Re: Godel's proof, truth, reality, self-awareness, and all that jazz
- From: "T.H. Ray" <thray123@xxxxxxx>
- Date: Sun, 16 Sep 2007 11:04:16 EDT
On 16 Sep., 14:58, "T.H. Ray" <thray...@xxxxxxx>Apparently, you are innocent of analysis.
wrote:
THR:IS
As working mathematicians here agree, mathematics
a liberal art. Get that point. No amount ofbraying
that you and Petry can do, changes the fact. Otherfacts
impinge: 1. Mathematical results often precedephysical
modeling based on those results (Riemanniangeometry,
e.g.)
Strange that nobody has use for finished infinity.
Just exactly what does the principle of exclusionunlessPerhaps, you would say,no map could be drawn
bysome
explorer actually measured the physical terrain
ofsome
arbitrary standard--a meter stick or the length
thehis
footsteps. Consider that if this were true (itisn't),
Einstein would not have had available to him
PythagoreanRiemannian geometry--the 4-dimensional
probabilisticTheorem
that cannot be "actually observed"--by which topattern
general relativity. Or consider the
themodels
by which we explain the "actual observation" of
inbehavior of light (and thus, quantum mechanics)
theThomas
Young's 2-slit experiment. One doesn't observe
didpath
that a particle didn't take,
because there is no particle and no path that it
quantumnot take
yet it turns out to be
important to understanding the theory.
WM:
That only seems so if one does not understand the
theory.
THR:
Huh? I would entertain a lecture from you on
mechanics. With sources.
There are most reliable *sources*, namely such which
release only a
single photon at a time. Experiments show that a
photon can only
interfere with itself (Dirac). Therefore we find that
a photon is
neither a particle nor a wave but something
intermediate which we have
no pictures for. Yes, you could learn such things in
my lessons (but
only in the summer semester).
(Pauli) have to do with the mathematics of probability
that characterize quantum mechanics? You might want
to take a harder look at your syllabus.
Yeah, sure. Your claim is well demonstrated to beyou
Some little research and reflection will inform
actuallythat
MOST of what we objectively know cannot be
observed.
WM:
Without observation we would know not more about
reality than the old
Greek who did not perfrom experiments.
THR:
Archimedes?
Was accused to prove by experiment his formulas (as
the saying is).
Found his famous density formula by self-experiment
(in the bath).
> Hero? Perhaps you mean the Greek
PHILOSOPHERS, a la Aristotle.
Yes, those before Archimedes (and many after him).
You are certainly notgeometers,
referring to the scientists. As far as the
Euclid et al, I dare say they were far moreacquainted
with reality than the narrow reality you havedefined
for yourself.
Euclid nearly never gave any practical calculation
but only derived
the formulas. Eratosthenes was quite different. So I
have to modify my
statement. It should read "many old Greek" instead of
"the old Greek".
false. I would drop it.
As Paulos said (in _Innumeracy_ IIRC), two cups ofWM:In
In both cases we have an approximation of truth.
onlybothcases we have
scientific characteristics. (Of course I include
mathematics"real mathematics
here.)
THR:
Your limited personal definition of "real
limits your result to what you personally believeis true.
No, to what can be verified by experiment, like 2
apples and 3 bananas
= 5 fruits.
popcorn and two cups of water does not amount to four
cups of soggy popcorn. Your examples are naive in the
extreme.
Sorry, I don't know what mean at all, by referencingresultsMathematical theorems, OTOH, are explicitlyconfined to
the domain in which they are true, and the
derived
therefrom explicitly live in the range of thatdomain.
WM:
Nevertheless they should be subject to the most
rigorous attempts to
prove them wrong.
THR:
They are! Check the literature.
Oh I know it from own experience. Check for instance:
http://groups.google.com/group/sci.math/browse_frm/thr
ead/16ebf68a5cc3b373?scoring=d&hl=de
your own thread.
mathematicsMathematics is a liberal art. Until one graspsthis fact,
one does not know enough mathematics to have "aview" of
what one personally believe mathematics "shouldbe."
WM
Unless you take my view you have no view. Roma
locuta, cause finita
est!
Regards, WM
THR:
As I have said and supported repeatedly, that
is a liberal art is NOT "my view." It is a fact
A fact like A <==> non-non-A?
Regards, WM
A = ~~A is the actual expression. That is, A is
identical to not-not-A. I don't know what you
even trying to say here. I find it incoherent.
Tom
.
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