The Logic Off Topic list

>I'm glad someone's
>interested in it.

Actually most mathematicians believe the beauty of mathematics in and of 
itself without any regard to real world applications. I remember when I 
was a student, one professor quoted some famous mathematicians said, 
about his work in math :
"I knit eight armed sweaters. If an octopus comes along and finds them 
useful thats fine." I think this was in regard to Hilbert spaces, which 
were invented in the 1920's in a purely mathematical context, but then 
decades later were found to be the perfect representation for quantum 
mechanics. Mathematics is full of these kinds of eventual applications. 
Galois who lived in the 1820's could not imagine that his theories would 
be useful for modem and satelitte error correcting codes in the future.

Most, but not all mathematicians, are musicians of some sort too. My 
graduate advisor used to play classical violin in community concerts as a 
hobby. As an undergraduate, we had a math club, and had a party at one of 
the professors' houses. Almost everyone there took a turn on the piano or 
guitar.

Mathematicians are very much artists.

By the way, just because i made a comment about the changing attitudes of 
women in our society doesn't have any reflection on my own love life or 
ability to 'get chicks'. I have no complaints - despite my knowledge of 
mathematics!

I made that comment just as an observation about society. I think that 
there was something about the 60's and 70's with all the talk of 
equality, which lead women to be more equal in all ways. Now, equality 
means 'equal pay' but not equal responsibility or other forms of 
equality. I was commenting on what I see all around me. In fact, young 
people in general seem so much more selfish and self-absorbed - but I'm 
sure my parents generation thought the same of us too.

>Actually most mathematicians believe the beauty of mathematics in and of
>itself without any regard to real world applications.
???? !!!! ****

"One would have to have completely forgotten the history of mathematics so 
as to not remember that the desire to know nature has had the most constant 
and also the happiest influence on its development".
Henri Poincare

"The scientist does not study nature because it is useful; he studies it 
because he delights in it, and he delights in it because it is beautiful. 
If nature were not beautiful, it would not be worth knowing, and if nature 
were not worth knowing, life would not be worth living. Of course I do not 
here speak of that beauty that strikes the senses, the beauty of qualities 
and appearances; not that I undervalue such beauty, far from it, but it has 
nothing to do with science; I mean that profounder beauty which comes from 
the harmonious order of the parts, and which a pure intelligence can grasp".
Henri Poincare

"The profound study of nature is the most fertile of all sources of 
mathematical discoveries".
Jean Baptiste Fourier

"Mathematics compares the most diverse phenomena and discovers the secret 
analogies that unite them".
Jean Baptiste Fourier

"Mathematical Analysis is as extensive as nature herself".
Jean Baptiste Fourier


Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

Thoughts from the mind of GAmoore@..., 09-11-2001:

>I made that comment just as an observation about society. I think that
>there was something about the 60's and 70's with all the talk of
>equality, which lead women to be more equal in all ways. Now, equality
>means 'equal pay' but not equal responsibility or other forms of
>equality.

Every research recently conducted in this field shows that women 
still get substantially less paid than men when performing the same 
kind of jobs or tasks.

So in fact you got it backwards: even when having the same 
responsibilty, they still don't get the same rewards.


cheers,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html

Thoughts from the mind of Kool Musick, 09-11-2001:

>  >Actually most mathematicians believe the beauty of mathematics in and of
>>itself without any regard to real world applications.
>???? !!!! ****

Yes, he's right (hey GA: see!  again I agree!  That's already 3 times 
this week!)

>"One would have to have completely forgotten the history of mathematics so
>as to not remember that the desire to know nature has had the most constant
>and also the happiest influence on its development".
>Henri Poincare

Not to the point.  GA says, rightfully, that most math-heads believe 
in, or are able to appreciate, the beauty of mathematics "in itself" 
-- contrary to most mathematical "laymen" who think mathematics is 
just a boring bunch of formulas and incomprehensible stuff, without 
any inherent "quality" or esthetics.

That doesn't mean they (mathematicians) don't care for applications, 
and it doesn't mean they can't be inspired by nature or any other 
real-world phenomena, or can't rejoice in the applicability of their 
discoveries.

>"The scientist does not study nature because it is useful; he studies it
>because he delights in it, and he delights in it because it is beautiful.

Which is not at all opposed to what GA says.  "Delight in nature" 
doesn't exclude the possibility to delight in pure abstract form as 
well.  Lots of people delight in nature, but very few delight in pure 
abstractions.

>"The profound study of nature is the most fertile of all sources of
>mathematical discoveries".
>Jean Baptiste Fourier

Ditto.

>"Mathematics compares the most diverse phenomena and discovers the secret
>analogies that unite them".
>Jean Baptiste Fourier

"Phenomena" could as well refer to abstract phenomena -- i.e. "pure" 
mathematics.

>"Mathematical Analysis is as extensive as nature herself".
>Jean Baptiste Fourier

Which, again, is not an argument.

Sorry Kool, but I think you missed the point this time...


tata,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html

Hi Hendrik Jan,

>Yes, he's right (hey GA: see!  again I agree!  That's already 3 times
>this week!)
Sigh. Not entirely.

Being a person greatly interested in the HISTORY of the subject, one has to 
bear in mind the appreciation of differences in the ways of thinking that 
seem 'normal' to us today; but that were not really accepted and would be 
hard to recognize and/or would seem strange to thinkers who existed prior 
to the time those differences became accepted. The 'real' differences 
between pure and applied mathematics, and between these and 'mathematical 
logic', and in fact between this and the 'history of mathematics' are in 
fact quite hard to state even today. It is also only recently that they 
have become properly recognized as differences important enough to be given 
names within the discipline.

Nowadays, we see the main differences between the pure and the applied 
variety, which is mainly the topic under debate here, as resting not only 
in the topics studied, but also in the approach to be taken to how given 
problems are to be solved. Both pure and applied mathematicians, of course, 
have to develop the important mathematical skills required that enable them 
to solve problems, but they tend to adopt different strategies. Since you 
teach mathematics yourself, you will be intuitively aware, at the very 
least, of this fact, although you may not have focused on those differences 
because they aren't that important in that a wrong answer is just a wrong 
answer, period. Pretty much, though, when you emphasize for example the 
specialized mathematical language of algebra as being the preferred method 
for learning and understanding mathematical concepts and as the preferred 
way to solve problems, then you are working more within the field of pure 
mathematics. In order to learn and progress in this field, it is necessary 
to present, more directly, the mathematical theories underlying those 
concepts (and also in a systematic and orderly way), to learn how to find 
exact value solutions to given equations, and to use formal mathematical 
reasoning and given models in the solving of problems. To return to applied 
mathematics, one teaches there more by the setting of challenging and 
interesting problems and activities that tend to be taken from real-life, 
or else that are devoted to the completion of a specific project set by the 
teacher. One encourages students to develop their mathematical skills in 
the mathematical operations under review more by getting them to do it 
often enough so that they understand the concepts. One also teachers more 
using graphs, constructing scales, diagrams and tables -- and these days 
using computers and spreadsheets. These are usually necessary when long and 
complex mathematical calculations are required. To the applied mathematics 
teacher the graphing and the spreadsheet operations are opportunities for 
the students to develop a very real competency in algebra, for example. 
This does not mean that pure mathematicians never use graphs! That is an 
absurdity, but I hope I have said enough for you to see that there is a 
difference between these approaches, even though the fundamental aim is the 
same -- to do mathematics well.

I have focused more broadly on the differences, though and in the 
applications, between pure and applied mathematics, but of course each 
specified division within mathematics does have its unique form of 
reasoning. Statistical theory has its particular form of reasoning and 
standard of proof; probability theory has its particular form of reasoning 
and standard of proof and so on and so forth. Many problems can in fact be 
solved through a variety of methods. I used to have a truly wonderful book 
that had over 200 methods for proving the Pythagoras Theorem which nicely 
demonstrated the very different kinds of methods of reasoning and proofs 
contained in mathematics.

But ... no matter that there may be different methods, what they all have 
in common, of course, is proof. This is easy to say, but the word 'proof' 
has had different meanings in different contexts, and has also had 
different meanings in historical epochs. What does seem to be broadly true, 
though is that proof is what mathematicians use to communicate a kind of 
quality of essential validity -- truth -- concerning a given piece of 
knowledge.

However, as with any language, the specific forms that 'proof' has taken 
has changed throughout the history of the subject -- as also, inevitably, 
the topics which that unique language can discuss. Mathematics has changed 
and the things mathematicians can prove has changed, as also the things 
that mathematicians try to prove has changed. These days, mathematicians 
can try to prove things that would have been impossible for them even to 
try to think about proving in earlier epochs simply because the nature of 
the language -- and therefore the nature of proof -- has changed so much. 
And essentially, in this context, what has changed is the nature and the 
perception of what it is to communicate, and what it is that can be 
communicated. But what does seem to have distinguished mathematics over the 
ages is the attempt to communicate a result or a discovery -- the 
excitement felt by the scribes in the Rhind Papyrus, for example, in 
presenting their information -- by using an argument or sequence of 
statements the aim and the end of which is to utterly convince the reader 
that the result present is truly valid. Of course, even coming by THAT 
understanding, by that kind of attempt to distill the essence of 
mathematics, requires a very modern perception of what it is that 
mathematics try to do within all the various branches, as opposed to what 
other disciplines try to do. It's hard to be sure, in fact, that even in 
the preceding statements, the real 'thing' or 'essence' that distinguishes 
mathematics has in fact been successfully captured. After all, there's a 
very good argument for saying that the whole idea of 'proof' transcends 
mathematics. Philosophers also try to use logical argument. So do lawyers. 
It's there in rhetoric both within and outside 'religious' arguments. Where 
many religious arguments fall down is in the original assumptions, and not 
in the argument that it built upon those assumptions. As you well know, 
many great scientists and mathematicians have been deeply religious, and 
have built impeccable proof structures built upon their religious 
assumptions whether they be Islamic, Jewish or whatever. If in the opinion 
of the reader the argument presented by that kind of a thinker (and Newton 
for example was very religious) falls down then the inconsistency can often 
be traced back to the speciousness (in the critic's eyes) of the initial 
assumptions.

Kool Musick quoted:
> >"One would have to have completely forgotten the history of mathematics so
> >as to not remember that the desire to know nature has had the most constant
> >and also the happiest influence on its development".
> >Henri Poincare

HJ said:

>Not to the point.
Well ... IMO it is exactly to the point, and I will try to explain why. 
Poincare was very well versed in the history of mathematics. It was what 
led him to his first great discoveries in maths, such as when he tackled 
the three body problem. He also clearly understood the nature of proof and 
the differences between pure and applied mathematics. When he presented his 
paper to the King of Oscar II of Sweden to claim his reward, his paper 
contained a section on why there was no 'exact' solution available. In this 
regard, though, he was a vast improvement on Euler in that Poincare 
outlined the reasons why, and pretty much put the issues concerned with 
treating dynamical systems on the map. All that was then left for the King 
to decide was whether or not Poincare had given 'the best solution 
possible', and whether or not a 'best solution' was good enough given that 
not even Poincare had given an exact solution, and had only really claimed 
that an exact solution was impossible. Luckily for Poincare, one of the 
judges was Weierstrass who wrote to the King's ambassador (I think it was) 
and said: "You may tell your Sovereign that this work cannot indeed be 
considered as furnishing the complete solution of the question proposed, 
but that it is nevertheless of such importance that its publication will 
inaugurate a new era in the history of Celestial Mechanics. The end which 
His Majesty had in view in opening the competition may therefore be 
considered as having been attained".

What Poincare had done was change the game yet again by changing the nature 
of proof, and by changing what was an acceptable solution. Pretty much -- 
creating a new branch of mathematics with new ways to tackle the solutions 
there was regarded as a 'correct' solution. I think this a pretty sensible 
and felicitous approach, don't you? But ... Poincare took the approach he 
did because he troubled to acquaint himself with the history of the subject 
... which was also actually the first thing that Andrew Wiley did when he 
decided that he was really rather interested in solving the Fermat problem. 
Surely a sensible thing to do.

>   GA says, rightfully, that most math-heads believe
>in, or are able to appreciate, the beauty of mathematics "in itself"
>-- contrary to most mathematical "laymen" who think mathematics is
>just a boring bunch of formulas and incomprehensible stuff, without
>any inherent "quality" or esthetics.

And ... my sole point is that this is a very modern approach. Earlier 
epochs did not really stress its importance in this kind of way, although 
they surely at least implicitly recognized it. Those were smart people and 
I'm quite sure that if we went back and pointed these things out to them 
they'd get the message within milliseconds. A separate issue would be 
whether or not, having recognized it, they'd look on it as particularly 
important. In that kind of way ... earlier mathematicians did see the 
difference between solving for the physical motions of the planets and 
solving for the motions of the planets by interpreting their behaviour with 
respect to the lives of mortal humans ... but by and large they just didn't 
see those differences as being particularly important. That's the 
historical record. Things in this regard have changed so much that nowadays 
most (but not all) respectable mathematicians distance themselves as far as 
possible from astrology. In fact many mathematicians take great exception 
to the very idea that their tools (i.e. physically determining the 
positions of the planets) are used in that kind of way at all and wish that 
those who do it would stop it. Yet ... do I really need to construct a list 
of all the mathematicians in history who made astrological predictions 
seeing it as not only their duty, but a very real part of their job 
description?

Forgive me if I erred, but all I was trying to say was that this was a very 
modern attitude and not really representative of the attitude to the 
subject that has generally prevailed. However, since it does appear that, 
statistically, most of the mathematicians who have ever lived are probably 
alive today (I once read that, but cannot remember where so cannot validate 
the assertion with a reference), I am more than happy to concede this point 
to the both of you and accept that 'most mathematicians who have lived' 
should take precedence over 'most of mathematical history'. Since my stock 
in trade is the history of mathematics, I hope you will accept that this is 
a pretty big concession for me to make and that you will accept it in the 
spirit in which it is offered.

> >"The scientist does not study nature because it is useful; he studies it
> >because he delights in it, and he delights in it because it is beautiful.
>
>Which is not at all opposed to what GA says.  "Delight in nature"
>doesn't exclude the possibility to delight in pure abstract form as
>well.  Lots of people delight in nature, but very few delight in pure
>abstractions.

And ... this is not at all what I was trying to say. Please excuse me for 
the fact that I had deemed it wisest to say nothing at all further about 
the underlying point that I was trying to make, but my experience of the 
L-OT list is that many people upon it are not really interested in the 
sharing and back and forth of information, but are rather more interested 
in always being right themselves. I tried to hint elliptically at what I 
was trying to say hoping that anyone who was really interested would work 
it out for themselves from the scant information I gave in those few 
quotes. I did not see the point in trying to elaborate any further on the 
matter because my experience is that it would have led nowhere but rather 
to another rather pointless exchange of emails. With you personally, 
however, I am perfectly willing to try to present the reasons as to why I 
sent in those quotes for I know that if you come back to me again it will 
be with  something that is not only intelligent, but that is also relevant 
to the points that I am trying to make; and that it will be in a genuine 
spirit of give-and-take. I just didn't want to write any words at all of my 
own and find myself getting absolutely nowhere at the end of it by which I 
mean having had my store of knowledge increased. I do not enjoy it when I 
can palpably feel the little store of knowledge that I have being sucked 
out of me by things that I am reading. I am a bit weird that way.

> >"The profound study of nature is the most fertile of all sources of
> >mathematical discoveries".
> >Jean Baptiste Fourier
Well ... I hope you will understand that in my view that quote was actually 
spot on, because Fourier lived before the times when the kinds of 
distinctions that you and I make were not really being made. (I had 
actually felt a bit like including a quotation from Vetruvius in my earlier 
email, actually, but refrained because what would have been the point, I 
had said to myself?!) I hate to belabour the point, but Fourier was a 
working mathematician in his day, and the attitude he evidences in the 
above statement was the generally accepted one of his day. Mathematicians 
simply did not make, in his day, the distinctions that we now make so 
easily. (I am willing to amend this too -- did make them but regarded them 
as 100% trivial if that would be better!). Laplace, Lagrange, Fourier, 
Euler and the like would not have recognized, for example, that there was a 
SEPARATE field of study called 'mathematical logic' although all of them 
would probably have recognized instantly what that particular subject was 
up to.


