Soduku solver

Soduku (Sudoku) is a Japanese number puzzle game that seems to be taking the world by storm. It’s played on a 9×9 grid. Each square can contain one of the numbers from 1 to 9 (inclusive). A given “problem” has some of the squares filled in, and you are required to fill in the remaining squares, satisfying the constraints:

Each row has to contain each of the numbers 1 through 9 exactly once.
Likewise for each column.
The board can be broken down into 9 3×3 squares (top-left, top-middle, top-right, etc.). Each of these has to contain each of the numbers 1 through 9 exactly once.

Anyway, these puzzles can get pretty tricky. Especially if you don’t know the third rule above — which until recently, I didn’t. Anyway, they’ve sufficient annoyed me now that I had to do something about it; so I wrote

The Langabi.name Soduku Solver

It’s not fancy, but is (in my opinion) very efficient. Enjoy!

Edit: Now available: an explanation of the method my solver uses, and the source code.

Complexity and abstraction

One of the key challenges that arises in almost any context is how to deal with complexity. Probably the most powerful tool we have to address it is abstraction — ignoring details in favour of a smaller set of information, at some “higher level”. I’ve been thinking recently about how abstraction appears, with varying success, in so many areas, and in particular what differentiates different problem areas in which abstraction is more or less effectives. This two-part post will meander vaguely through a few of those areas.

I’ll start, appropriately, in physics. Thermodynamics is an excellent example of abstraction at it’s best — macroscopic quantities of gas, say, have on the order of 10^27 molecules, but we can describe their behaviour very well using only the variables temperature, pressure and volume. Thermodynamics passes two test I’d like to propose for the appropriateness of abstraction:

There exists a useful cutoff scale. Considering the behaviour of the gas at “macroscopic” length scales is a well-defined, useful definition, since the molecules are so much smaller.
The different length scales decouple well; or to paraphrase, there is little behaviour loss from ignoring interactions at a smaller scale — thermodynamics describes the gas really well.

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Relaxation = information?

I’m addicted to high-information entertainment. Hey, so are most of you reading this. But it’s such a throw-away line that is ceases to mean much to us anymore. But I think I might really mean it.

I sometimes play the mental game, when I’m bored, of imagining what I would do if suddenly transplanted to times long ago. The immediate realisation is that while I have lots of good technological concepts, I don’t really know how to go about, say, finding iron ore or making those cotton spinning machines that were a part of the start of the industrial revolution. And even if I could take my reference material (ie. my laptop) along with me, I could spend my life trying to remember exactly how 1 volt was defined, so as to make a generator to power it.
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Asymmetries in scientific fields

I’ve just finished reading Michelle’s candidacy report, on some of the research she’s been doing into catalysts for certain reactions in organic chemistry. It’s highlighted for me some of the differences between different fields of research — and in particular, between theoretical physics, and the more experimental work that most other people at Caltech do.

Michelle’s report was very easy to read. That’s partially because it’s well written, but I’d say it’s also because the difficulty is in a different place to that of papers that I’m used to reading. “Reading” a longish string theory paper can take literally months — and even then, I can’t claim to understand everything that is being said. Reading Michelle’s report took a few hours, and while I didn’t understand all the jargon, I think I got the gist of the issues and approach that her research took.

On the other hand, having read Michelle’s report has brought me no nearer to actually being able to synthesise anything more interesting than a bowl of pasta and sauce. “Reading” the string theory paper, however, has involved working through the mathematics behind each step, at great length — sometimes hours for a single line. So once I’m finished, I’ve done a substantial portion of the work that was required to write the paper in the first place. The analogy would be me reading Michelle’s paper, and then making some of the reagents too — and that would take months too.
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Upgrading my memory

I’m proud to present the Official Langabi.name guide to Adding 256MB of RAM (memory) to your laptop:

Turn off your computer. Open the relevant part of your laptop to expose the memory slots. Check that you have a spare (unused) memory slot.
Remember (correctly) the result of the above check.
Assuming the success of the above steps, order a 256MB RAM chip for your laptop. Sites like Crucial allow you to order the correct RAM for the exact model of laptop that you have.
Wait for the RAM chip to arrive (allow approximately 3 days for shipping and damage. Though hopefully not much of the latter).
Turn off your computer. Touch a metal part of it to remove any static charge you might have. Open the appropriate part to expose the memory slots, and insert the RAM chip. Close the computer again, and turn it back on.
Live in eternal bliss. Or at least until software becomes yet more bloated.

All this can be had for the low, low price of 102.988 Del Taco “Taco Tuesday” tacos*. Or, if you must know, $36.79.

But wait, you say — there are surely lots of far more complete guides (with pictures!) on buying memory, all over the internet? True, but they all leave off the vital step 2.
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Only YOU have the power to Save Toby!

Only in the Internet age can someone make over $24 000, just by promising NOT to eat his pet. Have a look at Savetoby.com | Only YOU have the power to Save Toby!

This money-making ploy is right up there with some of the classics of our time, like selling your soul on eBay. The moral of the story: one part bored people surfing the net, one part instant virtual payment courtesy of PayPal, makes hitting the jackpot possible without even going to Vegas. Now I just need my big idea…

Thanks to my brother Martin for sending me this link. He occasionally does something useful, in between hijacking my friends’ computers to send me insults from their ICQ (instant messenger) accounts, in order to create much strife. I’m not sure why he wants this, but luckily I’ve seen through his shallow plan! 1-0 to me!

Lines, intersections and dimensions

Building on the interest in my post on knots and different dimensions, I thought I’d say a few words on some interesting issues on lines in different dimensions, as raised by a recent seminar. It’s an interesting mind game!

We explicitly consider only generic situations from here on, which means that we ignore special cases as physically unlikely. So parallel lines need not be considered — all lines will have some random angle between them.
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Why “Peak Oil” isn’t what really worries me

To flog a dead horse, here’s another post on oil depletion. This one is a few thoughts, mostly rebuttals to some points that have arisen about the validity of the argument around “Peak Oil” — that we’re a few years away from the greatest oil production we’ll ever see, and it’s downhill from there.

This post follows from my post on Price Elasticity of Oil, as well as this post on blogwaffe, and a whole collection of excellent, but scary, posts on Ted Brenner’s blog.

One of the more common replies to Peak Oil concerns is that oil production is not merely a function of how much oil there is in the ground, but rather a raft of other factors — such as the price of oil (determing what deposits are economical to drill), technology, investment in expanding existing fields, and political stability. I have two points here: the problems of keeping up with demand, and what higher prices mean.
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Good news and bad, in Africa

Two events happened in the last few days in Africa, one promising and one bad, which will have further knock-on effects in Africa and abroad. The good (with reservations) was the referral to the International Criminal Court (ICC) of the situation in Darfur, Sudan, for prosecution of individuals implicated in crimes against humanity. The bad was Mugabe’s successful stealing of yet another election in Zimbabwe. Oh, and apologies for yet another long post!
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The problem with point particles

Quantum mechanics is often viewed as a “weird” theory, with all sorts of non-intuitive predictions. However, there are more serious conceptual problems with classical mechanics, at least in its simpler formulations. One of these is what happens near point particles — in fact, point particles in classical mechanics lead to all sorts of infinities. I’ll say a little about this below, as well as talk about what quantum mechanics and string theory have to say about these short-distance infinities.
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