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MathGroup Archive 2007

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Re: Sometimes <space> means multiple

Well, well,...

To Point 1:	"very closely" is personal taste.  A cup of soup with a 
piece of hair in it is very closely resembles a cup of soup without 
it,... till you find that piece of hair in it.  From there on it is 
not a cup of soup at all :)

To Point 2:  <alt>+<shift>+<9> - for Mac users change <alt> for 
<option> - IS available for real multiplication and that would not 
just "very closely resemble" multiplication but it would be itself.

2 \[CenterDot] 3
2 \[CenterDot] 3

It just requires some intellectual braveness from WRI to make it happen.

To Point 3:
a.	I just have to scroll down a little to cite from Andrzej:
>>>>>> 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.
Being "shocked" is somewhat different from "I never wrote" , although 
I have to admit that for someone itmight look like a "very close 
resemblance" :)

b.  Never heard about that book.  I learned that little algebra I 
know from Andor Kert=E9sz, Jen=F6 Erd=F6s and K=E1lm=E1n Gy=F6ry.

To Point 4. /where Andrzej is falling out from himself like a ballast 
from a hot air balloon :)/

Apple's Mac is about as obscure to Wintel as Hungarian to English.  I 
bet that even Andrzej is using this obscure platform instead of 
attaching himself to the crowd with a wintel machine.  The US still 
would not have any "nukelar" weapons if four men - Szil=E1rd, Neumann, 
Wigner, Teller, using this obscure language - would not hatched that 
out by THINKING and discussing it in that obscure language.
  /Oppenheimer always fumigated about it but for the army the bomb 
was more important then to introduce a "Just English" policy.  Same 
thing happened later on with the Saturn V rocket but there Hungarian 
was replaced with German, and I bet that not too far from now similar 
achievements will be done by folks who will not speak English, but 
rather Chinese or Farsi - other obscure languages for the anglo world/
Well, in that pdf I cited - in that obscure language - especially on 
page 52 where the structure of a linear space is getting established, 
either nothing or the center dot is used for the multiplicative 
operation.  Neither "asterix" nor "space" is used.   If Erd=F6s just 
for a passing moment would have thought that "space" is "very 
closely  resemble" multiplication I am sure he would not hesitate to 
use it.  For him it was not even close.  When it comes to algebra or 
notation I go with Erd=F6s.  I never met anyone who paid as much 
attention to details than he.

As regarding to my "personal psychological needs" to "waste an 
inordinate amount of intellectual energy" I cannot add anything.  
Newbies always do it.  I hope experts are already scaled that obstacle.


On May 4, 2007, at 4:16 AM, Andrzej Kozlowski wrote:

> 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
> notation.
> 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
> multpilication".
> 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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>>>>>>> --
>>>>>>> Murray Eisenberg                     murray at
>>>>>>> Mathematics & Statistics Dept.
>>>>>>> Lederle Graduate Research Tower      phone 413 549-1020 (H)
>>>>>>> University of Massachusetts                413 545-2859 (W)
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>>>>> ----------------------------------------------
>>>>> Trying to argue with a politician is like lifting up the head of a
>>>>> corpse.
>>>>> (S. Lem: His Master Voice)

Rat race has one disadvantage: even if you win you remain a rat. 
(Lily Tomlin)

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