>"Phenomena" could as well refer to abstract phenomena -- i.e. "pure"
>mathematics.
Completely accepted -- because that's pretty much what all phenomena become 
once a mathematician starts looking at them from the point of view of the 
language of proof, which is the mathematicians' stock in trade. However, a 
directly related issue is the SOURCE of the phenomena that arouse the 
interest of a mathematician to study them so that they can prove something. 
And ... even within number theory as it was long practised, that source was 
the world of nature. Even Peano (1858-1932) was forced to keep the counting 
of things in mind when he tried to define that slippery concept we know as 
'number'. I gave his dates simply to try to indicate the recency of that 
phenomenon.

What was so outstanding in its day about Gauss' Disquisitiones Arithmeticae 
was the very way in which it helped to emplace number theory at the very 
heart of mathematics, and pure mathematics at that, as perhaps the prime 
exemplars of what mathematicians could and should reason about in and of 
themselves, and without regard for externals. It was a powerful revelation, 
and one that mathematicians quite rightly seized on. The methods and topics 
that Gauss directed himself towards in that kind of way helped to clarify 
what pure mathematics was ... as also did the methods and modes of study he 
directed at the physical problems he equally well delighted in. But ... as 
to the issue of what numbers actually are, not even Gauss really achieved a 
viable definition. To do that, you have to go to other arenas of 
mathematics, and mathematical logicians are even now trying to find and 
plug holes in the definition of number.

What else can I say but that pure mathematicians do not, and cannot have, 
defined objects that they can study 'in the abstract' -- nor methods that 
they can use to treat those objects -- until pure mathematics in itself 
exists as a properly defined subject area. By common consent, that process 
is generally regarded as starting properly with Gauss. But even there, you 
are dealing with somebody in whom mathematics of both the pure and the 
applied varieties took such an easy residence that it would be very foolish 
indeed to try to separate them out in that particular case. It is also 
regarded as not that constructive to try to separate them out too closely 
when dealing with the subject in earlier epochs ... even though it is often 
of great value to US to do so. Nowadays, it is easy to see their 
differences, and one can observe even at grade school level in which 
direction a given mathematician is the more likely to go simply by 
observing the topics they are interested in and the methods they prefer to 
use to solve the kinds of problems they seem to have a natural affinity for.

> >"Mathematical Analysis is as extensive as nature herself".
> >Jean Baptiste Fourier
>
>Which, again, is not an argument.
Fourier did not offer it as an argument, to be honest. He offered it as a 
way of describing a good picture. I think when he said it he was trying to 
convince the wife of one of his friends that what he spent the whole of his 
days doing was really worth while and really a beautiful thing to do. If 
you really want me to I can try and check out the exact context, but I'd 
rather you didn't ask, to be honest, because I have other things to do. The 
above is not a LOGICAL argument ... but it is certainly to me a convincing 
argument that mathematics is a beautiful subject that is well worth 
pursuing. That was all Fourier meant by it. If it does not strike you in 
that way or seems ridiculous, then that's quite fine by me, to be frank.

>Sorry Kool, but I think you missed the point this time...
And ... I have done my very best to indicate why I don't think I have. As 
far as I could see, the major point at issue was what has been the primary 
source of mathematical investigation, of mathematical proof, mathematical 
discovery, and of mathematical appreciation throughout its history. All I 
tried to say is that, contrary to the assertions made in GA Moore's 
original statement, the primary and principal object of study throughout 
mathematical history has been nature itself -- albeit when seen in a very 
particular kind of way. But ... it has been nature. It could not have been 
something abstract like number in and of itself, because the definition of 
number that we have today is very current, and it is only very recently, 
within the last 150 to 200 years, that it has been possible for 
mathematicians to think in those kinds of terms. As far as I can see the 
only way this is not so is if one adopts the 'brute number' approach -- 
i.e. to insist that since most of the mathematicians who have ever lived 
are either alive today or else have lived within the last hundred years 
then that should be the deciding factor in this matter. If that's the way 
the two of you want to play it then I bow my head humbly and respectfully 
concede the point, but this qualification simply was not made clear in the 
original assertion. I took it to mean that it was a statement that was 
being made as one to be accepted as true for all mathematicians through all 
historical epochs. That's all I can say, and I apologise in that case for 
having opened my big mouth.

Come to think of it, it's probably best if I keep my big mouth shut from 
here on in if this is the kind of palaver it's going to cause every time I 
open it.

If I have failed to present my case properly then it is simply because I 
have not learned as much from doing mathematics as you have ... but please 
do accept it from me that my love for the subject is absolutely no less 
than yours. I just became interested in a different side of it, that's all.

I do accept your contention that I might somehow have missed the point ... 
and I accept that contention enough to revisit the issue because I am 
genuinely not trying 'always to be right' or to such a degree that I ever 
refuse to change my mind and therefore stop learning anything. I would 
really much rather be wrong and then grow from it than to insist that I am 
always right and thus ossify. And that really is the truth. What's on 
earth's the point in anything else?

"The whole problem with the world is that fools and fanatics are always so 
certain of themselves, but wiser people so full of doubts".
Bertrand Russell.

I am not particularly wise, but I do have enough doubts about things, I 
hope, to be open to more things.

I hope it's OK if I contact you privately should I want further 
clarification on anything.

I thank you most sincerely for your kindness.

I also thank you for the complete lack of personal attacks in your email. 
It has certainly been a refreshing change from some of the stuff I have had 
to wade through recently. I look forward, therefore, to reading anything 
else you might have to say be it on this matter or on anything else.


Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

>>I made that comment just as an observation about society. I think that
>>there was something about the 60's and 70's with all the talk of
>>equality, which lead women to be more equal in all ways. Now, equality
>>means 'equal pay' but not equal responsibility or other forms of
>>equality.
>
>Every research recently conducted in this field shows that women 
>still get substantially less paid than men when performing the same 
>kind of jobs or tasks.
>
>So in fact you got it backwards: even when having the same 
>responsibilty, they still don't get the same rewards.

I hear that regularly too, but I think this is a classic 
misinterpretation of statistics, and I read an article to that affect 
about 6 years ago. I can tell you in my professional experience - both as 
a computer programmer and college professor - that there is absolutley no 
difference in pay at all  - for the same level of education and same 
years of experience. 

And in any area where there is a clear difference, there would be clear 
grounds for a lawsuit and humiliation for the company conducting such 
practices. 

So why the statistics? I suspect, and from what I have seen of the people 
I work with, women are more likely to have gone to lower ranked colleges, 
less likely to have PhDs, less likely to go into the more competitive job 
areas, and more likely to take time off for raising children. A 
significant number of women get married without going to college, and 
either after marriage or after kids are in school, or after kids are 
grown,... go back to school and enter the job market at a later age.

So I don't believe women are discriminated against in any way that I know 
of, or have seen! Perhaps such discrimination existed decades ago, but 
not in a systematic way now. On the other hand, men (in the US) 
contribute a great deal more around the house, to the kids, to the 
cooking, to the shopping, etc. And in the dating arena, women still want 
the guy to pay (depending on the woman) EVEN WITH EQUAL PAY.

I remember years ago, the talk of strip shows as demeaning to women - 
objectifying them as sexual objects. I recall when I was in NY (upstate) 
in the early 80's and when a bar turned to a strip bar, men and women 
were both out there walking picket lines in protest. However, instead of 
society rising to a higher standard of treating women as humans, I see 
the reverse. Men are now treated as sex objects too, the male stripping, 
etc. I see just as many advertisements featuring women in bikinis - even 
more so in fact. In fact, there is a law that you can't create a rap 
video without some fine ass, long legs, and bouncing betties.

Its the same thing with the cold war, every time we think human beings 
will rise to the occasion, they find new lows unimaginable before.

Kool Musick wrote:
>... which was also actually the first thing that Andrew Wiley did

OK sorry.
My fingers slipped or something.
I meant Wiles and not Wiley. In the year he received his 'Special Tribute' 
in the Fields Medal awards, the premier prize in mathematics, two of the 
four Fields Medal recipients (1998) received their prizes for their work in 
mathematical physics.

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

Thoughts from the mind of Kool Musick, 10-11-2001:

>Hi Hendrik Jan,
>
>>Yes, he's right (hey GA: see!  again I agree!  That's already 3 times
>>this week!)
>Sigh. Not entirely.

Also: sigh...  Why do you always have to write complete lectures in 
response to some posting?  True art is the art of "leaving out". 
Less words would have equally sufficed -- or would maybe even have 
been better, as such long postings tend to lose the readers 
attention, and hence don't help in getting your point across.

>Both pure and applied mathematicians, of course, have to develop the 
>important mathematical skills required that enable them to solve 
>problems, but they tend to adopt different strategies. Since you 
>teach mathematics yourself, you will be intuitively aware, at the 
>very least, of this fact, although you may not have focused on those 
>differences because they aren't that important in that a wrong 
>answer is just a wrong answer, period.

I'm very well (and more than just intuitively) aware of the 
differences between pure and applied mathematics, both in education 
and in formal research.

The subject however was not the difference between pure and applied 
maths, and I don't see how this has any bearing on the topic. 
GAmoore simply said that most mathematicians believe that mathematics 
is beautiful in and of itself, without the need to refer to 
applications of mathematics.
That, again, doesn't mean mathematicians can't appreciate a beautiful 
application.  They just are able to appreciate the beauty of pure 
abstraction _as well_, contrary to most non-beta's who see no beauty 
in pure abstraction.  They just see "square" stuff about formulas, 
theorems, proofs and numbers.

A testimony to this is the fact that _any_ half-decent mathematician 
knows what's meant when talking about a "beautiful proof".  The proof 
of the 4-colour-map theorem (or whatever it's called in English) is 
generally regarded to be an ugly proof, and people actually spend 
time to come up with a more esthetically satisfying one -- even 
though the plain _fact_ of the theorem has already been proven.  To a 
"layman" this most often seems absurd.  A proof is a proof, and it's 
all just boring stuff anyway, so why bother?

>These days, mathematicians can try to prove things that would have 
>been impossible for them even to try to think about proving in 
>earlier epochs simply because the nature of the language -- and 
>therefore the nature of proof -- has changed so much.

No, this is not true.  What constituted a proof 500 years ago still 
is a proof today.  What has changed is the scope of the field, and 
hence the amount of "tools" you can use to construct a proof.  The 
concept of what a valid proof is though has remained unchanged. 
Otherwise: why would we still study Euclid's "Elements" today (and 
not just for historical reasons, but to learn math from it)?

>After all, there's a very good argument for saying that the whole 
>idea of 'proof' transcends mathematics.

Yes.

>Philosophers also try to use logical argument. So do lawyers.

Yes, "try to use" is the correct expression :-).

>As you well know, many great scientists and mathematicians have been 
>deeply religious, and have built impeccable proof structures built 
>upon their religious assumptions whether they be Islamic, Jewish or 
>whatever.

Yes, I know.  And what is the point of that observation?

>Kool Musick quoted:
>>  >"One would have to have completely forgotten the history of mathematics so
>>  >as to not remember that the desire to know nature has had the most constant
>>  >and also the happiest influence on its development".
>>  >Henri Poincare
>
>HJ said:
>
>>Not to the point.

Note; I didn't say it isn't true what Poincare says here.  I just 
said it's not to the point.  I.e. it doesn't refute GA's claim that 
most mathematicians are able to appreciate "pure abstract beauty".

>Well ... IMO it is exactly to the point, and I will try to explain why.

OK, go ahead.

[...]
>What Poincare had done was change the game yet again by changing the nature
>of proof, and by changing what was an acceptable solution. Pretty much --
>creating a new branch of mathematics with new ways to tackle the solutions
>there was regarded as a 'correct' solution. I think this a pretty sensible
>and felicitous approach, don't you? But ... Poincare took the approach he
>did because he troubled to acquaint himself with the history of the subject
>... which was also actually the first thing that Andrew Wiley did when he
>decided that he was really rather interested in solving the Fermat problem.
>Surely a sensible thing to do.

Yes, of course.  However, I still fail to see the point you're trying 
to make.  Maybe you can write it down in one or two sentences.  I 
feel that this stream of words only confuses matters instead of 
clearing things up.  It might just be my non-native-English status 
that's playing a role here, but I fail to get the real sense of what 
you're trying to say.

>  >   GA says, rightfully, that most math-heads believe
>  >in, or are able to appreciate, the beauty of mathematics "in itself"
>  >-- contrary to most mathematical "laymen" who think mathematics is
>  >just a boring bunch of formulas and incomprehensible stuff, without
>  >any inherent "quality" or esthetics.
>
>And ... my sole point is that this is a very modern approach. Earlier
>epochs did not really stress its importance in this kind of way, although
>they surely at least implicitly recognized it.

Ah, so this is your point!  OK: so what?  Nobody said anything about 
the past, nobody claimed that mathematicians all over the centuries 
have always been in this or that mindset or whatever, and nobody 
argued that the way mathematics is viewed or appreciated has always 
been the same.

What or who exactly are you arguing with?  Again: this only seems to 
confuse matters instead of clearing anything up (as there initially 
was nothing unclear, as far as I can see).

And, as a sidenote to your comment above: the word "importance" was 
never used.  It's about appreciation.  Something quite different.

>  Those were smart people and
>I'm quite sure that if we went back and pointed these things out to them
>they'd get the message within milliseconds. A separate issue would be
>whether or not, having recognized it, they'd look on it as particularly
>important.

"Important": see above.

>However, since it does appear that, statistically, most of the 
>mathematicians who have ever lived are probably alive today (I once 
>read that, but cannot remember where so cannot validate the 
>assertion with a reference),

:-)  Funny fact.  I don't need any validation.  Some fact should just 
be taken at face value -- they're too good to allow them to be 
refuted by boring facts and validations :-).

>I am more than happy to concede this point to the both of you and 
>accept that 'most mathematicians who have lived' should take 
>precedence over 'most of mathematical history'.

I don't see why one should take precedence over the other, but then: 
I don't see the relevance of either option.

Again I fail to see what this has to do with the observation GA made. 
Every mathematician of whom we know anything at all (i.e. excluding 
Euclid and the likes) has been able to recognize the beauty of pure 
abstraction.  Otherwise they simple wouldn't have been able to become 
great mathematicians -- the whole stuff would just be too boring. 
Even when doing so-called applied maths, a large piece of the work 
(more than 50%) is still "just boring fiddling with numbers and 
formulas".  No-one in his right mind would do that sort of stuff if 
(s)he wasn't able to see the beauty of it.


>  > >"The scientist does not study nature because it is useful; he studies it
>>  >because he delights in it, and he delights in it because it is beautiful.
>>
>>Which is not at all opposed to what GA says.  "Delight in nature"
>>doesn't exclude the possibility to delight in pure abstract form as
>>well.  Lots of people delight in nature, but very few delight in pure
>>abstractions.
>
>And ... this is not at all what I was trying to say.

No, but it is what GA was trying to say.  And _that's_ what we're 
talking about.

GA, if I misinterpreted your words, feel free to step in and say so.

>With you personally, however, I am perfectly willing to try to 
>present the reasons as to why I sent in those quotes for I know that 
>if you come back to me again it will be with  something that is not 
>only intelligent, but that is also relevant to the points that I am 
>trying to make; and that it will be in a genuine spirit of 
>give-and-take.

Well, thanks for your trust, for starters.  Honestly.  But... if your 
point was _only_ to say something like "ok, mathematicians nowadays 
might be delighted by pure abstraction, but that hasn't always been 
so -- here are a few quotes to suggest otherwise", then 1) you should 
have said so from the onset, and 2) your first sentence in your reply 
to GA shouldn't have been "???? !!!! ****".  The latter suggested (to 
me at least) that you didn't agree with GA's remark.  And that, I 
still belief, is in error.

