THEOREM

Today I got up with this line in my head: don't worry about the soul. That has been fixed. As I was dreaming about walking around Riemann's zeta landscape, climbing the mountain and looking down to the zeros of the zeta function, I felt fixed in my soul. When plugged into Riemann's prime formula, each zero of the zeta function, or the points that correspond to the complex numbers, produces a wave corresponding to a pure musical tone. Simplified here, and in line with my own trivial thinking about Riemann's hypothesis—which, for the life of me, I don't know why I tend to think of on Sundays—the idea that one can chart exactly the occurrence of prime numbers on an infinite line, is fascinating. As we tend to think of the primes as occurring at random, the notion that one can orchestrate them, when one 'knows' them by plugging them into a harmonic scale, creates the illusion that the primes possess some sort of cosmic otherness.

Now, why the soul, via Riemann? Yes, because since March 18, when Grigori Perelman was announced to receive the first Clay Millenium Prize Problems Award for his resolution of the Poincaré conjecture (consisting of 1 million dollars, the prize was instituted in 2000 with view to be awarded to anyone who will come up with a proof for any of the 7 most intriguing mathematical conjectures), I've been thinking about the reason why I didn't become a mathematician myself. The story is too long and lousy, so I won't get into that, but I do want to mention the fact that there is out there a beautiful solution to such regretting anguish. Perleman, who is only two years older than me, and whom I would marry on the spot if he didn't live with his mother and was so sensitive—he declined the Fields medal in 2006, and gave up mathematics because he thinks that the discipline is now devoid of mathematicians with intact integrity—formulated a proof for what is called the soul theorem... The soul is in general not uniquely determined by the manifold...

I may not have become a mathematician, but by treading the landscape of analysis (the opposite, as it were, of algebra), I get a sense of the fact the even the greatest ironies in my life, if seen as symbolic inconveniences, can be orchestrated to yield the output zero, Riemann's laughter at incongruities. Schopenhauer once said: “every good joke is a disrupted syllogism.” The question of the soul is then, still, a question of what we choose to believe in. Today, I believe in numbers, even if, cosmically speaking, well, another long and lousy story...



Comments

Mark Daniel Cohen said…
"I expect a lousy story is nothing other than a suspended syllogism, and I know that every argument is a musical composition - you need only feel its structure. And therefore, I would humbly and inappropriately suggest what I ever suggest to myself - finish it. "
Camelia said…
Mark, what a lovely comment. Thank you for that. Suspended syllogisms are interesting. People talk about quantitative or mathematical syllogisms, which are utterly formless syllogisms. Form is good, but formlessness is more intriguing, as it requires, among other things, the notion of suspension. So, of course, some things are best left in the unfinished, formless, especially when they belong in a category that defies concrete understanding. You see, I don't think I understand myself why I never became a mathematician, apart from blaming it on ill circumstance, hence the lousy and inadequate feeling about it all. But perhaps some day I'll make it very simple. I'm good at that. At least.
Anonymous said…
As a mathematician myself and at the same time an admirer of literary talents I think this is an excellent post! I never thought of the Riemann's hypothesis in this way but I must admit this view makes it so much less depressing!
(Btw. I've been reading your posts for awhile- they're fresh, smart and snappy...any tips/strategies for writing like this? i.e. tips for writing math papers? ;))
Mark Daniel Cohen said…
"My pleasure. And it could well be much to the point that I came across your post while in the midst of reading James R. Newman - again. "
Camelia said…
I like anonymous mathematicians who think that my rantings are snappy and fresh. In fact this very comment so makes my fingers burn that I can't resist the temptation to deliver a set of threes on 'how to' write a 'smart' on top of it math paper. So here goes something:

1.Keep it simple. And yet allow yourself to move with ease between beliefs. In his youth Bertrand Russell was ready to swoon over the transcendental power of mathematics. In his 80s he dismissed his youthful enthusiasm calling it nonsense, and then referred to mathematics as being nothing other than the sum of tautologies. This being the case, you can start your paper with stating theorem X in elegant and composed prose, yet suggesting its vast beauty, only so that in the proof of theorem X you can start embellishing by using some other symbolic language than the strictly mathematical one. Look at music. My favorite contemporary violinist is Maxim Vengerov. Not only is he a smashing player but his master classes are a gem. He always entices people to bring to a very rigid structure of a Bach piece or something else that's demanding a good dose of imagination. Create a scenario, he says, and the sillier the better. In other words, be a mathematical hybrid between Rudolf Valentino and Groucho Marx.

