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| | ==Explanation== | | ==Explanation== |
| | + | {{incomplete|Created by a 2^64TH ITERATION OF A BOT - Please change this comment when editing this page. Do NOT delete this tag too soon.}} |
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| − | In this strip Black Hat begins by demonstrating the {{w|exponential growth}}, using a variation of the {{w|wheat and chessboard problem}}, a classic demonstration of this mathematical principle. Exponential growth involves an initial quantity being multiplied by any number greater than one again and again. It can cause small numbers to compound into very large numbers faster than might be intuitive. This principle is important in a number of real life applications, ranging from biological growth to inflation to reaction kinetics.
| + | {{w|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. |
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| − | This principle is often illustrated using a story that generally follows the narrative of a king of India (or elsewhere) wishing to thank a man for creating the game of {{w|chess}}, or perhaps some other chess-related service, and asked him to name his own reward. The man asks for a single grain of wheat (or, in some versions, rice) to be placed on the first square of a chessboard, and then for each subsequent square adding twice as many grains as the one before, until {{w|Wheat and chessboard problem|all 64 squares are filled}}. The king grants his strange request and immediately orders one wheat grain to be placed on the board, imagining this to be a trivial gift compared to the vast riches he had expected to be asked for. For the second square two more pieces are placed, and the square after has four pieces (the tale usually involves waiting a day between each placing of grains, delaying the unravelling and subsequent outcome of the story). However, by the 18th iteration, there are over 500,000 grains on the board in total and the king has to dig deep into his supply to continue to pay his dues. On the 23rd the king finds he owes more than 8 million additional grains. By the 32nd, the king finds himself owing over 4 billion grains (assuming he has come up with the almost equal amount summed up in the 31 previous iterations) and has to give up, realising the essential impossibility of the task. | + | 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 told him that he'd grant any wish. The man simply asked for a {{w|Wheat and chessboard problem|grain of wheat to be placed on a chess board and for it to double with each square on the board each day.}} 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, at this point he had to give up and offered the man another prize. |
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| − | In some versions of the story, the man is executed for embarrassing the king/being over-greedy; in others, he's rewarded for his cleverness; in yet others he becomes king himself as a consequence. There are also other versions that [https://www.comedy.co.uk/radio/finnemore_souvenir_programme/episodes/7/5/ subvert the well-known tale] by the king not being so naïve as to fall for the 'trick' played by the creator of the problem.
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| − | [[Black Hat]] initially appears to be using this example (with rice, rather than wheat), to demonstrate a mathematical principle, but actually turns out to be using it to "win" a chess match by covering the chess board in rice until his opponent quits out of frustration. Naturally, despite his claims that it's "nearly impossible to counter", under the International Chess Federation (FIDE)'s [https://www.fide.com/FIDE/handbook/LawsOfChess.pdf Laws of Chess], this would be illegal on several levels, as deliberately distracting or annoying your opponent is a violation, as is deliberately displacing the chess pieces. Black Hat being Black Hat, he likely simply doesn't care, and counts it as a win when his opponent stomps off out of annoyance.
| + | 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. |
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| − | {{w|Garry Kasparov}} and {{w|Antoly Karpov}} are both Russian chess grandmasters and former world champions. The two men famously competed for the world championship in the 1980s. The Kasparov gambit is an opening move in chess. The title text implies that Kasparov actually tried this method on Karpov, who attempted to consume all the rice with "increasingly large rice cookers", but eventually couldn't keep up. While this is obviously fictional, it fits with the principle of exponential growth. If exponential growth is unrestricted, it will eventually grow beyond the constraints of anything that could plausibly be built to contain it. | + | {{w|Garry Kasparov}} is a world renowned Russian chess master. He had the highest FIDE chess rating in the world-one of 2851 points-until {{w|Magnus Carlsen}} surpassed that in 2013 by 31 points. The Kasparov gambit is an opening move in chess. |
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| − | In any case, it appears that in his enthusiasm to enact his scheme, Black Hat has neglected to even set up his own pieces (or they have already been completely buried), never mind wait for the game to commence, so his opponent has nothing to resign from - indeed his king still appears to be standing as he walks away. | + | In 1984-85 Garry Kasparov played {{w|Anatoly Karpov}} in a 5-month-long 48-game championship tournament which was abandoned. In the 1986 rematch Garry Kasparov retained his world championship title. |
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| − | ==Math==
| + | In the 1984-85 match Kasparov was losing 4-0 with 6 points being required to win. Kasparov proceeded to draw 35 times before the match was abandoned. |
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| − | The amount of rice collected on each square of the chess board is listed below. It all sums up to around 400 billion tons (or {{w|tonne}}s, the various distinctions being not so important), taking each grain as weighing approximately 0.02 grams. This is 500 times the annual world production.
