Below are the 18 most recent journal entries recorded in Harald Andres Helfgott's LiveJournal:

Wednesday, April 19th, 2006
2:23 pm	Oh - I solved the problem mentioned in my first March entry a few weeks ago. (The one about f(p), I mean.) (3 Comments |Comment on this)
Wednesday, March 22nd, 2006
12:15 pm	That fashionable textual poster boy, Slavoj Zizek, often overstates his case for the sake of paradox, but this time around I could not agree with him more. I do not mean this at a general attitudinal level - he thinks as I do, down to the details. He seems to have picked my brain, the little a*****e. http://www.soapblox.net/liberilview/showDiary.do;jsessionid=950F0CEF86DC0F49B7F32256A77EC83D?diaryId=23 (Comment on this)
Saturday, March 4th, 2006
5:58 pm	In the last two weeks, I have put writing and editing largely aside to focus on solving two problems I have been considering for some time. I plan to keep this regime for the next week. So far, I have been able to solve neither problem. One of them involves generalising some earlier work of mine; some people seem rather interested in such an eventual generalisation. (So far, I have been able to ascertain that half of the proof goes through exactly as before, but the other half seems difficult to replace.) The other one can be stated as follows - Are there infinitely many prime numbers p such that p^3+2 is not divisible by any of 4, 9, 16, 25, 36...? The reply should be "yes". The same should hold for any cubic polynomial other than p^3+2 -- the polynomial p^3+2 was just an example. The question is fairly old - it was asked in the fifties by Erdos, and has remained open since then, though there are some partial results for specific polynomials. (A year and a half ago, I proved that the answer is "yes" when, instead of p^3+2, we have a cubic polynomial whose so-called discriminant happens to be a square. There are also some older results that show, for example, that, if f(p) is a polynomial of degree 7, then there are infinitely primes p such that f(p) is not divisible by any of 4, 9, 16, 26, 36 ...) (Oh, there are some silly polynomials for which the answer is "no" - say, 9 p^3 + 9, whose values are all divisible by 9, or, somewhat more subtly, 2p^3 - 2p, which is always divisible by 4. Forget about those - they can be easily catalogued.) I have an approach that seems to lead somewhere. Unfortunately, the last step involves a rather nasty optimization problem that I have been trying to solve for two months to no avail. There are some parameters that have to be chosen, and I seem unable to choose them so as to get a sufficiently good answer. Mind you, the values of the parameters themselves are irrelevant; what matters is the presumed fact that they exist. What may be my last assault will involve choosing these parameters randomly - with certain carefully set biases - and then showing that they work with positive probability. (I do not yet know whether this is true or even close to true.) Main idea of much of mathematics: if something happens a positive proportion of the time, then it happens *sometimes*. (Comment on this)
Tuesday, February 14th, 2006
6:28 pm	Oh, and another thing Not to be self-centered, but couldn't the anonymous person have left at least an anonymous thank-you note? I feel my brain has been flattened by a Jungian archetype. I do hope she got home safely. (Comment on this)
6:27 pm	Goodbye to Canada - in about five months. I have accepted Bristol's offer. h (2 Comments |Comment on this)
Friday, February 10th, 2006
2:57 pm	Apparitions in the snow As some of you know, I live in a one-room apartment on a third floor. Most of the apartment's back is taken by a large window-pane that does not open; a door on its side leads to a small balcony, which doubles as a fire escape. A steep spiral staircase runs down the side of the building. * * * It was about half an hour after midnight, between last Tuesday and Wednesday. I was dozing on some page proofs for a mathematics book; I had fallen asleep, or half-asleep, with the lights on. I was woken up by some loud knocking. An unknown girl was rapping on my window-pane. The snow, or the cold, had made the door stick; I pushed on the door while the girl pulled repeatedly - it would not open. I had to pick up a stool and hit the door again and again till it gave way. I let the girl in. She started sobbing. Up to that point, I had assumed that she had forgotten her keys. (She was in heavy winter clothes, with a long blue scarf, but that didn't make anything more or less probable; it must have been about -15C that night.) The