactly, [the archaeological description] establishes no hierarchy of value; it makes no radical difference.

Yes it does. The Church would fall apart if it turned out that what Christ actually said was 'fuck the Police!'  

It tries only to establish the regularity of statements.

Why bother? We soon understand that it would be highly irregular for a Doctor to say 'I'm a plumber. I've come to fix your sink. Please put your clothes back on.'  

The question of originality is all the more rare for the fact that the question of origins is never raised at all.

It is if some useful purpose is served by it. The discovery that when Christ said 'Fuck the Police' he was merely repeating what Moses said to the Buddha would have global repercussions. 

It is not necessary to be someone to produce a statement,

Though nobody who did not exist has yet produced any such thing- except of course the Holy Ghost who said 'Fuck the Police' to Leviathan.  

and the statement does not refer back to any Cogito or transcendtal subject that might render it possible,

We are welcome to make that imputation 

or to any ego that might pronounce it for the first time (or recommence it), or to any Spirit of the Age that could conserve, propagate and recuperate it.

Again, nothing can stop us doing so.  

There are many places from which any subject can produce the same statement, and they vary greatly. But precisely because different individuals can intervene in each case, a statement accumulates into a specific object which then becomes preserved, transmitted or repeated.

If people find it worthwhile doing so.  

This accumulation resembles the building up of a stock of provisions;

which is what keeps squirrels busy 

it is not the opposite of rarity, but an effect of this same rarity.

Squirrels aren't rare at all.  

In this way it replaces notions of origin and return to origins: like Bergsonian memory, a statement preserves itself within its own space

because doing so in Outer Space is difficult and costly 

and continues to exist while this space endures or is reconstituted.

That's not how my memory works. I still have vivid memories of the Sixties when I toured the world as a Secret Agent with a license to kill. Also, I was married to Mary Poppins.  

We must distinguish between three different realms of space which encircle any statement.

Only if must teach stupid shite.  

First of all there is collateral space, an associate or adjacent domain formed from other statements that are part of the same group.

Deleuze has some hazy notion that Weyl groups depend on the choice of Cartan sub-algebra for a Lie algebra. But statements have no unique or natural representation in point set topology. This is like pretending Pythagoras's theorem applies to Love Triangles.  

The question of knowing whether the space defines the group or, conversely, whether the group of statements defines the space, is immaterial.

Not if the statements are about mathematical group theory. If they are anything else, those statements are simply silly- like saying the hypotenuse of the Love Triangle is causing my dick to shrink.  

There is no homogeneous space that remains unlocalized:

No space doesn't have localized properties unless it isn't a space- i.e. the underlying set is not well-defined- like 'hypotenuse of the Love Triangle'.  

the two elements merge at the level of the rules of formation.

Elements of a set don't merge. A rule of formation of a set must forbid any such thing- otherwise the thing isn't well-defined and thus isn't a set.  

The important point is that these rules of formation cannot be reduced either to axioms, as in the case of propositions, or to a single context, as in the case of phrases.

Why not? Mathematics has advanced greatly in the former instance while the Law too has burgeoned in the latter. That's why mathematicians are respected while Contract Lawyers can get paid lots of money.  

Propositions refer vertically to axioms on a higher level

No. An axiom is merely a proposition which is assumed to be true. One can do 'reverse mathematics' and winnow out unnecessary axioms.  

which in turn determine certain constant and intrinsic factors and define a homogeneous system.

No. A homogenous system, in linear algebra, is one where either there is a unique or trivial solution. Alternatively, we may say it has no constant terms. This is stuff kids learn in their first year at Collidge- unless, like me, they are too busy wanking. 

The establishment of such homogeneous systems is indeed one of the conditions of linguistics.

No. Linguistics is about learning a lot of languages. It isn't about pretending Chomsky did anything useful. 

As for phrases, one of their members can be found in one system and another in a different system, in accordance with certain extrinsic variable factors.

