I've never managed to disagree with Richard Dawkins before, so this is a big moment for me. He must be getting old. In his latest book: 'The Magic of Reality' he asserts that it's impossible to turn a prince into a frog.
Easy:
Put a prince into a sealed glass box. Add lots of water and boil. Leave to cool. Introduce plant seeds and open the box to the air. Leave it until you have a nice pond. Introduce frogs (mating pair). Wait. Soon you will have many frogs, and they will be made mostly of prince.
The reverse transformation is harder because of the conservation of mass, but you can turn a lot of frogs into one prince, and it's actually easier. Sometimes you'll get princesses too.
I'm not sure that we'd learn much from the experiment though, so I imagine it might not get past the ethics committee. We'd have to do it as some sort of reality TV show. It's been a while since Dawkins did the Royal Society Christmas Lectures.
Friday, June 29, 2012
Thursday, June 28, 2012
Different Minds VIII (Surprise!)
So I've mentioned my new theory about different sorts of minds and how that explains how different people find that different things interfere with their ability to think.
And a lot of people seem to think it's plausible, and some people say that they think mainly in images, and some people seem to think that they think mainly in words.
And it appears that I myself do mathematical thinking in pictures, never in symbols (which is the opposite of how most mathmos work), but computer thinking in symbols, rarely in pictures (I often draw data-flow diagrams, or diagrams of data structures, or state machines or graphs on paper, but I can't do that sort of thinking without a piece of paper, because my working memory isn't good enough/large enough to hold the picture).
But the real shocker came when my friend Neil said "So you have a sort of inner narrator talking to you all the time?", and I said yes.
And Neil was quite surprised by this, because apparently he thinks entirely in pictures, and although he knows what the 'talking to yourself internally' voice sounds like he doesn't use it often.
And a bit later I was talking to my friend Gytha, who is a playwright, and she says that she doesn't have an inner voice either. She works out her plays in pictures, and she doesn't like the laborious process of turning them into words. She thinks that I'm the weird one, and she claims that that explains why I'm so articulate (because I'm always practising).
I hadn't realised that I was particularly articulate. But when a playwright who lives in Cambridge tells you that you are the second most articulate person that she knows, then you have to take that as evidence in favour, and come to think of it most other people seem to have trouble with easy things like 'giving speeches about something you care about with five minutes notice', which I've done a few times and which seems mainly to involve 'working out what you want to communicate and then just doing it'.
So am I the weird one? How often do you hear your inner voice? Does it speak in your native language, or is it speaking something else that needs translated into words?
And isn't it odd that we live in a world where other people have completely alien thought processes and yet we rarely notice.
If someone had written a science fiction story about an alien race that thought by forming and transforming pictures, I would have found it entertainingly weird, and probably dismissed it as an unlikely way of building a mind. But it appears that there are quite a lot of people whose brains work in just that way. And they think that the thing which to me is 'experience of being', is an alien concept.
There really are philosophical zombies. And I'm one of them.
Brainsss.....
Wednesday, June 27, 2012
Different Minds VII (A Theory)
By this time, I'd come up with the following theory of what was going on:
There are often several ways of thinking about the same thing. Some involve making and manipulating visual images. Some involve language.
When you're trying to think about something, you are actually using the bits of your brain whose real purpose is talking, or listening, or seeing (and reacting to the things you see).
If there's something going on nearby, it can activate one of these systems. For instance, if you see something flashing or moving that causes an alarm, that will refocus your visual system (all of it, including the brain part) to the suddenly interesting object. There's nothing you can do about this. An ancestor who was able to ignore things making sudden movements near him would one day ignore a snake. So he wouldn't be an ancestor of yours.
Similarly you can get alerts from your audio systems. Consider the famous cocktail-party effect, where you can be in a room with twenty conversations going on, and somebody in one of the conversations says your name, and suddenly you can hear that conversation above all the others.
What that means is that your audio system must be processing all the conversations, listening for interesting words, but not bringing them to conscious attention unless it detects something significant.
So even sounds that you don't realize are there are using bits of your brain.
So people thinking audio or language-type thoughts should do it much better in the quiet, and people thinking visual-type thoughts should do it better in the dark.
But worse than that, if you're thinking a visual thought and some sort of alert goes off (like seeing a movement, or something flashing, or a pattern being broken), then your entire visual system should be suddenly repurposed to assess the threat and YOU LOSE THE WHOLE THOUGHT.
And similarly for me, when I'm thinking about something, or reading, and some miserable bastard puts on the radiogramophone, that's it. Every so often something interesting (to my audio threat detection system) happens in the music, and my audio system focuses on it, and my stack of thoughts comes down and I have to build it up again. And once this has happened a few times, I am furiously angry and becoming averse to the very process of thinking.
Now this is kind of a weird theory, because it says that the programmers who don't notice ambient noise (and I would imagine this is all the programmers at github, because anyone like me would have managed to stand it for precisely one afternoon before walking out and never ever going back under any circumstances), are mainly thinking visual thoughts when doing their job.
Whereas the programmers like me (and I know a few examples), who don't notice the visual distractions must be thinking mostly language-type thoughts.
And this means that we are doing the same job in completely different ways. Which is kind of odd, if you think about it.
And there should be some people who can use either or both systems. I would imagine that those guys should be able to tolerate noise or visual distraction better than either Chris or I can, because they'll have alternative systems they can use, so they won't get completely stuck, but I would also imagine that they'd be much better at their jobs in a quiet and uncluttered environment where they can use both systems freely.
And if you are one of the people who uses only one system, then if you're able to learn to use the other one, you should become much better at what you do.
If you've got a theory, it should make predictions:
1/ An MRI scan of a man with music playing in the background should show audio activity
2/ There should be more activity if it's music with words.
3/ And even more if the words are in a language that the subject understands.
4/ Similarly for the visual stimuli, although you'd need to use an innocuous method of providing visual stimulation, and I can't think of any. Background music is ubiquitous and can usually be ignored. There isn't really such a thing as background television.
5/ Brain scans of people programming should show activity in visual areas if they identify as undisturbed by office noise.
6/ But should show activity in language-processing areas if they are disturbed by noise.
7/ Some people will show both or either. They should find that audio and visual noise reduce their productivity but do not disable them.
8/ People who are not disturbed by noise can become more effective thinkers by learning to think using the language parts of their brains as well.
9/ People who do not notice visual noise should learn to think visually.
10/ The best programmers will be driven up the wall by either.
Daniel Dennett says in 'Consciousness Explained', that he thinks that the inner dialogue starts when you use the bit of your brain which speaks to put thoughts into your own head via the bit of your brain that listens. Similarly he says that you can start off by drawing pictures to yourself and end up 'cutting out the middleman' and doing the same process entirely inside your head. Let's calls this sort of thing a feedback loop.
Further predictions:
11/ There will be other modes of thought I haven't thought of, wherever there's a feedback loop to be exploited. Maybe some people think using touch? or emotion? Perhaps that's why some people seem to be 'naturally good at sport' or 'emotionally literate'.
12/ Maybe these feedback loops can be trained too?
There are often several ways of thinking about the same thing. Some involve making and manipulating visual images. Some involve language.
When you're trying to think about something, you are actually using the bits of your brain whose real purpose is talking, or listening, or seeing (and reacting to the things you see).
If there's something going on nearby, it can activate one of these systems. For instance, if you see something flashing or moving that causes an alarm, that will refocus your visual system (all of it, including the brain part) to the suddenly interesting object. There's nothing you can do about this. An ancestor who was able to ignore things making sudden movements near him would one day ignore a snake. So he wouldn't be an ancestor of yours.
Similarly you can get alerts from your audio systems. Consider the famous cocktail-party effect, where you can be in a room with twenty conversations going on, and somebody in one of the conversations says your name, and suddenly you can hear that conversation above all the others.
What that means is that your audio system must be processing all the conversations, listening for interesting words, but not bringing them to conscious attention unless it detects something significant.
So even sounds that you don't realize are there are using bits of your brain.
So people thinking audio or language-type thoughts should do it much better in the quiet, and people thinking visual-type thoughts should do it better in the dark.
But worse than that, if you're thinking a visual thought and some sort of alert goes off (like seeing a movement, or something flashing, or a pattern being broken), then your entire visual system should be suddenly repurposed to assess the threat and YOU LOSE THE WHOLE THOUGHT.
And similarly for me, when I'm thinking about something, or reading, and some miserable bastard puts on the radiogramophone, that's it. Every so often something interesting (to my audio threat detection system) happens in the music, and my audio system focuses on it, and my stack of thoughts comes down and I have to build it up again. And once this has happened a few times, I am furiously angry and becoming averse to the very process of thinking.
Now this is kind of a weird theory, because it says that the programmers who don't notice ambient noise (and I would imagine this is all the programmers at github, because anyone like me would have managed to stand it for precisely one afternoon before walking out and never ever going back under any circumstances), are mainly thinking visual thoughts when doing their job.
Whereas the programmers like me (and I know a few examples), who don't notice the visual distractions must be thinking mostly language-type thoughts.
And this means that we are doing the same job in completely different ways. Which is kind of odd, if you think about it.
And there should be some people who can use either or both systems. I would imagine that those guys should be able to tolerate noise or visual distraction better than either Chris or I can, because they'll have alternative systems they can use, so they won't get completely stuck, but I would also imagine that they'd be much better at their jobs in a quiet and uncluttered environment where they can use both systems freely.
And if you are one of the people who uses only one system, then if you're able to learn to use the other one, you should become much better at what you do.
If you've got a theory, it should make predictions:
1/ An MRI scan of a man with music playing in the background should show audio activity
2/ There should be more activity if it's music with words.
3/ And even more if the words are in a language that the subject understands.
4/ Similarly for the visual stimuli, although you'd need to use an innocuous method of providing visual stimulation, and I can't think of any. Background music is ubiquitous and can usually be ignored. There isn't really such a thing as background television.
5/ Brain scans of people programming should show activity in visual areas if they identify as undisturbed by office noise.
6/ But should show activity in language-processing areas if they are disturbed by noise.
7/ Some people will show both or either. They should find that audio and visual noise reduce their productivity but do not disable them.
8/ People who are not disturbed by noise can become more effective thinkers by learning to think using the language parts of their brains as well.
9/ People who do not notice visual noise should learn to think visually.
10/ The best programmers will be driven up the wall by either.
Daniel Dennett says in 'Consciousness Explained', that he thinks that the inner dialogue starts when you use the bit of your brain which speaks to put thoughts into your own head via the bit of your brain that listens. Similarly he says that you can start off by drawing pictures to yourself and end up 'cutting out the middleman' and doing the same process entirely inside your head. Let's calls this sort of thing a feedback loop.
Further predictions:
11/ There will be other modes of thought I haven't thought of, wherever there's a feedback loop to be exploited. Maybe some people think using touch? or emotion? Perhaps that's why some people seem to be 'naturally good at sport' or 'emotionally literate'.
12/ Maybe these feedback loops can be trained too?
Tuesday, June 26, 2012
Different Minds VI (Clues)
A big clue came when one of my colleagues (another Chris), whom I know to be an exceptionally competent and intelligent man, said that although he literally hadn't noticed the noise, he also hated the overcrowded office because he was constantly distracted by people moving around in his peripheral vision.
I wondered why on earth that would be a problem. And he said that any visual distraction made it difficult to think. He looked at my computer screen and said "For instance, I couldn't get anything done with that messy arrangement of windows".
It hadn't occurred to me that my desktop was messy. I'd just opened various programs and moved the windows so that I could see them all.
So I asked him if he was disturbed by pictures hanging at odd angles, and he said that he couldn't think at all in a room where there was an odd hanging picture. WTF? I mean, if I noticed that a picture was at an angle, I'd fix it next time I was near the picture, but I'd be quite unlikely to notice unless it was about 20 degrees out, and even then I'd probably go through several cycles of forgetting about it and re-noticing before I got round to it.
Whereas to Chris, this was as annoying as music is to me. You can't think near it. It uses the bit of your brain that you want to use when you think.
At this point, I remembered an article I'd once read by Richard Feynman, describing how he'd taught himself to count time. With a bit of practice, he'd found that he could count at a nice even pace, and so could make accurate timings of things. But he'd noticed that there were some things he couldn't time like this, because he couldn't count while doing them.
So being Feynman, he made a list of all the things he could do, and all the things he couldn't do, and then he got colleagues to learn how to count evenly, and then got them to make lists of the things they could and couldn't do.
And to his amazement, the lists were not at all the same.
To cut a long story short, it turned out that some people were counting by saying the numbers to themselves, and some people were counting by looking at an imaginary clock and imagining it move. And that meant that different activities disrupted the process.
So I asked Chris what else he found interfering with his programming. And the list of things freaked me out completely.
One of them was the way the code was formatted.
Programming uses a lot of punctuation. For instance a piece of code might be formatted :
for(i=0;i<10;i++){do(thing)};
The punctuation lets the computer know where various bits of the program start and end. If you're talking to a human you might say 'Go and buy me 20 cigarettes and a mars bar', and it's obvious what that means, but computers are not terribly bright, and have trouble breaking the sentence up into its logical bits, so to help it 'parse' the sentence you have to say something like
Go; //and
Buy (me) {
20 * cigarettes ;
1 * mars bar ;
}
Come back;
This could be a real piece of code (meaning to do a thing 10 times):
for(i=0;i<10;i++){do(thing);}
But it's a bit dense for human eyes, so we tend to put extra spaces in to make it look better:
for( i = 0 ; i < 10 ; i++ ) {
do ( thing ) ;
}
They don't change the meaning, they just make it nicer to look at.
And programmers fight holy wars over where to put the damned spaces.
Here's another popular style:
for( i=0; i<10; i++ ) {
do( thing ); }
A lot of people seem to thing that this is terribly important. Most companies have a complicated document specifying exactly what the 'house style' is.
I have honestly never cared in the slightest. Even though I've never used the term 'special snowflake' about the people who do, it accurately sums up my attitude to anyone who'd get involved in an argument about where to put the damned spaces. If anyone tells me I'm doing it wrong, I usually let them reformat my code so that it suits them. I usually can't tell that they've done it afterwards, but it makes them happier, so what-ever...
But I've seen people get so angry about the issue that I thought they'd fight. And I've never known why.
The funny thing is, even though Chris could tell me exactly which bits of our codebase were well formatted and which weren't (In the same way that I can tell you which Cambridge pubs and cafes play music, which play music with words in it, and which tend to be quiet places suitable for thinking in), he didn't think that my stuff was badly formatted. So obviously even though I don't notice it, when I'm writing code, I have a consistent style I stick to. Except that I couldn't tell you what that style is. And I don't care about it.
Different Minds V (Asking around)
I thought I'd better check my assumption that people talking stops you programming.
Web searching produces contradictory results. Everyone agrees that it's a very complex task that needs lots of concentration.
Noisy crowded offices feature in several lists of 'top ten classic software mistakes'.
Tom DeMarco, a famous software productivity guru makes quiet and privacy the unconditional top recommendations in his famous book 'Peopleware', about how to manage software development. And has done experiments to back his advice up, which come to the conclusion that what is obvious (to me) is also true. You can't program well when people around you are talking.
A lot of programmers work very anti-social hours so that they can get things done when no-one else is around. (At the shop I'm talking about so many of the programmers were doing this that it actually got quite noisy and distracting in the evening. I tried coming in very early in the morning or at weekends to avoid the other avoiders. Anyone who knows me will tell you that I am not a mornings person, and I had to abandon this strategy because it was leaving me permanently exhausted).
