4th April, 2013
I am not very happy around strange abstract paintings, preferring portraiture; contemporary postmodernism underestimates picturesqueness, antagonistically mischaracterizing bourgeoisification, exhibitionistically, overenthusiastically overintellectualizing nonrepresentationalism.
27th March, 2013
A. Imagine that you could lift up into the air, and soar through the sky, just by gently fluttering your arms.
B. Yes, I’ve dreams like that. Lovely.
A. Where would you go?
B. Hmmm… I’m not sure. Maybe a cruise over the ocean to Rio?
A. What?? You seriously think you can flap your way to Brazil? What sort of lunatic are you?
As verbal entrapment goes, it’s hardly very clever or subtle. But A-san’s logic is identical to that from a recent Church of England press release.
The Church commissioned a survey which asked
“Irrespective of whether you currently pray or not, if you were to pray for something at the moment, what would it be for?”
19% of their interviewees were unwilling or unable to address this hypothetical scenario, either saying that they never prayed or that they didn’t know.
On the strength of this data, the Church announced that “Four out of five British adults believe in the power of prayer”, a statistic which is now making its way through the UK press.
I have just written to the CoE press office, reminding them of the Ninth Commandment: “You shall not bear false witness against your neighbour”.
13th April, 2012
Nightjack was an award-winning blog which ran from 2008-2009, written by an anonymous British police officer. In 2009, in what they claimed to be the public interest – but which struck many observers as an exercise in needless spite – The Times newspaper published an article exposing the author as Detective Constable Richard Horton.
Since then there have been claims and counter-claims about how that story came to press, culminating in the recent revelation that the Times likely misled both the High Court and its own readers.
We now know how Times journalist Patrick Foster knew Nightjack’s identity: he hacked his email account. What is interesting – and where considerations of computational complexity come in – is what happened next. Having found Nightjack’s identity through illegal means, Foster then approached Times lawyer Alastair Brett, and was advised to set to work on reproving Nightjack’s identity, purely through legally available sources. He was indeed later able to do this, with the result that the Times went to court and successfully fought off an injuction barring them from exposing Nightjack. But, critically, during the hearing, they omitted all mention of the original email hack, and spoke solely of Foster’s subsequent reproof.
Brett explained the thinking behind this advice in his testimony to the ongoing Leveson enquiry into the culture, practices, and ethics of the press:
“If he or any other journalist could identify Nightjack through legitimate sources and information in the public domain then we’ve got what I felt was a perfectly legitimate public interest story…
“He had to demonstrate to me that he could do it legitimately from outside in, and that’s what he did. He persuaded me that he was able, that the only person who could have been Nightjack was DC Horton…
“Rightly or wrongly I had believed you could separate the earlier misconduct by Mr Patrick Foster and you could then say that once he had done this legitimately then that could be presented to the court perfectly properly as he had done it legally. Now I accept that you say that the two are inextricably intertwined, but that, if I may say so is a subjective judgement. I happened to take the view that you could separate out the one from the other.”
Robert Jay QC, cross-questioning, makes the observation that the reproof was “a much easier exercise”, now that he “had the advantage of knowing the answer to his question”.
Of course this is true, but one might ask how much of an advantage he had. Is this a subjective judgement? Perhaps Foster could have determined the answer, legally, from the outset. In order to have a leg to stand on, the minimum he needed to establish was that Nighjack’s identity was in legal P, something which could discovered legally in polynomial time. All the reproof showed, however, was that it was in legal NP (as well as being in illegal P, of course). Are the two equal…? (And if they are, what is the polynomial mark-up…?)
David Allen Green has been monitoring the case since the beginning, and it was he who likened the identification to solving a maze ‘from the inside out’ (P) rather than ‘from the outside in’ (NP). He has an excellent run-down of the whole affair so far, at The New Statesman. (If you scroll down to the discussion of Oliver Kamm’s blogposts, you will also see how the Times went on to mislead its readers.)
The latest developments are that the Times’ editor James Harding has written to the hearing’s original judge to apologise, and that Nightjack is suing the Times for breach of confidence, misuse of private information and deceit. He is claiming aggravated and exemplary damages.
You can also watch Alastair Brett’s very uncomfortable evidence to the Leveson enquiry here. It begins at 72′, and the real drama starts at 129′, in which Lord Leveson accuses the Times of providing ‘utterly misleading’ evidence to the Court, an accusation which Brett essentially admits.
21st June, 2011
A mathematician confided
That the Möbius strip is one-sided
And you’ll get quite a laugh
If you cut one in half
For it stays in one piece, undivided!
A mathematician named Klein
Found the Möbius Loop quite divine
Said he, “If you glue
The edges of two
You get a weird bottle like mine!”
