I happen to think ln(x) is a damn fine idea, and log(x) without defining it but nevertheless secretly agreeing it is ln(x), is just obnoxious insistence on some sort of "you know what it means if you are part of the 'in' crowd" status symbol psychological bullshit. You know, where groups like to create pointless initiation rites, like hazing fraternity brothers and creating secret handshakes. Because otherwise they sadly wouldn't be able to feel like Real Men. There is nothing wrong with being less ambiguous and saving a letter at the same time. What's wrong is doing the opposite. And further, I like Knuth's (?) idea of lg(x)=log(x)/log(2) as well. And nobody ever seems to do it, but if anybody wanted to have a special one for log(x)/log(10), such as lt(x), I would have been ok with that too.
On 2015-02-28 22:27, Warren D Smith wrote:
I happen to think ln(x) is a damn fine idea, and log(x) without defining it but nevertheless secretly agreeing it is ln(x), is just obnoxious insistence on some sort of "you know what it means if you are part of the 'in' crowd" status symbol psychological bullshit. You know, where groups like to create pointless initiation rites, like hazing fraternity brothers and creating secret handshakes. Because otherwise they sadly wouldn't be able to feel like Real Men.
There is nothing wrong with being less ambiguous and saving a letter at the same time. What's wrong is doing the opposite.
And further, I like Knuth's (?) idea of lg(x)=log(x)/log(2) as well.
And nobody ever seems to do it, but if anybody wanted to have a special one for log(x)/log(10), such as lt(x), I would have been ok with that too.
I'm with Warren. Being friends with Knuth has *nothing* to do with it. Probably. --rwg
Here's an interesting footnote from the wikipedia article on logarithms: Some mathematicians disapprove of this notation. In his 1985 autobiography, Paul Halmos criticized what he considered the "childish ln notation," which he said no mathematician had ever used.[13] The notation was invented by Irving Stringham, a mathematician.[14][15] Sent from my iPhone
On Mar 1, 2015, at 01:27, Warren D Smith <warren.wds@gmail.com> wrote:
I happen to think ln(x) is a damn fine idea, and log(x) without defining it but nevertheless secretly agreeing it is ln(x), is just obnoxious insistence on some sort of "you know what it means if you are part of the 'in' crowd" status symbol psychological bullshit. You know, where groups like to create pointless initiation rites, like hazing fraternity brothers and creating secret handshakes. Because otherwise they sadly wouldn't be able to feel like Real Men.
There is nothing wrong with being less ambiguous and saving a letter at the same time. What's wrong is doing the opposite.
And further, I like Knuth's (?) idea of lg(x)=log(x)/log(2) as well.
And nobody ever seems to do it, but if anybody wanted to have a special one for log(x)/log(10), such as lt(x), I would have been ok with that too.
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In a book on pure mathematics, "log" could not reasonably mean anything other than natural logarithm; there should be no confusion about such usage. In a subject such as chemistry or astronomy, natural and common logarithms both appear, and it makes sense to use both "log" and "ln" to distinguish them. What absolutely irritates me is the use of j for √-1. -- Gene
On 3/1/2015 5:17 PM, Eugene Salamin via math-fun wrote:
In a book on pure mathematics, "log" could not reasonably mean anything other than natural logarithm; there should be no confusion about such usage. In a subject such as chemistry or astronomy, natural and common logarithms both appear, and it makes sense to use both "log" and "ln" to distinguish them. What absolutely irritates me is the use of j for √-1. That comes from electrical engineering practice. They liked j because they were already using i for current.
Brent
Using j as a square-root of -1 never bothered me, since you can use *any* purely-imaginary unit quaternion and (as long as you're consistent) you get a copy of the complex plane. Amusingly, working in the quaternions, complex conjugation is a special case of the other type of conjugation: (a + bi) = j (a - bi) j^-1 Sincerely, Adam P. Goucher
Sent: Monday, March 02, 2015 at 1:44 AM From: meekerdb <meekerdb@verizon.net> To: "Eugene Salamin" <gene_salamin@yahoo.com>, math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] ln
On 3/1/2015 5:17 PM, Eugene Salamin via math-fun wrote:
In a book on pure mathematics, "log" could not reasonably mean anything other than natural logarithm; there should be no confusion about such usage. In a subject such as chemistry or astronomy, natural and common logarithms both appear, and it makes sense to use both "log" and "ln" to distinguish them. What absolutely irritates me is the use of j for √-1. That comes from electrical engineering practice. They liked j because they were already using i for current.
