This
piece wouldn't have been called 'Nature isn't Mathematical' if it
weren't for the many other similar titles which I'd seen, such as: 'Everything in the Universe Is Made
of Math – Including You', 'What's the Universe Made Of? Math, Says
Scientist', 'Mathematics - The Language of the Universe', etc. Indeed
from Kurt Gödel to today's Max Tegmark (“the physical universe is
mathematics in a well-defined sense”) and ontic structural realism,
mathematical Platonism (or derivations thereof) seem to be in the
air. Though that's if being a realist about mathematics (or numbers) is the same as being a realist about the mathematical reality of... reality.

The
first thing to say is that the claim that 'nature is mathematical' hardly make sense. It's not even
that it's true or false. Taken literally, it's meaningless. So
perhaps it's all about how we should

*interpret*such a claim.
Some of the applications of Gödel's theorems to physics, for
example, simply don't seem to make sense. They verge on being Rylian
“category mistakes”. This bewilderment is brought about in full
awareness of the fact that there would hardly be physics without
mathematics. Indeed that's literally the case with quantum physics
and everything which goes with it.

However,
when John D. Barrow asks us
whether or not “the
operations of Nature may include such a non-finite system of axioms”
(as well as when he replies to his own question by saying that
“nature is consistent and complete but cannot be captured by a
finite set of axioms”), it can still be a philosophical struggle to
see the connection between mathematical systems or Godel's
metamathematics and reality/the world.

Strictly
speaking, Nature isn't any “mathematical system of axioms” and it
doesn't even “include” such things. Mathematics is

*applied*to Nature or it's used to*describe*Nature. Sure, ontic structural realists and other structural realists (in the philosophy of physics) would say that this distinction (i.e., between maths and physics) hardly makes sense when it comes to physics generally and it doesn't make any sense*at all*when it comes to quantum physics. However, surely there's still a distinction to be made here.
Similarly,
Nature is neither consistent/complete nor

*not*consistent/complete. It's what's applied to - or used to describe - nature that's complete/consistent. Again, certain physicists and philosophers of science may think that this distinction is hopelessly naive. Yet surely it's still a distinction worth making.
This
phenomenon is even encountered in contemporary philosophy of logic.

The
philosopher of logic and logician Graham Priest, for example, mentions the world
(or “reality”) when he talks of consistency and inconsistency.
When discussing the virtue of simplicity he
asks the following question:

“If
there is some reason for supposing that reality is, quite generally,
very consistent – say some sort of transcendental argument – then
inconsistency is clearly a negative criterion. If not, then perhaps
not.”

As
it is, how can the world be

*either*inconsistent or consistent?
What
we say about the world (whether in science, philosophy, mathematics, logic, fiction, etc.) may well be consistent or inconsistent (we may also say - with Spinoza later - that the world is “beautiful” or “ugly”). However, surely the world

*itself*can neither be consistent nor inconsistent.
Thus
within Graham Priest's logical and dialetheic context, claims of Nature's consistency or inconsistency don't seem to make sense. That
must surely also mean that inconsistency is neither a “negative
criterion” (as Priest puts it) nor a positive criterion when it
comes to Nature itself.

**Spinoza vs. Anthropocentrism or Anthropomorphism**

What
some philosophers of science and physicists are doing seems to
contravene Baruch Spinoza's words of warning about having an
anthropocentric or anthropomorphic (though that word is usually applied
to non-human animals) view of Nature. Spinoza's philosophical point
is that Nature can only... well,

*be*. Thus:
“I
would warn you that I do not attribute to nature either beauty or
deformity, order or confusion. Only in relation to our imagination
can things be called beautiful or ugly, well-ordered or confused.”

Spinoza
says Nature simply

*is*. All the rest is simply (in contemporary parlance) human psychological projection.
Thus there's
even a temptation to contradict Galileo's well-known claim about
Nature. Thus:

“Nature
is written in that great book which ever is before our eyes -- I mean
the universe -- but we cannot understand it if we do not first learn
the language and grasp the symbols in which it is written. The book
is written in mathematical language, and the symbols are triangles,
circles and other geometrical figures, without whose help it is
impossible to comprehend a single word of it; without which one
wanders in vain through a dark labyrinth.”

Surely
we must say that Nature's book isn't written in the language of
mathematics. We can say that Nature's book

*can be*written in the language mathematics. Indeed it often*is*written in the language of mathematics. Though Nature's book is not itself mathematical because that book - in a strong sense - didn't even exist until human beings wrote (some of) it.
Yet
perhaps I'm doing Galileo a disservice here because he does say that
“we cannot understand [Nature] if we do not first learn the
language and grasp the symbols in which it is written”. Galileo is talking about

*understanding*Nature here – not just Nature*as it is in itself*.
Nonetheless,
Galileo also says that the the “book is written in mathematical
language”. Thus he's talking about Nature

*as it is in itself*being mathematical. He's not even saying that mathematics is required to understand Nature. There is, therefore, an ambivalence between the idea that*Nature itself is mathematical*and the idea that*mathematics is required to understand Nature*.**The Mathematical Description of Disorder**

Another
point worth making is that if mathematics can explain or describe
random events or chaotic systems (which it can), then it can also
explain or describe just about

*everything*. What I mean by this is that it's always said that mathematics is perfect for describing or explaining the symmetrical, ordered and even beautiful aspects of nature. Yet, at the very same time, if I were to randomly throw an entire pack of cards on the floor, then that*mess-of-cards*could still be given a mathematical description. The disordered parts of that mess would be just as amenable to mathematical description as its (accidental) symmetries.
Similarly,
if I were to improvise “freely” on the piano, all the music I
played could be given a mathematical description. Both the
chaos and the order would be amenable to a mathematical description
and even a mathematical explanation. Indeed a black dot in the Sahara
desert could be described mathematically; as can probabilistic
events at the quantum level. It's possible that mathematicians can find different – or even contradictory –
symmetries in the same phenomenon.

In
a similar way, some of the mathematical studies of Bela Bartok's late
string quartets have found mathematical patterns and symmetries which
the composer was almost certainly unaware of. (See
this example; though it's not the one I'm familiar with.) True,
Bartok was indeed aware of the “golden ratio” and other mathematically formalisable aspects of his and other composers' music. Nonetheless, the analyses I'm referring aren't really formal in
nature. They're more like micro-analyses of the notes; and they serve, I believe, little purpose. Now there can
indeed be interesting formal aspects and symmetries in
music which composers aren't themselves aware of. Yet, at the same
time, a mathematician may still gratuitously apply numbers to specific passages of music in the same way he could do so the same to my

*mess-of-cards*.**********************************

***)**Kitty Ferguson, in her book*The Fire in the Equations*, writes:"It is very surprising to find, then, that the chorales Bach wrote himself contain quite a few parallel fifths. The rule forbidding them is a rule which Bach himself violated without the least compunction; in fact, it's doubtful whether he was even aware such a rule might exist." (238)

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