au miau --

I didn't say I didn't want higher order generalizations. What I said 
was that I didn't like the ones we had (and I don't like the ones we 
have now).

I do like abstract math, but I don't feel a slave to classical 
versions of it. In particular, one of the most important things about 
computing is change of state over time. For various reasons, most of 
classical math is weak in interesting ideas about this. And, I would 
say that our current ideas about this are weak.

Computing already is a kind of math, and what we need to do is to 
find better foundations for what is important about computing. To do 
that, we need to make lots of interesting artifacts and dynamic 
relationships. Classical math came by its foundations very late in 
its history, and only after there were lots of interesting 
relationships that looked like they could be grounded in theory.

P.S. Classes in Smalltalk-76 did not require metaclasses, yet the 
system was both very sound and very understandable. It could have 
easily had models of all of its parts.

P.P.S. An example of something for which Smalltalk has never had a 
useful model is a variable. This could be done right now -- it has 
been done successfully in other systems -- and it would lead to many 
useful extensions.

P.P.P.S. I think the way to sneak up on generalities today is to take 
a working system and try to rewrite it using the most useful 
abstractions that can be invented. Then criticize it.

Cheers,

Alan

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At 5:09 PM +0300 7/5/02, au miau wrote:
>I search the right way to do things in programming
>for a long time (and i have even the Fortran experience
>-IV(no 77)) .At the end i come to that definition for
>a good programmer :"A man who can solve any (solvable)
>problem starting at ground zero somewhere under assembler
>on any kind of computer arcitecture". My pre-last deffinition
>was: "Outstanding Smalltalk (or CLOS)programmer"-i'll explain
>why i drop that deffinition later.
>
>So, Alan Kay wrote:
>
>  "
>     Well, I think this is a confusion with "objects" and some of today's
>     "object-oriented systems". In the "Early History of Smalltalk" paper
>     I wrote back in '93, I seem to remember pointing out that the first
>     three principles of objects that came to me in '66:
>          * Everything is an object
>          * Objects communicate by sending messages (which thus must 
>be objects)
>          * Objects can remember (memory thus via objects)
>     had stood the test of time.
>  "
>
>"No vay Hoze"!!! When last time matematicians talk so careless for that
>what they called "Sets" (then this was the new foundation of their field
>same like "Objects" are foundation of programming now) they see what the
>result is they got a funny situation - known from these times as "Crisis
>in Foundations(of math)"(hint Russel's paradox and others you can get the
>same with Objects with that "Theory of Objects")
>
>1.This is an important problem!I think it is second time in Smalltalk
>and there is still no good answer what a higher order "obects" are
>in Smalltalk .
>Messages are not objects for sure they could be but they are not necessarily
>"objects"! Classes and Metaclasses are not Obcects too!
>You can reply now that abstract math is not that you are interested ,
>that objects are not sets or that computing happens in finite domain
>and there are no paradoxes . But first i like Smalltalk because it
>separates computer's brain and human brain and that you can use a
>Smalltalk program like a proof even if you can execute it and second
>why to replise computer logic with another non human logic ?
>
>2.At 60-ies A.Grothendieck had the same problem with categories, functors
>and so on (i.e. functor categories) at his famous "Seminair de Geometrie
>Algebrique du Boi Marie " (widely known like SGA 1 to 4)- i think it is
>something like XX sentury "Elements" . He solved the problem introducing
>Universes so if we think the class Object like something really very large
>a Grothendieck Univers analogy is obvious and that explains why Class and
>other subclass Object. I think that Grothendieck Universes are great
>invention that infact turn mathematics to more relative or using Derrida
>words deconstructive spirit . . .but the problem is that no one use universes
>now .I think most mathematicians think them unnatural and complex(definition
>is just 4 lines not very difficult to understand )
>So my question is :Is object oriented programing just a (bad name for)
>category theory a la Grothendieck ?
>
>3.Categories in math and your Classes do the same thing define a lower order
>things(objects in both cases) with higher order things . . . . unfortunately
>in both cases there is ifinite tower of metalevels and there is noting
>special in order 2 (objects(sets) are level 0 . . .) "Everything is an object"
>means "I can forget higher level structures " In mathematics that is
>"decategorification" and there is of course "categorification" no one of these
>is doable in uniqe way, so it is subject of study . . .in Smalltalk you know
>solution of everithing from 30 years .
>
>4.I can't wait to see mixed objects which are partialy Object partialy Class
>and partialy Metaclass .Part of ideas some of you express means that it could
>be possible. I have no idea how such objects will be debuged but it will be
>pretty funy...
>
>I come to Squeak 4 years ago , i was very very impressed because i understand
>that Alan Kay found the way to express category theoric thinking at a time
>i was just born . and my heart was full of respect and admiration ....
>and my expectations about how good you are was highest i ever had .
>But your idea about how good you are is really otside the limits of my world.
>I found here a man (L.R.) not brave enough to said to me that he thinks that
>i'm a jurk but brave enough to have ice cold heart and no respect to cause
>of paralised children ... and no one to say him it's not good.
>
>At the end it was my mistake to ask for a permision to have my project on SqF
>so i use the case to withdraw it .
>
>-----------------------------------------------------------------
>http://promo.abv.bg/spnet/spnet.phtml - ???? ?? 21.07 - 78 ???? 
>???????? + ??? 3MB ? ???? ??? + ????? ?? ????????? ?????????!


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