remainder of the story is confused somewhat by the fact that she was upset and speaking in French - with a Quebecois accent, as was to be expected - whereas I was somewhat surprised and had just been woken up. Having fallen asleep in my clothes, I must have looked unkempt; to boot, I couldn't help thinking that my being too friendly would frighten her. She told me she was being followed. She asked me for a phone. I spent the next couple of minutes scrambling for my cell-phone, which is the only phone I have, and which, of course, was not where it was supposed to be. She started sobbing again and, at the same time, laughing a little, at me, I assume; it seemed to me that she was trying to suppress one thing and the other. Finally, after having failed twice to find the phone under a dishcloth that was covering some articles and printouts on the table, I found the phone in my coat pocket. By then I had offered her a chair, which she had not taken. I had tried telling her that everything would turn out well, or something along those lines; apparently, the remark was not taken ill. I thought of whether I should offer her tea; it was only to be expected, but I do not think I did, at the end; she had not taken the chair, and, under the circumstances, the last thing I wanted was to be forward. Once the phone was found, she asked for a phone guide, which, of course, I didn't have. (She wanted to call a taxi to get home.) I told her she should feel free to call directory assistance; I suppose it was understood that she could call 911 instead of 411, but I did not want to press the matter. She did not use the phone, at the end; instead, she told me to walk with her outside, to see whether the two cars that were following her were still there. (I believe she said there were two.) So, I put on my coat and boots, and went with her to the door. She looked up and down the street, and told me the cars were not to be seen. I could not see anything myself, either. I asked her whether she wanted to be walked home, or to call a taxi; she said she didn't need either. The way I had phrased the former offer - avez-vous besoin de compagnie? - made me feel like a prostitute in an old French movie; I rephrased my offer, and she told me that she lived quite nearby, a couple of blocks down, and would not need anything. She shook my hand briskly and walked away. That was the last I heard of her. (5 Comments |Comment on this)
Thursday, February 9th, 2006
7:15 pm	A strange thing happened to me the night before yesterday - or, rather, it happened for the most part to somebody else. I do not know whether it is appropriate to post it here, since it does involve somebody else (whose identity is unknown to me). People who heard me tell it on the ifMUD - what is your opinion on the subject? (Comment on this)
Saturday, February 4th, 2006
1:03 pm	Another job offer! This time from Canada - a university in Montreal is making me an offer. (This one is tenure-track, rather than essentially-tenured-though-at-first-technically-on-probation - after all, Montreal *is* in North America.) I am now in London - just had what should be my last interview; I won't know whether I'll get an offer from IC until Monday. I have until Feb 15 to decide. Opinions? (4 Comments |Comment on this)
Friday, January 20th, 2006
11:05 pm	I have been offered a permanent post (as ultimus inter pares) at a rather nice place in the UK. (Rather nice in my opinion, at any rate.) My alimentation for the next fifty years should now be assured. (4 Comments |Comment on this)
Monday, January 2nd, 2006
8:33 pm	Spielberg's _Munich_ Spielberg's _Munich_ I did not know what to think at first, when the film showed the hostage-takers talking in what to almost all of the audience must have sounded like threatening gibberish. (There were no subtitles.) Neither did I a little later, when all Israeli characters were shown speaking in (accented) English - in Israel, among themselves. I was tempted to be disappointed, though enough intelligence had been shown up to that point that I was suspecting an alternative explanation. The game became clear shortly thereafter, when the squad arrived in Italy and started shadowing the Palestinian poet who has translated the 1001 Nights. A squad member (was it Avner, the central character?) watches the poet as the latter goes about buying milk and vegetables and speaking with the grocer - in Italian, and with the same gentle manner as he has shown throughout. Then the poet starts making a phone call from the store - in Arabic. Ominous music starts, and the squad member goes