There is an exceedingly simple proof that 1 + 2 + 4 + ... to the 64th term equals 264 - 1. Count in binary! Then you're going:
1 = 12
1+2 = 112
1+2+4 = 1112
...etc. So you end up with a string of 64 consecutive 1s. If you now added 1 to the total you would get the answer "0 and carry 1" all the way from the right to the left, making your answer 1 followed by 64 zeroes, that is 264. Hence 64 consecutive binary 1s = 264 - 1. If you want an approximate value for your answer then you need to know that 210 = 1000 to within 2.5%, so 220 = 1,000,000, 260 = 1,000,000,000,000,000,000, and 264 = 16,000,000,000,000,000,000 (or a little bit more. As long as you're getting all the gold in the universe, why quibble over loose change?). Of course, any of Hex's cheap Roundworld counterparts will do the exact calculation for you in less time than it takes Nobby Nobbs to lift your valuables.
--Captain Pedant 18:43, 4 September 2011 (CEST)
And what is the gold content of seawater?
Clever chemists have estimated that:-
To illustrate this point, it can be calculated that the oceans contain 8 x 106 tons of dissolved gold (value: about $1.1 x 1014) even though the gold content of sea water is only 6 x 10-14 % by weight.
Let's see if I've got this right: in a litre of sea water, weighing approximately just over one kilogram, the actual weight of gold content would be 0.0000000006 of a gram.
If a typical "gold-coloured coin" might weigh in at say 100grams, this would make the gold content by comparison 0.000000006g. Or less than might accidentally get in there during the smelting and refining processes of related base metals, , suggesting somebody has been conscientiously extracting the residual gold content...
Can it be extracted? Currently, not worth it:-
Although the dissolved gold content is not evenly distributed in the world's oceans - it is indicated that the seas around Japan and Alaska and the general North Pacific region have ten times more than elsewhere, suggesting major sub-oceanic deposits are there to be mined. (Dwarfs will make major contributions to submarine mining technology?)
Also, some species of marine lifeforms, mainly bacteria but going as high up the chain as some sponges, appear to preferentially harvest gold from seawater and retain it. Experiments, we are told, are proceeding...--AgProv 14:07, 5 September 2011 (CEST)
- At least on Roundworld, the idea is becoming more attractive. The source seemed to be using a 1980s gold price of $472 an ounce; at the recent $1886 those 8 million tons become $4.39 X 1014. I don't think you could call a 100g coin "typical"; it sounds like a Rhinu. --Old Dickens 16:04, 5 September 2011 (CEST)
It seems likely that there may be more gold in Discworld seawater that Roundworld sea water, mainly because of gold dissolved from the counterweight continent. --Confusion (talk) 01:46, 19 December 2013 (GMT)