>  > >"The profound study of nature is the most fertile of all sources of
>>  >mathematical discoveries".
>>  >Jean Baptiste Fourier
>Well ... I hope you will understand that in my view that quote was actually
>spot on,

No-one denied its truth, as far as I can see.

>Laplace, Lagrange, Fourier, Euler and the like would not have 
>recognized, for example, that there was a SEPARATE field of study 
>called 'mathematical logic' although all of them would probably have 
>recognized instantly what that particular subject was up to.

A non-issue, since mathematical logic is just a bit over 100 years old...

>as to the issue of what numbers actually are, not even Gauss really achieved a
>viable definition. To do that, you have to go to other arenas of 
>mathematics, and mathematical logicians are even now trying to find 
>and plug holes in the definition of number.

And so... ?

>What else can I say but that pure mathematicians do not, and cannot have,
>defined objects that they can study 'in the abstract' -- nor methods that
>they can use to treat those objects -- until pure mathematics in itself
>exists as a properly defined subject area.

This is rethoric.  Of course, if you think that pure mathematics is 
not a properly defined subject area, then there cannot even be such a 
thing as a "pure mathematician", and thus, obviously, these 
non-existent subjects can't have defined _anything_ -- simply because 
they (the subjects) don't exist.

In a more practical sense, this still doesn't hold.  There's no real 
reason a pure mathematician cannot define abstract concepts and 
figure out ways how to deal with them.  Set theory, especially the 
study of infinite sets, is a purely abstract thing.  Cantor figured 
out a way how to deal with them (and met great resistance initially). 
No problem there...

>  > >"Mathematical Analysis is as extensive as nature herself".
>>  >Jean Baptiste Fourier
>>
>>Which, again, is not an argument.
>Fourier did not offer it as an argument, to be honest.

No, but you seemed to be doing so.  For the record: I happen to agree 
with the above quote.  I just fail to see its relevance.

>I think when he said it he was trying to
>convince the wife of one of his friends that what he spent the whole of his
>days doing was really worth while and really a beautiful thing to do.

"A beautiful thing to do" -- exactly what GA said...

>The above is not a LOGICAL argument ... but it is certainly to me a convincing
>argument that mathematics is a beautiful subject that is well worth
>pursuing.

Again: exactly the point GA tried to make.

>  That was all Fourier meant by it. If it does not strike you in
>that way or seems ridiculous, then that's quite fine by me, to be frank.

No, not at all.  I agree wholeheartedly with it in fact.

>As far as I could see, the major point at issue was what has been the primary
>source of mathematical investigation, of mathematical proof, mathematical
>discovery, and of mathematical appreciation throughout its history.

No, not at all.  Either _you_ missed the point completely, or I did...

>  All I
>tried to say is that, contrary to the assertions made in GA Moore's
>original statement, the primary and principal object of study throughout
>mathematical history has been nature itself -- albeit when seen in a very
>particular kind of way.

Let me quote the first 3 lines of your reply to GA:
>  >Actually most mathematicians believe the beauty of mathematics in and of
>  >itself without any regard to real world applications.
>???? !!!! ****

Is there anything about "the primary and principal object of study throughout
mathematical history" in there?  I don't see it...

>But ... it has been nature.

Yes, of course it has been.  No-one in his right mind would deny that.

>It could not have been something abstract like number in and of 
>itself, because the definition of number that we have today is very 
>current, and it is only very recently, within the last 150 to 200 
>years, that it has been possible for mathematicians to think in 
>those kinds of terms.

It might have been some other abstract subject.  The history of one 
particular concept (i.e. the number-concept) is of no relevance. 
However, it (indeed) was _not_ some abstract subject.  Whether it 
could have been this or that is, again, of no relevance.

>If that's the way the two of you want to play it then I bow my head humbly

Stop pretending a kind of humility that's refuted by the length of 
your letters, the effort you take to be exact & precise, and the 
lengths to which you go to ensure you're ahead of any kind of 
"attack" that could follow.  This is something I don't like at all. 
Sorry.  And as for bowing one's head: bollocks.  No-one has to bow 
for anyone.  Ever.  If you fuck up, you just say "sorry" and that's 
it.  However, this is not about fucking up -- it's about different 
interpretations of what the subject at hand is.  Stooping low and 
bowing heads is a non-issue in such matters.
And "the two of us" don't want to play anything.  I don't know what 
you're suggesting here, but it doesn't give me a warm & cozy feeling.

>and respectfully concede the point, but this qualification simply 
>was not made clear in the original assertion. I took it to mean that 
>it was a statement that was being made as one to be accepted as true 
>for all mathematicians through all historical epochs. That's all I 
>can say, and I apologise in that case for having opened my big mouth.

1) I think you read way more things into GA's msg than were there. 
He simply said "most mathematicians appreciate pure abstraction". 
That's all.  No reference to present, future or history, no 
broad-sweeping claims, nothing of the kind.  Much like "most butchers 
don't trust beef from the UK" (mad-cows disease, in case you didn't 
know).  Of course this doesn't mean all butchers from all times all 
over the world have always distrusted English beef...

2) Even if GA meant it in such a general way, then you still haven't 
provided any convincing argument to refute such a statement.  The 
fact that mathematics has been driven forward by the need to solve 
practical problems, and the fact that many, if not all, 
mathematicians were interested in all kinds of applications is still 
_no_ argument against the simple statement that they're able to 
appreciate the abstract beauty of mathematics.  One doesn't exclude 
the other.
For all we know, Euclid or Phythagoras may well have been smitten 
with the beauty of abstractions.  Well, in fact Pythagoras most 
likely _was_.  His number based cosmology is, in a sense, highly 
abstract.

But let's not go there, as it's not the issue...

>"The whole problem with the world is that fools and fanatics are always so
>certain of themselves, but wiser people so full of doubts".
>Bertrand Russell.

Very wise...

>I hope it's OK if I contact you privately should I want further
>clarification on anything.

Of course.  Although I don't see what there would be to clarify.  As 
far as I can see this is a very simple matter which got complicated 
by the fact that you read things in GA's message that just weren't 
there.

>I thank you most sincerely for your kindness.

Oh, come on, cut the crap...

>I also thank you for the complete lack of personal attacks in your email.

Did I do better this time?  LOL!  :-)))

Seriously, I know I probably sound a bit "irked" in this letter. 
That's not meant that personally -- I hope you know me well enough by 
now.  I just tend to get that way when people make things 
unnecessarily complicated, as you seem to be doing in this case.  I 
know, a flaw in my character probably...  Trust me, I'm working on it.


keep cool ;),
HJ

-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html

Thoughts from the mind of GAmoore@..., 10-11-2001:

>  >Every research recently conducted in this field shows that women
>>still get substantially less paid than men when performing the same
>  >kind of jobs or tasks.
>
>I hear that regularly too, but I think this is a classic
>misinterpretation of statistics, and I read an article to that affect
>about 6 years ago.

There are many articles claiming the opposite.  So "I think" this one 
article of yours might not be a very persuasive argument.

>And in any area where there is a clear difference, there would be clear
>grounds for a lawsuit and humiliation for the company conducting such
>practices.

Such lawsuits are indeed being conducted ("conducted" -- is that how 
you say it in English?)

>So why the statistics? I suspect, and from what I have seen of the people
>I work with, women are more likely to have gone to lower ranked colleges,
>less likely to have PhDs,

Yes, that's indeed probably part of the story.  Still it's silly that 
2 people doing the same job get a different salary, solely depending 
on their degree.  But that's a whole topic in itself, I'm afraid...

>less likely to go into the more competitive job
>areas, and more likely to take time off for raising children.

Not relevant.  We're talking about men/women in similar jobs.  Not 
about male executives versus housewives.

>On the other hand, men (in the US) contribute a great deal more 
>around the house, to the kids, to the cooking, to the shopping, etc.

And women contribute a great deal more to the family's bank-account. 
What's your point?

>And in the dating arena, women still want
>the guy to pay (depending on the woman) EVEN WITH EQUAL PAY.

In the US maybe.  Not so over here.  And the few that do are the 
wrong kind of women :-).

>I remember years ago, the talk of strip shows as demeaning to women -

Which imo is bollocks.  These women most often work there out of free 
will,  They could have been waitresses or whatever, but being a 
stripper pays better.  I don't blame them.  Hell, I would maybe do 
the same if I even remotely had the body for it :-).  Sure beats a 
teaching-salary.  LOL!

>However, instead of society rising to a higher standard of treating 
>women as humans, I see the reverse. Men are now treated as sex 
>objects too, the male stripping, etc.

These men _choose_ to step into a role of sex-object.  Most likely 
_they_ don't mind at all -- otherwise they would have found a 
different job.

>Its the same thing with the cold war, every time we think human beings
>will rise to the occasion, they find new lows unimaginable before.

<plop> lose association -- on the news today: UNICEF has warned that 
in 6 months (or was it weeks?  I think so...) 100.000 children in 
Afghanistan will die because of malnutrition and the harsh winter. 
Talking about "lows"...


tata,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html

ROLFFFF, you forgot the Benz

> In fact, there is a law that you can't create a rap
> video without some fine ass, long legs, and bouncing betties.

Hendrik Jan wrote:

>Why do you always have to write complete lectures in
>response to some posting?
To be perfectly honest, I thought I was perfectly clear the first time 
around. When I in fact said absolutely nothing at all personally and just 
sent in a couple of quotes.

>True art is the art of "leaving out".
OK.

>Less words would have equally sufficed
Which is exactly what I tried.


>I'm very well (and more than just intuitively) aware of the
>differences between pure and applied mathematics, both in education
>and in formal research.
Then you should have got my point the first time around.

>The subject however was not the difference between pure and applied
>maths, and I don't see how this has any bearing on the topic.
If you don't see it then fair enough. Obviously, it would have been better 
if I had just have left it at the fact that you didn't see it the first 
time around.

>Again I fail to see what this has to do with the observation GA made.
>Every mathematician of whom we know anything at all (i.e. excluding
>Euclid and the likes) has been able to recognize the beauty of pure
>abstraction.
If one wants to exclude Euclid and the likes then that's quite fine. I did 
not realize, because it was not immediately apparent to me, that they were 
indeed to be excluded. I thought of them immediately. As also of all 
mathematicians up until about the time of Gauss. Simple. That's all. I just 
did not understand at the time that they were being excluded. That's all. 
Again simple.

>Well, thanks for your trust, for starters.  Honestly.  But... if your
>point was _only_ to say something like "ok, mathematicians nowadays
>might be delighted by pure abstraction, but that hasn't always been
>so -- here are a few quotes to suggest otherwise", then 1) you should
>have said so from the onset, and 2) your first sentence in your reply
>to GA shouldn't have been "???? !!!! ****".
I was trying to do what you have yourself suggested in this very email and 
say as little as possible.

>The latter suggested (to
>me at least) that you didn't agree with GA's remark.
Aaah

>And that, I still belief, is in error.
OK.

>This is rethoric.
If you say so.

>Of course, if you think that pure mathematics is
>not a properly defined subject area, then there cannot even be such a
>thing as a "pure mathematician", and thus, obviously, these
>non-existent subjects can't have defined _anything_ -- simply because
>they (the subjects) don't exist.
Yes.

>In a more practical sense, this still doesn't hold.
OK.

>  There's no real
>reason a pure mathematician cannot define abstract concepts and
>figure out ways how to deal with them.
I never denied this.

>Set theory, especially the
>study of infinite sets, is a purely abstract thing.
Yes.

>  Cantor figured
>out a way how to deal with them (and met great resistance initially).
>No problem there...
No problem at all.
Cantor (1845-1918) is post-Gaussian (1777-1855). I am sorry for having 
concentrated so much, in my own thoughts, on those mathematicians who 
worked before Gauss. As you have suggested above, maybe I should have 
realized sooner that we were ignoring Euclid and post-Euclideans. This was 
entirely my error. I am sorry.


> >Fourier did not offer it as an argument, to be honest.
>
>No, but you seemed to be doing so.
Then, again economy of words was working against me. I thought it was not 
only obvious what he meant, but also what I meant by quoting him.

>I just fail to see its relevance.
OK.

> >I think when he said it he was trying to
> >convince the wife of one of his friends that what he spent the whole of his
> >days doing was really worth while and really a beautiful thing to do.
>
>"A beautiful thing to do" -- exactly what GA said...
If you say so. It just did not seem that way to me.

> >As far as I could see, the major point at issue was what has been the 
> primary
> >source of mathematical investigation, of mathematical proof, mathematical
> >discovery, and of mathematical appreciation throughout its history.
>
>No, not at all.  Either _you_ missed the point completely, or I did...
Then let us say that it was me.


>Let me quote the first 3 lines of your reply to GA:
> >  >Actually most mathematicians believe the beauty of mathematics in and of
> >  >itself without any regard to real world applications.
> >???? !!!! ****

I see a 'most mathematicians there'. Like I said, my mind went immediately 
to Babylonians, Ancient Greeks, Euclid, Diophantes ... and all those other 
people who worked before Gauss. I am sorry about that. Next time I see most 
mathematicians I will try to remember that it means 'most of the 
mathematicians who have ever lived' rather than 'most of the historical 
period in which mathematics has been done'.

>Is there anything about "the primary and principal object of study throughout
>mathematical history" in there?  I don't see it...
Well ... it seemed that way to me. I read the 'without any regard to real 
world applications' bit, and to me it pointed like an arrow to the 
distinction between pure and applied mathematics because, as far as I 
understood it, by its very definition being applied to real world 
applications immediately means applied, and not pure, mathematics, and 
therefore the methods and practices of that discipline as opposed to the 
methods and practices of pure mathematics. You might not see a reference to 
'the primary and principal object study ...' in there, but I did. If it was 
wrong to draw from that an implicit reference to the Gaussian and 
post-Gaussian distinction between those two branches of mathematics and so 
on and so forth then I was wrong.


>It might have been some other abstract subject.  The history of one
>particular concept (i.e. the number-concept) is of no relevance.
If you say so. I had always understood that the history of mathematical 
thought was pretty much also an essay in the ability of human things to 
think abstractly, and carried to its supreme heights; and pretty much that 
when one tracks the history of mathematical objects one is charting the 
ability of human beings to be and to think abstractly. I simply gave 
number-concept as an example of the attempt to be abstract, and how 
difficult it has been to become, indeed, as abstract as we are today.

>Stop pretending a kind of humility that's refuted by the length of
>your letters, the effort you take to be exact & precise,
then ... what should I do when I think I have been totally clear in the 
first place, and evidently I have not.

>and the lengths to which you go to ensure you're ahead of any kind of
>"attack" that could follow.  This is something I don't like at all.
OK.

>And as for bowing one's head: bollocks.  No-one has to bow
>for anyone.  Ever.
Where I come from, that is what we do. It is as natural to me to bow my 
head on arrival and departure as it is to you to shake a hand. When, for 
example, I greet my mother, I bow my head. When I leave her, I bow my head. 
Thank you but I have absolutely no intention of stopping the habit. My 
mother is dear to me and it is my way of showing her so. I am entitled to 
it. You are free to interpret my actions how you wish. If you feel that it 
makes me subservient, then so be it. I repeat that I have no intention of 
stopping the habit.

>If you fuck up, you just say "sorry" and that's it.
And ... if I choose to bow my head at the same time, I shall do so. If I 
change my mind I'll let you know. I will try to remember, however, never -- 
ever -- to do it to you because it clearly deeply offends you. Will that do?

>However, this is not about fucking up -- it's about different
>interpretations of what the subject at hand is.
If you say so.

>Stooping low and bowing heads is a non-issue in such matters.
So ... would you rather I used expletives?

>1) I think you read way more things into GA's msg than were there.
>He simply said "most mathematicians appreciate pure abstraction".
>That's all.  No reference to present, future or history, no
>broad-sweeping claims, nothing of the kind.
Well ... I thought there were such references to present, past and the like 
because in his original statement there was a specific reference made to 
real-world applications.

