Blog Posts Escape from Lab
Yesterday I decided to put my blog posts into CVS. As part of doing that, I copied the blog articles tree. I must have made a mistake, because not all the files were copied in the way I wanted.

To prevent unfinished articles from getting out before they are ready, I have a Blosxom plugin that suppresses any article whose name is title.blog if it is accompanied by a title.notyet file. I can put the draft of an article in the .notyet file and then move it to .blog when it's ready to appear, or I can put the draft in .blog with an empty or symbolic-link .notyet alongside it, and then remove the .notyet file when the article is ready.

I also use this for articles that will never be ready. For example, a while back I got the idea that it might be funny if I were to poſt ſome articles with long medial letter 'ſ' as one ſees in Baroque printing and writing. To try out what this would look like I copied one of my articles---the one on Baroque writing ſtyle ſeemed appropriate---and changed the filename from baroque-style.blog to baroque-ftyle.blog. Then I created baroque-ftyle.notyet ſo that nobody would ever ſee my ſtrange experiment.

But somehow in the big shakeup last night, some of the notyet files got lost, and so this post and one other escaped from my laboratory into the outside world. As I explained in an earlier post, I can remove these from my web site, but aggregators like Bloglines.com will continue to display my error. it's tempting to blame this on Blosxom, or on CVS, or on the sysadmin, or something like that, but I think the most likely explanation for this one is that I screwed up all by myself.

The other escapee was an article about the optional second argument in Perl's built-in bless function, which in practice is never omitted. This article was so dull that I abandoned it in the middle, and instead addressed the issue in passing in an article on a different subject.

So if your aggregator is displaying an unfinished and boring article about one-argument bless, or a puzzling article that seems like a repeat of an earlier one, but with all the s's replaced with ſ's, that is why.

These errors might be interesting as meta-information about how I work. I had hoped not to discuss any such meta-issues here, but circumstances seem to have forced me to do it at least a little. One thing I think might be interesting is what my draft articles look like. Some people rough out an article first, then go back and fix it it. I don't do that. I write one paragraph, and then when it's ready, I write another paragraph. My rough drafts look almost the same as my finished product, right up to the point at which they stop abruptly, sometimes in the middle of a sentence.

Another thing you might infer from these errors is that I have a lot of junk sitting around that is probably never going to be used for anything. Since I started the blog, I've written about 85,000 words of articles that were released, and about 20,000 words of .notyet. Some of the .notyet stuff will eventually see the light of day, of course. For example, I have about 2500 words of addenda to this month's posts that are scheduled for release tomorrow, 1000 words about this month's Google queries and the nature of "authority" on the Web, 1000 words about the structure of the real numbers, 1300 words about the Grelling-Nelson paradox, and so on.

But I alſo have that 1100-word experiment about what happens to an article when you use long medial s's everywhere. (Can you believe I actually conſidered doing this in every one of my poſts? It's tempting, but just a little too idioſyncratic, even for me.) I have 500 words about why to attend a colloquium, how to convince everyone there that you're a genius, and what's wrong with education in general. I have 350 words that were at the front of my article about the 20 most important tools that explained in detail why most criticism of Forbes' list would be unfair; it wasted a whole page at the beginning of that article, so I chopped it out, but I couldn't bear to throw it away. I have two thirds of a 3000-word article written about why my brain is so unusual and how I've coped with its peculiar limitations. That one won't come out unless I can convince myself that anyone else will find it more than about ten percent as interesting as I find it.

[Other articles in category /oops] permanent link

The speed of electricity
For some reason I have needed to know this several times in the past few years: what is the speed of electricity? And for some reason, good answers are hard to come by.

(Warning: as with all my articles on physics, readers are cautioned that I do not know what I am talking about, but that I can talk a good game and make up plenty of plausible-sounding bullshit that sounds so convincing that I believe it myself. Beware of bullshit.)

If you do a Google search for "speed of electricity", the top hit is Bill Beaty's long discourse on the subject. In this brilliantly obtuse article, Beaty manages to answer just about every question you might have about everything except the speed of electricity, and does so in a way that piles confusion on confusion.

Here's the funny thing about electricity. To have electricity, you need moving electrons in the wire, but the electrons are not themselves the electricity. It's the motion, not the electrons. It's like that joke about the two rabbinical students who are arguing about what makes tea sweet. "It's the sugar," says the first one. "No," disagrees the other, "it's the stirring." With electricity, it really is the stirring.

We can understand this a little better with an analogy. Actually, several analogies, each of which, I think, illuminates the others. They will get progressively closer to the real truth of the matter, but readers are cautioned that these are just analogies, and so may be misleading, particularly if overextended. Also, even the best one is not really very good. I am introducing them primarily to explain why I think M. Beaty's answer is obtuse.

1. Consider a garden hose a hundred feet long. Suppose the hose is already full of water. You turn on the hose at one end, and water starts coming out the other end. Then you turn off the hose, and the water stops coming out. How long does it take for the water to stop coming out? It probably happens pretty darn fast, almost instantaneously.

   This shows that the "signal" travels from one end of the hose to the other at a high speed---and here's the key idea---at a much higher speed than the speed of the water itself. If the hose is one square inch in cross-section, its total volume is about 5.2 gallons. So if you're getting two gallons per minute out of it, that means that water that enters the hose at the faucet end doesn't come out the nozzle end until 156 seconds later, which is pretty darn slow. But it certainly isn't the case that you have to wait 156 seconds for the water to stop coming out after you turn off the faucet. That's just how long it would take to empty the hose. And similarly, you don't have to wait that long for water to start coming out when you turn the faucet on, unless the hose was empty to begin with.

   The water is like the electrons in the wire, and electricity is like that signal that travels from the faucet to the nozzle when you turn off the water. The electrons might be travelling pretty slowly, but the signal travels a lot faster.

2. You're waiting in the check-in line at the airport. One of the clerks calls "Can I help who's next?" and the lady at the front of the line steps up to the counter. Then the next guy in line steps up to the front of the line. Then the next person steps up. Eventually, the last person in line steps up. You can imagine that there's a "hole" that opens up at the front of the line, and the hole travels backwards through the line to the back end.

   How fast does the hole travel? Well, it depends. But one thing is sure: the speed at which the hole moves backward is not the same as the speed at which the people move forward. It might take the clerks another hour to process the sixty people in line. That does not mean that when they call "next", it will take an hour for the hole to move all the way to the back. In fact, the rate at which the hole moves is to a large extent independent of how fast the people in the line are moving forward.

   The people in the line are like electrons. The place at which the people are actually moving---the hole---is the electricity itself.

3. In the ocean, the waves start far out from shore, and then roll in toward the shore. But if you look at a cork bobbing on the waves, you see right away that even though the waves move toward the shore, the water is staying in pretty much the same place. The cork is not moving toward the shore; it's bobbing up and down, and it might well stay in the same place all day, bobbing up and down. It should be pretty clear that the speed with which the water and the cork are moving up and down is only distantly related to the speed with which the waves are coming in to shore. The water is like the electrons, and the wave is like the electricity.

4. A bomb explodes on a hill, and sometime later Ike on the next hill over hears the bang. This is because the exploding bomb compresses the air nearby, and then the compressed air expands, compressing the air a little way away again, and the compressed air expands and compresses the air a little way farther still, and so there's a wave of compression that spreads out from the bomb until eventually the air on the next hill is compressed and presses on Ike's eardrums. It's important to realize that no individual air molecule has traveled from hill A to hill B. Each air molecule stays in pretty much the same place, moving back and forth a bit, like the water in the water waves or the people in the airport queue. Each person in the airport line stays in pretty much the same place, even though the "hole" moves all the way from the front of the line to the back. Similarly, the air molecules all stay in pretty much the same place even as the compression wave goes from hill A to hill B. When you speak to someone across the room, the sound travels to them at a speed of 680 miles per hour, but they are not bowled over by hurricane-force winds. (Thanks to Aristotle Pagaltzis for suggesting that I point this out.) Here the air molecules are like the electrons in the wire, and the sound is like the electricity.

