Sunday, June 8, 2008

Millions of Billions

Another nerd post about Doctor Who.

The two most recent episodes of Doctor Who make some remarks about the number of non-human lifeforms. As the doctor says, there are "[over] a million million" entities on the planet.

A million million?

Clearly, he means, over 1012, or, 1000 000 000 000. And yet, in the previous episode, he refers to 109 as being a "billion", clearly following the American example. As such, why is it that he can't remain consistent and therefore refer to 1012 as being a trillion?

Or perhaps, the point of contention that Doctor Who is a [British] BBC production, and should therefore use traditional UK English as opposed to American English (also known as reformed British. They've also since ammended certain orthographical conventions like the single/double quotes, and connexion/connection). In which case, 109 should be "a thousand million", and 1012 should be "one billion".

The geek/mathematician in me demands that the great Doctor Who be at least consistent in his numbers! >.<

As point of reference, the traditional UK system of numbers works as follows:

106 = million
109 = thousand million
1012 = billion
1015 = thousand billion
1018 = trillion
Therefore, X-illion = 106x

For some reason, however, the Americans decided that "a thousand million" didn't sound nice enough, and decided to push up the use of prefixes, thus making there numbers significantly smaller. So in the American version:

106 = million
109 = billion
1012 = trillion
1015 = quadrillion
1018 = quintillion
So, for America, X-illion = 103(x+1)

Incidentally, the number system in East Asia, namely that used in China, Korea and Japan, goes by groups of 4s, or "myriads" (after the archaic Greek number "myriad" for 10000). Unfortunately, like most Chinese innovations, these namings aren't very productive; they don't really generate subsequently large numbers, since their names aren't derived from numbers themselves. But the cool part means that each number is named uniquely, and apparently from Buddhist sutra. Thus:

104 = man (萬)
108 = oku (億)
1012 = chou (兆)
1016 = kyou (京)
1020 = gai (垓)
1024 = shi (秭)
1028 = jou (穣)
1032 = kou (溝)
1036 = kan (澗)
1040 = sei (正)
1044 = sai (載)
1048 = goku (極)
1052 = kougasha (恒河沙)
1056 = asougi (阿僧祇)
1060 = nayuta (那由他)
1064 = fukashigi (不可思議)
1068 = muryou (無量)
1072 = taisuu (大数)

Fun stuff, eh? :D

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