away with the stern look of recognition on his face. He already knew he had the right man, but he has now truly identified him. In a work by a hack, written by a hack, this would have been a moment for groans; here the contrast with the intelligence the film had already shown was stark, and made it clear that a deliberate signal was being made. (I am still surprised at how many people seem to have missed it.) The scene was being seen from Avner's viewpoint. Unsurprisingly, Avner speaks a few European languages, but no Arabic. He feels threatened when it is spoken, and sees it as the aggressor language. The film follows Avner as his viewpoint evolves; we are, in fact, in a common situation in literature - while the story is not literally told in the first person (no voice-over says: "I, Avner, did not then know..."), it is told essentially from his viewpoint. After the initial action - which happen before he is introduced to us - we see very little that he cannot see. Overall, we have a much better idea of what is going on in his head than in anybody else's. Once the point of view is firmly established as that of a character - and thus distinct from an authorial view - the way the story is told is itself a commentary on the character's views. This technique goes back at least to Petronius (thanks, Auerbach); it would be silly to believe that it must be beyond Mr. Kushner, in the face of his repeated gestures towards it. In fact, I thought the film was particularly proficient in its display - partly implicit - of the evolution, or wavering, of Avner's viewpoint, and in its examination of the limitations of that viewpoint. These limitations are in part the inherent bounds to the strength and kind of questioning an adult individual of given personality and upbringing can subject himself to. In part, though, the limitations are simply those imposed by the knowledge of facts the character has. It is only consistent that we are made to share them. For example, not only does the extent of the involvement of many of the assassinated Palestinians in the Munich attacks seem as doubtful now as it does to Avner at the end - it seems nobody now claims that the poet was in fact involved at all, unless, of course, you consider being the PLO representative in Italy to constitute guilt by (indirect) association; for once, an appearance of innocence did not, it seems, deceive. Yet Avner has no way of knowing this; before the audience leaves the theatre and does some fact-checking, most of it does not know it either - and this is a consistent artistic choice, which also allows us to examine Avner's situation more sincerely than we might otherwise. One might make this last point with more complete confidence if the film did show some things that Avner must have known - for they were known by anybody who watched the news. Take, for example, the assassination in Norway, by misidentification, of a waiter that had nothing to do with the matter (unless you consider being of Arab extraction to constitute involvement in the matter!). This was accomplished by a different squad from that in which the presumed real-life counterpart to Avner was a member; still, the agents who killed the man were apprehended by the Norwegian authorities, the misidentification was made clear, and the perpetrators were sent to prison for a few months for the homicide - all of this was in the papers. There is much that was left out from _Munich_, presumably for the sake of finite running time; still, this was not the only departure of its kind from the actual occurences. In the raid in Lebanon, the wife of an assassination target is shown being taken away from her marital bed, and then her husband is machine-gunned out of her sight. In reality, the wife of one the main targets was killed herself, allegedly while trying to defend him. This is not shown. Of course, the film is a work of fiction, but a greater closeness to actual occurences of this kind might have put the film above the kind of suspicions of naive bias that diminish it both as a political reflection and as a work of art. (As it is, there are plenty of accusations of bias in the opposite direction from the usual quarters, but, since none of the accusers seems to have watched the film with any care, their comments may say a fair deal more about themselves than about the filmmaker; more to the point, they do not say, and may not be meant to say, anything about the film itself.) * * * Incidentally, there were subtitles at one point early in the film: when the German woman, citing Marcuse, makes a somewhat amusing little speech on (a)morality. That was quite nicely done: skepticism on the meaningfulness of moral questions is itself relativised, and, at the same time, Spielberg/Kushner show us that subtitles are allowed in their game, and thus their absence can have meaning. (Comment on this)