I believe that when someone asks for the speed of electricity, what they are typically after is something like: When I flip the switch on the wall, how long before the light goes on? Or: the ALU in my computer emits some bits. How long before those bits get to the output bus? Or again: I send a telegraph message from Nova Scotia to Ireland on an undersea cable. How long before the message arrives in Ireland? Or again: computers A and B are on the same branch of an ethernet, 10 meters apart. How long before a packet emitted by A's ethernet hardware gets to B's ethernet hardware?

M. Beaty's answer about the speed of the electrons is totally useless as an answer to this kind of question. It's a really detailed, interesting answer to a question to which hardly anyone was interested in the answer.

Here the analogy with the speed of sound really makes clear what is wrong with M. Beaty's answer. I set off a bomb on one hill. How long before Ike on the other hill a mile away hears the bang? Or, in short, "what is the speed of sound?" M. Beaty doesn't know what the speed of sound is, but he is glad to tell you about the speed at which the individual air molecules are moving back and forth, although this actually has very little to do with the speed of sound. He isn't going to tell you how long before the tsunami comes and sweeps away your village, but he has plenty to say about how fast the cork is bobbing up and down on the water.

That's all fine, but I don't think it's what people are looking for when they want the speed of electricity. So the individual charges in the wire are moving at 2.3 mm/s; who cares? As M. Beaty was at some pains to point out, the moving charges are not themselves the electricity, so why bring it up?

I wanted to end this article with a correct and pertinent answer to the question. For a while, I was afraid I was going to have to give up. At first, I just tried looking it up on the web. Many people said that the electricity travels at the speed of light, c. This seemed rather implausible to me, for various reasons. (That's another essay for another day.) And there was widespread disagreement about how fast it really was. For example:

• c
• 0.95c
• 0.75c
• 0.33c

But then I found this page on the characteristic impedance of coaxial cables and other wires, which seems rather more to the point than most of the pages I have found that purport to discuss the "speed of electricity" directly.

From this page, we learn that the thing I have been referring to as the "speed of electricity" is called, in electrical engineering jargon, the "velocity factor" of the wire. And it is a simple function of the "dielectric constant" not of the wire material itself, but of the insulation between the two current-carrying parts of the wire! (In typical physics fashion, the dielectric "constant" is anything but; it depends on the material of which the insulation is made, the temperature, and who knows what other stuff they aren't telling me. Dielectric constants in the rest of the article are for substances at room temperature.) The function is simply:

Wikipedia says that the dielectric constant of rubber is about 7 (and this website specifies 6.7 for neoprene) so we would expect the speed of electricity in rubber-insulated wire to be about 0.38c. This is not quite accurate, because the wires are also insulated by air and by the rest of the universe. But it might be close to that. (Remember that warning!)

The dielectric constant of air is very small---Wikipedia says 1.0005, and the other site gives 1.0548 for air at 100 atmospheres pressure---so if the wires are insulated only by air, the speed of electricity in the wires should be very close to the speed of light.

We can also work the calculation the other way: this web page says that signal propagation in an ethernet cable is about 0.66c, so we infer that the dielectric constant for the insulator is around 1/0.66² = 2.3. We look up this number in a a table of dielectric constants and guess from that that the insulator might be polyethylene or something like it. (This inference would be correct.)

What's the lower limit on signal propagation in wires? I found a reference to a material with a dielectric constant of 2880. Such a material, used as an insulator between two wires, would result in a velocity factor of about 2%, which is still 5600 km/s. this page mentions cement pastes with "effective dielectric constants" up around 90,000, yielding an effective velocity of 1/300 c, or 1000 km/s.

Finally, I should add that the formula above only applies for direct currents. For varying currents, such as are typical in AC power lines, the dielectric constant apparently varies with time (some constant!) and the analysis is more complicated.

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Approximations and the big hammer
In today's article about rational approximations to √3, I said that "basic algebra tells us that &radic(1-&epsilon) &asymp 1 - &epsilon/2 when &epsilon is small".

A lot of people I know would be tempted to invoke calculus for this, or might even think that calculus was required. They see the phrase "when &epsilon is small" or that the statement is one about limits, and that immediately says calculus.

Calculus is a powerful tool for producing all sorts of results like that one, but for that one in particular, it is a much bigger, heavier hammer than one needs. I think it's important to remember how much can be accomplished with more elementary methods.

The thing about &radic(1-&epsilon) is simple. First-year algebra tells us that (1 - &epsilon/2)² = 1 - ε + ε²/4. If &epsilon is small, then &epsilon²/4 is really small, so we won't lose much accuracy by disregarding it.

This gives us (1 - &epsilon/2)² ≈ 1 - ε, or, equivalently, 1 - &epsilon/2 ≈ √(1 - ε). Wasn't that simple?

[Other articles in category /math] permanent link

Archimedes and the square root of 3
In my recent discussion of why π might be about 3, I mentioned in passing that Archimedes, calculating the approximate value of π used 265/153 as a rational approximation to √3. The sudden appearance of the fraction 265/153 is likely to make almost anyone say "huh"? Certainly it made me say that. And even Dr. Chuck Lindsey, who wrote up the detailed explanation of Archimedes' work from which I learned about the 265/153 in the first place, says:

Throughout this proof, Archimedes uses several rational approximations to various square roots. Nowhere does he say how he got those approximations—they are simply stated without any explanation—so how he came up with some of these is anybody's guess.

Suppose you are a mathematician and you do not have a pocket calculator. You are sure to need some rational approximations to √3 somewhere along the line. So you should invest some time and effort into calculating some that you can store in the cupboard for when you need them. How can you do that?

You want to find pairs of integers a and b with a/b ≈ √3. Or, equivalently, you want a and b with a² ≈ 3b². But such pairs are easy to find: Simply make a list of perfect squares 1 4 9 16 25 36 49..., and their triples 3 12 27 48 75 108 147..., and look for numbers in one list that are close to numbers in the other list. 2² is close to 3·1², so √3 ≈ 2/1. 7² is close to 3·4², so √3 ≈ 7/4. 19² is close to 3·11², so √3 ≈ 19/11. 97² is close to 3·56², so √3 ≈ 97/56.

Even without the benefits of Hindu-Arabic numerals, this is not a very difficult or time-consuming calculation. You can carry out the tabulation to a couple of hundred entries in a few hours, and if you do you will find that 265² = 70225, and 3·153² is 70227, so that √3 ≈ 265/153.

Once you understand this, it's clear why Archimedes did not explain himself. By saying that √3 was approximately 265/153, had had exhausted the topic. By saying so, you are asserting no more and no less than that 3·153² ≈ 265²; if the reader is puzzled, all they have to do is spend a minute carrying out the multiplication to see that you are right. The only interesting point that remains is how you found those two integers in the first place, but that's not part of Archimedes' topic, and it's pretty obvious anyway.

In my article about the peculiarity of π, I briefly mentioned continued fractions, saying that if you truncate the continued fraction representation of a number, you get a rational number that is, in a certain sense, one of the best possible rational approximations to the original number. I'll eventually explain this in detail; in the meantime, I just want to point out that 265/153 is one of these best-possible approximations; the mathematics jargon is that 265/153 is one of the "convergents" of √3.

The approximation of √n by rationals leads one naturally to the so-called "Pell's equation", which asks for integer solutions to ax² - by² = ±1; these turn out to be closely related to the convergents of √(a/b). So even if you know nothing about continued fractions or convergents, you can find good approximations to surds.

Here's a method that I learned long ago from Patrick X. Gallagher of Columbia University. For concreteness, let's suppose we want an approximation to √3. We start by finding a solution of Pell's equation. As noted above, we can do this just by tabulating the squares. Deeper theory (involving the continued fractions again) guarantees that there is a solution. Pick one; let's say we have settled on 7 and 4, for which 7² ≈ 3·4².

Then write √3 = &radic(48/16) = √(49/16·48/49) = 7/4·&radic(48/49). 48/49 is close to 1, and basic algebra tells us that &radic(1-&epsilon) &asymp 1 - &epsilon/2 when &epsilon is small. So √3 &asymp 7/4 · (1 - 1/98). 7/4 is 1.75, but since we are multiplying by (1 - 1/98), the true approximation is about 1% less than this, or 1.7325. Which is very close—off by only about one part in 4000. Considering the very small amount of work we put in, this is pretty darn good. For a better approximation, choose a larger solution to Pell's equation.

