Posts tagged math
Posts tagged math
Stephen Wolfram, in a 2000 address to the MathML International Conference:
So, where did all the mathematical notation that we use today come from?
Well, that’s all bound up with the history of mathematics itself, so we have to talk a bit about that. People often have this view that mathematics is somehow the way it is because that’s the only conceivable way it could be. That somehow it’s capturing what arbitrary abstract systems are like.
One of the things that’s become very clear to me from the big science project that I’ve been doing for the past nine years is that such a view of mathematics is really not correct. Mathematics, as it’s practiced, isn’t about arbitrary abstract systems. It’s about the particular abstract system that happens to have been historically studied in mathematics. And if one traces things back, there seem to be three basic traditions from which essentially all of mathematics as we know it emerged: arithmetic, geometry, and logic.
If you read along with Wolfram’s text and this corresponding Wikipedia entry, Wolfram’s kooky writing voice really stands out. I can’t believe I read hundreds of pages of A New Kind of Science in that voice without going bonkers.
It’s Friday, so that means it’s time to learn about combinatorial explosion and the tragic future loneliness of robot teachers with anime!
The first part of it is a little boring, but please stick with it to the end. Everything that happens after the five and a half minute mark makes it worth it.
LADIES AND GENTLEMEN
Cliff Stoll is really excited to talk to you today about the Curta calculator.
Ian Sample wrote a piece for The Guardian on how a book about fish nearly bankrupted the Royal Society, nearly resulting in Isaac Newton’s hugely important Philosophiæ Naturalis Principia Mathematica, which stated Newton’s laws of motion and gravitation, never being published.
Though Ray and Willughby’s masterpiece delayed the publication of Newton’s Principia, it was saved from obscurity by Edmund Halley, then Clerk at the Royal Society, who raised the funds to publish the work, providing much of the money from his own pocket. The Principia was eventually published in 1687.
After publishing the work, the Royal Society told Halley it could no longer afford his salary and offered to pay him in unsold copies of the Historia Piscium instead.
Crazy paper by Tanya Khovanova and Alexey Radul on arXiv on Jewish discrimination in Russia:
In the summer of 1975, while I was in a Soviet math camp preparing to compete in the International Math Olympiad on behalf of the Soviet Union, my fellow team members and I were approached for help by Valera Senderov, a math teacher in one of Moscow’s best special math schools.
The Mathematics Department of Moscow State University, the most pres- tigious mathematics school in Russia, was at that time actively trying to keep Jewish students (and other “undesirables”) from enrolling in the department. One of the methods they used for doing this was to give the unwanted students a different set of problems on their oral exam. I was told that these problems were carefully designed to have elementary solutions (so that the Department could avoid scandals) that were nearly impossible to find. Any student who failed to answer could easily be rejected, so this system was an effective method of controlling admissions. These kinds of math problems were informally referred to as “Jewish” problems or “coffins”. “Coffins” is the literal translation from Russian; they have also been called “killer” problems in English.
These problems and their solutions were, of course, kept secret, but Valera Senderov and his friends had managed to collect a list. In 1975, they approached us to solve these problems, so that they could train the Jewish and other students in these mathematical ideas. Our team of the best eight Soviet students, during the month we had the problems, solved only half of them. True, that we had other priorities, but this fact speaks to the difficulty of these problems.
Twenty-one problems and solutions are given and they are insane.
French artist and architect Serge Salat is bringing his immersive installation “Beyond Infinity” to ten cities in China, including Beijing and Shanghai. In this installation, he has created a private cosmos where visitors are invited to journey through endless layers of space mapped out using cubic shapes, panels of mirrors, shifting lights, and music. “Beyond Infinity” is a multi-sensory, multimedia experience that blends Eastern Chinese with Western Renaissance, modern, and contemporary visual culture into a singular work.
I CAN SEE FOREVER
Here’s a bit of follow up on yesterday’s post about the inimitable Graphing Calculator.
Pacific Tech (the company that Ron and Greg started after GC 1.0 shipped) now sells two applications in the Mac App Store: Graphing Calculator Lite and Equation Editor.
Graphing Calculator Lite is currently $4.99 and seems to most of the features I remember Graphing Calculator having as a kid. Looks great.
They’re also selling a new piece of software, Equation Calculator for 99¢. It basically takes a lot of the symbolic manipulation features of GC and restyles them into an interface directed at doing calculation. There’s a full rundown of the features (and what’s missing in Graphing Calculator Lite) on Pacific Tech’s site.
I bought both.
One of my favorite pieces of software of all time is Graphing Calculator, a calculator application which can plot graphs of 2D and 3D functions. It shipped free with Apple computers in the ’90s, and I spent an enormous amount of time playing with the thing, even though I didn’t have a major understanding of how it worked the majority of the time.
Bear in mind I was (and still am) a tremendous nerd.
In 2004, Ron Avitzur, the lead designer/programmer/etc. for Graphing Calculator, wrote up a long piece about development of the program.
I used to be a contractor for Apple, working on a secret project. Unfortunately, the computer we were building never saw the light of day. The project was so plagued by politics and ego that when the engineers requested technical oversight, our manager hired a psychologist instead. In August 1993, the project was canceled. A year of my work evaporated, my contract ended, and I was unemployed.
I was frustrated by all the wasted effort, so I decided to uncancel my small part of the project. I had been paid to do a job, and I wanted to finish it. My electronic badge still opened Apple’s doors, so I just kept showing up.
Oh yes, Graphing Calculator was largely developed without pay by someone trespassing on Apple’s campus.
Wait, did I say “person”? Because I meant “people.”
I asked my friend Greg Robbins to help me. His contract in another division at Apple had just ended, so he told his manager that he would start reporting to me. She didn’t ask who I was and let him keep his office and badge. In turn, I told people that I was reporting to him.
In September, Apple Facilities tried to move people into our officially empty offices. They noticed us. The Facilities woman assumed that I had merely changed projects and had not yet moved to my new group, something that happened all the time. She asked what group I worked in, since it would be that group’s responsibility to find me space. When I told her the truth, she was not amused. She called Security, had them cancel our badges, and told us in no uncertain terms to leave the premises.
We were saved by the layoffs that began that month. Twenty percent of Apple’s fifteen thousand workers lost their jobs, but Greg and I were safe because we weren’t on the books in the first place and didn’t officially exist. Afterwards, there were plenty of empty offices. We found two and started sneaking into the building every day, waiting out in front for real employees to arrive and casually tailgating them through the door. Lots of people knew us and no one asked questions, since we wore our old badges as decoys.
It is an amazing, amazing story.
I would have been the coolest kid in math class if I could have “discovered” this on my TI-89.