Talk:Taxicab distance: Difference between revisions

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== Equilateral? ==

"Taxicab distance" sounds underspecific since it only states that the lattice is traversed in a "Manhattan/taxicab" manner, without any information on the length. I recommend adding "equilateral" to fully describe this kind of distance. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:27, 26 February 2023 (UTC)

: I believe that taxicab distance implies a length of 1 on every prime when it says the "number of primes". For comparison, [[Wilson height]] (sum of prime factors with repetitions) works in a similar way, but defines a length equal to the value of the prime to each prime. I'm not sure if different geometries (e.g. square lattice vs. hexagonal lattice) would give different results. I suppose if there are multiple distinct applications of taxicab distance, it might be worth giving them specific qualifiers, but I think "taxicab distance" should imply by default that we're working on a square lattice with edge length 1. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 15:52, 26 February 2023 (UTC)

:: I agree with Fredg999. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:45, 26 February 2023 (UTC)

:: I understood that reasoning, but there are different "defaults" in common use. For example, the Tenney harmonic distance is also a kind of taxicab distance and is used in a wider reach. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:24, 27 February 2023 (UTC)

::: I suppose the article could at least mention that taxicab distance is just the same thing as the 1-norm, and that it's quite common in RTT to scale the elements of vectors before taking their norm (such as with Tenney harmonic distance AKA log-product complexity), which is what Dave and I call a prescaled norm. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 23:31, 28 February 2023 (UTC)

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+== Equilateral? ==
+"Taxicab distance" sounds underspecific since it only states that the lattice is traversed in a "Manhattan/taxicab" manner, without any information on the length. I recommend adding "equilateral" to fully describe this kind of distance. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:27, 26 February 2023 (UTC)
+: I believe that taxicab distance implies a length of 1 on every prime when it says the "number of primes". For comparison, [[Wilson height]] (sum of prime factors with repetitions) works in a similar way, but defines a length equal to the value of the prime to each prime. I'm not sure if different geometries (e.g. square lattice vs. hexagonal lattice) would give different results. I suppose if there are multiple distinct applications of taxicab distance, it might be worth giving them specific qualifiers, but I think "taxicab distance" should imply by default that we're working on a square lattice with edge length 1. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 15:52, 26 February 2023 (UTC)
+:: I agree with Fredg999. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:45, 26 February 2023 (UTC)
+:: I understood that reasoning, but there are different "defaults" in common use. For example, the Tenney harmonic distance is also a kind of taxicab distance and is used in a wider reach. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:24, 27 February 2023 (UTC)
+::: I suppose the article could at least mention that taxicab distance is just the same thing as the 1-norm, and that it's quite common in RTT to scale the elements of vectors before taking their norm (such as with Tenney harmonic distance AKA log-product complexity), which is what Dave and I call a prescaled norm. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 23:31, 28 February 2023 (UTC)