More generally, Gallagher's method for approximating √n is: Find integers a and b for which a² ±1 = nb²; such integers are guaranteed to exist unless n is a perfect square. Then write √n = √(nb² / b²) = √((a² ± 1) / b²) = √(a²/b² · (a² ± 1)/a²) = a / b · √((a² ± 1) / a²) = a/b · √(1 ± 1/a²) ≈ a/b · (1 ± 1 / 2a²).

Who was Pell? Pell was nobody in particular, and "Pell's equation" is a complete misnomer. The problem was (in Europe) first studied and solved by Lord William Brouncker, who, among other things, was the founder and the first president of the Royal Society. The name "Pell's equation" was attached to the problem by Leonhard Euler, who got Pell and Brouncker confused—Pell wrote up and published an account of the work of Brouncker and John Wallis on the problem.

Order A Mathematician's Apology with kickback no kickback

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Blosxom sucks
Several people were upset at my recent discussion of Blosxom. Specifically, I said that it sucked. Strange to say, I meant this primarily as a compliment. I am going to explain myself here.

Before I start, I want to set your expectations appropriately. Bill James tells a story about how he answered the question "What is Sparky Anderson's strongest point as a [baseball team] manager?" with "His won-lost record". James was surprised to discover that when people read this with the preconceived idea that he disliked Anderson's management, they took "his record" as a disparagement, when he meant it as a compliment.

I hope that doesn't happen here. This article is a long compliment to Blosxom. It contains no disparagement of Blosxom whatsoever. I have technical criticisms of Blosxom; I left them out of this article to avoid confusion. So if I seem at any point to be saying something negative about Blosxom, please read it again, because that's not the way I meant it.

As I said in the original article, I made some effort to seek out the smallest, simplest, lightest-weight blogging software I could. I found Blosxom. It far surpassed my expectations. The manual is about three pages long. It was completely trivial to set up. Before I started looking, I hypothesized that someone must have written blog software where all you do is drop a text file in a directory somewhere and it magically shows up on the blog. That was exactly what Blosxom turned out to be. When I said it was a smashing success, I was not being sarcastic. It was a smashing success.

The success doesn't end there. As I anticipated, I wasn't satisfied for long with Blosxom's basic feature set. Its plugin interface let me add several features without tinkering with the base code. Most of these have to do with generating a staging area where I could view posts before they were generally available to the rest of the world. The first of these simply suppressed all articles whose filenames contained test. This required about six lines of code, and took about fifteen minutes to implement, most of which was time spent reading the plugin manual. My instance of Blosxom is now running nine plugins, of which I wrote eight; the ninth generates the atom-format syndication file.

The success of Blosxom continued. As I anticipated, I eventually reached a point at which the plugin interface was insufficient for what I wanted, and I had to start hacking on the base code. The base code is under 300 lines. Hacking on something that small is easy and rewarding.

I fully expect that the success of Blosxom will continue. Back in January, when I set it up, I foresaw that I would start with the basic features, that later I would need to write some plugins, and still later I would need to start hacking on the core. I also foresaw that the next stage would be that I would need to throw the whole thing away and rewrite it from scratch to work the way I wanted to. I'm almost at that final stage. And when I get there, I won't have to throw away my plugins. Blosxom is so small and simple that I'll be able to write a Blosxom-compatible replacement for Blosxom. Even in death, the glory of Blosxom will live on.

So what did I mean by saying that Blosxom sucks? I will explain.

Following Richard Gabriel, I think there are essentially two ways to do a software design:

1. You can try to do the Right Thing, where the Right Thing is very complex, subtle, and feature-complete.
2. You can take the "Worse-is-Better" approach, and try to cover most of the main features, more or less, while keeping the implementation as simple as possible.

Worse, because the Right Thing is very difficult to achieve, and very complex and subtle, it is rarely achieved. Instead, you get a complex and subtle system that is complexly and subtly screwed up. Often, the designer shoots for something complex, subtle, and correct, and instead ends up with a big pile of crap. I could cite examples here, but I think I've offended enough people for one day.

In contrast, with the "Worse-is-Better" approach, you do not try to do the Right Thing. You try to do the Good Enough Thing. You bang out something short and simple that seems like it might do the job, run it up the flagpole, and see if it flies. If not, you bang on it some more.

Whereas the Right Thing approach is hard to get correct, the Worse-is-Better approach is impossible to get correct. But it is very often a win, because it is much easier to achieve "good enough" than it is to achieve the Right Thing. You expend less effort in doing so, and the resulting system is often simple and easy to manage.

If you screw up with the Worse-is-Better approach, the end user might be able to fix the problem, because the system you have built is small and simple. It is hard to screw it up so badly that you end with nothing but a pile of crap. But even if you do, it will be a much smaller pile of crap than if you had tried to construct the Right Thing. I would very much prefer to clean up a small pile of crap than a big one.

Richard Gabriel isn't sure whether Worse-is-Better is better or worse than The Right Thing. As a philosophical question, I'm not sure either. But when I write software, I nearly always go for Worse is Better, for the usual reasons, which you might infer from the preceding discussion. And when I go looking for other people's software, I look for Worse is Better, because so very few people can carry out the Right Thing, and when they try, they usually end up with a big pile of crap.

When I went looking for blog software back in January, I was conscious that I was looking for the Worse-is-Better software to an even greater degree than usual. In addition to all the reasons I have given above, I was acutely conscious of the fact that I didn't really know what I wanted the software to do. And if you don't know what you want, the Right Thing is the Wrong Thing, because you are not going to understand why it is the Right Thing. You need some experience to see the point of all the complexity and subtlety of the Right Thing, and that was experience I knew I did not have. If you are as ignorant as I was, your best bet is to get some experience with the simplest possible thing, and re-evaluate your requirements later on.

When I found Blosxom, I was delighted, because it seemed clear to me that it was Worse-is-Better through and through. And my experience has confirmed that. Blosxom is a triumph of Worse-is-Better. I think it could serve as a textbook example.

Here is an example of a way in which Blosxom subscribes to the Worse-is-Better philosophy. A program that handles plugins seems to need some way to let the plugins negotiate amongst themselves about which ones will run and in what order. Consider Blosxom's filter callback. What if one plugin wants to force Blosxom to run its filter callback before the other plugins'? What if one plugin wants to stop all the subsequent plugins from applying their filters? What if one plugin filters out an article, but a later plugin wants to rescue it from the trash heap? All these are interesting and complex questions. The Apache module interface is an interesting and complex answer to some of these questions, an attempt to do The Right Thing. (A largely successful attempt, I should add.)

Faced with these interesting and complex questions, Blosxom sticks its head in the sand, and I say that without any intent to disparage Blosxom. The Blosxom answer is:

• Plugins run in alphabetic order.
• Each one gets its crack at a data structure that contains the articles.
• When all the plugins have run, Blosxom displays whatever's left in the data structure.

So Blosxom is a masterpiece of Worse-is-Better. I am a Worse-is-Better kind of guy anyway, and Worse-is-Better was exactly what I was looking for in this case, so I was very pleased with Blosxom, and I still am. I got more and better Worse-is-Better for my software dollar than usual.

When I stuck a "BLOSXOM SUX" icon on my blog pages, I was trying to express (in 80×15 pixels) my evaluation of Blosxom as a tremendously successful Worse-is-Better design. Because it might be the Wrong Thing instead of the Right Thing, but it was the Right Wrong Thing, and I'd sure rather have the Right Wrong Thing than the Wrong Right Thing.

And when I said that "Blosxom really sucks... in the best possible way", that's what I meant. In a world full of bloated, grossly over-featurized software that still doesn't do quite what you want, Blosxom is a spectacular counterexample. It's a slim, compact piece of software that doesn't do quite what you want---but because it is slim and compact, you can scratch your head over it for couple of minutes, take out the hammer and tongs, and get it adjusted the way you want.

Thanks, Rael. I think you did a hell of a job. I am truly sorry that was not clear from my earlier article.

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The 20 most important tools
Forbes magazine recently ran an article on The 20 Most Important Tools. I always groan when I hear that some big magazine has done something like that, because I know what kind of dumbass mistake they are going to make: they are going to put Post-It notes at #14. The Forbes folks did not make this mistake. None of their 20 items were complete losers.

