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by __MatrixMan__
763 days ago
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The acronyms refer to: https://en.wikipedia.org/wiki/Busy_beaver https://en.wikipedia.org/wiki/Ackermann_function As I understand it, the game around functions like this is to get as close to infinity as you can, but not quite, and then to try to uncover properties about what you find there. I'm under the impression that it's a certain kind of fun because the results are all way too large to work with computationally, so rather than comparing the values (which you can't calculate directly) you have to reason about the various algorithms that yield them. That's all I got. The gust of the post is greek to me. I wish I had more computer science and less software engineering under my belt. Then maybe this could be my kind of fun too. |
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In this case, we can actually name the number of symbols in terms of Knuth's up-arrow notation [0], which describes the sequence of operations starting with multiplication, exponentiation, repeated exponentiation (called tetration, e.g., 2↑↑5 = 2^[2^[2^[2^2]]]), repeated tetration (called pentation, e.g., 2↑↑↑5 = 2↑↑[2↑↑[2↑↑[2↑↑2]]]), and so on. This number is big enough that it needs 15 arrows in a row to describe it reasonably. So it's not just that the number is very large, it's that we can also put a neat lid over its value. For instance, we know it's still nothing compared to Graham's number, which can't be described with any reasonable number of up-arrows.
[0] https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation