Thursday, November 30, 2006

Hairiest Bug War Stories

I've seen a couple of bug-related items on the Net lately, and they reminded me of a piece in the April 1997 Communications of the ACM titled My hairiest bug war stories by Marc Eisenstadt. From this comes one of my favorite bug anecdotes about a program that only worked properly on Wednesdays:

"[Story B, excerpt] ...I once had a program that only worked properly on Wednesdays...The documentation claimed that the day of the week was returned in a doubleword, 8 bytes. In actual fact, Wednesday is 9 characters long, and the system routine actually expected 12 bytes of space to put the day of the week. Since I was supplying only 8 bytes, it was writing 4 bytes on top of storage area intended for another purpose. As it turned out, that space was where a "y" was supposed to be stored to compare to the users answer. Six days a week the system would wipe out the "y" with blanks, but on Wednesdays a "y" would be stored in its correct place. "

I found the entire original article online: here

Monday, November 27, 2006



Text: the Next GUI

Perhaps the point-and-click interface will go away some day. Repeatedly, I find myself going to Google and typing "XYZ store locator" after hopelessly fishing through the flashy stab at a GUI on the XYZ web site.

Today, it was my cable company's channel listing page. Impatience with the cable company web page set in quickly. When I gave Google the name of the cable company and the word "listings," I immediately wound up right where I wanted to be. Google's becoming a first line of attack.

Text. It's the new GUI.


I can only imagine our point-and-grunt troglodyte ancestors discovering the power and efficiency of language. Words, an effective form of communication. Who would have known?

Sunday, November 26, 2006

Beauty in Mathematical Proof

I've confessed to a bit of an addiction when it comes to books. One recent purchase is Q.E.D. Beauty in Mathematical Proof by Burkard Polster.

After Li: Dynamic Form in Nature, this is the second publication of Wooden Books I've purchased; these books are distinctive in their shape and design as (I hesitate in ever saying "cute") little hard cover editions devoted to mathematics, geometry, nature and design.

The subject matter of Q.E.D. falls in the intersection of things I find mathematically cool and things that may help spark mathematical interest in my children. In this case, we're talking about wonderful little proofs that demonstrate the beauty to be found in mathematics.

For example:



I'm going to work on collecting more of these over time. Sigh, too many projects, too little time. Here are a couple more neat proofs. Also Mathworld's Proof without Words has a good list of references on the subject.

Friday, November 24, 2006

What is Antihelp?

My brother deserves credit for introducing me to the concept of ANTIHELP. I see someone logged an Urban Dictionary entry for the term, but I find the definition given there unsatisfactory, because it doesn't properly identify the importance of intentions in the administration of ANTIHELP; nor does it recognize the distinctive characteristics of the outcome of ANTIHELP.

ANTIHELP is, of course, the fusion of "ANTI-" and "HELP." The general gist of "ANTI-" is well known; it implies "opposite," "against" and, most germane to this discussion, "opposite in effect." This is the ANTI- found in antigravity, the opposite of gravity, the imaginary force that would move the apple up from Newton's head and back into the tree before hurtling it off into outer space at ever increasing speed.

Good intentions are a key component of ANTIHELP. Malice is never a factor. When malice is involved, more appropriate words may be used, words such as SABOTAGE or SUBVERSION. Furthermore, ANTIHELP would be much less painful if malice were involved, because one would feel much more justified in feeling anger. It's infinitely harder to be angry when the subverter was simply trying to help.

ANTIHELP occurs when your mother-in-law comes to stay with you, washes all your dishes and stows every dish in the last place you'd look for it. It's a well-intentioned act of kindness that will leave you cussing things like "Where's the bleepin' sifter!" for months after she leaves.

On the balance sheet of help, she left you with 10 fewer minutes of dishwashing and an hour's worth of cussing and hunting for lost utensils. Note the deficit, the loss. ANTIHELP demands this deficit. You must be left worse off than if you had no help at all. No help at all is a zero. ANTIHELP always leaves one below zero. The absence of gravity isn't antigravity. In order to have antigravity, you need that force pushing in the opposite direction of gravity. So it is with ANTIHELP.

