Kindle Notes & Highlights
as the contorted plan, enacted in 2011, that it was meant to replace. So the justices opted for the extraordinary measure of adopting an independent outsider’s plan.
HyperLogLog is one of the most elegant mathematical solutions for counting distinct objects in big data applications, widely used in practice.
Since nominalist philosophers question whether there are any numbers (on the grounds that, were there to be such things, they would have to be abstract— nonspatiotemporal, acausal, mind- and language-independent—to serve as appropriate truthmakers for the claims of standard mathematics), they see fit to question claims such as “2 + 3 = 5” precisely because they logically imply the existence of objects such as the number 2, which, they take it, may fail to exist (as in our finite domain example) even though the general claim “any two things added to any three further things make five things” is
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Their ideas have come to be called Kolmogorov complexity theory or algorithmic information theory. They posited that a string is as complex as the length of the shortest computer program that can produce the string.
While a computer might find some pattern in a string, it cannot find the best pattern. We might find some short program that outputs a certain pattern, but there could exist an even shorter program. We will never know.
The smallest number that cannot be described in less than 15 words. This number needs 15, or 16, or even more words to describe it. It cannot be described by 12 words, or 13 words, or 14 words. However there is a major problem: The above phrase described the number in only 12 words. Our description of the number violated the description of the number. This is a contradiction.
As we age and suffer from ennui, we gain certain insights about the universe that we did not see before. We find better patterns. Maybe we get to see things more clearly. Or maybe not. We will never know. But we do know that the search is guaranteed to never end.
