My post on the 300th anniversary of the death of Gottfreid Leibniz just went live at the Wolfram Blog. Check it out.
I realized with some sheepishness, after writing about Bruce Sterling's story "The Black Swan," that I had only read secondhand accounts of Nassim Nicholas Taleb's Black Swan idea, but not his actual book of that title. So I ordered it, and now have read the book itself. A "black swan" as defined by Taleb, is an event of "rarity, extreme impact, and retrospective (though not prospective) predictability." Taleb is an exquant turned iconoclastic mathematician. This book was a bestseller, and like many bestsellers on arcane topics, it is chatty, opinionated, and a bit on the loose and sloppy side.
As I expected, I enjoyed the book a lot. His subject matter appeals both to my taste in mathematics and my aesthetic of fiction. (My favorite section of David Hartwell's The Dark Descent is The Fabulous Formless Darkenss, which is the section for what he and I call "nature of reality" horror  stories in which the parameters of what one thought was possible usually change for the worse.)
Other than having it confirm my belief system (always a pleasure), there were two basic things I got out of reading this.
As I told my husband (David Hartwell) while reading the book, for me this is partly a book about how David's way of doing things is right. The way David publishes books as an editor, the way he runs our small press, the way he collects books, the way he runs the family finances, etc. all tend to limit downside risks while at the same time leaving him exposed to positive Black Swans  serendipity. (Aren't I a good wife for blogging about how I just read a book that tells me how right my husband is?)
In the second half of the book Taleb spends a lot of wordage and emotion on condemning the "intellectual fraud" of the Bell Curve. I don't really need to be able to judge whether he is correct in terms of all of his examples. But it set me thinking about standardized testing.
Last week and this week, the school district is doing extensive testing of my son, which they do every three years. (This is separate from the group standardized testing.) When my husband I meet with the district in June, we will be presented with a sheaf of paper in which, page after page, our son will be raked in terms of percentiles and numbers of standard deviations from the norm. And we will try to make sense of all this data. Again.
Years ago, I read Stephen J. Gould's The Mismeasure of Man (another book which confirmed my belief systems) and I have a deep distrust of standardized testing anyway. And yet these tests mean something, and it is of crucial importance that I understand what. In past cycles of this, I've wasted a lot of time reading up on what is meant by "processing speed" and how to understand things like the results on subtests of IQ tests.
My son tends to produce an anomalous pattern of results on such tests, and so far no one has yet to be able to explain what this actually means, though  who knows  this year's tests may be different. (We expect to be having our independent expert read the results for us this time.)
So I'm reading along through Taleb's attack on the uses of the Bell Curve, and I realize that of course all of these tests are normed to Bell Curves. They wouldn't give them if they weren't. But all around me I see human attributes that do not fit that model: the ability to draw a recognizable portrait, the ability to play the piano, gender, eye color, etc. Many human differences are not meaningfully normalized to the Bell Curve.
And so I realized there was one further aspect of what these tests measure that I need to keep in mind: that the imposition of percentiles and standard deviations on what attributes are measured may be no more realistic than contemplating a spherical cow. We somehow need to try to consider whatever we're told each of these these tests are measuring is distributed BellCurvelike over the population, or whether it is a different kind of thing. I find this a bit daunting, though probably worth trying.
Just in time for Valentines Day, Wolfram Research releases Mathematica Home Edition for $295 (chocolates not included), a small fraction of the full professional edition price: Get it now your own and make your valentines with Mathematica! Find the true mathematical expressions of your love! (Or test out that new sexual geometry without injuring yourself  just kidding.)
Read all about it at MacWorld, MacNN, and Business Week.
My son Peter is really thrilled that decorating Easter eggs with Mathematica, something that he thought up, is used on the announcement page as an example.
(See also my post Who Among You are Geek Enough to Decorate Your Easter Eggs in Mathematica?)
