First years say the darndest things.

I have just finished marking 1/4 of the questions of a first year exam. But before I begin on what little meat there is in this story¹, perhaps a little explanation is in order about the paper² in question. It is a 'discrete mathematics and linear algebra' course. There are two such courses (covering exactly the same material) running simultaneously. One takes a year, and the other one half a year. The half year version begins half way into the full year version. The reader is perhaps under some misapprehension that the latter course, covering the same material in half the time, is full of the really bright and/or hard-working people. This is, sadly, not the case. In fact it is full of individuals who originally enrolled in the previous course who then took a long hard look at their assessment results and, looking down the barrel of an epic fail, decided to drop out of the full year version and enrol in the half year version instead. The reader is perhaps also under the misapprehension that they tend to put more effort into their second attempt.

Anyways, I want to talk to you about question 3 a): Write down the definition of a rational number. Most people answered this incorrectly, and here are some of the responses I received:

1. Any number that is not a fraction.
2. Any number which can be expressed as p/q where p,q ∈ ℝ and p ≤ q. ³
   
3. A number that exists rationally.
4. Any number that is not irrational.
5. A number that makes scence(sic).
6. Any number that doesn't believe in fairy tales⁴.
7. Definition of a rational number. There is a chap in class who I always thought was an ace but he has written less than I. I guess I am not the only person who was either stumped by this course or who didn't work on it hard enough & is now compelled to write Ramayamas in the answer sheet. Yay! 15 minutes to go. Actually 20 mins but I think I am going to make a run for it. Have no clue what I am writing and I think am simply allowing all thoughts to spill out onto paper. Possibly my constant scribbling is leading the guy next to me to get very worried as he isn't writing anything either. I wish I could go home for a bit. Really wish I could go home if only it wasn't 18 hours away.
   

¹Which may be safely characterised as being to world literature what a ham bone stew is to world cuisine. P.S. Fuck you, yes, this is a footnote. Despite your endless pay-outs on this front, I still like the fucking things.

²In New Zealand Universities 'courses' are called 'papers'. This caused some confusion for me when in casual conversation a great number of people started casually talking about papers they did in first year. I thought I was surrounded by geniuses. P.S. Yes, this is another footnote. Go to hell.

³I had to at least acknowledge internal consistency here. When asked to prove that √3 was irrational they said: √3 = 3/√3 and, since 3 > √3, √3 is irrational. The correct answers were kind of cute, too, actually (& not the way I've ever seen this answered). They reasoned as follows: Let p,q ∈ ℤ. Then the prime factorization of both p² and q² contain an even number of terms. Thus p²≠ 3q ² and so √3 ≠ p/q.

⁴This guy got marks.

Marking

To all those who think they know marking pain I would ask the following: Have you ever marked a first year linear algebra exam where they weren't allowed a calculator¹? If not, well let me just say that it's still full of the usual "hmm... I have no idea how to do this question, but if I waste the marker's time by asking them to painstakingly verify that this page of formal-looking statements is, in fact, gibberish .... well, this can only bode well for me"-type answers. In addition, you get people who write statements such as : "no calulator! ....1/52 ≈ 1/50, 1/50 ⋅ 102 = 2.04 ... so I'm going to write 1/52 ⋅ 102 as 2.04". Anyways, if ever you find yourself in such a situation I would advise you to do as I have. Print out a small pile of this comic, mark the offending answers down as harshly as your mood takes you, then staple a copy of said comic to their answer sheet.

¹Strictly this isn't true. They weren't allowed a graphics calculator, since they were being tested on (amongst other things) Gauss-Jordan elimination. Unfortunately, almost half the class in the exam I was supervising interpreted "not allowed a graphics calculator" to mean "allowed a graphics calculator", and so had to do the exam with no calculator at all. The questions weren't really such that you really needed one .... but there seems to have been an unfortunate correlation between those who owned only a graphics calculator and those who were scared of non-decimal fractions.

LOL

A conversation from my office:

Adam: I've just made an infinite injury argument in which requirements injure themselves.

