The folly of youth.....

The folly of youth. Read and weep. Weep as I  did some 40 years ago (ago, go). Never said I was perfect. Luckily I found a woman who accepts my past transgressions and puts up with my current lapses  

Sexually Transmitted Diseases (STDs) affect and blight the lives of up to 10% of our youth today. The social stigma and shame should not be underestimated. Also, knob rot hurts like fuck.

Here is my cautionary tale…….

Dat ain't me

Imagine a young Flaxen Saxon, brash, wickedly handsome, with long blond hair a flow, out with his mates on a Saturday night at the Brum Locarno Night Club and Abbatoir, circa 1974. All dressed in wide lapelled crushed velvet jackets and flairs.

Sometimes I’d leave at 3 o’clock in the morning covered in blood and snot. Sometimes I’d leave at 3 o’clock in the morning with a vaguely feminine form clamped to my arm. To be honest, it was sometimes difficult to distinguish the chicks from the fellas in them days. All that beer, flashing lights and strobes. In the disco, in the dark, mistakes were made. My opening gambit, was always: 'Are you a guy or a chick?'   Once in the alley, at the back of the nightclub, I would distract my ‘date’ with a humorous impression of Keith ‘Cheggers’ Chegwin. An impression I was particularly adept, whilst pissed.  In those days, I always kept a small squeezee bottle full of Domestos discretely inserted down my trousers. Whilst distracted, I would give my intended a quick squirt around the ‘bowl and rim’. I’ve always believed that prophylaxis is better than cure. Often I would add a couple of crushed Palma Violets just to show that I cared about feminine freshness.

As I’m sure you will remember, Domestos used to proudly announce that it killed 99.9% of all known germs. Alas, on one occasion I became a statistical outlier and anomaly. I had an inkling that something was amiss when two weeks later I expressed a small amount of bland, serous fluid. I thought the best course was to ‘wait and see’. Three months later my fireman’s helmet had the look of a busted pomegranate and issued forth a foul-smelling odour. As I lapsed in and out consciousness a moment of serene lucidity descended. My tumescent and weeping member popped up, winked and wiped a thick, yellow tear from its eye: ‘you dozy, fat, blond twat, catch the number 127 bus from Dudley Castle to Birmingham General Hospital.’ And then it kissed me. I decided to take a premed of seven pints of Bank’s bitter before alighting in Corporation Street. Although late at night, my swollen member gave off a faint ethereal glow and I was mysteriously guided to Ward 19.

Dr Mugumbo (for it is he) took a long drag on his cigarette, squinted and softly exclaimed: ‘Mr 74/3879, that’s not clap, that’s applause.’  After a vigorous course of antibiotics and scouring, the end of my cock sloughed off. Thereafter I was as good as new. Chastened, I never performed Keith Chegwin impersonations again.     

Take home message: Substitute the Parma Violets with 2 parts battery acid and 1 part Vim. Oh yes, and always listen to your cock.

Christianity and Evolution: Ponderings of a Part-time Biologist

Religion and evolution have never been happy bedfellows. While certain Christian denominations and Christian apologetics would have you believe that evolution is just an unproven theory and unlikely to be representative of how nature works in reality, scientists have universally embraced evolution as the best explanation for how organisms change through geological time. There is little doubt that selective environmental forces, together with genetic variation, are responsible for the vast array of life forms we see today. The evidence is overwhelming, has been for a long time, and has been garnered from many quarters of the natural sciences. When Darwin’s, ‘Origin of the Species’ was published in 1859, it was rapidly absorbed and accepted by the Victorian scientific community and equally reviled by the religious hierarchy. Religious leaders were right to be alarmed: the indisputable reality of the evolutionary process challenges firmly held and cherished Christian beliefs and tenets. Over the past 170 years, the way the church has reacted or evolved to evolutionary theory has been interesting. At one extreme we see fundamental bible literalists denying evolution outright, while at the other extreme we see liberal Christians embracing evolution wholeheartedly. The latter tread a dangerous path. On the one hand, they are concerned about losing their intellectual integrity if they deny evolution, on the other, they are in peril of losing their faith as the two belief systems are fundamentally incompatible. This hasn’t stopped savvy Christian thinkers from forcing some form of reconciliation.