Many people wear earplugs or earphones to work.
But some of those people are using their earphones to listen to loud music.
Those people are doing it to block out the ambient noise, and some of them say that it only works with instrumental music (no words), but some of them say that as long as they listen to songs they know well, it's not distracting.
And some programmers don't believe that there's a problem at all. They think that the people complaining about the noise are 'special snowflakes', or that they're trying to get offices for reasons of status. I wouldn't have been at all surprised by management types or HR people thinking this, but these are actual programmers saying this. Most programmers don't care about status. If they cared or noticed that sort of thing they'd stop wearing black T-shirts with the names of children's musicians on them covered in pizza stains. The ones that care about status signalling tend to become management.
One very successful and innovative shop I read about (Github) is actually proud to boast that they have rock music playing loud in their office. I could not have been more surprised if you had told me that they paid people to go around slapping their programmers with wet fish and stealing their computers.
So I asked the other people where I was working. After all we were all in the same environment.
And results were weird. Some people hated it like I did.
Some people found it just as distracting as me, but didn't care. They were getting paid whatever, it's only a job, isn't it like this everywhere?
Some people pointed me to sources of industrial strength ear-defenders.
Some people said what on earth is your problem? Can't you just shut out the noise?
And some people just didn't think it was that noisy.
I was reminded of a situation years ago where a colleague of mine was constantly complaining about the air-conditioning.
Apparently the air conditioning where we were working would randomly switch on and off every five minutes.
I tried to sympathise, but I hadn't the heart to tell him that I hadn't noticed that we had air conditioning before he'd started talking about it, and that even now I had to make an effort to tell whether it was on or not, and that I'd never noticed it switch on or off. Nobody else understood why it was a problem either. Chris found it absolutely infuriating and complained constantly. He eventually left over the issue. This was a sad thing because he was one of our better talents and we missed him badly.
Noise sensitivity is apparently a common symptom of Asperger's Syndrome, common amongst engineers and mathematicians. I wondered if that might be my problem.
I have some friends who are involved in autism research, and I asked them whether they thought I might have the syndrome. They were unanimous that there wasn't a chance. (Although one said "No, you're weird, but in a completely different way. Nothing like Asperger's.", which wasn't super-reassuring.)
Just to check that they weren't being nice to me, I did a couple of online tests, both of which said that I'm slightly less Asperger's than average. (Apparently that means that it's schizophrenia I should be worrying about. Sigh...)
Different Minds IV (Meta Open Plan Disaster)
So, I am sitting in an office where I am being very well paid despite being completely unproductive.
And it occurs to me that something is very wrong here. Once upon a time, engineers got offices to themselves, as is normal for lawyers and academics and other people who need to be able to think complex thoughts.
And yet somehow, over the last twenty years or so, open plan offices have become more and more popular amongst companies that do software for a living.
I can think of two obvious reasons why that could happen:
The first is cost. Obviously open-plan is a bit cheaper. But that's just ridiculous. Say that you rented a house in Cambridge for £1000/month. That would easily get you five large offices plus facilities, so we can put an upper bound on office cost of £200/person/month.
How much of that can you save by going open plan? Being generous, say half of it. Call it 160 hours, so you're saving ~ 50p / hour by having an open plan environment.
I'd guess that the average cost of engineering staff is a couple of orders of magnitude higher than that.
You wouldn't even notice a productivity change of 1%. By my own estimates, my productivity has been completely shredded by having people talking while I'm trying to think. Even if I'm wrong and I'm only down to working at half speed, cost can't even be an issue.
The second reason would be communication, which is extraordinarily important amongst a programming team (that's why outsourcing never works). But programmers talk much less in open-plan environments than they do normally, because they're conscious of disturbing other people. In every computer shop I've ever worked in, the interesting complicated conversations go on in the kitchen or in meeting rooms, where people can bounce ideas off each other without annoying everyone else.
In the particular shop I'm talking about, it was hard to have meetings in the kitchen because everyone was having meetings there, and what with people making tea and such, it was sometimes hard even to get in!
So I don't think it can be communication either. There definitely are communication problems in the traditional layout, but they're easy to solve by having common rooms with water-coolers and tea making facilities and whiteboards and sofas.
So the only reason I could think of why open plan has caught on is that the people making the decisions aren't programmers.
They actually don't realise that with their big open friendly spaces (and don't get me wrong, I'd much rather sit in a cafe that was all one room than in one divided into separate private rooms) they're completely screwing the productivity of their company.
But then I'm not sure that that explanation can work either. Because isn't the market supposed to sort that sort of thing out? Wouldn't a programming shop that did something that weird and horrific just go out of business, out-competed by its wiser siblings?
Apparently that hasn't happened either.
So I've run out of candidate explanations.
I notice that I am confused.
Different Minds III (Open plan disaster)
So the reason I am thinking so much about what it is like to be me these days is that I suspect that what it is like to be me is not what it is like to be some other persons I could mention.
And this all starts when I am working for a very nice bunch of guys who have an open plan office.
And when we are doing the initial dance, I have noticed that they have an open plan office, and I say "I hate and fear open plan offices, because I can get very little work done, and it is no fun, and I get angry and guilty and begin to hate life itself and then I resign."
But they are all: "Do not worry, it is as quiet as the grave in here, and we have lots of space for very few people, and we are very aware of the problem of noise for engineers, and we will make sure that it stays quiet. And anyway we are going to take over another floor of the building soon and then we will all be lost like dust specks in the vastness of intergalactic space."
And you cannot say fairer than that, so I take the job. Although being of a suspicious cast of mind I make sure that the contract specifies one hour's notice on either side and no hard feelings.
And indeed everything is very nice for a while.
But this company is being funded by the sort of venture capitalists who have more money than sense, and there are always new projects to start, and always new money to hire with, and the new-floor-taking-over does not go so well, and six months later we are crammed in so close that even though everyone is making an effort not to disturb anyone else, there is always someone nearby talking, and so I can't think any more.
Because computer programming is very hard. You need to remember so many things at once that it is not true. A lot of what is called 'software engineering' is in fact clever techniques for making the complexity go away by establishing standard patterns that are easier to remember. But of course once you have those techniques, you can hold more complexity in your head at once, so you do. The point is not only to use the new tools to do the old things more easily. The point is to do better things with the new tools.
The day to day experience of my job is like trying to remember very long telephone numbers whilst doing crosswords and playing chess.
I am not moaning. This is my favourite thing to do. I like it when my brain is working. But I cannot do it when other people are talking. Because they are using the bits of my brain that I need to use to talk to myself with!
Different Minds II (What it is like to be me)
Everyone generalizes from one example. At least, I do....For me, consciousness comes with a narrator. It's a bit like watching a film with a voiceover. There's a visual field, which goes all around even though I only see a broadish oval cone of it at once, that's full of colour and movement, and there are sounds, which are usually associated with a specific direction or thing or with one of the people I can see. Sometimes there are other human voices, which are streams of words which often have associated with them feelings like "probably to the left" or "middle-aged middle class male". Or both. Other times there are foreign voices, which have the associated labels, but sound like babble. With French, which I sort of speak, the streams of babble have occasional words in. If I concentrate on the French, then I hear babble with odd words in, and slightly later, some of the other words resolve, and meaning fragments and partial English translations come available (as separate things)
This bit is very like a film. It's more like a 3d colour multilingual film with very good surround sound and alas no subtitles, than a black and white silent, but it's very clearly the experience that cinema films are tending towards.
Which is odd, when you think about it. Because that's nothing like what the incoming information looks like, as countless eyeball-tracking and speech analysis experiments have shown.
But there's also a continuous narration that is a stream of words that are not in the outside, a "stream of consciousness". At the moment it's saying these words, very slowly as I type them. But if I stop typing then it carries on talking, thinking out the next sentence. I (the conscious perceiver) don't produce the words! I just listen to them.
If I like, I can direct the stream to the screen of my netbook. I can still hear the words, but they slow down a lot, and my fingers move in patterns I can't really perceive (just a flurry of movement, like watching a cloud of midges), and the words appear on the netbook screen.
Apart from the initial decision to start typing, this is nothing to do with me at all. I just watch the words appear. Sometimes I notice that one of the words is misspelled, or that I don't agree with what I've just written, so I backspace and do it again, hoping for a better result.
Sometimes I feel a sense of completeness, and at the same time I feel the little finger of my right hand stretch out to end the paragraph.
The narrator is always talking, whatever I'm doing.
I can stop the narration. If I do, then I become super-sensitive to the colors and sounds around me. But the state isn't stable. Even if there's no-one talking near me. I just tried it for a minute or so, and I watched a man walk past and noticed the articulation of all his joints as he walked, and heard the sound of his footsteps, and thought no words. But then there was a slight scraping noise off to the right hand side, (I am sitting in the blessedly silent Eagle), and I heard my voice say "the sound of a barrel". And then I started thinking again.
And if I somehow managed to hold the silent state stable, in an important sense "I" wouldn't be present any more. Nothing I'd call "thinking" would be going on. I'd just be sitting there waiting for alerts from various systems that monitor the world for sound and movement.
Of course I know that this can't be the truth. Sometimes I think about something (yesterday's mole problem is an example) for a while, can't think of the answer, forget about it for a bit, and then have a method of solution pop into my head by magic the following day (and it still took me an hour and a half to actually draw the diagram, even when I could already see how it was all going to pan out).
So a lot of the thinking must be unconscious, and I must have monitors set to alert me when some sub-process has found an important result. And presumably that doesn't stop when the narrator stops.
In fact, maybe the subprocesses can only work when the narrator releases the resources that it's using to narrate?
I wonder if it's possible to solve a problem by just sitting there deliberately not thinking and wait for the 'answer alert' to go off?
Different Minds I
All children wonder: "Is the red that my friend sees the same as the red I see?". "How would we ever know if he saw green where I see red and red where I see green?"
Partially this question is answered by colourblindness. If you see red and green as the same colour, then your experience of the world can't be anything like mine!
So I think we know that it doesn't necessarily 'feel the same' to different people to be human. And the Lord alone knows what it is like to be a pigeon, with four-colour vision, or a bat who sees with sonar.
I always thought that the biggest differences between human experiences would be between men and women. I notice that at least as far as anything to do with sex goes, women act completely differently from men, and I find it very hard to imagine what it would be like to be motivated in such a way that I would produce the observed behaviour.
But I can at least imagine what it might be like to be a woman. I don't know if my thoughts are anywhere near the truth, but at least I can think them.
Talking to various people over the last couple of months, I've begun to suspect that the differences between the experience of being between me and some of my closest friends are very much greater than the male/female differences.
Some of my friends claim that they don't have anything like what I'd call thoughts at all. And I really cannot imagine what that might be like.
The Angels' Share (Film)
After an hour or so of the usual, the repellent Glaswegian scum put on kilts and the film becomes the closest Ken Loach is going to get to a remake of Brigadoon.
It's coming to the end of its run and there were only ten people in the cinema. We nevertheless gave it a round of applause at the end. Go and see this marvel while it lasts.
It's coming to the end of its run and there were only ten people in the cinema. We nevertheless gave it a round of applause at the end. Go and see this marvel while it lasts.
Monday, June 25, 2012
The Hunger Games / Catching Fire / Mockingjay
I have no idea why I read these. I knew before I picked them up that they were 'young adult' fiction (which I take to mean no complexity, no sex and the predictable triumph of the obvious hero), and they are, but the pretty yellow bird on the black book made me curious.
And the first chapter led me on to the second. And so on. All the way through I was thinking 'Why are you reading these?', and yet I kept going and buying the next one.
They're really not bad, if you like that sort of thing. I have a strong desire to buy a mockingjay pin and fix it to my favourite tweed jacket. I am resisting that desire as hard as I can.
I imagine idealistic teens will love these books. If you have an idealistic teen then I have a complete set of three in their original beautiful covers. Free to a good home.
And the first chapter led me on to the second. And so on. All the way through I was thinking 'Why are you reading these?', and yet I kept going and buying the next one.
They're really not bad, if you like that sort of thing. I have a strong desire to buy a mockingjay pin and fix it to my favourite tweed jacket. I am resisting that desire as hard as I can.
I imagine idealistic teens will love these books. If you have an idealistic teen then I have a complete set of three in their original beautiful covers. Free to a good home.
Consciousness Explained (Daniel Dennett)
This glorious book is often referred to as 'Consciousness Denied'. Dennett takes a good look at the 'hard problem of consciousness' (What is the ghost in the machine?), and confronts it straight on.
The book is full of superb arguments and thought provoking examples and experiments, and throughout I kept wondering if I'd cease to exist mid-chapter.
In the course of the week it took to read this book, my entire view of what I am and how I work has turned upside down.
But still. Cogito ergo sum. I still buy that. I get the impression that Dennett does too.
This book is a mighty stride towards working out what it is that might be under the illusion of existing. But I'm still confused.
In fact I'm more confused. This is a very good thing and I cannot recommend this book too highly!
The book is full of superb arguments and thought provoking examples and experiments, and throughout I kept wondering if I'd cease to exist mid-chapter.
In the course of the week it took to read this book, my entire view of what I am and how I work has turned upside down.
But still. Cogito ergo sum. I still buy that. I get the impression that Dennett does too.
This book is a mighty stride towards working out what it is that might be under the illusion of existing. But I'm still confused.
In fact I'm more confused. This is a very good thing and I cannot recommend this book too highly!
Thinking Fast and Slow (Daniel Kahneman)
This book is absolutely life-changing. Kahneman and Tversky started the 'heuristics and biases' movement in psychology. Now he's written a popular account of the last twenty years of the research. I already knew about a lot of the stuff in here, but after reading this I feel very differently about it all. He has Feynman and Dawkins' gift of making the subject matter look obvious and the reader feel like a genius. The mark of the true master.
Mole Trouble
This from my friend Matt's eleven year old son Alex. The little sod solved it in his head. It took me an hour and a half, two pieces of paper and two pens:
You got a garden.
There is a mole.
It has dug five molehills in your lawn, in a line connected by a tunnel.
The mole is under one.
----
You hit a hole with your hammer.
If the mole is under the hole, it dies.
If it is not, it moves either left or right.
And repeat.
-----
Example
Call the hills 1 2 3 4 and 5.
The mole is under hill 2. You hit 3. It moves to 1. You hit 4. It moves to 2. You hit 1. It moves to 1 ......etc.
------
Can you kill the mole? How many whacks?
Wednesday, May 9, 2012
Pretty Fucking Safe
Imagine you live in an idyllic farming village, way up in the high mountains. There's no road, and the trek in is only for skilled mountaineers. As a result, you've literally never seen a stranger.
Your world consists of maybe one hundred people. You know all of them, you trust most of them.
It's not entirely paradise though. Legend has it that around 500 years ago, two men got into a drunken fight in the village pub and one of them was killed. People have been talking about it ever since. 1512 is known as 'the year of the murder'.
So I want you to imagine that you're lying in a field, not far from the village, and it's going dark, and you see a dark shadow moving around in the woods. What would your principal worry be?
How nice it would be to live in such a world. What would we need to do to turn our current crime-ridden society into such a safe place?
To start, let's look at the murder rate for modern Britain. Wikipedia tells me that it's 1.23 murders per 100,000 people per year.
What about our village?