Brent
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What bothers me is the unqualified use of sqrt(-1) to mean i, since I think that should always be described as a convention. Sometimes it seems to me we have no right to use a symbol for i, just because there is no way to distinguish between i and -i. Maybe we should be allowed only to refer to both of them at once. --Dan
On Mar 1, 2015, at 5:57 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Using j as a square-root of -1 never bothered me, since you can use *any* purely-imaginary unit quaternion and (as long as you're consistent) you get a copy of the complex plane.
Amusingly, working in the quaternions, complex conjugation is a special case of the other type of conjugation:
(a + bi) = j (a - bi) j^-1
Sincerely,
Adam P. Goucher
Sent: Monday, March 02, 2015 at 1:44 AM From: meekerdb <meekerdb@verizon.net> To: "Eugene Salamin" <gene_salamin@yahoo.com>, math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] ln
On 3/1/2015 5:17 PM, Eugene Salamin via math-fun wrote:
In a book on pure mathematics, "log" could not reasonably mean anything other than natural logarithm; there should be no confusion about such usage. In a subject such as chemistry or astronomy, natural and common logarithms both appear, and it makes sense to use both "log" and "ln" to distinguish them. What absolutely irritates me is the use of j for √-1. That comes from electrical engineering practice. They liked j because they were already using i for current.
Brent
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i is for the POSITIVE square root of -1. :-) ----- Quoting Dan Asimov <dasimov@earthlink.net>:
What bothers me is the unqualified use of sqrt(-1) to mean i, since I think that should always be described as a convention.
Sometimes it seems to me we have no right to use a symbol for i, just because there is no way to distinguish between i and -i. Maybe we should be allowed only to refer to both of them at once.
--Dan
On Mar 1, 2015, at 5:57 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Using j as a square-root of -1 never bothered me, since you can use *any* purely-imaginary unit quaternion and (as long as you're consistent) you get a copy of the complex plane.
Amusingly, working in the quaternions, complex conjugation is a special case of the other type of conjugation:
(a + bi) = j (a - bi) j^-1
Sincerely,
Adam P. Goucher
Sent: Monday, March 02, 2015 at 1:44 AM From: meekerdb <meekerdb@verizon.net> To: "Eugene Salamin" <gene_salamin@yahoo.com>, math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] ln
On 3/1/2015 5:17 PM, Eugene Salamin via math-fun wrote:
In a book on pure mathematics, "log" could not reasonably mean anything other than natural logarithm; there should be no confusion about such usage. In a subject such as chemistry or astronomy, natural and common logarithms both appear, and it makes sense to use both "log" and "ln" to distinguish them. What absolutely irritates me is the use of j for ?-1. That comes from electrical engineering practice. They liked j because they were already using i for current.
Brent
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On 2015-03-01 22:44, rcs@xmission.com wrote:
i is for the POSITIVE square root of -1. :-)
Macsyma: Is %I positive, negative, or zero? me: no Macsyma: Is %I positive, negative, or zero? me: no ... Jeff Golden: It's positive. Everybody knows that. --rwg
----- Quoting Dan Asimov <dasimov@earthlink.net>:
What bothers me is the unqualified use of sqrt(-1) to mean i, since I think that should always be described as a convention.
Sometimes it seems to me we have no right to use a symbol for i, just because there is no way to distinguish between i and -i. Maybe we should be allowed only to refer to both of them at once.
--Dan
On Mar 1, 2015, at 5:57 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
Using j as a square-root of -1 never bothered me, since you can use *any* purely-imaginary unit quaternion and (as long as you're consistent) you get a copy of the complex plane.
Amusingly, working in the quaternions, complex conjugation is a special case of the other type of conjugation:
(a + bi) = j (a - bi) j^-1
Sincerely,
Adam P. Goucher
Sent: Monday, March 02, 2015 at 1:44 AM From: meekerdb <meekerdb@verizon.net> To: "Eugene Salamin" <gene_salamin@yahoo.com>, math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] ln
On 3/1/2015 5:17 PM, Eugene Salamin via math-fun wrote:
In a book on pure mathematics, "log" could not reasonably mean anything other than natural logarithm; there should be no confusion about such usage. In a subject such as chemistry or astronomy, natural and common logarithms both appear, and it makes sense to use both "log" and "ln" to distinguish them. What absolutely irritates me is the use of j for ?-1. That comes from electrical engineering practice. They liked j because they were already using i for current.
