Children should wear bicycle helmets.

Simon Brooke Wrote:
in message , James Annan
') wrote:

Simon Brooke wrote:

Mathematics is falsifiable and has been falsified. No ifs, no buts,
no maybes. The incompleteness theorem, together with the
Entscheidungsproblem, drives a coach and horses through it.

This is just so wrong....it's hard to know where to start, except
perhaps with a polite suggestion that you distinguish between
subjects
where you have a clue, and those where you do not, in order that
people can judge whether anny of your others postings are worth
taking
seriously.

I should point out that I hold a degree in logic, and did postgraduate
research in metamathematics.


Mathematics is falsifiable - get outta here - you've gott be joking (or
talking nonsense)

What Wittgenstein said is apt he
(from http://c2.com/cgi/wiki?LittleWittgensteinQuote )

"Was sich ueberhaupt sagen laesst, laesst sich klar sagen: und wovon
man nicht reden kann, darueber muss man schweigen... Die Grenze wird
also nur in der Sprache gezogen werden koennen, und was jenseits der
Grenze liegt, wird einfach Unsinn sein."

Translation:

"What can be said, can be said with clarity: What can't be said, must
remain unsaid ... The language defines the limit, beyond that limit is
nonsense."

Or,

"Anything you can say at all, you can say clearly. Don't speak of
things you can't discuss. Poeple will only be able to see from what you
say where the border lies. Everything beyond that border is simply
nonsense."

The second sentence is hard, and I'm translating "Sprache" in the third
as "what you say" instead of "language".

Another go at the translation:

"What is sayable at all, lets itself be said clearly; and what you
cannot speak of, of that one should remain silent... The border is only
possible to draw in language, and what lays outside the border, is
simply madness."
Did James really say that?


--
RogerDodger

Dave Kahn Wrote:
RogerDodger wrote in
message ...
Mark Thompson Wrote:
(well,
I've never got my head around much of normal physics, let alone
quantum).

Don't sweat it - the physicist Richard Feynman is often quoted
expressing the idea that "understanding" quantum physics isn't
really
possible - quantum reality is just too weird to warrant claiming
that
it can be understood (his words were to that effect).

"What I am going to tell you about is what we teach our physics
students in the third or fourth year of graduate school... It is my
task to convince you not to turn away because you don't understand it.
You see my physics students don't understand it... That is because I
don't understand it. Nobody does."

- QED, The Strange Theory of Light and Matter.

--
Dave...

The quote I remember seeing was in John Barrow's book -The World within
the World- and was along the lines that Feynman recounted reading a
newspaper journalists report that there were only a dozen people in the
world who were able to understand relativity - Feynman goes on to say
(words to the effect) that relativity isn't too difficult to
understand, but as for quantum electrodynamics - that's another story -
nobody understands QED.
Mind you Feynman said this more than a couple of decades ago - I seem
to remember Leon Lederman and Murray Gell-Mann weren't of the same
opinion?

Roger


--
RogerDodger

Simon Brooke wrote:

We do indeed know something about mathematics. What we know is it is
dubious, uncertain, and inherently unreliable. We know this for
certain; we can prove it. There is no possibility of doubt.


Define "know" in respect of the absolute truth you are claiming.

Tony

Jon Senior wrote:
Tony Raven opined the following...

Yes but to synesthetes what they call red you call middle C.


An effect that can be achieved with around 45mg of LSD! ;-)

Jon

But not repeatedly with reliability.

Was that part of your conditioning and upbringing then?

Tony ;-)

in message , Tony Raven
') wrote:

Simon Brooke wrote:

We do indeed know something about mathematics. What we know is it is
dubious, uncertain, and inherently unreliable. We know this for
certain; we can prove it. There is no possibility of doubt.

Define "know" in respect of the absolute truth you are claiming.

Mathematics is a formal system; within that formal system it is possible
to derive proofs. One such proof which has been derived are Godel's
incompleteness theorem, which proves that it is possible to derive a
contradiction within the formal system - and, indeed, within any of a
broad class of possible alternative formal systems. Another is the
Entshcheidungsproblem, resolved by Church's thesis on the lambda
calculus and Turing's paper on computable numbers. What Church and
Turing (approaching the problem from different angles) proved is that
it is impossible to know for any given theorem whether it is provable
or not.

Within the context of the formal system, we are supposed to be able to
know things to be true or false. Of course, this sense of 'know' only
holds within the context of the formal system, but it is nevertheless a
strong sense. Godel's theorem, by encoding a paradox in number, proves
in a stronger sense that in fact even within a formal system you cannot
know whether things are true or false, because it is in itself an
example which is true only if it is false and vice versa.