Well, we have at least 500 years of murder records, and there's been one murder. There are one hundred people in the village, so that's fifty thousand people-years per murder, so on the same scale the murder rate looks like it might be around 2/100000 people/year.
So we're done. 21st century Britain (1.23), and indeed the whole of Western Europe (0-2), are around as safe as our village (probably somewhere between 1 and 3).
And yet, people worry all the time about horrible happenings. My own parents (who live in a remote village in the hills) have so many locks on their doors that it can be quite time-consuming to get in and out of the house. And they lock them when they are in.
But it's not just them. I live in Cambridge, one of England's safer cities. Pretty much everyone I know has a degree, and you can reasonably assume that the milkman is only milkmanning to support his interest in baroque Catalan poetry.
And yet when my female friends leave the pub alone, I offer to walk them home. And they often accept. Or indulge in expensive and fattening taxis because they don't feel safe. If they walk home alone, I worry about them.
I myself have been known to feel slightly wary walking down Regent Street (a wretched hive of scum and villany where young people go to enjoy themselves in much the same way that I did when I was their age) on a Friday night.
The control of violent crime is one of the most explosive and politically sensitive issues there is.
What could possibly be going on?
Easy.
You're a monkey. An extremely clever and dangerous monkey, but a monkey nevertheless.
And monkeys live in groups of one hundred or so. The same size as our village.
And if a monkey notices someone getting murdered every day, then it would be wise to be utterly terrified. Because there are not so many monkeys to go round, and chances are that if things continue like this, the monkey and everyone it knows will be dead in a few months.
So the monkey will be well advised to move heaven and earth to investigate what is causing all the killings, and fix it.
And this method of estimating the danger is hard wired. Because all our ancestors for a very long time indeed lived in groups of about the same size. So there's a simple rule: Murder every few hundred years-> not to worry, everything is perfectly safe, indeed unrealistically safe, things can't be this good. (Which is what you feel when you think of the village in the hills.). Murder every year or so-> worry a bit, keep your guard up, although it's probably wiser to worry about tigers and starvation and disease and such. Murder every week -> PANIC!! PANIC!!. And rightly so. This rule served our ancestors well for a long time.
But you're a monkey living in a society of 60 000 000 people, which is a number so big that your monkey-brain has trouble with the number of digits in it, let alone the actual number, which is ridiculously large and absolutely beyond imagining.
And you find murder very interesting indeed. The bookshop in which I am sitting has a whole section devoted to gruesome and horrifying imaginary murders that people have made up for entertainment, and another whole section devoted to artificially scary accounts of particularly awful and memorable murders that actually happened, and there is a whole entertainment industry devoted to gathering news of all the murders that happen throughout Great Britain (which is a very great number. 1.23*600/year, so a couple every day or so), and selecting the most scary, terrifying and thus entertaining ones and delivering these stories to your poor monkey-brain by Marconi-waves, which brain responds by following its ancient algorithm and getting into a God-almighty tizzy.
And that is the answer.
How do we turn our scary modern society into a tranquil mountain village where almost nothing bad ever happens?
It already is. Stop reading the newspapers. Stop watching the television. Stop reading murder mysteries. Stop watching detective fiction and true crime and CSI:whereever. They are misleading you about the state of the world.
Obviously this is a counsel of despair. It can't be done. Such things are way too interesting and enjoyable to ignore.
But at least try rank the fear with the other unpleasant self-inflicted side effects of modernity, like getting fat because incredible amounts of delicious and unnatural food are just lying around everywhere for the asking, and monkeys know to eat as much as possible in such circumstances because they may not last.
And do not say to yourself 'I live in the midst of dangerous chaos, which I would do well to fear'.
But rather say to yourself 'I live in the safest society there has ever been in the history of the world. Nevertheless, I fear crime, because I cannot help reading about crimes all the time, and this scares my brain, which is not really designed for this sort of thing.'
And try to relax a bit, and not do silly things like changing the way you vote on the basis of which of the various groups of political scum is pretending the hardest about how much they can do about a problem which effectively ceased to exist hundreds of years ago.
Or if you are a member of a group of political scum, try coming up with memorable crime-policies, like barbecueing anyone convicted of murder in Trafalgar Square, which will cost almost nothing, hurt almost no-one, and give everyone in the country a nice satisfying feeling of justice well and truly done, as well as providing an excellent source of entertainment for the sadist community.
But try not to believe that it will actually help. The problem is already solved.
Your world consists of maybe one hundred people. You know all of them, you trust most of them.
It's not entirely paradise though. Legend has it that around 500 years ago, two men got into a drunken fight in the village pub and one of them was killed. People have been talking about it ever since. 1512 is known as 'the year of the murder'.
So I want you to imagine that you're lying in a field, not far from the village, and it's going dark, and you see a dark shadow moving around in the woods. What would your principal worry be?
How nice it would be to live in such a world. What would we need to do to turn our current crime-ridden society into such a safe place?
To start, let's look at the murder rate for modern Britain. Wikipedia tells me that it's 1.23 murders per 100,000 people per year.
What about our village?
Well, we have at least 500 years of murder records, and there's been one murder. There are one hundred people in the village, so that's fifty thousand people-years per murder, so on the same scale the murder rate looks like it might be around 2/100000 people/year.
So we're done. 21st century Britain (1.23), and indeed the whole of Western Europe (0-2), are around as safe as our village (probably somewhere between 1 and 3).
And yet, people worry all the time about horrible happenings. My own parents (who live in a remote village in the hills) have so many locks on their doors that it can be quite time-consuming to get in and out of the house. And they lock them when they are in.
But it's not just them. I live in Cambridge, one of England's safer cities. Pretty much everyone I know has a degree, and you can reasonably assume that the milkman is only milkmanning to support his interest in baroque Catalan poetry.
And yet when my female friends leave the pub alone, I offer to walk them home. And they often accept. Or indulge in expensive and fattening taxis because they don't feel safe. If they walk home alone, I worry about them.
I myself have been known to feel slightly wary walking down Regent Street (a wretched hive of scum and villany where young people go to enjoy themselves in much the same way that I did when I was their age) on a Friday night.
The control of violent crime is one of the most explosive and politically sensitive issues there is.
What could possibly be going on?
Easy.
You're a monkey. An extremely clever and dangerous monkey, but a monkey nevertheless.
And monkeys live in groups of one hundred or so. The same size as our village.
And if a monkey notices someone getting murdered every day, then it would be wise to be utterly terrified. Because there are not so many monkeys to go round, and chances are that if things continue like this, the monkey and everyone it knows will be dead in a few months.
So the monkey will be well advised to move heaven and earth to investigate what is causing all the killings, and fix it.
And this method of estimating the danger is hard wired. Because all our ancestors for a very long time indeed lived in groups of about the same size. So there's a simple rule: Murder every few hundred years-> not to worry, everything is perfectly safe, indeed unrealistically safe, things can't be this good. (Which is what you feel when you think of the village in the hills.). Murder every year or so-> worry a bit, keep your guard up, although it's probably wiser to worry about tigers and starvation and disease and such. Murder every week -> PANIC!! PANIC!!. And rightly so. This rule served our ancestors well for a long time.
But you're a monkey living in a society of 60 000 000 people, which is a number so big that your monkey-brain has trouble with the number of digits in it, let alone the actual number, which is ridiculously large and absolutely beyond imagining.
And you find murder very interesting indeed. The bookshop in which I am sitting has a whole section devoted to gruesome and horrifying imaginary murders that people have made up for entertainment, and another whole section devoted to artificially scary accounts of particularly awful and memorable murders that actually happened, and there is a whole entertainment industry devoted to gathering news of all the murders that happen throughout Great Britain (which is a very great number. 1.23*600/year, so a couple every day or so), and selecting the most scary, terrifying and thus entertaining ones and delivering these stories to your poor monkey-brain by Marconi-waves, which brain responds by following its ancient algorithm and getting into a God-almighty tizzy.
And that is the answer.
How do we turn our scary modern society into a tranquil mountain village where almost nothing bad ever happens?
It already is. Stop reading the newspapers. Stop watching the television. Stop reading murder mysteries. Stop watching detective fiction and true crime and CSI:whereever. They are misleading you about the state of the world.
Obviously this is a counsel of despair. It can't be done. Such things are way too interesting and enjoyable to ignore.
But at least try rank the fear with the other unpleasant self-inflicted side effects of modernity, like getting fat because incredible amounts of delicious and unnatural food are just lying around everywhere for the asking, and monkeys know to eat as much as possible in such circumstances because they may not last.
And do not say to yourself 'I live in the midst of dangerous chaos, which I would do well to fear'.
But rather say to yourself 'I live in the safest society there has ever been in the history of the world. Nevertheless, I fear crime, because I cannot help reading about crimes all the time, and this scares my brain, which is not really designed for this sort of thing.'
And try to relax a bit, and not do silly things like changing the way you vote on the basis of which of the various groups of political scum is pretending the hardest about how much they can do about a problem which effectively ceased to exist hundreds of years ago.
Or if you are a member of a group of political scum, try coming up with memorable crime-policies, like barbecueing anyone convicted of murder in Trafalgar Square, which will cost almost nothing, hurt almost no-one, and give everyone in the country a nice satisfying feeling of justice well and truly done, as well as providing an excellent source of entertainment for the sadist community.
But try not to believe that it will actually help. The problem is already solved.
Monday, January 9, 2012
The Artist (film)
I've just been to see 'The Artist'. It's a bit early to call 'the film of the year', but I can't remember the last time I enjoyed going to the pictures so much.
It's a modern silent black and white film, with (necessarily) a very simple story, but it made me think that something important was lost when they started adding colour and sound.
Take hankies.
It's a modern silent black and white film, with (necessarily) a very simple story, but it made me think that something important was lost when they started adding colour and sound.
Take hankies.
Friday, June 17, 2011
Wildfire (again)
I wrote this article years ago, after the fall of the Northern Rock bank in England, which was the first run on an English bank in a hundred years. A while later, when it looked as though Greece was going to default on its debts, I put it back to the top since it had started to look like a prophecy.
It's now 17th June 2011. Last year Greece was bailed out on promise of economic reforms, but those reforms were exceedingly unpopular and have just brought down its government and it is again on the verge of default. The IMF has refused to supply money, effectively blackmailing Germany into paying Greece's debts.
This isn't a long term solution. The problem will recur. Similar problems have occurred in Ireland and Portugal, and been 'solved' by similar methods. The longer this sort of solution is attempted, the more catastrophic the eventual reckoning will be.
-------------------------------------------------------
Note of 10th May 2010
I've put this back to the top because of the financial crisis in Greece. It was originally written after the UK banking crisis that turned into the (first half of the most recent) depression. Sovereign debt default is the next stage of an inevitable process. We have to ask ourselves whether it is better to take the hit now, or put the crisis off again. Next time there may not be an entity large enough to organise a bailout.
I'm going to stick my neck out and make a prediction. Today is 10th May 2010. I predict that either Greece will default on its debts, or the EU will bail it out, and then within the next five years other EU nations will default. The resulting financial effects will domino, and there will be widespread bank defaults. No government will be able or willing to guarantee the banks this time. The turmoil will cause Japan to default on its debt, and the result of that will be a terrifying financial apocalypse the like of which has never been seen. There will be revolutions and wars.
-------------------------------------------------------
Original Article:
There are few good arguments from analogy. Anyway, here's mine:
Once upon a time, the forestry service put out wild fires.
Nowadays they start them.
Once upon a time, banks built solid marble buildings with Doric columns.
Nowadays they rent cheap offices with plastic chairs and nasty carpets.
And I think these facts are related.
Let's look at the war going on in the woods.
The natural enemies of plants are trees. If you have an expanse of open earth, the first things that grow there will be grasses and nettles. Grasses grow fastest of all, finding new earth with their wind-blown seeds and rapidly colonizing everywhere they can fix roots.
Nettles are next. Nettles have the trick of making poisons. Grazing animals don't eat them. Because animals eat the grass, the nettles are taller than the grass. So they can see the sun. Whilst the grasses, being short, die in the shade of the nettles.
A patch of open earth will soon be covered in grass. Soon after that it will be covered in nettles. The thick covering of nettles means that the grazing animals will not go there.
This opens up a place where trees can grow. Trees have the knack of making wood. Wood allows them to grow taller than the nettles. The trees get so tall that they can rise out of the nettle patch entirely, and then begin to spread their branches wide, spreading a vast carpet of leaves. Blotting out the sun. The nettles, which protected the trees from the grazing animals, die. But by this time the trees have grown so tall, and with such thick bark, that the grazing animals can't reach any edible bits of the tree. So the patch is covered in trees. And this is the final state of the world.
So we might wonder why grasses and nettles still exist, if they always lose.
The answer is fire.
A forest fire is an awful thing. Dry trees burn very well, and there is sufficient wood to create an inferno which is hot enough to set light to a tree.
Every so often, even in the oldest and most permanent forest, there will be a period of drought. The trees will become so dry that a lightning strike can set one burning. And the flames will set light to a nearby tree. And the fire will begin to rage through the dry woods, incinerating everything in its path. And nothing will stop it. Not even the arrival of the rains. Until the whole of the forest is a smouldering wreck, and everything is dead except the fire-tolerant seeds hidden in the ground.
Which will begin to grow. Grasses grow fastest, because they don't need to make wood or poison. But grazing animals eat them........
A forest fire is a dreadful thing. It moves faster than you can run. It destroys everything and everyone. You never want to be anywhere near one. Nothing escapes but birds.
So the forestry service used to put out forest fires. And this was a very good thing.
But the trees grew and kept growing until the density of wood in the forests was so high that one day there was a forest fire and it had so much fuel to feed on that the foresters could not put it out. And because there had not been a fire for so many years, a lot of people had got a little careless, and built their homes in the woods.
And the fire that burned was bigger and fiercer than a normal forest fire, because there was so much wood. And you do not ever want to be near even a normal forest fire.
So these days the forestry service starts forest fires. They keep the density of the trees low, and if you are skilled in the ways of the woods you can predict where the fires will go, and to an extent control them and protect people.
You never get the embarrassing situation that happens when there hasn't been a dry patch for a while, and lightning hasn't felt like striking much, and the woods are overgrown and dry and waiting like a tinder box for the spark that will unleash hell.
And who knows if this latest innovation of the foresters will have an unintended side-effect? So far it seems to work well.
What about banks?
Banking is a very risky business. You borrow money from people. And you lend money to people. But there is no symmetry.
People lend you money so that it will be safe. Once upon a time, you would build a nice strong building and charge people to keep their money in it, where it would be safe. This model has fallen out of fashion. But at any rate, people's primary motivation is that their money should not fall into the hands of the sort of person who is forever talking about giving it to the poor but whose favourite Maid is suspiciously well dressed for a girl who lives in the woods.
So you are sitting in a nice strong building full of money. And you can practically hear the outlaws plotting in the woods about tunnels and bulldozers and other ways of making what is inside the building cease to be inside it.
So you need to find some way to get rid of the stuff. And it turns out that there are plenty of people who are willing to take it off your hands and keep it safe for a while themselves. They do this by buying houses and setting up businesses and other wholesome things, and they have promised to pay the money back slowly, with some interest, and most importantly both you and the Sheriff know where they live.
And everything is going so swimmingly that you can barely believe your luck, until Crazy Jake walks into a bar and tells everyone that Mr Shylock put all of the town's money into a scheme to mine gold in the hills and it turns out that there ain't no more gold in them thar hills and all the money is gone.
