Bible-beater pilots

Hose****.

You're kidding right?

Well, first of all, you're mixing terms. "Hypothesis" is a term used
in scientific method, to propose something that is observed, but isn't
proven consistent. It doesn't exist in mathematics; proposals of
mathematic properties are called "theorems". But I set that aside;
this is casual conversation, after all.

I did not mix terms - I used the term that someone else used and asked for
elaboration. Not my confusion.


Bear with me here, everyone. I'm going to make a pretty good point or
two, in my opinion.

Can't wait...


Mathematical fundaments are composed of "Postulates", such as "A point
is defined as a location in space", "A line is defined as the
one-dimensional measure of distance between two points", and, "The
shortest distance between two points is a line".

Those are "postulates", specifically of Euclidean geometry. "Theorems"
arise from logical conclusions of the interactions of the postulates.
The ideas that triangles have certain properties, such as the sum of
their angles equalling pi radians, are "theorems".

Casually, these are sometimes called "laws", as in the "Law of
Cosines". Non-Euclidean geometries, necessary for doing things like
traversing the surface of a sphere (and none of us have *ever* done
that, oh, no!), does *not* have, as a postulate, that the shortest
distance between two points is a straight line; there are *no*
straight lines in spherical geometries.

Um, but the shortest distance between two points is STILL a stright line...
Unfortunately you can't travel through the earth.



For natural philosophers, people like physicists and mathemeticians,
the discovery (or rediscovery) of alternate but valid geometric
rulesets has resulted in several very useful discoveries, one of which
being Einstein's body of thought on relativity, flawed as we now know
it to be (but haven't come up with an all-encompassing replacement).

One other result of the re-examination of Euclidean thinking has been
the formulation of Theorems which deny the principal assumption of
great works like the _Principia Mathematica_, Goedel's Theorem
probably the most popular among them.

The upshot of Goedel's Incompleteness Theorem is mathematical proof
that "any self-consistent axiomatic system powerful enough to describe
integer arithmetic will allow for propositions about integers that can
neither be proven nor disproven from the axioms." [from the Wikipedia
article on Goedel]

Euclidean geometry is more powerful than integer arithmetic.

That is, logical systems powerful enough to be useful will contain
unprovable axioms. So the question, "Which [axiom or theorem] in
mathematics can't be proven or shown false that is the basis for all
other math?" is simply an utterly unanswerable question, given a
powerful enough system. Goedel proved it years ago. What *can* be said
is that "some axioms are unprovable, which doesn't mean they're false
or true."

I asked for which basic tenet was unprovable. My point was that the
original poster of this math == religion thread was not making sense.
There is nothing similar about them. Goedel (and Turing's equivalent with
the halting problem) have nothing to do with this conversation. You still
haven't answered the question - you have just tried to make the whole bit
sound more complicated than it is. And I am sure we are all impressed with
the disussion or Euclid, Theorems, incompleteness, etc.



Mathematics itself is today in a state alongside physics and most
natural science, of great uncertainty about the "Great Unknowables",
therefore, while depending on mathematical fundamentals will be
remarkably and consistently useful (can't compute a weight and balance
and then observe performance, or watch your climb rate go down as
altitude goes up, without noticing that), you just never know if your
system will stand up to new stuff.

Kind of like religion, that way, which works for most people. Until it
doesn't. Except for mine, of course. :-)


I still don't see how that is anything like religion.

On Sat, 22 Nov 2003 13:41:20 GMT, "Richard Hertz"
wrote:

Hose****.

Starting with fallacy. Not a good sign...

I did not mix terms - I used the term that someone else used and asked for
elaboration. Not my confusion.

OK, Usenet attribution mea culpa.

Um, but the shortest distance between two points is STILL a stright line...
Unfortunately you can't travel through the earth.

....thus necessitating the use of non-Euclidean geometries. Don't
forget that the point of philosophy really is to come up with useful
stuff.

I asked for which basic tenet was unprovable. My point was that the
original poster of this math == religion thread was not making sense.
There is nothing similar about them.
[...]
I still don't see how that is anything like religion.

The single undeniable similarity between math and religion is that
they are both philosophical systems, based on unproved (and maybe
unprovable) axioms and definitions.

Math: "A 'point' is defined as..."
Math: "The set of 'Integers' is defined as..."

(Aristotlean) Religion: "'God' is defined as..."
(Aristotlean) Religion: "'Sin' is defined as..."

You're right, of course, if you want to say that the similarity ends
there. But IMO involving the Incompleteness Theorem when talking about
complex axiomatic[1] systems is perfectly valid. The systems are
axiomatic and complex, whether you use the language of religion or the
language of mathematics to describe them. *Especially* orthodox
Christianity, whose apologist Thomas Aquinas (I'm told), made enough
of a significant case for basing scriptural understanding on
Aristotlean philosophical underpinnings that the comparison is
unavoidable.

Mathematics is also based on Euclidean rules of reasoning, the same
rules Aristotle used to build his thoughts. Therefore comparing the
two is not invalid.

you have just tried to make the whole bit
sound more complicated than it is.

So I have. It's because I believe that it is a far more complicated
problem than a blanket dismissal of "religion" can solve.

And I am sure we are all impressed with
the disussion or Euclid, Theorems, incompleteness, etc.

I hope so! It was more than a little bit of work.

Rob
[1] In theology I suppose they'd call it "dogmatic"

--
[You] don't make your kids P.C.-proof by keeping them
ignorant, you do it by helping them learn how to
educate themselves.

-- Orson Scott Card

"Richard Hertz" wrote in



straight lines in spherical geometries.

Um, but the shortest distance between two points is STILL a stright
line...

At non-relativistic speeds, it's so nearly a straight line as to be
inconsequential. But, at speeds approaching the speed of light, it isn't.
Unless you don't believe that the speed of light is a constant in vacuo.

le m

Happy,

Unless you don't believe that the speed of light is a constant in vacuo.


What's there not to believe? Anyone using GPS cannot deny Einstein - it
wouldn't work without relativity.

--
Thomas Borchert (EDDH)

Thomas Borchert wrote:
Unless you don't believe that the speed of light is a constant in vacuo.

What's there not to believe? Anyone using GPS cannot deny Einstein - it
wouldn't work without relativity.

Relativity has certainly been well-tested and (as you say) widely used.
However, there is serious discussion taking place concerning the
possibility of a variable speed of light as an alternative to inflation
during the early phases of the big bang.
See
http://www.iop.org/EJ/abstract/1475-7516/2003/07/004 and
http://www.arxiv.org/abs/gr-qc/0209014

Peter,

during the early phases of the big bang.


True. But that's been over for a while ;-)

--
Thomas Borchert (EDDH)

Peter wrote:

Thomas Borchert wrote:

Unless you don't believe that the speed of light is a constant in
vacuo.


What's there not to believe? Anyone using GPS cannot deny Einstein -
it wouldn't work without relativity.

Relativity has certainly been well-tested and (as you say) widely
used. However, there is serious discussion taking place concerning the
possibility of a variable speed of light as an alternative to
inflation during the early phases of the big bang.

Which demonstrates the fundamental difference between science and
religion - science
is falsifiable, and it is correctable. Religion is not. Science can say
"look here - here's
something that can't be explained by relativity, maybe we need to modify
our theories
a little bit."

When religion can propose a test that, if succesful, would disprove
the existance of God,
then will I be willing to grant it a status on par with science.

Rich Lemert