The same thing happened: something would look good at first and then turn out to be horrifying. For example, there was a book that started out with four pictures: first there was a windup toy; then there was an automobile; then there was a boy riding a bicycle; then there was something else. And underneath each picture it said, "What makes it go?"
I thought, "I know what it is: They're going to talk about mechanics, how the springs work inside the toy; about chemistry, how the engine of the automobile works; and biology, about how the muscles work."
It was the kind of thing my father would have talked about: "What makes it go? Everything goes because the sun is shining." And then we would have fun discussing it:
"No, the toy goes because the spring is wound up," I would say. "How did the spring get wound up?" he would ask.
"I wound it up."
"And how did you get moving?"
"From eating."
"And food grows only because the sun is shining. So it's because the sun is shining that all these things are moving." That would get the concept across that motion is simply the transformation of the sun's power.
I know I've posted this one before but I'm probably gonna post it each time I run across it.
That's chef Kin Jing Mark stretching and dividing dough into super-thin noodles. Seeing this when I was a kid made a great impression on me about the wonder of mathematics.
DARPA is soliciting research proposals for people wishing to solve one of twenty-three mathematical challenges, many of which deal with attempting to find a mathematical basis underlying biology.
What are the Fundamental Laws of Biology?: This question will remain front and center for the next 100 years. DARPA places this challenge last as finding these laws will undoubtedly require the mathematics developed in answering several of the questions listed above.
- The air in the Empire State Building weighs about 4 million pounds.
- The energy consumption of the world's population will be greater than the energy coming from the sun in less than 500 years. (Peak photons?)
What's surprising about such estimates is how often they are very close to the reality. This is especially true in a multi-step approximation, where over- and underestimates at various steps tend to cancel each other out, usually resulting in something not too far off from the truth.
Both Microsoft and Google use questions like these as part of their job interview process. We did a bunch of them in my freshman physics class; I loved them.
Banknote patterns fascinate me. I can get lost for hours in all the details, seeing how the patterns fit together, how the lettering works, the tiny security 'flaws' -- they're amazing. Central to banknote designs are Guilloche patterns, which can be created mechanically with a geometric lathe, or more likely these days, mathematically. The mathematical process attracted me immediately as I don't have a geometric lathe and nor do I have anywhere to put one. I do, however, have a computer, and at the point I first started playing with the designs (mid-2004) Illustrator and Photoshop had gained the ability to be scripted.
In case you're wondering, the most densely populated block group is one in New York County, New York -- 3,240 people in 0.0097 square miles, for about 330,000 per square mile. The least dense is in the North Slope Borough of Alaska -- 3 people in 3,246 square miles, or one per 1,082 square miles. The Manhattan block group I mention here is 360 million times more dense than the Alaska one; population densities vary over a huge range.
That's approximately the same range from the height of an iPod to the diameter of the Earth. (via fakeisthenewreal)
Benoit Mandelbrot and Paola Antonelli talk about, among other things, fractals, self-similarity in architecture, algorithms that could specify the creation of entire cities, visual mathematics, and generalists.
This has been for me an extraordinary pleasure because it means a certain misuse of Euclid is dead. Now, of course, I think that Euclid is marvelous, he produced one of the masterpieces of the human mind. But it was not meant to be used as a textbook by millions of students century after century. It was meant for a very small community of mathematicians who were describing their works to one another. It's a very complicated, very interesting book which I admire greatly. But to force beginners into a mathematics in this particular style was a decision taken by teachers and forced upon society. I don't feel that Euclid is the way to start learning mathematics. Learning mathematics should begin by learning the geometry of mountains, of humans. In a certain sense, the geometry of...well, of Mother Nature, and also of buildings, of great architecture.
Speaking of the Yankees, Derek Jeter always seems to get a lot of credit for those four World Series victories in five years but a quick look at the OBP stats for those years shows that Bernie Williams was the engine driving that offense. Jeter's a little overrated maybe?
