Dear Dr. Meyer:

The whale dived deep, feasted on despair, and rose again thoroughly sated. His fins mixed water and also are mixing metaphors. I am working now: I got a handle on how to deal with email, got in touch with some friends I had been ignoring......I really think despair is (or can be) fine medicine insolong as it is not shirked nor indulged in.

I spoke to Noam Elkies and was on the point of asking him about math books (I'm not sure if he's read Courant and Robbins). One thing I learned from studying math and physics (much too late to be any use for my education) is that it is tremendously helpful to have multiple books on similar material. Were I an undergraduate or graduate student now, I would, upon receiving the syllabus, immediately pick up the course text, but then also browse the library stacks for other books. And every one that seemed helpful, I would order. That might amount to five or six books, but never fewer than three, I should think.

The reason is that nearly every author fails to explain something clearly. Mathematics is so simple, but so complicated to understand, that it is impossible for any one author to keep track of all the ways a reader might get stuck. Of course there is some value in sitting there and puzzling things out, but it can also be an utter waste of time, because you never know how long you will be stuck on something for. 

I am sorry to say I spent countless hours in Yale and Brandeis libraries scratching my head, or giving up in frustration and pulling a copy of Herodotus off the shelf,, and reading about crocodiles on the Nile, or the men in Libya who have their faces on their chests, or the king of Ethiopia receiving messengers from Cambyses, stringing an immense bow in front of them, and then sending it back as a gift and a challenge to Cambyses-----which challenge he fails, and so, wisely, decides to leave Ethiopia alone.

I think someone must have told me about the many-books trick by sophomore or junior year, but I never did it. Amazon.com didn't exist in those days; the library would only let you check out books for a few weeks, and in any case by the time you got there the shelves were picked clean, because it only took one classmate who knew this trick to deplete them; textbooks are so breathtakingly expensive that it seems beyond robbery to multiply the cost by 3-5 (but one forgets that tuition is another order of magnitude!); finally, I had enough trouble finishing one book with the time left over from fencing practice.

But what I failed to grasp is that the point is not to read a book (as one might a novel or even a philosopher), but to understand. And so the irony is that with having five books on your shelf, you'd spend less time reading. When you reached the point of frustration you could thumb another book (one doesn't read all the books straight through; maybe you pick one to get a coherent view), and you'd rapidly get into a state of mental flow-----this, ironically, by discontinuating your process of reading.

And so in that spirit I went to my shelves today and found some more books that address some of the same foundational material as Courant and Robbins. (After I graduated I overcompensated for my failure by buying lots of math books, carting them around between apartments, and never reading them. Dare I say the time is at hand? Let us not be too regal.)

S.C. Kleene: Introduction to Meta-Mathematics.

This is a literary as well as mathematical masterpiece. I haven't read it all the way through. Much of the material might be of no interest to us. Chapters 1 and 2 I would read before anything else. 3 - 7 might be of interest too as they go into logic. Kleene was a seminal logician in his own right; nobody does it better.

The first five pages are, beyond that, wondrous.

Roger Penrose: The Road to Reality

Also an astonishing book: it attempts to give a quasi-popular but also rigorous account of all of mathematics and physics. Obviously this cannot be done in one book, however giant. However, Professor Penrose (whom I was fortunate enough to meet at the Science of Consciousness conference: I had the great privilege of sitting next to him at lunch, and had a probing conversation during which this remarkable man treated me as an equal), opens many philosophical questions, and skips over the excessive detail. At least the first seven chapters may be worth reading.

Sylvanus P. Thompson: Calculus Made Easy.

This is a classic and quite short book. Most calculus books for schools now are bloated, glossy pamphlets with all sorts of busywork that will never be needed by the student again. (I spent weeks figuring out how to calculate volumes of rotation by washers and discs and so forth; you never will need it again, because the next year you learn double and triple integrals!) They also descend into pedantry by demanding rigor. They do not use the reasoning that Newton and Leibniz used, but the problem is that is how they figured calculus out. Yes, Berkeley may have sniped about the "ghosts of departed quantities", but their methods worked. When you are in over your head with epsilons and deltas and Riemann sums you cannot comprehend how Newton came up with this idea in six weeks. The answer, I think, is he could not possibly have, had he been required to use the methods of Weierstrass.

The nineteenth-century level of rigor is tremendously important, but I think it is too much for a first exposure to calculus. It lies about how the subject came about. In any case, by 1960, Abraham Robinson was able to show that the concept of infinitesimals, which makes understanding the derivative so much easier, can be made rigorous with the help of modern model theory.


I have also a Princeton Encyclopedia of Mathematics, which must admit to having only perused, but which looks very good.

Prepending on a negative Covid result, I would be happy to drop these off with appropriate social distancing.

N.I.C.