Or intrinsic ones. A Judge may read into a phrase used in a law or contract stuff which isn't there for wholly intrinsic reasons- e.g. original intent, harmonious construction etc.  

A statement, however, is something completely different: it is inseparable from an inherent variant.

No. It can be separated from anything whatsoever. We do so all the time. 'My statement that you are a stupid bitch must be separated from the fact that I want us to do it doggie style while you say Deleuze level stooopid shit. After all, I talked dirty to you that time you wanted to fist yourself while watching Youtube videos of Rahul Gandhi.' 

Consequently, we never remain wholly within a single system but are continually passing from one to the other (even within a single language).

A system is merely a mental construct. We don't remain in it partially or wholly or on a part-time basis.  

A statement operates neither laterally nor vertically but transversally, and its rules are to be found on the same level as itself.

Thus when a witness gives a statement about the rules of grammar and that statement is 'Russian  is actually my cat which says 'miaow, miaow, miaow'' then you can find the rules of Russian grammar amongst those miaows. 

Perhaps Foucault and Labov are similar in this respect, especially when the latter demonstrates how a young Black can move back and forth between 'black English' and 'standard American' in accordance with rules which are in themselves variable or optional and which allow us to define regularities but not homogeneities.

French peeps thought young Black peeps say nothing but 'ooga booga, me rape yore white ass'.  

Even when they seem to operate within the same language, statements of a discursive formation move from description to observation, calculation, institution and prescription, and use several systems or languages in the process.

 A 'discursive formation' shapes and constructs social reality. What fucking 'social reality' have stupid French professors constructed? In any case, you have to do observation before you can do description. Calculation may not arise at all- e.g. in juristic contexts. Institutions or prescriptions too may be otiose. 

A group or family of statements is in fact 'formed' by rules of change or variation to be found on the same level, and these rules make the 'family' a medium for dispersion and heterogeneity, the very opposite of a homogeneity. 

No. We may classify statements into groups for some purpose. But they aren't formed by those groups. Considers the statement- 'I like smelly cheese'- which was made by a member of the Bourbaki group. It belongs to a family of statements made by other French people who like smelly cheese. It does not belong with the statements associated with Bourbaki as an approach to mathematics. Moreover, two members of Bourbaki might say very different things at the same time or at different times. 

This is the nature of the associate or adjacent space: each statement is inseparable via certain rules of change (vectors).

Some statements may be about vectors but, even if they are mathematical propositions, they are always separable. A vector is a quantity with magnitude and direction. There are different vector calculi to describe how they can change.  

And not only is each statement in this way inseparable from a multiplicity that is both 'rare' and regular, but each statement is itself a multiplicity, not a structure or a system.

Deleuze uses 'multiplicity' interchangeably with 'manifold'. Now a particular statement may describe a particular manifold but a description is not the thing it describes. No statement is a manifold anymore than a description of a cat can itself say miaow or lick its own arse.  

This topology of statements

there is no topology because there are no well defined sets 

contrasts both with the typology of propositions and with the dialectic of phrases. It is our belief that a statement, a family of statements, or a discursive formation is first of all defined for Foucault by certain inherent lines of variation

if they are 'inherent' then they are not a definition and can't define shit even for a shithead like Foucault. A property may inhere in a thing and a set may be defined as all the things with that property but a property is not the thing itself. It does not define what it may otherwise inhere in.  

or by a field of vectors which cut through the associate space:

a vector field is an assignment of a vector to each point in a space. There is no such thing as a 'field of vectors'. Any space can be associated with another space by an appropriate assignment.  

the statement therefore exists as a primitive function,

in which case it is its own derivative.  

or as the first meaning of the term 'regularity'.

Which it isn't. The first meaning of 'regularity' means being regular. In the case of statements, we might say that those statements which obey the usual rules of grammar are regular.  

