13th root of 9.1474397281474512894e199

[CurtC]

From the article http://news.yahoo.com/s/afp/20071211/od_afp/britainsciencerecordoffbeat;_ylt=Apc9AFJwYbRd8SkGS .BVm_oDW7oF
The world's fastest human calculator on Tuesday broke his own record for working out [the 13th root of] a 200-digit number using nothing but brain power to produce the answer in just over 70 seconds.

What technique does he use for this? Why specifically the 13th root - is there some shortcut? I thought at first that maybe there are only a few thousand possibilities for integers that produce a 200-digit 13th power, but I get something like 394 trillion of them.

ETA: oops, I should have titled the thread the 13th root of 9.1474397281474512894e199.

[Paul C. Anagnostopoulos]

As you wish.

[Fnord]

== 2,407,899,893,032,209.9999983726638087

[BenBurch]

It seems you can learn to do things like this; http://mathforum.org/dr.math/faq/faq.trachten.html

[boooeee]

It's possible that he used Newton's method. All it takes is a good initial guess.

If he's that good, he could probably come up with an initial guess of 2.4E+15 without too much work. After that, it takes about 3 or 4 iterations of Newton's method to get to his answer down to the nearest integer (which is apparently how the problem was stated). Each iteration involves taking powers of 12, powers of 13, and long division (plus some easy additions and subtractions). Definitely not trivial when you're taking a 15 digit number to the 13th power, but it seems possible for a savant calculator, within the timeframe.

There may be better tricks, but from my understanding, Newton's method converges pretty fast for this kind of problem.

[T-Diddy]

That's nothing. I read an article about an Autistic guy who learned Norwegian in a week and went over there and recited pi for several hours by calculating it in his head. He could pretty much go on forever.

[bokonon]

He wasn't calculating pi, he'd memorized it (to 20,000 places, if I recall correctly). And, he wasn't autistic.

[nimzov]

He wasn't calculating pi, he'd memorized it (to 20,000 places, if I recall correctly). And, he wasn't autistic.
You both are right. Some autistic (Daniel Tammet) and some non-autistics (Simon Plouffe, Haraguchi) persons have memorized thousands of pi decimals.

Was discused here:

http://forums.randi.org/showthread.php?t=76440&highlight=tammet&page=2

nimzo

[BenBurch]

Anybody can learn to estimate the result, thats not an issue at all

You only need to memorize 100 numbers, the base-10 logarithms to two places.

9.1 is .9590 add the magnitude and its is 199.9590 divide by thirteen and you have 15.3814 .3814 is just over 2.4 so, 2.4*10^15

Which I certify to you is good enough for most physics or engineering estimation.

And about as good as you could do on a slide rule.