Me: So, that would be an infinite self-injury argument, then ....... Wow. Recursion theory goes emo.

The hardest logic puzzle ever....

....is this, apparently. The problem being phrased there as follows:

Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which.

You can find various solutions on the page, so I won't detail the ones I came up with, exactly (the second of which being, I think not dissimilar to those found on wikipedia), in case you haven't seen it before and want to try and solve it yourself. I'm curious, though, about the following. To begin with, as a 'warm-up', I just attempted to find three questions that would work if the three gods spoke English. Having done so, the following thought occured to me: Why not just ask precisely these questions with "If 'ja' meant 'yes' and .." as a pre-amble to each of them. This thought shat me .... Do you think this is cheating? Settle (or at least expand upon) a discussion for me.

While chasing a Daemon, Fitz inadvertently finds god1.

On a point of business, dear reader, I recently found myself on the homepage of one Peter Gacs. This was, as it turns out, quite a timely visit. I had found myself, you see, at something of a spiritual impasse in my life. I mean, we've all heard the savage barbs in our time about mathematics research being a waste of time and having no relation to the "real" world.... and, well, I suppose we've learned to live with them². What was beginning to bother me, brothers and sisters, was this gnawing suspicion in the back of my mind that it also had no relation to the "not so real" world, or possibly "realer than real" world (depending on your point of view). The supernatural world. The spiritual world. I mean, sure, maths can teach you how to cheat at cards and pull chicks at parties .... but what has it got to say about witchcraft, magic and saving my immortal soul? I was beginning, com padre, with a deep and abiding sorrow to take the view that the answer to this question was "zilch". My interest was piqued, however, by the list of online publications of Mr Gacs which included the following titles: The Angel Wins, Clairvoyant Scheduling of Random Walks, The Clairvoyant Demon has a Hard Task³. Sadly, however, these just turned out to be cool titles. There were no concrete instructions to be found on how to actually summon such a clairvoyant demon. Via a tantalizing link on the same page, however, one learns that maths and physics can help you find god and rescue your immortal soul after all.

Yay team nerd!!!!!

¹Yeah, it occurs to me that this title makes the post sound a lot more interesting than it really is......

²Being mathematicians, we always come up with the wittiest of responses. "Your mum's pointless" I replied once. "Yeah, well ..... QUICK!!!! LOOK!!! BEHIND YOU!!!" is another favorite. Well, actually, Busty's wasn't bad.

³ Also on the list we find On playing "twenty questions" with a Liar. Another cool title, but I couldn't work it in to the current post angle, unfortunately.

Coffee and Statistics

People seem to spend an awful lot of their lives looking for stuff. For the most part, you might say people are looking for love, power or distraction. I, on the other hand, perhaps deciding that the first two items on this list will forever elude me¹ ...... actually, fuck ....... hang on. If I'm going to include such a big, pervasive category as 'distraction' I may as well forget the other two, hey? More importantly, the completion of the sentence "I, on the other hand,..." becomes stupid and banal because whatever the fuck follows is almost certainly a member of the "distraction" category² and hence my poignant little opening just collapses under its own weight. Ah, Shit. Oh, well, so accepting that the last few moments spent reading this post represent time wasted you'll never get back (sorry), let's just proceed with more of the let-down and say that much of my free time in the last week has been spent in a search for coffee.

Now that, I'm sure you're thinking, is a pretty stupid thing to spend too much time looking for. They sell the stuff in every supermarket in the country, it's one of the most widely consumed beverages on the planet and it's difficult to be placed at random in any moderately inhabited locale in the country without being within a few hundred metres of some cafe or eaterie claiming to be able to sell you an espresso. The problem is, dear reader, that when it comes to the set of cafes and eateries within walking distance of my current place of work these claims are lies!!!! Ask for a long black³ at any such establishment near me and what you get is this brackish liquid that smells vaguely like coffee but tastes like really bad tea - and frankly if black coffee doesn't induce a slight pain behind my left eye, well I'd say the vendor has failed in their contract with me, the consumer. And I mean it's not as though espresso machines are cheap, so how hard can it be to hire one fucking person who knows how to use the thing? Hmm? I mean I could bloody well do it if they'd just see fit to set up a coin-operated do-it-yourself machine..... actually, that's a really good idea..... I'll squirrel that away along with my plans to manufacture party tooter thingies⁴ that sound like an elephant and have an extension that looks like an elephant's trunk......... O.K. so, maybe this isn't the wisest thing to be worried about at present what with global warming and an imminent federal election and all, but I think we've all established by now that I'm a terribly petty person who gets rather worked up over small things. That, or possibly this is a lie and I just do it for effect. Who can say?

