Bugger!
The Ancient Greeks contributed so
much to rational thought and in so many diverse disciplines such as, natural
science, engineering, philosophy and mathematics; tis enough to make your head
swim. In many areas their contribution would not be equalled or excelled for
nearly two thousand years. And indeed it was the rediscovery of ancient Greek
treatises in the late middle ages which would act as an intellectual goad to
stimulate the explosion of Western thought which would define the renaissance
and scientific revolution of the 16th and 17th centuries.
What is even more surprising is that
the Greeks made important advances in pure mathematics with a mathematical
notion not particularly conducive to even the most basic arithmetical
manipulation. Consider trying to multiply 36 by 42, quickly, using Roman
numerals; the Greek system was similar to this. Therefore, even simple algebra
(as we understand it) was unknown to the Greeks and in fact nearly their entire
mathematics was based on geometry. All that they achieved was achieved with a
straight edge, a compass and a lot of contemplation. And what they achieved was
astonishing. From the ancient Greeks we obtain Pythagoras’ famous theorem
concerning right angled triangles; 2D geometry of various many sided figures;
conic solids; Pi; pesky irrational numbers and much more. We also obtain the
concept of 'proofs' based on logical reasoning ultimately derived from self
evident and impeachable axioms.
Pythagoras was probably one of the
most intellectually gifted men who have ever lived. He flourished on earth
about 532 BC (born ?570 BC) and he lived most of his later life in the Greek
colony of Croton in southern Italy.
It was here that he founded a school and attracted the greatest scholars of the
day. I said a school, but perhaps I should have said an 'aesthetic community'.
The Pythagoreans immersed themselves in pure mathematics to a fanatical degree.
They believed all was 'number' and that mathematics had a beautiful unifying
existence which underpinned and transcended everything (mathematics=God). This
was not to last. Pythagoras for all his lust for rigorous/vigorous proofs was
also a mystic. It is interesting to speculate why a man of such prodigious
intellectual gifts should be drawn to the irrational and esoteric. Isaac Newton
was also of this ilk. I could name others, but fundamentally, I'm an
intellectually lazy man. His community famously eschewed beans and women. Nor
were adherents allowed to pluck a garland, not allowed to sit on a quart
measure and never look in a mirror beside a light. All very sound advice, I'm
sure. I would never have been admitted to the hallowed halls of the
Pythagoreans due to my fondness/weakness for women and beans, although on a
good day I could probably give up the beans. Thus Pythagoras comes across as a
mixture of Einstein and the Dali Llama on acid go figure.
Any group espousing absolute and
fanatical beliefs is heading for a fall. Sadly, or gladly, the world is not
made that way. The Pythagorean love affair with simple, unsullied and sublime
number came a cropper due to the discovery of 'irrational numbers'. Up to this
time Pythagoras viewed numbers as perfect. The square root of 100 has a
beautiful symmetry. On the basis of pure number theory, the author can indulge
in rapture which is denied most mortal men. Sometimes mathematics is the only
solace I can find for a turbulent mind; I'm starting to digress. But one dark
day a Pythagorean student discovered the square root of 2, or at least the
geometrical equivalent. For his diligence and contribution to pure thought he
was drowned at sea. For his sake, I will expose the mathematical heresy here
and try not to get wet: The square root of 2= 1.4142135623746....... It goes on
forever with no elegant repeating sequence. As an aside, NASA has calculated
the square root of 2 to over 10 million digits. You would think they would be
better employed using their computing power sending ferrets to Mars or at least
developing cold fusion/illusion. This simple mathematical truth dealt the death
knell to the fundamentalist dogma of the Pythagoreans and therefore innocence
was lost. Their philosophy would never be the same again. They emerged
chastened and mayhap students developed a taste for the delights of beans and
women. As the sect soon died out I suspect they indulged in the former only.
Archimedes (287 BC  212 BC), a
savant of Syracuse in Sicily, was another great intellectual of
the ancient world. His contribution to knowledge was prodigious. He is mainly
remembered for his 'Eureka
moment' and a few of his engineering feats combating the fierce besieging
Romans, to which he ultimately succumbed. However, in his day he also made
substantial advances in mathematics, again using very simple geometric
techniques. His most interesting contribution relates to the calculation of the
area of a circle using many sided polygons. It is possible to calculate the
area of a circle, to within very narrow defining limits, using inscribed and
circumscribed polygons to the point of exhaustion. Fascinatingly, this
methodology anticipated infinitesimal calculus which would be independently
developed by Newton
and Leibnitz in the 17th century. As many are aware, calculus 'is' the tool
which formulates all fluid and dynamic functions of higher mathematics and therefore
is essential for understanding our world in motion.
So there we have it: a brief foray
into the exciting world of ancient Greek mathematics. They achieved much
considering the limitations under which they laboured. I wonder how their
mathematics would have evolved if they had had access to a flexible and
powerful notation which, we today, take for granted. Greek genius halted when
the Romans became Lords of the Mediterranean.
The Romans had no interest in abstract mathematics and applied themselves wholeheartedly
to war and politics, which for the Romans, was one of the same thing.

Mystical rigorousness is not a concept which springs readily to mind.
ReplyDeleteCan't agree more, Sir.
DeleteLike. And I liked the one you wrote before on time, though it makes my head bendy.
ReplyDeleteThe world is a very complex place, indeed. You should be wary of those who suggest otherwise, generally 'they be' politicians.
DeleteMr. Saxon, you great rollicking pansy, you have brought out my inner Grammar Nazi, to match your outer Regular Nazi.
ReplyDeleteParagraph 1, Line 1: "such as, as natural..."
Paragraph 2, Line 3: "multiple" > "multiply"
Paragraph 3, Line 12: "I've would never..."
It seems that I am not just your student, surrogate son, and object of affection (in the form of orifice exploration), but also your editor, too.
Indeed Matt, you are a demigod amongst mere men. I will edit as appropriate. I will attach the same diligence when marking your exam paper in two weeks. I can't give too much away, but a thorough grounding in ALL (26) theories concerning the hyperpolarisatuon of heterochromatin would not be wasted endeavour. Although you may struggle with the 'hetro' part of the concept.
ReplyDelete"...the delights of beans and women. As the sect soon died out I suspect they indulged in the former only..."
ReplyDeleteIndeed, one gets nowhere with the ladies by just farting around...
Ted, unless you hold the lady of your affections under the blanket whilst you fart. Considered a legitimate courting technique in Dudley.
DeleteAnd Tipton and Gornal, but not of course in upper crust Sedgley.
DeleteI hear tell that in Sedgley the paramours use sheets impregnated with charcoal to absorb the 'emanations'. Now that's class.
DeleteI believe what you are referring to is the practice known as the "Dutch Oven". I have also heard the urban legend that some poor individual has died from such an act  possibly through methane poisoning, knowing my "emanations". Still a rollicking good time, akin to such as autoerotic asphyxiation in terms of sheer sexual pleasure.
DeleteMatt, haven't you got an exam to study for? You don't get any extra marks for exchanging insane banter with a mad old fart. Arse bucket.
Delete