The second area is that of correlative space,

which has different dimensionality 

which is not to be confused with the associate space.

only if it has a canonical embedding or is separable. But, if you aint doing math, you can confuse the fuck out of such terms because there is nothing here but nonsense.  

Deleuze, it may be argued, was trying to justify stupid shite written by Foucault like the following- 

Not, of course, that it was political practice that from the early nineteenth century imposed on medicine such new objects as tissular lesions or the anatomo-physiological correlations;

No one was crazy enough to suggest any such thing. Nothing was 'imposed on medicine' save the need to get people to pay for it. 

but it opened up new fields for the mapping of medical objects

Maps are useful. As Science advances, it is useful for some of its practitioners to provide a 'map' of what currently falls under its rubric. There is nothing sinister about this.  

([...] the mass of the population administratively compartmented and supervised [. . .]

This simply did not happen.  

the great conscript armies [. . .]

Actually, universal conscription only came in 1905. Previously, you could pay for a substitute or, during the Revolutionary and Napoleonic period, simply run the fuck away.  

the institutions of hospital assistance that were defined at the end of the eighteenth and the beginning of the nineteenth centuries,

France was greatly behind Britain (whose Poor Laws go back to Tudor times) and, at a later point, Bismarck's Germany. It was only in 1902, that France got a public health law. Universal health coverage only dates back about 25 years. On the other hand, it must be said, France is a nation of hypochondriacs who are addicted to suppositories.  

in relation to the economic needs of the time and to the reciprocal position of the social classes).

This is nonsense. There was a Bourbon fucking restoration! France lagged behind not just England but even Germany which was poorer in the 1870s.  

One can also see the appearance of this relation of political practice to medical discourse in the status accorded to the doctor [. . .].

Medicine has always been high status though 'blood letting' may have been left to barbers. 

Deleuze, being French won't point out that Foucault was simply wrong about French history. Instead he writes

We might object that all Foucault is doing is refining a very classical analysis that relies on context.

This isn't true. The 'classical analysis' is that soldiers and surveillance and prisons and hospitals cost money. Poor countries won't have very much in the way of them. But this is also true if citizens aren't keen on paying a lot in taxes 

This would ignore the novelty of the criteria which he institutes, precisely in order to show that one can articulate a phrase or formulate a proposition without always occupying the same place in the corresponding statement, and without reproducing the same particular features.

Kids understand that by the time they are 5 years old. You can repeat what teechur said and raise a laugh because you aint the teechur and thus don't get to beat the shit out of horrible little boys. 

And if one is led to denounce false repetitions by determining the discursive formation to which a statement belongs, one equally uncovers certain isomorphisms or isotopisms lurking between distinct formations.

For Deleuze, mathsy stuff was always lurking here or there. If he liked Math so much, why didn't he marry it?  

 
Context explains nothing, since its nature varies according to the particular discursive formation or family of statements under consideration.

Only if there is an axiom of unrestricted comprehension. But if a 'discursive formation' is useful- e.g is Scientific, Juristic, Bureaucratic etc- then there will be 'admissibility' criteria or restricted comprehension.  

If the repetition of statements is subject to such strict conditions, this is not by virtue of external conditions

Start repeating nonsense in court and the Judge will send you to jail for contempt. Defunding has the same effect. External conditions matter because money and not being sent to jail and ass raped matters. 

but as a result of that internal materiality that makes repetition itself the power that a statement is alone in possessing.

Repeatedly farting or waving your dick around has the same internal materiality and can lead to the same sanctions. 

Foucault shows, then, that a curve, a graph, a pyramid are statements,

No. We may say that they are statements or cousins of my cat Mitzie. But such statements aren't particularly useful.  

but that what they represent is not a statement.

Unless we chose to see them as representing some stupid shit.  

Similarly the letters written out by me, AZERT, are a statement, even though these same letters do not form a statement on the keyboard.

Only in the sense that they are also kissing cousins of my imaginary cat.   

