Everything about Second Half Of The Chessboard totally explained
In
technology strategy, the
Second Half of the Chessboard is a phrase, coined by
Ray Kurzweil, in reference to the point where an
exponentially growing factor begins to have a significant economic impact on an organization's overall business strategy.
The term is derived from the fable of an
ancient Indian mathematician who according to the fable invented the game of chess. The emperor of India is so pleased with the game that he tells the mathematician he may have anything in his kingdom he wishes. The mathematician replies that he only asks for a meek amount of rice placed on the squares of his chessboard: one grain of rice on the first square, two for the second, four for the third
et cetera. Each successive square would have grains of rice double the number of the prior square until all 64 squares of the chessboard have had their said amounts.
(External Link
)
It turns out that while the amount of rice on the
first half of the chessboard is very large but economically viable for the emperor of India to provide, the amount on the
second half is so vastly larger that it would be impossible for any emperor, or even the entire world, to provide it.
Specifically, the total number of grains of rice on the
first half of the chessboard is 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 ... + 2,147,483,648, for a total of exactly 2
32 − 1 = 4,294,967,295 grains of rice, or about 100,000 kg of rice, with the mass of one grain of rice being roughly 25 mg
(External Link). This total amount is about 1/1,200
th of total rice production in India per annum (in 2005)
(External Link).
The total number of grains of rice on the
second half of the chessboard is 2
32 + 2
33 + 2
34 ... + 2
63, for a total of 2
64 − 2
32 grains of rice. On the 64th square of the chessboard alone there would be exactly 2
63 = 9,223,372,036,854,775,808 grains of rice, or more than a billion times as much on the entire first half of the chessboard. (For comparison
Archimedes, addressing
King Gelon of
Syracruse in
The Sand Reckoner, estimated that 10
63 ... or approximately 2
66 ... grains of
sand would fill the entire universe)! Current estimates of the number of
particles in the observable
universe vary from about 10
72 to around 10
87).
In total, on the entire chessboard there would be exactly 2
64 − 1 = 18,446,744,073,709,551,615 grains of rice.
Further Information
Get more info on 'Second Half Of The Chessboard'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://second_half_of_the_chessboard.totallyexplained.com">Second Half of the Chessboard Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
