## Second half of the chessboard[edit]

#
In technology strategy, the "second half of the chessboard" is a phrase, coined by Ray Kurzweil,^{[6]} in reference to the point where an exponentially growing factor begins to have a significant economic impact on an organization's overall business strategy. While the number of grains on the first half of the chessboard is large, the amount on the second half is vastly (2^{32} > 4 billion times) larger.
The number of grains of wheat on the first half of the chessboard is 1 + 2 + 4 + 8 + ... + 2,147,483,648, for a total of 4,294,967,295 (2^{32} − 1) grains, or about 279 tonnes of wheat (assuming 65 mg as the mass of one grain of wheat).^{[7]}
The number of grains of wheat 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. This is equal to the square of the number of grains on the first half of the board, plus itself. The first square of the second half alone contains more grains than the entire first half. On the 64th square of the chessboard alone there would be 2^{63} = 9,223,372,036,854,775,808 grains, more than two billion times as many as on the first half of the chessboard.
On the entire chessboard there would be 2^{64} − 1 = 18,446,744,073,709,551,615 grains of wheat, weighing about 1,199,000,000,000 metric tons. This is about 1,645 times the global production of wheat in 2014 (729,000,000 metric tons).^{[8]}

^{[6]}in reference to the point where an exponentially growing factor begins to have a significant economic impact on an organization's overall business strategy. While the number of grains on the first half of the chessboard is large, the amount on the second half is vastly (2

^{32}> 4 billion times) larger.

^{32}− 1) grains, or about 279 tonnes of wheat (assuming 65 mg as the mass of one grain of wheat).

^{[7]}

*second*half of the chessboard is 2

^{32}+ 2

^{33}+ 2

^{34}+ ... + 2

^{63}, for a total of 2

^{64}− 2

^{32}grains. This is equal to the square of the number of grains on the first half of the board, plus itself. The first square of the second half alone contains more grains than the entire first half. On the 64th square of the chessboard alone there would be 2

^{63}= 9,223,372,036,854,775,808 grains, more than two billion times as many as on the first half of the chessboard.

^{64}− 1 = 18,446,744,073,709,551,615 grains of wheat, weighing about 1,199,000,000,000 metric tons. This is about 1,645 times the global production of wheat in 2014 (729,000,000 metric tons).

^{[8]}

## Use[edit]

#
Carl Sagan titled the second chapter of his final book *The Persian Chessboard* and wrote that when referring to bacteria, "Exponentials can't go on forever, because they will gobble up everything."^{[9]} Similarly, *The Limits to Growth* uses the story to present suggested consequences of exponential growth: "Exponential growth never can go on very long in a finite space with finite resources."^{[10]}

*The Persian Chessboard*and wrote that when referring to bacteria, "Exponentials can't go on forever, because they will gobble up everything."

^{[9]}Similarly,

*The Limits to Growth*uses the story to present suggested consequences of exponential growth: "Exponential growth never can go on very long in a finite space with finite resources."

^{[10]}

# According to Nassim Taleb, in 2009, the banking sector lost in 18 months all the profits it ever made since the beginning of banking. Is this true?

This question previously had details. They are now in a comment.

5 Answers

you requested help to find good data: The National Information Center(NIC)

and EDGAR | Search Tools maybe are not the most easy to search webs, but the info is in there (you need to process it a little bit)

doublingis approximatelyequalto the sum ofallthe preceding growth!´´My researches have lead me to the Exponential Function. and Doubling TimesThe notion of doubling time dates to interest on loans in Babylonian mathematics. Clay tablets from circa 2000 BCE include the exercise "Given an interest rate of 1/60 per month (no compounding), come the doubling time." This yields an annual interest rate of 12/60 = 20%, and hence a doubling time of 100% growth/20% growth per year = 5 years.[1] [2] Further, repaying double the initial amount of a loan, after a fixed time, was common commercial practice of the period: a common Assyrian loan of 1900 BCE consisted of loaning 2 minas of gold, getting back 4 in five years,[1] and an Egyptian proverb of the time was "If wealth is placed where it bears interest, it comes back to you redoubled."[1][3]https://en.wikipedia.org/wiki/Doubling_time.

I have found a paper that researching money supply growth in the US, Japan and Germany states a doubling time of between 8 and 10 years. If Money supply growth doubles in 10 years then that is roughly equivalent to all money supply combined in previous periods. looked at it this way it is easy to see how a catastrophic collapse after a particularly large boom in money supply and hence Bank profits would cancel out all previous profit. I think it will take rather longer to reduce the notion back down to some empirical data but it does exist albeit used to demonstrate other concerns on money supply mainly regarding inflation and not the consequences of debt.