Christians should be afraid of evolution. Christian dogma and theology are primitive, pre-scientific beliefs. While it is true that Catholicism, and by extension some forms of Protestantism, has accrued a patina of Greek philosophy, lavishly applied, over the past two thousand years- a philosophy totally alien to its Judaic roots, by the way. It is also true, that the Neo-Platonism and Aristotelean foundation on which it rests has been thoroughly debunked. If you scratch the surface of Christianity you will reveal its atavistic and primal true self.

Here is a question for thoughtful Christians who seek to embrace evolution in all its manifestations and with all of its implications: how do they square a god of sublime mercy and love (have you read the Old Testament?) with a system that is based on wasteful misery? Evolution gets the job done, but at what cost? It is certainly not merciful. For every successful organism, there is a heap of dead compatriots extending out into the distant Eons. Evolution was not designed by a caring and loving deity, or a deity concerned with garnering resources. Perhaps god devolved this bit of reality to his adversary, Satan? According to Christianity, ‘Man’ is the pinnacle of ‘God’s Work’. Everything was put forth for us to thrive- humankind is at the centre of All. But to accept evolution is for the Christian, an abrogation/negation of our specialness in this world. Evolution demands/commands that we are but one in a teeming mound of organisms, a little smarter, perhaps, but not particularly special. Our dominance is a product of accidental not providential events. There is also the uncomfortable truth that in the past three billion, or so, years that life has existed on this planet, humankind only made its appearance 100,000 years ago. God took a while to get round to forming his favourite child. And if we are just another animal, what are the implications for the soul? Do amoebas have souls? And if not, why not?

To accept evolutionary theory as true, the Christian must be prepared to ditch the underpinning tenets of Christianity to such an extent that the term ‘Christian’ is an insubstantial vessel; hollow and devoid of content. To remain a ‘Good Christian’ there is a need to deny evolution as true. But here is the rub: evolution is true. The evidence supporting, the so-called theory, is implacable and scientifically impeccable. To deny evolution is akin to denying gravitational force.

Thus, what are we to make of this abomination? Can we make the supernatural edicts of Christianity mesh in harmonious accord with the intellectual rigour and the inevitability of evolution? You can try. There have been quite a few attempts by folk who are of the opinion that there is no problem in trying to form some accord between these two realms. And while they freely admit that religion and science exist as separate ‘Majestria’, they contend that they sometimes come into contact, and interact, on occasion. Imagine a Venn diagram, if you will, consisting of two circles with a portion of overlap. On reading Christian apologists who dare to tread/dread, into this territory, it is apparent that there is a woeful misunderstanding of the scientific method. The scientific method is a self-correcting process based on empirical data gathering and induction. It has no truck with the supernatural. By definition, science can only concern itself with the natural world. The supernatural, if it deigns to exist, is, by definition, beyond our ken and we can only speak of it in metaphor. In terms of reality, the concept does not resonate or can be considered compatible, with our reality.      

Let us be clear: religion, regardless of stripe, is predicated on the supernatural. In this way, theologians can appeal to the hiddenness of God and the lack of solid evidence for ‘His’ existence. But the serious theologian craves serious intellectual recognition. This paves the way for the introduction of faith. O wondrous faith! We are expected to take on board religious beliefs on the supposed epistemological process of faith. Beware, this is but a beguiling charade. On the basis of faith, you can believe in anything. Here is a worthwhile exercise: whenever a theologian argues for a belief in god, on the basis of faith, simply substitute the word ‘god’ with ‘fairy’. At the end of the argument are you convinced in the existence of fairies- of course not? That would be ridiculous, wouldn’t it? Nuff said, for now…….    

                       

Back into the Fray, Dear Friends

After nearly 18 months of retirement, the hallowed halls of science are beseeching me to return to the fold and once more I am being summoned (nay regaled ) to sally forth to uncover the arcane mysteries which assail the natural world…….