2.Know thyself. Write for yourself and strangers. Don't write for peers. Write for yourself and strangers. Thinking of how afraid Cantor was of that schmuck of Kronecker, and how he thought that he had to write for him, so that he wouldn't dismiss everything, makes me cringe. Waiting for others to recognize what you do is a waste of time. Sure, recognition is crucial if we want to score a good job, but the lack of it should not be turned into a personal failure. That's bound to depress the shit out of everybody. Perelman had the right idea when he decided to say to all: why don't you go fuck yourselves? People think he's crazy, but I'll tell you a secret: it won't surprise me at all if I met him on top of a mountain, digging the earth, and calculating the speed of clouds. While he wouldn't be of much use to the 'community', he sure as hell would make my day. A genius never thinks of himself as a genius. A genius knows what he knows, and that's all. If people want to know what a genius knows, then they will, and if they don't, they won't. This even has a wider application: generally, if people want to know you, they will, and if they don't, they won't. If you know what you give, and you're happy with that, you can't think of it as being your loss, if people decide not trust what you say, dismiss you, or telling you to go fuck yourself, which may also be the case.

3.Write for the occasion. Be fearless. Donald Barthelme once said: “Writing is a process of dealing with not-knowing, a forcing of what and how.” Force your limit, but also know it. Math is mysterious, it moves, and it demands. Whichever way the theorem goes, be grateful for having been allowed to experience getting there, wherever 'there' is. End your paper with 'thank you.'
Mark Daniel Cohen said…
"Thank you for referring me to your remarks on writing mathematics. The first and third thoughts are elegant and balletic. However, the second is indispensable. There is one moment's touch of qualification - if we want to score a good job - and I would put, and have put, and have spent my life putting the matter with no qualifications whatsoever - or so I've been told by the few friends I have left. (Actually, that should be in the singular.) Those who are like you will find you, and to be of concern to anyone else is humiliating. So too, to be concerned with them. I wish them well, I hope they have every success they desire, but they have no business here, and they would be happier some place else. ("Tell me what you think of me." "But I don't think of you.") Besides, the absence of the distraction is to the very soul of the purpose. Even the slightest habit of thought on anything other than what one is pursuing, and one will never have it. "Those who attain excellence, commonly spend life in one pursuit; for excellence is not often gained upon easier terms." - Samuel Johnson. And excellence is the only freedom. There is no other.