In this case we observe how a secret repetition animates the statement,

Nothing animates that shite. 

and the reader is once more faced with the theme of 'the tiny difference that paradoxically creates identity' which inspired the best pages of Raymond Roussel.

 which were still shit when compared with Agatha Christie. But then, Roussel had inherited money. 

A statement is in itself a repetition, even if what it repeats is 'something else' that none the less 'is strangely similar and almost identical to it'.

because it too is a cousin of my imaginary cat.  

So the greatest problem for Foucault would be to uncover the nature of these peculiar features presupposed by the statement.

Features they inherit from the grandmother of my imaginary cat.  

But The Archaeology of Knowledge stops at this point and does not attempt to deal with a problem that surpasses the limits of'knowledge'.

Because then it would be called 'the Archaeology of not just Knowledge but also Ignorance'.  

Foucault's readers become aware of the fact that we are entering into a new domain, that of power and its relation to knowledge, which is to be explained by the sequel to Archaeology.

What the French knew was that they had not been able to withstand Hitler's power. Maybe this was because they didn't know that Knowledge does not have an Archaeology or even an arse Professors could lick.  

But already we feel that AZERT, on the keyboard, represents the focal point of power or of powerrelations between the letters of the French alphabet, depending on which one crops up, and the typist's fingers, depending on which one is used.

The focal point of the power of cheese-eating surrender monkeys may indeed be their equivalent of QWERTY. Thankfully, De Gaulled provided them with nukes. Not having an offensive military doctrine means you may as well surrender.  

As Foucault explains, The Order of Things deals neither with things nor with words.

Nor with pineapples pushed up your rectum by the Pope while the Sun King stands by laughing maniacally. That is its chief flaw.  

It is not concerned with object or subject, nor does it examine phrases or propositions, grammatical analysis, logic or semantics.

Coz Foucault wasn't Chomsky.  

Statements are not in any sense portrayed as a synthesis of words and things,

because they feature only words.  

or as composite phrases or propositions. On the contrary, they precede the phrases or propositions which implicitly presuppose them,

No they don't. A statement may use wholly novel phrases and may express completely original and unique propositions. No presupposing necessarily arises in such cases.  

and lead to the formation of words and objects.

When Deleuze talks not just words but also Pineapples and Planets and Palaces erupt out of his mouth.  

There are two moments when Foucault goes back on this: in Madness and Civilization he has recourse too often to an 'experience' of madness that is already inscribed in a duality existing between the states of raw things and propositions; 

Madness is not such experienced in that manner though a particular lunatic, like Foucault, may pretend otherwise later on.  

and in The Birth of the Clinic he invokes a 'medical gaze' that still relies on a unitary subject whose position never changes with regard to objects.

Whereas when a Doctor looked at Deleuze, Deleuze would turn into pineapples in palaces on planets far far away.  

All the same, these lapses are perhaps fake.

Foucault may always have been genuinely crazier than a shit-house rat.  

It is no cause for regret that the romanticism which contributed to the beauty of Madness and Civilization has been abandoned in favour of a new positivism.

The earlier book had some purple passages. The latter was tedious shite.  

This rarefied form of positivism, which in itself is poetic, perhaps helps to rekindle a general experience in the dissemination of discursive formations or statements, an experience which is still that of madness; while it also reintroduces into the various locations at the heart of these formations a mobile site which is still that of a doctor, clinician, diagnostician or symptomatologist of civilizations (independently of any Weltanschauung).

Deleuze, poor fellow, was in poor health. That's why he topped himself by jumping out of the window. Still, he needn't have wasted his entire life writing pseudo-mathsy shite.  

And what is the conclusion to Archaeology if not an appeal to a general theory of production which must merge with revolutionary praxis,

coz French pedants are tough guys like Che Guevara- right?  

and where the acting 'discourse' is formed within an 'outside' that remains indifferent to my life and death?

I wouldn't have been indifferent if Deleuze jumped out of his window and put a dent in my new car.  