Friday, December 23rd, 2005
3:39 pm	I'm thinking of going to the cinema tonight (at Atwater?) in order to see _Munich_. http://www.cbc.ca/arts/film/munich.html Does anybody care to join me? h (1 Comment |Comment on this)
Monday, December 19th, 2005
4:22 pm	I am obsessed with Antarctica. (Comment on this)
Tuesday, October 11th, 2005
5:02 pm	Locro Or, Peruvian pumpkin stew. Ingredients: Plenty of pumpkin or squash A few potatoes, yellow-fleshed of preference Corn on the cob (a few cobs) Onions, garlic, salt, pepper and your favorite greenish spices (ad libitum) Queso fresco or feta cheese (a fair amount, in non-tiny blocks) Evaporated milk (250ml for a smallish pot, 500ml for a very large one) Instructions: (1a) Boil the potatoes; peel them either beforehand or thereafter. At the same time, boil the pumpkin/squash; peel it and seed it either beforehand or thereafter. (Warning: some peels are hard to remove, and some others have undesirably strong insulatory properties.) Boil the corn in the cob. (1b) In the meantime, fry the chopped onions and garlic, and add the spices. (2) Once (1a) and (1b) are done, put everything into a big pot with a little bit of water and some of the evaporated milk. Stir until the squash and cheese disintegrate. Add the rest of the evaporated milk. Boil for a tiny while more. Test for taste and adjust spices accordingly. (2 Comments |Comment on this)
Wednesday, September 7th, 2005
10:34 am	In memory of Joseph Rotblat - http://www.nytimes.com/2005/09/02/obituaries/02rotblat.html (Comment on this)
Sunday, June 19th, 2005
8:37 am	Just spent the night working - mostly organizational stuff. Also, it's high time I updated this journal with material from my Cuba trip... (Comment on this)
Saturday, January 22nd, 2005
1:12 pm	So, I just came back from brunch with some LiveJournal chaps and their associates. Some day I will do some anthropological field work on gamers; I have not witnessed a single game, ever, and the idea of the matter I have got from reading accounts thereof is very much incomplete. Oh, here "gaming" means "Gaming", much like "theory" sometimes means "Theory". I keep planning essays on politics and objectivity to post here, but I never actually write them. There are some interesting questions on ethical philosophy that I was discussing with a friend a few weeks ago. I haven't got around to answering him since then - I should do so soon. There is this article on Moral Saints by Susan Wolf - I think it's specious and, as it happens, also rather disgusting. Perhaps I should let my emotional reaction to it die off before I start analyzing it in detail. Oh, there is this thing about non-commutative groups. So, a large part of additive number theory revolves around the following situation. You have a set of integers - call it A - and consider all the possible sums of the form x+y with x and y both in A. So, you'd expect the set of all possible sums to be as large as (|A|^2)/2 or so, but sometimes it is much, much, much smaller, due to massive incest. (If A={1,...,n}, then the set A+A of all possible sums is {2,...,2n}, which is only twice as large as A - it certainly has many, many fewer than n^2/2 elements.) You then sit down to consider when such massive incest can occur, and step up old. Now, the question is - if A is not a subset of the integers, but rather a subset of something non-commutative -- something where x+y doesn't equal y+x -- can massive incest happen at all? That is, must A grow substantially when added to itself? (Comment on this)
Wednesday, October 27th, 2004
8:59 pm	Sigh. Now I have to take care of two rather obvious instances of cheating in my class. Vd. first line of Anna Karenina. (Comment on this)
Wednesday, October 20th, 2004
1:52 pm	Motorcycle diaries So, I finally saw the movie, and I liked it very much, after all. Dr. Hugo Pesce (the generous Lima doctor and hapless novelist - see the scenes between Cuzco and the leper colony) was a good friend of my grandfather's. I had often heard of his sterling character and arid prose. I suppose this speaks well of the accuracy of the movie's character depictions. (The "novel" Latitudes del Silencio was actually closer to a novelized memoir of Dr. Pesce's experiences as a physician in Andahuaylas, from what I've read elsewhere.) (Comment on this)