The topological part of my brain
Finds Möbius strips quite a strain
But I make you this pledge:
I’ll glue one at its edge
And build a real projective plane
Any more? (Or can anyone give me attributions for the Anons?)
6th June, 2011
A. B-san, may I aks you a question?
B. Please do.
A. Thank you. Are you an idiot?
B. That question is hardly of the intellectual calibre that I have come to expect from you, but I shall answer it nevertheless. No, A-san, I am not an idiot.
A. Are you entirely sure? I believe that I can demonstrate that you are indeed an idiot.
B. Are my trousers unbuttoned? Have I forgotten your birthday? If I have made some careless mistake you could tell me kindly rather than with insults.
A. Other than being somewhat old and ill-fitting, your trousers are fine. And my birthday is not for 3 months, as I believe you know. I do not have any such mistake in mind. Rather, I claim that I can demonstrate that you are an idiot using only this pen and paper. What is more, you will be forced by your own words to accept it. May I try?
B. I suppose so.
A. Very well. I shall write a sentence on this paper, and you must tell me whether or not you believe it.
B. What if I don’t know?
A. If you don’t know, then say you don’t believe it.
B. Hmm. It’s going to be one of those sentences which asserts its own falsity, isn’t it? Like that Cretan who said “all Cretans always lie”. Utterances like that can’t sensibly be called either true or false.
A. A good point, but my sentence is fully capable of supporting a truth value. Indeed, I shall attempt to persuade you that the sentence is true. And very likely I shall succeed. Nevertheless you will continue to insist that you do not believe it.
B. What? You say I will be convinced of your sentence’s truth, but at the same time I will refuse to believe it? That would indeed make me a supreme idiot.
A. Exactly! [Writes something down and hands it to B.]
B. [Reads] “Only idiots believe this sentence.”
A. So, do you believe it?
B. If I believe it, then I must be an idiot.
B. But I maintain that I am not an idiot. So, no, A-san, I do not believe this sentence.
A. That’s what I said when I first read it. And that’s what C-san and D-san said too. In fact, I expect your reaction is the same as that of any intelligent person.
B. I agree. Anyone who read that sentence and declared that they believed it would be a self-admitted idiot.
A. In other words, B-san, you are saying that only idiots believe that sentence.
A. Ok! Now read it again.
B. [Reads it again. Thinks.] Bollocks.
A. And B-san?
A. Your trousers are undone.
27th April, 2011
Having shamefully neglected this blog (and indeed having been enjoying a holiday in Hungary), I came back yesterday to find it overflowing with thousands of comments flogging fake Rolexes (or should that be Rolices?).
I’ve disabled comments as a temporary measure, while I fiddle around trying to install a spam-catcher. I hope I didn’t delete any real people’s comments during the clean-up operation, but if you notice anything missing, please let me know.
Meanwhile, here’s a video clip of British comedian Kenneth Williams talking about medicine. But I think his comment is equally applicable to many areas of science, and not least to mathematics:
10th February, 2011
[Update: I'm updating this post with more math raps as I find them, so scroll to the bottom for newer material.]
I can see the future. And what I see is math-rapping. So here’s a celebration of today’s trail-blazers:
First up, TRM:
Next we have the smooth-flowing Mr Mc E=MC2:
Now a massive youtube viral hit, WYKAMATH‘s What you know about math? (part 1):
And Part 2:
E=Mc2‘s The Math Rap
Stepping up the technicality is Essiness with One Geometry (The Poincaré Conjecture Rap)
Also by Essiness is Down With That (The Bolzano-Weierstrass Rap)
Am I missing any good ones?
UPDATE! Yes I am. The Kellers’ Pythagoras rap, worth watching as much for the video as the song:
…and an Eminem-style video from Brigham Young University’s Mathletics Team
19th November, 2010
I just ran into Tom Henderson’s Punk Math Manifesto:
The video’s an appeal for funds taken from Kickstarter, but it looks like the target’s already been reached. (Not that a few more pennies would go unappreciated, I’m sure.)
I definitely dig the philosophy, fleshed out in more detail in this interview. So it’ll be good to see the project develop.
Having said all that, punk’s not really my genre. Maybe I should try experimenting with some Jazz Geometry, or Death Metal Model Theory.
5th March, 2010
I’m currently having terrific fun playing around on Jeff Weeks’ flight simulator, Curved Spaces. Unlike most flight-simulators, the action takes place not in regular Euclidean space, but in a selection of 3-manifolds. (It’s also comforting that you don’t have to worry about crashing.) Highly recommended!
7th December, 2009
It’s a new one on me, but I like it:
Almost all natural numbers are very, very, very large.
We could extend it by saying that for any n, almost all natural numbers are veryn large. But that might not be so frivolous.