Just when I think I know a bit of math, I find a new unit of length or something and then I realize I will never know any math.
I cannot resist a good math article, or a good computer science tidbit, or a good history of math article, and I seem to have found all three of them in one place, Alex Bellos’s blog, in (as of this reading) in two entries about Alan Turing’s reading and study habits while at Sherborne School which he attended for what we in America would call high school.
First up is a list of the books that Turing borrowed from the school library.
The books are almost all ones about physics and mathematics, with two exceptions. One is The Escaping Club by A. J. Evans, which is about the author’s escape from an inescapable German prison camp in WWI, and the other the works of Lewis Carroll, which would seem out of place to someone who didn’t know that Charles Dodgson, aka Lewis Carroll, was a professor of mathematical logic at Oxford.
Then we have Alan Turing’s school reports, wherein we find out tidbits like the fact that he did not do very well in Latin.
As for math class, in Michaelmas term of 1926, his teacher writes: Works well. He is still very untidy. He must try to improve in this respect. I can only comment that tidiness isn’t everything.
By 1930, he is improved enough in math that he gets this comment: A really able mathematician. His trouble is his untidiness & poor style, but he has tried hard to improve in this. He sometimes fails over a simple problem by trying to do it by complicated methods, instead of by an elementary one.
So there we have the first sign of genius: the simple methods of problem solving are too easy for Turing, and he has to try to find the harder methods — don’t just look at a clock to see what time it is, but take the clock apart to see how it works and see why it says the time that it does.
The books themselves
I love it when people get caught out trying to snow others with fake math references. Now it’s the turn of Herman Cain.
Finding out that [Herman] Cain was a math major gives me the same flush of embarrassment I get when I hear that a Jew did something bad. As for bamboozling people with mathematics, thats just an old creationist trick.
In mathematics you don’t understand things. You just get used to them.
In Hungary, winters can be long (so I’m assuming). Before television, intelligent Hungarians tried many different pastimes to make it through those dark days. One of these, János Bolyai, resorted to non-Euclidean geometry.
Bolyai wasn’t warning his son off gambling, or poetry, or a poorly chosen love affair. He was trying to keep him away from non-Euclidean geometry.
I myself tend to contemplate the Cantor Set, but that’s just me. This looks like a tempting book, though.
“Everyone fails a math test,” my tutor told me, after I had failed one. I found out, as time went on, that those words were not just a consolation but the truth.
Math, for the vast majority of us non-child-geniuses and prodigies, is very difficult. However, you simply have to get through it. You do the work, and eventually get to understand not only how to get the right answer, and get it in a timely, efficient manner, but why the right answer is right. The mechanics of it have been revealed to you on your much-erased piece of scratch paper. You can now use it to climb further into the series of riddles and mysteries that is math.
You also learn why the wrong answer is wrong. You learn what won’t work, and why.
And now it seems as though other people besides me and my fellow math students see the value in this approach of getting things wrong for a while.
via Scientific American…
For years, many educators have championed “errorless learning," advising teachers (and students) to create study conditions that do not permit errors. For example, a classroom teacher might drill students repeatedly on the same multiplication problem, with very little delay between the first and second presentations of the problem, ensuring that the student gets the answer correct each time.
The idea embedded in this approach is that if students make errors, they will learn the errors and be prevented (or slowed) in learning the correct information. But research by Nate Kornell, Matthew Hays and Robert Bjork at U.C.L.A. that recently appeared in the Journal of Experimental Psychology: Learning, Memory and Cognition reveals that this worry is misplaced. In fact, they found, learning becomes better if conditions are arranged so that students make errors.
People remember things better, longer, if they are given very challenging tests on the material, tests at which they are bound to fail. In a series of experiments, they showed that if students make an unsuccessful attempt to retrieve information before receiving an answer, they remember the information better than in a control condition in which they simply study the information. Trying and failing to retrieve the answer is actually helpful to learning. It’s an idea that has obvious applications for education, but could be useful for anyone who is trying to learn new material of any kind.
I have enjoyed my visits to the Wolfram Alpha website, and am fascinated by what it can do.
However, tonight I found out that it cannot compute everything. There are limits.
It took place very late at night, and I have brought along three books for my efforts and travels (steep staircases at midnight require extra bravado. The three books fought against the cobwebs as I did to, and we ended up with an exceptional group. :dance:
- “Structure and Interpretation of Computer Programs, Second Edition” (Harold Abelson, Gerald Jay Sussman, Julie Sussman
- Mathematics and its History.
- Principles of Mathematical Analysis, AKA “Little Rudin” because it’s a thinner book than professor Rudin’s book called Real Analysis, which also treats the ideas in it a little more thoroughly, and which I don’t own a copy of.
Dentist: uneventful. Only screamed once. But seriously, folks… nothing to report, and only reporting the nothing because I’d promised you all I would.
I am noticing a rhythm to the days now, for the first time since my operation a year ago this last March. It’s a good rhythm, one I haven’t had at least since I’d drop Peter off to grade school and head to my math classes at the University of Cincinnati, an even longer time ago.
Having a rhythm to your days is a gift. What that rhythm contains is up to you, but the simple gift of enough days to find a rhythm, that’s a gift.
And having good blog friends is a gift, too. :D
Other Patti, Our Friend Sally, and I have just watched two very different movies. One was the stalwart and canonical western, Red River, with John Wayne and Montgomery Clift and Walter Brennan. That was a very satisfying movie, with an actual cattle drive in the middle of it — had to be, the way they kept getting all of those shots. This movie, however, promises no conspiracies, and delivers on their promise.
But I put up the “conspiracies” title, and I’ll stick to it, because the second movie we watched was The Number 23 with Jim Carrey not doing any comedy bits, not even dark comedy like in The Truman Show. Itn was visually stunning, which was why I went along with it, and Other Patti and Our Friend Sally got into the conspiracy bit. But I figured it’s just tricks with mathematics — you can find a number anywhere you want, and mess around with it until it becomes what you want it to become. Then you declare yourself cursed by a prime number (which is actually not an entity in its own right) and there you go.