Or more to the point, my old boss has managed to obtain funding for two days work and as no other bugger can eke out a viable living on such paltry terms he has turned to his old colleague to take up the slack. To be fair I could do with the diversion. Retirement is a funny old beast. For most it means transitioning from a full-time job racing at full tilt/tit, to zero: transitioning and reduction does not abide there. It can come as a shock to some folk, especially if they haven’t taken active preemptive measures to fill in the free time that retirement unlocks. I was lucky in that I have a set of extensive hobbies to which I could turn to keep mind and body whole and occupied.

I thought hard about the offer. It was not as if we really needed the extra cash. I receive a small ‘private’ pension and in 17 months I’ll be eligible for the state inspired variety. And, in addition, I have savings which earn a modest interest. That said, we could all do with a little extra cash and it would come in helpful in funding some of my interests. For instance, I always need a new bow, although Mrs S thinks that my current inventory of 25 bows is quite sufficient. She may have a point: I’m running out of wall space to hang them. But I have never been temperate when it comes to acquiring items (“Flaxen, you have never been temperate in anything that you do- ain't dat the sad truth”) which interest me and I feel no need/heed to change. So, I’ve decided to take my, old boss and friend, up, on his gracious offer.

My role will be different from my previous one. No longer will I be involved in teaching, admin, development and research. My job will be to soak up the routine practical and analytical work. I will be a donkey amongst thoroughbred horses. This holds no terrors: at my stage in life, I’m happy to relinquish the innovative work to younger and more nimble minds. Also, it will be an opportunity to catch up with old friends and colleagues. We have chosen to live in rural New Zealand, and perhaps the only downside is that we are socially isolated. I am not a social gadfly by nature and I’m usually okay with the isolation but I do miss the repartee and banter afforded by my old and slightly crazed, ex-colleagues.

Because I live 2 hours (by train) from work I will commute and stay overnight at my bosses’ place. I could stay with my son who lives in the centre of town, but I would have to catch a bus to get to the lab. I avoid public transport if I can help it- full of smelly, common, weird folk. Also, my son's live-in Danish girlfriend thinks I'm mentally unhinged.  Although my boss lives out in the northern suburbs, at least I will be able to get a lift into work (he knows I'm mentally unhinged).

So, I will see how it transpires. My initial contract/contact will run for three months with an option to renew. If I find the whole process tedious or onerous I will return to my life of idyll exile and rural contemplation. Arse.   

           
          

The Life of Pi

And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. (I Kings 7, 23)

According to the error-free and deity inspired bible, Pi is three.

 Pi            

We are introduced to the concept of ‘Pi’ sometime during our high school education. I don’t have to explain this interesting constant to modestly educated readers, but for completeness: Pi represents the ratio obtained when the circumference of a perfect circle is divided by the circle’s diameter. The resulting constant represents an ‘irrational number’. Thus, the ratio of the circumference divided by the diameter gives a number that cannot be expressed accurately by a fraction. When expressed as a decimal, the number continues, without a repeating sequence, unto infinity. As I recall, as a snotty school kid, I used the simple fraction 22/7 as a reasonable estimate for subsequent calculations. As an aside: Pi is a transcendental number or a real number that cannot be a root of a polynomial equation with integer coefficients- err, yes, methinks mathematicians have way too much time on their hands or is it chalk dust? Moving on…

Mathematicians are obsessed with the notion of mathematical proof and are not satisfied with large sets of data consistent with a conjecture. Thus, tis not enough to show that the non-repeating sequence extends to millions of decimal places and to declare Pi as irrational. There is a need to put forth an elegant mathematical proof which stands as a bastion of knowledge, forever. While scientists would be ecstatic with such a set of concordant data, mathematicians crave absolute perfection. There are a number of mathematical proofs available for Pi however, most rely on a knowledge of calculus and are rather technical and esoteric in nature: on these proofs, I shall say no more.
     
Pi has a long history. The ancient Babylonians, 4,000 years ago were familiar with this mathematical ratio and declared it to be: 3.125. The Egyptians were interested in Pi for reasons allied to the building of their magnificent edifices and for that purpose they were happy with a less accurate estimate of Pi, at 3.16.     

