This is the
talk page for discussing improvements to the
Logarithm article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Archives: 1, 2, 3, 4, 5, 6Auto-archiving period: 365 days |
Logarithm is a featured article; it (or a previous version of it) has been identified as one of the best articles produced by the Wikipedia community. Even so, if you can update or improve it, please do so. | ||||||||||||||||||||||
This article appeared on Wikipedia's Main Page as Today's featured article on June 5, 2011. | ||||||||||||||||||||||
|
This
level-3 vital article is rated FA-class on Wikipedia's
content assessment scale. It is of interest to multiple WikiProjects. | |||||||||||
|
This entire sections seems to be based on a single, vague, two paragraph description in Physics Today ( here), with the details being fleshed out through original research. Physics Today may a reliable source, but the article in question is obviously meant for a popular audience, and so is extremely lacking in detail, and does not cite any sources itself from which further detail might be found. If someone can find an academic paper, textbook or reference book that describes this algorithm then I'd be convinced that it belongs in Wikipedia, but as it stands I find its inclusion highly dubious at best. The section title might be taken to imply that the method is known as "Feynman's algorithm" in the literature, but can find no evidence that anyone aside from the editor who added this section called it that. If have no doubt that the method is, in fact valid, but this does not alone merit its inclusion since much of the detail seems to be the result of original research. -- RDBury ( talk) 03:11, 15 October 2020 (UTC)
It seems that Feynman rediscovered the "radix method", e.g. as described in "RADIX METHOD OF CALCULATING NATURAL LOGARITHMS IN BINARY NOTATION", which I can't actually find a copy of. But similar things are done with decimal radix as here. I think Danny Hillis's referenced brief description of the method is adequate, and the adaptation of it in the article is even more clear and correct. Dicklyon ( talk) 03:11, 17 November 2021 (UTC)
Okay, I'm a "noob" at editing Wikipedia pages (this is my second attempt in 15 years). So here goes:
In the "Particular bases" section of the Logarithm page, it says:
". . . in music theory, where a pitch ratio of two (the octave) is ubiquitous and the cent is the binary logarithm (scaled by 1200) of the ratio between two adjacent equally-tempered pitches in European classical music; . . ."
If you look at the Wikipedia definition of "Cent (music)" [1], and the Wikipedia definition of "Binary logarithm", it appears that there has been a transcription error between these two definitions [Cent (music) & Binary logarithm] and the Logarithm article, which may need to be harmonized.
Based on my music theory classes in college, a cent is 1/100th of the pitch ratio between two adjacent equal-tempered pitches (a interval of a semitone or half-tone) in European music, and 1200 cents make an octave - not a half-tone.
So should the above quoted text in the Logarithm article read: ". . . and the cent is the binary logarithm (scaled by 100) of the ratio between two adjacent equally-tempered-pitches in European classical music; . . ."?
Or would another way of re-writing this be better?
Or am I completely mistaken?
TimeriderTech ( talk) 01:10, 4 November 2021 (UTC)
Thank you both for chiming in on this! My attempt to create a new "Cent scale" sub-topic on the talk page for "Logarithm" didn't appear to go as planned, and I'm guessing that somebody silently helped me out. (Thanks! I promise I'll get better at editing.) It also makes me feel better that at least two other editors agree that there's a problem here. Thanks to you both! I'm going to ruminate on a better re-write of the erroneous sentence, incorporating the above input. Hopefully we can all find an alternative phrasing that corrects this mathematical error in a manner most pleasing and clear to read. 64.201.116.75 ( talk) 16:33, 4 November 2021 (UTC)
References
Really need a section on the units of a logarithm. For example, what is the unit of Log(10/seconds)? That is a common expression in first order rate equations, like nuclear decay.
From the integral definition of the natural log, "the area under the curve of a plot of 1/x versus x", it is clear that x can have any unit and that the logarithm is always unitless. The "area" under the curve has units of the x-axis times the units of the y-axis which, in all cases, is unity and unitless.
There are some discussion on the web suggestion things like "you can't take the logarithm of a number with units" (which is absurd, scientists and engineers do it all the time), to basically "there is a hidden and highly secret process in which the units disappear". Like "actually log(x*unit) is really log(x*unit/1*unit) so the units cancel", which is wrong.
The fact that the logarithm removes the units means that taking a logarithm is a lossy transform. There is no way, other than external knowledge, that allows the unit to be recovered by taking the exponent of the log. Therefore, e^(Ln(x)) <> x in all cases since the units have been lost. Jsluka ( talk) 18:49, 26 October 2022 (UTC)
Jacobolus surprisingly reverted an edit that removed a verbatim copy of a line two lines above that line. I'm re-reverting it after [ Discussion] with him. MüllerMarcus ( talk) 20:21, 20 October 2023 (UTC)
This is the
talk page for discussing improvements to the
Logarithm article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Archives: 1, 2, 3, 4, 5, 6Auto-archiving period: 365 days |
Logarithm is a featured article; it (or a previous version of it) has been identified as one of the best articles produced by the Wikipedia community. Even so, if you can update or improve it, please do so. | ||||||||||||||||||||||
This article appeared on Wikipedia's Main Page as Today's featured article on June 5, 2011. | ||||||||||||||||||||||
|
This
level-3 vital article is rated FA-class on Wikipedia's
content assessment scale. It is of interest to multiple WikiProjects. | |||||||||||
|
This entire sections seems to be based on a single, vague, two paragraph description in Physics Today ( here), with the details being fleshed out through original research. Physics Today may a reliable source, but the article in question is obviously meant for a popular audience, and so is extremely lacking in detail, and does not cite any sources itself from which further detail might be found. If someone can find an academic paper, textbook or reference book that describes this algorithm then I'd be convinced that it belongs in Wikipedia, but as it stands I find its inclusion highly dubious at best. The section title might be taken to imply that the method is known as "Feynman's algorithm" in the literature, but can find no evidence that anyone aside from the editor who added this section called it that. If have no doubt that the method is, in fact valid, but this does not alone merit its inclusion since much of the detail seems to be the result of original research. -- RDBury ( talk) 03:11, 15 October 2020 (UTC)
It seems that Feynman rediscovered the "radix method", e.g. as described in "RADIX METHOD OF CALCULATING NATURAL LOGARITHMS IN BINARY NOTATION", which I can't actually find a copy of. But similar things are done with decimal radix as here. I think Danny Hillis's referenced brief description of the method is adequate, and the adaptation of it in the article is even more clear and correct. Dicklyon ( talk) 03:11, 17 November 2021 (UTC)
Okay, I'm a "noob" at editing Wikipedia pages (this is my second attempt in 15 years). So here goes:
In the "Particular bases" section of the Logarithm page, it says:
". . . in music theory, where a pitch ratio of two (the octave) is ubiquitous and the cent is the binary logarithm (scaled by 1200) of the ratio between two adjacent equally-tempered pitches in European classical music; . . ."
If you look at the Wikipedia definition of "Cent (music)" [1], and the Wikipedia definition of "Binary logarithm", it appears that there has been a transcription error between these two definitions [Cent (music) & Binary logarithm] and the Logarithm article, which may need to be harmonized.
Based on my music theory classes in college, a cent is 1/100th of the pitch ratio between two adjacent equal-tempered pitches (a interval of a semitone or half-tone) in European music, and 1200 cents make an octave - not a half-tone.
So should the above quoted text in the Logarithm article read: ". . . and the cent is the binary logarithm (scaled by 100) of the ratio between two adjacent equally-tempered-pitches in European classical music; . . ."?
Or would another way of re-writing this be better?
Or am I completely mistaken?
TimeriderTech ( talk) 01:10, 4 November 2021 (UTC)
Thank you both for chiming in on this! My attempt to create a new "Cent scale" sub-topic on the talk page for "Logarithm" didn't appear to go as planned, and I'm guessing that somebody silently helped me out. (Thanks! I promise I'll get better at editing.) It also makes me feel better that at least two other editors agree that there's a problem here. Thanks to you both! I'm going to ruminate on a better re-write of the erroneous sentence, incorporating the above input. Hopefully we can all find an alternative phrasing that corrects this mathematical error in a manner most pleasing and clear to read. 64.201.116.75 ( talk) 16:33, 4 November 2021 (UTC)
References
Really need a section on the units of a logarithm. For example, what is the unit of Log(10/seconds)? That is a common expression in first order rate equations, like nuclear decay.
From the integral definition of the natural log, "the area under the curve of a plot of 1/x versus x", it is clear that x can have any unit and that the logarithm is always unitless. The "area" under the curve has units of the x-axis times the units of the y-axis which, in all cases, is unity and unitless.
There are some discussion on the web suggestion things like "you can't take the logarithm of a number with units" (which is absurd, scientists and engineers do it all the time), to basically "there is a hidden and highly secret process in which the units disappear". Like "actually log(x*unit) is really log(x*unit/1*unit) so the units cancel", which is wrong.
The fact that the logarithm removes the units means that taking a logarithm is a lossy transform. There is no way, other than external knowledge, that allows the unit to be recovered by taking the exponent of the log. Therefore, e^(Ln(x)) <> x in all cases since the units have been lost. Jsluka ( talk) 18:49, 26 October 2022 (UTC)
Jacobolus surprisingly reverted an edit that removed a verbatim copy of a line two lines above that line. I'm re-reverting it after [ Discussion] with him. MüllerMarcus ( talk) 20:21, 20 October 2023 (UTC)