The Logic Off Topic list

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


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