In fact, I think they did a pretty good job. They assembled a panel of experts, including Don Norman and Henry Petroski; they also polled their readers and their senior editors. The final list isn't the one I would have written, but I don't claim that it's worse than one I would have written.

Criticizing such a list is easy---too easy. To make the rules fair, it's not enough to identify items that I think should have been included. I must identify items that I think nearly everyone would agree should have been included.

Unfortunately, I think there are several of these.

First, to the good points of the list. It doesn't contain any major clinkers. And it does cover many vitally important tools. It provokes thought, which is never a bad thing. It was assembled thoughtfully, so one is not tempted to dismiss any item without first carefully considering why it is in there.

Here's the Forbes list:

1. The Knife
2. The Abacus
3. The Compass
4. The Pencil
5. The Harness
6. The Scythe
7. The Rifle
8. The Sword
9. Eyeglasses
10. The Saw
11. The Watch
12. The Lathe
13. The Needle
14. The Candle
15. The Scale
16. The Pot
17. The Telescope
18. The Level
19. The Fish Hook
20. The Chisel

Categories

Order The Pencil with kickback no kickback

But here is my first quibble: it's not really clear why some items stood for whole groups, and others didn't. The explanatory material points out that five other items on the list are special cases of the knife: the scythe, lathe, saw, chisel, and sword. The inclusion of the knife as #1 on the list is, I think, completely inarguable. The power and the antiquity of the knife would put it in the top twenty already.

Consider its unmatched versatility as well and you just push it up into first place, and beyond. Make a big knife, and you have a machete; bigger still, and you have a sword. Put a knife on the end of a stick and you have an axe; put it on a longer stick and you have a spear. Bend a knife into a circle and you have a sickle; make a bigger sickle and you have a scythe. Put two knives on a hinge or a spring and you have shears. Any of these could be argued to be in the top twenty. When you consider that all these tools are minor variations on the same device, you inevitably come to the conclusion that the knife is a tool that, like Babe Ruth among baseball players, is ridiculously overqualified even for inclusion with the greatest.

But Forbes people gave the sword a separate listing (#8), and a sword is just a big knife. It serves the same function as a knife and it serves it in the same mechanical way. So it's hard to understand why the Forbes people listed them separately. If you're going to list the sword separately, how can you omit the axe or the spear? Grouping the items is a good idea, because otherwise the list starts to look like the twenty most important ways to use a knife. But I would have argued for listing the sword, axe, chisel, and scythe under the heading of "knife".

I find the other knifelike devices less objectionable. The saw is fundamentally different from a knife, because it is made and used differently, and operates in a different way: it is many tiny knives all working in the same direction. And the lathe is not a special case of the knife, because the essential feature of the lathe is not the sharp part but the spinning part. (I wouldn't consider the lathe a small, portable implement, but more about that below.)

Pounding

No, I take it back. It's not like any of those things. Those things should all be described as analogous to leaving the hammer of the list of the twenty most important tools, not the other way around.

Was the hammer omitted because it's not a simple, portable physical implement? Clearly not.

Was the hammer omitted because it's an abstract fundamental machine, like the lever? Is a hammer really just a lever? Not unless a knife is just a wedge.

Is the hammer subsumed in one of the other items? I can't see any candidates. None of the other items is for pounding.

Did the Forbes panel just forget about it? That would have been weird enough. Two thousand Forbes readers, ten editors, and Henry Petroski all forgot about the hammer? Impossible. If you stop someone on the street and ask them to name a tool, odds are that they will say "hammer". And how can you make a list of the twenty most important tools, include the chisel as #20, and omit the hammer, without which the chisel is completely useless?

The article says:

We eventually came up with a list of more than 100 candidate tools. There was a great deal of overlap, so we collapsed similar items into a single category, and chose one tool to represent them. That left us with a final list of 33 items, each one a part of a particular class or style of tool; for instance, the spoon is representative of all eating utensils.

Also-rans

• spoon
• longbow
• broom
• paper clip
• computer mouse
• floppy disk
• syringe
• toothbrush
• barometer
• corkscrew
• gas chromatograph
• condom
• remote control

"Gas chromatograph" seems to be someone's attempt to steer the list away from ancient inventions and to include some modern tools on the list. This is a worthy purpose. But I wish that they had thought of a better representative than the gas chromatograph. It seems to me that most tools of modern invention serve only very specialized purposes. The gas chromatograph is not an exception. I've never used a gas chromatograph. I don't think I know anyone who has. I've never seen a gas chromatograph. I might well go to the grave without using one. How is it possible that the gas chromatograph is one of the 33 most important tools of all time, beating out the hammer?

With "syringe", I imagine the authors were thinking of the hypodermic needle, but maybe they really were thinking of the syringe in general, which would include the meat syringe, the vacuum pipette, and other similar devices. If the latter, I have no serious complaint; I just wanted to point out the possible misunderstanding.

"Paper clip" is just the kind of thing I was afraid would appear. The paper clip isn't one of the top hundred most important tools, perhaps not even one of the top thousand. If the hammer were annihilated, civilization would collapse within twenty-four hours. If the paper clip were annihilated, we would shrug, we would go back to using pins, staples, and ribbons to bind our papers, and life would go on. If the pin isn't qualified for the list, the paper clip isn't even close.

I was speechless at the inclusion of the corkscrew in a list of essential tools that omits both bottles and corks, reduced to incoherent spluttering. The best I could do was mutter "insane".

I don't know exactly what was intended by "remote control", but it doesn't satisfy the criteria. The idea of remote control is certainly important, but this is not a list of important ideas or important functions but important tools. If there were a truly universal remote control that I could carry around with me everywhere and use to open doors, extinguish lights, summon vehicles, and so on, I might agree. But each particular remote control is too specialized to be of any major value.

Putting the computer mouse on the list of the twenty (or even 33) most important tools is like putting the pastrami on rye on the list of the twenty most important foods. Tasty, yes. Important? Surely not. In the same class as the soybean? Absurd.

The floppy disk is already obsolete.

Other comparisons

The telescope

But the telescope has a cousin, the microscope. Is the telescope's scientific value comparable to that of the microscope? I would argue that it is not. Certainly the microscope is much more widely used, in almost any branch of science you could name except astronomy. The telescope enabled the discovery that the earth is not the center of the universe, a discovery of vast philosophical importance. Did the microscope lead to fundamental discoveries of equal importance? I would argue that the discovery of microorganisms was at least as important in every way.

Arguing that "X is in the list, so Y should be too" is a slippery slope that leads to a really fat list in which each mistaken inclusion justifies a dozen more. I won't make that argument in this article. But the reverse argument, that "Y isn't in the list so X shouldn't be either", is much safer. If the microscope isn't important enough to make the list, then neither is the telescope.

The level

I'm boggled; I don't know what the level is doing there. But the fact that my most serious complaint about any particular item is with item #18 shows how well-done I think the list is overall.

Sewing

There are small, portable lathes. But there are also small, portable looms, hand looms, and so on. I think the loom has a better claim to being a tool in this sense than a lathe does. Cloth is surely one of the ten most important technological inventions of all time, up there with the knife, the gun, and the pot. Cloth does not belong on the Forbes list, because it is not a tool. But omission of the loom surprises me.

Grinding

Male bias?

The pot made the list, but not the potter's wheel. An important omission, perhaps? I think not, that a good argument could be made that the potter's wheel was only an incremental improvement, not suitable for the top twenty.

I do wonder what happened to rope; here I could only imagine that they decided it wasn't a "tool". (M. Ewalt says that he is at a loss to explain the omission of rope.) And where's the basket? Here I can't imagine what the argument was.

Carrying

The bag! Where is the bag?

I will say it again: Where is the bag?

Is the bag a small, portable implement? Yes, almost by definition. "Stop for a minute and think about what you've done today--every job you've accomplished, every task you've completed." begins the Forbes article. Did I have my bag with me? I did indeed. I started the day by opening up a bag of grapes to eat for breakfast. Then I made my lunch and put it in a bag, which I put into another, larger bag with my pens and work papers. Then I carried it all to work on my bicycle. Without the bag, I couldn't have carried these things to work. Could I have gotten that stuff to work without a bag? No, I would not have had my hands free to steer the bicycle. What if I had walked, instead of riding? Still probably not; I would have dropped all the stuff.

