020081018 - Through History's Lense

This is a thought experiment. Imagine that the situation in Iraq continues to improve, that a stable democracy is established, and - whether it's a consequence of the Iraqi democracy or not - that democracy flourishes in the Middle East. A region that has plagued the world with its troubles for centuries becomes as peaceful as Western Europe is today.

If this happens then I think there is a very good chance that George Bush Jr. will get the credit. Because people will forget the other sides of his Presidency, good and bad. Instead they'll see a visionary statesman who made hard decisions and was not afraid to be unpopular. Whether that's fair or not, and whether it's right is entirely beside the point. George Bush Jr., probably posthumously, will become the greatest President America ever had.

020081003 - The 2D Rotation Matrix

Sometimes my mathematical weakness is a bit embarrassing - a while back I set myself the task of rederiving the vector equations which determine the instantaneous velocity vector of a point mass in a circular orbit around another point mass. This stumped me. So I went back to square 1 and just worked on the rotation matrix instead. That took me longer than I would have liked, but I got there in the end. Now I can do it any time. The useful things I fill my time with.

Oh, and check out Polya's book. It's a good read and I wish I'd read it before tackling this problem.

020080729 - Judgements and the Sunk Cost Fallacy

A judgement or an opinion is a sunk cost. Even after it's been loudly and publically pronounced it's still very nearly a sunk cost. And too often our pronounced judgements seem to entice us into committing the nearly-sunk costs fallacy. Even after it has become obvious that it's a bad idea we'll stay the course anyway. In fact, the more wrong it is, the more tightly we cling to it. A dispassionate observer might think we thought that by holding on to our opinion tightly enough, reality might relent. You see this in the markets all the time, when someone rides an investment all the way down to zero. I've done it in the markets, fortunately not all the time.

The “sunk costs fallacy” occurs when we let costs already incurred and which are impossible to recover affect our decision, when the only things that should affect our decision are costs yet to come and the benefit. A non-refundable movie ticket is an example of a sunk cost. Forcing yourself to watch the movie even if there's something else you'd rather do is an example of the fallcy.

Why do I say judgements aren't quite a sunk cost though? Because changing them may incur a cost, as the allegedly “flip-flop Kerry” found out to his chagrin. Sometimes you shouldn't change your mind, even when you know you're wrong. But even when you think you shouldn't you probably still should. Our inevitable cognitive biases mean that we'll over-estimate the costs of changing, and under-estimate the costs of staying the course. Never making a judgement isn't an option either. It seems to me that it's almost always better to have made up your mind, even if it turns out to be wrong. At least then you have something to change.

OK, I'm done sermonising.

020080722 - Chess Boards

GameKnot has a really powerful chess game analysis application. But it only works when you're online. So I've crudely hacked it up. Now it works offline as well. Full credit to them for the application itself though - it works very well! Downloadable here as a tar.gz of an mht file for Internet Explorer, and here as a tar.gz of the files for use with FireFox.

020080602 - Dealing with Dimensions

I don't know about you, but I have trouble visualising anything with more than 3 dimensions. And until recently I couldn't really even do 3. I certainly thought I could, but then I realised I was almost always thinking of a 2 or 2.5D projection of 3 dimensions, which isn't quite the same thing. Some practice means I can intuitively get up to 3 now. But back to 4, and a neat little trick.

If the dimensions that you're dealing with fall naturally into groups of 2 or 3, and if those groups are largely independent of each other, and if you can put them into some kind of order (it doesn't have to be objective, just reasonable) then I've found that the following thought process helps.

Pick your first cluster of two or three dimensions and imagine what they look like. Get a firm picture of this in your mind. Now, holding that, take your next group and get a firm picture in your mind of this group and its characteristics. Now, for every single point in your first group there will be an instance of your second group. Repeat, recursively, until you run out of dimensions or stack space.

That's it, that's all there is to it. It doesn't work if the states in each dimension are all mutually dependent, but for something like fuzzy uncertainty (the source of this model for me) it works quite well, and even for something as complex as space-time it can give you a good first draft. So what is four-dimensional space-time? Well, imagine time, it's a one dimensional line. Associated with every single point on this line will be a complete 3D universe. The state of each 3D universe will depend on the state of the previous one (optionally of the immediately future one, or in fact any other 3D universe, the model is causally neutral and specifying this is just a matter of how you mentally characterise each “instance of 3D space-time”), and so their are dependencies, but I think a mental model like this is at least a start. You can imagine the universe progressing down the time line in a Newtonian way, and it all runs like clockwork.

Of course, the underlying physics is a lot more complicated than that. For one thing this mental model doesn't deal with relativity very well, where your velocity down the time line also depends on your velocity in the other 3 dimensions. That's the kind of dependency I don't think this recursive trick can handle. Really this whole mental nesting of dimensions is most appropriate for mathematical models with nice crisp boundaries, but it's a start, and maybe someone can extend it more completely to complex phenomena with mutually dependent dimensions. Fingers crossed.

020080529 - Antireduction

One of the key problems in biological and social sciences is that the classic reductionist model of science does not work. After understanding or specifying the components of an atom, the properties of the components and their interactions with each other then you fully understand the atom. However, even after fully specifying the neural pathways of a nematode worm and how each neuron and cell in the worm interacts, we still do not understand how the worm swallows. This is the problem.

In a quick and dirty essay inspired by discussions in the Conceptual Foundations of Systems Biology seminar series and available here, I argue that understanding involves both reduction and antireduction, and that the antireduction is implicit and invisible in sciences such as physics and chemistry. Inspired by Werner's logical model of agent's, social structures and communication I speculate about a way that the problem of antireduction could plausibly be addressed.

020080511 - The Black Swan

I'm really in two minds about this book. On the one hand, it's brilliant. On the other, it's circular. Read more here.

020080317 - Epistemic Translucency

Two books, one fiction, one not. Both kind of about the same thing. An Instance of the Fingerpost is a beautiful, artistic illustration of how our perceptions change as we get new (still partial, still erroneous) information. The Psychology of Intelligence Analysis addresses the question of how we cut through all the clutter and make good decisions, precisely when faced with this kind of beautiful confusion. You can read my brief reviews and find links at the bottom here and here, respectively.

020080122 - Initial Thoughts on Academic Style

So the absurdly short story…

I've taken this initial ramble and converted it into fuller essay on what I think good writing style is. You can find it here and if you have any comments or feedback you should definitely pass them on!