Now Crazy Jake is a big fat liar. At the most you only put a very small amount of spare money of your own into that scheme and yes, it is gone, but no one need care particularly because there is plenty of money in the bank to go round.
But people are a suspicious lot, and a few people pop round, not at all concerned, really, to ask for their money back so that they can keep it under the bed instead.
And a few people come round as normal to ask if they can have their money back because they have bills to pay.
And towards the end of the day you realise that the bank is out of cash. But everything will be alright tomorrow, you promise, because there are lots of interest payments on loans due in.
Tomorrow there is a line round the bank half a mile long. Because a couple of non-crazy people have been talking about how they asked the bank for some of their money back and the bank didn't have any money.
And you are a dead man. If you don't actually get hung from a lamp-post on the spot, you will be carted off to a dungeon somewhere and kept there forever. Crazy Jake has killed you as randomly and with as little malice as a lightning bolt hits a tree.
And the only people who are happy are the people that you lent all the money to, because their creditor is dead. And maybe the mess will all get sorted out eventually and they will be paying their interest to the people who've lost all their money by trusting it to you. And maybe it won't.
This is called a bank run, and it is why banking is a risky business.
Bank runs used to happen all the time. You can see black and white footage of huge queues round banks. Bank runs feature frequently in Westerns.
Banking is a very risky business, entered into by gamblers of the bravest and most reckless kind.
There is no way round it. The problem is that you are making money by lending long term and borrowing short term. That is what a bank does. If you aren't doing that, you aren't a bank.
Imagine that you are a gambler of the most reckless kind, who has a way to make large amounts of money at the price of occasionally and unpredictably being hung from a lamp-post.
To make it work, you need to get people to trust you with their money. These people may or may not be fools, but they certainly know about bank runs. They know that if a bank is behaving recklessly, it may suddenly cease to exist.
What should you build your building out of?
You should build it out of stone. And you should face the stone with marble. It should look as though it has been built out of pure money, by people who have lots of money, and intend to be around for a very long time.
Sober, serious, professional people. People who wear suits.
The minute you start to express the slightest bit of creativity, imagination or flair, the minute you're caught renting an office, as though you hadn't got the slightest intention of lasting for ten thousand years, then people will begin to take their money out and put it with more serious people. And we know what happens then.
Now once upon a time, this was what banks looked like. English towns are full of great big solid old banks built along classical lines, with lovely solid sounding names like 'The Trustees Savings Bank", or "The National Westminster Bank". Boring as hell, but lovely safe places to trust with money. Of course, they weren't actually. That's why they had to try so hard to look as though they were.
When I was a little boy, there was a new bank startup in England called "William's and Glyn's". I thought that that was a really nice name, and sounded very human and decent. They offered high interest rates and good service and they advertised heavily. And my father wouldn't put his money anywhere near them, because they sounded like they were just a couple of guys who'd started a bank.
But nowadays, banks don't look all solid like they used to. All the lovely solid marble buildings that look as though they will last for ten thousand years have been converted into public houses.
The last time I went into a physical bank, I found myself sneering at the crappy quality of the furniture. And anyone who knows me will tell you that I am not one to care too much about the quality of furniture. But this stuff was made out of formica, and it wobbled.
They don't even have sensible names any more. They're called "Natwest" or "Floyd's TSB" or "Egg". They're behaving like people who've been christened Thucydides by unworldly parents, and who have decided that they prefer to be called Diddy.
What has changed? Nothing recently. There hasn't been a serious bank run for years and years.
What has happened is that recently, the folk memory of bank runs has vanished. No one can remember what they were any more. So trusting money to a bank has stopped being scary. It will be safe. They will look after it carefully.
In fact trusting money to a bunch of gamblers to gamble with has started to seem like the boring option. Real men stick their life's savings in stocks and shares, or in exotic derivative instruments like property prices in areas where no more property can be built. Safe as houses.
What changed?
Government got involved in banking. A government can prevent a bank run. All it has to do is say: "Don't worry about your money. We guarantee that we will pay it all back if the bank fails."
The government can make this guarantee, because it has guns and tanks. So if it needs money it can steal it.
So if the government makes the guarantee, it is believed. Panic over. No-one needs to worry about whether their bank is solvent. No bank runs.
That's why we haven't seen a bank run in a while.
I believe that bank runs work the same as wildfires:
Lightning struck a while back. Through heroic efforts by all the governments in the world, a vast amount of money was stolen, and the fire was put out by pouring all this money over it. No one got hurt.
But the woods are still full of dry tinder. Be very afraid.
It's now 17th June 2011. Last year Greece was bailed out on promise of economic reforms, but those reforms were exceedingly unpopular and have just brought down its government and it is again on the verge of default. The IMF has refused to supply money, effectively blackmailing Germany into paying Greece's debts.
This isn't a long term solution. The problem will recur. Similar problems have occurred in Ireland and Portugal, and been 'solved' by similar methods. The longer this sort of solution is attempted, the more catastrophic the eventual reckoning will be.
-------------------------------------------------------
Note of 10th May 2010
I've put this back to the top because of the financial crisis in Greece. It was originally written after the UK banking crisis that turned into the (first half of the most recent) depression. Sovereign debt default is the next stage of an inevitable process. We have to ask ourselves whether it is better to take the hit now, or put the crisis off again. Next time there may not be an entity large enough to organise a bailout.
I'm going to stick my neck out and make a prediction. Today is 10th May 2010. I predict that either Greece will default on its debts, or the EU will bail it out, and then within the next five years other EU nations will default. The resulting financial effects will domino, and there will be widespread bank defaults. No government will be able or willing to guarantee the banks this time. The turmoil will cause Japan to default on its debt, and the result of that will be a terrifying financial apocalypse the like of which has never been seen. There will be revolutions and wars.
-------------------------------------------------------
Original Article:
There are few good arguments from analogy. Anyway, here's mine:
Once upon a time, the forestry service put out wild fires.
Nowadays they start them.
Once upon a time, banks built solid marble buildings with Doric columns.
Nowadays they rent cheap offices with plastic chairs and nasty carpets.
And I think these facts are related.
Let's look at the war going on in the woods.
The natural enemies of plants are trees. If you have an expanse of open earth, the first things that grow there will be grasses and nettles. Grasses grow fastest of all, finding new earth with their wind-blown seeds and rapidly colonizing everywhere they can fix roots.
Nettles are next. Nettles have the trick of making poisons. Grazing animals don't eat them. Because animals eat the grass, the nettles are taller than the grass. So they can see the sun. Whilst the grasses, being short, die in the shade of the nettles.
A patch of open earth will soon be covered in grass. Soon after that it will be covered in nettles. The thick covering of nettles means that the grazing animals will not go there.
This opens up a place where trees can grow. Trees have the knack of making wood. Wood allows them to grow taller than the nettles. The trees get so tall that they can rise out of the nettle patch entirely, and then begin to spread their branches wide, spreading a vast carpet of leaves. Blotting out the sun. The nettles, which protected the trees from the grazing animals, die. But by this time the trees have grown so tall, and with such thick bark, that the grazing animals can't reach any edible bits of the tree. So the patch is covered in trees. And this is the final state of the world.
So we might wonder why grasses and nettles still exist, if they always lose.
The answer is fire.
A forest fire is an awful thing. Dry trees burn very well, and there is sufficient wood to create an inferno which is hot enough to set light to a tree.
Every so often, even in the oldest and most permanent forest, there will be a period of drought. The trees will become so dry that a lightning strike can set one burning. And the flames will set light to a nearby tree. And the fire will begin to rage through the dry woods, incinerating everything in its path. And nothing will stop it. Not even the arrival of the rains. Until the whole of the forest is a smouldering wreck, and everything is dead except the fire-tolerant seeds hidden in the ground.
Which will begin to grow. Grasses grow fastest, because they don't need to make wood or poison. But grazing animals eat them........
A forest fire is a dreadful thing. It moves faster than you can run. It destroys everything and everyone. You never want to be anywhere near one. Nothing escapes but birds.
So the forestry service used to put out forest fires. And this was a very good thing.
But the trees grew and kept growing until the density of wood in the forests was so high that one day there was a forest fire and it had so much fuel to feed on that the foresters could not put it out. And because there had not been a fire for so many years, a lot of people had got a little careless, and built their homes in the woods.
And the fire that burned was bigger and fiercer than a normal forest fire, because there was so much wood. And you do not ever want to be near even a normal forest fire.
So these days the forestry service starts forest fires. They keep the density of the trees low, and if you are skilled in the ways of the woods you can predict where the fires will go, and to an extent control them and protect people.
You never get the embarrassing situation that happens when there hasn't been a dry patch for a while, and lightning hasn't felt like striking much, and the woods are overgrown and dry and waiting like a tinder box for the spark that will unleash hell.
And who knows if this latest innovation of the foresters will have an unintended side-effect? So far it seems to work well.
What about banks?
Banking is a very risky business. You borrow money from people. And you lend money to people. But there is no symmetry.
People lend you money so that it will be safe. Once upon a time, you would build a nice strong building and charge people to keep their money in it, where it would be safe. This model has fallen out of fashion. But at any rate, people's primary motivation is that their money should not fall into the hands of the sort of person who is forever talking about giving it to the poor but whose favourite Maid is suspiciously well dressed for a girl who lives in the woods.
So you are sitting in a nice strong building full of money. And you can practically hear the outlaws plotting in the woods about tunnels and bulldozers and other ways of making what is inside the building cease to be inside it.
So you need to find some way to get rid of the stuff. And it turns out that there are plenty of people who are willing to take it off your hands and keep it safe for a while themselves. They do this by buying houses and setting up businesses and other wholesome things, and they have promised to pay the money back slowly, with some interest, and most importantly both you and the Sheriff know where they live.
And everything is going so swimmingly that you can barely believe your luck, until Crazy Jake walks into a bar and tells everyone that Mr Shylock put all of the town's money into a scheme to mine gold in the hills and it turns out that there ain't no more gold in them thar hills and all the money is gone.
Now Crazy Jake is a big fat liar. At the most you only put a very small amount of spare money of your own into that scheme and yes, it is gone, but no one need care particularly because there is plenty of money in the bank to go round.
But people are a suspicious lot, and a few people pop round, not at all concerned, really, to ask for their money back so that they can keep it under the bed instead.
And a few people come round as normal to ask if they can have their money back because they have bills to pay.
And towards the end of the day you realise that the bank is out of cash. But everything will be alright tomorrow, you promise, because there are lots of interest payments on loans due in.
Tomorrow there is a line round the bank half a mile long. Because a couple of non-crazy people have been talking about how they asked the bank for some of their money back and the bank didn't have any money.
And you are a dead man. If you don't actually get hung from a lamp-post on the spot, you will be carted off to a dungeon somewhere and kept there forever. Crazy Jake has killed you as randomly and with as little malice as a lightning bolt hits a tree.
And the only people who are happy are the people that you lent all the money to, because their creditor is dead. And maybe the mess will all get sorted out eventually and they will be paying their interest to the people who've lost all their money by trusting it to you. And maybe it won't.
This is called a bank run, and it is why banking is a risky business.
Bank runs used to happen all the time. You can see black and white footage of huge queues round banks. Bank runs feature frequently in Westerns.
Banking is a very risky business, entered into by gamblers of the bravest and most reckless kind.
There is no way round it. The problem is that you are making money by lending long term and borrowing short term. That is what a bank does. If you aren't doing that, you aren't a bank.
Imagine that you are a gambler of the most reckless kind, who has a way to make large amounts of money at the price of occasionally and unpredictably being hung from a lamp-post.
To make it work, you need to get people to trust you with their money. These people may or may not be fools, but they certainly know about bank runs. They know that if a bank is behaving recklessly, it may suddenly cease to exist.
What should you build your building out of?
You should build it out of stone. And you should face the stone with marble. It should look as though it has been built out of pure money, by people who have lots of money, and intend to be around for a very long time.
Sober, serious, professional people. People who wear suits.
The minute you start to express the slightest bit of creativity, imagination or flair, the minute you're caught renting an office, as though you hadn't got the slightest intention of lasting for ten thousand years, then people will begin to take their money out and put it with more serious people. And we know what happens then.
Now once upon a time, this was what banks looked like. English towns are full of great big solid old banks built along classical lines, with lovely solid sounding names like 'The Trustees Savings Bank", or "The National Westminster Bank". Boring as hell, but lovely safe places to trust with money. Of course, they weren't actually. That's why they had to try so hard to look as though they were.
When I was a little boy, there was a new bank startup in England called "William's and Glyn's". I thought that that was a really nice name, and sounded very human and decent. They offered high interest rates and good service and they advertised heavily. And my father wouldn't put his money anywhere near them, because they sounded like they were just a couple of guys who'd started a bank.
But nowadays, banks don't look all solid like they used to. All the lovely solid marble buildings that look as though they will last for ten thousand years have been converted into public houses.
The last time I went into a physical bank, I found myself sneering at the crappy quality of the furniture. And anyone who knows me will tell you that I am not one to care too much about the quality of furniture. But this stuff was made out of formica, and it wobbled.
They don't even have sensible names any more. They're called "Natwest" or "Floyd's TSB" or "Egg". They're behaving like people who've been christened Thucydides by unworldly parents, and who have decided that they prefer to be called Diddy.
What has changed? Nothing recently. There hasn't been a serious bank run for years and years.
What has happened is that recently, the folk memory of bank runs has vanished. No one can remember what they were any more. So trusting money to a bank has stopped being scary. It will be safe. They will look after it carefully.
In fact trusting money to a bunch of gamblers to gamble with has started to seem like the boring option. Real men stick their life's savings in stocks and shares, or in exotic derivative instruments like property prices in areas where no more property can be built. Safe as houses.
What changed?
Government got involved in banking. A government can prevent a bank run. All it has to do is say: "Don't worry about your money. We guarantee that we will pay it all back if the bank fails."
The government can make this guarantee, because it has guns and tanks. So if it needs money it can steal it.
So if the government makes the guarantee, it is believed. Panic over. No-one needs to worry about whether their bank is solvent. No bank runs.
That's why we haven't seen a bank run in a while.
I believe that bank runs work the same as wildfires:
Lightning struck a while back. Through heroic efforts by all the governments in the world, a vast amount of money was stolen, and the fire was put out by pouring all this money over it. No one got hurt.
But the woods are still full of dry tinder. Be very afraid.
Thursday, June 9, 2011
Overconfidence Bias
The other day, a friend and I are out throwing cricket balls to one another.
I believe that when practising a skill, you should set the difficulty of the thing you're practising to the point where you fail one time in ten. Then you're getting positive emotional reinforcement from your successes, while constantly practising things that are still challenging, and pushing yourself periodically. If you're practising a skill that is in fact dangerous, then this also gives you a reasonable chance of avoiding injury, if the usual failure case is to not get injured.
I felt that the throws Joe was giving me were getting below the one in ten level, i.e. I seemed to be catching most of them routinely without having to try too hard, and I was about to ask him to make them harder.
Instead, we started counting successes and failures.
Over the next twenty or so throws, the total number of catches was 14, and I dropped the ball seven times. i.e. the true rate was about one in three.
Both Joe and I thought that this was due to getting freaked out by suddenly making success/failure a thing that was noticed, or possibly getting distracted by the effort of counting. So we carried on. Neither of us thought that the throws had got more difficult because of the counting.
Over the next twenty throws, the proportion of catches rose, until after about seventy-five, the proportion was 60 to 15. I'd completely stopped worrying about counting, and I'm pretty sure that the effort of remembering the two numbers wasn't interfering.