The bag, guys!. Which of you comes to work in the morning without a bag? I just polled the folks in my office; thirteen of fourteen brought bags to work today. Which of you carries your groceries home from the store without a bag? Paleolithic people carried their food in bags too. Did you use a lathe today? No? A telescope? No? A level? A fish hook? A candle? Did you use a bag today? I bet you did. Where is the bag?

The only container on the Forbes list is the pot. Could the bag be considered to be included under the pot? M. Ewalt says that it was, and it was omitted for that reason. I believe this is a serious error. The bag is fundamentally different from the pot. I can sum up the difference in one sentence: the pot is for storage; the bag is for transportation.

Each one has several advantages not possessed by the other. Unlike the pot, the bag is lightweight and easy to carry; pots are bulky. You can sling the bag over your shoulder. The bag is much more accommodating of funny-shaped objects: It's much easier to put a hacked-up animal or a heterogeneous bunch of random stuff into a bag than into a pot. My bag today contains some pads of paper, a package of crackers, another bag of pens, a toy octopus, and a bag of potato chips. None of this stuff would fit well into a pot. The bag collapses when it's empty; the pot doesn't.

The pot has several big advantages over the bag:

1. The pot is rigid. It tends to protect its contents more than a bag would, both from thumping and banging, and from rodents, which can gnaw through bags but not through pots.

2. The pot is impermeable. This means that it is easy to clean, which is an important health and safety issue. Solids, such as grain or beans, are protected from damp when stored in pots, but not in bags. And the pot, being impermeable, can be used to store liquids such as food and lighting oils; making a bag for storing liquids is possible but nontrivial. (Sometimes permeability is an advantage; we store dirty laundry in bags and baskets, never pots.)

3. The pot is fireproof, and so can be used for cooking. Being both fireproof and impermeable, the pot enables the preparation of soup, which increases the supply of available food and the energy that can be extracted from the food.

I have no objection to Forbes' inclusion of the pot on their list, none at all. In fact, I think that it should be put higher than #16. But the bag needs to be listed too.

Other possible omissions

Revised list

Linguists found a while ago that if you ask subjects to judge whether certain utterances are grammatically correct or not, they have some difficulty doing it, and their answers do not show a lot of agreement with other subjects'. But if you allow them an "I'm not sure" category, they have a lot less difficulty, and you do see a lot of agreement about which utterances people are unsure about. I think a similar method may be warranted here. Instead of the tools that are in or out of the list, I'm going to make two lists: tools that I'm sure are in the list, and tools that I'm not sure are out of the list.

The Big Eight, tools that I think you'd have to be crazy to omit, are:

1. Knife (includes sword, axe, scythe, chisel, spear, shears, scissors)
2. Hammer (includes club, mace, sledgehammer, mallet)
3. Bag (includes wineskin, water skin, leather bottle, purse)
4. Pot (includes plate, bowl, pitcher, rigid bottle, mortar)
5. Rope (includes string and thread)
6. Harness (includes collar and yoke)
7. Pen (includes pencil, writing brush, etc.)
8. Gun (includes rifle and musket, but not cannon)

1. Compass
2. Plumb line (includes level)
3. Sewing needle
4. Candle (includes lamp, lantern, torch)
5. Ladder
6. Eyeglasses (includes contact lenses)
7. Saw
8. Balance
9. Fishhook
10. Lathe
11. Abacus (includes counting board)
12. Microscope

The other adjustments are minor: The pot got a big promotion, from #16 to #4. The pencil is represented by the pen, instead of the other way around. The rifle is teamed with the musket as "the gun". The telescope is replaced with the microscope. The level is replaced with the plumb line. The scale is replaced by the balance, which is more a terminological difference than anything else.

The omission of mine that worries me the most is the basket. I left it out because although it didn't seem very much like either the pot or the bag, it did seem too much like both of them. I worry about omitting the pin, but I'm not sure it qualifies as a "tool".

If I were to get another 13 slots, I might include:

1. Basket
2. Broom
3. Horn
4. Pry bar
5. Quern
6. Radio (Walkie-talkies)
7. Scraper
8. Shovel
9. Spoon
10. Tape
11. Tongs
12. Touchstone
13. Welding torch

[Other articles in category /tech] permanent link

Mysteries of color perception
Color perception is incredibly complicated, and almost the only generalization of it that can be made is "everything you think you know is probably wrong." The color wheel, for example, is totally going to flummox the aliens, when they arrive. "What the heck do you mean, 'violet is a mixture of red and blue'? Violet is nothing like red. Violet is less like red than any other color except ultraviolet! Red is even less like violet than it is like blue, for heaven's sake. What is wrong with you people?"

Well, what is wrong with us is that, because of an engineering oddity in our color sensation system, we think red and violet look somewhat similar, and more alike than red and green.

But anyway, my real point was to note that the colors in look a lot different against a gray background than they do against the blue background in the bar on the left. People who read this blog through an aggregator are just going to have to click through the link for once.

[Other articles in category /aliens] permanent link

Who farted?
The software that generates these web pages from my blog entries is Blosxom. When I decided I wanted to try blogging, I did a web search for something like "simplest possible blogging software", and found a page that discussed Bryar. So I located the Bryar manual. The first sentence in the Bryar manual says "Bryar is a piece of blog production software, similar in style to (but considerably more complex than) Rael Dornfest's blosxom." So I dropped Bryar and got Blosxom. This was a smashing success: It was running within ten minutes. Now, two months later, I'm thinking about moving everything to Bryar, because Blosxom really sucks. . But for me it was a huge success, and I probably wouldn't have started a blog if I hadn't found it. It sucks in the best possible way: because it's drastically under-designed and excessively lightweight. That is much better than sucking because it is drastically over-designed and excessively heavyweight. It also sucks in some less ambivalent ways, but I'm not here (today) to criticize Blosxom, so let's move on.

Until the big move to Bryar, I've been writing plugins for Blosxom. When I was shopping for blog software, one of my requirements that that the thing be small and simple enough to be hackable, since I was sure I would inevitably want to do something that couldn't be accomplished any other way. With Blosxom, that happened a lot sooner than it should have (the plugin interface is inadequate), but the fallback position of hacking the base code worked quite well, because it is fairly small and fairly simple.

Most recently, I had to hack the Blosxom core to get the menu you can see on the left side of the page, with the titles of the recent posts. This should have been possible with a plugin. You need a callback (story) in the plugin that is invoked once per article, to accumulate a list of title-URL pairs, and then you need another callback (stories_done) that is invoked once after all the articles have been scanned, to generate the menu and set up a template variable for insertion into the template. Then, when Blosxom fills the template, it can insert the menu that was set up by the plugin.

With stock Blosxom, however, this is impossible. The first problem you encounter is that there is no stories_done callback. This is only a minor problem, because you can just have a global variable that holds the complete menu so far at all times; each time story is invoked, it can throw away the incomplete menu that it generated last time and replace it with a revised version. After the final call to story, the complete menu really is complete:

        sub story {
          my ($pkg, $path, $filename, $story_ref, $title_ref, $body_ref,
                 $dir, $date) = @_;
          return unless $dir eq "" && $date eq "";
          return unless $blosxom::flavour eq "html";
          my $link = qq{<a href="$blosxom::url$path/$filename.$blosxom::flavour">} .
                     qq{<span class=menuitem>$$title_ref</span></a>};
          push @menu, $link;
          $menu = join "&nbsp;/ ", @menu;
        }

But it turns out that this doesn't work, and I don't think there is a reasonable way to get what I wanted without hacking the base code. (Blosxom being what it is, hacking the base code is a reasonable solution.) This is because of a really bad architecture decision inside of Blosxom. The page is made up of three independent components, called the "head", the "body", and the "foot". There are separate templates of each of these. And when Blosxom generates a page, it does so in this sequence:

1. Fill "head" template and append result to output
2. Process articles
3. Fill "body" template and append result to output
4. Fill "foot" template and append result to output

So I had to go in and hack the Blosxom core to make it fractionally less spiky:

1. Process articles
2. Fill "head" template and append result to output
3. Fill "body" template and append result to output
4. Fill "foot" template and append result to output

1. Process articles
2. Fill and output templates:
   1. Fill "head" template and append result to output
   2. Fill "body" template and append result to output
   3. Fill "foot" template and append result to output

        #include head
        #include body
        #include foot

Anyway, the real point of this note is to discuss was the debugging technique I used to fix Blosxom after I made this core change, which broke the output. The menu was showing up where I wanted, but now all the date headers (like the "Sat, 18 Mar 2006" one just above) appeared at the very top of the page body, before all the articles.