Brent
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When a square root of -1 appears more than once in an exposition, it is necessary to have a way of indicating whether two such occurrences are the same or different square roots. The use of i and -i satisfies that requirement. -- Gene From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, March 1, 2015 7:13 PM Subject: Re: [math-fun] ln What bothers me is the unqualified use of sqrt(-1) to mean i, since I think that should always be described as a convention. Sometimes it seems to me we have no right to use a symbol for i, just because there is no way to distinguish between i and -i. Maybe we should be allowed only to refer to both of them at once. --Dan
Yes, good point. Surely it's less trouble if we pretend it makes sense to refer to i and -i separately. But of course, given that U and V are each a root of X^2 + 1 , we could equally tell whether they are the same or different according as UV = -1 or UV = +1 , without referring to either of them separately. --Dan
On Mar 2, 2015, at 10:19 AM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
When a square root of -1 appears more than once in an exposition, it is necessary to have a way of indicating whether two such occurrences are the same or different square roots. The use of i and -i satisfies that requirement. -- Gene
From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, March 1, 2015 7:13 PM Subject: Re: [math-fun] ln
What bothers me is the unqualified use of sqrt(-1) to mean i, since I think that should always be described as a convention.
Sometimes it seems to me we have no right to use a symbol for i, just because there is no way to distinguish between i and -i. Maybe we should be allowed only to refer to both of them at once.
--Dan
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Sheesh -- of *course* you can tell i from -i. When you draw the complex plane, i is the one at (0,1), and -i is the one at (0,-1). Obviously. On Mon, Mar 2, 2015 at 2:18 PM, Dan Asimov <asimov@msri.org> wrote:
Yes, good point. Surely it's less trouble if we pretend it makes sense to refer to i and -i separately.
But of course, given that U and V are each a root of
X^2 + 1
, we could equally tell whether they are the same or different according as
UV = -1 or UV = +1
, without referring to either of them separately.
--Dan
On Mar 2, 2015, at 10:19 AM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
When a square root of -1 appears more than once in an exposition, it is necessary to have a way of indicating whether two such occurrences are the same or different square roots. The use of i and -i satisfies that requirement. -- Gene
From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, March 1, 2015 7:13 PM Subject: Re: [math-fun] ln
What bothers me is the unqualified use of sqrt(-1) to mean i, since I think that should always be described as a convention.
Sometimes it seems to me we have no right to use a symbol for i, just because there is no way to distinguish between i and -i. Maybe we should be allowed only to refer to both of them at once.
--Dan
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-- Forewarned is worth an octopus in the bush.
But what if you inadvertently placed -i at (1,0) instead of i. --Dan
On Mar 2, 2015, at 11:35 AM, Michael Kleber <michael.kleber@gmail.com> wrote:
Sheesh -- of *course* you can tell i from -i. When you draw the complex plane, i is the one at (0,1), and -i is the one at (0,-1). Obviously.
On Mon, Mar 2, 2015 at 2:18 PM, Dan Asimov <asimov@msri.org> wrote:
Yes, good point. Surely it's less trouble if we pretend it makes sense to refer to i and -i separately.
But of course, given that U and V are each a root of
X^2 + 1
, we could equally tell whether they are the same or different according as
UV = -1 or UV = +1
, without referring to either of them separately.
--Dan
On Mar 2, 2015, at 10:19 AM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
When a square root of -1 appears more than once in an exposition, it is necessary to have a way of indicating whether two such occurrences are the same or different square roots. The use of i and -i satisfies that requirement. -- Gene
From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, March 1, 2015 7:13 PM Subject: Re: [math-fun] ln
What bothers me is the unqualified use of sqrt(-1) to mean i, since I think that should always be described as a convention.
Sometimes it seems to me we have no right to use a symbol for i, just because there is no way to distinguish between i and -i. Maybe we should be allowed only to refer to both of them at once.
--Dan
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-- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Given an unadorned plane, you get the complex numbers by *choosing* 1) a point for the origin, 2) a line for the real numbers, 3) which side of the line is positive 4) a unit length, and 5) a handedness. Each of the five choices gives a symmetry: 1) translation, 2) rotation, 3) negation, 4) scaling, and 5) complex conjugation. On Mon, Mar 2, 2015 at 11:51 AM, Dan Asimov <asimov@msri.org> wrote:
But what if you inadvertently placed -i at (1,0) instead of i.
--Dan
On Mar 2, 2015, at 11:35 AM, Michael Kleber <michael.kleber@gmail.com> wrote:
Sheesh -- of *course* you can tell i from -i. When you draw the complex plane, i is the one at (0,1), and -i is the one at (0,-1). Obviously.