Flickr Camera Finder

Last week Flickr added a Camera Finder, which makes it possible to search for photos taken with various cameras as well as chart cameras by popularity. Most of the best pictures on Flickr have been adjusted and sharpened, so one should be careful with one's assumptions, but I still feel this is a great addition to Flickr.



Thursday, November 23, 2006

Tiling & Recursion

Still playing around with Canvas (1, 2). Each endeavor needs some purpose, so here's the question behind today's plaything:

What's the optimal way to recursively tile a circle with rectangles?

Maybe I've somehow managed to look in all the wrong places, but preliminary searches haven't brought me to the answer. This problem has to have been solved 1000 times.

But, anyhow, following is a link to an applet demonstrating my stab at the problem (although I'm not sure it's optimal).

Enter a value to set the number of levels of recursion (1 - 8). The total area of the tiles is returned after each tiling. The perfect answer is, of course, Pi.


Happy Thanksgiving!

Wednesday, November 22, 2006

Cafe Scientique

The Sacramento Bee writes about science cafes springing up around the globe:

"In a lecture theater, you expect to be lectured to, but in a cafe, you expect to have a conversation," said Duncan Dallas, a retired TV producer who founded the first "Cafe Scientifique" in the English city of Leeds in 1998.

Today, there are a couple of hundred similar venues scattered from Tokyo to Warsaw, Poland, to Rio de Janeiro, Brazil, some unrelated and others modeled after Dallas' venture. American science cafes have sprung up in Chicago, Dayton, Ohio, Los Angeles, New York and at least two dozen other cities, although not in Sacramento, so far."


On Being Virtually Cool

I've a rant in me or two. The basic idea behind this one is this:

If it ain't cool in the real world, perhaps the virtual equivalent ain't cool either.

What if brick and mortar companies behaved like software companies and online vendors? (I'll let you deduce identities.)

Begin imaginary metaphorical sequence... diddle-a-doot, diddle-a-doot, diddle-a-doot...

So I'm driving to work this morning, just clipping along nicely, when all of a sudden a man with a sign is standing right in the middle of the road in front of me. I bring my car to a stop, roll down the window. He leans in and says, "Hey, I'm a representive of your car manufacturer. There's been a recall. We need to replace a few parts. If you're busy now, we can do it later."

I tell him I'd prefer to do it later. He gets out of the way. I go back to clipping down the freeway. Five minutes later, guess who? I stop the car again. Lather, rinse and repeat. Induction tells me he's going to be pulling this stunt and stopping me every five minutes until I let him change the muffler bearing, and induction is right.

Not really cool. Not virtually cool either.

And don't get me going...

I was out shopping the other day. When I asked a store clerk about the price of an item, he coyly said, "I'll tell you, if you put it in your shopping cart." As I exited, employees kept popping signs in my face. I had to bat them away one by one to get out of the place.

When I tried to exit through the revolving door, it kept spinning me around and plopping me right back inside. Somehow the store creators had come to the conclusion that "EXIT" means people want to stay. (A knuckle sandwich was in order.)

diddle-a-doot, diddle-a-doot, diddle-a-doot...

Monday, November 20, 2006

Edge of Blade Runner

The Big Picture links to a great British Channel 4 documentary on Blade Runner via Google Video. Highly recommended, if you love the film.



Why do our brains seem so noisy?

"In the November issue of Nature Neuroscience, the Rochester study shows that the brain's cortex uses seemingly chaotic, or 'noisy,' signals to represent the ambiguities of the real world--and that this noise dramatically enhances the brain's processing, enabling us to make decisions in an uncertain world."
(via Statistical Modeling...)

The Last Man Who Knew Everything

"We don't like polymaths any more. Perhaps it's because even being a monomath is too difficult now; even specialists specialise only in a small subset of their specialty, and learning is an either/or business. The wave/particle duality of light or the practice of medicine, but not both. Making a serious breakthrough in the deciphering of Egyptian hieroglyphs or serving with distinction on the Board of Longitude, but not both. That's the modern way.