The way Blosxom generates output is by appending it to a variable $output, which eventually accumulates all the output, and is printed once, right at the very end. I had found the code that generated the "head" part of the output; this code ended with $output .= $head to append the head part to the complete output. I moved this section down, past the (much more complicated) section that scanned the articles themselves, so that the "head" template, when filled, would have access to information (such as menus) accumulated while scanning the articles.

But apparently some other part of the program was inserting the date headers into the output while scanning the articles. I had to find this. The right thing to do would have been just to search the code for $output. This was not sure to work: there might have been dozens of appearances of $output, making it a difficult task to determine which one was the responsible appearance. Also, any of the plugins, not all of which were written by me, could have been modifying $output, so it would not have been enough just to search the base code.

Still, I should have started by searching for $output, under the look-under-the-lamppost principle. (If you lose your wallet in a dark street start by looking under the lamppost. The wallet might not be there, but you will not waste much time on the search.) If I had looked under the lamppost, I would have found the lost wallet:

      $curdate ne $date and $curdate = $date and $output .= $date;

Perl has a feature called tie that allows a variable to be enchanted so that accesses to it are handled by programmer-defined methods instead of by Perl's usual internal processes. When a tied variable $foo is stored into, a STORE method is called, and passed the value to be stored; it is the responsibility of STORE to put this value somewhere that it can be accessed again later by its counterpart, the FETCH method.

There are a lot of problems with this feature. It has an unusually strong risk of creating incomprehensible code by being misused, since when you see something like $this = $that you have no way to know whether $this and $that are tied, and that what you think is an assignment expression is actually STORE($this, FETCH($that)), and so is invoking two hook functions that could have completely arbitrary effects. Another, related problem is that the compiler can't know that either, which tends to disable the possibility of performing just about any compile-time optimization you could possibly think of. Perhaps you would like to turn this:

        for (1 .. 1000000) { $this = $that }

        $this = $that;

But tie is really useful for certain kinds of debugging. In this case the question is "who was responsible for inserting those date headers into $output?" We can answer the question by tieing $output and supplying a STORE callback that issues a report whenever $output is modified. The code looks like this:

        package who_farted;

        sub TIESCALAR {
          my ($package, $fh) = @_;
          my $value = "";
          bless { value => \$value, fh => $fh } ;
        }

        sub FETCH {
          my $self = shift;
          ${$self->{value}};
        }

        sub STORE {
          my ($self, $val) = @_;
          my $fh = $self->{fh};
          print $fh "Someone stored '$val' into \$output\n";
          ${$self->{value}} = $val;
        }

        sub st {
          my @stack;
          my $spack = __PACKAGE__;
          my $N = 1;
          while (my @c = caller($N)) {
            my (undef, $file, $line, $sub) = @c;
            next if $sub =~ /^\Q$spack\E::/o;
            push @stack, "$sub ($file:$line)";
          } continue { $N++ }
          @stack;
        }

The real STORE dumps the stack trace, and takes some pains to announce whether the value of $output was entirely overwritten or appended to:

        sub STORE {
          my ($self, $val) = @_;
          my $old = $ {$self->{value}};
          my $olen = length($old);
          my ($act, $what) = ("set to", $val);
          if (substr($val, 0, $olen) eq $old) {
            ($act, $what) = ("appended", substr($val, $olen));
          }
          $what =~ tr/\n/ /;
          $what =~ s/\s+$//;
          my $fh = $self->{fh};
          print $fh "var $act '$what'\n";
          print $fh "  $_\n" for st();
          print $fh "\n";
          ${$self->{value}} = $val;
        }

        open my($DIAGNOSTIC), ">", "/tmp/who-farted" or die $!;
        tie $output, 'who_farted', $DIAGNOSTIC;

A somewhat more useful version of this technique comes in handy in situations where you have some program, say a CGI program, that is generating the wrong output; maybe there is a "1" somewhere in the middle of the output and you don't know what part of the program printed "1" to STDOUT. You can adapt the technique to watch STDOUT instead of a variable. It's simpler in some ways, because STDOUT is written to but never read from, so you can eliminate the FETCH method and the data store:

        package who_farted;

        sub rig_fh {
          my ($handle, $diagnostic) = shift;
          my $mode = shift || "<";
          open my($aux_handle), "$mode&=", $handle or die $!;
          tie *$handle, __PACKAGE__, $aux_handle, $diagnostic;
        }

        sub TIEHANDLE {
          my ($package, $aux_handle, $diagnostic) = @_;
          bless [$aux_handle, $diagnostic] => $package;
        }

        sub PRINT {
          my ($aux_handle, $diagnostic) = @$self;
          print $aux_handle @_;
          my $str = join("", @_);
          print $diagnostic "$str:\n";
          print $diagnostic "  $_\n" for st();
          print $diagnostic "\n";
        }

Something it might be worth pointing out about the code I showed here is that it uses the very rare one-argument form of bless:

        package who_farted;

        sub TIESCALAR {
          my ($package, $fh) = @_;
          my $value = "";
          bless { value => \$value, fh => $fh } ;
        }

"Take advantage of" is the wrong phrase here, because, as I said, there is not actually any advantage to doing it this way. And although I was sure that who_farted would never be inherited, I might have been wrong; I have been wrong about such things before. A smart programmer requires only ten years to learn that you should not do things the wrong way, even if you are sure it will not matter. So I violated this rule and potentially sabotaged my future maintenance efforts (on the day when the class is subclassed) and I got nothing, absolutely nothing in return.

Yes. It is completely pointless. A little Dada to brighten your day. Anyone who cannot imagine a lobster-handed train conductor sleeping in a pile of celestial globes is an idiot.

[Other articles in category /oops] permanent link

More on Emotions
In yesterday's long article about emotions, I described the difficulty like this:

There's another kind of embarrassment that occurs when you see something you shouldn't. For example, you walk into a room and see your mother-in-law putting on her bra. You are likely to feel embarrassed. What's the connection with the embarrassment you feel when you fall off a ledge? I don't know; I'm not even sure they are the same. Perhaps we need a new word.

I also thought of another emotion that was not on my list of basic emotions, but seems different from the others. This emotion does not, so far as I know, have a word in English. It is the emotion felt (by most people) when regarding a happy baby, the one that evokes the "Awwww!" response.

This is a very powerful response in most people, for evolutionarily obvious reasons. It is so powerful that it is even activated by baby animals, dolls, koala bears, toy ducks, and, in general, anything small and round. Even, to a slight extent, ball bearings. (Don't you find ball bearings at least a little bit cute? I certainly do.)

The aliens might or might not have this emotion. If they are aliens who habitually protect and raise their young, I think it is inevitable. The aliens might be the type to eat their young, in which case they probably will not feel this way, although they might still have that response to their eggs, in which case expect them to feel warmly about ball bearings.

I also gave some more thought to Ashley, the Pacemate who claimed that her most embarrassing moment was crashing into the back of a trash truck and totaling her car. I tried to understand why I found this such a strange response. The conclusion I finally came to was that I had found it inappropriate because I would have expected fear, anger, or guilt to predominate. If Ashley is in a vehicle colision severe enough to ruin her car, I felt, she should experience fear for her own safety or that of others, anger at having wrecked her car, guilt at having carelessly damaged someone else's property or health. But embarrassment suggested to me that her primary concern was for her reputation: now the whole world thinks that Ashley is a bad driver.

If you don't see what I'm getting at here, the following situational change might make it clearer:

Most Embarrassing moment

Ashley (alternate universe version): Crashing into the back of a school bus full of kids and totaling my car!