On Mon, Mar 2, 2015 at 2:18 PM, Dan Asimov <asimov@msri.org> wrote:
Yes, good point. Surely it's less trouble if we pretend it makes sense to refer to i and -i separately.
But of course, given that U and V are each a root of
X^2 + 1
, we could equally tell whether they are the same or different according as
UV = -1 or UV = +1
, without referring to either of them separately.
--Dan
On Mar 2, 2015, at 10:19 AM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
When a square root of -1 appears more than once in an exposition, it is necessary to have a way of indicating whether two such occurrences are the same or different square roots. The use of i and -i satisfies that requirement. -- Gene
From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, March 1, 2015 7:13 PM Subject: Re: [math-fun] ln
What bothers me is the unqualified use of sqrt(-1) to mean i, since I think that should always be described as a convention.
Sometimes it seems to me we have no right to use a symbol for i, just because there is no way to distinguish between i and -i. Maybe we should be allowed only to refer to both of them at once.
--Dan
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Below the distinction should be made that 5) constitutes a symmetry of the complex numbers; 1) -- 4) are symmetries of your graph paper! WFL On 3/2/15, Mike Stay <metaweta@gmail.com> wrote:
Given an unadorned plane, you get the complex numbers by *choosing* 1) a point for the origin, 2) a line for the real numbers, 3) which side of the line is positive 4) a unit length, and 5) a handedness.
Each of the five choices gives a symmetry: 1) translation, 2) rotation, 3) negation, 4) scaling, and 5) complex conjugation.
On Mon, Mar 2, 2015 at 11:51 AM, Dan Asimov <asimov@msri.org> wrote:
But what if you inadvertently placed -i at (1,0) instead of i.
--Dan
On Mar 2, 2015, at 11:35 AM, Michael Kleber <michael.kleber@gmail.com> wrote:
Sheesh -- of *course* you can tell i from -i. When you draw the complex plane, i is the one at (0,1), and -i is the one at (0,-1). Obviously.
On Mon, Mar 2, 2015 at 2:18 PM, Dan Asimov <asimov@msri.org> wrote:
Yes, good point. Surely it's less trouble if we pretend it makes sense to refer to i and -i separately.
But of course, given that U and V are each a root of
X^2 + 1
, we could equally tell whether they are the same or different according as
UV = -1 or UV = +1
, without referring to either of them separately.
--Dan
On Mar 2, 2015, at 10:19 AM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
When a square root of -1 appears more than once in an exposition, it is necessary to have a way of indicating whether two such occurrences are the same or different square roots. The use of i and -i satisfies that requirement. -- Gene
From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, March 1, 2015 7:13 PM Subject: Re: [math-fun] ln
What bothers me is the unqualified use of sqrt(-1) to mean i, since I think that should always be described as a convention.
Sometimes it seems to me we have no right to use a symbol for i, just because there is no way to distinguish between i and -i. Maybe we should be allowed only to refer to both of them at once.
--Dan
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There's a slightly less facetious way to make this distinction: (1) is only an automorphism of C as a metric space; (2,3,4) are also automorphisms of C as an additive group; (5) is also an automorphism of C as a ring (or field). APG
Sent: Monday, March 02, 2015 at 11:51 PM From: "Fred Lunnon" <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] ln
Below the distinction should be made that 5) constitutes a symmetry of the complex numbers; 1) -- 4) are symmetries of your graph paper!
WFL
On 3/2/15, Mike Stay <metaweta@gmail.com> wrote:
Given an unadorned plane, you get the complex numbers by *choosing* 1) a point for the origin, 2) a line for the real numbers, 3) which side of the line is positive 4) a unit length, and 5) a handedness.
Each of the five choices gives a symmetry: 1) translation, 2) rotation, 3) negation, 4) scaling, and 5) complex conjugation.
On Mon, Mar 2, 2015 at 11:51 AM, Dan Asimov <asimov@msri.org> wrote:
But what if you inadvertently placed -i at (1,0) instead of i.
--Dan
On Mar 2, 2015, at 11:35 AM, Michael Kleber <michael.kleber@gmail.com> wrote:
Sheesh -- of *course* you can tell i from -i. When you draw the complex plane, i is the one at (0,1), and -i is the one at (0,-1). Obviously.
