Talk:Wilson norm: Difference between revisions
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== Extract fact from main Height article to here == | == Extract fact from main Height article to here == | ||
Presently the information about the historical origin of this terminology is only found on the page for [[Height]] in general: | Presently the information about the historical origin of this terminology is only found on the page for [[Height]] in general: | ||
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== errors in "L1 Norm on Monzos" formula == | == errors in "L1 Norm on Monzos" formula == | ||
It looks like we're missing a multiplication 2 in there and have an extra multiplication by 3. (Edit: I forgot to sign this the first time around, in April 2022) --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:22, 11 December 2022 (UTC) | It looks like we're missing a multiplication 2 in there and have an extra multiplication by 3. (Edit: I forgot to sign this the first time around, in April 2022) --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:22, 11 December 2022 (UTC) | ||
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== This metric is flawed == | == 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''. | 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''. | ||
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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) | 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) | ||
: You're correct that Wilson weights prime 3 less than Tenney relative to prime 2. Whether it's a flaw is debatable. | |||
: I have a section to add to this article where I'll address the extrapolation on Tenney and Wilson and note that fact along the way. | |||
: —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:21, 1 November 2025 (UTC) | |||