Jeff Hamrick of the Wolfram Research Special Projects Group has done a blog post giving instructions for using Mathematica to analyze the US Presidential Election. He shows how to pull polling data into Mathematica and how to use some of the Mathematica 6 data libraries to create your own Red State/BlueState maps.
I think this is very interesting stuff because, for those of you with Mathematica out there, you don't have to rely on how other people choose to analyze and map this data. If you have questions of your own you can introduce your own data and draw your own maps. I will be very curious to see what people come up with.
Yifan Hu at Wolfram Research has come up with a computer model of the I35 bridge that shows how the bridge could have collapsed with the failure of only 3 pieces. He explains:
The picture below shows the computed stresses in a simple 2D model of the I35W bridge, with red meaning more stress. (I got the geometry from news pictures.) There are definitely aspects of the model that are not realistic. For example, the weight of the trusses themselves isn't included. And, of course, it's in 2D.
So what happens if one of the trusses weakens?
It's easy to include this in the computation by adding an upper bound on the stress in that truss. That just adds another inequalitywhich FindMinimum has no problem with.
One can actually compute all this in real time inside Manipulate. Here's an animation of the result:
One sees that when the truss with maximal stress weakens (shown in yellow), the stress spreads out to other parts of the bridge. If one weakens the next truss, then the stress propagates further. And when one weakens yet another truss, then the constraints can't be satisfied at all any moreso there is no static equilibrium for the bridge, and the bridge cannot stay standing.
See it HERE.
In a short essay "The Space of All Possible Bridge Shapes," composed in response to the Minneapolis bridge collapse, Stephen Wolfram suggests design principles that could lead to stronger bridges:
. . . it's been known for a while that the best networks don't have that kind of simple structure. In fact, they almost seem in some ways quite random.
Well, what about bridges? I strongly suspect that there are much better truss structures for bridges than the classic ones from the 1800sbut they won't look so simple.
I suspect one can do quite well by using simple rules to generate the structure. But as we know from NKS, just because the rules to generate something are simple, it doesn't mean the thing itself will look simple at all.
Two students at our NKS Summer School (Rafal Kicinger and Tom Speller) have investigated creating practical truss structures this wayand the results seem very promising.
So what should the bridges of the future look like? Probably a lot less regular than today. Because I suspect the most robust structures will end up being ones with quite a lot of apparent randomness.
Did you know that there exists a "Conservapedia," a conservative reaction to Wikipedia? I discovered this fascinating fact via the Liberal Avenger, which was making fun of their entry on the Moon. My favorite page on Conservapedia is their entry entitled Examples of Bias in Wikipedia. Here are a few choice bits:
 Wikipedia allows the use of B.C.E. instead of B.C. and C.E. instead of A.D. The dates are based on the birth of Jesus, so why pretend otherwise? Conservapedia is Christianfriendly and exposes the CE deception. . . .
 Wikipedia often uses foreign spelling of words, even though most English speaking users are American. Look up "Most Favored Nation" on Wikipedia and it automatically converts the spelling to the British spelling "Most Favoured Nation", even there there are far more American than British users. Look up "Division of labor" on Wikipedia and it automatically converts to the British spelling "Division of labour," then insists on the British spelling for "specialization" also. Enter "Hapsburg" (the European ruling family) and Wikipedia automatically changes the spelling to Habsburg, even though the American spelling has always been "Hapsburg". Within entries British spellings appear in the silliest of places, even when the topic is American. Conservapedia favors American spellings of words. . . .
 Wikipedia has many entries on mathematical concepts, but lacks any entry on the basic concept of an elementary proof. Elementary proofs require a rigor lacking in many mathematical claims promoted on Wikipedia. . . .
 The Wikipedia entry for the Piltdown Man omits many key facts, such as how it was taught in schools for an entire generation and how the dating methodology used by evolutionists is fraudulent. . . .
Oh, goodness. I wonder which mathematical claims were felt to be unchristian or subject to liberal bias.
Conservapedia is aparently a project of Andy Schafly, son of Phyllis.
(Notably absent from the Conservapedia entry on algebra is a discussion of the Arabic origin of the word.)

