Sorry to break this off, but this part involves something on which a
comment is warranted. First, math is a broad area in which all the
statements are "true in all possible worlds." This applies to arithmetic
and number theory, geometry, the calculus, complexity theory, and all the
rest of the special areas. This does not mean that all the theorems apply
equally to all situations. Both "one line parallel to a given straight
line can be drawn through a point on the plane not on the given line" and
"there are no parallel lines" cannot be true when applied within any
world simultaneously. They hold only in Euclidean and Riemannian
geometries. Something similar holds for ordinary and modular arithmetics.
Since within a specific mathematical calculus or system all statements or
theorems are proved "true," if a set of interpreted statements holds, one
may interpret other theorems in the expectation that they will also yield
physical truths. There is no guarantee that the process will yield an
unending series of truths. Changes may be required at some point. This is
seen most obviously in Newton's work, which may be viewed as an
interpreted Euclidean geometry. Everything worked for a couple of
centuries. But the next step was Einstein's interpreted Riemannian
geometry (Special Theory) which provided for Newton's results as a
limiting case. The math gets stickier with the General Theory.
As I see it, the problem from the empirical side is collecting enough
data on which a discipline can be based; on the theoretical, a system
that fits the observations, so that predictions can be made. This leads
to expansion and testing. I recall a report in the 50s that the
mathematics of something Einstein produced was so difficult that only
three persons living had the background to understand it. One of them had
taken the time to work through the math (18 months ?) and announced that
it was consistent. The report quoted him, "I'm only a mathematician. I
can't comment on the physics." I'm only a philosopher, so I don't know
what Einstein had presented, nor whether it was an advance or a dead end.
But I suspect that one reason the applicability of mathematics is lauded
is that the dead ends are not pursued and are soon forgotten. This type
of selectivity certainly functions in other areas of human recall. So I'm
not too surprised that our mathematics fit the world.
Dave
On Thu, 9 Aug 2001 19:00:21 +0100 "iain.strachan2"
<iain.strachan2@ntlworld.com> writes:
in part
>
> Concerning the possibility of mathematical relationships
> underpinning the words of Scripture - yes, it is an amazing
> phenomenon, and one that seems ridiculous and hard to believe. But
> I should like to quote from John Polkinghorne's book "The Particle
> Play". Polkinghorne was a Professor of Mathematical Physics at
> Cambridge, who later became an Anglican minister. He is equally
> amazed that mathematics underpins the natural world, and relates it
> to God's Word as the creative agent:
>
> "I am very struck by the fact, ... that mathematics, which
> essentially is the abstract free creation of the human mind,
> repeatedly provides the indispensible clue to the understanding of
> the physical world. This happening is so common a process that most
> of the time we take it for granted.. At root it creates the
> _possibility_ of science, of our understanding the workings of the
> world. It seems to me a remarkable fact. I believe - I cannot
> prove it - that it is one aspect, perhaps rather a small one really,
> of the logos doctrine of Christianity. Israel developed an idea of
> the Word of God who was his agent in the creation of the world. The
> prologue to John's gospel not only makes the astonishing
> identification of the Word with Jesus of Nazareth, but also says
> that the Word is the true light that enlightens every man."
>
> Throughout the ages, people have always played with numbers,
> equations, geometry and so forth - it is almost a recreation, and
> for some mathematicians, it becomes an obsession. I read the other
> day how the pure mathematician John H. Conway learned pi to 1000
> decimal places, and so did his wife. They would go for walks to
> Grantchester taking it in turn to recite 20 digits to each other.
>
> But Polkinghorne draws attention to the fact that this peculiar
> obsession that mathematicians have created - in many cases just for
> their own amusement, is at the heart of the physical world, and is
> associated with creation ( implying that God is a mathematician).
>
> I therefore do not think it is an unfitting topic of conversation to
> speculate the possibility that these numerical phenomena are yet
> another aspect of the "logos" Creator that lies behind it all. The
> word "logos" has, I understand many different meanings; "word",
> "rational utternace" , "principle", and so forth. I think one should
> not try and decide which is the "right" translation or meaning;
> maybe they are all valid - it is common practice for a poet to
> choose a word for its multiple associations. It is appealing to
> think of "logos" as "scientific principle", and that leads to the
> mathematics that underlies the physical world. But maybe also the
> possibility of a literal reading should not be ignored. "Logos"
> maybe really does mean "word" - it is by God's literal words that
> things happen. Is it therefore not unreasonable to suppose that the
> words themselves may be mathematical objects - deliberately
> contrived to be so by God's continuing interaction with people's
> apparently arbitrary choices?
>
> George, if I've misconstrued what you intended in this topic, and
> that all you intended to do was spawn off a different thread, rather
> than wipe out the existing one, then I apologise. I think both
> topics are worth of study and objective discussion.
>
> Iain.
>
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