So that's pretty strong - as strong as any knowledge can ever be. Within
the formalism which it describes it violates the formalism.

But if you think mathematics is truth preserving, then you must think
that the incompleteness theorem is truth preserving, since it obeys all
the rules of mathematics. But the incompleteness theorem demonstrates
that mathematics is not truth preserving.

Knowledge is like that: the more you examine what you think you know,
the slippier it becomes.

--
(Simon Brooke) http://www.jasmine.org.uk/~simon/
;; Generally Not Used
;; Except by Middle Aged Computer Scientists

in message , Jon Senior
jon_AT_restlesslemon_DOTco_DOT_uk ('') wrote:

Simon Brooke opined the following...
Now you're running very close to a working definition of magic.
You're saying 'I know this is broken in unpredictable ways but I will
continue to trust it'. At least an understanding of the Universe
based on any given religion could possibly be correct; an
understanding of the Universe based on mathematics cannot be - and
that is _certain_.

But it's not broken in unpredictable ways. We know (You said so
yourself) where it is broken.

No: we know that you can't predict where it's broken. That is what 'On
Computable Numbers' proves. Read it, it's a good paper:
URL:http://www.emula3.com/docs/OnComputableNumbers.pdf

In 1917, David Hilbert stated a series of problems which needed to be
solved before mathematics would be complete. What was needed, he said,
were proofs that:

(1) every mathematical question be solvable in principle;

(2) every result be checkable;

(3) every mathematical question be decidable in a finite number of
steps (the 'Entscheidungsproblem').

He was convinced that all of them could be proved, and would be proved
quickly. During the twentieth century each of them in turn was proved
to be false. Yet most engineers and scientists continue to work with
mathematics as if Hilbert was right.

From the point of view of science, the aim is to have a model that be
predictive. Although the purists would hate it, the model does not
have to be an accurate representation of the real world, just that the
figures it provides match the real world ones.

How can it be predictive if it is based on an underlying formalism which
is flawed in provably unpredictable ways?

Good answers would be 'science isn't based on mathematics', or 'well,
that's one of the limitations of knowledge we just have to live with'.
In practice, I choose the second; but it makes it pretty hard to claim
science is somehow different from religion.

--
(Simon Brooke) http://www.jasmine.org.uk/~simon/

;; Men never do evil so completely and cheerfully as when they
;; do it from *religious*conviction." *********--*Pascal

Tony Raven opined the following...
But not repeatedly with reliability.

True. Although I believe that it can repeat on you in later years with
surprising consequences.

Was that part of your conditioning and upbringing then?

Thankfully not. Although were I to go down the route of experimenting
with strange chemicals, I think that LSD would be pretty high on the
list of things to try.

Jon

Simon Brooke wrote:

So that's pretty strong - as strong as any knowledge can ever be. Within
the formalism which it describes it violates the formalism.


Which comes back to it all being based on man-made constructs and only
having value if you beleive in those constructs having an absolute truth
beyond man. Kind of like religion really ;-)

Tony

Simon Brooke opined the following...
No: we know that you can't predict where it's broken. That is what 'On
Computable Numbers' proves. Read it, it's a good paper:
URL:http://www.emula3.com/docs/OnComputableNumbers.pdf

It's on my list of things to do... right after learning Polish! ;-)

How can it be predictive if it is based on an underlying formalism which
is flawed in provably unpredictable ways?

Because it has and continues to successfully predict.

Simplistic example:

Imagine that some property in nature is governed by the following
equation.

y = 2x + (3x / (2x + x))

We have a model of the system which uses the equation

y = 2x + 1

Our model is inaccurate as it does not follow the correct real-world
equation, but the answers we produce are the same.

That was a very simplistic example but it does illustrate the point that
it is not necessary to be identical to be predictive.

Good answers would be 'science isn't based on mathematics', or 'well,
that's one of the limitations of knowledge we just have to live with'.
In practice, I choose the second; but it makes it pretty hard to claim
science is somehow different from religion.

Except as I explained earlier. Science (regardless of underlying
contructs) has predictive abilities. No religion has ever predicted
successfully. This is a very important distinction to someone who is
trying to decide what to believe.

Put simply: Science is predictive. Religion is retrospective.

Jon

Jon Senior wrote:

Simplistic example:

Imagine that some property in nature is governed by the following
equation.

y = 2x + (3x / (2x + x))

We have a model of the system which uses the equation

y = 2x + 1

What's the difference?

--
Eiron.