π (Pi) is odd,
wouldn’t you agree? π is simply this: the circumference of a circle divided by
its diameter. Hypothetically, at least, each of these has an exact value, but
when you divide one by the other, there is no exact value: it can be calculated
indefinitely, with an infinite number of decimal points, without any repeating
pattern of numbers. Now the number 1/3, when expressed as a decimal also
extends to infinity; but the digits repeat forever: 0.33333... π does not do
that; π cannot, in fact, be expressed as a ratio of integers in this way. This
has always seemed very weird to me, slightly mysterious. It seems to suggest
some kind of open-ended-ness in the universe that we inhabit, especially as π
plays such an important role in this universe. Not surprisingly, π (together
with a few similar numbers) is also known as a

*transcendental*number, that is (I suggest skipping the rest of this sentence, if you become queasy in the face of mathematics), a number that is not the root of any nonzero polynomial having rational coefficients.
It is perhaps worth pointing out that, although π plays in an important part in
equations of cosmology, it is not a physical constant, in the way that, say,
the speed of light or the strength of the various attractive forces in the
universe are physical constants. It describes no property of reality. It in
fact describes the relationship between two aspects of a pure concept: the perfect circle. No such
thing exists, except in our minds. That we can conceive such things, and that
there is such amazing coherence to mathematical concepts, is truly astonishing.
Mathematics itself is transcendent, in the sense that it is beyond any mere
physical manifestation of it. The number “3”, for example, “exists”
independently of any group of three objects that we might encounter. And within
that transcendent system called mathematics, π is further transcendent. Mathematics exists purely as a set of
logically coherent concepts. Then, surprisingly, within this very system, we
encounter “irrational” numbers such as π. Equally surprisingly, these concepts
somehow “apply” to reality in some way.

Is it any wonder that human beings have always felt that
there was something mysterious or even mystical about numbers? You do not have
to believe that numbers have any magical or predictive capacity for this to be
true. Once again, these magical and semi- or pseudo-religious interpretations
obscure what is truly mysterious about numbers; but it is easy to see how one
could slip into magical thinking. I emphasise here, as I have done time and
time again in these pages, that the universe is wonderful and surprising in its
own right, without having to ground that in any other being or reality. I stand
in awe of, but do not worship, this universe into which we have come into
being.

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