Indefinite vs. Infinite

Francois-Rene Rideau rideau@clipper.ens.fr
Fri, 17 Mar 95 21:47:52 MET

```">>" is me (Fare)
">" is Jecel
>>    To me, the system shall not provide any finite system of resources.
>> There should be a generic way to multiplex and share resources. Users may
>> then be able to multiplex and share their own share, etc, recursively,
>> indefinitely. Else, there will always be problems, because if you can't
>> multiplex, it means you've got a security hole. This is why POSIX is
>> bullshix: no generic multiplexing, only specific, finite one.
>
> I am not sure I understand. Computer resources are not continuous. How
> can you multiplex indefinately? This is very obvious with things like
> a modem+a single phone line, for example, but is valid even for disk
> space and CPu time. How do you achieve fairness among the users?
>
There definitely seems to be confusion between infinite and indefinite.
I understand there is, because I myself happen to have been fully aware of
the distinction for no so long a time, thanks to my non-standard studies in
mathematical logic (I particularly recommend books on non-standard analysis).
Indefinite means finite, but not bounded. Infinite is really another
quite bigger kind of abstraction.
Confusion may come from the fact that what the mathematicians commonly
call "infinitely small" really is indefinitely small, i.e. every time smaller,
as small as you want, etc.
Now, when it comes to real data, the physicists will tell you that in
actual input, indefinite no more exists (not to talk about infinite), and
at most becomes "small enough" or "big enough".

That's just the same for TUNES: from the theoretic specification point of
view, the only requirement for the system to run is its being finitely founded,
and by providing generic operators, its dynamic founding level is indefinite.
Now, given a running system at some moment, you can actually compute this
founding level, and see how finite it is, so the a posteriori abstraction level
is bounded; but there is no static a priori bound to it, and it may grow with
time.

Thus, as for multiplexing resources, we don't impose any static a priori
bound on resources being multiplexed; they may be indefinitely multiplexed.
Still, at any moment, they are finitely multiplexed.

Was I clear enough ? If not, I hope I can be indefinitely clearer, though
I'm sure I'll always be finitely clear ;)

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