I think we were observing learning actually happening, as the rate changed from one in three to one in four.
We ended the session there, since we were both bored, but I really can't now believe that I'm capable of catching nine out of ten similar throws.
And so I wondered for a bit what it is that makes a person (I'm assuming I'm typical!) who can do something one time in three, and has done it lots recently, and presumably failed one third of the time, believe sincerely that they are likely to succeed nine times out of ten.
A little research brings up the term Overconfidence Bias, which seems somewhat related, where people back their own judgements to be right 'with 90% confidence', and then get it right about 40% of the time.
Afterwards the thought occurred to me that I must have been miscalibrating my 9/10 rule all my life.
I used it to learn to ski and to learn to row, and at the moment I'm trying to use it to learn to catch cricket balls, and I imagine in various other contexts where I was learning to do some physical skill.
And then it occurred to me that I had no idea why I believed that that was the right ratio anyway.
I just seem to have come up with it once, tried it, found that it worked, and then adopted it as an article of belief without ever trying any other way of learning physical skills.
That also sounds like overconfidence, but actually it's called the Congruence Bias.
If you have a theory, you test it by doing what it says to do and seeing if it works.
And in fact if that's all you do, that's a terrible way of testing a theory. You should be looking into the dark and asking if, when you try something else, do you still get good results.
But it's hard to do this.
I'm now thinking 'I should try catching really hard throws'.
But I don't want to. I know what will happen. I'll get my fingers broken and my hands hurt and I'll teach myself to fear the ball even more than I already do.
I'm thinking 'I should try to catch really easy throws'.
But I don't want to. It will be very boring and I'll learn nothing from it.
It is difficult, this 'rationality'. Once you start looking at what you believe and why, and what you do and why, you find all sorts of odd things going on.
I believe that when practising a skill, you should set the difficulty of the thing you're practising to the point where you fail one time in ten. Then you're getting positive emotional reinforcement from your successes, while constantly practising things that are still challenging, and pushing yourself periodically. If you're practising a skill that is in fact dangerous, then this also gives you a reasonable chance of avoiding injury, if the usual failure case is to not get injured.
I felt that the throws Joe was giving me were getting below the one in ten level, i.e. I seemed to be catching most of them routinely without having to try too hard, and I was about to ask him to make them harder.
Instead, we started counting successes and failures.
Over the next twenty or so throws, the total number of catches was 14, and I dropped the ball seven times. i.e. the true rate was about one in three.
Both Joe and I thought that this was due to getting freaked out by suddenly making success/failure a thing that was noticed, or possibly getting distracted by the effort of counting. So we carried on. Neither of us thought that the throws had got more difficult because of the counting.
Over the next twenty throws, the proportion of catches rose, until after about seventy-five, the proportion was 60 to 15. I'd completely stopped worrying about counting, and I'm pretty sure that the effort of remembering the two numbers wasn't interfering.
I think we were observing learning actually happening, as the rate changed from one in three to one in four.
We ended the session there, since we were both bored, but I really can't now believe that I'm capable of catching nine out of ten similar throws.
And so I wondered for a bit what it is that makes a person (I'm assuming I'm typical!) who can do something one time in three, and has done it lots recently, and presumably failed one third of the time, believe sincerely that they are likely to succeed nine times out of ten.
A little research brings up the term Overconfidence Bias, which seems somewhat related, where people back their own judgements to be right 'with 90% confidence', and then get it right about 40% of the time.
Afterwards the thought occurred to me that I must have been miscalibrating my 9/10 rule all my life.
I used it to learn to ski and to learn to row, and at the moment I'm trying to use it to learn to catch cricket balls, and I imagine in various other contexts where I was learning to do some physical skill.
And then it occurred to me that I had no idea why I believed that that was the right ratio anyway.
I just seem to have come up with it once, tried it, found that it worked, and then adopted it as an article of belief without ever trying any other way of learning physical skills.
That also sounds like overconfidence, but actually it's called the Congruence Bias.
If you have a theory, you test it by doing what it says to do and seeing if it works.
And in fact if that's all you do, that's a terrible way of testing a theory. You should be looking into the dark and asking if, when you try something else, do you still get good results.
But it's hard to do this.
I'm now thinking 'I should try catching really hard throws'.
But I don't want to. I know what will happen. I'll get my fingers broken and my hands hurt and I'll teach myself to fear the ball even more than I already do.
I'm thinking 'I should try to catch really easy throws'.
But I don't want to. It will be very boring and I'll learn nothing from it.
It is difficult, this 'rationality'. Once you start looking at what you believe and why, and what you do and why, you find all sorts of odd things going on.
Monday, May 9, 2011
Super Injunction
How is a super injunction supposed to work? Am I allowed to say that Jeremy Clarkson is having an affair with Jemima Khan? Or not?
Sunday, April 17, 2011
Mother's Day Flowers
Credit where credit is due. This year I remembered Mother's Day the day before, and it's a bit too far to drive for a day (I think. I know some people do 300 mile round trips for fun!).
I thought about asking my sister to take something to Mum for me, but that seemed a bit lame, so I found a Sheffield florist on-line and asked them if they could deliver on the day, which was a Sunday.
I asked for their advice on what to send, and then managed to give them an old credit card number which had expired. They rang back later and told me very apologetically that it hadn't got through, but luckily I realized what I'd done and gave them the new one.
They produced a really nice bunch of tulips for about £35 and delivered them at 11 o'clock on Sunday morning. I think they did the delivery themselves rather than using a parcel service. My parents live a fairly long way out of Sheffield itself so it must have been a long trip on what I assume is their busiest day of the year.
I was at a cricket net at the time, and when I got home I had 6 missed calls, all from Mum. (She doesn't normally do that.) Of course I rang back. A couple of days later she sent me a hand-made thank you card and the picture above.
So I'm pretty happy with Katie Peckett ( http://www.katiepeckett.com/ ), Sheffield Florist, 0114 2664985, and I thought I'd give them a plug on my blog.
I've no idea whether they're a big or a small operation, but although their website makes them look like a large and expanding firm, their service was as personal and obliging as if I'd rung a friendly corner shop.
I asked for their advice on what to send, and then managed to give them an old credit card number which had expired. They rang back later and told me very apologetically that it hadn't got through, but luckily I realized what I'd done and gave them the new one.
They produced a really nice bunch of tulips for about £35 and delivered them at 11 o'clock on Sunday morning. I think they did the delivery themselves rather than using a parcel service. My parents live a fairly long way out of Sheffield itself so it must have been a long trip on what I assume is their busiest day of the year.
I was at a cricket net at the time, and when I got home I had 6 missed calls, all from Mum. (She doesn't normally do that.) Of course I rang back. A couple of days later she sent me a hand-made thank you card and the picture above.
So I'm pretty happy with Katie Peckett ( http://www.katiepeckett.com/ ), Sheffield Florist, 0114 2664985, and I thought I'd give them a plug on my blog.
I've no idea whether they're a big or a small operation, but although their website makes them look like a large and expanding firm, their service was as personal and obliging as if I'd rung a friendly corner shop.
Tuesday, April 5, 2011
The Rise of the Machines
I made the last post from Chrome rather than Firefox. I haven't installed adblock in Chrome. My screen is now covered in adverts for pest control firms. I think the singularity may be some years off yet.
The Demon out of Nightmare
Imagine what it's like to be hunted by the basilisk.
Just a look will turn you to stone. You are naked, weaponless, powerless to hurt it unless you can get close enough to kill it with your bare hands.
The basilisk can disguise itself well. It can lie motionless for hours, and when it does you can't see it until you're very close, but if it sees you first, you are dead.
It can move faster than you. It can fly across the ground faster than any living creature can run. It can rise into the air and see a huge area at once, and it can kill over all that radius. It has sharper eyes than any natural being.
It has the power to control the world itself. Sometimes, even when it is nowhere near, plants or rocks will suddenly coil and deform, wrapping round you. Very often, when you are running from it, you will find that it has created a ravine or a gully or a trap in front of you, cornering you. Sometimes the ground itself will grow teeth, and bite into your legs, holding you in place. Once you are trapped, all you can do is wait in agony for the basilisk to come.
Often it will not even bother to come and kill you. It will just leave you to starve in agony, tearing at your wounds, trying to get free.
It knows your habits and your favourite places. Sometimes it can sense you over the horizon.
It can communicate silently with other basilisks, summon them to join its hunt, coordinate so that there is always one basilisk in your path, waiting for you.
Sometimes a basilisk will not kill you when it can.
In those cases your fate will be worse than death. You will be enslaved and worked to death, or you will be imprisoned forever in a tiny cage, to go mad with boredom and misery and lack of companionship. Either you will be castrated, or the children of your brief, brutal, forced matings will share your fate.
Often after years of imprisonment and every conceivable form of violation you will be eaten anyway.
Until recently, basilisks were only mythical demons. They were said to live in forests and savannahs where the wise did not go. They were few, and they did not stray from their territories.
But recently, they have discovered a new source of magical power. Always the deadliest things in the world, they have grown in deadliness to surreal levels. Nothing can stand against them. All creatures fear them, except a few inexplicable terrible allies, slaves swollen on the profits of their collaboration with evil.
And the basilisk breed. Where once they were few, a deadly but rare predator, now they grow without limit. Suddenly they are millions, tens of millions, hundreds, billions and they will not stop multiplying until there is nothing left of the world but basilisks. And there is nothing in the world that can stop them, or that will even dare to try.
Perhaps I am laying it on a bit thick here? My monsters are too terrifying to be believed, you say?
I killed an ant yesterday. It was walking across our stainless steel sink. I turned the tap on and it swirled down the plughole. I don't have a big problem with ants. In fact I like them. It's just that they're not the sort of thing one likes to have in the house. If I hadn't been feeling a bit ill, and only dressed in my dressing gown, I'd have caught it in a glass and put it outside, like I did with yesterday's enormous hornet.
I think most people would have used fly spray on the (huge and terrifying) hornet. I was feeling brave.
Oh yes. The basilisks can magic the very air so that it kills you when you breathe it by filling your lungs with knives. There's no way to tell the magic air. The first warning you get is when your lungs start to fill with knives.
Sometimes they use different magic that makes you go to sleep so they can put you in their cages. Sometimes they use a type which burns your eyes and skin away. Sometimes they just set the entire world around you on fire. There's no way to tell what sort of mood they'll be in.
Imagine what it's like to be a creature 'sharing' a world with a higher intelligence.
Saturday, January 29, 2011
Thursday, January 27, 2011
£500 if you can find me a job
That worked a treat. And the lucky winner was Simon.
It was fun, but a short contract. Now I'd like another one, so I repeat:
If, within the next six months, I take a job which lasts longer than one month, and that is not obtained through an agency, then on the day the first cheque from that job cashes, I'll give £500 to the person who provided the crucial introduction.
If there are a number of people involved somehow, then I'll apportion it fairly between them. And if the timing conditions above are not quite met, or if someone points me at a short contract which the £500 penalty makes not worth taking, then I'll do something fair and proportional anyway. (The thing Simon pointed me at only lasted three weeks and I paid him in full anyway, because it was neat.)
And this offer applies even to personal friends, and to old contacts who I have not got round to calling yet, and to people who are themselves offering work, because why wouldn't it?
And obviously if I find one through my own efforts then I'll keep the money. But my word is generally thought to be good, and I have made a public promise on my own blog to this effect, so if I cheat you you can blacken my name and ruin my reputation for honesty, which is worth much more to me than £500.
Anyhow, if you're interested in helping out, my CV is at http://www.aspden.com, and any advice on how it could be improved will be gratefully received.
It was fun, but a short contract. Now I'd like another one, so I repeat:
If, within the next six months, I take a job which lasts longer than one month, and that is not obtained through an agency, then on the day the first cheque from that job cashes, I'll give £500 to the person who provided the crucial introduction.
If there are a number of people involved somehow, then I'll apportion it fairly between them. And if the timing conditions above are not quite met, or if someone points me at a short contract which the £500 penalty makes not worth taking, then I'll do something fair and proportional anyway. (The thing Simon pointed me at only lasted three weeks and I paid him in full anyway, because it was neat.)
And this offer applies even to personal friends, and to old contacts who I have not got round to calling yet, and to people who are themselves offering work, because why wouldn't it?
And obviously if I find one through my own efforts then I'll keep the money. But my word is generally thought to be good, and I have made a public promise on my own blog to this effect, so if I cheat you you can blacken my name and ruin my reputation for honesty, which is worth much more to me than £500.
Anyhow, if you're interested in helping out, my CV is at http://www.aspden.com, and any advice on how it could be improved will be gratefully received.
Thursday, January 20, 2011
Uncle Boonmee Who Can Recall His Past Lives (Film)
Tedious bewildering rubbish. Apparently the six different reels are all shot in a different style and they each echo a different blah blah blah...
Made me want to stuff the Palme d'Or up the arse of the Guardian film critic.
And don't get me wrong. I usually love pretentious foreign rubbish.
Made me want to stuff the Palme d'Or up the arse of the Guardian film critic.
And don't get me wrong. I usually love pretentious foreign rubbish.
Friday, January 7, 2011
An Idea for Teaching Times Tables to Children
Fully 50% of the table is useless, and has been since the introduction of the metric system in 1970.
So only do 2-9 x 2-9. That's 64 facts to memorize.
First get them to write it out by addition. If they can't do this then you may want to work on addition instead!
Everyone stands in a ring. The teacher's current favourite starts. Their job is to ask their fellows questions they can't answer.
The current favourite starts. He should pick someone. It's ok to pick on the weakest! Ask them a question. If they can't do it, you get another go. If they can, then they become 'it' and it's their turn to persecute.
I'd imagine that after half an hour of this, your whole group will be table perfect.
So only do 2-9 x 2-9. That's 64 facts to memorize.
First get them to write it out by addition. If they can't do this then you may want to work on addition instead!
Everyone stands in a ring. The teacher's current favourite starts. Their job is to ask their fellows questions they can't answer.
The current favourite starts. He should pick someone. It's ok to pick on the weakest! Ask them a question. If they can't do it, you get another go. If they can, then they become 'it' and it's their turn to persecute.
I'd imagine that after half an hour of this, your whole group will be table perfect.
Wednesday, January 5, 2011
Effortless Superiority
This isn't a boast. It starts off sounding like one. Actually it's a confession of utter stupidity, blindness and laziness. I write it as catharsis now it's far too late, and as a warning.
There is a phrase, 'Effortless Superiority'. I've always thought it was the motto of one of the Oxford Colleges, but apparently not.
I used to take it seriously. As an ideal.
I don't know my times tables. I never had to learn them. I can work out what they have to be if I need them. I could do that fast enough to beat all the other children at primary school on arithmetic tests by an overwhelming margin. So I never bothered learning the tables, or practising multiplication. I just used to sit around thinking about other things, and then win the test anyway.
I was told at primary school. At *primary* school. That I'd never amount to anything, because I was too lazy. That I'd never get any 'O' levels (0). By a teacher called Mr Nicholson. He made a special point of telling my parents the same thing. I thought he was an idiot. I think my parents probably did too.
I never did any work at school. I certainly never did any homework. I did usually pay attention in class. It was often interesting.
Once or twice I remember finding something mathematical that I didn't understand immediately.
Come to think of it, I still can't do integration by substitution. I remember noticing that I couldn't, and deciding that it must be a silly, uninteresting special purpose trick.