The great Greek scientist, engineer and mathematician, Archimedes (287 BC-212 BC) was obsessed with Pi and was not content with previous estimates. Although he was aware that Pi was an irrational number, and therefore any solution generated would always be an approximation, he nonetheless set out to develop a methodology for a better estimate. Archimedes approach was innovative and ingenious. He inscribed a many-sided polygon within a circle and did the same on the outside of the circle. Thus, he was able to calculate the circumference of both polygons. By utilising polygons with 96 sides he was able to calculate an upper and lower limit of Pi (3.1408 and 3.1429). Therefore he found an approximation of Pi bound between these limits- clever fellow that Archimedes. It is possible that he was working on refining his estimate during the siege of Syracuse by the Romans in 212 BC. When a Roman soldier burst into his room he was so absorbed with his circles that he did not heed the soldier’s command. The soldier was so aggrieved at this imagined sleight that he felt a wave of indignation and relinquished his frustration by stabbing the distracted polymath unto death. Needless to say, Archimedes' mathematical ability was never the same again.

As mentioned in a previous post, mathematics (and science) in the West went into a sad decline after the death of Archimedes and would not be revived until the middle ages. In the 15^th century, Nilakantha (remember him?) formulated an equation for the enumeration of Pi, based on an infinite series. Thus he saved his contemporary savants from drawing peskily large circles. It is to be noted, however, that his method only gives an estimation of Pi. The more terms added, the closer the estimation becomes. After five terms, the number is within 0.002 of the correct value of Pi. Since Nilakantha there have been numerous attempts to define equations for the calculation of Pi, with varying degrees of sophistication and accuracy. I’m not inclined to place the various computations here- a simple Gogle search will satisfy my reader’s mathematical expectations and perhaps, curiosity. In our wonderful modern age and with the advent of ultra-fast computers, it has been possible to calculate Pi to several trillion digits.    

Why bother you say? In fact, all useful calculations involving Pi only require the constant to reveal forth four decimal points, anything more is simply a mathematical extravagance. I suppose you might ask why mountaineers climb mount Everest or why some folk drink intemperately every Saturday night? However, extravagant Pi calculations are of some practical utility and can be used to test the efficiency of ‘supercomputers’ and have found a role in the generation of random numbers necessary for encryption. Modern-day spies are therefore grateful and indebted to Pi's irrationality.   

The 14^th of March is ‘Pi Day’: tis a celebration of all things Pi and is usually an excuse for nerds and geeks to consume inordinate (or coordinate) amounts of homophone Pie. And if your craving for all things Pi is not satiated, or slaked, by one day of celebration, don’t despair, because several months later you can revel in ‘Pi Approximation Day’ on the 22^nd of July (ie 22/7). 

To end this post I will simply state (note the clarity and innate beauty): 3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146......

This fraction is only bounded by infinity.

        

All is Sophistry.......

On occasion, I feel so moved to resurrect an old post for the edification of my 'newish' readership. Of course, it has nothing to do with me being a fundamentally lazy arse...... O, no. Anyway, this is one from my 'Blue Period'. A time when I was trying to 'wing it' without the medication. It has always been a dilemma: If I don't take my meds my creativity runs riot and the thoughts tumble through my brain like tumbly (not a real word) things. But on the downside, I sometimes take note of the voices exhorting me to burn stuff- although, not necessarily a bad thing (see link). When medicated, the cacophony in my head is leashed however, my creativity suffers according. But at least the good Burghers of Tipton can sleep secure in their beds at night without getting their bed shirts singed, spontaneous combustion excepted.   

How many angels can you fit on the head of a pin? Don't laugh, this was a hot topic for debate amongst Clerics, c1332. This is a surprisingly subtle question and raises further questions about the fundamental nature of our existence. Anyway, if angels are not made of matter and are pure 'spiritual energy', whatever that means, then they are without dimension and form and occupy no space. Having said that however, ultimately all matter can be reduced to waves and therefore solid matter is but an illusion, although a very persistent one. What is perceived as matter is really ‘a whizz’ of wave radiation bound by forces which are poorly understood.