Called "Hilbert" after the influential German mathematician, David Hilbert, the newly licensed software will be browser accessible and, utilizing AJAX technologies, will emulate the desktop version of the software with remarkable fidelity. "The magic of AJAX will allow OST to combine or 'mash-up' Mathematica with other web-based technologies to deliver and support high quality science and mathematics courses online such as the Calculus&Mathematica courses currently taught through NetMath at the University of Illinois and other universities," explains Scott Gray, Director of the O'Reilly School of Technology.
Hilbert should be available before the end of the year.
Infinite Jest once again proved finite, although it's taken me since August to get through it. This book was such a revelation the first time through that I was afraid of a reread letdown but I enjoyed it even more this time around...and got much more out of the experience too.
Right as I was finishing the book, I read a transcription of an interview with Wallace in which interviewer Michael Silverblatt asked him about the fractal-like structure of the novel:
MICHAEL SILVERBLATT: I don't know how, exactly, to talk about this book, so I'm going to be reliant upon you to kind of guide me. But something came into my head that may be entirely imaginary, which seemed to be that the book was written in fractals.
DAVID FOSTER WALLACE: Expand on that.
MS: It occurred to me that the way in which the material is presented allows for a subject to be announced in a small form, then there seems to be a fan of subject matter, other subjects, and then it comes back in a second form containing the other subjects in small, and then comes back again as if what were being described were -- and I don't know this kind of science, but it just -- I said to myself this must be fractals.
DFW: It's -- I've heard you were an acute reader. That's one of the things, structurally, that's going on. It's actually structured like something called a Sierpinski Gasket, which is a very primitive kind of pyramidical fractal, although what was structured as a Sierpinski Gasket was the first- was the draft that I delivered to Michael in '94, and it went through some I think 'mercy cuts', so it's probably kind of a lopsided Sierpinski Gasket now. But it's interesting, that's one of the structural ways that it's supposed to kind of come together.
MS: "Michael" is Michael Pietsche, the editor at Little, Brown. What is a Sierpinski Gasket?
DFW: It would be almost im- ... I would almost have to show you. It's kind of a design that a man named Sierpinski I believe developed -- it was quite a bit before the introduction of fractals and before any of the kind of technologies that fractals are a really useful metaphor for. But it looks basically like a pyramid on acid --
To answer Silverblatt's question, a Sierpinski Gasket is constructed by taking a triangle, removing a triangle-shaped piece out of the middle, then doing the same for the remaining pieces, and so on and so forth, like so:
The result is an object of infinite boundary and zero area -- almost literally everything and nothing at the same time. A Sierpinski Gasket is also self-similar...any smaller triangular portion is an exact replica of the whole gasket. You can see why Wallace would have wanted to structure his novel in this fashion.
What's sort of great about it is that it will happen to everybody if you live long enough. If you were born in 2000, it happens instantaneously. The people who were born at the end of the century have to take care of themselves.
Basically, as the leaf grows it is constrained to a 2-d surface, but the cells of some leaves reproduce fast enough to require more surface area than a pi-r-squared plane surface can provide. Its only recourse is to buckle out-of-plane, giving the wrinkles. Since the exuberant growth continues as the leaf grows outward, the buckling process repeats and you get the multi-scale (ripples on ripples on ripples) shape that you see in kale and daffodils.
Cadaeic Cadenza is a 3834-word story by Mike Keith where each word in sequence has the same number of letters as the corresponding digit in pi. (thx, mark, who has more info on constrained writing) Related: The Feynman point is the sequence of six 9s which begins 762 digits into pi. "[Feynman] once stated during a lecture he would like to memorize the digits of pi until that point, so he could recite them and quip 'nine nine nine nine nine nine and so on.'"
On March 14, 1998, I made the first post to this little site. And I'm still standin' (yeah yeah yeah). Here's to 9 more years. Actually, I'll settle for making it to 10. Baby steps.
And if that weren't enough excitement for one day, it's also Pi Day. (Whoa, the Pi Day web site uses Silkscreen!) I bet the Pi Dayers are really looking forward to 2015 when they can extend the fun to two additional decimal places.
