Talk:Taxicab distance

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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. 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. --Fredg999 (talk) 15:52, 26 February 2023 (UTC)

I agree with Fredg999. --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. 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. --Cmloegcmluin (talk) 23:31, 28 February 2023 (UTC)