Cosmological Koans by Anthony Aguirre

Author:Anthony Aguirre
Language: eng
Format: epub, mobi
Publisher: W. W. Norton & Company
Published: 2019-03-14T16:00:00+00:00

Our minds are quite good at understanding small numbers like 3 and 46: we can crisply picture 3 objects, and we have a clear, if hazy, sense of what 46 of pretty much anything looks like. When confronted with numbers in the millions or billions, we can achieve some comprehension by imagining comparisons such as fine grains of sand in a glass (about a million) or a swimming pool (a trillion or more), or—at a stretch—mustard seeds in a 10-km cubic volume (about 1020). But we are quite helpless when it comes to a number like 10120, let alone 1010120, which are the sorts of numbers that can arise when we are discussing the possibility space of physical systems in our universe.

Such vast yet meaningful numbers easily arise combinatorially—when there are many factors in combination, each of which can take on many values. In a lottery we might have 6 balls of 40 possible values each, giving 406 (about 4 billion) possibilities. A game of chess has many moves, with many possibilities each; Claude Shannon estimated 10120 possible sequences of them. Similarly, a half hour of playing the Tibetan game of Sho could entail about 120 rolls of two dice, thus at least 12120 possible games. As asserted to the monk, a game in which the dice are rolled once per thousand years would take about 105 years, and only after about 105 × 12120 ≈ 10134 years would the game start to be genuinely repetitive, all possible sequences having been run through about once, on average. But that’s an incredibly long time. Compared to this, the age of the observable universe—about 1010 years—would be inexpressibly evanescent. The timescale is so long that we need new words for it. Following the Buddha, let’s denote by kalpa any of these superlong timescales, like 10(some two-or-more-digit integer) years.

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