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Re: Re: Re: Re: Re: Log[x]//TraditionalForm

Of course what Murray meant by "advanced" meant "advanced 
mathematics". ( I myself wrote "aimed at mathematicians"). I think 
most people will agree that physics is "what physicist do" and 
engineering is "what engineers do" so presumably mathematics is what 
mathematicians do. (Others might use it but they do not normally *do* 
it, with the exception of a few "borderline cases", most notably   
Edward Witten).  And Murray's (and mine) point was that in advanced 
books meant for mathematicians the notation ln is (almost) never used, 
which of course does not mean that it isn't used in very advanced 
texts in physics etc.   There are several reasons why mathematicians 
do not like the notation ln. One is that in text on analysis the only 
logarithms ever considered are the "natural" ones. As there is no need 
for any other logarithms there is no need for any special notation for 
"natural logarithms" (they are the only ones). Moreover, the usual one 
dimensional logarithm is only a special case of the inverse of the 
exponential map in the theory of Lie Groups (or even manifolds with 
connection) and these logarithms do not involve any basis and nobody, 
not  even physicists writes ln for the inverse of the general 
exponential map.
Someone the same thread suggested that the "criterion"  for an 
"advanced  book" should be whether it uses the notation log or ln, and 
probably thought himself very witty. However, this immediately brought 
to my mind a very famous story, which played a big role in the history 
of mathematics and which has a lot to do with this issue

Just a few days after the unexpected death of his father, Galois took 
the the entrance examination to the =C9cole Polytechnique for the second 
time. It became a legend in the history of mathematics. He was aware 
that a refusal would be final this time, if he would flunk again. The 
examiners, though being recognized mathematicians, were not capable of 
detecting the mathematical genius of Evariste Galois. One of the two 
examiners asked the fatal question: He should describe the theory of 
the arithmetic logarithms. Galois criticized immediately the question, 
and mentioned to professor Dinet that there are no arithmetic 
logarithms. Why didn't he simply ask for the theory of the logarithms? 
Thereupon Galois refused to explain some propositions concerning 
logarithms. He said that it was completely obvious! This was 
apparently the dot on the i: He failed the examination.
(Quoted  from http://www.galois-group.net/g/EN/fate.html)

Evariste Galois was certainly a very "advanced" mathematician. His 
examiner Charles Louis Dinet, in the words of the historian E.T. Bell, 
was =93not worthy enough to sharpen his (Galois) pencil=94.

Andrzej Kozlowski

On 7 Feb 2009, at 08:38, Curtis Osterhoudt wrote:

>   =46rom what I've seen, (most of) the physics books published 
> recently (and going so far back as 1953, though Morse & Feshbach's 
> _Methods_of_Theoretical_Physics_ was "renewed" --- whatever that 
> means --- in 1981) have the "ln" notation, rather than "log". This 
> is pretty much true across the spectrum, from optics to acoustics to 
> math methods to GR to fluid mechanics to classical dynamics and 
> electrodynamics, and so forth. It's also true at all levels, from 
> undergraduate texts to very specialized texts. In that respect, 
> there's no "more advanced course" to go on to, unless it's more 
> associated with maths in the stead of physics. Maybe we're still to 
> attached to our Napier's Bones.
>
>   Once one is in the field, it should almost always be obvious from 
> context what base logarithm is being used, unless (and this one is a 
> large pet peeve of mine) the authors are inconsistent, or mix 
> notation. Students have no call to be confused by such little 
> things :)
>
>                     C.O.
>
>
>
>
> On Friday 06 February 2009 02:14:24 am Murray Eisenberg wrote:
>> So far as I have seen, almost any recently published, high-selling
>> textbook in calculus -- as distinct from advanced calculus or 
>> analysis
>> -- aimed at the U.S. market uses ln rather than log for the natural
>> logarithm.
>>
>> No wonder students are confused when they go on to a more advanced
>> course and suddenly it's log, not ln.
>>
>> Then of course there's the issue that computer scientists often use 
>> log
>> to mean base-2 log.
>>
>> Andrzej Kozlowski wrote:
>>> Tthe notation ln seems to have become essentially extinct since the
>>> disappearance of slide rules. It fact, was almost never used in 
>>> books
>>> on analysis or calculus aimed at mathematicians. I have just 
>>> checked and
>>> Dieudonne, Foundations of Modern Analysis, published in 1969 uses 
>>> log,
>>> Apostol, Calculus, published in 1967 uses log, Rudin, "Principles of
>>> Modern Analysis", published in 1964 uses L after remarking that "the
>>> usual notation is, of corse, log"), Rudin "Real and complex 
>>> analysis",
>>> published in 1970 uses (naturally) log. Of 5 books that I have 
>>> looked
>>> at only one, Fichtenholtz - A course of differential and integral
>>> calculus (in Russian) published in 1966 uses ln, which is presumably
>>> because it was aimed at engineers, who in those days still used 
>>> slide
>>> rules (at least in Russia). (In spite of that, it is still a rather
>>> good book).
>>>
>>> Andrzej Kozlowski
>>>
>>>
>>> On 4 Feb 2009, at 11:18, Murray Eisenberg wrote:
>>>
>>>> No, in mathematics log x or log(x) is a perfectly acceptable, 
>>>> perhaps
>>>> the predominant, notation for the base-e, natural logarithm.
>>>>
>>>> In calculus books, ln x or ln(x) is typically used for that --  
>>>> so as
>>>> not to confuse students who were taught that log means the base-10
>>>> logarithm.
>>>>
>>>> O.T.: P.S. M.I.T. has an all-male a cappella singing group named 
>>>> the
>>>> "Logarhythms".
>>>>
>>>> slawek wrote:
>>>>> The natural logarithm function in "traditional form" in 
>>>>> Mathematica
>>>>> (version
>>>>> 6.0.2.0)
>>>>>
>>>>> Log[x]//TraditionalForm
>>>>> log(x)
>>>>>
>>>>> This is "not a bug but a feature", but in mathematics the natural
>>>>> logarithm
>>>>> is just ln(x) or even ln x.
>>>>> The true traditional notation use log for decimal logarithm, ln 
>>>>> for
>>>>> natural
>>>>> logarithm, lb for binary logarithm, and
>>>>> log_{b}x  for logarithm with base b. Unfortunatelly in most 
>>>>> computer
>>>>> programs (see FORTRAN) LOG
>>>>> stands for natural logarithm (an exception is Pascal).
>>>>>
>>>>> Nevertheless, how to force to use ln(x) instead log(x) ?
>>>>>
>>>>> The brute way is use /.Log->ln//TraditionalForm.
>>>>>
>>>>> Is any more elegant way to do this?
>>>>>
>>>>> slawek
>>>>>
>>>>>
>>>> --
>>>> Murray Eisenberg                     murray at math.umass.edu
>>>> Mathematics & Statistics Dept.
>>>> Lederle Graduate Research Tower      phone 413 549-1020 (H)
>>>> University of Massachusetts                413 545-2859 (W)
>>>> 710 North Pleasant Street            fax   413 545-1801
>>>> Amherst, MA 01003-9305
>>>>
>>>
>>>
>>
>
>
>
> --
> =========================
==========================
=========
> Curtis Osterhoudt
> cfo at remove_this.lanl.and_this.gov
> PGP Key ID: 0x4DCA2A10
> Please avoid sending me Word or PowerPoint attachments
> See http://www.gnu.org/philosophy/no-word-attachments.html
> =========================
==========================
=========
>
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