The mysterious genius of Athens

Consider these names: Socrates, Plato, Pericles, Sophocles, Euripides, Aristophanes, Aeschylus, Xenophon, Thucydides, Anaxagoras, Demosthenes, Alcibiades, Phidias and Simonides. Consider also these lesser known names: Aspasia, Aristippus, Polynotos, Lycurgos, Lysias, Protagoras, and Praxiteles.

What do all these people have in common - apart from being known by but a single name?

The answer is more surprising than at first it seems. They are all Athenians, from Ancient Athens. Does that shock you? It did me. It shocked me because I troubled myself to find out a little more about Ancient Athens and its Golden Age. What I learnt is both humbling and terrible news for the modern era.

The first thing that should be noted is that all of these people lived in the period 440 BC to about 380 BC. This is the Golden Age of Athens. As you will have noted the first of the two lists is unequivocally a list of some of the greatest geniuses who ever lived - accounted by not only their impact and reputation in their own times, but by their subsequent effects on the development of Western civilization and rational thought. Without their impetus, most of what we enjoy today, would not have come to being. The underlying way of thinking would not have evolved. So, we owe a debt of great gratitude to these early rational thinkers and scientific philosophers - and playwrights, too, (for inventing the theatre), among other achievements.

The second list are also regarded as geniuses, but are of lesser reputation - but still, they are all Athenian - and that, in itself, is telling.

You see, I tried to find the population of Athens at the time in question. I saw estimates varying from just 90,000 people to a high of 250,000. The highest estimate, according to one historian, implied that were about 60,000 adult males in Athens at the time. This estimate is not just for Athens but for the city plus the entire surrounding territory of Attica, on which Athens stood. So, it is actually an over-estimate for Athens itself. (Quite a few estimates for Athens' population placed it at around 100,000 - so divide all these calculations by 2.5, if that figure is correct for the city of Athens, proper).

So, the largest estimate of the possible pool from which all these geniuses - and some of them were great geniuses indeed - is drawn - is just 60,000 men.

Think long about that. A significant number of the greatest thinkers in Ancient times were drawn from a pool of just 60,000 men! (At the highest estimate).

How many geniuses are there today in a gathering of 60,000 men in a typical developed country? I mean, true geniuses - people of genuine creative power? I would be surprised if there was even one, really surprised.

How many true geniuses are there alive in the world's 6,000,000,000 plus people, today? Very, very few.

How many should there be? Well, let us use Ancient Athens as our template - and just so you don't accuse me of massaging the figures, let us use a worst case scenario. Let us count the number of major geniuses in Athens in the list above - and forget about the ones of lesser reputation, in the first instance. There are 14 major geniuses in the list above - for a population of no more than 250,000 (including children and slaves - who didn't really have much chance of participating - so this actually dilutes the true impression of Athenians, proper).

How many great geniuses would there be in the world today, for a population of six billion?

Well it is 14 divided by 250,000 multiplied by 6,000,000,000. That gives us a total of: 336,000.

There would be a third of a million geniuses on a par with Plato and Socrates alive today, if modern humans were as the Ancient Athenians had been.

I, for one, do not believe that there are a third of a million such individuals alive today. It may even be that such a number of great geniuses have never, in fact, lived, in the whole history of the human race. (Had they lived, one would expect history to be littered with many more great men and women than seems to be the case).

Now, that calculation only looked at those geniuses of greatest reputation in Ancient Athens. Let us consider the whole list - but remember that these lists may have accidentally excluded other great names, too. So, it will be, if anything, an underestimate of the true situation.

Doing the calculation for the second list of seven names gives another 168,000 geniuses who should be alive today - but most probably aren't.

Now, it doesn't make sense that the lesser names should be half as numerous as the greater ones. Clearly, therefore, my list is incomplete. So this is just a rough guide to the situation. There should be several lesser names for every greater one. Remember though that these lesser names are geniuses too - great enough to be remembered by some two and a half millenia later. So they are not insignificant.

Adding the two estimates gives us at total of 504,000 geniuses for the modern world. That is enough to populate a sizable city. Yet, I doubt the actual number is great enough to fill a sizable hotel.

The conclusion we can draw from this is either something is wrong about modern man - or something was great about Athenian man. It is basically the same, relative, conclusion.