On 09/10/2020 10:22 PM, Nikola Chubrich wrote:
> Dear Dr. Meyer:
>
> I will take your unreading of my letter and raise you one. Replies tomorrow!
>
> I was chatting (as this line-by-line text medium on Facebook is called; there was something on Unix called Ntalk that did the same thing, but I'm not sure if you ever used online chatrooms) with a friend of mine I met through holotropic breathwork. She's a psychiatrist, and she was in the mood to listen. So in spite of being hungry, and tired, and very much risking not falling asleep if I push it too late, I said what was on my mind while she was listening.
>
> It comes out like a kind of poetry, sometimes, this chat. And you may find it of interest.
>
> (Another evil of Facebook: they make it purposefully difficult to get content out of their environment. To put a chat in another format, first you have to manually scroll through and copy-paste it (and this is, I suspect, intentionally defective: the copied area sometimes disappears and you have to start over again). Then, when you paste it, it comes out like this:
>
> well thanks for thanking me!
> You sent
> about an hour ago
> I presume I may infer I am not merely being a nuisance?
> You sent
> about an hour ago
> and thanks also for the virtual hug
> You sent
> about an hour ago
> I so much needed a hug last night I wanted to drive up to Portsmouth and wake my mom up and ask her to give me a hug
> You sent
> about an hour ago
> but the intention travels across space and even time
> .......
>
> Nobody really needs to see "You sent, about an hour ago". So I wanted to get her what I had written formatted in one document, so she wouldn't have to scroll through a tiny narrow chat window. This pisses people off sometimes (typical response: shut up. Or: you sent me a novel.). I have managed to convince a few people to put up with this, and they are worth their existence in gold: because the sense of having someone, however virtually, however distant, hanging on your every word, is a wonderful spur to composition.
>
> So racing against time and tiredness and hunger, I spent about twenty minutes manually deleting Facebook's deterring filter. Thanks, Mr. Zuckerberg.
>
> I really need to learn Vi. I tried to learn Emacs once, but I think you might be right to use vi. I guess you would use vi to do that kind of thing automatically? Or Sed? Or Awk?
>
> Anyway, here is the whole thing, should you find it of any interest. And I shall have to defer reading your two letters until tomorrow!
>
> Guten nacht.
>
> Nikola.
>
> * * *
>
> well thanks for thanking me!
> I presume I may infer I am not merely being a nuisance?
> and thanks also for the virtual hug
> I so much needed a hug last night I wanted to drive up to Portsmouth and wake my mom up and ask her to give me a hug
> but the intention travels across space and even time
> so maybe that was you tonight last night
> when I had this crushing despair for about two hours
> wondered whether I should give in and grab some Ativan
> but resolved, as I learned in Breathwork, to sit with it
> go deeper
> and so I came out the other side
> perhaps with the help of your atemporal, anageonistic embrace
> had a fitful dream for about forty-five minutes
> woke up into a sneezing fit
> took some Zzquil (which is also an antihistamine)
> found it totally failed to put me to sleep
> didn't panic
> rose with the dawn
> spun grand narratives in my mind, in the shower, sitting on the toilet (sorry for the details) giving time to my gut, because Lithium wrecked it and had caused ulcerative colitis again
> twirling a cocktail umbrella between my fingertips
> thinking, thinking
> but not repetitively
> going out
> going out
> and then coming back
> and instead of writing down a grand narrative
> as I always had tended to wish to do
> I sat down and started organizing my email
> finally dealing with taxes
> reaching out to a bunch of friends I was afraid to talk to all summer
> talking to one on the phone for about an hour or two
> found my mind
> that I thought I had lost
> had come back better then before
> and I kept doing the taxes
> and found it a delight
> almost like a form of meditation
> never had anything like that before
> and you put your finger on it:
> rhythm
> to be able to swing from one thing to the next
> during the day yesterday: totally unable to think clearly
> essentially making up stuff to get through a required therapy session at 4:00
> feeling desperately tired
> unable to fall asleep
> experience the most intense despair, perhaps of my life
> my body as if wrapped with a sheet of despair
> and during that unable to imagine that there will ever be anything else
> and then coming out that
> and having a day of learning and functioning
> rhythm
> that is what you said
> and the thing is
> I can never, never say
> "I got it done"
> "I'm through"
> "I'm a changed man"
> because I have absolutely no idea what tomorrow will be like
> not just in external vicissitudes
> I might well wake up befogged and unable to access any of my seeming superpowers of today
> feeling it was all an illusion
> falling still worse into despair
> because I'll think to myself:
> "I thought I had it figured out"
> "I really did"
> and that supposition mocking me the more
> and maybe the next day will be like that too
> and the next
> for a week
> or two
> and then there'll be another day of being awake
> maybe not as awake
> even though, during the dark sleeping days
> I am incapable of that faith
> can only distract myself with repetitious nonsense on the internet
> watching Elon Musk's rocket launch
> twirling twirling twirling
> or thinking about how now my life is over
> I'm 43
> no real friends
> no prospects
> parents getting older
> selling the house
> terrible relationship with my brother
> that's it
> I'll be hanging out in an apartment the rest of my life
> peering out the blinds
> or running out of money
> and ending up in some dump for mentally disabled people
> I have to acknowledge that could happen
> it would be dishonest to even say
> "I don't think I will"
> I've said that so many times to myself before
> at least 80% of the time effectively denying to myself I even said it to myself
> even though I obviously did
> and it's wrong every time
> there is always the potential of another foolishness around the bed
> so I cannot know nor claim what tomorrow will bring
> but there it is again, what you said
> rhythm
> there are larger rhythms
> the waves beneath the ripples
> the swells beneath the waves
> it's all a rhythm
> and so I am quite capable of saying now
> even though I may be incapable of saying this tomorrow
> (and remind me, if you will, as Odysseus's crewmen did after they unstopped the wax from his ears and restrained him from the sirens)
> that even if I were to face ten years of unremitting despair
> it would be worth it if I learned something
> and to say still more
> not desiring to tempt God
> but if God the father, or God the mother (the concavities being determined by where \you are) finds that there is no other way to teach what he must teach
> than ten years of despair
> then so be it
> Thy will be done
> but perhaps I may indulge in a bit of optimism
> that I have had at least practice
> for one day
> of being able to shift from despair
> to possibly mad flights of fancy
> to a learner and a doer
> and perhaps I shall not be able to do it again
> like that beginner's luck
> the time you get it
> slip the ball in the basket effortlessly
> only to find that tomorrow
> pursuant to whatever dreams, known or unknown
> have wiped your slate clean
> you are unable
> perhaps you never will be again
> but I know how this is
> from learning violin
> one day you learn vibrato
> you make the instrument sing
> and then a month of scrapulous sawing
> and it comes back a little more reliably
> a little stronger
> so perhaps that is how it will be
> perhaps
> and so I'll make dinner
> (getting too late)
> and perhaps I'll get to sleep well tonight
> or not
> maybe I won't be able to shut my mind off
> or maybe I'll fall into that despair again
> but as I sit here
> I have no desire to grab the Ativan, or the Remeron, or the Ambien, or the Thorazine
> to make sure I sleep tonight
> God gives me a marathon, well then, time to run it
> time to learn not to take the easy outs
> after four years of breathwork and several of psychedelics
> learning to navigate those states
> I went five nights straight over Christmas without sleeping
> until I was having closed-eye visual hallucinations
> and while waking, freezing up into brief catatonias, then emerging
> and I came back
> after a fashion
> then made more mistakes
> but I came back
> I didn't freak out
> and it was all useful
> that night I listened to Rachmaninoff's Rhapsody on a Theme of Paganini
> saw rectalinear forms going down and sideways
> like those green Japanese characters in The Matrix, if you have ever seen that
> and seeing this suddenly realizing what the Rhapsody is about
> having all my life listened to it
> simply thinking it a lush concert piece
> perhaps a bit Hollywood
> and realizing what Rachmaninoff was doing
> an Orthodox mystic from the birch-filled forests of Russia
> having to enfold himself and fit into the expression of a St. Petersburg sophisticate
> and then, that world being destroyed in Revolution
> having to do it Again
> into brash, overwrought America
> and having to pretend to be that
> and he does all of it, in that piece
> a monk chanting on a distant island in the midst of Russia
> and that chant becoming the lush sparkle of a noble lady's necklace in St. Petersburg
> and that sparkle becoming the booming voice of America
> but inside all of it, the monk
> I'd never heard that before
> all the years I had listened to that piece
> I had to be able to \see it as well
> and that was on night five of no sleep
> so it's not like I'm going to force myself to stay up to try to get there again
> I'm not a total fool
> but if that's what's in the cards
> well
> let's see what happens
> good night!
>
> * * *
>
> I have resisted the temptation to clean it up, reformat beyond removing the automated interjection, or explain what I mean more clearly. Should you think it worthwhile to do so, I will do so.



