Comments on: The Cute to its Roob

By: Benjamin Nelson

Benjamin Nelson — Sat, 29 Jul 2006 02:53:32 +0000

Molly (#12), you could do that, if people named their discoveries plainly. But they don’t, so you can’t.

By: chris y

chris y — Thu, 27 Jul 2006 09:17:28 +0000

#19 How true. See, when I was 8 and had never heard of algebra, I wouldn’t have made that error.

By: eudoxis

eudoxis — Thu, 27 Jul 2006 00:43:21 +0000

That reminds me of a Vedic Math book I recently picked up. 16 sutras! The problem with the nifty tricks is that they work for a great many numbers, but not all numbers.

It’s an odd phenomenon that when a particular problem has been solved it seems to be easier for subsequent generations to solve. It’s almost as if a new piece of information has been added to the Platonic universe, now accessible to all.

Not to diminish the fun tricks that people come up with, but students of mathematics go through the derivations of ancient mathematical discoveries on their own all the time. Remember geometry and the Euclidian ideas you had to discover on your own? My son is presently at a number theory camp where, on a daily basis, the students are asked to derive proofs based on, often, unfamiliar material. There’s some rumbling of the “I’m not Gauss” sort, but the students do come up with the proofs. Once the 3 minute mile is broken, the 3 minute mile is easy to run.

By: BruceR

BruceR — Wed, 26 Jul 2006 19:47:37 +0000

#8, you’re missing a “-1”, I believe.

By: J. Ellenberg

J. Ellenberg — Wed, 26 Jul 2006 16:26:52 +0000

I once had a calculus student who had thought quite hard about the meaning of infinitesimals, and had in some sense independently arrived at the conclusion that nonstandard analysis could be interesting. He called his infinitesimals “Brian numbers,” after himself. So I set up a meeting between him and the person in our department who knew nonstandard analysis. Unfortunately, once Brian found out that others had walked the path before him and that “Brian numbers” was not going to become standard notation, he lost all interest.

By: pdf23ds

pdf23ds — Wed, 26 Jul 2006 16:13:31 +0000

The ambiguity is caused be the alternate interpretation that “as long as they’re whole numbers” applies only to the cubed number.

By: Henry

Henry — Wed, 26 Jul 2006 15:20:38 +0000

Your essential disclaimer “as long as they’re whole numbers” needs to be clearer; namely, that it applies both to the cube root and the “quite large sounding number”.

But surely any number that has a whole number as a cube root is itself ipso facto a whole number???

By: Jeffrey

Jeffrey — Wed, 26 Jul 2006 15:14:12 +0000

Your essential disclaimer “as long as they’re whole numbers” needs to be clearer; namely, that it applies both to the cube root and the “quite large sounding number”.

For example, try applying your method to the number 207,646. Your method gives an answer of 56, whereas the real answer is 59.2162893.

By: kharris

kharris — Wed, 26 Jul 2006 14:54:51 +0000

I think Belle has the key to Chris Y’s question. Kids do the same operation over and over. In those repetitions, kids have the opportunity to see patterns if they exist. Later in life, we use intermingle various operations. Less opportunity to recognize patterns. Could Wolfram’s assertion of a “discovery” be “youthful” in a similar sense? Seeing things that other have seen, but not knowing that others have seen them?

By: coujou

coujou — Wed, 26 Jul 2006 12:58:23 +0000

Here is a method to calculate cube roots of 9 digit numbers. I didn’t “discover” it myself (except if you count finding the web page as a discovery).

http://www.1729.com/blog/CubeRoots.html

By: mollymooly

mollymooly — Wed, 26 Jul 2006 12:41:13 +0000

Number 5: “not knowing whether or not the ideas you have are truly original or not”. Wouldn’t it be great if there was a way to find out? A kind of “engine” for “searching” some vast repository of knowledge? Gee, I think I’m on to something here…

By: Jacob T. Levy

Jacob T. Levy — Wed, 26 Jul 2006 12:30:46 +0000

My third-grade pattern discovery was squares and odds:

n^{2 + (2n+1) = (n+1)}2

not that I knew the notation at the time, or how to prove it algebraically; I just wrote down lots of square numbers in a sequence down one side of the page, and the sequence of odd numbers down the other side and finding that the gaps between sequential squares were sequential off numbers. I was ver excited, but nothing seemed to follow from it, and there was no one around to show me how to abstract it into the algebraic form.

By: chris y

chris y — Wed, 26 Jul 2006 12:24:42 +0000

I imagine if I had to do 20 long division problems a night for a while it might come back to me.

Or you could use the calculator on your PC, which is why nobody under 25 can do arithmetic any more.

[Disclaimer: if Belle is in fact in her teens, I apologise fulsomely]

By: Belle Waring

Belle Waring — Wed, 26 Jul 2006 12:16:24 +0000

when I was 10 I “discovered” short division because I was tired of writing out long division. my teacher wasn’t very happy about it because I wasn’t showing my work. I’ve completely forgotten now, but I imagine if I had to do 20 long division problems a night for a while it might come back to me.

By: chris y

chris y — Wed, 26 Jul 2006 10:49:45 +0000

I get the impression that small kids do this a lot. I had several blinding “insights” about numbers when I was 7 or 8 which came down to using pattern recognition to solve simple equations. A number of my friends used to do the same sort of thing.

I wonder if children are innately better at seeing such patterns than most adults[e.g. “Daddy, if you multiply a number by itself it’s always one more than if you multiply the number below it by the one above it” : n^2 = (n-1) * (n+1)]. Are competent mathematicians the people who don’t lose this ability in later life? And why do the rest of us not keep it?