While I was looking for pictures of soap bubbles spanning minimal surfaces for yesterday's post, I came across a cool site about wooden sculptures of minimal surfaces.
Archive for February, 2006
Minimal surfaces
Friday, February 17th, 2006Analog quantum computers
Thursday, February 16th, 2006Quantum computers are really difficult to build. No-one has yet managed to build one that can do something that a classical computer can't do more quickly and easily. However, if someone does manage to build a quantum computer of reasonable power it could make all sorts of computations possible that aren't practical today. For example, a quantum computer might be able to solve chess (predict whether black or white would win, or if it would be a draw, if both players made the best possible moves).
Current avenues of research for quantum computers seem to mostly involve building something that looks sort of similar to a classical computer, with bits and gates that can hold both 0s and 1s at the same time (and which can be entangled with other gates/bits).
This article got me wondering if there might be another (possibly easier) way to go about quantum computing. Imagine you have an irreguarly shaped loop of wire, that bends and twists at all sorts of strange angles in three dimensions. For some reason you wish to find the surface which has that loop as its perimeter, but with the smallest possible area. This is quite a difficult problem computationally, but extremely easy physically - to solve it all you need to do is put some detergent in some water and dip your loop of wire into it. The resulting soap bubble film will be exactly the surface you are looking for. The difficult problem is made easy by the massively parallel nature of the many molecules of soap and water.
Suppose we found a physical way to solve a certain class of hard computing problems ("NP complete problems", to use a technical term). There is a theorem in computer science that (effectively) says if you can solve one NP complete problem, you can solve them all by rephrasing the unsolved problem in terms of the solved one. So all we would need to do would be to find a physical "computer" that could solve a particlar type of NP complete problem.
Quantum mechanics is extremely difficult to simulate on a computer, because every particle is "spread out" and computations must be done at each point in space to figure out what what will happen. There are some shortcuts for simple situations, but even moderately complex molecules are beyond our ability to simulate with a high degree of accuracy.
Perhaps it would be possible to solve some NP complete problem that would take centuries to solve with today's computers by transforming it into some physical problem which could be solved by a quantum-mechanical analog computer (maybe something like a Bose-Einstein condensate interacting with atoms fixed in particular positions on some substrate), reading off the answer and then transforming it back into the answer of the original problem.
[Edited to add] Since writing this I have realized that analog quantum computers don't really add anything because you can effectively only measure digital information. Even when making a measurement of some analog quantity your instruments are only so accurate so there will be a finite number of significant figures that you actually read off.
Cheese slicing algorithm
Wednesday, February 15th, 2006While I was making my daily cheese sandwich the other morning, I got to thinking about the optimal algorithm for slicing cheese.
I use a Swedish cheese slicer for my cheese slicing needs. This works great until you get to the end of a block of cheese - if you are careless and always slice the same side, you are likely to get a large thin block of cheese which is almost impossible to slice any further on the wide side but which is still too thick for sandwich purposes. You then need to slice it on one of the long thin sides, which leads both to long thin slices of cheese, and to a block of cheese that is still long in one dimension but short in the other two.
So it seems that the ideal algorithm is to always slice the cheese on the smallest side, so that the shape of the block always approximates a cube (of gradually shrinking size). But that means that you're always rotating the block - you really want to get a few slices out of a side before you rotate, and there must be some optimal rate of rotation to minimize both fiddliness and rotation. You also get a number of very small slices of cheese at the end of a block, but in practice this does not seem to be a big problem.
Yes, I know I put too much thought into this.
Infinite loop on floor 1
Tuesday, February 14th, 2006The other day, I got into a loop trying to find a conference room on the first floor of the building where I work. Normally there is a fairly simple algorithm for finding a conference room in a Microsoft building:
- Wander about
- Stop when you find the room, or when you find a sign. If you found a sign,
- Find the line of the sign which has a range of room numbers including the number you want
- Go in the direction of the arrow on that line of the sign, and back to step 2.
However, I was foiled on this particular morning as sign A pointed in the direction of sign B, and sign B pointed in the direction of sign A, but the conference room in question was not in between the two signs! Fortunately, I realized the problem after only 3 or 4 iterations, and was not late to my meeting.
The future of computer interaction?
Monday, February 13th, 2006I was going to post this seriously cool link today, but Slashdot and Fark beat me to it, so you probably saw it already.
Range of sizes
Sunday, February 12th, 2006According to the Guinness book of World Records, the shortest adult human ever recorded was 57cm (1 foot 10.4 inches) tall, and the tallest was 272cm (8 feet 11.1 inches) tall. But these are extremes. 95% of human heights fall within a range of about one foot.
This is roughly what it would look like if a 272cm tall man stood next to a 57cm tall man. Similarly with the largest and smallest recorded dogs:
I wonder what life would be like for a population of people whose sizes varied much more widely, for example if individuals as tall as 100m and as short as 10cm were not uncommon (but in which the total volume of the people whose size lies in some interval would be roughly proportional to the size of the interval, so there would be a lot more small people than large people). I imagine that such a population would have incredible architecture, as their buildings would have be extremely large (for the tallest people) yet extremely detailed (to be useful for the smallest people).
