Replying to LO25146 --
[Host's Note: I corrected this msg in the archive at Judy's request on
8/25. ..Rick]
Shalom Andrew, At and All,
Andrew, you mentioned Bletchley Park and Alan Turing in one of your
previous mails (have you been there, already?). While reading your moving
words about TRUTH and the way it is both, given once AND revealing itself
in our experience (emerging), and while meeting your rhetoric question,
At: "Is Truth a becoming, rather than merely a being?", it re-occurred to
me that Turing actually simulated (by the famous Machine, bearing his own
name) the nature of such emergence of TRUTH in the reality called Number's
Theory.
It is easy to relate to Number Theory (like to any other mathematical
theory) mainly because it is SIMPLE. Simplicity celebrates in theoretical
mathematics due to the fact that statements bear exact "truth values",
precisely measurable. For example the statement "the product of two odd
numbers is odd" has truth value "T" in Number Theory (can't write NT - it
is already occupied), while the statement "the sum of two primes is a
prime" has truth value "F". What about the proposition "there are only
finitely many perfect numbers"? The truth value here depends on additional
knowledge (like the definition of "perfect" in the language of
mathematicians), but it is not different from the other two -
mathematicians agree on it's truth value.
Number Theory, like any other theory is SIMPLE also because its TRUTH can
be given at once - all you need is a sheet of paper and a pen (usually a
few lines will suffice - the rest of the page can be used for creative
emergence like painting). Number Theory's TRUTH also reveals itself when
rules of inference (taken from another Theory, in fact Meta-Theory: Logic)
are applied and re-applied on certain propositions (called "theorems").
At 1937, Turing invented (I would say "constructed" - just because I'm
well known for not being practical), a Machine (TM is occupied too) that
actually "produces" theorems. By "working" (that's what machines do?) this
machine "delivers" propositions in Number Theory, with truth value "T" -
it brings TRUTH into being ... one piece at a time.
Well, as we all know, people did that before, and quite efficiently (with
all respect) too. People keep doing it (what are all those mathematicians
paid for?) - so who needs this machine? shall we fire mathematicians,
reduce overhead?
Turing's Machine can work forever. Seriously ... it can do it. Will it
mean that this machine can reveal ALL TRUTH? Does it matter? Yes! because
this IS something you can't count on me to do, neither on more talented
mathematicians.
I wouldn't have written all this just for itself - it was long written in
books. I wrote it because I think we can borrow some logical arguments to
get a "T" or 2 (two sugar, please).
To a certain degree I see an analogy between Turing's Machine (a lot more
can be told about this machine, Alan Turing and even A. Church) and what
we actually do as we are learning (be-coming): We reveal TRUTH by our
deeds - and NATURE provides us with feedbacks, one at a time.
Unlike any machine (even if well bread) we are equipped with consciousness.
Unlike Turing's Machine we pre-tend to search for TRUTH but tend to "prove"
the same theorems again and again (even odd mathematicians prove a theorem
only once).
How come?
Andrew, I assume you needed room for new "T"s - how courageous of you!!!
Judy
I used "we" meaning myself and people like me - nobody should take it
personally ;-))
Dr. Judy R. Tal
LCL-Learning Cycles (1999)
+972 3 6997903
+972 54 666294
judyt@netvision.net.il
--Judy Tal <judyt@netvision.net.il>
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