Wednesday, December 12, 2007

The Root Problem

The 13th root of a number is a figure that must be multiplied 13 times by itself to reach the original. For example, the 13th root of one is one, the 13th root of 8,192 is two, and of 96,889,010,407 is seven. the situation for a 200 digit number always begins with a two, whereas that for a 100 digit number always begins with a four. The 13th root of a number will usually have approximately one thirteen the number of digits of the original. So the 13th root of a 100 digit number has eight digits and that of a 200 digit number has 19 digits. There are more than 3.9 trillion possible solutions for the 13th root of a 200 digit number.

The above is taken from today's Telegraph. Yesterday Alexis Lemaire broke the world speed record for calculating the 13th root of a 200 digit number generated at random. He didn't use a calculator and finished the job in 70.2 seconds. Mr Lemaire is working on an artificial intelligence PhD at the University of Reims. His plan is to download the way his brain works to a computer programme. He calls this mind uploading. At last there may be someone who could master the formula by which National Assembly money is distributed to local authorities in Wales.

1 comment:

Dr. Christopher Wood said...

I haven't read that article, but even a stunted kid like me from a relatively poor family living in a council house realized that an easy way to calculate the root of most numbers is to have previously memorized the log tables, and the anti-log tables and be good at mental division. (E.g., the log of
8,192 is 3.9134 and dividing by 13 gets you 0.3010 - which any school kid brought up without a calculator worth his/her weight in mustard would know that .301 is the log of 2.

Anyways, … for some tricksters, once you know the log and antilog tables you can appear to have fantastic mental arithmetic skills and "make friends"; in BBC RED DWARF lexicon, "... be a genius again". You will learn that certain log numbers have a form, a form that can burst organs, smash balls and stop Gordon Brown in his tracks (OK, a line mutated from Frank Herbert’s DUNE).

At a stroke you will be able to work out power numbers, divide big numbers just by converting the number to a log number, performing a subtraction, and antiloging and vola, the answer in around 5 seconds, but stretch it out to 20 seconds with various facial contortions to add drama and other things and you will earn pats on the back from morons and evil stares from real mathematicians).

I can write the code to do this in less than a paragraph of computer code, so why even bother with the Telegraph geni-ass?