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Exponential Growth

Title text: Karpov's construction of a series of increasingly large rice cookers led to a protracted deadlock, but exponential growth won in the end.

Explanation

This explanation may be incomplete or incorrect: Created by an INFINITELY NESTED SET OF RICE COOKERS - Please change this comment when editing this page. No mention of the title text yet.

Exponential growth is the principle that if you keep multiplying a number by a value larger than 1, you will pretty quickly get very large numbers. Even if you start with 1 and simply double it each time, you'll have a 10-digit number after about 30 iterations.

This principle is often illustrated using the story "Game of Rice". A King of India wished to reward a man for creating a new game of Chess, and offered a wish. The man simply asked for a a single grain of wheat to be placed on the first square of a chessboard and that each day the next square have twice as many grains as the one before, until all 64 squares are filled. The king granted his strange request and ordered one wheat grain to be placed on the board. The second day two more pieces were placed on the square next to that and the day after four pieces on the next. However, by day 20 there was over 500,000 grains on the board. The king had to dig into his own stock pile to pay his dues. On day 24 the king owed 8 million grains. By day 32 the king owed over 2 billion pieces of grain, and had to give up. In some versions of the story the man is executed for embarrassing the king, in others, he's rewarded for his cleverness, in some even becoming King himself.

Since a chessboard contains 64 squares, the final square would contain 2^63 (approximately 9.2 quintillion) grains. This would be around 600 billion tonnes of wheat (even in modern times, this is more than 750 years of global wheat output). Worse, that's just for the final square -- adding up all the squares would require about double that (2^64-1 which is approximately 18.4 quintillion grains).

Instead of this being a (possibly apocryphal) story, Black Hat used it literally during a game of chess to annoy his opponent into quitting. Black Hat begins describing the metaphor, only to reveal it wasn't a metaphor at all. Black Hat had been playing actual Chess games, and tried to force his opponent to resign by burying the chess pieces in rice, as implied by the multiple large sacks bluntly labelled 'rice' on his side of the chessboard. This is not the first comic to feature large quantities of rice labelled in this manner - in 1598: Salvage, a gargantuan tank of rice has simply the word 'rice' written on the side in equally gargantuan capital letters.

Garry Kasparov is a world renowned Russian chess master. He had the highest FIDE chess rating in the world - one of 2851 points - until Magnus Carlsen surpassed that in 2013 by 31 points. The Kasparov gambit is an opening move in chess, a variation of the Sicilian Defense.

In 1984-85 Garry Kasparov played Anatoly Karpov in a 5-month-long 48-game championship tournament which was abandoned. In the 1984-85 match Kasparov was losing 4-0 with 6 wins being required to win. Kasparov proceeded to draw 35 times before the match was abandoned.

In a 1985 rematch, Kasparov defeated Karpov for the world championship title, which he retained in their next rematch in 1986.

There are several articles in the International Chess Federation (FIDE)'s Laws of Chess that might prevent Black Hat from winning in this way:

• 7.3 "If a player displaces one or more pieces, he shall re-establish the correct position (...). The arbiter may penalise the player who displaced the pieces."
• 12.1 "The players shall take no action that will bring the game of chess into disrepute."
• 12.6 "It is forbidden to distract or annoy the opponent in any manner whatsoever. (...)"

The amount of rice collected on each square of the chess board is listed below. It all sums up to around 400 billion tons (each grain weighing approximately 0.02 grams), or 500 times the annual world production. The last day would be 200 billion tons. But the implicit implication of this doubling is that the amount of rice you put on tomorrow is exactly equal to the amount of rice already on the board, plus one extra grain. So there were around 200 billion tons already, before the last square needs ~200 billion more.

• First row:
  • a1: 1 grain
  • a2: 2 grains
  • a3: 4 ...
  • a4: 8
  • a5: 16
  • a6: 32
  • a7: 64
  • a8: 128
• Second row
  • b1: 256
  • b2: 512
  • b3: 1,024
  • b4: 2,048
  • b5: 4,096
  • b6: 8,192
  • b7: 16,384
  • b8: 32,768

• First of each row

• • c1: 65,536 grains (~ 1 kg)
  • d1: 16,777,216 (~ 400 kg)
  • e1: 4,294,967,296 (~ 100 tons)
  • f1: 1,099,511,627,776 (~ 25,000 tons)
  • g1: 281,474,976,710,656 (~ 6 million tons)

• ...

• Eighth row
  • h1: 72,057,594,037,927,936 (~ 1.5 billion tons, more than the 2022 world harvest)
  • h2: 144,115,188,075,855,872
  • h3: 288,230,376,151,711,744
  • h4: 576,460,752,303,423,488
  • h5: 1,152,921,504,606,846,976
  • h6: 2,305,843,009,213,693,952
  • h7: 4,611,686,018,427,387,904
  • h8: 9,223,372,036,854,775,808 (~ 200 billion tons)

Example on chessboard (SVG diagram)

Transcript

This transcript is incomplete. Please help editing it! Thanks.

[Black Hat is talking to Cueball standing next to him, arm raised.]

Black Hat: Exponential growth is very powerful.

[Closeup on Black Hat. Next to him is an image of the lower left part of a chessboard. The four leftmost squares in the bottom row have grains of rice on them -- one, two, four, and eight grains respectively.]

Black Hat: A chessboard has 64 squares.

Black Hat: Say you put one grain of rice on the first square, then two grains on the second, then four, then eight, doubling each time.

[Black Hat has emptied a bag of rice on a chessboard. There are two additional bags next to him and a pile of rice already on the table. A small pile of rice is growing at Black Hat's feet. A frustrated Hairy is walking away, fists clenched. On Hairy's side of the chessboard there is a white King and Pawn]

[Caption above panel, representing Black Hat continuing to speak:]

If you keep this up, your opponent will resign in frustration.

It's called Kasparov's Grain Gambit. Nearly impossible to counter.

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