| + | Instead of this being a (possibly apocryphal) story, [[Black Hat]] used it literally during a game of chess to annoy his opponent into quitting. |
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| − | The last day, alone, would require 200 billion tons. But the implicit nature of this doubling is that the amount of rice you put on at any stage 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 required a virtually identical additional amount.
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| | * First row: | | * First row: |
| − | ** a1: 1 grain | + | ** a1: 1 |
| − | ** a2: 2 grains | + | ** a2: 2 |
| − | ** a3: 4 ... | + | ** a3: 4 |
| | ** a4: 8 | | ** a4: 8 |
| | ** a5: 16 | | ** a5: 16 |
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| | ** b7: 16,384 | | ** b7: 16,384 |
| | ** b8: 32,768 | | ** b8: 32,768 |
| − | * First column of third to seventh rows | + | : |
| − | ** c1: 65,536 grains (~ 1 kg) | + | * First of each row |
| − | ** d1: 16,777,216 (~ 400 kg) | + | : |
| − | ** e1: 4,294,967,296 (~ 100 tons) | + | ** c1: 65,536 |
| − | ** f1: 1,099,511,627,776 (~ 25,000 tons) | + | ** d1: 16,777,216 |
| − | ** g1: 281,474,976,710,656 (~ 6 million tons) | + | ** e1: 4,294,967,300 |
| − | * Eighth row, in detail | + | ** f1: 1,099,511,630,000 |
| − | ** h1: 72,057,594,037,927,936 (~ 1.5 billion tons, more than the 2022 world harvest) | + | ** g1: 281,474,977,000,000 |
| − | ** 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 | + | * Eighth row |
| − | ** h6: 2,305,843,009,213,693,952 | + | ** h1: 72,057,594,040,000,000 |
| − | ** h7: 4,611,686,018,427,387,904 | + | ** h2: 144,115,188,100,000,000 |
| − | ** h8: 9,223,372,036,854,775,808 (~ 200 billion tons) | + | ** h3: 288,230,376,200,000,000 |
| − | * Total: 18,446,744,073,709,551,615
| + | ** h4: 576,460,752,300,000,000 |
| − | | + | ** h5: 1,152,921,505,000,000,000 |
| − | [https://upload.wikimedia.org/wikipedia/commons/e/e7/Wheat_Chessboard_with_line.svg Example on the chessboard (SVG diagram)]
| + | ** h6: 2,305,843,009,000,000,000 |
| | + | ** h7: 4,611,686,018,000,000,000 |
| | + | ** h8: 9,223,372,037,000,000,000 |
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| | ==Transcript== | | ==Transcript== |
| − | | + | {{incomplete transcript|Do NOT delete this tag too soon.}} |
| − | :[Black Hat is talking to Cueball standing next to him, arm raised.] | + | :[Black Hat is talking to Cueball standing next to him.] |
| | :Black Hat: Exponential growth is very powerful. | | :Black Hat: Exponential growth is very powerful. |
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| | :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: Say you put one grain of rice on the first square, then two grains on the second, then four, then eight, doubling each time. |
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| − | :[Black Hat has emptied a bag of rice on a chessboard. There are two additional bags next to him, each labeled "Rice", and a pile of rice already on the table. Some rice has spilled off, and 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] | + | :[Black Hat has emptied a bag of rice on a chessboard. There are several bags next to him and a pile of rice already on the table. A frustrated Hairy is walking away, fists clenched.] |
| | :[Caption above panel, representing Black Hat continuing to speak:] | | :[Caption above panel, representing Black Hat continuing to speak:] |
| | :If you keep this up, your opponent will resign in frustration. | | :If you keep this up, your opponent will resign in frustration. |