Some of the argument for this thought is in the current issue of Hyperion, in the dedication to James Rossant, which I wrote. I suppose I was talking about more than just him. "
Camelia said…
Mark, you nailed precisely what I was also saying in brackets. Last night I watched—again—the documentary: Glenn Gould, Hereafter. Every time he gets to the point where he passionately and very sanely discredits the so-called benefits of being a public performer, my hair rises. At some point he has this discussion with Yehudi Menuhin, who is in favor of the energy that the crowd gives him, and who tells Glenn: 'if I have to follow your argument and only record, not perform, then I would have to conclude that you're basically happy with only showing people how to climb a mountain on TV, rather than giving them the possibility to go there with you and try real alpinism on their own.' To this Glenn says: 'nonsense.' He sticks to his belief that making music, which he is adamant about, should be the concern of every performer, and that independent of insufferable reviewers and gatekeepers or rich bourgeois snobs who only pretend to understand what you do. So he climbs his own mountain, he climbs the microphone, and from there he plays for himself and strangers. And this is exactly what manages to touch people: his undisturbed excellence. His refusal to be anyone's pet, and his refusal to follow idiotic, conventional, and scared peers. Oh, Glenn was beautiful. He was sublime in his relentless. “People like you will find you,” you say. Indeed they do. Even if it is only for the hereafter. In the documentary, I like how Bruno Monsaingeon, the director, captures the total intimacy between Gould and his strangers, which is shown to be far more valuable than that between him and his concert hall audience. An Italian tourist is shown to have imaginary conversations with Gould while in Toronto, tracing his steps: 'Glenn, my love,' she asks him in a most moving moment of genuine concern: 'is it true that you took so many pills? Why did you do it? Do you have a girl, are you engaged? Glenn, you gave me so much, my most beautiful moments in my life.' Another, a Russian, disseminates her concept of Gouldanizzare, of being galvanized by Gould to everyone she knows. She has turned this into her life project, that everyone she knows must know Gould like she does. So, this is what excellence does. It makes us forget about ourselves and appreciate the mountain we each climb, with Gould, others, or by ourselves, if we should be so lucky to be able to afford it. When you're on top, or flying, it is hard to feel humiliated.
Anonymous said…
Thanks Camelia and Mark for your comments and direct references! Your suggestions make me realize that indeed my biggest fear is to be judged negatively by the others (yes, I am a woman in an academic environment dominated by sometimes overly serious guys etc...)
But I love making up stories, love simple and elegant things turning complex, and appreciate originality- let's see how my phd thesis will turn out, now that I got a new positive perspective on writing it!
Camelia said…
You're welcome. As to measuring up to the seriousness of the guys, I don't want to sound patronizing and say, get over it honey, or maybe I do, now that I think of it. Yet if I'm allowed another word that is not fueled by aggressiveness, I'll say what I say to myself: measure up to your own imagination, and you'll do fine. What do you work on?
Mark Daniel Cohen said…
Yes, exactly. The only humiliation I know is self-betrayal, which of course does not arise with the uncompromising dedication to a purpose. And I am baffled - not in dispute but baffled - by the Menuhin posture you recount about obtaining energy from the crowd - depending on their energy as far as I can tell. I simply do not understand this kind of thinking, this kind of feeling. It eludes me utterly - I do not sense the allure of it. To be dependent on others for the achievement of one's own goal - to be dependent in this - and what then has one discovered, and what has one to offer as a gift, for that matter? What good is one to oneself, or to anyone else if that becomes the issue - where is the generosity in that? Not to show people how to climb a mountain but to give them the chance to go there with you. Am I missing something here? Sounds strangely similar, to adopt someone else's form of thought, to giving someone a fish rather than teaching him how to fish. A further failure. But then - I study Nietzsche far more than I adopt him - or anyone else in fact - but if ever he was indispensable, it was in this: "Neither rule nor obey" - and there is something of both in this.

Thank you for reminding me of the Glenn Gould film. I have not seen it in some time, but I have left behind Gould's example and inspiration for no more than a few days, perhaps weeks, at a time. I keep something of his on me at all times, along with a few other imperatives. And I must admit you have read my mind, with your point about touching people with one's undisturbed excellence. (Great adjective) To find the beauty (that hardly seems the word any longer), the entrancement, in the impeccable expression, no, the impeccable gesture, the exquisite curve, rather than mutual wallowing in joint commiserations, in collective self-pities, which we pretend are sympathies and are generous. I will be doing an essay (if that's the word for what I'm aiming at) for Hyperion, probably in October, on the Super-Massive Black Hole in the center of the galaxy - most galaxies - an aesthetics essay that will touch on this matter of excellence rather than, well, rather than a number of things we've taken as the proper objectives of art. But, that will come, later.

For now, I'll be presumptuous on your forbearance and offer you a reciprocal gesture, in response to the moments of poetry you've offered me and many of us through your blog and in Hyperion. There is a poem of mine in which you might locate something of interest. You will find it at http://homepage.mac.com/cohenmd1/Poetry/Hollow.html

It is one small piece of a much larger project - rather, a mission - and it is an example, for good or for ill, of what I have managed by way of keeping no one's counsel but my own.
Camelia said…
Mark, thanks, again. While reading your wonderful poem I had a strong feeling that what it wants to say is that you can't lose that which you never had, but that which is nonetheless contained by everything that you did have. Contrary to popular belief, if everything and nothing coexist simultaneously, they do not annul each other, but form a kind of geometry that lends itself to touch rather than dimension, however nonsensical this might sound. Your excessive on purpose alliteration presses on and I was reminded of Borges's story Tlön, Uqbar, Orbis Tertius, where he says this: “Centuries and centuries of idealism have not failed to influence reality.” Your phrase: “and face to face to fan in symmetries” struck a core, a hollow one these days, as it renders the situation of reductio ad absurdum powerful in its impotence. Yes, I'm thinking... Listen, I'd love to publish your project with EyeCorner Press. Just say the word, if you're interested, and I'd even write a nice introduction, if you want.
Mark Daniel Cohen said…
Camelia, several points, and the most important is last.