>  Much like "most butchers
>don't trust beef from the UK" (mad-cows disease, in case you didn't
>know).  Of course this doesn't mean all butchers from all times all
>over the world have always distrusted English beef...
Maybe not all ... but when someone says most, and a person knows that the 
history of mathematics can be roughly and importantly divided into two 
important eras, pre-Gauss and post-Gauss, and that the first period is the 
vast bulk of human history while the second is only about 400 years, this 
at first seems to be a rather lop-sided interpretation of most. That's 
simply the way it seemed to me.

>2) Even if GA meant it in such a general way, then you still haven't
>provided any convincing argument to refute such a statement.
OK. If pointing to the Gaussian divide as an important marker in the 
ability of humans to think abstractly and appreciate abstraction in the 
sense that I thought was meant by GA Moore's original statement is not 
sufficient then that's fine.

>For all we know, Euclid or Phythagoras may well have been smitten
>with the beauty of abstractions.
Possibly so. But ... they wrote precious little about it. The history of 
aesthetics, however, does not give any positive indicators for this ... 
although that is certainly not definitive either.

>Well, in fact Pythagoras most
>likely _was_.
Most likely? Most probably. Definitely?

>His number based cosmology is, in a sense, highly abstract.
Maybe so.

>But let's not go there, as it's not the issue...
Quite.


> >"The whole problem with the world is that fools and fanatics are always so
> >certain of themselves, but wiser people so full of doubts".
> >Bertrand Russell.
>Very wise...
I think so too.

> >I hope it's OK if I contact you privately should I want further
> >clarification on anything.
>
>Of course.  Although I don't see what there would be to clarify.
OK.

>  As
>far as I can see this is a very simple matter which got complicated
>by the fact that you read things in GA's message that just weren't
>there.
Well ... they were clearly there to me.

> >I thank you most sincerely for your kindness.
>Oh, come on, cut the crap...
Sorry you felt it was. It was not. I have come to have the greatest respect 
for you, and although you quite obviously do not remember, you helped me an 
awful lot when I had some problems with sysex, as also with key commands. 
Out of all the people in the Logic Users Group you were not only the only 
person who had a solution, you were also patient with me when I did not at 
first understand your solution. So ... I was thanking you sincerely for 
your kindness because I did appreciate those things. You may have forgotten 
... indeed you obviously have. But ... I still remember. I did not say this 
to offend you but to thank you. I regret that it had the contrary effect.

> >I also thank you for the complete lack of personal attacks in your email.
>Did I do better this time?  LOL!  :-)))
What answer do you want me to give?

>Seriously, I know I probably sound a bit "irked" in this letter.
Not really.

>That's not meant that personally -- I hope you know me well enough by
>now.
I'm beginning to wonder, actually. When I thank you, you attack me. When I 
am respectful to you, you treat me as a hypocrite. What should I do? Attack 
you in return in the hope that I will receive kindness? The problem I have 
with that is that you have given me no cause whatever to attack you ... so 
I will not.

>I just tend to get that way when people make things
>unnecessarily complicated,
I kept things very simple as far as I can recall. Sent in a few quotes 
which as far as I was concerned made my point completely.

>I know, a flaw in my character probably...  Trust me, I'm working on it.
I honestly wish you well.

I have quite given up trying to work out how any of my remarks will be 
received by you, to be honest. You may take it as you wish. It's up to you.

>keep cool ;),

That I always work on. It is hard some times.

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

Hi Kool,

>  >Why do you always have to write complete lectures in
>>response to some posting?
>To be perfectly honest, I thought I was perfectly clear the first time
>around. When I in fact said absolutely nothing at all personally and just
>sent in a couple of quotes.

OK then.  But apparently there _was_ room for misunderstanding. 
(isn't there always? :-)

>  >I'm very well (and more than just intuitively) aware of the
>>differences between pure and applied mathematics, both in education
>>and in formal research.
>Then you should have got my point the first time around.

Well, I failed to see the relevance of the quotes in relation to the 
statement by GA.  My fault maybe, or not.  But this isn't about "what 
is who's fault" now, is it?  At least, I do hope it isn't...

>  >Again I fail to see what this has to do with the observation GA made.
>>Every mathematician of whom we know anything at all (i.e. excluding
>>Euclid and the likes) has been able to recognize the beauty of pure
>>abstraction.
>If one wants to exclude Euclid and the likes then that's quite fine. I did
>not realize, because it was not immediately apparent to me, that they were
>indeed to be excluded. I thought of them immediately. As also of all
>mathematicians up until about the time of Gauss. Simple. That's all. I just
>did not understand at the time that they were being excluded. That's all.
>Again simple.

No, no, you get me wrong, sorry.  I didn't mean that Euclid et al 
need to be excluded because this-or-that doesn't hold for them, or 
because GA's remark somehow magically "clearly" suggested they be 
left out.
I meant to say (and thought I said) that we simply don't know enough 
about the ancient Greek mathematicians to be able to judge how 
exactly they viewed mathematics, beauty of abstraction and such. 
There's simply not enough reliable written history on that subject, 
as far as I know.  About people like Gauss and such we _do_ know 
quite a lot, including sometimes how they thought about maths, 
abstraction, beauty, etc.

>As you have suggested above, maybe I should have realized sooner 
>that we were ignoring Euclid and post-Euclideans. This was entirely 
>my error. I am sorry.

You don't have to be sorry for anything.  First of all, GA never said 
anything about excluding or including whomever --- that was me, 
interpreting GA's statement.  Second, as I explained above, the 
exclusion was meant to limit the scope to those mathmaticians we know 
enough about to be able to say anything sensible about their 
conception of abstract beauty.  Third, even if you had not understood 
something properly in whatever previous post, there's still no reason 
to "be sorry".  Not getting some point is not someone's fault.  Like 
I said earlier: I do hope this entire discussion is not about who's 
to blame, who's fault is what, etc.
As far as I'm concerned, it's just an exchange of thoughts.  And it 
was my impression that you took GA's remark to mean something else 
than what he intended to say.  I simply tried to correct that, that's 
all.
And about my somewhat irritated tone yesterday: I'm sorry, I should 
have been more friendly.  But I felt a lot of "sorry"s and "I'm 
humble" stuff in your previous letter, and that somewhat got to me. 
To me it felt as if you were somewhat 'humiliating' yourself, while 
at the same time quite strongly trying to make a point.  To me these 
didn't match -- cognitive dissonance or whatever.  If you want to 
make a point, make it.  If you want to say "sorry, I didn't get it", 
then say so.  But mixing the two is just ... confusing or so... 
(rather struggling at the moment with the fact that I'm no native 
speaker, so please bear with me).

Maybe I got your intention all wrong. I.e. the "bow my head" stuff 
was (of course!) not meant as an insult to your culture or heritage 
or mother.  Of course!  You should know me well enough.  To me it 
sounded simply like a kind of "overdone modesty" or what do you call 
it.  If I understood you wrong, then I hereby apologize.  Sincerely.

>  >No, not at all.  Either _you_ missed the point completely, or I did...
>Then let us say that it was me.

Why you?

>  >Let me quote the first 3 lines of your reply to GA:
>>  >  >Actually most mathematicians believe the beauty of mathematics in and of
>>  >  >itself without any regard to real world applications.
>>  >???? !!!! ****
>
>I see a 'most mathematicians there'. Like I said, my mind went immediately
>to Babylonians, Ancient Greeks, Euclid, Diophantes ... and all those other
>people who worked before Gauss.

OK.  My mind didn't.  Just as with the butcher example.  Or "most 
teachers think they're underpaid" -- which to me clearly means 
"teachers in this day and age".  Different interpretation.  No 
problem.

>I am sorry about that. Next time I see most mathematicians I will 
>try to remember that it means 'most of the mathematicians who have 
>ever lived' rather than 'most of the historical period in which 
>mathematics has been done'.

Now, this is the kind of stuff that I find ... annoying, if I may say 
so, or puzzling.  As if an incidental meaning of some words in one 
particular context would define them for all eternity.  And as if you 
have to humbly bow to adjust yourself to the incidental 
interpretation two other guys give to a bunch of words in some 
particular context.  I find such an attitude truly incomprehensible. 
Maybe it's a cultural difference, but then it's one I very much don't 
understand.  To me it feels as if it leaves no room for anything 
else.  It feels like "ok, you have won, I humbly admit it", in which 
the other apparently is the "winner", and yet your "modesty" in fact 
makes you the _true_ "winner".  Not unlike Socrates did when talking 
to pupils: "Ah, so you understand the nature of <big concept>.  Well, 
then please tell me, an old man, all about it so that I may learn 
from you".  And then in the end crush the poor kid completely with 
his unequalled mastery of dialectic argument.

Do you understand what I'm trying to say?  I don't say your 
intentions are like Socrates'.  I just say that to me it sometimes 
feels that way, leaving completely and honestly open the option that 
I may completely misunderstand your intentions.

As far as I'm concerned, I have a problem with people adjusting 
themselves to me "in modesty".  I prefer the opposite: I like people 
to have their own opinions.  Strong opinions, preferably.  And not 
shy away from defending them when needed.  Things like "I'm sorry, 
I'll use those words the way you want me to in the future" is 
perpendicular to that.
Again this is not meant in any offensive way.  Remember, this stuff 
is quite subtle and requires accurate phrasing, and I'm still no 
native English speaker (yes, despite my command of the English 
language, that _does_ play a role at times).  I'm just genuinely 
puzzled.  I know you're a person "of good intent", and yet I feel a 
certain irritation or annoyance at the "humble" tone you sometimes 
use.  That could entirely be me, so please don't start apologizing 
again.

>  >And as for bowing one's head: bollocks.  No-one has to bow
>>for anyone.  Ever.
>Where I come from, that is what we do. It is as natural to me to bow my
>head on arrival and departure as it is to you to shake a hand. When, for
>example, I greet my mother, I bow my head. When I leave her, I bow my head.
>Thank you but I have absolutely no intention of stopping the habit. My
>mother is dear to me and it is my way of showing her so. I am entitled to
>it. You are free to interpret my actions how you wish. If you feel that it
>makes me subservient, then so be it. I repeat that I have no intention of
>stopping the habit.

OK, OK, chill out...  As I explained above, this might be a cultural 
difference.  To me (and probably to many westerners) "bowing one's 
head" has a ring of subservience, and that's what I reacted to.  Not 
to any other meaning of the phrase, like "showing someone's dear to 
you" and such.

>  >If you fuck up, you just say "sorry" and that's it.
>And ... if I choose to bow my head at the same time, I shall do so. If I
>change my mind I'll let you know. I will try to remember, however, never --
>ever -- to do it to you because it clearly deeply offends you. Will that do?

Ahw, come on, this is driving matters way to far...

>  >For all we know, Euclid or Phythagoras may well have been smitten
>>with the beauty of abstractions.
>Possibly so. But ... they wrote precious little about it.

That's why I suggested to leave them out of the discussion.

>  > >I thank you most sincerely for your kindness.
>>Oh, come on, cut the crap...
>Sorry you felt it was. It was not. I have come to have the greatest respect
>for you, and although you quite obviously do not remember, you helped me an
>awful lot when I had some problems with sysex, as also with key commands.

Why the "quite obviously"?

As for respect: I've come to respect you at least as much as you've 
come to respect me.  That's precisely the reason I take the effort to 
write about the things that annoy or puzzle me.  If I didn't respect 
you, I would have better things to do with my time than try to 
communicate with you about non-trivial matters.
Maybe the problem indeed is one of culture.  Your background is 
probably totaly different than my "say what you mean straight out, 
without fuzziness" Dutch background.

>Out of all the people in the Logic Users Group you were not only the only
>person who had a solution, you were also patient with me when I did not at
>first understand your solution.

I get paid to be patient with students ;-).

>So ... I was thanking you sincerely for your kindness because I did 
>appreciate those things.

Uhm... in your last letter, on beauty & abstraction, you thanked me 
for things I did for you way back in the past...?  No, indeed, I 
hadn't understood it that way. Mainly because there was no reference 
to what you thanked me for, so naturally I assumed it was for 
something recent, like something I did or said in my last letter on 
this same subject.

>  You may have forgotten ... indeed you obviously have.

I never forget my own kindness :-)).

>  >Seriously, I know I probably sound a bit "irked" in this letter.
>Not really.

I do think I did.  I _was_ a bit irked, at least.

>  >That's not meant that personally -- I hope you know me well enough by
>>now.
>I'm beginning to wonder, actually. When I thank you, you attack me. When I
>am respectful to you, you treat me as a hypocrite. What should I do?

It felt as if you thanked me for something you shouldn't thank me 
for.  And as for the respectful/hypocrite thing: I tried to explain 
that in the bit about Socrates.  I hope you understood what I tried 
to say there.
I don't want to offend you, much as you don't want to offend me (I 
suppose).  However, I did feel a bit offended at your tone of 
humility and modesty.  I may have misinterpreted that tone, and if 
that's the case I apologize, truly.

>I have quite given up trying to work out how any of my remarks will be
>received by you, to be honest. You may take it as you wish. It's up to you.

No, it's not up to me.  It's up to us.  Communication is a two-way 
street.  That's probably why you take the effort to write back.  It 
certainly is the reason why _I_ take the effort to write back.

>  >keep cool ;),
>
>That I always work on. It is hard some times.

"Life is suffering", Buddha, 2600 BC.  Oh well, the consolation is 
that we _all_ suffer equally in the end...


be well,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html

Kool Musick said:

> >To be perfectly honest, I thought I was perfectly clear the first time
> >around. When I in fact said absolutely nothing at all personally and just
> >sent in a couple of quotes.

Hendrik Jan said:
>OK then.  But apparently there _was_ room for misunderstanding.
Obviously.

>(isn't there always? :-)
Seems so!!

>But this isn't about "what
>is who's fault" now, is it?
No.

>At least, I do hope it isn't...
Likewise.


>No, no, you get me wrong, sorry.  I didn't mean that Euclid et al
>need to be excluded because this-or-that doesn't hold for them, or
>because GA's remark somehow magically "clearly" suggested they be
>left out.
>I meant to say (and thought I said) that we simply don't know enough
>about the ancient Greek mathematicians to be able to judge how
>exactly they viewed mathematics, beauty of abstraction and such.
>There's simply not enough reliable written history on that subject,
>as far as I know.
Well. There is quite a lot actually, to act as a reasonable basis for 
surmising. For example, and more specifically, there was the ancient Greek 
attitude to the first couple of proofs in projective geometry where it is 
pretty clear what they did and did not appreciate. They simply did not see 
that the proofs concerning what we now call Pascal's theorem, as but one 
example was quite simply in a very different category of proofs from other 
geometric proofs in that it transcends mensuration. Same for their work on 
conic sections. Absolutely no realization  of the different parameters 
involved. This does not negate that those things were proofs, but it does 
give a pretty clear indication of the kind of ways in which they were 
prepared to abstract. In addition to that, there are writings about 
architecture, pottery and stuff like that and the principles underlying how 
such things should be created, and what it took to make them beautiful. 
Your point that there is nothing definitive in the records is well taken, 
but to be honest, for there to BE anything definitive, then they would have 
had to have an attitude to those things that is pretty much like ours so 
that they could write about it. What aestheticians and historians of 
mathematics do is therefore go by the evidence regarding what their 
attitude to beauty was in those various departments, look at what the 
mathematicians actually said, draw the surely reasonable premise that 
mathematicians, many of whom were also architects and the like, probably 
did not have an attitude towards beauty in general that was much different 
from any one else's and proceed from there.

To be honest, absolutely THE most powerful argument that there is for the 
contrary position (i.e. the one that you are GA  Moore are supporting but 
that goes against the weight of 'the most reasonable evidence' is when GA 
Moore pointed out that when Archimedes died, what he wanted put on his 
grave was that beautiful theorem.