Anyways, on the statistics half of things (what I seem to be spending most of my non-free time on at the moment....). Does it strike anyone else as terribly odd that statistics is generally so very boring? I mean, take probability theory to start with. I mean, this is basically measure theory and analysis, right? Nothing wrong with those, and in any case I've gone and done courses in probability theory and I've found it to be a perfectly interesting subject. So now consider the idea of applying probability theory to the independent world around you. This is, philosophically, really rather interesting too. This is kind of foundational meta-science type stuff in the same way as set theory and logic can be thought of as meta-mathematics. And yet, when you move on to the class of stuff taken as falling under the umbrella category of 'statistics' which is, essentially, just applied probability theory, well, it all seems so dull and I'm buggered if I can work out why this should be so.

¹go on, cue the violins you bastards

²And, in point of fact, it will be

³ I've never been game to ask for a short one.

⁴ You know the ones I'm talking about. You blow on them and get a 'toot' sound, while pneumatically extending this colourful paper thing.

"Oh the humanity", or what I remember of wine and cheese

Well, first of all, I was reminded last night that I haven't blogged the last Red Room Trivia, so lets just warm my wine-pickled brain up by recalling that to you now. This was the last red-room trivia for the year and it was (and let's be fair to it) completely crap. This is more than mere sour grapes on account of the fact that we didn't win. Anyone failing to notice, by virtue of Rupert's novelty sombrero, that there was to be a theme should probably have cottoned on when they got their answer sheet. This was a photocopy of a hand-scrawled job with "Gringo Trivia" written on the top, two columns and "horizontal" lines about as straight as Molly Meldrum. Rupert, however, feeling that the point had not been sufficiently well made announced that it was to be a Spanish-themed trivia. This was unfortunate for me given that, when it became apparent we had put the wrong nationality for South American Paulo Coelho, the night's theme lent me sufficient confidence to bet Geoff $10 that we could at least be sure that the answer wasn't Brazillian. This was not a wise investment ladies and gentlemen. So not only is this son of a bitch responsible for The Alchemist, he went and lost me $10. Anyways, Two rounds of ten questions became two rounds of 5 instead¹ . So, how do we sum up this, the last Red Room trivia for the year? I'm inclined to paraphrase T.S. Eliot myself: This, my friends, is the way trivia ends, not with a bang, but a whimper. Were the comic book guy from the Simpsons present, we might instead say WORST. TRIVIA. EVER. Perhaps we said it best, though, with our answer to the question "What is the English translation of 'Naranja'?". We wrote the following:

Naranja: "So, this is the way trivia dies. To thunderous applause...."

Which, I feel, also gets across our nerd credentials.

Anyways...... to get back to the original post title. Wine and cheese. Why oh why, dear reader, do we look forward so to this event? A mathematics department wine and cheese night sounds superficially so very civilised. "Sure," we seem to be saying "like many departments we see fit to hold an end-of-semester get-together. However, unlike yours, ours is no mere seedy booze-up. No Sir. We hold a wine and cheese night at which members of an intellectual elite sample fine wine and cheeses whilst discussing sundry philosophical difficulties with the axiom of choice." In fact, it is of course the case that the MSS wine and cheese night differs from your average seedy booze-up only in as much as there's more cheese involved, and in that probability of hearing the phrase "mathematician celebrity head" is significantly higher.

