i) To think Number “in its being” is to nominate an ontological schema in which numbers (whole, real, infinitesimal…) are given. There is no way to “think Number” without such a gesture of nomination: attempts to derive the being of Number from some other given (the extensionality of concepts; the totality of the thinkable; the permutations of a syntax) either founder in contradiction or yield only a castrated, procedural numericality. A novel axiomatic is required.

ii) Ontological thought is not divination, but nomination. To think something in its being is not to intuit, via some extra-rational means, its eternal essence, perceiving it as it might appear in divine ideation, but to determine what there is within the ontological situation (the count-as-one of the resources of ontology in general) that delivers it to thought.

iii) Through the inscription of a new schema within the ontological situation, we are able to separate Number, thought in its being, from those numbers - numerical beings - that are accessible to our thought. We are able to think a great profusion of numbers, but our thinking of Number tells us that the numbers we are presently able to think are an immeasurably tiny subset of the numbers that there are.

iv) Not even a subset, because the numbers that there are do not form a set. The being of Number is an inconsistent multiplicity: no consistent presentation of all of Number is possible. Our access to Number is through this or that numerical situation, this or that consistent presentation of numericality. No such presentation can exhaust the being of Number.

v) What is presented within the ontological situation, wherein Number is thought in its being through the inscription of an ontological schema, is not the being of Number (which cannot be consistently presented) but the thinking of Number in its being. The ontological schema of Number is a being, a consistent multiplicity (in this case, the doctrine of “surreal numbers”). That of which it is the schema is not a being, but the inconsistent multiplicity of the being of Number itself.

vi) There is no mystery about this. In mathematics there are sets, which must be well-founded and consistent, and proper classes, which are “larger” than sets in that no set can “contain” them. A proper class may be regarded as supplying a “law of the count” for all of the sets that can be drawn from the class; but this “descent” from inconsistent multiplicity to consistent presentation is not the predicative separation of a subset from a set. Neither is it necessarily the determination of a finite section of the infinite. The “largeness” of a proper class is not the vastness of infinity, but the non-containability of the class within any set, even an infinitely large one. A proper class is unpresentable, but the ontological schema of the class (which determines the property that every set within the class must have) is a presentation: what it presents is that there is something which is nevertheless itself unpresentable.

vii) Thus, the question of what is or is not accessible to us of Number is not primarily a question of our limited mental powers - the poverty of our mathematics, its irrecusible subservience to our “species being”, or any such pragmatic or empirical limitation. Such limitations no doubt exist, but the separation we have been speaking of between Number, thought in its being, and the numbers to which any particular numerical presentation may provide access, is not an empirical separation. No being that thinks - that organises its thoughts into consistent multiplicities - can think all of Number at once. But a being that thinks can indeed think that this is so, and for what reasons.

viii) The “ancestral” time prior to the emergence of any animal consciousness is (by definition) inaccessible to thought as something present to it. Thought and the ancestral have never been present to each other, face-to-face. The claim of science to be able to identify the “arche-fossil” (the object residing within the depths of ancestrality) and define its properties does not rest on any powers of mystical divination: the scientist does not presume to be an intimate of the Creator, privileged to share His innermost thoughts. Neither is mathematics conceived of, in neo-Platonist fashion, as a bridge between the human and divine, a means of deciphering the inscription within nature of its maker’s mark. In any case, the unpresentable can no more be present within the Creator’s thoughts than it can within ours.

ix) However, as we have seen, mathematics is able to think that something is that is not thinkable in its totality under the sign of presence. It is this thought that breaks the correlationist circle; for correlationism insists on thinking even the absences in its thought under the sign of presence, as if marking off a register. Its “lacunae” are so many rogues, truants, inscrutable oriental gentlemen; they are not thought in their being, but as components of the being of a thought. The arche-fossil cannot be thought in this way.

x) Neither is it claimed that the arche-fossil is somehow seized by mathematics, which succeeds in apprehending it through the achievement of a higher level of technical refinement than other kinds of thought - smarter detectives, better surveillance equipment. This is not a sales pitch: we are not declaring that mathematics reaches the parts other disciplines cannot reach. What is significant about mathematics is that we may recognise here and there in the work of mathematicians the gesture of inscribing a new form in the ontological situation. Only a gesture of this kind can determine that the arche-fossil is, quite separately from how it is for us.

xi) This act of recognition Badiou calls an evental nomination: the decision that such and such an axiomatisation shall be determined as fixing the being of that which it axiomatises. Meillassoux emphasises the groundlessness of any such decision: it is certainly possible to think the being of Number otherwise than through the schema of the “surreal numbers”, or being in general otherwise than through the Z-F axiomatisation of sets. This emphasis on the contingency of nomination is detectable in the name that Meillassoux gives to the venture of ontological thought: speculative realism.

xii) Speculative realism is a realism because it concerns what is, and not merely what our thought is able to grasp in its totality under the sign of presence. It is speculative because there is no possible ground for the act of evental nomination on which its procedure depends: it must set out anew the terms of its investigation, and proceed on the basis of a fidelity to those terms. We are still in a sense in the situation Lyotard described as that of postmodern science: that of legitimation by paralogy, oriented towards a thought of the sublime.