Having made the analysis explicit for myself, and pinned down what seemed strange to me about Ashley's embarrassment, it no longer seems so strange to me. Here's why: It wasn't a school bus, but a garbage truck. Garbage trucks are big and heavy. The occupants were much less likely to have been injured than was Ashley herself, partly because they were in a truck and also because Ashley struck the back of the truck and not the front. The truck was almost certainly less severely damaged than Ashley's car was, perhaps nearly unscathed. And of course it was impossible that the truck's cargo was damaged. So a large part of the motivation for fear and guilt is erased, simply because the other vehicle in the collision was a garbage truck. I would have been angry that my car was wrecked, but if Ashley isn't, who am I to judge? Probably she's just a better person than I am.

But I still find the reaction odd. I wonder if some of what Ashley takes to be embarrassment isn't actually disgust. But at least I no longer find it completely bizarre.

Finally, thinking about this led me to identify another emotion that I think might belong on the master list: relief.

[Other articles in category /aliens] permanent link

Emotions
I was planning to write another article about π, and its appearance in Coulomb's law, or perhaps an article about how to calculate the volume of a higher-dimensional analogue of a sphere.

But John Speno says he always skips the math stuff on my blog, and the last couple of days have been unrelievedly mathematical. So instead, John, I have written an article about the comparison of emotions, whether the 18-toed Sirian ghost worms will understand why you are holding your nose, Homer Simpson, the evolutionary justification for disgust, the Indiana Pacers cheerleading squad, Paris Hilton, and maggots. Skip this, I dare you.

But one day she pushed the idea too far and asserted that those were the only emotions there are.

That's clearly wrong. Even discounting emotions that might be considered variations on the big four, such as: (anger) rage, annoyance, resentment, frustration, (sadness) grief, disappointment, remorse, loneliness, (happiness) delight, joy, pride, (fear) nervousness, dread, terror, panic, and so on, we still have:

• Boredom
• Disgust
• Envy
• Guilt
• Jealousy
• Lust
• Shame
• Surprise

Some of these may require explanation. People sometimes use the word "disgust" metaphorically to refer to a feeling that is really nine parts anger to one part boredom, as when they say they are disgusted with the state of American politics. But that's not what I mean by it here. The disgust I'm referring to is the feeling you have when you have been on vacation and come back to discover that the power went out while you were away and the meat in the refrigerator has spoiled and slid out onto the kitchen floor where it is now festering with thousands of squirming, white, eyeless maggots, and the instant you see it, your reaction is to (a) turn away, (b) hold your nose, and (c) vomit. I suppose it's possible that some people would have that very reaction to American politics; it's certainly understandable. But I don't think that's what people usually mean when they say that politics disgusts them. Or if they do mean it, they mean it only in a hyperbolic sense.

People often confuse guilt and shame, but they are really orthogonal. You feel guilt when you have done something you believe is ethically or morally wrong. You feel shame when other people observe you doing something that they shouldn't see, whether or not that thing is ethically or morally wrong. The problem is with the observing, not with the thing that is being observed. I think the following example will help clear up the confusion: One might or might not feel guilty about picking one's nose, although I think most people don't feel guilty when they do it. But even someone who picks their nose entirely without guilt, probably feels ashamed if someone else catches them in the act.

The other two that are often confused are envy and jealousy. Here I think the confusion is caused simply because people don't know what the words mean. Envy is what you feel when you want what someone else has; you can envy someone else's car or their lunch or their special relationship with their lover. Jealousy is much more specific. You are jealous when you have a special relationship with a person, and you are afraid that you are going to lose them to a third person. You can envy someone else's possession of a ham sandwich, but jealousy of a ham sandwich is impossible.

I might be willing to believe the proposition these eight, plus the original four (anger, sadness, happiness, and fear) constitute a complete set of "primary colors" for human emotion, and that you can consider the others as being mixtures of various amounts of these twelve. For example, you go up on stage to accept an award, and your trousers fall off, and you feel embarrassed. What is embarrassment? It's maybe five parts shame, two parts fear, and one part surprise. Take away any of these three things, and you no longer have embarrassment, but something else. Add in anger and you have humiliation.

If someone wants to argue that jealousy is compounded from fear, anger, and envy, and should be removed from the list in favor of affection or confusion, I won't complain. The list is necessarily dependent on culture, and even more so on the individual making it. Not every culture will have anything like jealousy; perhaps most won't. Romantic love seems to be a uniquely European invention, dating from around the 13th century.

Another problem with the list is that even within one culture, there may not be agreement on which kinds of feelings qualify as emotions. Does hunger qualify? Or fatigue? It seems to me that some emotions are more rooted in the physical processes of the body, and others less so. Guilt is at the "high" end of that scale: it refers to a feeling you have in your mind when you have done something that you feel you shouldn't have. It is hardly associated with the body at all. A brain in a vat could feel guilt, and probably does. At the "low" end of the scale is disgust, the experience of which is much less about an the social constructions in your mind than it is about your stomach trying to turn itself inside out. I think hunger and fatigue are even farther down the scale of body-vs-mind than disgust; below even those is pain, and at the very bottom are feelings like the one you have in your arm when you open a door, which is purely physical and has no emotional content whatsoever. The counterparts at the top end of the scale are plans, analyses, and the like, which are purely mental and have no emotional content. Emotion is somewhere in between, and I can imagine that someone else could want to exclude disgust or guilt from a list of emotions because they were too far down from the middle of the scale.

An exercise I love to do is to try to consider what we will have in common with the space aliens. For example, do the space aliens consider the P=NP problem interesting? Do the space aliens consider the set of real numbers as a fundamental object, or as an obscure construction only of interest to set theorists? I will probably address these topics in future articles. Meanwhile, this article, believe it or not, started out as a discussion of whether the space aliens, when they arrive, will already know how to play chess. (Well, obviously not. But it is less obvious that they will not already know how to play go. I will write that article sooner or later.)

But now we might ask what kinds of emotions the aliens will have. The question seems at first glance to be completely impossible. But I believe that partial answers are possible.

As emotions get higher up on the body-to-mind scale, it becomes less likely that they will be shared by the aliens; such emotions are not even cross-cultural among humans. Our experience of guilt is very much dependent on our culture, and in particular on our relationship to law and authority, much of which is the result of two thousand years of Christian philosophizing. The converse is that emotions that are low on the body-to-mind scale are much more universal among people. Perhaps not everyone feels guilt. But everyone feels disgust.

Disgust is particularly easy to analyze from the point of view of natural selection. It is to a large extent an aversion to dangerous biohazards: rotten food and carcasses; decay, including mold, and things that look like mold; excrement, vomit, and other body substances that should be inside but that have come out; disembowelment and bodily mutilation; deformity and disease. Rotting meat is extremely poisonous, so an automatic aversion reaction makes evolutionary sense: the people who turned away in disgust lived longer than the people who saw an opportunity for a free lunch. Excrement, and particularly human excrement, harbors bacteria dangerous to humans, so an automatic aversion reaction makes evolutionary sense. Deformity is similar. Perhaps whatever caused it is not contagious—but perhaps it is, and evolution wants to stay on the safe side.

I think it is inevitable that the aliens will have these same kinds of reactions, for the same reasons. Aliens will have a strong aversion reaction if you put them in front of a chunk of rotting alien flesh, or show them an alien with its internal organs on the outside. Why? Because those things are dangerous to aliens, and so all the aliens who didn't have that reaction have died long ago of horrible diseases. I don't think it's a big step to identify this reaction with disgust.

Similarly, aliens might not have eyes, if they come from a place with no ambient short-wavelength electromagnetic radiation; say, the surface of Jupiter. But the aliens will have chemical senses, analogous to smell and taste, because there are chemicals everywhere. Every life form on earth has chemical senses, even down to bacteria. This is because you cannot use the Homer Simpson strategy of ingesting everything you encounter; you would quickly die. (Homer is fictitious, or he would be dead long ago.) You need some way of distinguishing which items are food, so that you can eat the things that are food and ignore the other things. So you need to have a sense of smell and taste.

What happens when you smell or taste something that is really harmful? You had better have some kind of aversion reaction, and you do, because all the 18-toed Sirian ghost worms without those reactions ate stuff that disagreed with them, and died young; you are the product of a long line of ghost worms that do have a sense of smell and feel disgust when they wander into a biohazard zone.

