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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 a 2^64TH ITERATION OF A BOT - Please change this comment when editing this page. No mention of the title text yet.

In this strip Black Hat begins by demonstrating the exponential growth, using a variation of the 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.

The earliest versions of this story come from India and involve a man (the inventor of chess, in some tellings), who, being offered a reward by a king, asked that a single grain of wheat 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. Following this pattern the next day two pieces of wheat were placed on the second square, and four pieces of wheat the day after on the third. In the story, the king generally laughs off such a reward as being trivial, but soon learns that the reward would be impossible to pay. 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). 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.

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 Laws of Chess, this would be illegal on several levels, as deliberately distracting or annoying your opponent is 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.

Garry Kasparov and Anatoly 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.

Needless to say, this process would be impossible to do. ^{[citation needed]}

Transcript

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

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

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 (either a8, b8, c8, and d8 or h1, g1, f1, and e1) 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 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:]

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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