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Those problems always bothered me. I think that for any sequence of numbers there is an infinite number of next-in-sequence solutions regardless of the sequence
by mtreis86 8y ago
Those problems always bothered me. I think that for any sequence of numbers there is an infinite number of next-in-sequence solutions regardless of the sequence length or numbers contained. One may be more obvious but you can put any number next and find a pattern that matches. Example - what if those are a sequence of digits in pi.
- cabaalis 8y agoI think "What comes next?" is an incomplete question, without any context. "What comes next in the sequence of (blah)?" is a complete question with full context. But that question wouldn't make anybody feel superior. "Identify as many sequences as you can which fit this set of numbers, and tell me the next number in each sequence" is the non-trick actually being asked.
- jameshart 8y agoI think the only sane approach is to apply a Kolmogorov-shaded Occam's Razor, and select, from the set of possible sequences which fit the pattern, the one which has the simplest generating function.
- CamperBob2 8y agoThat can be tricky in itself, though. 1, 2, 3, 4, .... might be a sequence of positive integers, or it might be a subset of pseudo-random digits emitted by a maximal-length shift register sequence. Someone recently pointed out to me that if you were designing hardware to (e.g.) refresh all memory locations in a system, or otherwise visit a set of 2^n sequential locations in no particular order, then using a maximal-length shift register of the appropriate width is actually simpler than a 'simple' adder or subtractor. That could be seen as a literal interpretation of Kolmogorov complexity.