Francis Galton (February 16, 1822 to January 17, 1911) once noted concerning the Athenian situation that, for Ancient Athens to have possessed so many geniuses, that the average intelligence of its population would have had to have been "two grades above the mean for a modern European" (That is a 19th century human, who, I propose, would have been genetically superior to people of today for reasons to be discussed elsewhere). For Francis Galton, a grade equated to about 10 IQ points in the current way of looking at it. So, in Francis Galton's estimate, for there to have been so many geniuses, in such a small place as Ancient Athens, the mean IQ of the Athenian population must have been about an IQ of 120.

No nation, city or race on Earth in the modern world comes remotely close to such a figure. By comparison the mean IQ of our "world leader" - the United States is just 98. The highest is Hong Kong at a mean of 107. As for races and IQ, the highest is for the Ashkenazi Jews at just over 107 mean according to the biggest study I could find (and therefore likely to be the most representative), with a sample size of 1,236 Ashkenazi Jews, by Backman in 1972.

So, Athenian man (and woman) stood far above modern people in mean intelligence. Such a huge disparity in mean intelligence, would have led to a situation in which gifted people - by modern reckoning of that term, were super-abundant. A significant proportion of the population would have tested as "gifted or above". If the mean IQ was, in fact, 120 for Ancient Athens, then assuming a standard deviation of 15 about that mean (as it is today in the West), then fully 25 % of the population would have tested at the gifted range of 130 or above. One in four Athenians would have been considered gifted by modern standards, by this reckoning.

Let us look a little deeper. One in four would have been moderately gifted (IQ 130); One in twenty-one would have been highly gifted (IQ 145 and above); one in two hundred and sixty one would have been exceptionally gifted (IQ 160 and above) and one in thirty-one thousand five hundred and sixty would have been profoundly gifted (IQ 180 and above). By the way, this suggests one Athenian had an IQ of 187 (one in a quarter of a million).

Now even these figures will be an underestimate of the true situation because they use a normal curve to derive the probabilities - whereas the true, observed curve is trimodal, with higher than expected upper and lower occurrences of IQ.

By comparison, for the modern world, using the rarity expected in a normal distribution of standard deviation 15, gives 1 in 44, moderately gifted, 1 in 741 highly gifted, 1 in 31,560 exceptionally gifted, 1 in 20,696,000 will be profoundly gifted (or say fifteen people in the United states, today).

These figures can only, therefore, give you a feel for the situation - but an incredible one it is. Were modern men as gifted as Ancient Athenians, genius would be more common than footballers. Such a world would be far different from the one we actually have. Presumably, we would be far more advanced culturally, scientifically and technologically.

Yet, we are not as the Athenians were. Neither are the modern Greeks. Their mean IQ is a saddening 92.

What happened, then, to the great Athens and their superhuman Athenians? Well, plague took a lot of them (including Pericles) - one third in one bite. Then Sparta took a lot more of them, by defeating them. The sterility (and military discipline) of Sparta triumphed over the genius of Athens. In 338 B.C Philip II of Macedon (Alexander the Great's dad) conquered Athens ending its independence. Athens never shone again, as once it had.

(If you would like to learn more of Ainan Celeste Cawley, a scientific child prodigy, aged seven years and nine months, or his gifted brothers, Fintan, four years and two months, and Tiarnan, nineteen months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, College, University, Chemistry, Science, genetics, left-handedness, precocity, child prodigy, child genius, baby genius, adult genius, savant, gifted adults and gifted children in general. Thanks.)

Of Genius, Wealth and Poverty

We live in a world that worships money - and accords both respect and awe to those able to accumulate vast quantities of this magical stuff. Many, indeed, confuse "wealthy", with "brilliant". Yet, is this conflation a necessary truth?

There are many ways to become wealthy and not all of them involve great brilliance - in fact, most of them involve little more than doing what someone else has done, before, with a better marketing plan in place. I could say, "Look at Microsoft.", but I won't. In short, being rich does not mean being a genius. Nor does its corrollary apply: being poor does not mean one is dumb.

This latter point is essential to grasp. You see, I have recently received a letter from an American pointing out that, in her country, the poor are discounted on the issue of giftedness: no-one believes that a gifted child could emerge from a poor family - and so they are often overlooked. This is a very odd take on the issue of giftedness and shows that those who think so are unaware that wealth and IQ are not strongly correlated. There are rich bright people, yes - but there are also dumb rich people - and poor bright people - and poor dumb people (perhaps not the best combination, that one).

