On 07 Oct 2014, at 00:02, John Mikes wrote:
Brent: thank you so much for formulating some of my potential (and
not yet formulated) replies in a much better format than I could
ever do. Chris seems to be "in reverse" - describing SOME natural
observations do not mean Nature being created to FIT those
observations (which are temporary, anyway, within our few millennia
of developing human logic. They change.
We 'learn'.
I wrote once to Bruno - supporting my disbelief in "numbers" being
the base of the World-entire that so far I failed to find in nature
any natural 'object' that makes a difference if it consists of
35,479 or 35,379 parts.
I have less doubt about 2+2=4 than about the existence of nature or
natural objects. Typically I am agnostic if there is anything more
than number relations. After Gödel and Cantor we know they challenge
already all reductionist complete theories.
Also I asked if he could identify "number" for me beyond the little
written 'lines' - added together and counted? (3, or 5).
All what asked is to shere the belief in 0, and the belief that all
numbers have successor, that 0 is different from all successor of
numbers, that if too numbers are different, their successors are
different, together wit the usual recursive definition of addition and
multiplication:
x + 0 = x
x + the successor of y = the successor of x+y.
x * 0 = 0
x * the successor of y = x + (x * y) (for example 5 * 7 = 5 + (5 *
6) OK?
For the ontology, we don't need no more, to get a web of machine's
dreams, with a pretty complex mathematical structure.
Does nature have some stable referents in the ways those dreams can
glue? Open problem.
I do not want to get involved with Chris in a math-related
argumentation: my math is less than his inventory used nonchallantly
in his language. As I already confessed: the last time I studied
math was in 1947 preparing for my first Ph.D. (chem-phys-math).
Representing the little we so far learned of Nature by HUMAN MATH is
a great achievement. But it is a "NOT VICE VERSA".
It can be sometimes. Now physicists are responsible for the existence
of math which have been used to solve problem in number theory. Nature
does provide light on the number theoretical reality. It go both way.
Keep in mind that since Gödel we have learned that the arithmetical
reality kicks back. It is not what we thought, and machines and finite
entities are not what we thought they can be. There is a transfinite
complexity and infinite degrees of unsolvability.
Not human math has organized nature, rather we found more-or-less
fitting math-matches to it.
It is your theory that there is something like human math, which could
be different from the math of dolphin or from alien.
May be you are right, but assuming we are machine, then it is more
physics and nature which might be different, although we can be
reassured it is basically the same for all self-referentially correct
machine (but this is an ideal concept, non constructive, cf mechanism
= vaccine against reductionism)
(More-or-less? our technology is great - ALMOST. There are acidents,
illnesses, wars, revolutions, disasters we are not prepared for etc.
in spite of the 'best' math applied in design and forecast.)
The mathematical reality itself cannot be secured.
We chat about the infinity, even put the sign into our math-
expressions, but it is beyond our capabilities - as a NOUN. We can
identify the adjective 'infinite' (into more than just the circle-
line) but the CONCEPT is more than we can swallow (today).
We can propose theories, and for the mathematical infinities there is
the theory of ordinals and cardinal by Cantor.
I know I was abrupt and tried to write something fast, please forgive.
JohnM
No problem John, it is hard to sum up in few words.
The mathematical, even just the arithmetical, reality is a sort of
mess, full of surprises. Theories are reflected in the matter subject,
like the physicist obey the SWE in physics (or should), Above some
threshold of complexity, bigger complexities develop from the inside,
this happened more than once on this planet, but here we are spectator
of it.
It is just a theorem in rigorous theology: assuming computationalism,
Church thesis rehabilitates Pythagorean version of Neoplatonism.
Nature emerges from the statistical first person interference of
infinities of dreams which occur in arithmetic.
I am agnostic on computationalism and on its consequences. I just give
a "theorem" in a theory. You can add selection or collapse sort of
axioms, but in all case, you will need some magic to keep the
computationalist hypothesis in the process.
You don't seem so much agnostic on computationalism, it seems to me.
Isn't it?
Bruno
On Sun, Oct 5, 2014 at 8:56 PM, meekerdb <[email protected]> wrote:
On 10/5/2014 4:34 PM, 'Chris de Morsella' via Everything List wrote:
Mathematics is human thinking, we are smart to have mastered SOME
of it (not all, as the progression of math shows).
John M
John one question that comes to mind then is: if math is the
cultural accumulated product of human thought over the arc of the
history of recorded culture, then what about all the mathematical
and geometric patterns that appear and reappear in nature quite
apart from any human cultural input. For example how ratios such as
the golden ratio (e.g. 1·618034 approximately), or the Fibonacci
series manifest in things as diverse as conch shells to the spiral
arms of [spiral] galaxies.
But notice that they appear approximately and finitely - quite
different than the mathematical abstraction a idealization.
And in geometry the ratio of a radius to a circumference has been
very closely approximated by human cultural achievement, but this
ratio certainly is not a human cultural invention... is it?
Again, "approximately" and by our best current theories space is not
Euclidean and maybe not even a continuum.
There exists a large number of such ratios in geometry, math and in
nature itself. Certainly these precisely defined relationships
existed before there were hominids on this planet...
What exists is theory dependent. Within Euclidean geometry there is
a line passing through any two points - and always has been. What
the mean about "nature itself" is a different question; one that
depends on operational definitions that interpret the
relationships. What is a "point"? a "line"? How does one
determine whether a "line passes through a point"?
I think you are making the error of taking our theories to be facts
and then expressing amazement at how good our theories are at
describing the facts.
in fact can you even conceive of a time or universe where these
basic mathematical ratios do not hold true? Perhaps you can, but it
would be a bizarre universe utterly unlike the one in which we
inhabit.
Even the most basic stuff... say the concept of the set. Is this just
a human cultural invention? Certainly on one level it is, we have
developed a theory of sets and incorporate and manipulate sets at
so many levels of human activity, but does this fact of our
cultural discovery of set theory and wide employ of the techniques
and structures it provides us with translate into the much more
fundamental claim that set theory itself only exists in so far as
humans have invented it. Would not some alien culture (biological
or with some artificial substrate) come discover the same set
theory as we have? If not... then why? I am arguing that there is
something fundamental about an abstract something such as a set...
even an empty set. The kinds of operations the manner in which it
selectively includes "likes" while excluding "unlikes".
What about fractals? Purely a human artifact? Then explain how
fractals show up all over nature from ferns to snowflakes?
And... the infinite set of countable natural numbers [e.g. 1, 2, 3...
N]? Is this purely a human cultural invention with no independent
existence outside of human culture?
Would it make any difference if there were only 10^10^10 particles
in the universe? Wouldn't it be an inconvenience only in some
mathematical proofs?
Brent
As you can see from my questions... If that is I understood your
position of course <grin>... I think that there is strong evidence
for many kinds of mathematically precise relationships in nature,
that many quite clear patterns exist and repeat across many scales
and domains in the natural universe (outside of human culture).
It seems to me that math is better defined as our accumulated human
cultural achievement in understanding basic fundamental laws and
patterns of the universe we inhabit. It is our human cultural
discovery of something a lot deeper and vaster than what can
possibly be contained in the meager store of our species
accumulated musings over the last handful of millennia.
Cheers,
Chris
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