On Mon, Mar 2, 2015 at 2:18 PM, Dan Asimov <asimov@msri.org> wrote:
Yes, good point. Surely it's less trouble if we pretend it makes sense to refer to i and -i separately.
But of course, given that U and V are each a root of
X^2 + 1
, we could equally tell whether they are the same or different according as
UV = -1 or UV = +1
, without referring to either of them separately.
--Dan
On Mar 2, 2015, at 10:19 AM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
When a square root of -1 appears more than once in an exposition, it is necessary to have a way of indicating whether two such occurrences are the same or different square roots. The use of i and -i satisfies that requirement. -- Gene
From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, March 1, 2015 7:13 PM Subject: Re: [math-fun] ln
What bothers me is the unqualified use of sqrt(-1) to mean i, since I think that should always be described as a convention.
Sometimes it seems to me we have no right to use a symbol for i, just because there is no way to distinguish between i and -i. Maybe we should be allowed only to refer to both of them at once.
--Dan
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I thought "ln" was invented by the French, maybe even Napier, standing for logarithme naturale. --Dan
On Mar 1, 2015, at 4:33 PM, Victor S. Miller <victorsmiller@gmail.com> wrote:
. . .
Some mathematicians disapprove of this notation [ln for log_e]. In his 1985 autobiography, Paul Halmos criticized what he considered the "childish ln notation," which he said no mathematician had ever used.[13] The notation was invented by Irving Stringham, a mathematician.[14][15]
John Napier was Scottish, rather than French.
Sent: Monday, March 02, 2015 at 3:16 AM From: "Dan Asimov" <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] ln
I thought "ln" was invented by the French, maybe even Napier, standing for logarithme naturale.
--Dan
On Mar 1, 2015, at 4:33 PM, Victor S. Miller <victorsmiller@gmail.com> wrote:
. . .
Some mathematicians disapprove of this notation [ln for log_e]. In his 1985 autobiography, Paul Halmos criticized what he considered the "childish ln notation," which he said no mathematician had ever used.[13] The notation was invented by Irving Stringham, a mathematician.[14][15]
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On Mar 1, 2015, at 7:51 PM, Adam P. Goucher <apgoucher@gmx.com> wrote:
John Napier was Scottish, rather than French.
Yes, and for that matter I can't even find any suggestion that Napier worked in base e. And natural logarithm in French appears to actually be "logarithme naturel" instead of what I wrote. While googling about this, I came across some comments by Europeans who said they learned that ln is an abbreviation for the Latin phrase (approximately) logarithmum naturalis. Maybe the origin of ln notation is in doubt, but I'm pretty sure how it became widespread in the U.S. and maybe the world: The calculus book by George B. Thomas was the number one calculus book used in college and high school courses for many years*. It is used all over the world. That book probably helped popularize the ln notation more than any other. --Dan _________________________ * The first edition came out in 1952, it's now in its 13th edition. Of course it has been overshadowed by other books in recent years, especially those by James Stewart.
Sent: Monday, March 02, 2015 at 3:16 AM From: "Dan Asimov <dasimov@earthlink.net>
I thought "ln" was invented by the French, maybe even Napier, standing for logarithme naturale.
On Mar 1, 2015, at 4:33 PM, Victor S. Miller <victorsmiller@gmail.com> wrote: . . . Some mathematicians disapprove of this notation [ln for log_e]. In his 1985 autobiography, Paul Halmos criticized what he considered the "childish ln notation," which he said no mathematician had ever used.[13] The notation was invented by Irving Stringham, a mathematician.[14][15]
On 01/03/2015 06:27, Warren D Smith wrote:
I happen to think ln(x) is a damn fine idea, and log(x) without defining it but nevertheless secretly agreeing it is ln(x), is just obnoxious insistence on some sort of "you know what it means if you are part of the 'in' crowd" status symbol psychological bullshit.