On one particular occasion (a problem in dynamics. something to do with balls on wire hoops.) I was worried that there was a maths-thing I couldn't do, and so I worked through a couple of examples in the back of the textbook, and I remember the light dawning.
That should have been a clue. But it was lost in the noise.
I remember learning a table of German vocabulary once for an exam. It took about half an hour, and I got it perfectly. I thought this was an utter waste of time. I don't know why I did it. When I took the exam and got a near perfect score, and it was obvious that if I hadn't bothered I'd still have aced it, I remember thinking that that had been a complete waste of half an hour in which I could have been doing something more interesting. (1)
When A-level Chemistry got to the point where I had to learn the colours of the transition metal ions, a table of apparently random text which must have had oooh, twenty entries? I gave up the subject. I am not joking. I remember asking the teacher if I could carry on doing the practicals, which I enjoyed, and not come to the theory lessons. He wouldn't let me, so I just gave up the course entirely. I used to spend the time in the school canteen (we had a nice sixth form common room where you could smoke) playing pool.
I was still entered for the exam, so I took it anyway. Despite having only gone to the first year of a two year course, I got a B because I could deduce most of the required answers from physics and from what I remembered of 'Teach Yourself Organic Chemistry', and 'Asimov on Chemistry', which I'd devoured when I was about ten years old.
Chemistry had been my first love. The first thing I was passionate about. I used to make little plasticene models of hydrocarbons and take them to school, where I would try to persuade Mr Nicholson to hang them from wires on the ceiling to represent my idea of what a gas was.
When, at around ten or eleven, I had my first fevered dreams about the bodies of women, I also had equally fevered dreams about space-filling molecular models of such exotica as DNA, which could be purchased for insanely high prices from glossy catalogues that my father would bring home from work, along with copies of New Scientist donated by his friends.
And in spite of never lifting a finger I was always clearly the best at anything intellectual. I seem to remember, back in 1986 or whenever, thinking that I was probably the cleverest sixth-former in my home city, on the basis that I didn't know anyone who'd done as well at A-level as me.
The thing is, this might actually have been true.
I've mentioned where my B at chemistry came from. My A at physics, and my grade 1 at physics S-level (a special form of super-A level that most people don't know about), came on the back of exams that I'd taken while coming down from LSD, which I'd taken a couple of days before in the sure knowledge that I'd have straightened up enough by the time of the exam to sail it anyway. This was, to say the least, not the first experience I'd had with drugs, and even allowing for the after effects of acid I knew I wasn't going to have any trouble with Physics.
By that time, I'd decided that I wanted to be a mathematician. That seemed to be the subject where everything was obvious. Nothing needed to be learnt or memorized. People just said things that were obviously true, and once you'd heard them it was like you'd been born knowing them, and it had just taken someone to draw attention to the memory.
Slightly to my surprise, Cambridge University turned me down when I applied there.
I'd taken my maths A-level a year early and got a B, so that was the only evidence they had at the interview. And in the interview, they'd asked me a question I couldn't do.
My school were furious, disbelieving. With my typical modesty, I decided that Cambridge were wrong.
I had been planning a year off (taking drugs) anyway, and so I asked London if they'd hold open their unconditional offer of a place, and I applied to Cambridge again. To the same college. Chosen because I thought it was the prettiest one and because it was both particularly hard to get into and top of the academic table of Colleges at the time. To do what was famously the hardest maths course in the world, at what I thought was the best university in the world.
Don't misunderstand. I didn't decide to work harder or anything. I just thought they had been wrong, and I'd give them another chance to make the right decision.
I sat my A-levels, S-levels, and STEPS (Cambridge Entrance Exam), and aced them apart from the B in Chemistry and dropping a grade or two in one of the two STEP papers, which it turned out didn't matter.
King's gave me a second interview, and I did really well on this one. They accepted me.
At College I had the disturbing experience of not being the brightest person I knew any more.
There were people who'd been to public schools, who'd been prodigies and competed in scary things called Olympiads that I'd never heard of, and who had been appropriately stretched by gifted teachers. There were other people from comprehensive schools like me, but who'd worked insanely hard to get in.
I reckoned that I was about halfway up my group of twelve. But several of them have told me since that they were scared stiff of me, who didn't seem to try, and had had a standard state education, and yet who seemed given to flashes of insight.
I'm not sure that I actually did anything you'd call 'work' in the first year. But they did have this supervision system, where you'd get question lists handed out and you were supposed to solve as many as possible before going to see one of the Fellows about them.
I used to have a go at these sheets. I used to find that I could do the first five or six questions without trouble, and then everything else would be too hard. But if you turned up to the supervision, the Fellow in question would then explain how to do the remaining five or six.
I thought that's what they were for.
In my first year exams I came in about the top ten per cent of my year. I scored below a couple of my college-mates, both of whom were super-educated public school kids, and obviously very bright as well.
I figured that was good enough. I had girls and alcohol to worry about. I was up to my neck in both. I'd given up on drugs because they were all boring except for LSD, and I'd given up on LSD because I'd had one too many bad trips. But I'd filled the gap with heavy drinking and socializing. Mainly I think because it got you laid, but it was also great fun in itself.
So in the second year, I just gave up. I still went to all my lectures, because I enjoyed them. In fact despite near-constant partying, I think I missed two lectures in my entire time at college. I didn't love mathematics any less than I had.
But I no longer had any sort of go at the example sheets. I just turned up to supervisions and got the supervisors to explain how to do the problems. I could usually do the first couple off the top of my head anyway. As far as I know, my teachers still thought I was pretty good, because of my initial solid first, and the fact that I asked the right questions about the subjects I found interesting.
And at the end of the second year, I got a second. I was about half way up the list. I remember that my teachers seemed quite disappointed, and my reputation took a bit of a hit.
I'd been expecting it. I'd deliberately taken the year off, but I was never under any illusions about what my capabilities were. I knew that if I'd actually practised answering exam questions I'd be able to do them faster, and the tripos exam was like every other exam that I'd ever sat, a speed test rather than a test of understanding. I still knew how all the questions worked, it just took me more time to solve them than I was allowed to spend. The reason that other people were doing better than me was because I hadn't *cheated* by practising doing exam questions. I understood it all as well as they did. Most of them were just half-remembering formulae they'd picked up from spending many sleepless nights revising.
Everything was going according to plan.
The plan that I'd had, ever since I first thought what I should do as an adult, to sail effortlessly into a tenured academic job (when I'd been growing up, that had been a very easy thing to do), and to carry on learning and teaching and who knows, maybe think of something new and interesting one day. It had never really occurred to me to do anything else. If I thought about the 'real world' at all, then it was as a sort of sewer, filled with people who did tedious and unchallenging things because they wanted money. Academic salaries and PhD grants weren't great in the way that they had once been, but still plenty enough to support a studenty lifestyle, and that was all I wanted. I saw myself as being one of those kindly unmarried dons who hangs around in college and lives in college rooms, and lets the undergraduates substitute for the children he would have had if he hadn't been devoted to his craft. It looked great.
But if I wanted to do a PhD in pure mathematics (2), I needed a first-class degree. There was no funding available otherwise.
So I went back to my first year routine of having a half-hearted go at the example sheets before heading off to supervisions to have it all explained face to face. To be spoon-fed the answers without having made the effort to think of them myself.
It was a bit harder this time, because as well as having to work out what the new stuff was about, I realised that I hadn't really understood the second year stuff even though I thought I had (3), and so I needed to work out how all that worked while working out what the new stuff meant.
But it all worked out OK, almost. I was actually good enough to start catching up again.
I didn't bother with the third year computer project, despite that I'd been programming since the age of 10, would have found it very easy, and it was worth a full third of the credit that I'd need to get a first (4).
I didn't want to do something that I wouldn't learn anything from. I wanted to be a mathematician, not a programmer. And I was already as good a programmer as I'd ever need to be. (4.5)
By the time the final exam was close enough to worry about, my first was in the bag.
I had actually stooped to trying my hand at some past papers under exam conditions, which I still thought was cheating, but getting a first looked important enough to cheat at, and after the first couple of papers, I'd got good enough at it to reliably score the marks necessary for a first.
Rather to my surprise, (remember that this was the first time I'd ever taken an exam seriously enough to practise doing it), I found that I rather enjoyed the process. And even more surprisingly, learning to do the questions quickly actually seemed to make the ideas behind them clearer and more beautiful. They achieved a sort of focus that they hadn't had before.
Knowing that I was going to do well in the exam, I took Easter term pretty much off. The sunshine was lovely, this was my last year with all my friends, there was punting to do, and cricket to play, and riverside pubs to sit in, and parties to go to, and not many lectures to go to, and I understood enough subjects in enough detail to be confident that even if the questions turned out to be particularly hard, I'd pass. (I thought anything lower than a first was a fail.)
And of course I failed (5).
I have excuses, of course, for the failure of my confident prediction. The questions in my particular favourite subjects deviated from their usual predictable patterns. The first paper was much harder than I expected. One particular topology (one of the two subjects where I really could have given the lectures) question was so incomprehensible that all I could do for an answer was to draw a picture and write underneath 'It works because of this'. I had no idea how to do a formal proof as asked for.
My finals were four exams over two days, three hours each. After the first day I knew I'd done badly. I couldn't sleep for worry. The questions in the third and fourth exams were more in line with normal, but I actually managed to go to sleep in the fourth one because I was so tired after two gruelling days awake.
When the results came out I wasn't surprised. I'd calculated my mark afterwards, and it was on the line between a second and a first. I fell just the wrong side. (5.5)
Cambridge Mathematics has a charming tradition of reading out the results at a big ceremony in the Senate House. They read out the names of everyone who has got a first, in alphabetical order. I remember the list of names going Aa.... Ab..... Ascot (or something), Bagg...
Bagg was my college mate Jenny. As soon as I heard her name I knew I'd screwed it. Without any previous warning in about twenty one years, I'd managed to be not as good at something as I needed to be.
That was pretty much the end for me.
No first meant no PhD funding in the thing I wanted to do. I didn't have a plan B. It literally hadn't occurred to me in the month or so before the exam that I could fail it.
I fell on my feet after a fashion. Someone told me of a PhD place for a specific project in London (at Imperial College, which is a pretty damned good university), which had its funding allocated already, but where the student in question had dropped out. I rang the man who controlled the funding, he invited me to London, we talked for an hour and the place was mine.
But it didn't work out. I didn't get on particularly well with my supervisor, I wasn't interested in the thing I was supposed to be studying, he wasn't interested in any of my ideas, and there was no one else to talk to.
I'd been looking forward to London. I'd always enjoyed going there as a boy. But it turned out to be awful. A lonely wasteland of concrete and filth. And being an academic didn't look like much fun in London. More of a sort of glorified schoolteacher job, and not that glorified either.
And then my intuition failed. One day I was trying to read a research paper, and I found out that it was just squiggles. No pictures, no handle on what it meant. Not even a vague feeling that if I tried just changing this bit, something would happen. It was suddenly all greek to me.
I understood, for the first time in my life, what it was to not understand a piece of mathematics.
And I figured that was the end of the line. All my life I'd watched people give up maths, because it didn't seem to mean anything to them. I knew that however hard they tried, it wouldn't ever make proper sense to them like it did to me.
It just seemed that that had happened to me. There's obviously a point beyond which you can't go, and it just so happened that mine was about half-way through a PhD.
I don't think it occurred to me that I might be able to work my way through this. That just wasn't the way I thought it worked. By that time I didn't care anyway. Two years in London had put me off the whole idea of academia.
I moved back to Cambridge because that's where most of the people I liked lived.
At about this time, I started to run out of money. The near limitless ability of the 1980s British State to subsidize lazy good-for-nothing layabouts who thought the world owed them a living had met its match in me. I had an overdraft, accounted for pretty much exactly by six years of booze and cigars. Even though today's self-funded students will laugh at my tiny £6000 debt, it seemed to me that I was so poor that I had to give up smoking. I even gave up 2000AD, a comic that I'd read regularly since I was a boy, because the 50p it cost every two weeks was a noticeable expense.
Of course when the PhD funding ran out, I managed to start drawing unemployment benefit. But this wasn't quite as much, so there was further belt tightening to be done, and I didn't fancy it. My supervisor said that I'd got about another six months work to do before I'd be able to hand in a doctorate, and I was pretty sure that meant about twelve months. Also it was going to be a complete piece of shit. Nobody would ever read it out of interest, and I wasn't in the least interested in writing it.
I got a job, programming. It was great fun, it turned out. People actually gave you things to do that they didn't know how to do themselves, but they were usually quite easy things, so they were usually done quickly, and (and this was the real revelation) people were actually grateful when you solved their problems. I mean that you felt like you'd done them a favour. This was a revelation to me. I loved it. After about two months I had this awful dream where I'd gone back to London to try to finish my PhD. I woke up in a cold sweat of terror, and at that point I knew I was never going to be Dr Aspden. Which was strange. I'd always thought that Mr was what you were called from about 16 to about 24. Like a sort of probationary title. It was like I'd been told I'd never be able to get a driving licence.
I got used to being mediocre. I was good enough to have got a Cambridge maths degree. I was probably top quartile. But there are a fair number of people like that in the world.
I've thoroughly enjoyed it. I'm pretty good at what I do, and it's fun.
I took up other hobbies. I'd always liked playing sports, even though I was useless at it, and, almost by accident, I took up rowing, which is the local sport here, for townies as well as the university.
There was no reason to expect to be anything other than rubbish at rowing. I'm average height, stronger than most men my size, but not vastly so, and I smoke, which doesn't go well with a sport where the chief physical variable is a capacity for consuming oxygen.
And I was. Terrible at it. For years.
But I enjoyed it, and I practised it, and I got good at it. I was never in a million years going to be any sort of star at it, even in the rather limited competitive environment of Cambridge town. But I ended up being, if not actually any good, better than I would ever have believed possible to start with.
And somehow it taught me that if you work at something, you get better at it.
And I decided a few years ago that I should learn LISP, an antique computer language out of the dark ages, because there seemed to be something special about the way LISP people talked.
So I got the standard textbook Structure and Interpretation of Computer Programs, and I found it harder than most things about computers. But I was damned if I was going to let some sort of computer-thing be hard, because nothing in computers is even a bit hard. So I did the exercises in the book to see if they would make it clear, and found that solving carefully chosen example problems is fun, and you know what, the more of the exercises I solved, the more I understood the book, and the better I understood, the more of the book I could read.
And it taught me that if you work at something intellectual, you get better at it.
Which I didn't believe for the first thirty years of my life.
I thought that you were born good at things. I thought if you weren't good at things, working hard at them was just a path to ruining your life with fruitless toil, to fail one level higher than you would have failed anyway. To be honest, I still believe something like that, just not as extreme a version as I once did.
Why would I not have believed this? You cannot move without people praising the special quality of genius. You cannot read without finding out that authors and poets and musicians have their works come to them fully formed. The special genius of my heroes, Feynman, Einstein, Newton, Conway, Von Neumann is trumpeted from rooftops. You never hear that they lifted a finger apart from doing exactly what seemed most amusing to them at the time.
And it had been absolutely true for me for twenty years. I'd been told over and over again that I needed to work harder. And every time I'd ignored the advice and turned out to be right.
And when I was twenty one the 'problem of induction' hit me over the head with a whisky bottle during my final exams. And I was stone dead and I didn't even notice because twenty years of confirming evidence isn't overturned by a human mind just like that.