Rule of thumb to avoid photographing people with their eyes closed: divide the number of people by three (or by two if the light is bad). That means that if you're taking a photo of 12 people, you need to take at least 4 photos to have a good chance of getting a photo with everyone's eyes open. (via photojojo)
Update:Jeff writes: "Way back when we only used film I learned you could tell before looking at the photo whether someone blinked by asking them what color was the flash. If it was white or bluish white, then their eyes were open. If it was orange, then their eyes were closed and they had 'seen' the flash through their eyelids."
A look at Saks Fifth Avenue's new logo and identity. The identity system consists of cutting up the logo into patterns....98,137,610,226,945,526,221,323,127,451,938,506, 431,029,735,326,490,840,972,261,848,186,538, 906,070,058,088,365,083,852,800,000,000,000 possible patterns.
Last month I covered the hubbub surrounding the still-potential proof of the Poincare conjecture. The best take on the situation was a New Yorker article by Sylvia Nasar and David Gruber, detailing the barest glimpse of the behind-the-scenes workings of the mathematics community, particularly those involving Grigory Perelman, a recluse Russian mathematician who unveiled his potential Poincare proof in 2002 and Shing-Tung Yau, a Chinese mathematician who, the article suggested, was out for more than his fair share of the credit in this matter.
After declining the Fields Medal, the Nobel Prize of mathematics, Perelman has quit mathematics and lives quietly in his native Russia. Yau, however, is upset at his portrayal (both literally and literary) in the New Yorker article and has written a letter to the New Yorker asking them to make a prominent correction and apologize for an illustration of Yau that accompanied the article. From the letter:
I write in the hope of enlisting your immediate assistance, as well as the assistance of The New Yorker, in undoing, to the extent possible, the literally world-wide damage done to Dr. Yau's reputation as a result of the publication of your article. I also write to outline for you, on a preliminary basis, but in some detail, several of the more egregious and actionable errors which you made in the article, and the demonstrably shoddy "journalism" which resulted in their publication.
The letter, addressed to the two authors as well as the fact-checker on the article and CC'd to David Remnick and the New Yorker's general counsel, runs 12 pages, so you may want to have a look at the press release instead. A webcast discussing all the details of the letter is being held at noon on September 20...information on how to tune in will be available at Dr. Yau's web site. (thx, david)
As I mentioned yesterday, the New Yorker published an article by Sylvia Nasar1 and David Gruber about the recent proof of the Poincare Conjecture2. (Previous coverage in the NY Times and the Guardian.) The article, which is unavailable from the New Yorker's web site (they've now made it available), contains the only interview I've seen with Grigory Perelman, the Russian mathematician who published a potential proof of the conjecture in late 2002, gave a series of lectures in the US, and then went back to Russia. Since then, he hasn't communicated with anyone about the proof, has quit mathematics, and recently refused the Fields Medal, the most prestigious award that mathematics has to offer, saying:
It was completely irrelevent for me. Everybody understood that if the proof is correct then no other recognition is needed.
Meanwhile, a Chinese group of mathematicians, led by Shing-Tung Yau3, are claiming that Perelman's proof was too complicated and are offering a reworked proof instead of Perelman's. That is, they're claiming the first complete proof of the conjecture. Yau The active director of Yau's mathematics institute explained the relative contributions thusly:
Hamilton contributed over fifty per cent; the Russian, Perelman, about twenty five per cent; and the Chinese, Yau, Zhu, and Cao et al., about thirty per cent. (Evidently, simple addition can sometimes trip up even a mathematician.)
Clearly the Chinese gave more than 100% in solving this proof, but Yau is regarded by some mathematicians as attempting to grab glory that does not belong to him. John Morgan, a mathematician at Columbia University, says:
Perelman already did it and what he did was complete and correct. I don't seen anything that [Yau et al.] did different.
Yau wants to be associated with the proof of the Poincare Conjecture, to have China associated with it, and for his student, Zhu, to be elevated in status by it. The $1 million in prize money for the proof of the conjecture offered by the Clay Mathematics Institute can't be far from Yau's mind as well. For his part, Grigory Perelman won't say whether he'll accept the prize money until it is offered. Stay tuned, I guess.
