Re: Sometimes <space> means multiple

*To*: mathgroup at smc.vnet.net*Subject*: [mg75567] Re: [mg75532] Sometimes <space> means multiple*From*: János <janos.lobb at yale.edu>*Date*: Sat, 5 May 2007 06:04:38 -0400 (EDT)*References*: <200704270918.FAA23598@smc.vnet.net> <200704290714.DAA21234@smc.vnet.net> <200704300738.DAA22373@smc.vnet.net> <200705010719.DAA07230@smc.vnet.net> <200705020751.DAA05016@smc.vnet.net> <200705030746.DAA17296@smc.vnet.net> <C5565DB1-9FCE-4F3A-994E-12BF2776F3D9@mimuw.edu.pl> <200705040816.EAA04967@smc.vnet.net>

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. 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 >>>>>>>> >>>>>>>> ***************************************************************= >>>>>>>> *= > >>>>>>>> * >>>>>>>> This e-mail and any files transmitted with it may be >>>>>>>> proprietary == >>> >>>>>>>> >>>>>>>> and are intended solely for the use of the individual or entity >>>>>>>> to == >>>>> >>>>>>>> >>>>>>>> whom they are addressed. If you have received this e-mail in = >>>>>>>> >>>>>>>> error please notify the sender. Please note that any views or >>>>>>>> opinions presented in this e-mail are solely those of the >>>>>>>> author == >>> >>>>>>>> >>>>>>>> and do not necessarily represent those of ITT Corporation. >>>>>>>> The == > >>>>>>>> >>>>>>>> recipient should check this e-mail and any attachments for >>>>>>>> the == > >>>>>>>> >>>>>>>> presence of viruses. ITT accepts no liability for any damage = >>>>>>>> >>>>>>>> caused by any virus transmitted by this e-mail. >>>>>>>> ***************************************************************= >>>>>>>> *= > >>>>>>>> **= >>> >>>>>>>> * >>>>>>>> =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)

**Follow-Ups**:**Re: Re: Sometimes <space> means multiple***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**Re: Re: Re: RE: Re: Sometimes <space> means multiple***From:*János <janos.lobb@yale.edu>

**Re: Re: Re: Re: RE: Re: Sometimes <space> means multiple***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Re: Re: Re: Re: RE: Re: Sometimes <space> means multiple***From:*János <janos.lobb@yale.edu>

**Re: Re: Re: Re: Re: Re: RE: Re: Sometimes <space> means multiple***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>