But contemplation of angels as 'energy' is not as simple as envisioning angels as photons. Angels are sentient and therefore their 'energy' is not the energy we are familiar with. Angels are supernatural entities and therefore reside outside the natural world and by extension are not subject to causality. Even if we could persuade a host of angels to gravitate toward the vicinity of a pinhead they would defy measurement. This is but one aspect of the discourse. 

This raises the question of how sentient supernatural beings can interact with us at all. In the distant past angels apparently communed with man; tis in the bible- look it up........

According to the Bible, angels can connect with the natural world and therefore, during this interactive interlude, they must be subject to natural law and hence causation. So, let us take a different tack for sophistry's sake.

"The medieval doctors of divinity who did not pretend to settle how many angels could dance on the point of a needle cut a very poor figure as far as romantic credulity is concerned beside the modern physicists who have settled to the billionth of a millimetre every movement and position in the dance of the electrons." 

According to Thomas Aquinas, the ultimate Catholic scholar and medieval ‘Angelic Doctor’, no two angels can occupy the same space. This is in accord with quantum physics and abides with the Pauli Exclusion Principle. The next point concerns the size of the pinhead under question: to wit, the size of a standard pinhead. In order to move this argument along it is necessary to make an assumption. 

For our purposes, said size will be a sphere of 1Angstrom diameter with an associated mass of 9.5 x 10^-29kg. Also, we need to note that space is not infinitely divisible. This limit is denoted as the Planck length, or 1.6 x 10-35 m. Next, we need to decide the information carried by a standard angel. Note: I have made no allusion to mass. In fact, in this simple case, I’m assuming mass-less angels. The introduction of mass into the equation will result in ‘reducto ad absurdum’- which would make the whole argument just silly. So for our purposes, I will assume that angels comprise of ‘one bit’ of information. They cannot be less than this information limit and logically remain within our reality. There is one last concept to be introduced before we begin our calculation. The Bekenstein bound (k) or universal entropy bound is a limit on the entropy that can be contained in a physical system or object with a given size and total energy. It follows: In a system of diameter D and mass M, less than kDM distinguishable bits can exist, where k=2.57686 x 10⁴³ bit/metre kg. From this, we can derive an upper limit of 2.448 x 10⁵ angels on our pinhead.    

There are some clever bastards who demand that the angels should be 'a dancing'. This introduces a whole new set of thermodynamic and velocity parameters into our hypothetical situation which will undoubtedly alter the upper limit of angels gyrating on the pinhead- basically, these bastards can fuck off. 

Makes me want to burn stuff.

The Lizard Connection

 

David Icke in repose

Let me introduce you to the entity called David Icke. In the 1970s David was a professional football player resplendent in the English football league (c’mon the baggies). When his career ended due to an auto-immune condition (rheumatoid arthritis) he became a sports commentator on the tele. He was articulate, opinionated, popular and obviously intelligent. In 1990 he had an epiphany while in a Ryde bookstore on the Isle of Wight. Apparently, a voice commanded him to go to the ‘Psychic Section’ and it was there that he espied a book written by a psychic living in Brighton. He felt compelled to visit the psychic and during the interview, she told him he was about to become an important recipient of supernatural and psychic messages. From that moment the ‘scales fell from his eyes’ and a worldwide conspiracy became evident…… Subsequently, he popped up on a popular talk show, ‘The Terry Wobegone Show’. He appeared in a turquoise tracksuit and calmly announced he was the son of god and the world was about to end. The audience did not seem to be overly impressed and greeted the revelation with howls of derision and laughter. Overnight he went from a respected television personality to a full-blown fruit loop and a bona fide swivel-eyed, looney. Although his views have evolved over the intervening years, as described graphically in his 20 or so books, there are a few consistent themes. In the following paragraph, I’ll outline a few of his ideas: read and weep.