Thomas Young, who lived from 1773 to 1829, felt no such constraints. While he may not have been the last 'man who knew everything', he made significant progress in the fields of Egyptology, optics and the physics of light, and serious contributions to many other disciplines."
The New Statesman
(via 3 Quarks Daily)

Milton Friedman, R.I.P.

"For right-of-center American libertarians, Milton Friedman was a powerful leader. For left-of-center American liberals, Milton Friedman was an enlightened adversary, and one whose view is now ascendant. We are all the stronger for his work. We will miss him."
Brad DeLong writes at Salon

Charging Batteries without Wires

New MIT research reveals a way to send wireless energy to mobile phones and laptops. Technology Review

Brilliant Minds Forecast The Next 50 Years

Articles such as this always intrigue me...

"What will be the biggest breakthrough of the next 50 years? As part of our 50th anniversary celebrations we asked over 70 of the world's most brilliant scientists for their ideas."
The New Scientist

Where the Story Ends

Time recently released the All-TIME 100 Albums list, which is the sort of thing that always leaves me a little wrankled, I guess, because the best little gems tend to get swept aside by best sellers coming easily to the memory, presumably, of music journalists brainstorming on a deadline.

What makes for an all time greatest disc? My answer is this: You still find yourself listening to it 5 years later--maybe 10--or 15--or even more. One such disc in my collection is Reading, Writing & Arithmetic by The Sundays, released in 1990.

I found a fairly recent (2004) re-review by John Polewich at Stylus who writes 14 years after the The Sundays debut:

"It takes some time before even the joy on its surface starts to shimmer--but once it does, Reading, Writing, and Arithmetic slowly begins to reveal itself. Only a few weeks later will one, while patiently watching the ripples on that surface, finally spot the tiny sparks of light that flicker beneath it like small, silvery fish. And perhaps a few months later, won over by the intensity of those sparks, one will begin to think about the album. "

In my humble opinion, it's one of the finest pop discs I own--even though it probably never stood a chance of making Time's list. Here's a link to the excellent video for Here's Where the Story Ends featuring Harriet Wheeler and her beautiful, dreamy voice.

Sunday, November 19, 2006

Feedback Loops

After a little more experimentation with ExplorerCanvas, I've come to the conclusion rendering the Lorenz attractor with Javascript doesn't translate into seriously responsive software. Depending on how far you go with it, it's not intolerably slow in Firefox, but the combination of IE and ExplorerCanvas required more cycles than my patience would allow. I don't mean to denigrate anything here--and it's not like I tried to optimize it in any way--I'm just trying to get an idea of limits. Oh well, it's pretty, isn't it?

Continuing on with a feedback loop theme...

One of the zillion books on my wannareadlist is Dark Hero of the Information Age: In Search of Norbert Wiener The Father of Cybernetics (link).

If you're a fan of Weiner, I recommend reading the Amazon review by his former student John C. Kotelly, which contains a number of great personal anecdotes. (You'll find it on this Amazon page.) The review by Alwyn Scott is also well worth the read. Thanks to both of them for taking the time.

Saturday, November 18, 2006

SVD: The Applet

Given my web traffic patterns, it seems I am becoming an unwitting explicator of the Singular Value Decomposition. My original intent was simply sharing some ideas with the graphically inclined. There are certainly many who can more write capably on this, but it's a subject I find cool and there appears to be sufficient outside interest, so I guess I'll carry on when I feel inclined.

Lately curiosity has been pulling me into experiments with JavaScript and ExplorerCanvas. I decided to combine these two pursuits with the SVD to see if I could construct something useful, and I managed to stumble my way through enough HTML, JavaScript and Canvas code to make a little SVD applet.

When it comes to the state of vector graphics on the Web, the situation feels almost criminal. Some of this feeling may be due to my experiences as an advocate of SVG (Scalable Vector Graphics). This is an area where open standards would be [would have been] great, but the players seem to insist on fighting for total domination. In the process, it feels like the Balkan world of vector on the Net has been set back years.