Attendance seemed lower than last semester to me, and we were a little worried that it wasn't going to be a real wine and cheese night anyway on account of how....... hmmm.... a small digression is in order here. So as to avoid naming too many names un-necessarily I'm going to institute a coding system and the lecturer in question here shall be code named "Mrs Robinson". Most of you will know who I'm talking about. Anyways we were a little worried that it wasn't going to be a real wine and cheese night on account of how Mrs Robinson took a while to show up and at first didn't appear to be drinking. Luckily, this state of affairs did not persist. It was, to be certain, something of a shame that "Dustin Hoffman" had at this point left, but before too long Mrs R. was crawling around, throwing a tennis ball at people and throwing water all over Claire - so there was a happy ending on that front at least. I remember the night finishing with a group of us climbing onto the roof of the maths building and, rather predictably I suppose, urinating over the side². I also remember sundry trips into the strange, strange mind of Mary Waterhouse. Apart from that the reader can probably fill in most of the remaining blanks themselves from the last booze-up they attended. I'm just going to go and lie down now......

¹ My cries of "why not one round of ten with two prizes given out Rupert? Can't we end this farce now?" went sadly unheeded.

²you'd be amazed how far you can reach

I'm βringing Sεxy βack

Sam introduces himself on his blog as "Sexy Mathematician Sam". Sadly, however, if we exclude the laudable Hot Mathematician website and, of course, Sam's questionable characterisation of himself - it would appear that the web is not altogether kind to us when it comes to appreciating the raw, unbridled sexual power of the mathematics community¹.

It is time to redress this imbalance. I propose, dear reader², that we hereby compile a list of candidates in a quest to uncover the the sexiest mathematician of all time a-la Dave's classic and terribly popular 'what's your favourite cardinal?' poll³. You can nominate yourself if you like, and yes, Martin, you can nominate Victor.

I wish to propose the following two candidates.

Geralomo Cardano , of Cardano's Method fame - a method which has the dual distinctions of 1 Victor Scharashkin's actually expecting us to remember the fucking thing on a 4th year Galois theory exam⁴ and 2 not really being Cardano's anyway. Apart from his dashing good looks, debonair smile and raw animal magnetism he has the following to commend him as a hard-drinking, hard-living, devil-may-care hornbag:

1. After wheedling the general solution to the cubic from his friend with the promise not to tell anyone else, he promptly published it.
2. He was a professional gambler who published posthumously a book on, amongst other things, effective cheating methods.
3. He was convivted of Heresy, with his own son contributing to the prosecution.
4. Having predicted astrologically the date of his own death, he killed himself on said day.

If I had my druthers (I'm bringing back the word "druthers" too, incidentally) the young and hip would be wearing the visage of Cardano, not Che Guevara proudly on their chest^5.
Kurt Gödel , the man himself. And when I say "the man", I mean this in the sense of "who's the man?" Kurt's the man. As I go through the following I challenge you, ladies, to tell me you wouldn't hit that.

1. He looked like a relative of Count Dracula.
2. He married a night-club dancer. Up high, Kurt.
3. He proved results which ran counter to, not only the entire generation of which he was a part, but pretty much everyone who went before him.
4. Not only did he proved the mutual exclusiveness of the completeness and consistency of formal arithmetic on upwards - he did so by inserting into formal arithmetic an analogue of the statement "this statement is unprovable" - leading one to the inescapable conclusion that people were uncomfortable about his work not due to point 3., but because no-body likes a smart-arse.
5. When being naturalised as a U.S. citizen he lectured the judge on the U.S. constitution and explained to him a loop-hole he'd found while Albert Einstein sat in the background saying "It's allright,........he's with me".
6. He was completely, irretrievably insane - dying of starvation presumably because he thought that ghosts lived in his fridge.
7. Whenever asked the question "What are you rebelling against?", he'd always answer with an Arnold-Schwarzenegger like voice "Vat Haf You Got".

Over to you.......

¹Clio Cresswell doesn't, doesn't count.

²And I probably really do mean "reader" - singular, here.

³I still go with aleph₁ . There's something I can relate to in the least cardinal in a state of identity crisis.
⁴Bastard!!!!!
⁵ Having bought said shirt at some trendy expensive boutique and failed to appreciate the irony