He believes that aliens from another galaxy came to earth several thousand years ago. He calls these aliens, Archons and they are depicted as tall reptile-like creatures. The Archons manipulated human DNA to produce human/alien hybrids. These hybrids have become the leaders of the world and are in collusion to manipulate and control world events. Apparently, the goal of the lizard hybrids is to cause worldwide strife and discontent which releases negative energy. The Archons, residing in their ‘other galaxy’ home are able to feed and gain sustenance from this energy. Also, the moon is hollow and contains reptile aliens, probably on holiday from their home galaxy. They use the moon as a base to broadcast mind-controlling beams in order to manipulate the way, we humans, think and behave. The Queen, the Clintons, the Bush family and apparently Justine Beiber are part human/lizard alien. We don’t observe their natural form as they are able to shapeshift through the dimensions.

So why am I bothering to write about a man who is clearly delusional? David Icke interests me for several reasons: firstly, I honestly believe that he is sincere and earnest in his beliefs. I do not think he is a charlatan or conman in the American tel-evangelist mould. Of course, I may be wrong and it is possible the whole, ‘lizard alien’ conspiracy is a means to fleece the gullible. I suggest my readers listen to the man in action on YouTube in order that they may form their own opinion (refer to the link below). Secondly, David Icke has seemingly/seamlessly tapped into the modern preoccupation with ‘new age’ sensibilities and other- world consciousness. A hash of pseudo-scientific, Eastern spiritual and other associated nonsense. From this wobbly edifice, he speaks to packed auditoriums throughout the world holding forth for eight or 10 hours to an enthralled and captivated audience.

There is no doubt that David Icke has charisma- a quality difficult to define but you know it when you see it. How otherwise is he able to keep people seated and presumably listening for such long periods? I’ve listened to a few of his monologues and I was struck by the way he introduces and delivers his fantastical/phantasmal material without a shred of evidence or coherent progression. He talks a lot about energy and like a lot of ‘New Age folk,’ he appears to have no idea of what energy actually is.  
  
I don’t think Mr Icke is mad in any conventional sense. Although, I suspect, like me, he doesn’t always take his medication, prescribed or otherwise. When he holds forth on topics not related to lizard folk and a hollow moon he makes a lot of sense. I watched a video of Icke discussing the transgender movement and I found myself in agreement with many of the points he raised. He also makes some very salient points about the world we live in, none of which are particularly controversial or new. A lot of his non-delusional material is actually commonplace and mundane: it is the delivery which makes it appear novel and supposedly interesting. His ideas concerning the control of society by powerful and rich oligarchies would ring true if espoused 2,000 years ago: truly there is nothing new under the sun. Again, I suggest my readers listen to him in action- it is difficult to paraphrase all of his opinions and ideas, mainly because he holds forth on everything and at great length. His mind must be a tumult of ideas and competing voices- reminds me of someone I know. I must admit to a grudging respect for Icke. Whatever his motivation for doing what he does, he clearly is imbued with astonishing energy (whatever that is) and a singularity of purpose which is frankly admirable. I cannot dislike a man for doing what he thinks is right, although, I disagree with much of what he has to say.

I would be interested in what my readers think of David Icke: Is he a charlatan?; a man of vision?; a true prophet of our times?; or madder than mad Jack MacMad on a particularly mad day? Let me know what you think of this rather strange and driven, man. 

In this video he talks a lot of sense. In other videos, not so much.

On Ancient Greek Mathematics

Now, where did I leave my car keys......

As moderns, all we can do is gape in wonder at the intellectual achievements of the ancient Greeks. With the eclipse of Greece following their conquest by Rome, Greek genius descended unto stasis. In the West, their achievements would not be matched for over a Millenium.

Mathematics is the epitome of clarity of thought. The scientific method, although powerful, can only give us mere mortals a side shifted glance at true knowledge. To view knowledge full-on there is only one vision, and that vision is mathematics. Only mathematics can lead fragile humans to true knowledge. One plus one is always two, at least in base ten, regardless of context and intellectual stance. To think otherwise is to contemplate the mind of a madman, or perhaps a genius.   
   
The ancient Greeks were the first civilisation to undertake mathematics for its own sake regardless of any practical application. The ancient Egyptians had developed their own mathematics but it was subject to matters of state and engineering. It was a practical discipline and there is no evidence that the Egyptians had any abstract concept of mathematics that was not allied to the practical and mundane.