Laptop fixing
Saturday, February 11th, 2006"Puck", my laptop, developed a loose connection in its power connector over the past few days so today I set about fixing it. The actual fixing was fairly easy (I just had to unsolder the offending connector, clean and tighten the contacts and solder it back on to the laptop's motherboard) but the process of taking the machine apart and putting it back together again took the best part of the day.
There was an awful lot of dust, fluff, hair and food crumbs in there (the CPU cooler was especially full of dust and fluff which explains why there wasn't as much airflow through it as there used to be). This is why my can of compressed air ran out half way through. Also, I didn't have quite the right screwdrivers for the job, so I left a bit early to pick up Gennie from work and stopped at Fry's on the way.
The CPU must have become really hot at some point in the past because when I removed the CPU cooler (to clean the fan) a small area of the thermal compound had clearly been heated much more than the rest, and was baked right on to the heatsink. I wonder what the part of the CPU directly over that part of the heatsink does... I eventually managed to scrape it all off and replaced the heatsink using some fresh thermal compound. It is running much cooler now (Prime95 has been running for a good half an hour now and the exhaust still isn't burning my fingers). I suspect the thermal contact was never very good in the first place and that the fan now no longer needs to continually run at full speed to stop the CPU overheating.
Amazingly, when I put it all back together again it worked first time. This makes a pleasant change from when I took my previous laptop, "Jack" apart and killed it in the process. In my defense, I didn't know about thermal grease then. It is nice to know that I can fix a laptop.
The fan is still a little bit on the noisy side so I had a look online to see if I could find a replacement (Fry's didn't have anything suitable). There only seems to be one place in the entire world that sells the right sort of fan, and they were sold out. I suspect this particular model of laptop (a Samsung VM8000) often has fans fail. I also had a look on eBay to see if anyone was selling VM8000s (either working or for parts). I found two interesting things - someone selling a working one for £225, and someone was selling one that has exactly the same problem that "Puck" had this morning for £20. So (assuming those are fair prices) I have effectively made £205 (about $400) today. Maybe if I get bored of working for Microsoft I should start a business buying broken laptops, refurbishing them and then selling them. I know that there are people who make a living doing this.
Thought for the day
Friday, February 10th, 2006Nobody has the right to not be offended. Discuss.
The undiscovered colour
Sunday, February 5th, 2006I'm reading a great book at the moment, Dave Gorman's Googlewhack adventure. This book chronicles the epic procrastination techniques Dave Gorman used to avoid starting to write a novel. The novel he was going to write was about a guy who sees a brand new colour in a dream and travels the world searching for an example of it.
Sounds pretty far fetched, no? Well, quite by accident I came across this page in which a physicist Andrew Hamilton comes up with an entirely new colour.
In case you're put off by the maths on that page, here's a basic explanation. The human eye contains 3 types of colour receptors (call them red, green and blue for the sake of argument). When we see a particular colour, these receptors are triggered in some ratio - the ratio determines the hue of the colour you are looking at. The red receptors detect long wavelengths, the blue receptors detect short wavelengths and the green receptors detect wavelengths in between. However, even when looking at even the purest green light the red and/or blue receptors are triggered to some extent because their ranges of sensitivity all overlap.
So what would you see if you could trigger just the green receptors? It would be a colour that no-one had ever seen before, since light with this colour isn't physically possible. Hamilton hypothesizes that this colour (which he calls "psychedelic aquamarine") would be the colour you got if you took the colour of the water around the reefs of Heron Island in the Great Barrier Reef of Australia and subtracted white to make the colour even more saturated:
In this picture, psychedelic aquamarine would be to the bottom left image as the top right image is to the top left image. When I tried to apply the same transformation the bottom left image that I applied to the top left image to get the top right image, nothing happened (which is hardly surprising since obviously my computer is not capable of displaying psychedelic aquamarine).
According to Hamilton, people who are red/green colour-blind see psychadelic aquamarine all the time, whenever they look at something which us non-colour-blind people would see as red. Such a colour would stimulate the green receptors, but not the blue receptors (as it's too red) nor the red receptors (since these don't exist in such people). However, since we can only describe colours by mentioning things which are that colour, a colour-blind person's description of psychendelic aquamarine would probably sound very much like a colour-seeing person's description of the colour red.
I wonder if it would be possible to make a machine that would allow people to see this colour. It would have to work by scanning someone's retinas, identifying where the green receptors are and firing out photons in such directions that they only hit the green receptors. If someone built such a machine and stared into it, would they just see a very vivid (bluish) green or would they have the incredible experience of seeing a brand new colour that they would never have seen before?
[Update 8/8/2011] It turns out that it is possible to see psychedelic aquamarine with no special equipment, due to the fact that colour receptors get fatigued if they look at the same colour for a long time. The Eclipse of Mars illusion (about halfway down the page) exploits this fact to enable you to see psychedelic aquamarine. Try it - it's extremely impressive!
Actor needed
Friday, February 3rd, 2006Anyone in the Seattle area want to try their hand at acting? My theatre troupe is staging a new play and we are short one actor to play:
Cory “Crash” Callahan, Director of Security. Everybody loves Crash. Ruddy, stocky, strong, slow-talking ex-cop and two-fisted whiskey-drinking Irishman. He watches everything and everyone, and doesn’t miss much.
The play is a version of the story of Julius Caesar set in a modern office environment (Crash is the counterpart of Casca in the original play).
Rehearsals start Monday and the show will go in March. Please forward to anyone who you think might be interested.