Zeno of Elea is credited with being the
originator of a number of famous paradoxes - of which Achilles and the Tortoise is probably the best known. I reckon Zeno
was something of a one-trick pony - a lot of his repertoire was based around a
single concept - the problem of visualising an infinite number of infinitesimal
events. Once you've got the hang of that, his stuff is probably not worth
spending much time on. At least not if you have as little imagination as I do.
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| Zeno |
His Paradox
of the Millet Seed may be described - and debunked - very briefly thus:
A single millet seed, when it falls, makes
no sound; however, if you drop a ton of millet seed it will definitely make a
noise. The implication is that a very large number of zeroes adds up to
something greater than zero, which Zeno identified as obvious nonsense. Without
getting into a philosophical discussion of infinity, this is flawed from the
outset. When Zeno says that a single seed makes no sound, what he means is that
we/he cannot hear it. There will be some disturbance of the air, even for one
seed, so the point at issue becomes the threshold of human hearing, which,
apart from anything else, varies from individual to individual. For example,
you could drop a large iron bucket next to my mother and she would be unaware
of it.
Achilles
and the Tortoise is rather different, but again
depends on the infinite divisibility of time and space. Achilles (who must have
been a hustler) challenges a tortoise to a race, and gives the tortoise a
start. By the time Achilles reaches the spot where the tortoise started, the
tortoise will still be a small distance ahead. By the time Achilles has run
this additional distance, the tortoise will still be slightly ahead. And so on
- forever, says Zeno. Achilles will never catch him.
Where this puzzle falls down is that the
infinite series of incremental distances during which Achilles fails to
overtake the tortoise does not add up to the full race distance - it adds up to
the point at which Achilles catches up with the tortoise. It does not require a
celebrated ancient scholar to understand that there will be some point in the
race at which Achilles catches up with his opponent, and that at all points
before that he will not yet have caught him. After that, of course, Achilles
disappears into the distance. The process of summing to infinity the decreasing
steps only serves to mask what is obvious anyway, though it does raise the separate
issue that Achilles would have to be careful to make sure that he didn't give
the tortoise too much of a start, or philosophy as we know it would never
recover.
A related, everyday paradox is that of the application
of a simplified description to something which is really rather complicated. The
example I have in mind is the concept of baldness. A man with no hair at all is
obviously bald. A man with a lot of hair is not bald. A man with exactly one hair
on his head is probably bald, but what about two hairs, three, 5374? - how many
hairs does he require to stop being bald? The problem here is obviously one of
terminology; "bald" is a rather crude on/off term - we really can't
consider this seriously without some definitions and a lot of counting. For
practical purposes, if someone describes someone else as bald, then they
normally mean "the impression I got was that they didn't have much
hair", which is not very precise but seems to serve for most everyday
situations, without wasting too much time on the matter.
There are many such words - what is a
"tall" person? Taller than average? Taller than me? Very unusually
tall? There is a whiff of percentiles and survey data in there which is all a
bit wearying, so we don't normally worry about it.
Tall.
OK.
Enough. For today's post I only wish
to consider the matter of baldness, so I guess we are in Zeno's millet seed
country.
I visit my hairdresser every four or five
weeks - five if it was cut very short last time. Normally a Thursday morning.
My haircuts are quick and inexpensive, since I do not have much hair. Every
time, we have the same discussion, as I glower in the mirror at the thinning
section at the front - I ask her if she thinks it is yet time to get rid of
that front bit. Not yet, she says - it is still hanging in there. If at any time I find that we are performing some trick to
pretend that I have more hair than I really have then a klaxon will sound and
we will stop and reconsider. Similarly, I have asked my wife to kill me if she
ever finds me performing any kind of comb-over.
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| We'll be in touch |
Reasons? Well, just personal baggage
really. Mr Trump is a shining illustration of why we shouldn't do this,
probably, but this train of thought is really triggered by the fact that today
is the eleventh anniversary of my dad's death, and my memories of my dad are
always dominated by the adventures to which he subjected us with his damned
hair. If I must learn just one thing from my father, please let it be that.
Before anyone feels moved to offer
condolences on this sad anniversary, please don't bother. My dad and I were
never very close, unfortunately. He was a very clever man, but a very
difficult, uncomfortable one. If it were possible to be given no capacity for
empathy at all then he must have been close. With my dad, you could agree with
him, and do what he said, or you could disagree with him, and fight about it,
or you could do what I did, and move some hundreds of miles away, to get on
with your own life. I don't feel bitter about any of this, by the way -
everyone is different, everyone has to deal with things in his own way.