Giftedness is not a measure of wealth - it is a measure of mind - and great minds may emerge in the most unpromising of circumstances. History can teach us much here. I have already written of Carl Friedrich Gauss - a great child prodigy and a great genius level mathematician. What I did not stress enough, perhaps, was that his family were a very poor one. His father was a stone mason - a manual worker - and had the limited resources one expects of manual workers in most societies. Yet, this did not stop the young Gauss from being born a prodigy, and turning out to be the "greatest mathematician of his Age", according to many of his peers.

Another great mathematician, born in poverty, was Srinavasa Ramanujan. Born in 1887 in abject circumstances, he nursed a brilliance for mathematics by his own private efforts. He only emerged into prominence on writing a letter to G.H Hardy, the Cambridge mathematician, enclosing 120 mathematical statements of his own devising. Hardy, rather open-mindedly, invited him to Cambridge and the great young genius, was recognized. We all have something to thank him for. His work (the partition theory) is behind the operations of automatic teller machines (ATMs) and without his ideas, we would not be able to get a hold of our funds, so readily.

Both of these great men, were born poor - and both became great mathematical geniuses. Their poverty did not prevent them from being great. There are many such cases throughout history. Poverty does not connote stupidity - and wealth does not connote genius (I could bore you with cases of stupid, rich people but the living ones would sue and the dead ones are too uninteresting to bother with.)

So, to my American reader, I would like to send assurance that gifted people can, do and have emerged from poor backgrounds - and would like to urge those in America, who seek to identify gifted people, to be more open-minded in their pursuit of them. Do not assume intelligence in a rich kid - or dumbness in a poor one. Have an open mind when evaluating each and every one. For intelligence, creativity and genius, may emerge from any background, rich or poor.

(If you would like to read of Ainan Celeste Cawley, a scientific child prodigy, aged seven years and eight months, or his gifted brothers, Fintan, four years and one month, and Tiarnan, eighteen months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted adults and gifted children in general. Thanks.)

Are geniuses ever satisfied?

What is it that drives a genius ever on, to deeper understandings, greater works, more complete statements? I would say that one key attribute is dissatisfaction.

Yet, dissatisfaction at the work already achieved, has a dark side to it, too. Perhaps the genius is unable to fully appreciate their own work, so high are their aims and, perhaps, so low are their achievements, in comparison.

I am led to the words of two great geniuses to support this view that they appear dissatisfied with their works.

Albert Einstein once said: "If I had my life to live over again, I would be a plumber."

Surely, only great dissatisfaction with what he had achieved - or the life that he had had to lead to achieve it - could ever have motivated such words. Looking back over his life, his personal assessment was that a life of manual labour would have been preferable.

Another, too, who expressed dissatisfaction with his creative life, was Leonardo da Vinci - whose last words I have elsewhere recorded: "I have offended God and Man by doing so little with my life."

These words, too, point to an essential dissatisfaction with his achievements: somehow, great though they appear to others, he felt that they didn't make the grade.

Are we to assess a genius on their own unachievably high standards - or on the external standards of others looking on, at their works. I think the latter is healthier. Einstein and da Vinci may not have thought much of their work - but to the rest of us, their lives seem little short of miraculous.

A genius may need that sense of dissatisfaction to drive them on to greater things. It may, in fact, be a key attribute of great minds - but we must not let their self-assessment provide us with our view of their works. The judgement should be by the standards of the rest of society - otherwise we may not be able to see geniuses for what they are at all. It doesn't seem that they see themselves as we see them. That, in itself, is interesting.

Perhaps a genius needs society to tell them just how significant their works are. That society may, of course, be one of a different time, since some geniuses are not recognized in their own times. Whenever it is, however, society should not be shy in rewarding a genius with recognition - because, more than others, perhaps, they need this positive feedback - since so many of them seem to be unable to see it in themselves.

(If you would like to read of Ainan Celeste Cawley, a scientific child prodigy, aged seven years and six months, and his gifted brothers, Fintan, three, and Tiarnan, sixteen months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted adults and gifted children in general. Thanks.)

Johann Carl Friedrich Gauss

Some of history's greatest thinkers began life as child prodigies. What is interesting, to me, is that not everyone seems to know this.

Johann Carl Friedrich Gauss was a classic and remarkable case of child prodigy, emerging from an unpromising background. He was born on the 30th April 1777 in Brunswick, Germany. Neither of his parents were educated - indeed, his father was a stone mason. So, the young Gauss was very much on his own, in his early education. Yet, he was not without success. By the age of three he had somehow taught himself reading and arithmetic to a proficient degree.

One day, his father was adding up some figures, on paper, concerning the family finances. The young Gauss, three, peered over at his father's work and pointed out an arithmetical error - which Gauss had checked in his head.

