The Logic Off Topic list

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