lederhosen

Via Weaselking: Conway's Game of Life used to run Conway's Game of Life.

(More on the 'metapixel' used to power this here.)

Thing 1: I've been doing the free machine learning e-course from Stanford. I can thoroughly recommend it* and if you missed it there's another offering in January.

Thing 2: Stanford are also offering a whole bunch of other free online courses. The PGM one looks like it might be work-relevant, and I think I might do the game theory one on my own time.

Thing 3: The course forums are pretty good, in general, but there's this one guy who makes me cry every time I see his comments. In this case, the OP produced a graph that looked good near the fitting points, but produced negative results (nonsensical in context) elsewhere**. Response, in the original punctuation:

HOLY FLOW CHARTS....I have never have seen negative Water Flow Across a DAM... When the Level Transmitter shows a ZERO LEVEL....you only get SPLASH flow across the Dam (wind and waves cause Splashing). A secondary flow sensor should pick up this random flow. When the Level Signal goes positive you should get a flow signal that follows Weir Flow Charts...I think it is a 3/2 or 5/2 power or something in between depending on how it is constructed.

Modelling it with a Chart showing NEGATIVE FLOW would get you FIRED...recommend erasing everything < than "ZERO" FLOW...the Stanford computers might pick that up as an ERROR in the CALCULATIONS...

Translated into English: "You should censor the results that are obviously wrong, to make the graph look better, without considering what those results might imply for the accuracy of the other results that don't LOOK wrong."

...and that, right there, is a "I would never ever hire you" button.

*although I still don't like their explanation of back propagation - not sure whether I've misunderstood it, or whether it's just a bad explanation of something that should just be "calculate the gradient of the cost function".

**Kids, JUST SAY NO to extrapolating from eighth-order polynomial fits. Please.

Rey and I are gradually working through our moving boxes, unpacking stuff to keep and picking as much as we can for garage sales/rubbish, because we have Way Too Much Stuff.

Today, my old programmable calculator (HP 20S). I didn't use it for academic work much because they didn't allow programmables*, but I'm fond of it. I won it in a maths competition, and I used its 100-line memory to create a dice roller for D&D.

Now of course it's hopelessly obsolete, but I still feel bad about just tossing it in the bin. Does anybody run a Home For Old Calculators or something?

*Except for the maths department at ANU, who had a fairly liberal open-book policy.

Sad moment: Archive-bingeing a newly-discovered webcomic, and spending several minutes trying to get past a broken 'next page' button before realising that no, the button's not broken, that's all there is so far.*

Sadder moment: It only updates once a week? O NOES!

(In two days' time, we can has house of our own! Hooray!)


*I only figured this out after attempting to guess URLs. That said, I've encountered some comics where URL-guessing really did let me see several days into the future...

So, this story about Daryl Bem's alleged experimental evidence for precognition has been doing the rounds.

I was going to launch into a lengthy post about the problems with this experiment, but four Dutch researchers have already produced a very good response that covers all the points I was going to make and several more.

In brief: when you have a large long-running experiment and you get to chose the analysis techniques, exclusion criteria, and the stopping point after looking at the results, it is really easy to find 'significant' patterns.

One of my favourite demonstrations of this is Brendan McKay's 'Bible Code' work, in which he shows how 'Moby Dick' predicted the assassinations of Indira Gandhi, JFK, Rene Moawad, Leon Trotsky, MLK, Yitzhak Rabin, and others.

In case anybody doubts that 7x13=28, I wrote some SAS code to test it:

%let officers=9+4; /* 9 lieutenants, 4 captains */
%let donuts_per_officer=4+3; /* 4 plain, 3 fancy */

data total_needed;
officers=&officers;
donuts_per_officer=&donuts_per_officer;
total_donuts_needed=&officers*&donuts_per_officer;
run;

Result confirmed!

It's probably a sad thing that my first reaction to this theoretical ecology of vampires is neither "who cares", nor "wow, that's cool", but "wait, I think there's an error in that first expression".

Answers to the other day's questions below the cut.

( Read more... )

(Partly, I think, suggested by a passage in Oliver Sacks' Uncle Tungsten in which he discusses music and the periodic table.)

I know several of my artistic friends are tired of hearing lines like "You're so lucky to have that talent!" when a big part of their 'talent' comes not from luck but years of hard work.

For most media, that's the nature of art - people won't see the hard-earned technique unless they actively look for it, but the creative aspect is there for all to perceive. You can look at a Renoir and enjoy it without knowing a thing about Renoir's painting technique; you can listen to Beethoven's Ninth Symphony and feel its beauty and vibrancy without the faintest idea of how to read music, much less how to score for an entire orchestra.

Beethoven, of course, was deaf.

By the time the Ninth was finally performed, he was so utterly deaf that he was still attempting to conduct it several bars after the orchestra had finished, and he had to be turned around to see that the audience were applauding. For him, I presume, technique was the only medium through which he could know what he was writing, and hear it, if not with his ears, then at least in his mind.

Mathematics is a little like that. At first, the technique relates to things that we can perceive directly - we can lay out apples in a square, two by two, and see that two-squared is four; with a little bit of balancing, we can sit another layer of apples on top of the first four and see that two-cubed is eight. This is something comparable, perhaps, to playing a few notes on a scale and hearing what they sound like.

But take it a little further - what about two-to-the-fourth? - and we can't see it any more. We can still build physical analogies of one sort or another (imagine a second apple inside each apple, perhaps?) but they swiftly become so complicated or so bizarre that we can no longer visualise them in a way that lets us grasp the work we're trying to do; we have to build it inside our heads, a strange sort of shape beyond anything our physical senses can capture.

For the last six months, I've been working on a multi-stage sampling project, immersed in the mathematics that involves; I wish I could describe how that feels inside my head. It's a little like a telescope, with four or five stages that fold into one another; it's a little like an orrery, with a cloud of tiny satellites - each of them, viewed from a certain angle, represents a person - orbiting a swarm of invisible moonlets, which in turn orbit moons, each captive to a planet, each planet captive to the invisible sun at the heart of the system. But it's not really any of these things; trying to describe these structures in terms of things we can see is like trying to turn paintings into music.

So the only way I can share that with anybody else if if they've learned the relevant technique - and even then, they'll need to spend some time staring at the dry equations in order to go from 'notes' to 'music'. I suspect this is part of the problem: most people never get enough exposure to the technique that they're able to get past it to see what it represents. It's like staring at a Pointillist painting, and seeing only a sea of coloured dots.

To get very far with mathematics, you need to reach that level of comfort with the underlying technique, internalise it and practice to the point where you can forget it. I can learn how to press a key on a piano and produce a note of whatever pitch and volume I want, but that isn't enough to make me a musician**; knowing the rules of logic is vital as a first step in mathematics, but it doesn't take me very far on the road to doing what I want in the medium. A musician can listen to music they've never heard before, and guess what the next notes will be; there are similar instincts at work when I'm doing my job. Logic tells me what steps I can and can't take, but instinct guides me in choosing which of those countless possibilities will get me closer to where I want to be. It is a creative process in its own fashion, and knowing where that process will begin and end doesn't detract from that creativity, any more than painting loses its creativity when you're looking at a model.

Not, of course, that the distinction between 'technique' and 'creation' is sharply drawn. In mathematics especially, yesterday's creation is tomorrow's technique - and sometimes technique, picked apart and re-evaluated a la Godel etc, becomes creation again.


*Mind you, a good knowledge of technique almost always increases the ability to appreciate art - it's just that you can get a long way even without it.
**Sadly, I had almost ten years of piano lessons without ever really figuring out that there was more to music than pushing the keys in the right way at the right time.