In time, Gauss came to the attention of the Duke of Brunswick and, as was the custom of the day - and a good custom it was too - Gauss was to receive the patronage and support of the Duke of Brunswick, throughout much of his career. The Duke awarded Gauss a fellowship to the Collegium Carolinum, which he attended from 1792 to 1795 and thence he went to the University of Gottingen, which he attended from 1795 to 1798.

It was while at the University that Gauss began the train of mathematical breakthroughs that were to characterize his work and life. In 1796, he proved that any polygon with a number of sides equal to a Fermat prime may be constructed with a compass and straightedge. This was a major mathematical discovery since the problem of construction of such shapes had bedevilled mathematicians since the Ancient Greeks. It took the young Gauss to finally solve it.

Admission to University seems to have electrified Gauss into creative action. The construction problem was solved on March 30, 1796. A few days later, on April 8th, he proved the Quadratic Reciprocity law, which allowed one to determine the solvability of any quadratic function in modular arithmetic.

Modular arithmetic? Oh, he invented that, too. Then he came up with the Prime Number Theorem about the distribution of primes amongst all integers, on May 31st. On July 1oth he discovered that any positive integer is the sum of, at most, three triangular numbers. On October 1st, he published some work on the number of solutions of polynomials with coefficients in finite fields.

This outburst of creativity was not a solitary occurrence in Gauss' life. He went on to make lifelong contributions in many fields. I wrote in detail of that one year to give you some idea of what he was capable of. In 1799, he proved the fundamental theorem of algebra. In 1801, he published his book on number theory, Disquisitiones Arithmeticae, a magnum opus which he had actually completed at the age of 21, though he delayed publishing (this was a chronic tendency of his, failing to publish until, in his perfectionism, he was satisfied with his work. Had he published all that was later to be found in his notebooks, it is estimated that he would have advanced mathematics fifty years, single-handedly. However, in delaying publication, other mathematicians often got to publish Gaussian results before he did, though he had reached the same conclusions decades ahead of them).

In that same year, 1801, Giuseppe Piazzi discovered the planetoid Ceres. He tracked it for a few months, across three degrees of sky, but was unable to locate it again. (It had been lost behind the glare of the sun.) The astronomers of the time were unable to calculate an orbit sufficiently well on so little information to be able to predict the path of an object. Gauss, however, just 23 at the time, took on the project. In three months of work, he revolutionized how orbital calculations were performed, devising an approach which still stands as the foundation of such calculations today. He accurately stated where the object could be expected to be seen in the night sky - and Ceres was duly found again. This single piece of work catapulted Gauss to fame - and was later key in securing him the lifelong position of astronomer at Gottingen.

Gauss' achievement with Ceres puzzled many, for it seemed a feat beyond possibility. He was asked how he had done such an intricate calculation. He replied: "I used logarithms." When asked how he had looked up so many logarithms in so short a time, he dumbfounded them, by saying: "Who needs to look them up? I calculated them in my head."

Thus Gauss carried into his adult life the childhood ability as a mental calculator that he had shown at the age of three.

Gauss put his mental calculation to another practical use through performing a geodesic survey of the state of Hanover. In so doing, he developed what we know today as the Normal Distribution - or more properly, Gaussian distribution.

In the 1820s he collaborated with the physicist Wilhelm Weber and contributed much to the areas of optics, acoustics, mechanics and magnetism. Indeed, in 1833 he invented the telegraph, which was to later revolutionize communications that century.

Subsequent to his death on February 23rd, 1855, his brain was taken from his skull and weighed. It was, perhaps not surprisingly, significantly heavier than usual, at 1,492 grams and, the examiner stated that it was "highly and deeply convoluted". It was theorized that this unusual manifestation of the brain accounted for his genius.

Johann Carl Friedrich Gauss, began life as a self-educated child prodigy, born of uneducated parents, who could not, therefore, assist him but, by the end of his days, he was accounted, by many, as "the greatest mathematician since antiquity".

(If you would like to read about Ainan Celeste Cawley, seven years and six months, a scientific child prodigy, or his gifted brothers, Fintan, three, or Tiarnan, sixteen months, please go to: http://scientific-child-prodigy.blogspot.com/2006/10/scientific-child-prodigy-guide.html I also write of gifted education, IQ, intelligence, child prodigy, child genius, baby genius, adult genius, savant, the creatively gifted, gifted children and gifted adults in general. Thanks.)