English Chess Forum

Does anyone have any practical examples of using base numbers? Base 2 is binary - computers easy.
Base n?

Mr Sad

Hexadecimal is also used in computers, most notably graphics displays

Many years ago, when programming in machine code, it was useful to know how to use base 4, base 8 and base 16, the grandly named hexadeximal, was all but essential.

Lots of things are still bought and sold in dozens. Eggs for instance.

I understand base 24 and base 60 are used every day . An explanation of base 60 is that there are 12 sections on the fingers and folding the fingers on the other hand allows you to count 5 lots of 12. This method may have been used by shepherds during Roman times.

Again I seem to remember that base 60 came from the Babylonians, look how many factors it has.
A pupil stumped me years ago by asking why we had 60 minutes in an hour and 60 seconds in a minute, and I had no idea.
A little research then revealed that the name came from the Latin when the Romans, who seemed to hoover up everything, called the divisions 'pars minutiae' and 'pars secundus'.
Also used in geometry, minutes and seconds of arc.

One interesting point is that say the dozen 12 base: 13 doesn't exist so this would = 10

So if you ask for a bakers dozen you get 10 though end up with 13 dernary rolls.

From horse racing we use bases 220, 8 and 105.

How about base 92,955,807.27? I haven't used this one since yesterday.

Gavin Strachan wrote:One interesting point is that say the dozen 12 base: 13 doesn't exist so this would = 10

So if you ask for a bakers dozen you get 10 though end up with 13 dernary rolls.

actually, in base 12, 13 would be written as 11. 12 is 10

I seem to recall reading somewhere that counting in twelves had greater practical use than tens because 12 could be split into more whole numbers than 10. Three quarters of 12 is 9, half of 12 is 6, one third is 4, a quarter is 2, and a sixth is 2. Try that with 10!

Hex is amazing because 16 is both 2^4 and 4^2 and as far as I know, no other number has this property, for instance 2^3 <>3^2 this probably makes 16 very special!

Usually you work out the nth number of pi by knowing its previous value, ie you have to work out all the previous values of pi to know the nth value of pi, there is an equation to work out the nth term of pi without knowing its previous value. Here is the kicker it only works in hex!

Plouffe formula

It gets better - there are 20 different amino acids constructed from a base four arrangement ACTG, 4^3 = 64, 64 = 16 X 2 X 2.

Where this starts to get interesting is when we consider morphogenesis, ie start out with one cell and end up with elephants, understanding the mathematics of morphogenesis, in the context of genetics, will teach us the mathematics of life.

And explain why most chess players are useless at explaining themselves

Times tables are much easier in base 12

multiples of 3
3 6 9 10 13 16 19 20 23 26

multiples of 4
4 8 10 14 18 20 24 28

multiples of 6
6 10 16 20 26 30

multiples of 8
8 14 20 28 34 40

multiples of 9
9 16 23 30 39 46 53

multiples of ten, eleven, twelve and thirteen also follow nice sequences

You can add Crash Dumps and Symmetrix Device ID's (http://en.wikipedia.org/wiki/EMC_Symmetrix) to your list of practical examples in Hex.

And of course 6 x 9 = 42 (base 13)