[2] Poincare (properly written as Poincaré) is pronounced Pwan-cah-RAY, not Poyn-care as I said it up until a few weeks ago. ↩
[3] Yau proved a conjecture by Eugenio Calabi which gave birth to a highly useful mathematical structure called a Calabi-Yau manifold; Yau won the Fields Medal for it. The C-Y manifold is important in string theory and Andrew Wiles used it as part of his proof of Fermat's Last Theorem. In short, Yau is a mathematical stud, no question. ↩
Benford's Law describes a curious phenomenon about the counterintuitive distribution of numbers in sets of non-random data:
A phenomenological law also called the first digit law, first digit phenomenon, or leading digit phenomenon. Benford's law states that in listings, tables of statistics, etc., the digit 1 tends to occur with probability ~30%, much greater than the expected 11.1% (i.e., one digit out of 9). Benford's law can be observed, for instance, by examining tables of logarithms and noting that the first pages are much more worn and smudged than later pages (Newcomb 1881). While Benford's law unquestionably applies to many situations in the real world, a satisfactory explanation has been given only recently through the work of Hill (1996).
I first heard of Benford's Law in connection with the IRS using it to detect tax fraud. If you're cheating on your taxes, you might fill in amounts of money somewhat at random, the distribution of which would not match that of actual financial data. So if the digit "1" shows up on Al Capone's tax return about 15% of the time (as opposed to the expected 30%), the IRS can reasonably assume they should take a closer look at Mr. Capone's return.
Since I installed Movable Type 3.15 back in March 2005, I have been using its "post to the future" option pretty regularly to post my remaindered links...and have been using it almost exclusively for the last few months[1]. That means I'm saving the entries in draft, manually changing the dates and times, and then setting the entries to post at some point in the future. For example, an entry with a timestamp like "2006-02-20 22:19:09" when I wrote the draft might get changed to something like "2006-02-21 08:41:09" for future posting at around 8:41 am the next morning. The point is, I'm choosing basically random numbers for the timestamps of my remaindered links, particularly for the hours and minutes digits. I'm "cheating"...committing post timestamp fraud.
That got me thinking...can I use the distribution of numbers in these post timestamps to detect my cheating? Hoping that I could (or this would be a lot of work wasted), I whipped up a MT template that produced two long strings of numbers: 1) one of all the hours and minutes digits from the post timestamps from May 2005 to the present (i.e. the cheating period), 2) and one of all the hours and minutes digits from Dec 2002 - Jan 2005 (i.e. the control group). Then I used a PHP script to count the numbers in each string, dumped the results into Excel, and graphed the two distributions together. And here's what they look like, followed by a table of the values used to produce the chart:
Digit
5/05-now
12/02-1/05
Difference
1
31.76%
33.46%
1.70%
2
11.76%
14.65%
2.89%
3
10.30%
9.96%
0.34%
4
10.44%
9.58%
0.86%
5
10.02%
10.52%
0.51%
6
4.83%
5.40%
0.57%
7
5.66%
4.96%
0.70%
8
7.62%
4.65%
2.97%
9
7.60%
6.81%
0.79%
As expected, 1 & 2 show up less than they should during the cheating period, but not overly so[2]. The real fingerprint of the crime lies with the 8s. The number 8 shows up during the cheating period ~64% more than expected. After thinking about it for awhile, I came up with an explanation for the abundance of 8s. I often schedule posts between 8am-9am so that there's stuff on the site for the early-morning browse and I usually finish off the day with something between 6pm-7pm (18:00 - 19:00). Not exactly the glaring evidence I was expecting, but you can still tell.
The obvious next question is, can this technqiue be utilized for anything useful? How about detecting comment, trackback. or ping spam? I imagine IPs and timestamps from these types of spam are forged to at least some extent. The difficulties are getting enough data to be statistically significant (one forged timestamp isn't enough to tell anything) and having "clean" data to compare it against. In my case, I knew when and where to look for the cheating...it's unclear if someone who didn't know about the timestamp tampering would have been able to detect it. I bet companies with services that deal with huge amounts of spam (Gmail, Yahoo Mail, Hotmail, TypePad, Technorati) could use this technique to filter out the unwanted emails, comments, trackbacks, or pings...although there's probably better methods for doing so.