I like the idea behind ExplorerCanvas. If you can't beat 'em, join 'em (with an adapter). The basic idea is a Canvas implementation in IE. By leveraging Microsoft's VML, ExplorerCanvas makes it possible to write vector code (Canvas) that works in Firefox, Safari, Opera and IE. Check out the ExplorerCanvas site for more info.

My experiences with ExplorerCanvas revealed some bugs and unimplemented features. Rendering transformed arcs, for example, didn't work, so I wound up creating my own paths. Inconsistencies in line style scaling between IE and Firefox, etc. That said, the project looks like a promising undertaking.

For background on this applet, I recommend you read this post and probably the one before it. In the applet, you can specify a 2x2 matrix A. The effect of A on the unit circle is shown. You can see the relationship between the vectors of V and U as well as the relationship between S and the scale of the axes of the resulting ellipse.


(p.s. please make a comment or send me a note if you find any bugs... software is made to be broken. Also, if you're flying blind, small numbers less than four will work best.)

The Whole of the Moon

Another video link.

This The Whole of the Moon from the Waterboys excellent 1985 release This is the Sea. In the video, you'll find Mike Scott singing vocals with keyboard accompaniment by the talented Karl Wallinger, who went on to create World Party.

Scott studied literature and philosophy at the University of Edinburgh, undoubtedly one factor contributing to his thoughtful lyrics. I've seen him in concert a couple times, and both times he put on a great performance. The band's Irish influences show through more clearly in Fisherman's Blues, which was featured on the Good Will Hunting sountrack.

Wednesday, November 15, 2006

On claims of multipier effects...

In the past few months (must have been the election season), I've heard claims of economic multiplier effects and, as usual, they have left me highly skeptical.

The general form of such claims is "every dollar invested in {insert proponent's economic activity here} generates..." some multiplier of a dollar (5X, 7X, 10X or whatever) in terms of economic benefits.

I'm not an economist, but it sure seems to me that on the first level of analysis any dollar directed at A is a dollar not directed at B, C or D. Even if the claimed multiplier effect exists, we're still left with questions of which alternatives to A also have multiplier effects and whether or not any hypothetical multiplier effects associated with B, C or D are even greater.

The opportunity costs are never mentioned or considered.

Supercomputing's Next Revolution

Recent Wired article on GPGPU:

"On Wednesday, Nvidia announced the industry's first C-compiler development environment for the GPU, called CUDA, a move that will make it easier to tap the GPU for custom applications, from product design to number crunching. Nvidia general manager for GPU computing, Andy Keane, said the company created a completely new architecture for its newest GPU, the GeForce 8800, adding a cache that allows the chip to work in two modes--one for graphics that uses "stream processing" and a second so-called load-store mode for more complex logic-based operations."


Saturday, November 11, 2006

Stranger than Fiction

Recent film viewings include Talladega Nights, Borat, and Stranger than Fiction. The film I'd most like to note is the last one, Stranger than Fiction. Perhaps the primary impetus behind this post is the Metacritic score of Borat (89) vs. Stranger than Fiction (67). There's some sort of grave injustice in scoring Stranger than Fiction 22 points lower than Borat.

As far as story structure goes, Stranger than Fiction is multi-leveled, self-referential metafiction in a vein similar to the work of Charlie Kaufman (Adaptation, Eternal Sunshine for the Spotless Mind) and the more recent metatale of Tristram Shandy.

The film casts Will Ferrell as Harold Crick, intentionally and appropriately the dullest character Ferrell's ever played by far. Many critics damn director Marc Forster (Monster's Ball, Finding Neverland) for underplaying Ferrell, but this clearly wasn't supposed to be a madcap Ferrell film; the character's dullness is crucial to the story. A typically zany Ferrell would have resulted in a different film altogether, and it certainly would have ruined this one.

The basic premise is one in which inconsequential I.R.S. agent Harold Crick (Ferrell) suddenly begins hearing the voice of Kay Eiffel (Emma Thompson), a celebrated author coincidentally writing the tragic tale of a tax man's life. I don't want to hammer out any spoilers. This much is revealed in all the previews.

