How to get to Lagarto’s new academy

Single-handed

I’ve been reading Halfway to Venus, Sarah Anderson’s memoir about having one arm: an experience enriched for me by the fact that when I met her on the train I never even noticed the empty sleeve.

She says at one point that being one-armed is in some ways more disabling than being one-legged, since losing a leg makes locomotion difficult but losing an arm transforms one’s life completely. My first thought was that I hadn’t thought of it like that – and naturally my second thought was: how would having only one arm transform one’s jiu-jitsu?

The answer is that it doesn’t stop one from becoming a black belt. A One-Armed Guide to Jiu Jitsu describes exactly how the black belt Aaron Lapointe deals with the situation, and his opponents. Like any black belt’s description of his own game, it makes one think more deeply about one’s own.

Off to Breakin’ Convention this weekend, and coincidentally ILL-Abilities will be performing again.

More self-indulgence

You can tell I’ve got some serious work on when I’m on here instead. Here’s another Proof from THE BOOK.

Write down 10 numbers. Any 10 whole numbers. They don’t even all need to be different.

Then:

1. either one of them is a multiple of 10,
2. or a sequence of them adds up to a multiple of 10.

For instance, if I write down 3 1 4 1 5 9 2 6 5 3, then 4+1+5=10 and 5+9+2+6+5+3=30.

(Note: the division into case 1 and case 2 is purely artificial. A mathematician would be happy with “a sequence of 1 number adds up to a multiple of 10″ but real people aren’t.)

Dangerous to exceed the stated doze

In the days when I did not suffer from insomnia on trains the way I do now, the nearest railway station to home was Tonbridge, about 45 minutes from London.

The next station after Tonbridge was Ashford, 30 minutes further down the line. This was not theoretical knowledge. I knew it from experience.

It follows that when, one day, I woke up and the train was stationary at Tonbridge, I moved with lightning rapidity. I gathered together bag, coat, books, magazines, whatever, and tumbled with them, in a heap, onto the platform.

I was safe.

I then looked round and realised, one by one, three things.

1. I was in London, at Waterloo East station, which looks a lot like Tonbridge.
2. But it was all right, I had not leapt off the train 42 minutes too early, because…
3. … I was not travelling home from London at all, I was travelling to London from home, for a party.

Another good software disaster

The good software disasters are the ones where nothing goes wrong and everything works.

Knight Capital’s suicide bid on 1 August 2012 was one of those. They have never admitted what caused them to buy shares at the offer price and immediately sell them back at the (lower) bid price, losing a little money each time, between 40  and 100 times a second, on many different shares, for almost half an hour, but the description at Nanex, although based on inference, seems close to the truth of how software development works:

1. They developed some new market-making software: software to offer shares to people who want them and to bid for shares at a lower price from people who don’t.
2. They had to test this.
3. So they wrote a test program which placed orders to buy at the offer price, to see that the market-making software handled them properly, and which placed orders to sell at the bid price – very fast, to make sure that the software could handle high volumes of transactions.
4. The tests worked.
5. So they linked the market-making software into New York Stock Exchange’s systems, and at 9.30am on 1 August 2012, it went live.
6. It worked.
7. They accidentally included the test program in the software that went live.
8. It worked too.
9. So, many times a second, Knight Capital asked to buy a share at the offer price and immediately afterwards asked to sell it at the bid price, losing a little money every time and driving the prices wild.
10. If the test order went to Knight Capital’s own market-making software, nothing much happened. Knight Capital was losing money to Knight Capital. But when it went to another market-maker, it was a real purchase or a real sale. Knight Capital lost a quarter of a million dollars every second. In half an hour, the rest of Wall Street was 440 million dollars richer at Knight Capital’s expense.

Because the test program was a test program and not doing real trades, there was no need for it to record the trades it was making, so it didn’t. The only way to tell what was happening while it was happening was to watch the monitors go wild. Here is a series of monitor pictures, at increasing levels of zoom, from the middle of the Knightmare. They are actually rather pretty.

But the thing to remember is that at all times and in all ways, all the software worked exactly as it was designed to work.

Pure self-indulgence

Well, almost pure.

I was leafing through Aigner and Ziegler’s Proofs from THE BOOK, which is a compendium of the most beautiful results in mathematics, and I came across a very simple puzzle which Paul Erdös used to use when he wanted to see if someone was really a mathematician. Here it is, without the algebra:

Think of the numbers from 1 to 100. Prove that if you make a collection of any 51 numbers between 1 and 100, at least one number in your collection will be divisible by some other number in your collection.

I am not a real mathematician. I am not patient enough. Knowing I’d regret it for the rest of my life, I read the solution. It is indeed very beautiful. To atone for my crime and assuage my anguish, here is the proof in a form that I think everyone will be able to follow. Try it. It’s fun.

Duck for Freedom

DuckDuckGo is Google for anarchists.

It doesn’t track or remember anything you search for. It doesn’t synthesize an identity for you based on your searches. It doesn’t target advertisements at you based on your searches. And so on. DuckDuckGo is a Google that you don’t pay for with your soul.

This is a Good Thing.

Using mathematics

Publishers tell one that each equation one includes in a book halves its sales. Hence the phenomenon of completely incomprehensible books which would have made sense if the author had only been allowed to say what he was talking about: João Magueijo and Marcus du Sautoy are notable victims.

The back page of La Recherche, always a good source of the information that really matters (it once reported a paper which established a negative correlation between designer stubble and life expectancy), now weighs in on the other side. A new paper reports that adding a random line of nonsense mathematics to the abstract of an academic paper on sociology or anthropology made the paper seem more authoritative – though the effect seemed to be confined to non-mathematical readers.

The Beautiful Result

I recently worked out a formula in celestial mechanics which is so beautiful, I was stunned by it for a week.

It isn’t just the unexpected simplicity of the formula. It’s the fact that it’s one in the eye for the scientists. They are always contrasting how things look (to us) with how things really are (in the scientists’ eyes), and of course the idea is that Reality trumps Appearance every time.

Except now.

The beautiful one-in-the-eye-for-the-scientists formula says that the height of the tides depends on two things and two things only: what the Moon is made of (green cheese would make smaller tides than rock) and how big it looks when we look up at it. What about how big the Moon really is? And how far away it really is? Neither of these things matters in the slightest. Reality is irrelevant: it is Appearance that counts.

Beauty should be shared; and a beautiful result must have a proof that lives up to it. To me, this means a proof that is as pure and limpid and natural as the things it talks about, not line after line of algebra. Algebra does have beauty in some people’s eyes, but only because the beauty of what is underneath the algebra shines through the symbols. I’d rather try and communicate the beauty directly.

Here is my attempt.

Crowdsourcing in a nutshell

One of the things we are promised the Web will do for us is answer all our questions without anybody having to be paid to collect and collate the information. Whatever you ask, someone will know the answer.

Only an out-of-date cynic would say that a random person with no known credentials may not be the best source of information.

What this out-of-date cynic did was look at Yahoo! Answers. I wasn’t looking round for a target to croticize: I genuinely wanted to know the atmospheric pressure at 3000 metres, because I’ve skied at that height and I’ve been able to breathe.