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MathGroup Archive 2007

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Re: Re: Re: Re: Re: Re: RE: Re: Sometimes <space> means multiple

  • To: mathgroup at
  • Subject: [mg75532] Re: [mg75500] Re: [mg75474] Re: [mg75442] Re: [mg75426] Re: [mg75423] Re: [mg75364] RE: [mg75358] Re: Sometimes <space> means multiple
  • From: Andrzej Kozlowski <akoz at>
  • Date: Fri, 4 May 2007 04:16:08 -0400 (EDT)
  • References: <> <> <> <> <> <> <>

I think a summary of the main points may be helpful to others who 
have not followed this discussion.

1. In traditional mathematical notation "nothing" is the most 
commonly used symbol for multiplication. Mathematica allows one to 
use this traditional notation in all situations where it is 
unambiguous. In all situation where using "nothing" would lead to 
ambiguity an empty space is used, which produces (in traditional 
form) output that very closely resembles traditional mathematical 

2. InputForm (like the syntax of other programing languages such as C 
etc) is based on ASCII so the relevant question is only which of the 
ASCII characters should be used to denote multiplication. Of all the 
available characters only the period and the asterisk are ever used 
to denote binary operations. The first one is not available since it 
is already used for Dot product. Nobody ever claimed that ASCII is 
the ideal solution for mathematical typesetting, only that it was all 
that there was available for InputForm.

3. I never wrote that the asterisk (*) is commonly used to denote 
multiplication. I only wrote that it is sometimes used to denote a 
binary operation. It is, of course, done when the operation is not 
the standard multiplication and one does not want to use notations 
that could be confused wiht standard multiplication. Anybody with the 
slightest acquaintance with  abstract algebra literature could easily 
come up with such examples. I will just refer to the first book I 
picked up form my shelf, which is probably the most famous and widely 
used algebra textbook in the world:Van Der Waerden's "Algebra". This 
notation can be found in Chapter 13, section 97 entitled "Star 
The fact that the asterisk is used to denote some sort of 
multiplication makes it a better choice for ordinary multiplication 
that characters that are never used for any such purpose.

4. There is no point at all, (not counting personal psychological 
needs of the poster) to post links to papers written in an obscure 
language, particularly by an author whose large number of papers 
written in English are easily available. (and whose lectures, by the 
way,  I have personally attended and still have hand written notes 
from them). Even if it were true that this particualr mathematician 
never used a "star" to denote anything at all, what sort of 
"intellectual value" does this have as an argument in the context of 
this thread?

Andrzej Kozlowski

On 3 May 2007, at 18:05, Andrzej Kozlowski wrote:

> I suggest trying read other people posts before wasting what seems 
> to be an inordinate amount of intellectual energy on replying to them.
> Andrzej Kozlowski
> On 3 May 2007, at 16:46, J=E1nos wrote:
>> Just to be sure I looked up Jen=F6 Erd=F6s selected teachings 
>> again at
>> and found no usage of "space" or "asterix" or "star" in any shape or
>> form there for multiplication.  I could see only nothing or the
>> central point for multiplication.
>> So when someone is claiming that the virtuosity of Mathematica to
>> convert "a b" into "a*b" and vice verse is the best thing after
>> sliced bread, I am not impressed.
>> With the best,
>> J=E1nos
>> P.S.  If you can read Hungarian, you will find that the pdf listed
>> above is one of the finest work a real mathematician ever produced.
>> On May 2, 2007, at 3:51 AM, Andrzej Kozlowski wrote:
>>> I think I can see some advantages to "intellectual laziness". It
>>> might, for example, stop people writing long posts when they have no
>>> point to make.
>>> So to make it short: it was already pointed by someone else that
>>> Mathematica's use of "space" for multiplication is simply the
>>> nearest =
>>> approximation to using nothing at all - by far the most common
>>> convention in algebra. Mathematica does allow "nothing" to be used
>>> when  no ambiguity results; in other cases space is used, which
>>> approximates rather well what one can see in books an d papers on
>>> algebra.
>>> In InputForm asterisk is used because central dot is not available
>>> in =
>>> ASCII and ordinary dot is used, naturally, for dot product. Asterisk
>>> is sometimes used in books on algebra do denote binary operations,
>>> probably more often than "x" (which can, of course,  be used in
>>> TraditionalForm in Mathematica).
>>> Intellectual laziness (presumably due to infection) prevents me from
>>> writing any more on this subject.
>>> Andrzej Kozlowski
>>> On 1 May 2007, at 16:19, J=E1nos wrote:
>>>> I think the reason for "space" used as multiply is the typical 
>>>> anglo-
>>>> american intellectual laziness :)  /Old Hungarian proverb:  "Whose
>>>> shirt it is not, should not take it on"/
>>>> Steve just did not want to type an extra character when he came up
>>>> with the design - that is it.  He was also constrained by the 
>>>> ASCII ==
>>>> 7 =
>>>> bit.
>>>> If I look back on my education for multiplication in elementary
>>>> school a dot was use on the "middle of the lane".  On a Mac it is
>>>> <Option>+<Shift>+<9>.
>>>> Now to use that would have been more painful than just <Shift>+<8>,
>>>> wouldn't it ?.
>>>> The <Shift>+<8> came to the math circles via computers and with
>>>> punch =
>>>> cards where the restrictive ASCII 7 bit ruled the world and "a" and
>>>> "b" had to be tightened with SOMETHING.
>>>> Looking many professional journal pdfs one thing is sure.  Neither
>>>> the "space" nor the "star" is used for multiplication.  It is still
>>>> the dot on the "middle of the lane", a small "x" or nothing.  That
>>>> is, I never see "a*b" or "a b" as a multiplication of a and b but
>>>> rather I see "ab" or "a=B7b".
>>>> With the best,
>>>> J=E1nos
>>>> P.S.  If I take the "a b" to its ultimate test and "try" it in pre-
>>>> fix " ab" or post-fix "ab " that shows clearly the dumbness of the
>>>> usage of space in its pure naked form :)
>>>> On Apr 30, 2007, at 3:38 AM, Andrzej Kozlowski wrote:
>>>>> I compltely agree. I also think that any comparisons between C+
>>>>> + and
>>>>> Mathematica in this respect are completely off the mark, unless of
>>>>> course sombody decides to develop an analogue of 
>>>>> "TradtitionalForm"
>>>>> for C++.
>>>>> I would also like to point out the following obvious but not
>>>>> insignificant fact. Enter  a b (or 2 3  if you prefer) and
>>>>> convert to
>>>>> InputForm. You will obtain an explicit asterisk in place of the
>>>>> space. Conversely, enter a*b and convert to TraditionalForm (or =