Needless to say, Harold is troubled by the prospect of having his life narrated to him by the mysterious British female voice inside his head, and solving the mystery provides the engine for much of the surface-level plot. In addition to Ferrell and Thompson, Maggie Gyllenhall and Dustin Hoffman offer up wonderful performances.

I believe it's true to say the more acquainted you are with literary theory, the more enjoyable this film will be. My wife teaches the subject, and I'm sure this will be one of her very favorite films of the year; it may even wind up being one of her favorites of all time. (That said, I enjoyed it immensely as well.)

If you know a deus ex machina when you see one, there are a couple more laughs in the film for you. So it goes with a quite a few other laughs, and so it goes with a number of great ironies (those who are irony-impaired will undoubtedly enjoy this film less than those who are irony-enabled).

That said, you don't need a degree in literary theory to enjoy the film, just a brain. This is where I think many critics fail to do the film justice. It's one thing to not like the film, but those who bemoan the demure performance of Ferrell without bothering to credit the film's puckish ironies and clever writing simply aren't doing it justice. It leaves me wondering if some of these critics missed many of the best jokes.

Roger Ebert got it: "Stranger Than Fiction is a meditation on life, art and romance, and on the kinds of responsibility we have. Such an uncommonly intelligent film does not often get made. It could have pumped up its emotion to blockbuster level, but that would be false to the premise, which requires us to enter the lives of these specific quiet, sweet, worthy people..."

(4 / 5)

Ich mochte ein eisbaer sein...

Musical boredom sets in all too quickly for me, but the upside is never tiring of exploring the universe of music. Mentioned before, Nouvelle Vague spins bossa nova reanimations of classic eighties alternatives. (Currently, I am most attached to their take on New Order's Confusion.)

This morning YouTube adventures led me to the excellent video for Nouvelle Vague's Eisbaer. There's nothing quite like Brazilian rhythms backing a French chanteuse singing the quarter-century-old German lyrics of a Swiss band, especially with the sixties feel of the video. Excellent!

Line Rider

Thanks to my brother for introducing me to Line Rider, a silly Flash-based time waster.

Draw a line with the pencil, click the play button, Line Rider appears and virtual physics does the rest.

Line Rider

(Here's how the pros do it on YouTube: link)

Friday, November 10, 2006


In the late 1980s, I bought a copy of Floodland by The Sisters of Mercy. From time to time, it still makes its way onto the playlist. Via YouTube, this is 1959.

On Rebates

This morning I heard a piece on NPR regarding vendors of consumer electronics. The subject of rebates arose and predictable disapproval and poo-pooing of rebates ensued. It's certainly not the first time I've seen rebates dissed. People seem to hate rebates. I don't. I like them. Let me explain why.

When people think of rebates they tend to think "Why don't you just give my my thirty bucks back RIGHT NOW ALREADY!" In order to understand rebates, however, you need to look at rebates through the eyes of the vendor.

When vendors offer a $30 rebate, they don't assume everyone who buys one unit of the product will submit one rebate. If the vendor had to discount every unit sold by $30, the rebate wouldn't be offered at all--at least in such a large denomination, because it would be economically unfeasible for the vendor to make such an offering.

In reality, only a relatively small percentage of people actually go to the trouble of submitting rebates. Vendors know this, and that knowledge factors into the size of the rebate offered. When vendors offer a $30 rebate, it's often the case that only 10% of buyers actually go to the trouble of jumping through the hoops and properly submitting the rebate. Through the eyes of a vendor, the bottom line is an average rebate per unit of $3.

If you're among the 10% (or other small percentage) who successfully submit the rebate, you not only receive the average $3 rebate per unit due to you from an egalitarian perspective (what a buyer would get in a world where everyone got a rebate)--you also receive the average rebate per unit due to the other 90% of buyers who didn't send in the rebate (i.e., in this case $27).

Basically, you get 10X (or some other relatively large factor) more back in a world where only the rebate hoop jumpers get their money back than you would get back in a world where everyone got a rebate; e.g., $30 back vs. $3 back. That's a good thing, IMHO.

In the parlance of economists, this is a form of price discrimination. Check out the Wikipedia entry for more information.