[1] I've been doing this to achieve a more regular publishing schedule for kottke.org. I typically do a lot of work in the evening and at night and instead of posting all the links in a bunch from 10pm to 1am, I space them out over the course of the next day. Not a big deal because increasing few of the links I feature are time-sensitive and it's better for readers who check back several times a day for updates...they've always got a little something new to read.
[2] You'll also notice that the distributions don't quite follow Benford's Law either. Because of the constraints on which digits can appear in timestamps (e.g. you can never have a timestamp of 71:95), some digits appear proportionally more or less than they would in statistical data. Here's the distribution of digits of every possible time from 00:00 to 23:59:
Three economists share a cab, getting off at three different destinations. How do they split the fare? For answers, you might look to John Nash or the Talmud.
Here's a sampling of the rest of the AIGA Design Conference, stuff that I haven't covered yet and didn't belong in a post of it's own:
Juan Enriquez gave what was probably my favorite talk about what's going on in the world of genetics right now. I've heard him give a variation of this talk before (at PopTech, I think). He started off talking about coding systems and how when they get more efficient (in the way that the Romance languages are more efficient than Chinese languages), the more powerful they become in human hands. Binary is very powerful because you can encode text, images, video, etc. using just two symbols, 1 and 0. Segue to DNA, a four symbol language to make living organisms...obviously quite powerful in human hands.
Enriquez: All life is imperfectly transmitted code. That's what evolution is, and without the imperfections, there would be no life. The little differences over long periods of time are what's important.
Enriquez again: The mosquito is a flying hypodermic needle. That's how it delivers malaria to humans. We could use that same capability for vaccinating cows against disease.
1. Design is the easy part. 2. Learn from your clients, bosses, collaborators, and colleagues. 3. Content is king. 4. Read. Read. Read. 5. Think first, then design. 6. Never forget how lucky you are. Enjoy yourself.
Nicholas Negroponte: If programmers got paid to remove code from sofware instead of writing new code, software would be a whole lot better.
Negroponte also shared a story about outfitting the kids in a school in Cambodia with laptops; the kids' first English word was "Google", and from what Negroponte said, that was followed closely by "Skype". He also said the children's parents loved the laptops because at night, it was the brightest light in the house.
Ben Karlin and Paula Scher on the challenges of making America, The Book: Books are more daunting than doing TV because print allows for a much greater density of jokes. In trying to shoot the cover image, they found that bald eagles cannot be used live for marketing or advertising purposes. The solution? A golden eagle and Photoshop. And for a spread depicting all the Supreme Court Justices in the buff, they struggled -- even with the Web -- to find nude photos of older people until they found a Vermont nudist colony willing to send them photos because they were big fans of The Daily Show.
Bill Strickland blew the doors off the conference with his account of the work he's doing in "curing cancer" -- his term for revitalizing violent and crime-ridden neighborhoods -- in Pittsburgh. I can't do justice to his talk, so two short anecdotes. Strickland said he realized that "poor people never have a nice day" so when he built his buildings in these poor black neighbohoods, he put nice fountains out front so that people coming into the building know that they're entering a space where it's possible to have a good day. Another time, a bigwig of some sort was visiting the center and asked Strickland about the flowers he saw everywhere. Flowers in the hood? How'd these get here? Strickland told him "you don't need a task force or study group to buy flowers" and that he'd just got in his car, bought some flowers, brought them back, and set them around the place. His point in all this was creating a place where people feel less dissimilar to each other...black, white, rich, poor, everybody has a right to flowers and an education and to be treated with respect and to have a nice day. You start treating people like that, and surprise!, they thrive. Strickland's inner city programs have produced Fulbright Scholars, Pulitzer Prize winners, and tons of college graduates.
I caught 30 minutes of David Peters' presentation of Typecast: The Art of the Typographic Film Title and realized I should have gotten there in time to see the whole thing. I could sit and watch cool movie titles all day long. Among the titles he showed were Bullit, Panic Room, Dr. Strangelove, Barbarella, The Island of Dr. Moreau, and Superman. The title sequence for Napoleon Dynamite (which was discussed on Design Observer last year) was shown later in the main hall.