>>>>> even
>>>>> StandardForm). You will get a space instead of the asterisk.
>>>>> This, in
>>>>> my opinion,  is exactly how it should be. In fact, I am somewhat
>>>>> shocked that anyone would claim otherwise.
>>>>> Andrzej Kozlowski
>>>>> On 29 Apr 2007, at 16:14, Murray Eisenberg wrote:
>>>>>> Why "mistake"?  Why not allow Mathematica to mimic as much of
>>>>>> traditional mathematical notation as possible without running 
>>>>>> into
>>>>>> genuine ambiguity?
>>>>>> After all, it's really convenient to be able to use 2 Exp[x] and
>>>>>> Cos[2
>>>>>> t] -- and even 2Exp[x] and Cos[2t] -- without having to insert an
>>>>>> extra,
>>>>>> distracting multiplication symbol.  Then the usage in 2 4, for
>>>>>> example,
>>>>>> just extends that.
>>>>>> In my own work, I ordinarily include an explicit multiplication
>>>>>> symbol
>>>>>> -- and I prefer the multiplication sign one gets from Esc * Esc
>>>>>> instead
>>>>>> of the FORTRANish * -- when the factors are numbers.  There's
>>>>>> nothing to
>>>>>> prevent you from doing that if you don't like the implicit
>>>>>> multiplication indicated by a space.
>>>>>> Virgilio, Vincent - SSD wrote:
>>>>>>> Personally, I think it was a mistake to overload the meaning of
>>>>>>> "space"
>>>>>>> to multiply. I bet Wolfram Inc. would reverse that decision now,
>>>>>>> if it
>>>>>>> wasn't for backward compatibility.
>>>>>>> I like to compare Mathematica to C++. Somewhere in his writings,
>>>>>>> Bjarne
>>>>>>> Stroustrup mentions the same issue, and his decision not to
>>>>>>> overload
>>>>>>> whitespace. I think the question also arises on the Boost 
>>>>>>> mailing
>>>>>>> lists
>>>>>>> now and then, mostly tongue-in-cheek.
>>>>>>> (Corrections welcome.)
>>>>>>> Vince Virgilio
>>>>>>> -----Original Message-----
>>>>>>> From: Bill Rowe [mailto:readnewsciv at]
>>>>>>> Sent: Thursday, April 26, 2007 3:35 AM
>>>>>>> To: mathgroup at
>>>>>>> Subject: [mg75364] [mg75358] Re: Sometimes <space> means
>>>>>>> multiple , sometimes not
>>>>>>> On 4/25/07 at 5:27 AM, siewsk at wrote:
>>>>>>>> As a newbie, I was taught that <space> character in Mathematica
>>>>>>>> means
>>>>>>>> multiple. But sometimes it does not.
>>>>>>>> For example:
>>>>>>> <examples snipped>
>>>>>>> Mathematica allows spaces to be placed before or after any
>>>>>>> operation.
>>>>>>> Consequently, a space is only interpreted as a multiply when 
>>>>>>> there
>>>>>>> is no
>>>>>>> other operator or other possible interpretation.
>>>>>>> So, -4 -2 is the same as -4 - 2 or -4-2 and gives -6 but
>>>>>>>      -4 (-2) will yield 8
>>>>>>> --
>>>>>>> To reply via email subtract one hundred and four
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>>>>>>> **=
>>>>>>> *
>>>>>>> =0D
>>>>>> --
>>>>>> Murray Eisenberg                     murray at
>>>>>> 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
>>>> ----------------------------------------------
>>>> Trying to argue with a politician is like lifting up the head of a
>>>> corpse.
>>>> (S. Lem: His Master Voice)

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