For discursive formations are real practices,

Only if they actually change 'social reality'- e.g. by getting everybody to twerk the way Beyonce did. Otherwise they are just a failed attempt at pedantry or a pure case of mental illness.  

and far from being a universal logos their languages are transient and tend to promote and sometimes even to express mutation.

Deleuze could have turned into Prof. Xavier from the X-men if only he'd switched to English- right?  

So this is our definition of a group of statements, or even a single statement: they are multiplicities.

i.e. manifolds. A Lie group is also a smooth manifold.  

It was Riemann in the field of physics and mathematics who dreamed up the notion of 'multiplicity' and different kinds of multiplicities.

In a specific mathematical context.  

The philosophical importance of this notion then appeared in Husserl's Formal and Transcendental Logic, and in Bergson's Essay on the Immediate Given of Awareness (where he tries to define duration as a type of multiplicity to be contrasted with spatial multiplicities, rather as Riemann had distinguished between discrete and continuous multiplicities).

Like Husserl, Bergson started off as a mathsy dude. Maybe if he'd chosen English rather than French citizenship, he would have collaborated with Russell who shared his literary gifts. However, it was Einstein, not Russell or Husserl or Bergson who understood the true import of Reimann's work which Weyl, Cartan etc. elaborated on. Deleuze has done most to revive interest in Bergson but there are more math savvy ways- e.g. invoking concurrency problems in higher dimensional spaces- of saving anything attractive we find about his thought. 

But the notion died out in these two areas, either because it became obscured by a newly restored simple dualism arising from a distinction made between genres, or because it tended to assume the status of an axiomatic system.

I suppose Deleuze is thinking of Russell's criticism of Bergson and the manner in which Norbert Weiner brought in ordered pairs to overcome problems of reducibility in set theory.

One indefatigable scholar of Deleuze who tries to make out his math wasn't crap is Martin Calamari who writes-

As is well known, Deleuze's first reference to Riemann is found in the second Chapter of Bergsonism (1966). The underlying issue lies in Bergson's distinction between (quantitative and qualitative) multiplicities,

Bergson thinks that things treated quantitatively- e.g. sheep in a flock- must be differentiable spatially (i.e. by location). This is not the case. Consider the names of Allah in Islam. There is a given number for the approved names but there is no spatial distinction.  

and the attempt to overcome the classical dichotomy between the One and the Multiple by affirming a substantive multiplicity.

The thing is nominal, not substantive. Suppose we define a 'flock of sheep' as 50 sheep. We may say, 'Abraham had twenty flocks of sheep' and from this an agronomist may conclude that he must have had access to, or ownership of, 20 hectares of pasturage. That may appear 'substantive'.  But we could also say 'the God of Abraham had 99 names according to Islam' though, clearly, this is not substantive. It is purely nominal. 

On the background of this philosophical problem, Deleuze synthesises, in a particularly dense passage, one of the key aspects of Riemann's theory of 'multiplicities' (manifolds):

A manifold is a set of points, or topology, which is 'locally' Euclidean. It has nothing to do with 'multiplicities'. Rather, it dealt with a situation where the occupied space has curvature but there is no access to the coordinate system of an 'embedding' Euclidean space. But a 'manifold' represents a unity- that of a space which has one curvature at the infinitesmal or purely local level but a different curvature macroscopically or globally. But, that is provided by a 'connector'- e.g. of a Cartan type. 

'In fact, this problem dates back to a scholar of genius, Riemann, a physicist and mathematician.

A mathematician of genius. He wasn't a 'philosopher' or a 'physicist'. Gerte Hermann, however, was both a neo-Kantian and a mathematical physicist who showed Von Neumann's proof re. hidden variables was wrong- a result similar to Bell's. She was an actual Social Democrat savant who proved very useful to her country. 