I am happy to agree -- as a romantic -- that Archimedes wanted it because 
of something inside himself that I do agree with about 'mathematical 
beauty' because in my heart I do think that Archimedes had a very special 
reason, and one that I also have in my heart. However, I am not prepared to 
extrapolate from that feeling of empathy with Archimedes back through the 
ages to a more general statement about the general attitude of Greek 
mathematicians to their subject and to their general attitude to 'proof' 
and such like because the weight of the evidence points, very reasonably, 
to the contrary.

>  About people like Gauss and such we _do_ know
>quite a lot, including sometimes how they thought about maths,
>abstraction, beauty, etc.
Which was pretty much their point, actually. About Gauss and so forth we 
KNOW. Many times I have tried to point to the fact that at Gauss there came 
a big shift. Don't know how many times I have to repeat this.

Up until then, we do not KNOW, so we must look at the evidence and draw the 
most reasonable conclusions we can from the evidence. Now, the 
mathematician in me would like to believe that Euclid and others had much 
the same attitude towards the beauty of their subject as Gauss and Riemann 
did ... but this is simply not supported by the evidence we have, because 
the evidence we have is that attitudes changed dramatically.

>You don't have to be sorry for anything.  First of all, GA never said
>anything about excluding or including whomever --- that was me,
>interpreting GA's statement.
I understand that you were offering your own understanding according to 
your own interpretation, but so also was I according to mine. I read what 
he said and by what I knew of the history of thought, the history of 
aesthetics, and the documented history of mathematics, much as the artist 
in me would like to agree with him, the assertion which he seemed to me to 
be making was not supported by the evidence.

>Second, as I explained above, the
>exclusion was meant to limit the scope to those mathmaticians we know
>enough about to be able to say anything sensible about their
>conception of abstract beauty.
As I have said, in the eyes of those who study the history of Greek thought 
and Greek attitudes to beauty inside and outside mathematics, there IS 
enough to draw sensible conclusions. But then again, there's enough 
evidence also to debate those conclusions. But to be honest, the only 
'evidence' to the contrary position is arguments like 'well why ELSE would 
Archimedes wanted to have that model on his grave?'. I don't know why, but 
I do suspect, and my reasons for suspecting are the same as GAM's, that 
somehow from deep inside himself Archimedes had a way of looking at 
mathematical objects that was remarkably similar in its essence to anyone 
who enjoys mathematical beauty today. I am all for feeling that kind of 
kinship with Archimedes. But extrapolating from a heart-to-heart 
communication to a statement about mathematical beauty in general and 
across the ages seems to me to be rather a grand step to take given the 
historical record.

>Third, even if you had not understood
>something properly in whatever previous post, there's still no reason
>to "be sorry".  Not getting some point is not someone's fault.
Let's just say that you and I obviously have different interpretations by 
the word 'sorry'. Sometimes by 'sorry' I only mean ... 'I wish I had 
understood what you are saying earlier so that the energy we have wasted in 
trying to clarify things to each other need not have been expended'. I do 
not say it to be subservient, but simply to indicate something along the 
lines of I wish we had a closer and more accurate means of communication, 
you and I, because it would save a lot of our joint energies.

>Like
>I said earlier: I do hope this entire discussion is not about who's
>to blame, who's fault is what, etc.
Don't think it is.

>As far as I'm concerned, it's just an exchange of thoughts.
Yes.

>And it
>was my impression that you took GA's remark to mean something else
>than what he intended to say.
OK

>I simply tried to correct that, that's all.
OK. But I didn't accept the thrust of your correction. That's also all. The 
figure of Gauss, and Newton and Liebniz who led up to Gauss, as also people 
like Cardano who indicated the existence of imaginary numbers ... all these 
things taken together caused a seismic shift in the concept of mathematics, 
in the very concept of proof, and in what it was felt mathematicians were 
actually doing. Things like astrology gradually got dumped, for example. 
Used to be that a person was a good mathematician if he was a successful 
astrologer. That's how it was for centuries. Very sorry, but I don't see 
any mathematical beauty in a good astrological prediction, but even Kepler 
was inclined to think that if had made a good prediction then he had done a 
good job of work. I do not agree with him. But I can understand why he 
thought that way given the history of the subject and the time in which he 
worked. Then there was all that mumbo jumbo he had about cosmic solids. He 
really thought it beautiful. As a 'work of art'. maybe. But as a 
mathematical demonstration? Yet ... there were people who thought, at the 
time, that it was a demonstration of mathematics at its best.

Am I being any clearer? I just wanted to point out that before making a 
statement of any kind such as I thought GAM was making, one had to be very 
careful indeed about what was being claimed.

>And about my somewhat irritated tone yesterday: I'm sorry, I should
>have been more friendly.
Should have been's fine by me. That I always try to respond to.

>But I felt a lot of "sorry"s and "I'm
>humble" stuff in your previous letter, and that somewhat got to me.
Sorry about that. We were simply not understanding each other. I was doing 
my best to clarify. When I wrote nothing, you got annoyed and didn't my 
point; when I wrote lots, you got annoyed and didn't get my point either. I 
felt a bit stuck, actually. So I just kept saying sorry.

>To me it felt as if you were somewhat 'humiliating' yourself, while
>at the same time quite strongly trying to make a point.
I am not in the humiliate yourself business, thank you. I was being sorry 
for having put you to the 'trouble' of having had to work so hard to try to 
get your point across to little old me who didn't understand it; and I was 
also being sorry for the yet more trouble I was putting you to because I 
still didn't agree with it.

>To me these
>didn't match -- cognitive dissonance or whatever.  If you want to
>make a point, make it.  If you want to say "sorry, I didn't get it",
>then say so.
What I said was sorry, I still didn't accept it. Not sorry, I didn't get 
it. I still don't accept it. Sorry about that. But ... I have given copious 
reasons.

>Maybe I got your intention all wrong.
I think so.

>I.e. the "bow my head" stuff was (of course!) not meant as an insult to 
>your culture or heritage or mother.
Maybe not. But my life experience is to receive many such insults, to be 
frank and honest with you.

>Of course!  You should know me well enough.
I do. At least, I hope I do.

>To me it
>sounded simply like a kind of "overdone modesty" or what do you call
>it.
It was not intended as overdone modesty.

>If I understood you wrong, then I hereby apologize.  Sincerely.
Lotta sorry's going around now, seems to me. Maybe we should share them 
around a bit!!!

> >  >No, not at all.  Either _you_ missed the point completely, or I did...
> >Then let us say that it was me.
>Why you?
Because you are a very intelligent person, and I agree with most of the 
things you say. Therefore, if you are saying something and I am not getting 
it then chances are that it is my own position, and not yours, that need 
re-evaluating. No disrespect to you, but I have found it the best way to 
increase my knowledge -- to admit that maybe the other guy had a point. 
Didn't work with neurolinguistic programming, though. Hard as I tried, and 
I did try very hard, I found a lot of it to be a bogus kind of '60's warm 
cuddly feely stuff. Not that I'm against warm cuddly feely, but I didn't 
find the practix of it particularly convincing, no matter how noble the 
ideas. So ... my attempts to concede that the other guy might have a point 
don't always work, but at least I make the effort.

> >I see a 'most mathematicians there'. Like I said, my mind went immediately
> >to Babylonians, Ancient Greeks, Euclid, Diophantes ... and all those other
> >people who worked before Gauss.
>
>OK.  My mind didn't.

I kind of think that's all that's going on here.

>Different interpretation.  No problem.
OK.

> >I am sorry about that. Next time I see most mathematicians I will
> >try to remember that it means 'most of the mathematicians who have
> >ever lived' rather than 'most of the historical period in which
> >mathematics has been done'.
>
>Now, this is the kind of stuff that I find ... annoying, if I may say
>so, or puzzling.  As if an incidental meaning of some words in one
>particular context would define them for all eternity.
No. It means that next time I read 'most mathematicians', I shall keep more 
clearly at the front of my mind that the person who using that expression 
is probably using it in a very different way from me.

>And as if you
>have to humbly bow to adjust yourself to the incidental
>interpretation two other guys give to a bunch of words in some
>particular context.
And ... what's wrong with adjusting my understanding of affairs after 
interacting with two people? No word has an absolute meaning.

>I find such an attitude truly incomprehensible.
OK.

>Maybe it's a cultural difference, but then it's one I very much don't
>understand.
As above, OK.

>To me it feels as if it leaves no room for anything else.
Seems to me that all I've done is recognize that the word 'most' when used 
in conjunction with the word 'mathematicians' can mean something a tad 
different from what I first assume.

>It feels like "ok, you have won, I humbly admit it",
You have not won anything. I have. I have extended my meaning and 
understanding of a phrase.

>in which the other apparently is the "winner", and yet your "modesty" in fact
>makes you the _true_ "winner".
Yes ... I am the true winner. I have extended my meaning and understanding 
of a phrase.

>And then in the end crush the poor kid completely with
>his unequalled mastery of dialectic argument.
I am not aware of having made any attempt whatever to crush you. Anyway, I 
have a healthy respect for your mastery of dialectic argument.

>Do you understand what I'm trying to say?
Possibly.

>I don't say your intentions are like Socrates'.
They are not. Not in any way, shape or form. At least, in so far as the 
crushing bit is concerned.

>I just say that to me it sometimes feels that way,
OK.

>As far as I'm concerned, I have a problem with people adjusting
>themselves to me "in modesty".
I think my life will be easier if I leave this as your problem and do not 
take it on myself. All I will do is extend my meaning of certain words.

>I prefer the opposite: I like people
>to have their own opinions.
Am I then a person with no opinions?

>Strong opinions, preferably.
Are my opinions then weak ones?

>And not
>shy away from defending them when needed.
I have defended my opinions. When I tried to defend them thoroughly, and by 
covering the more obvious of the objections that I could think of, you 
criticized me for lecturing.

>Things like "I'm sorry,
>I'll use those words the way you want me to in the future" is
>perpendicular to that.
OK. But as far as I can see, I have my own way, plus I have added your way. 
I have not given up my way. I shall just be careful in future that others 
might interpret the phrase 'most mathematicians' differently from me, and I 
shall take it into account. Is something wrong with that?

>Again this is not meant in any offensive way.
OK

>Remember, this stuff
>is quite subtle and requires accurate phrasing,
I tried that. You just criticized me for lecturing. And for writing many 
words. It was exactly my motivation that the ancient mathematical concept 
of 'beauty', especially 'in mathematics' before around the time of Gauss, 
and the associated attitude to proof was subtle ... and subtly different 
from the modern kind ... and I did my level best to elucidate those 
differences in a clear and understandable way.

Clearly, I failed. I wish I had succeeded. (Please notice that I did 
actually manage to avoid a 'sorry' there!!)

>I'm just genuinely
>puzzled.  I know you're a person "of good intent", and yet I feel a
>certain irritation or annoyance at the "humble" tone you sometimes
>use.  That could entirely be me, so please don't start apologizing
>again.
Then ... I will say nothing.

> >  >If you fuck up, you just say "sorry" and that's it.
> >And ... if I choose to bow my head at the same time, I shall do so. If I
> >change my mind I'll let you know. I will try to remember, however, never --
> >ever -- to do it to you because it clearly deeply offends you. Will that do?
>Ahw, come on, this is driving matters way to far...
Then ... what should I do? Just being myself quite obviously isn't working.


> >  >For all we know, Euclid or Phythagoras may well have been smitten
> >>with the beauty of abstractions.
> >Possibly so. But ... they wrote precious little about it.
>That's why I suggested to leave them out of the discussion.
Then ... take out the 'most' in 'most mathematicians'. That's my view on 
the matter. If it's kept in, then people like me will always put up their 
hands and raise doubts and ask questions.

> >Sorry you felt it was. It was not. I have come to have the greatest respect
> >for you, and although you quite obviously do not remember, you helped me an
> >awful lot when I had some problems with sysex, as also with key commands.
>Why the "quite obviously"?
Because I simply felt that if you had remembered, then you would understand 
why I continue to be grateful to you.

>As for respect: I've come to respect you at least as much as you've
>come to respect me.
That's nice. You must have been on the same neurolinguistic programming 
course!! (Sorry Tony if you're reading ... just a little joke there!!!)

>Maybe the problem indeed is one of culture.  Your background is
>probably totaly different than my "say what you mean straight out,
>without fuzziness" Dutch background.
My background is certainly very different. But ... please don't run away 
with the idea that I don't say what I mean straight out. It just tends to 
come out differently when I do it, that's all.

>I get paid to be patient with students ;-).
OK. What's your fee? Do you take credit cards?!!!

>Uhm... in your last letter, on beauty & abstraction, you thanked me
>for things I did for you way back in the past...?
Yes. Seemed relevant to me because it shapes my general attitude to you.

>No, indeed, I hadn't understood it that way.
OK.

>  Mainly because there was no reference
>to what you thanked me for, so naturally I assumed it was for
>something recent, like something I did or said in my last letter on
>this same subject.

Why should there be. In any case, you seem to get annoyed when I have that 
attitude of gratitude as a general principle ... how much MORE annoyed 
would you get if I prefaced it every time with a long list of the wonders 
that you have done for me over many years?!! I've just written my will, 
actually, just in case!!! Easier for me to remember that you are a person 
who has been most kind to me and work on that basis. Sorry if it sometimes 
annoys you that I treat you that way and say that, but I think that you're 
just going to have to get used to it to be honest.

> >  You may have forgotten ... indeed you obviously have.
>I never forget my own kindness :-)).
Glad to hear it. I wouldn't want to be the one to have to help you raise 
your self-esteem!!

> >  >Seriously, I know I probably sound a bit "irked" in this letter.
> >Not really.
>I do think I did.  I _was_ a bit irked, at least.
OK.

>It felt as if you thanked me for something you shouldn't thank me
>for.
I should not have gratitude for, or continue to remember, your kindness to 
me? Strange, that.


>I don't want to offend you, much as you don't want to offend me (I
>suppose).
You suppose correctly.

>However, I did feel a bit offended at your tone of
>humility and modesty.  I may have misinterpreted that tone, and if
>that's the case I apologize, truly.
You got any other choruses?!!

> >I have quite given up trying to work out how any of my remarks will be
> >received by you, to be honest. You may take it as you wish. It's up to you.
>
>No, it's not up to me.  It's up to us.
Very very true. Nice point.


>be well,
You also

Here's to many years of successfully sorting little communication problems.

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

Thoughts from the mind of Kool Musick, 11-11-2001:

>  >I meant to say (and thought I said) that we simply don't know enough
>>about the ancient Greek mathematicians to be able to judge how
>>exactly they viewed mathematics, beauty of abstraction and such.
>>There's simply not enough reliable written history on that subject,
>>as far as I know.
>Well. There is quite a lot actually, to act as a reasonable basis for
>surmising.
[interesting stuff deleted for brevity]

Didn't know this.  Interesting.  Thanks.

>Your point that there is nothing definitive in the records is well taken,
>but to be honest, for there to BE anything definitive, then they would have
>had to have an attitude to those things that is pretty much like ours so
>that they could write about it.

Uhm... are you implying that the fact that they didn't write about it 
must mean they thought about it differently than we do?  Because with 
that I wouldn't agree.  IMO there's no way we can figure out why they 
did or did not write about something.  But maybe I misunderstand what 
you're saying here.

>  >  About people like Gauss and such we _do_ know
>>quite a lot, including sometimes how they thought about maths,
>>abstraction, beauty, etc.
>Which was pretty much their point, actually. About Gauss and so forth we
>KNOW. Many times I have tried to point to the fact that at Gauss there came
>a big shift. Don't know how many times I have to repeat this.

I _did_ get your point, believe me.

>I don't know why, but
>I do suspect, and my reasons for suspecting are the same as GAM's, that
>somehow from deep inside himself Archimedes had a way of looking at
>mathematical objects that was remarkably similar in its essence to anyone
>who enjoys mathematical beauty today. I am all for feeling that kind of
>kinship with Archimedes. But extrapolating from a heart-to-heart
>communication to a statement about mathematical beauty in general and
>across the ages seems to me to be rather a grand step to take given the
>historical record.

Which is why I suggested to leave them out of the discussion.