Almost you could forgive them for having invented emo.

Comment in Slashdot discussion of Iranian nuclear program:

| Violence creates more violence.

Quite interestingly, so does XML.

Two more guitar things. Clean:

Noisy:

My submission to Roger’s Profanisaurus made it into this month’s Viz (May issue, no. 175).

This may be the first time an entry in the Profanisaurus has ever featured the word “ontological” (or the phrase “radically divergent”). Then again, it may not. One of my favourite definitions from a few months ago contained the word “corvoid”. Viz has frequently illustrated the truth of J. P. Donleavy’s observation that the power of a coarse word may be greatly amplified if it is combined with an erudite one (Donleavy’s own, unsurpassed, example beginning “you unconscionable…”). The admirable Richard Seymour is also an accomplished practitioner in this area.

Annoyingly, I didn’t get a pencil - probably because I submitted online, and didn’t therefore supply a proper (non-email) address. Next time inspiration strikes, I’ll use the post.

I did briefly consider trying to work something up about well-pointedness, but the recondite element is just too recondite and the coarse element too bloody obvious (not that this is always necessarily an obstacle). However, I do think there is an immediate and urgent requirement for someone to come up with a definition of “Boris Johnson” that matches Dan Savage’s appropriation of “Santorum” for stomach-turning filthiness.

Just stumbled across VBCorLib, a backport into VB6 of many of the common classes, exception types etc. of the .Net framework. This strikes me as heroically sad. The saddest thing of all is that I might have occasion to use it. Who’d have thought I’d still be writing VBA, eight years after my first attempts at automating myself out of a job using only Excel and what I could remember of BBC Basic?

High spin    sloughing

thises

    thats

lens-flare

One about how traumatised he was when someone bared their bum at him at a concert:

One about…well, goodness only knows what, to be honest.

I like that it contains references to the Northern Line, a tube line I had never been on when I first learned the song about ten years ago and now use on a daily basis. Is the line about to “falling so far on a silver spoon” a reference to cooking up heroin, or just, y’know, symbolism? Anyways, I think we can reasonably surmise that he was feeling a bit low when he wrote this one. And most of the others, come to that.

Two short little things: O Waley Waley

and The Star of the County Down.

Kids! Just because you can do this, doesn’t mean you should:

Do as I say, not as I do!

This is how metal should be: horrible, perverse and sickening.

Love that guy’s witchy hat

Hilarious blissblogger post about Goldfrapp’s recent turn to “weird folk”. I claim a no-prize for recognising the contents page at the end as belonging to C. S. Lewis’s That Hideous Strength, from which the Belbury Poly derived their name…

demi-vierge

A perennial favourite. I do wonder who it is who wants to know, and why. Perplexed readers of D. H. Lawrence, by the looks of things. And maybe people looking to improve their rating on the…

chastity point system

I love this idea! As Augustine might have said, O Lord make me three and a half points chaster, but not yet. Presumably part of abstinence-based sex education, an idea the potentially revolutionary kernel of which has yet I feel to be grasped (unless you count Lysistrata. Or, come to think of it, Nova Express).

metallica react to torture claims

A story that somehow completely passed me by. Unless it’s about the US army playing Metallica at high volume to stress detainees, in which case it’s disgustingly familiar.

no future lee edelman summary chapter 1

Fun little book, but I fear the moment has passed. “Reproductive futurism” is still a handy coinage, though, and I can’t absolutely promise never to refer to anybody as a sinthommosexual ever again.

no rational being can fear a thing it will not feel

Larkin’s “specious stuff”. I do think he invented his own particular way of being scared of death - or more exactly of being dead - which is quite an accomplishment really.

carol anne duffy admired

Not on this blog she isn’t.

what does dominic mean?

If I could tell you, I would let you know.

April, the new album by Mark Kozelek’s Sun Kil Moon, is very good indeed.

This marvellous person is Dr Eugenia Cheng, and she is going to tell you about natural transformations:

There’s a whole series of these on YouTube. I wish they started with some more basic topics: I’m still strugging a bit with things like limits and equalisers.

I also wish I understood why it was “mon-oid”, but “moan-ad”.

A night-visiting song:

Happiness plays at most a fleeting role in Alan Garner’s Red Shift, while like The Owl Service before it is a book about trauma and traumatic memory, about the unhappiness of repetition. The lesson Garner draws from myth and history is that there are recurring patterns of human interaction, repeatable configurations of intersubjective violence. The mythic story is both an abstract template of experience and, as narrative, a realization of that experience, a way of binding its emotional energies into a concrete form (like the plates in The Owl Service, literally imprinted with the form of the lady of flowers/owls). The power of myth is a power of repetition: Garner’s characters find themselves seized by myths and compelled to act out (or work through) their assigned roles within them.