Riemann defined as 'multiplicities' those things (les choses)

meromorphic functions- i.e a ratio of well behaved functions. But functions aren't things.  

that could be determined in terms of their dimensions or their independent variables.

things aren't 'determined' by any thing other than the fact that they exist as things. Nothing relating to a function is necessarily a thing.  

He distinguished between discrete multiplicities and continuous multiplicities.

Because functions are distinguished in that way. Things may be, but then again, for all we know, they may not. All we can say is that 'perspectivally' this distinction can usefully arise whether it is true or not. Had Deleuze read Gerte, he might have preferred a notion of 'splitting of Truth' as the basis for an analysis of 'Schizophrenia & Capitalism'. The fact is the latter must have 'ontologically dysphoric' goods and services if the Lancastrian characteristic space does not coincide with the underlying commodity configuration space. If people with a modicum of math and econ want to 'repair' Deleuze, they could do so easily enough just as we do with Keynes or Marx or other such shitheads.  

The former contain the principle of their own metric ( portaient le principe de leur métrique)

No they don't. For one purpose, a flock is 50 sheep. For another, e.g. that of a meat packing plant, a flock of sheep is what generates 1000 kg of usable mutton. Thus, for a particular breed of sheep from a particular ranch, flock is 30 sheep. For an inferior breed from a shittier ranch, it is 60 sheep. Gerte's Nelsonian 'Neo-Kantianism' just cashes out as Pragmatism. Pity she didn't have a penis. Had she done so, everybody would have understood that the Universe aint locally real. What is accessible can't contain any fucking general principle because it is essentially stochastic. 

(the measure of one of their parts being given by the number of elements they contain) (la mesure d'une de leurs parties étant donnée par le nombre des éléments qu'elles contenaient).

Coz, in reality, all sheep are the same weight or are equal for all possible purposes- right?  

The latter found a metrical principle in something else, even if only in phenomena unfolding in them or in the forces acting in them (ne fût-ce que dans les phénomènes se déroulant en elles ou dans les forces agissant en elles). (Deleuze 1988: 39/31-2)'

A family is a 'continuous multiplicity'- till it goes extinct. It has no 'metrical principle' precisely because nice peeps, like my Mum & Dad, can have a wholly horrible and useless son. Who could have predicted that in advance? What 'principle' so unfolds in families such that they never suffer the birth of a fucking useless imbecile of a son? 

To this passage Deleuze adds a very important footnote. First, he refers to Riemann's famous Habilitation lecture 'On the Hypotheses Which Lie at the Foundation of Geometry', dating to 1854 (but only published posthumously in 1868). As is known, it is in this lecture that Riemann first introduces the concept of manifold or manifoldness (Mannigfaltigkeit). Second, he refers to one of the major works of mathematical physics of the early twentieth century: Space, Time, Matter (1918), by the German mathematician Hermann Weyl 

whose wife was Husserl's student but who moved in a Brouwerian direction. But, ultimately, what is that? Pragmatism. It's where Grete and Frank Ramsey were heading. Or so I fondly believe not because but despite and therefore because I'm as stupid as shit- i.e. a useless tosser. 

 Weyl's book constitutes the first detailed exposition of Albert Einstein's general theory of relativity; as well as, starting in subsequent editions -on which the French translation adopted by Deleuze is based -Weyl's original elaboration of the first unified field theory.

gauge field which corresponds to the Lie algebra of a group generator. This is the stepping stone to Kaluza-Klein, Super-symmetry, String theory etc.  

Finally, Deleuze suggests that even Husserl, although differently than Bergson, was influenced by Riemann's theory.

He developed a theory of manifolds as an ontological form. The French see Husserl as a bridge between Reimann and Bourbaki.  

Now, while the philosophical importance of Riemann for Bergson and Husserl will be frequently repeated in Deleuze's works, except for a passing mention (which we will encounter), Deleuze never referred to Weyl again.

Grete could be said to be the bridge between Weyl and Nelson type neo-Kantianism and its progressive Social Democratic agenda.  

 

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