Although the Egyptians initially influenced Greek mathematics of the 7^th and 6^th centuries BC, the Greeks expanded and developed mathematical principles far beyond anything envisioned by the Egyptians. The Greeks, as far as we are aware, were the first ancient culture to undertake rigorous mathematical proofs to underpin their geometrical conjectures.     
   
In the realm of abstract mathematics, the Greeks were supreme for their time and managed to squeeze everything that could be possibly imagined from a straight edge and a compass. They achieved much even though their mathematics was limited by their crude number notation and the absence of the concept of zero. Like the Romans, the Greeks substituted letters for numbers. The system was additive and unlike the system we use today, the position of the numbers was not important. Thus, the development of algebra was denied to them. It can be argued that the development of algebra and its advanced offshoot/offspring, calculus, is the most majestic and exquisite branches of mathematics; they are certainly the most practical. And even though Greek mathematics, of the time, could not work with abstract numbers and notational substitutions, they did manage to develop a form of geometric proto-calculus under the auspices of the last great mathematician of Western antiquity, Archimedes.  The death of Archimedes in 235 BC, at the hands of a Roman soldier, signalled the end of Greek mathematics in any innovative sense. Archimedes’ calculation of the area of two-dimensional figures by the product of the infinitesimal anticipates the great insights of Newton and Leibnitz in the 17^th century.

Up until a hundred years ago, Euclid’s 14 books on geometry, ‘The Elements’, were an essential study for Victorian grammar school pupils. All of geometry is laid bare in these worthy tomes. These books are crammed with ancient mathematical wisdom and wonderful expositions of mathematical proofs. The basic geometrical axioms established by ancient Greek thinkers is probably one of their greatest legacies.

Most folk have heard of Pythagoras and the theorem that bears his name, although it is unlikely that Pythagoras ‘invented’ this theorem himself. Why he has become associated with this cardinal rule has been lost in the vast (nay extensive) mists of time. Pythagoras and his acolytes flourished in the 6^th century BC and were a rather a strange bunch. If they were existent today we would describe them as a cult. They espoused some rather odd ideas and they were obsessed with numbers. To the Pythagoreans, everything was related to number and they extended their mathematical insight into the realm of musical harmony. When one of their acolytes discovered irrational numbers (a number that cannot be expressed as a fraction) he was taken out to sea and drowned. In this way, they hoped to suppress this seditious and dangerous notion. With the discovery of irrational numbers, mathematics lost its impeccable perfection and symmetry at least in the eyes of the Pythagoreans. The discovery that ‘rogue numbers’ had an abstract existence was a serious blow to this rather weird aesthetic sect- they would never be the same again. I’ve discussed Pythagoras, and his followers, previously in this blog: here is the link.

Alexander the Great’s conquest of Persia and parts of India introduced the Greeks to Babylonian astronomy. During his excursions, Alexander founded a number of cities throughout the former Persian empire, the greatest, of course, was Alexandria in northern Egypt. Egyptian Alexandria became a seat of great learning and knowledge and attracted eminent mathematicians and philosophers throughout the Hellenistic world.

With the subjection of the Greeks by Rome and their integration within the Roman Empire, innovative mathematics ceased. The pragmatic/phlegmatic Romans had little time for abstract mathematical concepts. If maths could help with the building of straight roads or the manufacture of engines of war, all well and good, however, the Romans had no interest or aptitude for mathematics in general, especially in the abstract. And it is probably true that all Roman mathematics was wholly dependent and derivative from Greek ideas and principles.                            

Western mathematics would languish until invigorated by Indian mathematical concepts, transmitted through contact with the Muslims, during the early middle ages. The power of ‘Arabic numerals’, our current counting system, was quickly recognised by the scholars of the day, although the Catholic church was against it (O, what a surprise!). It allowed Western mathematics to develop beyond geometry and expand into new and exciting mathematical territory. From the Hindus, the West came to understand the concept of zero. The importance of this simple (?is it) concept cannot be underestimated and historically, together with the development of the positional decimal number system, represents perhaps the most important insight in the development of mathematical theory.

Perhaps, I will be so moved by zero’s noble and lofty countenance, that I will pen a post dedicated to its magnificence: I’ll put it on the list for future contemplation.