I've posted a bunch of photos from the Wolfram Technology Conference 2006. Enjoy!
In the comments section, in the context of whether one is more likely to survive the collapse of a building using the duckandcover technique or the triangle of life technique (taking refuge next to furniture, not under it), Jonathan Post tells the following story:
When we had "duck & cover" nuclear drills at my Robert Fulton elementary school (P.S. #8), in the late 1950s, I refused to get under my desk, and got sent to the principal's office. I explained to him that we were directly across the East River from downtown Manhattan, and that Wall Street could be ground zero. I explained that the radius of the fireball varied with the 2/3 power of megatonnage, and that the desk would not give even a microsecond of protection. He agreed, and told me not to tell all this to the other students, as it might frighten them. For that matter, he advised me not to scare the teachers. I did not leave my baby teeth for a "tooth fairy." Rather, I had my Mom snailmail them to someone who was researching Strontium90 levels in teeth, for fallout research.
Pakistan has about 2 percent of the world's population living on less than 0.7 percent of the world's land.
Q: What portion of the world's population lives in areas affected by the earthquake? How can you tell? How many of those are under age 18?
Show your work.
Extra credit: What is the population density in the most severely affected areas?
ALSO, there is a fascinating piece by an Indian seismologist, Arun Bapat, about what is to be learned from this earthquake tragedy, including some risk factors to that population your trying to do math about that might not have occurred to you:
. . . let us examine the fate of conventional structures. Press reports and television coverage indicate that there has been extensive damage in the mountainous areas of this region. The area in the vicinity of earthquake epicentre is situated at an altitude of 2,000 to 3,000 meters. Seismic vibrations have more amplitude at higher elevations. For example, take a 30storeyed building. It will have the least vibrations at the level of the ground floor but, as you go higher, the amplitude of the vibrations increase. The earthquake damage in Baramulla, Uri, Poonch, and so on, which are located at heights of about 1,500 to 2000 metres, and at a distance of about 60 to 90 km from the epicentre, was therefore more severe, as compared to the damage at Islamabad or Haripur, which are at a distance of about 60 to 90 km, but situated at an elevation of about 500 metres or so.
Follow the link to the Indian Express news story, "Is there anybody out there?" It is the first one I've seen to give any account of what I've suspected was going on in the quakeravaged hills.
Even in the fuzzy Digital Globe satellite images from 1999  the best I could get of the region over the internet  it is apparent on my nice large monitor that the mountainsides are terraced with farmlands, and their creases are dotted with small white rectangles suggestive of roofs. There were people down there.
Given confidence at my own skills as a cinematographer by a look through the GoogleVideo, I opened my own account and I uploaded this bad little clip I shot on the 28th of September of my kids in their first encounter with Peter Overmann's Wolfram Tones. It took a while for the busy folks at Google Video to approve my clip, but now it has finally been unleashed upon the public.
Back on the 28th,when I first uploaded it, I wrote:
After dinner this evening, I sat my son Peter, who has just started 3rd grade, down at my computer and let him play with Wolfram Tones for the first time. The first interesting thing that happened was that my daughter Elizabeth, who turns 3 in October, started jamming to the Wolfram Tomes soundtrack on the toy piano in the living room. (I had gotten the video camera out to film Peter, and she started while I was getting set up.) After about 10 minutes of fiddling, Peter came up with something he really liked.
I got out the video camera for a kind of personal notetaking to watch how Peter used the program. What happened while I was getting the camera out and turned on, I find quite remarkable: Elizabeth's jamming along with the music coming from the computer is something she usually only does with live music, implying that somehow the music coming from WolframTones passed the Turning test for her.
I know that lots of other mommies foist their children on their husbands and go to conferences all by themselves, but I haven't done anything like that since my children were born, and Peter turns eight next month. So, yippeee, I'm going to the Wolfram Technology Conference and I won't have to interrupt a conversation even once to say, Get down from there! or Don't eat that! (Or at least, I don't think I will.)