We can push this even further. I conjecture that we can even predict some of the aliens' body language. When presented with something that smells bad—say rotten food—an alien's response will be to hold its nose, if it has an olfactory sense that can be disabled by closing the organ off from the outside world. If the alien asks me what I think of Paris Hilton, and I hold my nose, the alien will understand that Paris Hilton is being insulted, and will understand something of the way in which Paris Hilton is being insulted. Chemical senses, I think, must be so universal that even noseless aliens will understand the gesture, once the structure and function of the human nose is explained to them. "Oh, I see," says the alien. "You have closed off your chemical sense organ so that Ms. Hilton's noxious effluvia cannot penetrate. Yes, I quite understand! Unfortunately, for us it is not possible since our olfactory bulbs are distributed throughout our skins. But I am sure we have all wanted to do something like that at one time or another."

Disgust, being one of the lowest emotions on the mind-body scale, is one of the easiest to attribute to the aliens. Even going a little higher is risky. Will the aliens feel lust? Quite possibly. Even a giant amoeba that reproduces by fission might feel something akin to lust when the time comes, a powerful urge to divide in two. Will the aliens feel anger? Perhaps, but here we're on shaky ground.

Long ago, I had a conversation with Matthew Stone, in which he told me how different cultures have different notions of even apparently simple emotions such as rage. Rage, he said, is characterized by the following situation: you want something, but there is some insurmountable obstacle to your getting it, and so you are frustrated. When you become enraged, your response is to attack the obstacle and try to destroy it.

But, said M. Stone, in Polish, when you want something, and there is an insurmountable obstacle, and you are frustrated, you do not have a fit of rage in which you go nuts and attack the obstacle. Instead, you have a fit of złost, in which you go nuts and attack everything around you at random.

Or, in some other culture that I forget, if you want something to which there is an insurmountable obstacle, and you are frustrated, then you have a fit of some emotion I don't remember the name of, in which you go nuts and kill yourself.

These seem to me to be distinctly different from rage, if not fundamentally so. Variations on jealousy are even easier to invent.

I don't know how much of all this is true, how much was wrong before M. Stone heard it, how much he said that was right but I misunderstood, and how much I understood correctly but got wrong between then and now. It might all be nonsense. But one can still get some mileage out of attributing złost, rather than rage, to the aliens.

Embarrassment is another one of the more universal emotions. I've seen my cat act embarrassed, typically when he falls off of a ledge, or tries to jump from A to B but only makes it partway, and goes splat.

There's another kind of embarrassment that occurs when you see something you shouldn't. For example, you walk into a room and see your mother-in-law putting on her bra. You are likely to feel embarrassed. What's the connection with the embarrassment you feel when you fall off a ledge? I don't know; I'm not even sure they are the same. Perhaps we need a new word.

The Indiana Pacers basketball team has a web site on which they list the "most embarrassing moments" of each of their cheerleaders, the Pacemates. (I keep wanting to call them the "Pacemakers", but even I know that is wrong.)

When I first planned to discuss this, it was because my random sample of responses picked up mostly strange ones, and I was ready to conclude that the Pacemates and I were not of the same species. I planned to complain that none of the Pacemates had apparently ever farted in public. But a more thorough survey revealed that the Pacemates were much less surprising in their embarrassment than I had originally thought. As embarrassing moments go, you would be hard-pressed to find a more typical example than that of falling down in the middle of a carefully-choreographed public dance exhibition, and that is mostly what they said. Both I and my cat can understand the embarrassment of these mishaps:

Lindsay: I usually don't get embarrassed, but one time, I did fall off stage at a national dance competition.

Darcy: Last year during Pacers player introductions when the lights were out, Boomer ran into me and knocked me down to the floor!

Amanda: When I was cheering at an IU game, I went back for a back handspring and in the middle of Assembly Hall court, I landed flat on my head.

Kim: When I was in sixth grade, I slipped and fell on the ice trying to get on the school bus. I had on a skirt and dress shoes and was carrying my trumpet!

I find it rather comforting that the Pacemates are embarrassed by the same things that embarrass me or my cat or both. I had been worried that all the embarrassing moments would be strange and puzzling, like this one:

Ashley: Crashing into the back of a trash truck and totaling my car!

Nikki: During speech class of my freshman year of college, I was giving a speech on the health care industry and I...well, let's just say for the rest of the semester, my classmates nicknamed me "Toot-Toot!"

[Other articles in category /aliens] permanent link

Why pi is 3
At the end of my post about why π is so peculiar, I said:

Simon [Cozens] also asked me why the number came out to be around 3, rather than around 5 or 57, and there I was on much shakier ground. I did not have any clever insights, and all I could do was itemize a bunch of stuff that seemed to bear on the issue. It will probably appear here in a future article.

Several people have written to me to point this out, and nobody has pointed out anything different, which I think supports my contention that this is the most obviously germane fact available.

Also, as I replied to M. Cozens:

I do not know any way to calculate the perimeter of a circle without considering it as a limiting case of a polygon with a lot of very short sides, so I think any investigation of why pi is 3.14 and not something else will have to start here.

(This raises an interesting question: with a 96-gon, you would expect the bounds to involve things like √3, like the hexagon does. Where do the weird fractions 10/71 and 1/7 come from? Answer: A bound of the type 2√3 was of limited use to the Greeks, because it replaces the poorly-understood number π with another poorly-understood number √3. So Archimedes replaced surds with rational approximations; for example, early on he replaces √3 with the rational approximation 265/153. (See Dr. Chuck Lindsey's detailed explanation.) I'd like to work through this and see what he would have come up with if he had done the exact calculation, but it'll take me some time.)

Anyway, the other items I sent to M. Cozens were:

2. The shortest curve that can enclose a unit area has length 2π. (Or conversely, the largest area that can be enclosed by a unit path is 1/4π.)

The "wordless" proof of the Pythagorean theorem shows that I'll have to be very careful in making the extension from length to area in Manhattan:

Independent of the metric, this proof demonstrates that the two small white thingies on the left have the same area as the large white thingy on the right, In Euclidean space, this equality establishes the Pythagorean theorem. It had better not do so in Manhattan, because the Pythagorean theorem is false in Manhattan; in the diagram, c is not equal to √(a² + b²) but to a + b.

I think I've convinced myself that a square with side s in Manhattan still has area s². And I'm pretty sure that those two white thingies on the left are squares, and so have areas a² and b², respectively.

But this implies that the large white thing on the right has area a² + b², and therefore that it is not a square, and does not have area c² as labeled, because c = a + b, and c² is not equal to a² + b².

Squares in Manhattan are required to have edges that are parallel to the coordinate axes. I think. I don't know where to go next; maybe I'll figure it out on the way home from work today.

The next item is my second favorite, after the observation about the inscribed hexagon:

3. If you put a penny on the table, then you can get at most six other pennies to touch it at the same time. This is closely related to the fact that 6 is the largest integer less than 2π. Analogous results hold in higher dimensions. The area of a sphere is 4π, or about 12.5; you can get 12 spheres to touch another sphere at the same time, but not 13.

After this item, I was pretty much out of circle-related facts. So I switched tactics and tried to look at things that seemed completely unrelated to circles:

4. &pi satisfies the equation:

x - x³/6 + x⁵/120 - x⁷/5040 + ... = 0

This was the only thing I could come up with that seemed both fairly elementary, and at the same time a good way to get π out without putting it in to begin with.

So I started trying to come up with ways to get π that seem to have nothing to do with circles. The infinite polynomial was the first thing I came up with.

It can be related to the circles, but not easily, which I think is an advantage. You need to be able to relate it to circles, or else it doesn't tell you anything about why the perimeter of the circle is pi. But it mustn't be too closely related, because I think that items 1-3 probably exhaust what can be gotten directly from the circles.

Item 5 was the Buffon's needle problem, but I said the the appearance of π there appeared to be an obvious consequence of its appearing as the perimeter of a unit circle, so let's pass on to the next thing.

6. The probability that two randomly-selected integers are relatively prime is 6/π². I said:

This gets π out, without putting it in anywhere obvious, but does not seem to me to be elementary. And how you could relate it to the circle, I have no idea.