Again, you read my thoughts, very concretely: a kind of geometry that lends itself to touch. I am working on several philosophy books simultaneously, one of which, and the most personal for me, is titled Treatise on Poetic Reason. One of its axioms is the proposition that all thought, prior to acquiring semiotic character, is geometric - that thought is fundamentally geometric. (This is a result of one of my arguments with Kant - not an argument with him actually, but my contention that Kant's writing of the first Critique several decades prior to Gauss was deadly to his objective.) Another of the book's axioms asserts that geometry is not visual but tactile. (As is sculpture, both points being obvious, I think, the moment one considers them - at least, it took me that long, ultimately.)

(By the way, you'll probably enjoy this thought - the book is organized like Wittgenstein's Tractatus - geometrically, the numbering being a coordinate system - except that Wittgenstein worked in two dimensions, and this book will work in three - http://www.facebook.com/l/6a1f3;xxx.xxx.xxx)
Second, thank you for the reminder about Tlön - it's been too long since I entered Borges - I've not been home since the accident and I'm foreign to my library, although the iPad has helped enormously. Along with Shakespeare, Mallarme, Beckett, and Hopkins (for sound, I suppose that's self-evident), he's essential to my mission.

And - most important - Thank you for your offer to publish my work (it's my real work) in EyeCorner Press. I would be honored for you to publish the work and, in particular, honored to have you write an introduction. I must give you a better idea what I meant by mission - not really an orchestrated project.

My mission, my real work, is poetry - as I understand poetry, which is very English language, very traditional, very Shakespearean in sound and technique. It is also very Beckett, I believe - there are perhaps a thousand ways to go about explaining this, which means I shouldn't try, so I'll save that for another time - reading it is the most explanatory.

What is available is a number of lyric poems, most of them longer than The Hollow at the Core, a large number of translations of poems, some of which have been published in Hyperion, and a one-act verse drama, which is - I'm told and I believe - the most successful example of my literary objective.
Please let me know what you'd like to see, and what you think would be appropriate content for a book. I can make my suggestions but of course, they'll be more meaningful when I can discuss material you've read.

Thank you so much for the offer, and for the obvious compliment implicit in the proposal. It is greatly appreciated, which is no contradiction to my basic posture. I believe it's all a zero sum game - the less one hungers for general, anonymous approval, the more one can relish individual, personal appreciation.
Camelia said…
My dear Mark,

Jesus fucking Christ, I want to say, but I don't want to sound ever so vulgar, on telepathic things and the like. You're on with the publishing of your work. And I shall be most delighted if you designed the whole thing yourself. Give me a camera-ready file, and I'll "fling the monster to the public" (Churchill's words) in a snap. We don't want to waste time. Send me whatever you think is appropriate and resonates with you the best, and I'll throw myself at writing an introduction with the best of my energy. I'm quite sure that I'll have no problem tapping into your thinking. As for some geometry in philosophy, I'd say it's about time someone other than Borges remembers it. “We already know that in Tlön the subject of knowledge is one and eternal.” Yes, I read for the writing that astounds, not the truth. The only truth I believe in is the one I can catch in the astonished eye. There is enough knowledge in it to confirm my certitudes as there is enough mystery in it to keep me in a state of marvel if I lived forever.
Mark Daniel Cohen said…
Exceptional, and well phrased - the vulgarity is only in the intention and not the language, and its other name is Philistinism, from which you certainly do not suffer.

It will take a while for me to be able to put this together, but then, I'm sure there's no rush, not for doing something that's been waiting to happen. Of course, I remain in my convalescence, although I am getting very impatient to be up and about my life again. In the meantime, I have just finished a book (well, the introductory essay for an artist's book), this last issue of Hyperion, an article in the latest issue of Sculpture magazine, my day job (managed by people who don't want to understand what it means to be on disability, something that is going to be resolved before very long - I'm not pleased), and the next issue of Hyperion. Not a bad work load for someone laid up from a rather serious care accident. But then - if you can, you must - unfortunately, much of the world exploits that near natural law, which is the beginning of my argument in defense of elitism. (Nobody wants it eradicated - if it were, they'd have to do their own work.)

