Talk:Wilson norm: Difference between revisions

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I'm just posting here as a reminder to admins about these two requests, in case they all missed them the first time. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:58, 6 May 2023 (UTC)

== This metric is flawed ==

While the overall idea of prioritizing lower limits makes sense, there's a bit of a flaw. For example, 2048/1 has a Wilson norm of 22, while 2187/1 has a Wilson norm of 21. If primes are weighted by ''1/log<sub>2</sub>(p)'', then this views factors of 3 as less complex than factors of 2, and prime 5 is barely more complex than 2. I propose a modified version, where if a/b is a ratio, each prime factor ''q'' of ''ab'' increases the norm of ''a/b'' by ''q-1'', rather than ''q''. This brings much more weight to prime 2, and lower limits in general. Here is a list of {{nowrap|(increase in Wilson norm)/(increase in Tenney norm)}} and {{nowrap|(increase in Wilson norm)/(increase in my norm)}} per factor of each prime in ''ab'' for a ratio ''a/b''.

2: Wilson/Tenney: 2.000; Mine/Tenney: 1.000

3: W/T: 1.893; M/T: 1.262

5: W/T: 2.153; M/T: 1.723

7: W/T: 2.493; M/T: 2.137

11: W/T: 3.180; M/T: 2.891

13: W/T: 3.513; M/T: 3.243

17: W/T: 4.159; M/T: 3.914

19: W/T: 4.473; M/T: 4.237

As you can see, the wilson norm sees prime 13 as over half as important as 2, while mine sees 13 as less than a third as important as 2. My norm sees prime 3 as somewhat less important than 2, and prime 5 is seen as considerably more complex.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 06:10, 1 November 2025 (UTC)

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 I'm just posting here as a reminder to admins about these two requests, in case they all missed them the first time. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:58, 6 May 2023 (UTC)
+== This metric is flawed ==
+While the overall idea of prioritizing lower limits makes sense, there's a bit of a flaw. For example, 2048/1 has a Wilson norm of 22, while 2187/1 has a Wilson norm of 21. If primes are weighted by ''1/log<sub>2</sub>(p)'', then this views factors of 3 as less complex than factors of 2, and prime 5 is barely more complex than 2. I propose a modified version, where if a/b is a ratio, each prime factor ''q'' of ''ab'' increases the norm of ''a/b'' by ''q-1'', rather than ''q''. This brings much more weight to prime 2, and lower limits in general. Here is a list of {{nowrap|(increase in Wilson norm)/(increase in Tenney norm)}} and {{nowrap|(increase in Wilson norm)/(increase in my norm)}} per factor of each prime in ''ab'' for a ratio ''a/b''.
+: Wilson/Tenney: 2.000; Mine/Tenney: 1.000
+: W/T: 1.893; M/T: 1.262
+: W/T: 2.153; M/T: 1.723
+: W/T: 2.493; M/T: 2.137
+: W/T: 3.180; M/T: 2.891
+: W/T: 3.513; M/T: 3.243
+: W/T: 4.159; M/T: 3.914
+: W/T: 4.473; M/T: 4.237
+As you can see, the wilson norm sees prime 13 as over half as important as 2, while mine sees 13 as less than a third as important as 2. My norm sees prime 3 as somewhat less important than 2, and prime 5 is seen as considerably more complex.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 06:10, 1 November 2025 (UTC)