DON’T COUNT ON IT
As far as the laws of mathematics refer to reality, they are not
certain; as far as they are certain, they do not refer to reality – Albert
Einstein.
Mathematics is extremely useful and endlessly
fascinating. In the right hands, it can predict and explain almost everything
in the universe, and is the foundation of engineering, architecture, science
and technology. It can even be used to dissect musical harmonies and to lend
‘scientific’ credibility to spurious statistics and correlations.
Speaking as someone who failed his maths O-level
twice (or was it three times?), I came into this world as ripe for bamboozling
as anyone, and bamboozled I was – we all were – from the moment we were taught
to recite the one-times table (I kid you not) at Foxhole infants’ school:
‘One times one is one.’
With you so far.
‘Two times one is two.’
Ah, here is where we run into trouble. We’re back
to the old problem of applied blanket nomenclature that undermines taxonomy.
We look out at the car park and see two cars. Two
ones are two. But is the second car an exact duplicate of the first?
‘No. One car is blue and the other black.’
One is also a Citroën and the other a SEAT.
‘To me, a car is a car.’
Then you have a future as a statistician, or a
conductor of bogus studies, but don’t go alone into a car showroom or the
witness box.
‘A chair is still a chair,’ says legendary lyricist
Hal David, ‘even when there’s no one sitting there.’ And, lexicographically, he
is correct. Both the chair’s persistence and the metamorphosis of his house
into a home occur without major structural alteration.
But the chair is not any chair or every chair. It
is only a chair at all because ‘chair’ is the convenient English code for
communicating its general use and characteristics to others. In reality, it is
billions of tiny particles and impulses moving in an area restricted by an
imposed form. None of these impulses or particles is present in another chair,
and no two of them are identical in the present one.
What’s worse is that the chair that was once one is
no longer the one it was, because its constituent atoms, molecules and little
spinning and sparking things are never static, even in the apparent equilibrium
of chairdom.
Ergo, not only is once two not really two, but once
one is no longer one. You could chant, ‘Once one was one,’ but both the
incantation and its uses would be limited.
So what are we left with?
‘Nothing.’
Not exactly. The old alma mater didn’t dwell on the
zero end of things. ‘One times nothing is nothing.’ ‘Two times nothing is still
nothing.’
‘There’s nothing in the paper; nothing on the
telly.’ But the paper is never blank and the TV never silent, so these are
specialised forms of nothing – the absence of something specific.
An absolute zero cannot exist as part of the
material universe. If it did, guess what – schlonk,
no universe!
One day, in our remedial maths class at Torquay
Grammar, the harassed master was explaining a method of solving what I think
were quadratic equations (I’ve never since found much call for them).
‘So we call this one zero,’ quoth he. ‘Yes,
Randle?’
‘Why, sir?’
‘Why?’
‘Yes, sir.’
He pondered for a while, searching the musty
corners of the magisterial cranium for inspiration, and at length resolved to
let me know on Monday.
I still feel slightly guilty at the thought of him
spending an entire weekend poring over mathematical tomes and scratching
algebraic formulæ on the walls of his cave, but, true to his word, he came back
to me at the start of the next school week, chalk spattered, an even more
faraway look in his good eye, brandishing a sheaf of inscrutable foolscap, to
deliver his findings.
‘We’ve always done it that way,’ he announced.
Although it hardly kept me awake at night, this
conundrum continued to puzzle me for an improper fraction of my life, until it
dawned on me that it’s not really zero in any absolute sense that we’re looking
at – not nothing – but an absence of mathematical value – the arbitrary
baseline where the positive value ceases, or runs out. You could call it
‘not-one’.
Rather than making one of the equations equal zero,
you are reducing it to its starting point and, by so doing, you are able to
solve the x or y of the other (if you happen to know what you’re doing).
Absolute zero is not approached. Instead we have a
theoretical zero of mathematics, something of which I would be very much in
favour.
From BLINDED WITH SCIENCE available from The Book Depository
From BLINDED WITH SCIENCE available from The Book Depository
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