I will consider what I'd like to include in the volume. In the meantime, I'm going to email you the one-act drama. It will be either the core of the volume or the entire volume - I'm thinking in one of those two directions. It is titled Coarctate: Antigone's Return - the title itself is a story. (I needed a word with a very specific meaning, and did not know such a word. I then heard the word "Coarctate" in my head. Looked it up in the OED and found it means exactly what I needed to say, and the latest citation in the OED was over 200 years ago. Telepathic indeed.)

Please email me directly, so that I can be sure I've got your proper email address, and I'll send the play to you.

In short, it's a go.
Anonymous said…
I'm back- just to answer your question - I work on topics in theoretical computer science- on algorithms for massive data sets and error correcting codes. My research
is mainly mathematical, with more abstract 'philosophical' implications than actual real-life applications...In any case will be reading your blog for inspiration! ;)
James said…
Perhaps it was your Riemann post, but I dreamt someone (you?) offered me the chance to be digitized. Of course, I didn't understand what that meant, but the voice was very persuasive -- slightly teasing, slightly amused.

I sensed it was something menacing, but the persuader's logic was infallible. My position was, "I'm afraid, I don't know what it means to be 'digitized,' what if it is irreversible and permanent and what if it means to be extinguished?" and Your, or rather the persuader's, convincing retort, was "Oh but you must experience it, and if you do, it will give me pleasure!"

Naturally, I agreed. The persuader smiled a wicked smile, giggled, and instantly i was reduced to zeros and ones -- powerless, vulnerable to infinite manipulation.

For some reason this seemed too embarrassing to post on your blog, but, of course, i defer to You.
Camelia said…
James, it gets published. Every word of it. And I tell you why. Because here we are not concerned with ethical issues of the sort that distinguishes between what's appropriate and what's not. The only thing that concerns us here is insisting on our bullet-proof classical formation which invites to a courteous consideration of one another. If one is courteous, even the potentially embarrassing thing becomes more than just embarrassing and therefore more interesting. The fact that you elected to send your text to me before you posted it, thus deferring to me, is already interesting from a psychological point of view. You want my consent because you like to see me consent not so much to what you wrote but to your submission to my text. This is more interesting already than the ordinary situation, even though establishing clear-cut power relations like this is as basic as it gets: I get to dominate and you say thank you. And I say thank you in return for making me laugh, and, well, for the implicit rest. This is psychology 101. Now, if we move past this, however, I can say that it's dangerous to dream of numbers, or becoming one. Though it is not more dangerous than experiencing numbers in real life. That can get very complex. If I had more time, I'd explain. Meanwhile, here's a thought: we give in to our transgressions when excelling in complexity may be more challenging than we can handle. We are relentless in our excess when we cannot be resilient in our excellence. But as any good metaphysician would know, there is always a middle way. Keep on thinking. There's a lot of pleasure right there, if you care to recognize it on that level which exceeds the banal. So, thank you.
James said…
Oh my. . . Your response is terrific. I hadn't quite realized the implicit submission in my writing first to you -- but it couldn't be clearer! There is something wonderful (for me, at least) in submission -- and (perhaps for you) in dominance.

Numbers are a realm of the abstract, unconstrained by the checks and balances of ordinary life. After all, one way of becoming a number is to become a statistic. And becoming a number can mean forfeiting one's individuality and personality.

And so the wish to become one is quite puzzling -- unless it's another form of submission. Perhaps being digitized means having all of one's qualities and aspects (including one's soul) converted to strings of numbers, infinitely long, like the threads of a stocking, infinitely stretchable, but forever useless once broken. . . .
Camelia said…
James, thanks again. That's the nice thing about the bloody infinities. That they never end. And the more complex the infinity, the better. But how many understand that, and the possible application of an infinite string of thoughts to real life? A few mathematicians perhaps, and then a few ordinary people who are not afraid of anything. It's a mighty thing to be fearless and infinitely open to all sorts, regardless of observing sometimes contradictory belief and behavior. It all comes down to making a few damn good distinctions.

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