The metaphor Garner uses for this process is one of energetic accumulation and discharge: like a battery storing electricity, the myth holds emotional energies in reserve. The person seized by a myth becomes a conductor for its energies, undergoing in the process a partial loss of selfhood and autonomy. It is not a coincidence that Garner’s main characters tend to be adolescents who experience their own passions as both inner turmoil and alien compulsion, as if sexuality were a kind of haunting and sex itself a kind of poltergeist activity.

Red Shift is putatively a “Tam Lin” story, a story about possession and rescue. In two of the book’s three overlapping narratives, the male epileptic character is rescued from his own inner violence by the steadfast love of a long-suffering woman. In the third story, the pattern appears to be broken: the relationship between Tom and Jan reaches a point of crisis from which it may not recover. (The book’s - literally - cryptic endnote has suggested a possible reconciliation to some readers, and a threat of suicide to others). Unable to go all the way with Tom in his “debasement”, Jan ultimately refuses the role to which the myth would have committed her: “It would like to go now, please. It feels sick. It’s had enough. It has a train to catch.”

It can’t go on; and in Red Shift it apparently does not. By referring to herself in the third person, as an “it”, Jan separates the debased object of Tom’s sexual jealousy and rage from the “I” who had loved him. Love cannot survive this separation: in the person I love there is always an “it”, an intractable element which refuses narcissistic identification; conversely, to be loved is to be “it” for another, to experience oneself as containing a part which is literally unloveable. Jan identifies this as the reason why there is always a period of surprise and resentment when they meet again after being apart: “The longer I’m away from you, the more certain my love for you becomes. Because we don’t have each other, we have memories, and these memories simplify themselves. We forget our flaws and create ideals of each other. Then, when we meet, the difference shows”.

What is always disastrous in love is to try to force this point – to demand to be “wholly and completely” loved, not in spite of one’s faults but because of them; or to seek to possess and control that in the other which one cannot love as oneself. This is what Tom’s jealousy of Jan’s former affair with a German wine-grower drives him to attempt, to blot out the “it” of his own shameful inferiority by obsessing over sexual performance:

“Catch up,” he said. “Rub out. My mistakes. My clumsiness. Next time it’ll be all right, every time, and it isn’t. Next time will make up for him – and me. Never. Poached eggs. Galactic. Red shift. The further they go, the faster they leave. They sky’s emptying. God, this wind’s cold.”

(“Next time it’ll be all right, every time, and it isn’t” - very Beckettian formulation, that). The consequence of this obsession is that he, too, becomes reduced to an “it”: as Jan says, just prior to the above quotation: “You used to give so much, oh, it was marvelous to be with, everything new and giving, like colour for the first time. Now you’re all one thing, and I don’t know what to do”. The unfortunate truth is that Tom’s cleverness, wit and powers of invention, the marvels he is able to produce for her, the shared poem of their lovers’ language, do not finally have any traction over the real of sex.

But what is this real? For Tom, sexual shame is correlated with class anxiety (“More of a caravan sticks to you than an old fry-up”); his parents’ simultaneous prohibition and noisy enjoyment (at close quarters) of sex; overhearing his father saying “I’ll not beg” to his mother, a line he repeats almost unconsciously to Jan. The German wine-grower Jan slept with before him was a well-off, indulgent, older man - “that warm man”, Jan calls him, contrasting with Tom’s repeated cry of “Tom’s a-cold” – whereas Tom is callow, spiky and skint. Whereas for Jan her first sexual experiences enable her to grow more fully into herself, becoming the person who first attracted Tom’s attention and interest, for Tom the gateway of sex opens onto a maelstrom of insecurity: it is precisely as a sexual being that he is most unloveable, lapsing into a variety of borrowed poses from disgust-filled puritan to callous working-class tough.

Red Shift is such a bleak book that it is easy to overlook the compelling portrait of real happiness that Garner makes of the early part of Jan and Tom’s love affair (paralleled by the scenes with Alison and Gwyn in The Owl Service). The problem the book poses is how the happiness of love can accommodate the real of sex, when the latter is indexed to humiliation, shame and violence; it suggests that the means available to Tom’s doubles from past ages (represented by the votive axe, or “thunderstone”, which Tom in turn acquires but gives away to a museum) are no longer accessible in the present day. But Red Shift itself is such powerful myth-making, or myth-retelling, that it may perhaps become a touchstone in its own right for some of its readers.

Finished re-reading Red Shift today, which quotes Sweet William (”I’ll dye my petticoats crimson red”) amongst others. Another song about mislaid virginity (but aren’t they all?) seems appropriate:

While we’re on the subject of folk: here’s a quick quiz: what was Prince Heathen’s name? It’s not a trick question. Child doesn’t give an answer, and neither does any version of the song that I know of, but he is named in the hagiography of Saint Margaret of Antioch, and it’s definitely the same story…

The devil made me do it.

This one is more recognisably music…