Thursday, November 09, 2006


Sunset II

Wednesday, November 08, 2006


What's new?

Lately, it seems ignorance has been falling down and going boom, but anyhow...

I'm a bit behind on media plugs, so here are a few things to which I give thumbs up.

Recently, I made it to an excellent Shawn Colvin concert promoting her new disc These Four Walls. If you like her music and you have the chance, she does good.

Corrine Bailey Rae has created a great disc; hardly breaking news, it's simply a matter of giving credit where it's due. Nice work!

There's a certain kindred spirit I find in Michael Shermer, so I'm probably not a good source for impartiality in giving thumbs up to Why Darwin Matters--another nice contribution towards the end of seeing ignorance fall down and go boom.

Recently, I enjoyed a book talk by Marjane Satrapi, Iranian author of the graphic novel Persepolis and refugee from Islamic fundamentalism. She insists on calling her work "comics" and seems to eschew the term "graphic novel."

Finally, high praise for the 5th edition of David Flanagan's Javascript: The Definitive Guide. If you are considering buying a book on the subject, this is the one to get. Definitive.

Tuesday, November 07, 2006

Teaching Kids Math - I

I spent some time helping my stepson with his 7th grade math homework last night. In the process, I taught him how to do work with units; e.g., treating units like numbers, calculating unit conversions via unit cancellation, etc.

As far as my own experiences go, I don't recall learning many of these techniques until some time after 7th grade, but I think these are simple and very helpful techniques that should be taught to students earlier rather than later.

There are a number of good unit tutorials for kids here and here at Drexel's Ask Doctor Math.

Saturday, November 04, 2006

Why the Bell Curve?

There seem to be countless times in my life where I've said, "I wish I would have known that a long time ago!" or "Why didn't you say so?!?!" More specifically, I'm refering to times when key insights came, insights crucial to understanding some concept. More often than not, the insights came in the form of an example showing a great underlying truth with undeniable clarity.

As a parent who spends too much time on the road, I often find myself thinking about good examples to offer my children, in hopes of sparing them painful paths from "I don't get it!" to "Why didn't you say so?!?!" As a stab (no promises) toward such an end, I'm writing this post.

In order to understand most things, I think you have to get your empirical hands dirty. I think it's hard to gain real understanding working purely in abstract terms (if you can avoid it). The way to get your hands dirty in this particular case is by playing Yahtzee, a game I believe most people have played at one time or another in their lives.

Yahtzee consists of 5 dice. After rolling the dice, one attempts to fulfill one of several possible objectives, most of which resemble poker hands (four of a kind, three of a kind, a full house, etc.) If you've played Yahtzee, you know that the most pleasing rolls are those that reveal the most sixes, because there are a number of objectives best fulfilled with lots of sixes.

Here's a chart showing the chances of rolling 1, 2, 3, 4, 5 and 6 with a single die. If the die is fair and properly designed, the chance of each number is 1/6 (or 0.166666...). Notice that the chart is flat, which outcomes all numbers are equally likely.

Let's look at the possible sums resulting from rolling two dice. The two least likely sums are two and twelve. The reason is there's only one way to get those sums--you have to roll either 2 ones or 2 sixes. The chances of rolling either sum is 1/6 * 1/6, or 1/36. On the other hand, rolling a sum of seven is much easier, because there are so many combinations that add up to seven (1+6, 6+1, 2+5, 5+2, 3+4, 4+3).

It's important to consider the shape of the chart going from one die to the sum of two dice. The first chart was flat, with all outcomes equally probable. The second chart looks like a tent; it's triangular, high in the middle where sums are most likely and short at each end where sums are least likely.

Let's move on to three dice. Again, we'll look at the possible sums of all dice and the odds of getting those sums. The smallest possible sum is 3. To get it, you need to roll 3 ones. The largest possible sum is 18, coming from three sixes. It's hard to get the extremes with three dice, the chances of rolling three ones is 1/6 * 1/6 * 1/6, or 1/216. The chances of rolling three sixes is also 1/216. On the other hand, by looking at the chart, you can infer there are many ways to roll a sum of 10 or 11. This is the peak of the chart. The chances of each roll is 1/8, a.k.a 0.125. The chances of summing to either 10 or 11 is 1/8 + 1/8 = 1/4, which is 0.25.

