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Re: Re: Sometimes <space> means multiple
I see nothing worth commenting in this strange monologue, except
perhaps to remark that the people whose names you drop so readily had
more in common than jus the language of the country they happened to
be born in. They sure acheived great things will never know whether
that language was a help or a hindrance. Who knows, they might have
achieved even more had they been born speaking a non-obsure language,
like, for example, Grisha Perelman ;-)
Andrzej
On 5 May 2007, at 19:04, J=E1nos wrote:
> 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. =46rom 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.
>
> In[1]:=
> 2 \[CenterDot] 3
> Out[1]=
> 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:
> <snip>
>>>>>>> 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.
> </snip>
> 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.
>
> J=E1nos
>
>
> 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
>>>>
>>>> http://www.math.klte.hu/~szekely/Jeno11.pdf
>>>>
>>>> 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 sbcglobal.net]
>>>>>>>>> Sent: Thursday, April 26, 2007 3:35 AM
>>>>>>>>> To: mathgroup at smc.vnet.net
>>>>>>>>> Subject: [mg75364] [mg75358] Re: Sometimes <space> means
>>>>>>>>> multiple , sometimes not
>>>>>>>>>
>>>>>>>>> On 4/25/07 at 5:27 AM, siewsk at bp.com 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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>
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>>
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>>>>>>>>> *=
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>>>>>>>>> *=
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>>>>>>>>> **=
>>>>
>>>>>>>>> *
>>>>>>>>> =0D
>>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>>> 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
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> ----------------------------------------------
>>>>>> 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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