And I've only just noticed.
Recently, I was asked to teach a young friend enough maths to get him onto an engineering degree. I loved doing this. Sitting down and talking with him and taking him through trial problems and trying to work out where his mental blocks were and blowing them away was the best fun I've had in ages. And he's now doing his engineering degree, although he's going to screw it up by, ironically, spending so much time rowing really seriously that he'll be too tired to think about engineering.
And I've been reading the collected works of the brilliant philosopher Eliezer Yudkowsky, who's built a whole philosophy and predicted the entire future of the human race convincingly using amongst other intellectual tools Bayes' Theorem, a trivial piece of arithmetic with profound implications.
And I figured if I'm going to understand Eliezer Yudkowsky's thoughts I'd better understand Bayes' Theorem and its consequences as well as he does, which I'm still arrogant enough to think that I can do.
And so from a combination of these effects, I've started doing mathematics, recreationally, for the first time in my life. And indeed mathematics at all, for the first time in about fifteen years.
And it turns out I'm pretty damned good at it. I shouldn't be, because I'm forty years old now, and no one's as good at maths at forty as they were at twenty. But if my powers have declined I can't tell.
I'm reading David MacKay's beautiful book Information Theory, Inference, and Learning Algorithms, and it's like reading a thriller. I've patiently worked through the examples in the first two or three chapters, even the ones that look boring, because I remember that the boring looking examples in SICP always turned out to teach unique and thrilling lessons.
I've sort of got my head round the introductions to Information Theory and Inference, and I think I already see why the Noisy-Channel Coding Theorem is going to turn out to be true in chapter 6 or wherever it is, and why it is also going to turn out to be of little practical value. And I can't wait to find out if I'm right.
And this has brought back memories, and when I start remembering things these days I start writing, and all this has come out like a flood, and suddenly it occurs to me, because I promise you that the above is as true as my fallible memory can make it, that I may actually have been as good as I once thought I was.
And fuck the research angle and doctorates and names on interesting discoveries. I love teaching. And I'm good at it. And that's what I should have been doing with my life. Teaching mathematics and computers to bright young people. I would have loved it. And I didn't do it. And it's too late now.
And I want to call bullshit on the idea of Effortless Superiority, which it now occurs to me I may have been the only human on the planet stupid enough to take seriously (6).
Footnotes
(0) English school leaving exams. A-levels are the optional ones two years later, on which University Entrance depends, S-levels are a special form of A-levels, on the same syllabus but the questions are much harder. STEP is similar to S-level, but set by Cambridge University and used as part of its entrance requirement.
(1) Even though I was good at foreign languages, they seemed like a completely stupid rigmarole. It wasn't like they were any use for anything except passing foreign language tests.
Somehow, at around this same time, I was teaching myself Latin to O-level standard out of a book my father had left lying around where I could find it. Latin was interesting and useful, because you could read about the Roman Empire and other cool things in the Romans' own words. And you could see where lots of our words came from. And their poetry was better than ours.
I've wondered if I'd have done modern languages for my degree if my school had managed to make living German and French anything like as interesting as Francis Kinchin Smith managed to make dead Latin and Greek in his two Teach Yourself ... books. Cheap self-help manuals that were doubtless intended by the publishers to be read only as far as the third chapter. From the love and care and scholarship and cleverness lavished on them I think Francis had higher goals for them. I wonder if he ever got fan mail? If I could go back and write it I would. What did a child know? I've just googled him. He died in 1958 apparently. Too early for him to have got my letter even if I had thought to write. The fact that I can remember his name after 28 years tells you how much I liked those books. I wish I'd had a chance to tell him.
But the tedium of French and German was as nothing compared to the horror of Music and the Calvary of Religious Education.
How, how for the love of Christ did they manage to make Music boring to a human child?
And for that matter, the King James Bible is one of my favourite books.
I am as bleak an atheist as it is possible to be, and yet I often read the Gospel According to St Matthew on Easter Day. I wonder how many Christians do?
(2) By this time I'd begun to despise applied maths, which seemed to be a bag of stupid half-understood magic tricks that was overdue to be swept away by computer simulation. Weirdly it only seems to be taught like that in Cambridge. In London later on I found it interesting again.
(3) As someone once pointed out, what the hell did I think it meant for someone to understand something if they couldn't use it fluently?
(4) I had done some computer stuff in the second year out of interest, but I'd found that it didn't teach me anything interesting. I already knew how to program. I can't even remember whether I bothered completing it.
(4.5) I know, I know, I was a moron. But actually it did look singularly unchallenging. Now if they'd taught SCHEME rather than matrix multiplication algorithms, who knows...
(5) got a second.
(5.5) As I remember, the topology question that I'd drawn the answer to was bastard hard, only a couple of people had attempted it, and my picture had been given almost the maximum mark. So in fact I needn't have worried. If I'd known that, I might have been able to sleep that night.
(6) I'm not whining for the sake of it, by the way. I've loved life, and I'd do the first forty years over again exactly the same way like a shot if I had the chance.
But if you recognise yourself in the above, young person, for God's sake do the exercises in the textbooks, and practise exam questions. It's not cheating. It helps you understand. A lot.
If you do the exercises, and play with the examples, then you will find that your intuition, already powerful, starts to get brighter, and rather than finding as I did that as you go forward, you start to run out of dry places to stand in the swamp, until eventually there's nowhere new to go, you'll find that as you brighten the swamp recedes ahead of you faster than you can walk.
On the other hand, if you find yourself working every hour God sends on something and you're not enjoying it for its own sake, give up. Nothing's worth that sort of life. I still think success probably comes fairly easily if you're any good. What I'm trying to warn against is pig-headedly not lifting a fucking finger to practise something you enjoy because you think that's something lesser beings have to do to make up for being lesser.
"If at first you don't succeed, try, and try again. Then give up. No sense making a fool of yourself." -- Homer
Some bits of text from the essay I started writing before it turned into the above whine.
Right until halfway into a PhD that I didn't find interesting. At that point the wellspring failed, and within twelve months of realising that it was gone I wasn't a mathematician any more. Part of the problem was that I'd never had to try at anything before, and I didn't know how to deal with anything that required effort.
Would you believe that at the time I sat my finals, I still thought that practising exam questions was cheating. I thought it was vulgar. Like you were trying to fool the examiners into thinking you were cleverer than you were.
I realized that I wasn't clever enough to bank on a first (I mean I still thought I'd get one, it's just that I'd realized there was a *chance* I wouldn't), so towards the end of my third year, I cheated a bit. But it was far too little too late, and it didn't help. I got the second I'd feared.
This only confirmed me in my belief that it was silly to try. That nothing that had to be worked at was worth having. It was easy to maintain this belief.
Lots of people have to try very hard to get into university. They slog away at A-levels, ruining evenings and weekends that should be spent being young and happy. And when they crowbar their way in, somehow managing to convince an interviewer far cleverer than they are that the lights are on in their heads, they find that it's all ashes. For nothing.
For it gets harder once you're not at school. And the only strategy these people have is to work harder. But they already worked as hard as they could.
They react predictably. They burn the candle at both ends for three years, and at the end of it they scrape low seconds and thirds. Some, released from parental pressure, realize that the game isn't worth it and drop out, pretending they didn't care in the first place.
I was terrified of being one of these people. I guess I still am.
There is a phrase, 'Effortless Superiority'. I've always thought it was the motto of one of the Oxford Colleges, but apparently not.
I used to take it seriously. As an ideal.
I don't know my times tables. I never had to learn them. I can work out what they have to be if I need them. I could do that fast enough to beat all the other children at primary school on arithmetic tests by an overwhelming margin. So I never bothered learning the tables, or practising multiplication. I just used to sit around thinking about other things, and then win the test anyway.
I was told at primary school. At *primary* school. That I'd never amount to anything, because I was too lazy. That I'd never get any 'O' levels (0). By a teacher called Mr Nicholson. He made a special point of telling my parents the same thing. I thought he was an idiot. I think my parents probably did too.
I never did any work at school. I certainly never did any homework. I did usually pay attention in class. It was often interesting.
Once or twice I remember finding something mathematical that I didn't understand immediately.
Come to think of it, I still can't do integration by substitution. I remember noticing that I couldn't, and deciding that it must be a silly, uninteresting special purpose trick.
On one particular occasion (a problem in dynamics. something to do with balls on wire hoops.) I was worried that there was a maths-thing I couldn't do, and so I worked through a couple of examples in the back of the textbook, and I remember the light dawning.
That should have been a clue. But it was lost in the noise.
I remember learning a table of German vocabulary once for an exam. It took about half an hour, and I got it perfectly. I thought this was an utter waste of time. I don't know why I did it. When I took the exam and got a near perfect score, and it was obvious that if I hadn't bothered I'd still have aced it, I remember thinking that that had been a complete waste of half an hour in which I could have been doing something more interesting. (1)
When A-level Chemistry got to the point where I had to learn the colours of the transition metal ions, a table of apparently random text which must have had oooh, twenty entries? I gave up the subject. I am not joking. I remember asking the teacher if I could carry on doing the practicals, which I enjoyed, and not come to the theory lessons. He wouldn't let me, so I just gave up the course entirely. I used to spend the time in the school canteen (we had a nice sixth form common room where you could smoke) playing pool.
I was still entered for the exam, so I took it anyway. Despite having only gone to the first year of a two year course, I got a B because I could deduce most of the required answers from physics and from what I remembered of 'Teach Yourself Organic Chemistry', and 'Asimov on Chemistry', which I'd devoured when I was about ten years old.
Chemistry had been my first love. The first thing I was passionate about. I used to make little plasticene models of hydrocarbons and take them to school, where I would try to persuade Mr Nicholson to hang them from wires on the ceiling to represent my idea of what a gas was.
When, at around ten or eleven, I had my first fevered dreams about the bodies of women, I also had equally fevered dreams about space-filling molecular models of such exotica as DNA, which could be purchased for insanely high prices from glossy catalogues that my father would bring home from work, along with copies of New Scientist donated by his friends.
And in spite of never lifting a finger I was always clearly the best at anything intellectual. I seem to remember, back in 1986 or whenever, thinking that I was probably the cleverest sixth-former in my home city, on the basis that I didn't know anyone who'd done as well at A-level as me.
The thing is, this might actually have been true.
I've mentioned where my B at chemistry came from. My A at physics, and my grade 1 at physics S-level (a special form of super-A level that most people don't know about), came on the back of exams that I'd taken while coming down from LSD, which I'd taken a couple of days before in the sure knowledge that I'd have straightened up enough by the time of the exam to sail it anyway. This was, to say the least, not the first experience I'd had with drugs, and even allowing for the after effects of acid I knew I wasn't going to have any trouble with Physics.
By that time, I'd decided that I wanted to be a mathematician. That seemed to be the subject where everything was obvious. Nothing needed to be learnt or memorized. People just said things that were obviously true, and once you'd heard them it was like you'd been born knowing them, and it had just taken someone to draw attention to the memory.
Slightly to my surprise, Cambridge University turned me down when I applied there.
I'd taken my maths A-level a year early and got a B, so that was the only evidence they had at the interview. And in the interview, they'd asked me a question I couldn't do.
My school were furious, disbelieving. With my typical modesty, I decided that Cambridge were wrong.
I had been planning a year off (taking drugs) anyway, and so I asked London if they'd hold open their unconditional offer of a place, and I applied to Cambridge again. To the same college. Chosen because I thought it was the prettiest one and because it was both particularly hard to get into and top of the academic table of Colleges at the time. To do what was famously the hardest maths course in the world, at what I thought was the best university in the world.
Don't misunderstand. I didn't decide to work harder or anything. I just thought they had been wrong, and I'd give them another chance to make the right decision.
I sat my A-levels, S-levels, and STEPS (Cambridge Entrance Exam), and aced them apart from the B in Chemistry and dropping a grade or two in one of the two STEP papers, which it turned out didn't matter.
King's gave me a second interview, and I did really well on this one. They accepted me.
At College I had the disturbing experience of not being the brightest person I knew any more.
There were people who'd been to public schools, who'd been prodigies and competed in scary things called Olympiads that I'd never heard of, and who had been appropriately stretched by gifted teachers. There were other people from comprehensive schools like me, but who'd worked insanely hard to get in.
I reckoned that I was about halfway up my group of twelve. But several of them have told me since that they were scared stiff of me, who didn't seem to try, and had had a standard state education, and yet who seemed given to flashes of insight.
I'm not sure that I actually did anything you'd call 'work' in the first year. But they did have this supervision system, where you'd get question lists handed out and you were supposed to solve as many as possible before going to see one of the Fellows about them.
I used to have a go at these sheets. I used to find that I could do the first five or six questions without trouble, and then everything else would be too hard. But if you turned up to the supervision, the Fellow in question would then explain how to do the remaining five or six.
I thought that's what they were for.
In my first year exams I came in about the top ten per cent of my year. I scored below a couple of my college-mates, both of whom were super-educated public school kids, and obviously very bright as well.
I figured that was good enough. I had girls and alcohol to worry about. I was up to my neck in both. I'd given up on drugs because they were all boring except for LSD, and I'd given up on LSD because I'd had one too many bad trips. But I'd filled the gap with heavy drinking and socializing. Mainly I think because it got you laid, but it was also great fun in itself.
So in the second year, I just gave up. I still went to all my lectures, because I enjoyed them. In fact despite near-constant partying, I think I missed two lectures in my entire time at college. I didn't love mathematics any less than I had.
But I no longer had any sort of go at the example sheets. I just turned up to supervisions and got the supervisors to explain how to do the problems. I could usually do the first couple off the top of my head anyway. As far as I know, my teachers still thought I was pretty good, because of my initial solid first, and the fact that I asked the right questions about the subjects I found interesting.
And at the end of the second year, I got a second. I was about half way up the list. I remember that my teachers seemed quite disappointed, and my reputation took a bit of a hit.
I'd been expecting it. I'd deliberately taken the year off, but I was never under any illusions about what my capabilities were. I knew that if I'd actually practised answering exam questions I'd be able to do them faster, and the tripos exam was like every other exam that I'd ever sat, a speed test rather than a test of understanding. I still knew how all the questions worked, it just took me more time to solve them than I was allowed to spend. The reason that other people were doing better than me was because I hadn't *cheated* by practising doing exam questions. I understood it all as well as they did. Most of them were just half-remembering formulae they'd picked up from spending many sleepless nights revising.
Everything was going according to plan.
The plan that I'd had, ever since I first thought what I should do as an adult, to sail effortlessly into a tenured academic job (when I'd been growing up, that had been a very easy thing to do), and to carry on learning and teaching and who knows, maybe think of something new and interesting one day. It had never really occurred to me to do anything else. If I thought about the 'real world' at all, then it was as a sort of sewer, filled with people who did tedious and unchallenging things because they wanted money. Academic salaries and PhD grants weren't great in the way that they had once been, but still plenty enough to support a studenty lifestyle, and that was all I wanted. I saw myself as being one of those kindly unmarried dons who hangs around in college and lives in college rooms, and lets the undergraduates substitute for the children he would have had if he hadn't been devoted to his craft. It looked great.
But if I wanted to do a PhD in pure mathematics (2), I needed a first-class degree. There was no funding available otherwise.
So I went back to my first year routine of having a half-hearted go at the example sheets before heading off to supervisions to have it all explained face to face. To be spoon-fed the answers without having made the effort to think of them myself.