Once again, it's important to consider the shape of the chart. It's not flat. Nor is it as triangular as it was before. It's starting to look more like a curve. Keep watching the shape as we move on to four dice and five dice.

The next chart shows the sums possible with four dice. The lowest possible sum is now four (1+1+1+1), and the highest possible sum is twenty-four (6+6+6+6). The chances of getting either is 1/6 * 1/6 * 1/6 * 1/6, or 1/1296. Now the most likely sum is fourteen, the chances of which are just a little better than 1/10.

If you're thinking that the chart is starting to look like a bell curve, that's exactly what you should be thinking. This is one of the most important things to realize in this example.

Finally, take a look at the case of five dice. Now the smallest possible sum is five (1+1+1+1+1). The largest possible sum is thirty (5+5+5+5+5). The chances of rolling either is 1/6 * 1/6 * 1/6 * 1/6 * 1/6, which amounts to 1/7776. This is also why people who have played Yahtzee scream when they roll five sixes on the first roll. It's like winning a miniature lottery, quite unlikely.

At the point of five dice, the shape of the chart really looks like a bell curve. The more dice we add, the better this definition gets. Also, the more dice we add to our equation, the harder it is to get to the extremes of all ones or all sixes (this fact is worthy of an extra thought or two), because it's 1/6 to get the first one, 1/6 to get the second one, 1/6 to get the third one, and so on.

There many names for the bell curve. Engineers tend to call it the Gaussian Curve. Statisticians call it the Normal Distribution. An amazing thing about it, is you always get this sort of curve when you sum up random things. The random things don't even have to be of the same kind of things; had we used a combination of six-sided and seven-sided (or whatever-sided) dice or even counted heads and tails of coin flips, we still would have wound up with a bell curve (slightly wider or taller, perhaps, but still a bell curve).

A profound implication is that there's a certain order that arises from randomness. People often scream "Entropy!" and assume more and more randomness produces greater and greater chaos, but it's not true (at least in the sense I mean here*). More and more randomness tends to make our conception of normal possible.

The thought of randomness making normal possible is counterintuitive. Shouldn't more randomness produce greater chaos*? Nope. Why? Because when you combine all sorts of random forces, many of them tend to counteract each other. The name for this phenomenon is the Central Limit Theorem.

For every six increasing the sum of your dice, there's a good chance there's a one decreasing it. You only wind up at the extremes when all of the random forces are going in the same direction with respect to the center, which isn't very likely for the same reason it's hard to roll all ones or all sixes.

Countless phenomena in the real world are the result of summing random factors, whether it's the shuffling of the genes that contribute to how tall we are or measurement errors made by astronomers. This is why the Normal Distribution is so common, and it's why the related statistical tools and methods are so useful and important.

"I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the 'Law of Frequency of Error.' The law would have been personified by the Greeks and deified, if they had known it. It reigns with serenity and in complete self-effacement amidst the wildest of confusion." -- Sir Francis Galton (1889)

For more information, research Central Limit Theorem and Normal Distribution.

(*This is the wrong place to go into the Shannon entropy of the Gaussian!)

Friday, November 03, 2006

Longevity Tips for Mice

If you're a fat mouse, drink red wine (Red Wine Extends Life of Fat Mice). Fat or skinny, consider moving to a colder climate (Cold Mice Live Longer) and starving yourself (Low-Calorie Diet Slows Aging in Mice), but be forewarned that red wine, indeed, contains calories.

If you starve yourself and go from being a fat mouse to a skinny mouse, I'm presently uncertain of the value of red wine. Beyond that, if you work your way into my cupboards, dig into my fortified cereals (Folate-Deficient Mice Prone to Colorectal Cancer).

(And, if you're wandering around my furnace, you may want to avoid the peanut butter in the mouse traps, because it's probably covered with alfatoxin.)

Update: scientists make blind mice see again! (Sources say they're plotting against farmer's wife.)