[ExI] The "Unreasonable" Effectiveness of Mathematics in theNatural Sciences

[Mike Dougherty]

On Mon, Sep 29, 2008 at 4:17 PM, Jef Allbright <jef at jefallbright.net> wrote:
> I think you've roughly grokked an aspect of the simple something I've
> been trying to say.  Frankly, I'm repeatedly boggled by how this
> concept is so apparently alien to so many, but then, I've always felt
> quite alien.

Perhaps that's the best one can hope for?

>> Within a particular context, the best approximation of truth may be
>> verified as good enough.
>
> Well, you're still displaying the presumption of a point of view
> somehow outside the system from which to distinguish "best
> approximation" from "good enough" approximation, and your use of
> "verified" seems again to imply some reference standard outside the
> system.  But further down, you seem to have captured at least part,
> which is why I said you've (only) roughly grokked my point.

I presume those viewpoints due to a lack of rigorous definition.
"Best" could either mean the highest achievable or highest yet
achieved.  I used verified within the scope of a single context in the
manner that "people like chocolate" can be verified by specifying a
sample group of people and asking them to confirm their satisfaction
with chocolate.  A more rigorous definition of 'people' may be
required (are children considered people?  are cannibals considered
people?  I meant "normal" people, so define another adjective, etc.)
Clearly that's a ridiculous perversion of the question; we should
focus on "like" to the extent that we are probing the preference of
the aforementioned collection of individual persons.  It's amazing we
can communicate despite all the ways communication can fail.

> It's like the (oversimplified) difference between Positivism and
> Pragmatism:  For the Positivist, beliefs are expressions about
> reality.  For the Pragmatist, beliefs are expressions of reality. The
> distinction is the functional relationship of the observer to the
> observed.

fwiw - I consider myself reasonably intelligent, but I'm completely
lost by that analogy.  I was thinking of mis-applying Heisenberg
Uncertainty:  the more succinctly you try to define the words, the
greater the potential for misunderstanding the message.  If you agree,
then it probably proves this point.  If you disagree, then it also
probably proves this point.

>> If this principle can be used to
>> correctly predict the situation in new contexts, this further measures
>> the principle's approach to an ideal Truth.  Since it is arguably
>> impossible to have verified truth in absolutely every context,
>
> Why do you say "arguably"?  How might it not be impossible (unless one
> were to argue from Providence)?

You got me.  I admit to superfluous language.  I believe
it["arguably"] was intended to provide an escape route when (for
example) Lee called me out on using "impossible" when I am not in a
position to defend the absolute.  You correctly followed my thinking
though, it is impossible to exhaustively verify a transcendental form.
 The tools available for mathmeticians to deal with this kind of
problem do not have standard analogues in philosophy.  [I freely admit
my ignorance of the completeness of tools employed by philosophy]  *

> Here we go again, speaking of the "asymptotic limit to the maximum
> measurable 'truth'" as if it were meaningful (could be functionally modeled with its
> effective interactions.)

Agreed.  Cross-domain use of terms magnifies their ambiguity.
Eventually words lose their meaning altogether, no?

> Stop trying to model "Truth" in your statements about truth and the
> problem disappears, with nothing (actual) lost.

How Zen.  If you can remove the thing from its description, can that
thing be properly described?

"stop trying to eff the ineffable"



* Intentionally stripping adjectives from this paragraph forward gave
me a better appreciation of your form of argument.  Sentences may lose
nuance, but gain simplicity.  A subject/verb/object primitive can be
accepted or rejected.  It can be difficult to force natural language
into simplistic constructs.  I would agree that doing so is a
worthwhile exercise.  ... as would 'dereferencing'(?) ambiguous
pronouns such as "it" and "they"