>Let's just say that you and I obviously have different interpretations by
>the word 'sorry'. Sometimes by 'sorry' I only mean ... 'I wish I had
>understood what you are saying earlier so that the energy we have wasted in
>trying to clarify things to each other need not have been expended'.

Ah, ok, that _is_ a misunderstanding then.  Probably to do with the 
"emotional charge" of some words.  As a non-native speaker, it is 
often difficult to really, exactly, understand the precise nuance or 
connotations of some words -- and most often this is the case with 
the seemingly simplest words.  Like "brother", which is a word I 
sometimes use (well, the Dutch translation) to address certain 
friends.  But I've come to understand that when a white man says 
"brother" to an Afro-American in the Bronx, he can get his butt 
kicked, since only Af-Am's are allowed to call each other "brother". 
Apparently in certain contexts this simple word has far reaching 
connotations that I, as non-native, am not always aware of.  Oh 
man... maybe Af-Am is insulting too...  help...

Or did I get this one wrong too? :-)

>I do
>not say it to be subservient, but simply to indicate something along the
>lines of I wish we had a closer and more accurate means of communication,
>you and I, because it would save a lot of our joint energies.

OK, from now on I'll interpret it this way.  Thanks for the clarification.

>  >I simply tried to correct that, that's all.
>OK. But I didn't accept the thrust of your correction.

Which you have every right to do of course.

>Then there was all that mumbo jumbo he had about cosmic solids. He
>really thought it beautiful. As a 'work of art'. maybe. But as a
>mathematical demonstration? Yet ... there were people who thought, at the
>time, that it was a demonstration of mathematics at its best.

:-).  But then: what could be more beautiful than an abstract science 
being able to explain the entire cosmos with a basically simple 
model?  Isn't that every scientist's wet dream?

>Am I being any clearer? I just wanted to point out that before making a
>statement of any kind such as I thought GAM was making, one had to be very
>careful indeed about what was being claimed.

Sure I understand what you mean.  The essence of my reply was just 
that I thought you made things more complicated than they were ever 
intended.

>  >But I felt a lot of "sorry"s and "I'm
>>humble" stuff in your previous letter, and that somewhat got to me.
>Sorry about that. We were simply not understanding each other. I was doing
>my best to clarify. When I wrote nothing, you got annoyed and didn't my
>point; when I wrote lots, you got annoyed and didn't get my point either. I
>felt a bit stuck, actually. So I just kept saying sorry.

:-)  So that's what you do when feeling stuck?  Keep saying sorry? 
Ahw, sorry, I shouldn't laugh about that, but I can't help it raises 
a kind of funny picture in my mind.  Like someone bumping into a 
brick wall and then apologizing to the wall or so.  I don't know why 
-- probably the time of day.  it's been a rather heavy day -- lots of 
difficult things going on, in between all the emails.  OK, sorry, I 
won't laugh anymore.  And if I once more say "sorry" myself, then... 
Oh no, sorry... :-))

>  >To me it felt as if you were somewhat 'humiliating' yourself, while
>>at the same time quite strongly trying to make a point.
>I am not in the humiliate yourself business, thank you.

OK, forget it.  I'll never suggest such a thing again.

>I was being sorry for having put you to the 'trouble' of having had 
>to work so hard to try to get your point across to little old me who 
>didn't understand it;

I have the impression there's precious little "little" and "old" about you.

>and I was also being sorry for the yet more trouble I was putting 
>you to because I still didn't agree with it.

As if you _have_ to agree.  Of course you needn't...

>  >I.e. the "bow my head" stuff was (of course!) not meant as an insult to
>>your culture or heritage or mother.
>Maybe not. But my life experience is to receive many such insults, to be
>frank and honest with you.

OK, but then, to paraphrase what you said above: I'm not in the 
humiliate-others business.

>  >To me it
>>sounded simply like a kind of "overdone modesty" or what do you call
>>it.
>It was not intended as overdone modesty.

OK, got it.

>  >If I understood you wrong, then I hereby apologize.  Sincerely.
>Lotta sorry's going around now, seems to me. Maybe we should share them
>around a bit!!!

Hey, my girlfriend just bought me an entirely new box of sorry's.  I 
don't know if I'm that eager to share them with who-knows on the list 
though.  After all, I like them way too much myself.  Selfish little 
bastard that I am...

>  > >  >No, not at all.  Either _you_ missed the point completely, or I did...
>>  >Then let us say that it was me.
>>Why you?
>Because you are a very intelligent person,

So are you...

>and I agree with most of the things you say.

You ought to. :-)

>Therefore, if you are saying something and I am not getting
>it then chances are that it is my own position, and not yours, that need
>re-evaluating.

Mwah... I wouldn't disregard my own position so easily if I were you.

>  > >I see a 'most mathematicians there'. Like I said, my mind went immediately
>>  >to Babylonians, Ancient Greeks, Euclid, Diophantes ... and all those other
>>  >people who worked before Gauss.
>>
>>OK.  My mind didn't.
>
>I kind of think that's all that's going on here.

Indeed.

>  > >I am sorry about that. Next time I see most mathematicians I will
>>  >try to remember that it means 'most of the mathematicians who have
>>  >ever lived' rather than 'most of the historical period in which
>>  >mathematics has been done'.
>>
>>Now, this is the kind of stuff that I find ... annoying, if I may say
>>so, or puzzling.  As if an incidental meaning of some words in one
>>particular context would define them for all eternity.
>No. It means that next time I read 'most mathematicians', I shall keep more
>clearly at the front of my mind that the person who using that expression
>is probably using it in a very different way from me.

Replace "probably" by "possibly" maybe...

>  >And as if you
>>have to humbly bow to adjust yourself to the incidental
>>interpretation two other guys give to a bunch of words in some
>>particular context.
>And ... what's wrong with adjusting my understanding of affairs after
>interacting with two people? No word has an absolute meaning.

Exactly: this holds for interpretations or meanings given by me or GA 
or whoever else as well.

>  >To me it feels as if it leaves no room for anything else.
>Seems to me that all I've done is recognize that the word 'most' when used
>in conjunction with the word 'mathematicians' can mean something a tad
>different from what I first assume.

Yes, it _can_ mean something different.  But what you previously said 
(or what I thought you said) was that you'll accept that from now it 
it _does_ mean something different.  Simply because I and/or GA says 
so.  And that, of course, makes no sense.

>  >As far as I'm concerned, I have a problem with people adjusting
>>themselves to me "in modesty".
>I think my life will be easier if I leave this as your problem and do not
>take it on myself.

Very wise :-).  Every man's got to deal with his own shortcomings in 
the end, hasn't he?

>  >I prefer the opposite: I like people
>>to have their own opinions.
>Am I then a person with no opinions?

No.

>  >Strong opinions, preferably.
>Are my opinions then weak ones?

No.

>  >And not
>>shy away from defending them when needed.
>I have defended my opinions. When I tried to defend them thoroughly, and by
>covering the more obvious of the objections that I could think of, you
>criticized me for lecturing.

OK.  But the point of the foregoing was found in the following;

>  >Things like "I'm sorry,
>>I'll use those words the way you want me to in the future" is
>>perpendicular to that.
>OK. But as far as I can see, I have my own way, plus I have added your way.
>I have not given up my way. I shall just be careful in future that others
>might interpret the phrase 'most mathematicians' differently from me, and I
>shall take it into account. Is something wrong with that?

No.

>  >Remember, this stuff
>>is quite subtle and requires accurate phrasing,
>I tried that.

I was referring to my own troubles with accurate phrasing, enlarged 
by the fact that I;m no native English speaker.

>You just criticized me for lecturing. And for writing many
>words. It was exactly my motivation that the ancient mathematical concept
>of 'beauty', especially 'in mathematics' before around the time of Gauss,
>and the associated attitude to proof was subtle ... and subtly different
>from the modern kind ... and I did my level best to elucidate those
>differences in a clear and understandable way.
>
>Clearly, I failed. I wish I had succeeded. (Please notice that I did
>actually manage to avoid a 'sorry' there!!)

:-)  Again: maybe it's just my non-nativeness that gives me trouble 
reading such long posts.  To me, it feels as if the real meaning gets 
somewhat lost in the large amount of words.  But again, that's 
probably me.

>  > >  >For all we know, Euclid or Phythagoras may well have been smitten
>>  >>with the beauty of abstractions.
>>  >Possibly so. But ... they wrote precious little about it.
>>That's why I suggested to leave them out of the discussion.
>Then ... take out the 'most' in 'most mathematicians'. That's my view on
>the matter. If it's kept in, then people like me will always put up their
>hands and raise doubts and ask questions.

Leaving out "most" would yield a statement like "mathematicians 
appreciate the beauty of abstractions", which is far _more_ 
generalising than inserting "most" before "mathematicians".

And yes, I know this is a lousy rethoric remark.  It's not to be 
taken seriously.

>  >As for respect: I've come to respect you at least as much as you've
>>come to respect me.
>That's nice. You must have been on the same neurolinguistic programming
>course!! (Sorry Tony if you're reading ... just a little joke there!!!)

No, this has nothing to do with 60ies cuddly fuzzy feelie stuff.  I 
was just being honest and straightforward.

>In any case, you seem to get annoyed when I have that
>attitude of gratitude as a general principle ... how much MORE annoyed
>would you get if I prefaced it every time with a long list of the wonders
>that you have done for me over many years?!!

Well, I don't know...  You could always give it a try, couldn't you? 
At least that way the others in this group would see, time and time 
again, what a wonderful sort of person I really am.  And what's good 
for my reputation is good for me, isn't it?  :-))
But seriously, if anything, I think that an attitude of a kind of 
friendship (or whatever you want to call our "relationship") would be 
more appropriate.  I think you're on OK-guy, and so when you have a 
problem I try to help you out.  I suppose you'd do the same for me. 
Gratitude does have its place there but, imo, shouldn't be the 
dominant feeling.  More like "[HJ|Kool] is an OK-kind-of-guy".

Oh well, what are we talking about...?  this does start sounding like 
fuzzy feelie etc.

>  >It felt as if you thanked me for something you shouldn't thank me
>>for.
>I should not have gratitude for, or continue to remember, your kindness to
>me? Strange, that.

No no no.  You're free to thank me for anything "good" I did for/to 
you, obviously.  At the time however, I had the feeling you said 
"thank you" in reference to something else -- something which had, 
imo, very little to do with doing something "good".

>Here's to many years of successfully sorting little communication problems.

I'll have a whiskey to that.  Cheers.


tata,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html

>>  >I meant to say (and thought I said) that we simply don't know enough
>>>about the ancient Greek mathematicians to be able to judge how
>>>exactly they viewed mathematics, beauty of abstraction and such.
>>>There's simply not enough reliable written history on that subject,
>>>as far as I know.

Well there was a cult around Pythagorus I think. Euclid's books were 
famous for millenia but some were destroyed in the fire in the library in 
Alexandria.

>>Then there was all that mumbo jumbo he had about cosmic solids. He
>>really thought it beautiful. As a 'work of art'. maybe. But as a
>>mathematical demonstration? Yet ... there were people who thought, at the
>>time, that it was a demonstration of mathematics at its best.

What mumbo-jumbo? Actually, the n-sphere is a good example of the 
abstractness of mathematics (the unit sphere in n-dimensions given by the 
equation (x_1)^2 + (x_2)^2 + ..... + (x_n)^2 = 1) - something that would 
take n dimensions to visualize, but nonetheless exists as though it were 
a household object for mathematicians.

Hendrik Jan wrote:

>[interesting stuff deleted for brevity]
>Didn't know this.  Interesting.  Thanks.
You're welcome. Glad you found it interesting. Not many people around here 
to talk that kind of stuff over with, so it's a pleasure.


>Uhm... are you implying that the fact that they didn't write about it
>must mean they thought about it differently than we do?
No must. Just a probably ... and enough of a doubt, when combined with the 
little we DO know to make the proposition basically one that should be 
doubted rather than (glibly) accepted.

>Because with
>that I wouldn't agree.  IMO there's no way we can figure out why they
>did or did not write about something.  But maybe I misunderstand what
>you're saying here.
I don't think you're exactly misunderstanding. I am saying that we can't 
KNOW, but we can conjecture from the fact that the famous Greek 
mathematicians we know about also did things like architecture, and in the 
record of the arts that we have regarding what they thought were sound 
principles for that, there is no record of the kind of abstractionist 
beautifying under debate. It's a hotly debated topic for example whether 
thinkers of that era distinguished between 'good' and 'beautiful' and 
'well-made' (i.e. does the job it's intended to do well) in the easy kind 
of way we do. Thus it could be that to them a 'beautiful proof' was 'good' 
in the sense that it was moral; or that it was 'beautiful' in the sense of 
concise ... the possibilities are endless. Therefore, better to accord to 
them principles and thoughts we can be reasonably certain they did have -- 
from the evidence -- than attribute to them principles of our own and that 
we can't really be sure of.

I must repeat, though, that in my view GA Moore's argument about the 
Archimedes tomb is emotionally convincing and satisfying to me -- and 
therefore IMO likely to be correct -- about Archimedes at the very least, 
and therefore that it was also probably applicable to others of his ilk 
like Apollonius. I must still reluctantly say, though, that there's no 
EVIDENCE that would concord with the more general statement of this kind 
that is being made.

>Which is why I suggested to leave them out of the discussion.
I agree ... but in that case it calls into question the whole issue of what 
is meant by 'most mathematicians'. We are leaving out rather a lot of 
mathematicians over 'most' of the historical epochs in which mathematics 
has been done. Rather devalues the assertion IMO but that's probably just me.

[Regarding 'sorry']
>Ah, ok, that _is_ a misunderstanding then.  Probably to do with the
>"emotional charge" of some words.
Most likely.

>But I've come to understand that when a white man says
>"brother" to an Afro-American in the Bronx, he can get his butt
>kicked,
Could happen indeed.

>Apparently in certain contexts this simple word has far reaching
>connotations that I, as non-native, am not always aware of.
Yup.

>Oh man... maybe Af-Am is insulting too...  help...
I'm not sure about that. I'll have to check the latest reprint of the 
Politically Correct Dictionary.

> >Then there was all that mumbo jumbo he had about cosmic solids. He
> >really thought it beautiful. As a 'work of art'. maybe. But as a
> >mathematical demonstration? Yet ... there were people who thought, at the
> >time, that it was a demonstration of mathematics at its best.
>:-).  But then: what could be more beautiful than an abstract science
>being able to explain the entire cosmos with a basically simple
>model?  Isn't that every scientist's wet dream?
I would really like to believe that that is what Kepler intended. However, 
in Kepler's case it is really very doubtful. I honestly don't think, and 
nor do most of the people who write about him, think that this was Kepler's 
intent. He was filled through and through with Pythagorean mysticism and 
what pleased him was not the elegance of the pattern, or anything to do 
with it, but the simple fact that God had revealed the true meaning of 
number. God had done so in several other ways also, including by giving him 
visions. To Kepler, those other visions were all of a piece with his 
mystical cosmic solid system, and there doesn't seem to be any sign that 
the truly mathematical side of it evoked any more appreciation in him than 
the witchcraft that gave him the same kind of knowledge.His Mysterium 
Cosmographicum was certainly brilliant but in the same kind of way that a 
good theological book can be brilliant. It is also true that his 
presentation fused mathematics, imagination and aesthetics together, but 
this was done in a very Aristotelian rather than mathematical manner. 
That's to say, it was not mathematically logical, but simply 
philosophically or theologically logical.

>Sure I understand what you mean.  The essence of my reply was just
>that I thought you made things more complicated than they were ever
>intended.
I only tried to explain the basis for my disagreement. I guess that would 
inevitably complicate things, because on the face of it GAM's original 
assertion does on the face of it seem very simple. Since I wasn't prepared 
to take it at face value, I guess inevitably I was making it complicated.

>:-)  So that's what you do when feeling stuck?  Keep saying sorry?
>Ahw, sorry, I shouldn't laugh about that, but I can't help it raises
>a kind of funny picture in my mind.
That's OK.

