What is Expressiveness in a Computer Language

[Marshall]

Chris F Clark wrote:
> Chris F Clark (I) wrote:
>
> > I'm particularly interested if something unsound (and perhaps
> > ambiguous) could be called a type system.  I definitely consider such
> > things type systems.
>
> "Marshall" <marshall.spight at gmail.com> wrote:
>
> > I don't understand. You are saying you prefer to investigate the
> > unsound over the sound?
> ...
> > Again, I cannot understand this. In a technical realm, vagueness
> > is the opposite of understanding.
>
> At the risk of injecting too much irrelevant philosophy into the
> discussion, I will with great trepdiation reply.

I agree this is OT, but I'm not sure about the source of trepidation.


> First in the abstrtact: No, understanding is approximating.

Agreed.


> The world is inherently vague.

Our understanding of the world is vague. The world itself is
not at all vague.


> We make false symbolic models of the world which
> are consistent, but at some level they do not reflect reality,

Yes...

> because reality isn't consistent.

What?!


> Only by abtracting away the inherent
> infinite amout of subtlety present in the real universe can we come to
> comprehensible models.

Sure. (Although I object to "infinite.")


> Those models can be consistent, but they are
> not the universe.  The models in their consistency, prove things which
> are not true about the real universe.

Sure, sure, sure. None of these is a reaon to prefer the unsound
over the sound.


> Now in the concrete: In my work productivity is ultimately important.
> Therefore, we live by the 80-20 rule in numerous variations.  One of
> ths things we do to achieve productivity is simplify things.  In fact,
> we are more interested in an unsound simplification that is right 80%
> of the time, but takes only 20% of the effort to compute, than a
> completely sound (100% right) model which takes 100% of the time to
> compute (which is 5 times as long).  We are playing the probabilities.

What you are describing is using a precise mathematical function
to approximate a different precise mathematical function. This
argues for the value of approximation functions, which I do not
dispute. But this does not in any way support the idea of vague
trumping precise, informal trumping formal, or unsoundness as
an end in itself.


> It's not that we don't respect the sound underpining, the model which
> is consistent and establishes certain truths.  However, what we want
> is the rule of thumb which is far simpler and approximates the sound
> model with reasonable accuracy.  In particular, we accept two types of
> unsoundness in the model.  One, we accept a model which gives wrong
> answers which are detectable.  We code tests to catch those cases, and
> use a different model to get the right answer.  Two, we accept a model
> which gets the right answer only when over-provisioned.  for example,
> if we know a loop will occassionaly not converge in the n-steps that
> it theoretically should, we will run the loop for n+m steps until the
> approximation also converges--even if that requires allocating m extra
> copies of some small element than are theoretically necessary.  A
> small waste of a small resource, is ok if it saves a waste of a more
> critical resource--the most critical resource of all being our project
> timeliness.

Υes, I'm quite familiar with modelling, abstraction, approximation,
etc. However nothing about those endevours suggests to me
that unsoundness is any kind of goal.


> Marshall's last point:
>
> > I flipped a coin to see who would win the election; it came
> > up "Bush". Therefore I *knew* who was going to win the
> > election before it happened. See the probem?
>
> Flipping one coin to determine an election is not playing the
> probabilities correctly.  You need a plausible explanation for why the
> coin should predict the right answer and a track record of it being
> correct.  If you had a coin that had correctly predicted the previous
> 42 presidencies and you had an explanation why the coin was right,
> then it would be credible and I would be willing to wager that it
> could also predict that the coin could tell us who the 44th president
> would be.  One flip and no explanation is not sufficient.  (And to the
> abstract point, to me that is all knowledge is, some convincing amount
> of examples and a plausible explanation--anyone who thinks they have
> more is appealing to a "knowledge" of the universe that I don't
> accept.)

I used a coin toss; I could also have used a psycic hotline. There
is an explanation for why those things work, but the explanation
is unsound.


> Look at where that got Russell and Whitehead.

Universal acclaim, such that their names will be praised for
centuries to come?


> I'm just trying to be "honest" about that fact and find ways to
> compensate for my own failures.

Limitation != failure.


Marshal