Eventually, of course, my parents became
old and less able to cope, so they moved up to Scotland to be near me, which was
the right thing to do, and I am happy to believe they enjoyed their last years up
here together, and I certainly had to get involved in a lot of running around
to help them, which is probably as it should be. My mum is still alive, and is now safely resident in a splendid little care home very close to my house,
with which we are very pleased, but my dad's passing, though it was a shock at
the time, meant mostly that my life suddenly became a lot more
peaceful, and of course I got the opportunity to shuffle one more place up the
queue for the Reaper.
Oh yes - the hair. When I was a little boy
it became apparent that my dad was going bald. He must have been in his 20s. He
had a bald patch on the crown of his head which he concealed by combing his
hair over the patch, and keeping it in place with Brylcreem. All was revealed
when he was sitting at the kitchen table, studying for his engineering exams -
while his mind was elsewhere, he would wind a pencil into the long bits of
hair, and tease them out to remarkable heights. Hey. My dad was baldy.
As the years passed, though most of this
was out of my sight, this became more of a problem. By the time he moved up
here, he must have had very little hair on top of his head, but he attempted to
conceal this with the most complex edifice of hair from the edges. This was
combed across from all directions - if you stood behind him, there was a
strange horizontal parting above his neck, from which the hair headed upwards.
These partings were all over the place, with hair heading in unnatural
directions - the impression was that his cap probably screwed into place. He
also was a devotee of Grecian 2000
dye - I don't know what shade he used, but the effect on his (presumably white)
hair was of a vague nicotine stain - like pee-holes in the snow. And everything
was cemented into place to combat the forces of gravity and weather with
copious amounts of Harmony hairspray.
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| This progression does not seem to include my dad's shade |
The cap was the life-saver, of course, but
it took him ages to get ready to go anywhere, and he always had his comb with
him.
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| What could go wrong? |
On one occasion he had what was probably a
mini-stroke - he fell into a flower-bed in his garden, and just disappeared. By
the time the ambulance arrived he was indoors and sitting up and obviously
recovering, but the ambulance could not leave until he had found his comb and
arranged his hair. While they were waiting, the ambulance driver suggested to my mum that
they might cut his hair in hospital, if only because of the impossibility of
keeping it up to spec.
She, for the one and only time I ever
heard, very quietly said, "Let's hope they cut it, and we can all get some
bloody peace".
I'd never thought about it before, but she
must have been required to help with this palaver. She must have washed and
dyed his hair for decades - he certainly wouldn't have been able to do it all
himself. She must also have cut it for him, since any self-respecting
professional would just have refused. She was, in fact, an accomplice. Poor
woman - presumably this was just to keep him happy.
I wonder what it was he thought he was
doing? By this time, I guess it had just become a ritual (not unlike 50mm x
45mm MDF bases, I suppose), which had become somehow essential. Whom did he
think he was fooling? What (to be blunt) did he think he looked like?
If my mother had been so inclined, or if he
had had any friends (he didn't), then someone might have said, years earlier,
that having a weird, nicotine-coloured pavlova on top of his head did not give
the impression of hair, not to anyone, and that from the back, in fact, all
this effort produced something not unlike a polar bear's arse. Not a worthwhile
investment of time. Ridiculous. And all that combing and spraying while the
world waited to go out for a walk was pointless.
Eventually, after a long and unusually
healthy life, he started getting some angina problems. His medication was not
very successful, he had periods of irregular pulse which were causing some
alarm, and it was decided to take him into hospital in Edinburgh for tests. I
was there when he left in the ambulance - once again there was something of a
drama while he prepared his hair, but he was sitting up in the ambulance when he went.
The tests didn't go very well, and he was
transferred to the Royal Infirmary, outside the south side of Edinburgh. While
there he became ill, and then died, quickly and without much discomfort. All
over. It was unexpected - a bit of a shock, to be sure.
The next morning I drove to the Royal
Infirmary to sign the paperwork, and to collect my dad's possessions, which
were in a couple of plastic carrier bags. His clothes, his spectacles, his
shoes, his raincoat, his toilet bag, his cap, his wallet and the eternal comb. That seemed
a bit weird - that's all you get back. I dropped the comb in the car park while
I was stowing the bags, and I just put it in the litter bin. I was not going to
waste any more time on that, thank you.
When my mum became too ill to live at home
any more, I cleared her house. By this time my dad had been dead for nearly nine
years, but his coiffure was still very much in evidence. All the armchairs and
much of the bedding were stained with Grecian
2000 - very recognisable shade of Old
Nicotine - and I found warehouse-sized cartons of Harmony aerosols in the cupboard in the spare room and in the
attic.
And I bet he thought that no-one ever knew.
Your secret is safe with us, Baldy.