>Like someone bumping into a brick wall and then apologizing to the wall or so.
That's what I used to do, I guess, when I was given complex differential 
calculus stuff to do and I just couldn't get it right.

>OK, but then, to paraphrase what you said above: I'm not in the
>humiliate-others business.
Nicely put. And I never thought you were, or tried to imply that you were.

 >>Why you?
> >Because you are a very intelligent person,
>So are you...
Thanks.

> >and I agree with most of the things you say.
>You ought to. :-)
I keep trying to!!!!

> >Therefore, if you are saying something and I am not getting
> >it then chances are that it is my own position, and not yours, that need
> >re-evaluating.
>Mwah... I wouldn't disregard my own position so easily if I were you.
Re-valuating is not the same thing as disregarding.

> >And ... what's wrong with adjusting my understanding of affairs after
> >interacting with two people? No word has an absolute meaning.
>Exactly: this holds for interpretations or meanings given by me or GA
>or whoever else as well.
True. But ... I simply can't do anything about whether or not you are 
prepared to re-evalute YOUR understandings and meanings of 'most 
mathematicians' etc. I can only work on whether or not I am prepared to 
re-evaluate mine. At the very least, surely, next time either the one of 
you makes a similar remark and someone else disagrees, you might have some 
idea why. That's all I can hope. But ... I can only HOPE in your cases. For 
myself, I can make sure that it is definitely the case that I consider 
other issues than the ones first come to my mind.


>Yes, it _can_ mean something different.  But what you previously said
>(or what I thought you said) was that you'll accept that from now it
>it _does_ mean something different.  Simply because I and/or GA says
>so.  And that, of course, makes no sense.
I agree it makes no sense. I meant 'can' and not 'does'.

> >>As far as I'm concerned, I have a problem with people adjusting
> >>themselves to me "in modesty".
> >I think my life will be easier if I leave this as your problem and do not
> >take it on myself.
>Very wise :-).  Every man's got to deal with his own shortcomings in
>the end, hasn't he?
Yes.

> >>Remember, this stuff
> >>is quite subtle and requires accurate phrasing,
> >I tried that.
>
>I was referring to my own troubles with accurate phrasing, enlarged
>by the fact that I;m no native English speaker.
I accept that ... but ... I was also remembering that GAM was reading ... 
and he has a very sharp eye for spotting the hole in an argument. I think 
he reads too much theology, to be honest (just a joke!!!!). So ... I was 
trying to anticipate and plug those holes so that I wouldn't have to do so 
later. Of course, if the whole position is faulty then no amount of detail 
can cover it up, which might be basically what you were criticizing me for? 
I.e. my position was faulty, then it could not really be salvaged by any 
number of facts. However, since I did not feel my position to be faulty but 
rather a subtle one that might not have been considered due to a certain 
lack of information regarding the historiography of mathematical reasoning, 
I tried to defend my position by presenting those facts but in a close knit 
way that left no holes in it for people as well versed in dialectical 
argumentation as you and GAM. The two of you just don't make it easy for 
those of us who tend to get by with bluster and slipshod arguments, you 
know!! I was just trying to cover my bases and make my position look not 
only reasonable, but well-thought out and justified. The only way to do 
that was present evidence in the form of information that you might not 
have known and that you might not therefore have considered.

That's all, really. What GAM at first said had a great deal of plausible 
face value, and in order to explain why I did not accept it a great deal of 
underground stuff seemed to me to be required.

>:-)  Again: maybe it's just my non-nativeness that gives me trouble
>reading such long posts.  To me, it feels as if the real meaning gets
>somewhat lost in the large amount of words.  But again, that's
>probably me.
Not entirely you, I think. Like I said, you two are not easy people to 
debate anything with and I was doing my best to present a thorough and 
convincing argument. Since you fiercely believed what you were saying, you 
were making it very hard work for me to present the alternative case. Very 
hard work indeed. I am still not entirely certain I have succeeded, but I 
don't think it matters any more because I think we've all learned a great 
deal we didn't know before to carry forwards with us ... which I think is 
good thing.

>Leaving out "most" would yield a statement like "mathematicians
>appreciate the beauty of abstractions", which is far _more_
>generalising than inserting "most" before "mathematicians".
Yes. But another statement would be 'I think' or 'in my opinion, most 
mathematicians in history have appreciated the beauty of abstractions'. 
Those conditionals turn it into a very different kind of statement. There 
were no conditionals of any kind in the original assertion, and a 
conviction seemed to be apparent there that something truthful and 
revealing had been said about all mathematicians in history. That simply 
was not so IMO and that's all I have tried to point out.

>And yes, I know this is a lousy rethoric remark.  It's not to be
>taken seriously.
Should have read this first, I guess.

> >  >As for respect: I've come to respect you at least as much as you've
> >>come to respect me.
> >That's nice. You must have been on the same neurolinguistic programming
> >course!! (Sorry Tony if you're reading ... just a little joke there!!!)
>
>No, this has nothing to do with 60ies cuddly fuzzy feelie stuff.  I
>was just being honest and straightforward.
Oh dear. I _knew_ you were being serious. I, on the other hand, was trying 
to make a joke.

>... that way the others in this group would see, time and time
>again, what a wonderful sort of person I really am.  And what's good
>for my reputation is good for me, isn't it?  :-))
That's indeed so. I'll give some thought to the matter. (Another joke!!!)

>But seriously, if anything, I think that an attitude of a kind of
>friendship (or whatever you want to call our "relationship") would be
>more appropriate.  I think you're on OK-guy, and so when you have a
>problem I try to help you out.  I suppose you'd do the same for me.
>Gratitude does have its place there but, imo, shouldn't be the
>dominant feeling.  More like "[HJ|Kool] is an OK-kind-of-guy".
Gratitude is not the dominant feeling. But it is there. I weigh it in my 
way. You weigh it in yours.

>Oh well, what are we talking about...?  this does start sounding like
>fuzzy feelie etc.
It's all that neurolinguistic programming you've been doing.

> >Here's to many years of successfully sorting little communication problems.
>
>I'll have a whiskey to that.  Cheers.
Make it a good expensive whiskey. (On your own credit card, though!!).

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

GA Moore wrote:

>Well there was a cult around Pythagorus I think.
Yes.

>Euclid's books were
>famous for millenia but some were destroyed in the fire in the library in
>Alexandria.

Not to put too fine a point on it, this was a most heinous crime against 
humanity for which Christians and Muslims were jointly responsible. At one 
of those burnings they were stoking the fires for over a week!! Imagine!!! 
All those books and manuscripts lovingly gathered over the centuries just 
GONE in wanton acts of sheer savagery.

And then there was that manuscript that showed up out of the blue in 18 
something or other where an old theorem by Archimedes had been covered over 
to put a prayer on.

Grrr. All that lost knowledge. Grrrrrrrrrrrrrrrrrrrrrrrr

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

At 03:30 PM 11/11/01, you wrote:
> >>Then there was all that mumbo jumbo he had about cosmic solids. He
> >>really thought it beautiful. As a 'work of art'. maybe. But as a
> >>mathematical demonstration? Yet ... there were people who thought, at the
> >>time, that it was a demonstration of mathematics at its best.
>
>What mumbo-jumbo? Actually, the n-sphere is a good example of the
>abstractness of mathematics (the unit sphere in n-dimensions given by the
>equation (x_1)^2 + (x_2)^2 + ..... + (x_n)^2 = 1) - something that would
>take n dimensions to visualize, but nonetheless exists as though it were
>a household object for mathematicians.

I don't doubt any of that. However, that's not what so delighted Kepler. I 
meant to refer to his Aristotelian mumbo-jumbo ... all that stuff about the 
planets and their 'meaning'.

"The orbit of the Earth is a circle: round the sphere to which this circle 
belongs, describe a dodecahedron ... <snip> ... Now inscribe in the Earth's 
orbit an icosahedron ... <snip> Inscribe an octahedron in the orbit of 
Venus; the circle inscribed in it will be Mercury's orbit. This is the 
reason for the number of the planets". But ... he didn't stop there. He 
then went on to philosophise about the numerological significance of all 
those numbers, and therefore the role in life that each planet played 
because of its number and position. To him, that was a part of the beauty 
... not just the abstract mathematical patterning of it all.

This would not be so bad if it were not for the context in which it were 
written. Kepler was not in the least interested in mathematical beauty. He 
was after a Divine, harmonious order for the solar system, and if he could 
find it in prayer, good enough; if he could find it in witchcraft; good 
enough; and if he could find it in Platonic solids, also good enough.

In his defence, however, Kepler did also say the following:
"We do not ask for what useful purpose the birds do sing, for song is their 
pleasure since they were created for singing. Similarly,we ought not ask 
why the human mind troubles to fathom the secrets of the heavens. The 
diversity of the phenomena of Nature is so great, and the treasures hidden 
in the heavens so rich, precisely in order that the human mind shall never 
be lacking in fresh nourishment."

That bespeaks, I guess, an appreciation of abstract patterns. However ... 
Kepler had great difficulty in accepting that the model is completely false 
and that the interplanetary distances it predicts are inaccurate. The 
mathematician in him qua scientist had great difficulty accepting this 
because he wanted to cling to both the truth and the beauty of the pattern. 
This is probably a good example of the difficulties of equating truth and 
beauty because the two are not always equivalent -- but then again the 
whole point of Kepler's presentation was not just that it was a pretty 
pattern but that it was true.

Thomas Huxley referred to this kind of thing as: 'the great tragedy of 
science, the slaying of a beautiful hypothesis by an ugly fact'. I have 
always loved that quote!!

When Kepler's idea was no longer true, it also was not pretty any more. 
However, he was forced to accept their speciousness eventually because he 
himself found different laws that worked much better. When he found his new 
laws and published them, his whole attitude made them very difficult to 
find or appreciate. His New Astronomy was a complete mess and contained not 
only the valuable information about his three laws, but a lot of guff, 
philosophising -- and also intricate information about all the wrong 
guesses he had made, every bogus hypothesis he had had, every blind alley 
he had explored. He was not really that interested in the beauty of any of 
it. If one can conclude anything it was that his three laws of planetary 
motion were not particularly beautiful. They were just true.

All in all, the case of Kepler is confusing in this regard, and he is 
actually a much better candidate for discussing this whole issue of 
mathematical beauty because he really did stand at an important crossroads. 
Things moved from simple prettiness to their utility in terms of 
computational excellence and conciseness and a new kind of elegance -- 
which Kepler just didn't seem to appreciate. Even though he was a prime 
architect in introducing it.

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

Kool Musick wrote:

>You're welcome. Glad you found it interesting. Not many people around here
>to talk that kind of stuff over with, so it's a pleasure.

Please ... before anyone gets hot under the collar I meant 'here' in my 
physical house here where I live ... and not 'here' this L-OT list.

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

Thoughts from the mind of Kool Musick, 11-11-2001:
>It's a hotly debated topic for example whether
>thinkers of that era distinguished between 'good' and 'beautiful' and
>'well-made' (i.e. does the job it's intended to do well) in the easy kind
>of way we do. Thus it could be that to them a 'beautiful proof' was 'good'
>in the sense that it was moral; or that it was 'beautiful' in the sense of
>concise ... the possibilities are endless.

Yes, this is an extremely interesting and subtle topic when studying 
anything that has to do with ancient Greece culture and value 
judgements.  One of the dominant words in Greek thinking was "arete", 
which nowadays often gets translated as "virtue" -- i.e. with a kind 
of ethical connotation.  However, it covered much more than virtue 
alone.  Art could have "arete", and a warrior could.  Probably a 
mathematical proof could also have "arete".  A more proper 
translation would probably be something like "excellence", in a 
rather broad sense.  The tale of Ulysses is one about a man "gaining 
arete" -- i.e. proving his excellence.  Some one with arete was a 
good fighter but at the same time a good scholar, a thinker, 
craftsman, father and husband.  It was someone who excelled at as 
many things as possible.
So yes, indeed, terms like good, beautiful, moral, just, high-quality 
nowadays all have different meanings or nuances, whereas in the old 
days, it all was part of "excellence".  Lots of confusion can rise 
from an improper understanding of such pivotal concepts.

Geesh, apparently my years at the philosophy department haven't all 
been wasted :-).

>I only tried to explain the basis for my disagreement. I guess that would
>inevitably complicate things, because on the face of it GAM's original
>assertion does on the face of it seem very simple. Since I wasn't prepared
>to take it at face value, I guess inevitably I was making it complicated.

It's a pity this whole discussion apparently couldn't have been as 
simple as this:
---
GA: most mathematicians appreciate pure abstract beauty.

Kool: if that's supposed to hold for all mathematicians past and 
present, I don't think that's true.  There are arguments suggesting 
that the beauty of abstraction was only appreciated relatively 
recently, and that in "the old times" much (or all?) of the beauty of 
mathematics was found in its applicability to (sometimes) urgent and 
practical problems.

GA: Oh yes, sure.  I just meant to talk about living mathematicians. 
or at least about recent (few centuries) mathematics.

HJ: Agreed too (if I had said anything at all in such a clear and 
simple exchange of thoughts)
---
That would have spared all of us an awful lot of typing, wouldn't it?

>But ... I simply can't do anything about whether or not you are
>prepared to re-evalute YOUR understandings and meanings of 'most
>mathematicians' etc. I can only work on whether or not I am prepared to
>re-evaluate mine.

See directly above.

>Of course, if the whole position is faulty then no amount of detail
>can cover it up, which might be basically what you were criticizing me for?

No.  When talking about different _interpretations_ there's no such 
thing as "faulty".  And neither is there the need to re-evaluate your 
viewpoint or whatever.  Both interpretations are equally valid.  When 
talking about "all mathematicians past and present" you made a valid 
point.  When talking about "all living or 'recently' living 
mathematicians", GA had a valid point.  The difference is only in the 
interpretation of the word "most", and no value judgement can be 
attached to such interpretations.

>The two of you just don't make it easy for those of us who tend to 
>get by with bluster and slipshod arguments, you know!!

You, of all people, are certainly _not_ in the category of "those of 
us... slipshod arguments", so I don't see how the above applies to 
you.

>  >And yes, I know this is a lousy rethoric remark.  It's not to be
>>taken seriously.
>Should have read this first, I guess.

Yeah. That's one of the things I try to teach my students: first read 
the question very carefully before attempting to give any answers :-).

>  > >Here's to many years of successfully sorting little 
>communication problems.
>>
>>I'll have a whiskey to that.  Cheers.
>Make it a good expensive whiskey. (On your own credit card, though!!).

Lagavullin.  16 years old, wonderful single malt Scottish whiskey. 
Anything cheaper than that I find undrinkable.  I'm a snob, 
sometimes...


cheers,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html

HJ wrote:

>Yes, this is an extremely interesting and subtle topic when studying
>anything that has to do with ancient Greece culture and value
>judgements.

And ... the fact that the original statement was in fact a value judgement 
and not the definitive statement of fact that it purported to be was 
exactly one of the points I was trying to make. I simply felt that since it 
was nothing more than a value judgement it should have been -- and was not 
-- labelled as such. And ... then granted that as a statement of fact it 
seemed to me to be clearly untrue when taken generally -- which was the 
overall tenor it seemed to have --  then at the very least it was in need 
of extreme qualification so that its limited parameters of relevance were 
somewhat clearer.

>Art could have "arete", and a warrior could.  Probably a
>mathematical proof could also have "arete".
I would tend to agree with you.

>A more proper
>translation would probably be something like "excellence", in a
>rather broad sense.  The tale of Ulysses is one about a man "gaining
>arete" -- i.e. proving his excellence.
And I would again agree with you by saying that a statement gains in a very 
great deal of arete once it has been taken through the process of proof and 
so becomes a theorem. That's a view that I'm quite sure you share. I am not 
for a moment pretending to speak for what them guys back then actually did 
have in their heads. I am just agreeing with you that that's also how I 
feel about these things.

>  Lots of confusion can rise
>from an improper understanding of such pivotal concepts.
Ain't that the truth/


>Geesh, apparently my years at the philosophy department haven't all
>been wasted :-).
"Apparently". (!!!)


