Hi Alan,

--- Alan Kay <Alan.Kay at squeakland.org> wrote:
> Hi Rob --
> 
> At 6:19 PM -0800 11/14/03, Rob Withers wrote:
> >Alan, these posts are always so stimulating.  Could
> >you tell me a little about abstact algebras and how
> >you relate them to computers sending messages to
> other
> >computers?  Is it related to defining languages, in
> >some way?
> 
> Originally, algebra was a symbolic form of
> arithmetic. In the 19th 
> century, mathematicians realized that there were
> lots of other 
> systems that had some of the properties of numbers,
> and they gave 
> such systems with various overlaps to numbers, names
> such as groups, 
> fields, rings, etc., and algebras. This then became
> a useful metaphor 
> and goal: to try to find common properties of
> systems and abstract 
> them into the simplest schemes that covered all of
> them.  So, e.g, a 
> number of the object-like systems I saw in the 60s,
> such as 
> Sketchpad, used a particular offset in the layout to
> find the pointer 
> to (say) the display subroutine for that kind of
> object. Today we 
> call that polymorphism, but this term is borrowed
> from theory of 
> functions and is not quite right. In any case, once
> you have an 
> inside and an outside, and try to do everything
> through embedded 
> procedures of some kind, you have set up the
> possibility for an 
> "algebra" of meaning that could extend over all
> objects. Clearly, a 
> good job of this cuts down the size and nomenclature
> of the concept 
> space. This thinking was before APL, but not before
> Iverson's book 
> that defined a more comprehensive version of APL,
> and it occured to 
> me that you could go much further than Iverson did
> with what I called 
> "generic procedures".

We have a system of objects in an image, and there is
an algebra defined for these objects.  These objects
can be transformed by "primitive" operations.   Is our
algebra defined by the Interpreter, both it's
bytecodes and msg lookup mechanism? 

So there must be an extended definition of what is an
object in this system.  An object has identity, state
and a class, with a method dictionary filled with
procedures.  Then all functions are recursive in a
sense, due to the fact that they can invoke any
primitive operation or recurse with another msg send
to any visible object.

It has nothing to do with Smalltalk, the language.  We
can have any number of languages describing functions
in this algebraic system!  Wow!  I feel like I am
starting to get the mathematical underpinnings of what
we really have here.

> 
> >
> >you also wrote:
> >
> >>  An interesting consequence of this structure was
> >>  that protection was
> >>  complete in ST-72, and all messages could be
> >>  serialized if the object
> >>  wanted (we did not bother with this because we
> were
> >>  working on
> >>  different kinds of problems -- but Hewitt
> thought
> >>  about it a lot).
> >
> >Could you say a little more about why protection
> was
> >ensured?
> 
> In the very same way that a computer on the Internet
> is quite 
> intrinsically safe -- no outside entity can force
> anything because 
> the computer has to run some of its own code before
> anything can be 
> admitted and acted upon. To hurt a computer it has
> to have stupid and 
> foolable SW. The ST-72 objects were only given a
> pointer to the 
> message and the knowledge that a message was trying
> to be sent. They 
> had to do the rest of the work to receive the
> message, and they had 
> full power to act or not.

ok.  It sounds expensive.  This topic has probably
been discussed elsewhere - currently squeak can walk
it's stack and get inside.


> >  Also, I like the implications of serializing
> >all msgs.  How did this work in these systems?
> 
> As I said, we didn't do very much about this, but
> part of the style 
> that the first Simula used, and the later Hewitt
> Actors inspired by 
> ST-72 were very much concerned about serializing.
> Again, thinking of 
> an object as a computer, it was quite possible to
> make objects that 
> would implement ques, etc., that would handle or
> reject messages in 
> serial order. This is part of Dave Reed's scheme in
> his '78 MIT 
> thesis and in his part of Croquet.

I am reading it again.  I misunderstood "serializing"
to mean encoding a msg into a flat representation,
rather than ordering multiple msg sends.

thank you,
Rob