It was a bit harder this time, because as well as having to work out what the new stuff was about, I realised that I hadn't really understood the second year stuff even though I thought I had (3), and so I needed to work out how all that worked while working out what the new stuff meant.
But it all worked out OK, almost. I was actually good enough to start catching up again.
I didn't bother with the third year computer project, despite that I'd been programming since the age of 10, would have found it very easy, and it was worth a full third of the credit that I'd need to get a first (4).
I didn't want to do something that I wouldn't learn anything from. I wanted to be a mathematician, not a programmer. And I was already as good a programmer as I'd ever need to be. (4.5)
By the time the final exam was close enough to worry about, my first was in the bag.
I had actually stooped to trying my hand at some past papers under exam conditions, which I still thought was cheating, but getting a first looked important enough to cheat at, and after the first couple of papers, I'd got good enough at it to reliably score the marks necessary for a first.
Rather to my surprise, (remember that this was the first time I'd ever taken an exam seriously enough to practise doing it), I found that I rather enjoyed the process. And even more surprisingly, learning to do the questions quickly actually seemed to make the ideas behind them clearer and more beautiful. They achieved a sort of focus that they hadn't had before.
Knowing that I was going to do well in the exam, I took Easter term pretty much off. The sunshine was lovely, this was my last year with all my friends, there was punting to do, and cricket to play, and riverside pubs to sit in, and parties to go to, and not many lectures to go to, and I understood enough subjects in enough detail to be confident that even if the questions turned out to be particularly hard, I'd pass. (I thought anything lower than a first was a fail.)
And of course I failed (5).
I have excuses, of course, for the failure of my confident prediction. The questions in my particular favourite subjects deviated from their usual predictable patterns. The first paper was much harder than I expected. One particular topology (one of the two subjects where I really could have given the lectures) question was so incomprehensible that all I could do for an answer was to draw a picture and write underneath 'It works because of this'. I had no idea how to do a formal proof as asked for.
My finals were four exams over two days, three hours each. After the first day I knew I'd done badly. I couldn't sleep for worry. The questions in the third and fourth exams were more in line with normal, but I actually managed to go to sleep in the fourth one because I was so tired after two gruelling days awake.
When the results came out I wasn't surprised. I'd calculated my mark afterwards, and it was on the line between a second and a first. I fell just the wrong side. (5.5)
Cambridge Mathematics has a charming tradition of reading out the results at a big ceremony in the Senate House. They read out the names of everyone who has got a first, in alphabetical order. I remember the list of names going Aa.... Ab..... Ascot (or something), Bagg...
Bagg was my college mate Jenny. As soon as I heard her name I knew I'd screwed it. Without any previous warning in about twenty one years, I'd managed to be not as good at something as I needed to be.
That was pretty much the end for me.
No first meant no PhD funding in the thing I wanted to do. I didn't have a plan B. It literally hadn't occurred to me in the month or so before the exam that I could fail it.
I fell on my feet after a fashion. Someone told me of a PhD place for a specific project in London (at Imperial College, which is a pretty damned good university), which had its funding allocated already, but where the student in question had dropped out. I rang the man who controlled the funding, he invited me to London, we talked for an hour and the place was mine.
But it didn't work out. I didn't get on particularly well with my supervisor, I wasn't interested in the thing I was supposed to be studying, he wasn't interested in any of my ideas, and there was no one else to talk to.
I'd been looking forward to London. I'd always enjoyed going there as a boy. But it turned out to be awful. A lonely wasteland of concrete and filth. And being an academic didn't look like much fun in London. More of a sort of glorified schoolteacher job, and not that glorified either.
And then my intuition failed. One day I was trying to read a research paper, and I found out that it was just squiggles. No pictures, no handle on what it meant. Not even a vague feeling that if I tried just changing this bit, something would happen. It was suddenly all greek to me.
I understood, for the first time in my life, what it was to not understand a piece of mathematics.
And I figured that was the end of the line. All my life I'd watched people give up maths, because it didn't seem to mean anything to them. I knew that however hard they tried, it wouldn't ever make proper sense to them like it did to me.
It just seemed that that had happened to me. There's obviously a point beyond which you can't go, and it just so happened that mine was about half-way through a PhD.
I don't think it occurred to me that I might be able to work my way through this. That just wasn't the way I thought it worked. By that time I didn't care anyway. Two years in London had put me off the whole idea of academia.
I moved back to Cambridge because that's where most of the people I liked lived.
At about this time, I started to run out of money. The near limitless ability of the 1980s British State to subsidize lazy good-for-nothing layabouts who thought the world owed them a living had met its match in me. I had an overdraft, accounted for pretty much exactly by six years of booze and cigars. Even though today's self-funded students will laugh at my tiny £6000 debt, it seemed to me that I was so poor that I had to give up smoking. I even gave up 2000AD, a comic that I'd read regularly since I was a boy, because the 50p it cost every two weeks was a noticeable expense.
Of course when the PhD funding ran out, I managed to start drawing unemployment benefit. But this wasn't quite as much, so there was further belt tightening to be done, and I didn't fancy it. My supervisor said that I'd got about another six months work to do before I'd be able to hand in a doctorate, and I was pretty sure that meant about twelve months. Also it was going to be a complete piece of shit. Nobody would ever read it out of interest, and I wasn't in the least interested in writing it.
I got a job, programming. It was great fun, it turned out. People actually gave you things to do that they didn't know how to do themselves, but they were usually quite easy things, so they were usually done quickly, and (and this was the real revelation) people were actually grateful when you solved their problems. I mean that you felt like you'd done them a favour. This was a revelation to me. I loved it. After about two months I had this awful dream where I'd gone back to London to try to finish my PhD. I woke up in a cold sweat of terror, and at that point I knew I was never going to be Dr Aspden. Which was strange. I'd always thought that Mr was what you were called from about 16 to about 24. Like a sort of probationary title. It was like I'd been told I'd never be able to get a driving licence.
I got used to being mediocre. I was good enough to have got a Cambridge maths degree. I was probably top quartile. But there are a fair number of people like that in the world.
I've thoroughly enjoyed it. I'm pretty good at what I do, and it's fun.
I took up other hobbies. I'd always liked playing sports, even though I was useless at it, and, almost by accident, I took up rowing, which is the local sport here, for townies as well as the university.
There was no reason to expect to be anything other than rubbish at rowing. I'm average height, stronger than most men my size, but not vastly so, and I smoke, which doesn't go well with a sport where the chief physical variable is a capacity for consuming oxygen.
And I was. Terrible at it. For years.
But I enjoyed it, and I practised it, and I got good at it. I was never in a million years going to be any sort of star at it, even in the rather limited competitive environment of Cambridge town. But I ended up being, if not actually any good, better than I would ever have believed possible to start with.
And somehow it taught me that if you work at something, you get better at it.
And I decided a few years ago that I should learn LISP, an antique computer language out of the dark ages, because there seemed to be something special about the way LISP people talked.
So I got the standard textbook Structure and Interpretation of Computer Programs, and I found it harder than most things about computers. But I was damned if I was going to let some sort of computer-thing be hard, because nothing in computers is even a bit hard. So I did the exercises in the book to see if they would make it clear, and found that solving carefully chosen example problems is fun, and you know what, the more of the exercises I solved, the more I understood the book, and the better I understood, the more of the book I could read.
And it taught me that if you work at something intellectual, you get better at it.
Which I didn't believe for the first thirty years of my life.
I thought that you were born good at things. I thought if you weren't good at things, working hard at them was just a path to ruining your life with fruitless toil, to fail one level higher than you would have failed anyway. To be honest, I still believe something like that, just not as extreme a version as I once did.
Why would I not have believed this? You cannot move without people praising the special quality of genius. You cannot read without finding out that authors and poets and musicians have their works come to them fully formed. The special genius of my heroes, Feynman, Einstein, Newton, Conway, Von Neumann is trumpeted from rooftops. You never hear that they lifted a finger apart from doing exactly what seemed most amusing to them at the time.
And it had been absolutely true for me for twenty years. I'd been told over and over again that I needed to work harder. And every time I'd ignored the advice and turned out to be right.
And when I was twenty one the 'problem of induction' hit me over the head with a whisky bottle during my final exams. And I was stone dead and I didn't even notice because twenty years of confirming evidence isn't overturned by a human mind just like that.
And I've only just noticed.
Recently, I was asked to teach a young friend enough maths to get him onto an engineering degree. I loved doing this. Sitting down and talking with him and taking him through trial problems and trying to work out where his mental blocks were and blowing them away was the best fun I've had in ages. And he's now doing his engineering degree, although he's going to screw it up by, ironically, spending so much time rowing really seriously that he'll be too tired to think about engineering.
And I've been reading the collected works of the brilliant philosopher Eliezer Yudkowsky, who's built a whole philosophy and predicted the entire future of the human race convincingly using amongst other intellectual tools Bayes' Theorem, a trivial piece of arithmetic with profound implications.
And I figured if I'm going to understand Eliezer Yudkowsky's thoughts I'd better understand Bayes' Theorem and its consequences as well as he does, which I'm still arrogant enough to think that I can do.
And so from a combination of these effects, I've started doing mathematics, recreationally, for the first time in my life. And indeed mathematics at all, for the first time in about fifteen years.
And it turns out I'm pretty damned good at it. I shouldn't be, because I'm forty years old now, and no one's as good at maths at forty as they were at twenty. But if my powers have declined I can't tell.
I'm reading David MacKay's beautiful book Information Theory, Inference, and Learning Algorithms, and it's like reading a thriller. I've patiently worked through the examples in the first two or three chapters, even the ones that look boring, because I remember that the boring looking examples in SICP always turned out to teach unique and thrilling lessons.
I've sort of got my head round the introductions to Information Theory and Inference, and I think I already see why the Noisy-Channel Coding Theorem is going to turn out to be true in chapter 6 or wherever it is, and why it is also going to turn out to be of little practical value. And I can't wait to find out if I'm right.
And this has brought back memories, and when I start remembering things these days I start writing, and all this has come out like a flood, and suddenly it occurs to me, because I promise you that the above is as true as my fallible memory can make it, that I may actually have been as good as I once thought I was.
And fuck the research angle and doctorates and names on interesting discoveries. I love teaching. And I'm good at it. And that's what I should have been doing with my life. Teaching mathematics and computers to bright young people. I would have loved it. And I didn't do it. And it's too late now.
And I want to call bullshit on the idea of Effortless Superiority, which it now occurs to me I may have been the only human on the planet stupid enough to take seriously (6).
Footnotes
(0) English school leaving exams. A-levels are the optional ones two years later, on which University Entrance depends, S-levels are a special form of A-levels, on the same syllabus but the questions are much harder. STEP is similar to S-level, but set by Cambridge University and used as part of its entrance requirement.
(1) Even though I was good at foreign languages, they seemed like a completely stupid rigmarole. It wasn't like they were any use for anything except passing foreign language tests.
Somehow, at around this same time, I was teaching myself Latin to O-level standard out of a book my father had left lying around where I could find it. Latin was interesting and useful, because you could read about the Roman Empire and other cool things in the Romans' own words. And you could see where lots of our words came from. And their poetry was better than ours.
I've wondered if I'd have done modern languages for my degree if my school had managed to make living German and French anything like as interesting as Francis Kinchin Smith managed to make dead Latin and Greek in his two Teach Yourself ... books. Cheap self-help manuals that were doubtless intended by the publishers to be read only as far as the third chapter. From the love and care and scholarship and cleverness lavished on them I think Francis had higher goals for them. I wonder if he ever got fan mail? If I could go back and write it I would. What did a child know? I've just googled him. He died in 1958 apparently. Too early for him to have got my letter even if I had thought to write. The fact that I can remember his name after 28 years tells you how much I liked those books. I wish I'd had a chance to tell him.
But the tedium of French and German was as nothing compared to the horror of Music and the Calvary of Religious Education.
How, how for the love of Christ did they manage to make Music boring to a human child?
And for that matter, the King James Bible is one of my favourite books.
I am as bleak an atheist as it is possible to be, and yet I often read the Gospel According to St Matthew on Easter Day. I wonder how many Christians do?
(2) By this time I'd begun to despise applied maths, which seemed to be a bag of stupid half-understood magic tricks that was overdue to be swept away by computer simulation. Weirdly it only seems to be taught like that in Cambridge. In London later on I found it interesting again.
(3) As someone once pointed out, what the hell did I think it meant for someone to understand something if they couldn't use it fluently?
(4) I had done some computer stuff in the second year out of interest, but I'd found that it didn't teach me anything interesting. I already knew how to program. I can't even remember whether I bothered completing it.
(4.5) I know, I know, I was a moron. But actually it did look singularly unchallenging. Now if they'd taught SCHEME rather than matrix multiplication algorithms, who knows...
(5) got a second.
(5.5) As I remember, the topology question that I'd drawn the answer to was bastard hard, only a couple of people had attempted it, and my picture had been given almost the maximum mark. So in fact I needn't have worried. If I'd known that, I might have been able to sleep that night.
(6) I'm not whining for the sake of it, by the way. I've loved life, and I'd do the first forty years over again exactly the same way like a shot if I had the chance.
But if you recognise yourself in the above, young person, for God's sake do the exercises in the textbooks, and practise exam questions. It's not cheating. It helps you understand. A lot.
If you do the exercises, and play with the examples, then you will find that your intuition, already powerful, starts to get brighter, and rather than finding as I did that as you go forward, you start to run out of dry places to stand in the swamp, until eventually there's nowhere new to go, you'll find that as you brighten the swamp recedes ahead of you faster than you can walk.
On the other hand, if you find yourself working every hour God sends on something and you're not enjoying it for its own sake, give up. Nothing's worth that sort of life. I still think success probably comes fairly easily if you're any good. What I'm trying to warn against is pig-headedly not lifting a fucking finger to practise something you enjoy because you think that's something lesser beings have to do to make up for being lesser.
"If at first you don't succeed, try, and try again. Then give up. No sense making a fool of yourself." -- Homer
Some bits of text from the essay I started writing before it turned into the above whine.
Right until halfway into a PhD that I didn't find interesting. At that point the wellspring failed, and within twelve months of realising that it was gone I wasn't a mathematician any more. Part of the problem was that I'd never had to try at anything before, and I didn't know how to deal with anything that required effort.
Would you believe that at the time I sat my finals, I still thought that practising exam questions was cheating. I thought it was vulgar. Like you were trying to fool the examiners into thinking you were cleverer than you were.
I realized that I wasn't clever enough to bank on a first (I mean I still thought I'd get one, it's just that I'd realized there was a *chance* I wouldn't), so towards the end of my third year, I cheated a bit. But it was far too little too late, and it didn't help. I got the second I'd feared.
This only confirmed me in my belief that it was silly to try. That nothing that had to be worked at was worth having. It was easy to maintain this belief.
Lots of people have to try very hard to get into university. They slog away at A-levels, ruining evenings and weekends that should be spent being young and happy. And when they crowbar their way in, somehow managing to convince an interviewer far cleverer than they are that the lights are on in their heads, they find that it's all ashes. For nothing.
For it gets harder once you're not at school. And the only strategy these people have is to work harder. But they already worked as hard as they could.
They react predictably. They burn the candle at both ends for three years, and at the end of it they scrape low seconds and thirds. Some, released from parental pressure, realize that the game isn't worth it and drop out, pretending they didn't care in the first place.
I was terrified of being one of these people. I guess I still am.
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