>It's a pity this whole discussion apparently couldn't have been as
>simple as this:
>---
>GA: most mathematicians appreciate pure abstract beauty.
>Kool: if that's supposed to hold for all mathematicians past and
>present, I don't think that's true.  There are arguments suggesting
>that the beauty of abstraction was only appreciated relatively
>recently, and that in "the old times" much (or all?) of the beauty of
>mathematics was found in its applicability to (sometimes) urgent and
>practical problems.
>GA: Oh yes, sure.  I just meant to talk about living mathematicians.
>or at least about recent (few centuries) mathematics.
>HJ: Agreed too (if I had said anything at all in such a clear and
>simple exchange of thoughts)
>---
>That would have spared all of us an awful lot of typing, wouldn't it?

Yes it would.


> >Of course, if the whole position is faulty then no amount of detail
> >can cover it up, which might be basically what you were criticizing me for?
>
>No.  When talking about different _interpretations_ there's no such
>thing as "faulty".
That is true. However, the original assertion was presented as -- and was 
also initially defended as -- a statement of fact. And in the area of 
things asserted as facts, faultiness is sometimes possible.

>And neither is there the need to re-evaluate your
>viewpoint or whatever.  Both interpretations are equally valid.
Yes. And as for the interpretation, I think we all three agree that 
Archimedes and those others, by any reasonable standard we have today given 
how WE understand those words, was most probably in touch with how we view 
things. These are still not matters of fact, though. Just a way to get a 
warm fuzzy feeling about Archimedes. Which I don't object to in the least. 
Go Archimedes.

>When
>talking about "all mathematicians past and present" you made a valid
>point.  When talking about "all living or 'recently' living
>mathematicians", GA had a valid point.  The difference is only in the
>interpretation of the word "most", and no value judgement can be
>attached to such interpretations.
And ... the interpretation of 'most' is exactly what I addressed.

When I tried to say that IF by 'most' he/you meant 'all those after Gauss 
then fine'; and that if he/you meant 'most of history' then not fine; I 
still met with strenuous objections -- including statements that I didn't 
properly understand what was going on and that I had misunderstood and so 
forth.

> >The two of you just don't make it easy for those of us who tend to
> >get by with bluster and slipshod arguments, you know!!
>You, of all people, are certainly _not_ in the category of "those of
>us... slipshod arguments", so I don't see how the above applies to
>you.
Well ... I do try very hard not to use bluster and slipshod arguments, but 
that's what I've been accused of in the past. Not by you. When I say 
something, I try to base it on solid facts and my experience and knowledge. 
If I don't have the grounds and backings for such things, I try very hard 
not to pretend that I have it.


>Lagavullin.  16 years old, wonderful single malt Scottish whiskey.
>Anything cheaper than that I find undrinkable.  I'm a snob,
>sometimes...

OK. You reach out for that credit card ... and help yourself to another whisky.

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

--- In logic-ot@y..., Kool Musick <koolmusick@y...> wrote:
> GA Moore wrote:
> >Euclid's books were
> >famous for millenia but some were destroyed in the fire in the library in
> >Alexandria.
> 
> Not to put too fine a point on it, this was a most heinous crime against 
> humanity for which Christians and Muslims were jointly responsible. At one 
> of those burnings they were stoking the fires for over a week!! Imagine!!! 
> All those books and manuscripts lovingly gathered over the centuries just 
> GONE in wanton acts of sheer savagery.

Damn! These were the Talibans of the past.

Lets bom the Vatican. No, just kidding, :-). No more wars please.
Peace, 
Yoonchi.

Thoughts from the mind of Kool Musick, 12-11-2001:

>And ... the fact that the original statement was in fact a value judgement
>and not the definitive statement of fact that it purported to be was
>exactly one of the points I was trying to make. I simply felt that since it
>was nothing more than a value judgement it should have been -- and was not
>-- labelled as such. And ... then granted that as a statement of fact it
>seemed to me to be clearly untrue when taken generally -- which was the
>overall tenor it seemed to have --  then at the very least it was in need
>of extreme qualification so that its limited parameters of relevance were
>somewhat clearer.

Man... I get a headache trying to read & comprehend this... :-)

>  >It's a pity this whole discussion apparently couldn't have been as
>  >simple as this:
>  >[...]
>  >That would have spared all of us an awful lot of typing, wouldn't it?
>
>Yes it would.

Glad you agree :-).  That was, just to clarify one of my previous 
letters a bit more, the reason for my somewhat being annoyed at your 
longish, and for me sometimes fuzzy, postings -- the realisation that 
this entire discussion could have fitted on a single sheet of paper.

>And as for the interpretation, I think we all three agree that
>Archimedes and those others, by any reasonable standard we have today given
>how WE understand those words, was most probably in touch with how we view
>things.

So... let's leave it at that, ok?  I know what your point is/was, and 
you know mine, and GA probably knows them too.  So we all understand 
each other, and can move on to more important aspects of life, right?

>  >Lagavullin.  16 years old, wonderful single malt Scottish whiskey.
>  >Anything cheaper than that I find undrinkable.  I'm a snob,
>>sometimes...
>
>OK. You reach out for that credit card ... and help yourself to 
>another whisky.

Nah, not every night.  Just occasionally.  I'm not much into alcohol, 
generally.  Good whiskey is like a bonbon -- have one and savour it, 
have too many and spoil the good taste.


cheers,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html

>> Not to put too fine a point on it, this was a most heinous crime against 
>> humanity for which Christians and Muslims were jointly responsible. 

Mr. Kool, would you care to explain that statement? I never heard that 
before.

>Damn! These were the Talibans of the past.
>Lets bom the Vatican. No, just kidding, :-). No more wars please.

I don't think the Taliban's bombing of the ancient Buddhist statues was 
funny in the least. If you don't want to bomb these Taliban/Al Qaeda 
gentlemen who took power in Afganistan in the same way Al Capone would 
have liked to have taken charge of Chicago, should we send them 
chocolates and roses so they'll cheer up and put on thier smiley faces, 
and stop bombing our embassies, naval vessels, and major cities? Maybe we 
should ask them real politely to stop killing our innocent civilians, and 
then they'll listen to us.

GA Moore wrote:

>  > > Euclid's books were
>  > > famous for millenia but some were destroyed in the fire in the 
> library in
>  > > Alexandria.

Kool Musick wrote:
>  > Not to put too fine a point on it, this was a most heinous crime against
>  > humanity for which Christians and Muslims were jointly responsible. At 
> one
>  > of those burnings they were stoking the fires for over a week!! 
> Imagine!!!
>  > All those books and manuscripts lovingly gathered over the centuries just
>  > GONE in wanton acts of sheer savagery.

GA Moore wrote:
>Mr. Kool, would you care to explain that statement? I never heard that
>before.

I'll do my best!!

The first really big disaster that befell the Great Library seems to have 
been Julius Caesar. Unfortunately, the earliest descriptions we have of the 
Alexandrine War are simply toadying, were written by his family, and simply 
do not mention anything, good or bad, about his escapades in Alexandria. He 
does seem to have destroyed a good part of it, however, as a stratagem in 
the war. According to Livy 400,000 scrolls and books, all house in grain 
depots near the harbor became ashes when Caesar decided to torch Cleopatra 
and her brother's brother fleet. Plutarch, Gellius, Seneca and Livy all 
agree that Caesar burnt those stacks. There's a lot of justifiable 
finger-pointing but admittedly no hard evidence ... probably because he and 
his cronies had the good sense to destroy it. It seems that some Reading 
Rooms survived, but very many books perished. Much of this loss seems to 
have been made good by Anthony, who gave Cleopatra some 200,000 books and 
rolls from the library then based in Pergamum.

The next great disaster was at the hands of the Christians under the 
Emperor Theodosius. However, defenders of the Catholic Church say that this 
is a fiction perpetrated by Edward Gibbon who was certainly no lover of the 
Church and who lambasted it somewhat unmercifully in his history. Christian 
apologetics have argued that Gibbon not only wanted to attack Christians, 
but absolve the Arabs (who also engaged in book-burning) of all possible 
blame for anything. Unfortunately, a lot of other Western sources used 
Gibbon, knowingly or unknowingly, as their primary reference.

The flash-point seems to have been the attempt by Patriarch Cyril to expel 
the Jews. The prefect (can't remember his name) objected to the order and 
an army of monks promptly ran riot and laid the entire city to the sword. 
One of the things they did was kill Hypatia, one of the very few notable 
women mathematicians in history never mind in antiquity. The mob of monks 
happened to see her driving home alone and without her attendants (her 
father was himself a famous mathematician of the day and also an official 
of the city. By all accounts Hypatia was a great beauty as well as one of 
the better mathematicians of that era. She apparently had many suitors but 
rejected them all. To the mob she epitomized everything they hated about 
pagans and their heretical mathematics and science. She was dragged from 
her chariot and stripped. The monks then armed themselves with abalone 
shells and flayed her flesh from her bones. She was then burned and had her 
ashes spread in the Library. Patriarch Cyril was eventually made a saint 
for all of this.

The library was ransacked for its gold and silver ... and then torched so 
that later generations of Christians would never have to face being led 
astray from the one true path by the teachings in the ancient books. Not 
all the books were destroyed (enough were left for the Arabs to do much the 
same thing a while later), but one archaeologist who worked a dig there 
recently (I cannot remember his name) said that of the few things that were 
found, if they had remained in existence then the Industrial Revolution 
would certainly have occurred about 1500 years before it did. Amongst the 
documents lost in this particular escapade were, apparently, complete 
details on how to build a pyramid. Of the 123 plays that Sophocles was 
known to have written and that are now known to have been in the Library, 
only seven have survived. Luckily, one of those is Oedipus Rex. Emperor 
Theodosius wanted all non-Christian destroyed. Only the works of Aristotle 
survived because he was essential in that Christian scholars had decided 
that his syllogistic and other logical principles were a gift directly to 
them, via the pagans, in order that they could prove the existence of 
Christ and His plan for humanity.

Next, we get to the Arabs. This one's a bit confusing. Until Gibbon wrote, 
the generally accepted story was that when the Muslims captured Alexandria 
somewhere around 640, a Greek scholar who happened to be a friend of the 
conquering general, Amrou, sent a message to his friend asking if he could 
please receive the gift of the library so that he could carry on with his 
scholarship. Amrou felt unable to make the decision and consulted with 
Caliph Omar who gave the famous answer:

If these writings of the Greeks agree with the Koran then they are useless, 
and so do not need to be preserved; and if they disagree with the Koran 
then they are pernicious and should be destroyed.

Caliph Omar then instructed that the remaining books be used to stoke the 
fires of all the Alexandria baths because they were short of wood. The Arab 
historian Ibn al-Kifti said:

'the number of baths was well known, but I have forgotten it. 'They say 
that it took six months to burn all that mass of material.'

A Greek scholar called Eutychius estimated, however, that there were four 
thousand.

Obviously, some of the tales that have come down through the ages about the 
library and the various ways in which it and its contents were destroyed do 
not meet present day standards of accuracy or veracity. Particularly when 
you have good reason to throw scepticism on them all for some agenda of 
your own. Something, however, happened to all those books because there was 
definitely a library, and there are compendiums of what was in it. We do 
not have those books today, and there were rather a lot to bet rid of. 
Something happened. Personally, my money's on the sheer stupidity and 
short-sightedness of various idiots and bigots. But ... that's just me.

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

Kool Musick wrote:
> > Not to put too fine a point on it, this was a most heinous crime against
> > humanity for which Christians and Muslims were jointly responsible. At one
> > of those burnings they were stoking the fires for over a week!! Imagine!!!
> > All those books and manuscripts lovingly gathered over the centuries just
> > GONE in wanton acts of sheer savagery.

Yoonchi wrote:
>Damn! These were the Talibans of the past.
>Lets bom the Vatican. No, just kidding, :-). No more wars please.

Hmm!!
I really didn't think I was suggesting a war, actually.

The various Alexandria burnings happened some 2,000 years ago now ... so I 
think it's kind of well past time that any sort of war of revenge or 
retribution should be initiated, to be honest! Please don't anyone start 
one on my behalf.

I also kind of thought that I was saying that I really don't see how a War 
On Books served any purpose, but that it had rather hurt things instead ... 
as all wars seem to do.

I guess I should have thought more clearly that someone or other might feel 
motivated to stand up and try to defend those burnings. I never thought of 
that. If anyone does want to stand up and defend them then I'll just say 
that I respectfully disagree with them and simply leave it at that. They 
are burned and they are gone and that's a fact.

Also ... on my mother's side, my grandfather was the first literate member 
of our family; and on my father's side my father was. I have relatives who 
still haven't learned to do this. My experience, therefore, is not that 
deep in this regard. And ... because of this, I guess, I have learned to 
love and appreciate books possibly in a way that's a bit different from 
those who, through a different heritage, are able to take it for granted. 
It is pretty close to incomprehensible to me why anyone would want to do 
something like this.

I was not suggesting a war. I was not trying to get one to start. I was 
just trying to say that as someone who loves books and learning and who has 
spent a lot of time studying ancient knowledge, it truly grieves me to 
think of everything that was lost. When I read GA Moore's post I remembered 
Alexandria from the few studies I did in early Christian and Muslim 
theology and that was about it, really. Nothing more. Certainly no 
incitement to violence.

>Peace,

Peace to you also.

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

Hendrik Jan wrote:

>Man... I get a headache trying to read & comprehend this... :-)
In that case don't try. Way too complicated. Keep it simple. Just ... read 
and comprehend instead. (!!!!)

>Glad you agree :-).  That was, just to clarify one of my previous
>letters a bit more, the reason for my somewhat being annoyed at your
>longish, and for me sometimes fuzzy, postings -- the realisation that
>this entire discussion could have fitted on a single sheet of paper.
With all due respect -- and I hate to repeat myself -- but you also got 
annoyed when I said absolutely nothing and just sent in a few quotes. 
Personally, I thought that Poincare and Fourier between them had made my 
point perfectly adequately.

KM:
> >OK. You reach out for that credit card ... and help yourself to
> >another whisky.

HJV:
>Nah, not every night.  Just occasionally.  I'm not much into alcohol,
>generally.  Good whiskey is like a bonbon -- have one and savour it,
>have too many and spoil the good taste.
OK. Just use the credit card a lot then and leave that good stuff for your 
descendants yet unborn. They'll thank you for it. You'll feel much better, too.

Kool Musick
Keep Musick Kool


_________________________________________________________
Do You Yahoo!?
Get your free @... address at http://mail.yahoo.com

Thoughts from the mind of Kool Musick, 13-11-2001:

>Hendrik Jan wrote:
>  >Glad you agree :-).  That was, just to clarify one of my previous
>>letters a bit more, the reason for my somewhat being annoyed at your
>>longish, and for me sometimes fuzzy, postings -- the realisation that
>>this entire discussion could have fitted on a single sheet of paper.
>With all due respect -- and I hate to repeat myself -- but you also got
>annoyed when I said absolutely nothing and just sent in a few quotes.
>Personally, I thought that Poincare and Fourier between them had made my
>point perfectly adequately.

OK, OK... you win...

>KM:
>>  >OK. You reach out for that credit card ... and help yourself to
>>  >another whisky.
>
>HJV:
>>Nah, not every night.  Just occasionally.  I'm not much into alcohol,
>>generally.  Good whiskey is like a bonbon -- have one and savour it,
>>have too many and spoil the good taste.
>OK. Just use the credit card a lot then and leave that good stuff for your
>descendants yet unborn. They'll thank you for it. You'll feel much 
>better, too.

I'm afraid I'll use that credit card for way different purposes. 
Like LA5 and stuff like that.  Ouch...  Will have to wait a bit with 
that descendants-stuff.  Yet another argument with the Lovely Lady...

tata,
HJ
-- 
     Hendrik Jan Veenstra
     email: mailto:h@...
     www:   http://www.ision.nl/users/h/index.html