"ln" is no more immediately obvious than "log"; in either case you need to know what the notation means to do anything useful with it. The same goes for every other bit of mathematical notation there is. What's "secret" about it? Only the fact that in some other communities other than that of pure mathematicians it happens that "log" is used to mean something else. That isn't the result of any kind of in-crowd status-symbol psychological bullshit. It's just that if you happen to need one kind of logarithm much more often than others it's natural (ha!) to use "log" to denote that; and it happens that for pure mathematicians that happened with the natural log, while for engineers and schoolteachers it happened with the base-10 log. Natural logs are still much the most, er, natural kind in pure mathematics (though maybe base-2 logs are more important now than they were 50 years ago). There's less excuse for the dominance of base-10 logs in engineering and school teaching, now that slide rules and log tables have been so thoroughly supplanted by other means of computation. But of course the real reason why the notation persists in both cases is simply tradition: changing would require lots of people to abandon the notation they're used to for very little benefit, and invalidate lots of existing textbooks, journal articles, etc. It might be no bad thing if pure mathematicians and engineers and schoolteachers all got together and agreed never again to use unqualified "log" to denote any particular base, and to use (say) "lg" for base 2, "ln" for base e, and "ld" for base 10. Realistically, though, it's not going to happen. (Also, "ln" is distractingly hard to read because lowercase-l looks like capital-I and digit-1 and so forth and needs all the extra context it can get, and "ln" is harder to say than "log"; that agreement would be pretty much a pure loss for the pure mathematicians.) Among people who aren't pure mathematicians it is common to write angles in degrees, and common -- albeit sloppy -- to leave off the degree signs. Is it in-crowd status-symbol psychological bullshit for mathematicians to define the sine function so that its period is 2pi rather than 360? Among people who aren't pure mathematicians it is common to use terms like "compact", "real", "manifold", "similar", etc., with meanings very different from those pure mathematicians give them. Is it in-crowd status symbol psychological bullshit for pure mathematicians to use their meanings for these words? Of course not. Same for "log". -- g
Gareth's post is very well written. As I see it, the only problem is that "being in the same community" is not an equivalence relation — so there are overlapping groups that tend to use the same notation for different things. I almost always use ln when I mean natural log, just because it's unambiguous. I'm not sure about other countries (though googling had shown that many Europeans use ln). But as for the U.S.: I don't see any good argument *against* everyone's using ln to mean natural log. Virtually everyone who knows what natural log means has seen that notation when they took calculus. And that will avoid any confusion between log_10 and log_e. Who knows how many bridges already fell down for just this reason? --Dan P.S. And while we're at it, let's standardize the meaning of "natural numbers" and the symbol N for them — or else come up with new notation that is unambiguous. Gareth wrote: ----- "ln" is no more immediately obvious than "log"; in either case you need to know what the notation means to do anything useful with it. The same goes for every other bit of mathematical notation there is. What's "secret" about it? Only the fact that in some other communities other than that of pure mathematicians it happens that "log" is used to mean something else. That isn't the result of any kind of in-crowd status-symbol psychological bullshit. It's just that if you happen to need one kind of logarithm much more often than others it's natural (ha!) to use "log" to denote that; and it happens that for pure mathematicians that happened with the natural log, while for engineers and schoolteachers it happened with the base-10 log. Natural logs are still much the most, er, natural kind in pure mathematics (though maybe base-2 logs are more important now than they were 50 years ago). There's less excuse for the dominance of base-10 logs in engineering and school teaching, now that slide rules and log tables have been so thoroughly supplanted by other means of computation. But of course the real reason why the notation persists in both cases is simply tradition: changing would require lots of people to abandon the notation they're used to for very little benefit, and invalidate lots of existing textbooks, journal articles, etc. It might be no bad thing if pure mathematicians and engineers and schoolteachers all got together and agreed never again to use unqualified "log" to denote any particular base, and to use (say) "lg" for base 2, "ln" for base e, and "ld" for base 10. Realistically, though, it's not going to happen. (Also, "ln" is distractingly hard to read because lowercase-l looks like capital-I and digit-1 and so forth and needs all the extra context it can get, and "ln" is harder to say than "log"; that agreement would be pretty much a pure loss for the pure mathematicians.) Among people who aren't pure mathematicians it is common to write angles in degrees, and common -- albeit sloppy -- to leave off the degree signs. Is it in-crowd status-symbol psychological bullshit for mathematicians to define the sine function so that its period is 2pi rather than 360? Among people who aren't pure mathematicians it is common to use terms like "compact", "real", "manifold", "similar", etc., with meanings very different from those pure mathematicians give them. Is it in-crowd status symbol psychological bullshit for pure mathematicians to use their meanings for these words? Of course not. Same for "log". -----
The fact that mathematics has dialects and jargons simply affirms that it is a living language in active use. Rigor is good, but rigor mortis is not.
participants (14)
-
Adam P. Goucher -
Dan Asimov -
Dan Asimov -
David Wilson -
Eugene Salamin -
Fred Lunnon -
Gareth McCaughan -
meekerdb -
Michael Kleber -
Mike Stay -
rcs＠xmission.com -
rwg -
Victor S. Miller -
Warren D Smith