At the closing party at the Museum of Science, we checked out the cool Mathematica exhibit that was designed by Charles and Ray Eames, two designers who were also pretty big science/math nerds.
And some final thoughts from others at the conference. Peter Merholz says that "form-makers", which make up the vast majority of the AIGA audience, "are being passed by those who are attempting to use design to serve more strategic ends". (That's an interesting thought...) A pair of reviews from Speak Up: Bryony was a bit disappointed with the opening Design Gala but left, like everyone else, in love with emcee John Hockenberry while Armin noted that the preservation of digital files is a big concern for museums in building a collection of graphic design pieces...in 35 years, how are you going load that Quark file or run that Flash movie?
The list of the 100 greatest theorems in mathematics is topped by The Irrationality of the Square Root of 2 from that nutball Pythagoras. Jesus, who does Godel have to sleep with to get higher on this list...I mean, all the man did was destroy math! (I know, I know, oversimplification, please don't send me any email....) (via cyn-c)
Fun little quiz on eight grade math...can you pass? I got 9/10 (got tripped up on what I thought was a trick question but wasn't...erroneous! erroneous!).
The competitive Scrabble world is starting to see some top-notch players for whom English is not their native language. At he highest level of competition, "Scrabble's secret is that it's a math game: board geometry, strategic decision making, probability and chance." And sometimes it's better not knowing English so the player can focus solely on the memorization of patterns and gameplay. Interesting stuff.
xThink Calculator is a math calculation program that recognizes handwritten input from a Tablet PC (check out the screenshots). Pretty darn nifty and reminiscent of Denim, a tool for UI design. (thx nick)
"The hairy ball theorem of algebraic topology states that, in layman's terms, 'one cannot comb the hair on a ball in a smooth manner'". Heh. Looks like Wikipedia has some new measures in placeto deal with spam/trolls: "This page has been protected from editing to deal with vandalism."
They wonder whether the digits contain a hidden rule, an as yet unseen architecture, close to the mind of God. A subtle and fantastic order may appear in the digits of pi way out there somewhere; no one knows. No one has ever proved, for example, that pi does not turn into nothing but nines and zeros, spattered to infinity in some peculiar arrangement. If we were to explore the digits of pi far enough, they might resolve into a breathtaking numerical pattern, as knotty as "The Book of Kells," and it might mean something. It might be a small but interesting message from God, hidden in the crypt of the circle, awaiting notice by a mathematician.
The Chudnovsky article also reminds me of Contact by Carl Sagan in which pi is prominently featured as well.
According to Wolfram Research's Mathworld, the current world record for the calculation of digits in pi is 1241100000000 digits, held by Japanese computer scientists Kanada, Ushio and Kuroda. Kanada is named in the article as the Chudnovskys main competitor at the time.
(Oh, and as for patterns hidden in pi, we've already found one. It's called the circle. Just because humans discovered circles first and pi later shouldn't mean that the latter is derived from the former.)
DFW is a favorite of mine, but I was disappointed in Everything and More. Perhaps I wasn't part of the intended audience, but with an interest in all things Wallace, a college degree in physics, a general interest in mathematics, and avid reader of popular science books, if not me, then for whom was this book written?
Mostly I was bothered by Wallace's signature writing style, which usually challenges the reader in delightful ways. In E&M, he ratcheted his style up to such a degree that it became as obfuscating as the math he was trying to explain. Not that he should have used only words of four letters or less, but a greater degree of clarity and simplicity would have been appreciated to let the parodoxical beauty and the beautiful paradox of transfinite math show (which Jim Holt did more successfully than Wallace in his New Yorker review of the book).
You're visiting kottke.org. All content by Jason Kottke (contact me) unless otherwise noted, with some restrictions on its use. Good luck will come to those who dig around in the archives. If you've reached this point by accident, I suggest panic. In memory of DFW, rest in peace. Thanks for everything.
