Thanks very much for your reply, er, feedback.
The feedback loop is of course what makes the complex possible from the simple, makes it all work and, speaking efficiently, makes it alive. It is all so… elegant.
I have to interject something that occurs to me in the first cause argument and your post, at the risk of cliché: Godel’s Incompleteness Theorem. Can’t quite tie it all up, but something about self-referencing and creation needing something outside creation to explain it.
Thanks very much for the Rosenr reference. Your recommendation is enough for me to look it up.
That's a really interesting way of thinking about Gödel's Incompleteness Theorem, D-fendr. I happen to agree with Eugene Wigner's remark about "the unreasonable effectiveness of mathematics in the natural sciences." That somehow, mathematical structures are good tools for exploring the phenomenal world, evidently because the natural world — the Creation — itself has some sort of commensurate, intelligible structure.
Regarding Number Theory and the problem of undecidability within the theory — Gödel's main interest leading to the development of the Incompleteness Theorem — Robert Rosen has some interesting observations:
Number Theory has historically been plagued with conjectures (really inductions, based on limited experience or sampling with small numbers), which no one has ever been able either to prove or produce a counterexample (disprove). Is Fermat's Last Theorem a theorem? How about the Goldbach Conjecture, that every even number is the sum of two odd primes? Is Number Theory general enough, even in principle, to cope with these very specific situations?Or to put it really crudely, there can be truthful statements within a given system of axioms that are not provable from that system's particular set of axioms.
The situation is made even more interesting as a result of Gödel's celebrated work on undecidability in Number Theory.... In brief, Gödel showed how to represent assertions about Number Theory within Number Theory. On this basis, he was able to show that Number Theory was not finitely axiomatizable. In other words: given any finite set of axioms for Number Theory, there are always propositions that are in some sense theorems but are unprovable from those axioms.... The conclusion here is that every finitely axiomatized system is too special, in some abstract, absolute sense. But there is no way of telling whether a specific assertion or conjecture about numbers is provable, or disprovable, or undecidable (unprovable) within such a system. — Life Itself, p. 35.
A "finitely axiomatized system" is "too special" — meaning, one gathers, that it does not exemplify the general case, speaking universally. It is also the construction of a human mind — which also is limited by finitude.
And so it seems to me that Gödel's Incompleteness Theorem points to a "Beyond" — to a "something about self-referencing and creation needing something outside creation to explain it." :^)
I just loved this:
The feedback loop is of course what makes the complex possible from the simple, makes it all work and, speaking efficiently, makes it alive. It is all so… elegant.Oh so beautifully said — especially the "so...elegant" part!
Thanks so much for writing, D-fendr!