Dear Nikola,

It's time for an answer to your two letters, for both of which I thank you.

In reply to the "mathematics"letter: a) I am much appreciative of your generosity, but I ask that you spend no money in buying books (or anything else) for me.  Miserly as I am myself, I ask that you save your money and spend it only on necessities for yourself, so that you will never be impoverished. b) studying and exploring issues in mathematics is on a list of priorities in my mind, where it competes with other imperatives of my fantasy. I don't know when I will be ready for mathematics books other than the volumes of Courant, his "What is Mathematics", his "Calculus", and his "Methods of Mathematical Physics," which are presently on my book shelves. I may at sometime in the future appeal to you for help with a specific mathematics question, and if at that time it seemed best to you to answer my question by lending me a book which you already own, I would accept your offer.  But this morning I am not yet prepared with any question.

Concerning the Facebook fragments, which you sent me, (and for which I thank you), you write:
"I have resisted the temptation to clean it up, reformat beyond removing the automated interjection, or explain what I mean more clearly.  Should you think it worthwhile to do so, I will do so."
My advice, (which I hesitate to give), is that you should write, and that you should write what is most meaningful to you.  It seems to me that these fragments might serve as seeds for dialogues, for poems or essays, the composition of which might provide your life with additional meaning and structure. For myself, I shall avoid the constraints of Facebook and rely on e-mail to communicate with individuals, and on my website, or on printed books, for publication.

Stay well and content. Please give my regards to your parents.

EJM
~