Talk:Taxicab distance: Difference between revisions

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~~= ARCHIVED WIKISPACES DISCUSSION BELOW =~~

~~'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''~~

~~<span style~~=~~"color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.~~

== Equilateral? ==

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"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)

~~== Title~~ of ~~this page ==~~

: 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)

"~~factor limit commas~~" ~~seems like~~ a ~~bad name for~~ a ~~page about~~ a ~~complexity measure~~.

- ~~'''genewardsmith''' September 03, 2011, 08~~:24:~~54 AM~~ UTC~~-0700~~

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

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~~how's' "commas by taxicab distance"?~~

~~- '''xenjacob''' September 03, 2011, 10~~:06:~~13 AM UTC-0700~~

:: 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)

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OK, ~~if you plan to talk only about commas~~ and ~~not intervals~~ in ~~general~~.

- '~~''genewardsmith''' September 03~~, ~~2011, 10~~:09:~~09 AM~~ UTC~~-0700~~

::: 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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-= ARCHIVED WIKISPACES DISCUSSION BELOW =
+{{WSArchiveLink}}
-'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
-<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.
+== Equilateral? ==
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+"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)
-== Title of this page ==
+: 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)
-"factor limit commas" seems like a bad name for a page about a complexity measure.
-- '''genewardsmith''' September 03, 2011, 08:24:54 AM UTC-0700
+:: I agree with Fredg999. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:45, 26 February 2023 (UTC)
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-how's' "commas by taxicab distance"?
-- '''xenjacob''' September 03, 2011, 10:06:13 AM UTC-0700
+:: 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)
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-OK, if you plan to talk only about commas and not intervals in general.
-- '''genewardsmith''' September 03, 2011, 10:09:09 AM UTC-0700
+::: 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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