Although the Colosseum served for many centuries as a centre of hideous spectacle and barbarous cruelty, at the time of its construction Romans saw it as part of the rightful restoration into public hands of land which had been illegally expropriated by the despised Emperor Nero. At the very heart of Rome, from the Palatine to the Esquiline, Nero had built a large private estate, the symbolism of which had been plain to everyone. Nero had even blocked the people's access to the Sacre Via, Rome's most sacred thoroughfare and, in a city which traditionally frowned upon ostentation in private dwellings even for the rich, built himself a huge and magnificent palace which became known as the Domus Aurea or "Golden House". On a ridge on the northern face of the Palatine, Nero had erected for himself a colossal 36 metre high bronze statue and in the middle of the palace grounds was a large artificial lake.

After Nero's eventual disgrace and death, his successors competed with one another to break up his estate and to replace it with structures of public utility. To this end, Emperor Vespasian filled in the lake and built the Amphitheatrum Flavium. He also moved closer to it the Colossus of Nero which he changed to represent to the god of the Sun. It is this combination statue and amphitheatre which much later led to the site being known as the Colosseum.

Considering the watery origins of the site, it seems somehow appropriate that some of the earliest spectacles held there had an aquatic theme. Following precedents set by Julius Caesar and Augustus, the amphitheatre was used as a venue for naumachia, mock sea battles which were designed to thrill and divert the masses. Being located very close to a major aqueduct, the arena of the Colosseum was filled with water up to a height of 1.5 metres. Then scale replicas of naval vessels were floated on the water and manned with presumably very reluctant crews of prisoners who were forced to battle for their lives.

The exhibitions were normally reenactment of famous naval engagements between two fleets such as the Battle of Actium ("Augustus" vs. "Mark Anthony"), the Battle of Salamina ("Greeks" vs. "Persians") etc. They usually involved a large number of ships and thousands of combatants. Clemency was sometimes granted to the victors of these battles but, as with other gladiatorial events, this apparently happened very rarely.

After examining detailed images of the bones of Ebu Gogo, John Hawks has now come out unambiguously on the side of Jacob, Thorne and Henneberg . He now thinks that the Homo floresiensis skull and bones are definitely indicative of some sort of kind of pathology and one that is in a single individual rather than the contemporary population. He doesn't go on to speculate what this pathology is other than it disqualifies in his mind the possibility that this represents a new species. Professor Teuku Jacob has argued since the beginning that the bones are most likely those of a pygmy human being (a type that still inhabits the region) albeit one with some sort of growth abnormality such as microcephaly.

I've been following John's blog for quite a while and he has always had something interesting to say in the Ebu Gogo debate. Previously, he has even floated the possibility that the bones might have been australopithecine , an extremely archaic human type distinct from Homo erectus. He now emphatically disavows ...

...any suggestion that LB1 or any of the Flores fossils are australopithecines. Along with four of the best anatomists that I know, I had the opportunity to see detailed pictures of the LB1 postcrania.

The specimen is beyond any doubt or question pathological.

This is very clearly shown by many details that are either not depicted or are not clear in the photos in the original Nature paper. It is not my place to provide more information about these details; my understanding is that a thorough presentation of them is forthcoming. I will say that this specimen has morphological characters that would indicate severe developmental abnormalities even if the skull had never been found . This is in no way a close call.

It remains to be shown whether the pathology in the specimen explains its brain size. Examination of the endocast shows features that are highly unusual. It would seem to me remarkable if the occurrence of these features was purely coincidental with the postcranial and cranial pathology.

My suggestion of australopithecine affinity was based strongly on the anatomy of the pelvis and the size of the brain. Since the specimen is pathological, I no longer trust that either feature characterized the Flores population rather than this single individual.

I also saw the other skeletal specimens. These have not been described, so I will not talk about them, although their existence has been widely cited as evidence that LB1 was typical of its population. A look at the rest of the sample lends little credence to this idea.

The bottom line is that this specimen cannot be assumed to be representative of the population from which it came. Any interpretation that starts with the assumption that LB1 is normal should be viewed with extreme skepticism.

Honestly, people spout a lot of crap about the Golden Ratio .

I mean that, to paraphrase the Willard character out of Apocalypse Now , there's just so much bullshit piling up on this subject that you practically need wings to stay above it. The Golden Ratio, once a pristine jewel of geometrical truth and simplicity, has become a deity for a cult of hyperlinking headnodders whose chief devotional practice seems to be to handwave their way from one disconnected and unexamined falsehood to another.

Like many cults, the founding myth of this one is the belief that its truths are very old - that this is the occult wisdom of the ancients. In fact, it is actually quite modern and has its roots not with, say, Pythagoras or ancient Egypt but rather with the restless young men of German Romanticism.

While the ancients certainly knew and understood about the Golden Ratio, they didn't invest it with any special significance apart from its obvious geometrical utility. Some Renaissance thinkers, on the other hand did see a mystical significance in the number (which they dubbed the "divine proportion") but this fancy was of a very different nature to the modern version. For a start, these were mathematicians with a strongly Christian Platonist worldview. The Golden Ratio was divine because of its importance in the construction of the Platonic solids and other polyhedra .

Modern devotees of the Golden Ratio by comparison are in general rather feeble at geometry. Their main interests lie in divining Golden Rectangles (i.e. rectangles where the ratio of the sides are equal to the Golden Ratio) from photographs of churches and paintings. Golden Rectangles, they argue, have always been appreciated as the most aesthetically pleasing of all rectangles and this is why they were used extensively in the architecture of classical temples, most notably in the Parthenon in Athens.

The reality is however that there is not a shred of evidence to support this claim. When actually measured the Parthenon does not exhibit any definitive Golden Ratios. In fact after close examination it becomes clear that the temple's construction is not very precise with things such as column height and spacing varying all over the place. Apart from this, there is good reason to think that the Greeks probably didn't have used the Golden Ratio in their architecture. For one thing, the number is irrational (in fact it is the most irrational of all irrational numbers ) something that would have made it extremely difficult to work with using their system of whole numbers and ratios. Vitruvius, the only ancient author whose work on architecture has survived, briefly mentions that the architect of the Parthenon, Ictinos, actually wrote a book which explained its proportions but unfortunately he doesn't elaborate any further. Despite this knowledge, however, Vitruvius makes absolutely no reference to the Golden Ratio anywhere in his work, staying instead with simpler rules of proportion.

A creature which has been greatly misused by Golden Ratio cultists is the poor old Nautilus pompilius . As if being pushed to near extinction wasn't bad enough, the beautiful spiral shell of this animal, which is a relative of the octopus, has become a sort of totem for graphic designers who never fail to resort to it whenever they need a graphic to grace an article or book cover that might even tangentially refer to the Golden Ratio (one might imagine that being a totem and being collected to extinction are two not necessarily unrelated phenomena).

Certainly, there is no question that the nautilus spiral is mathematically interesting. D'arcy Thompson pointed out in his 1917 classic On Growth and Form , that the shell grows in the shape of a logarithmic or equiangular spiral and this enables the creature inside to grow steadily without needing to change its shape. Also a recent mathematical study was made to measure the fractal dimension of these shells .

The logarithmic spiral is certainly a nifty curve in its own right, so much so that Jakob Bernoulli dubbed them Spiral Miribilis and even had one engraved on his tombstone (alas it turned out as an Archimedian spiral). But w hile it is rare to find an article featuring the Golden Ratio that doesn't feature a luscious image of one of these shells, the reality is that there is no real connection between them. There are certainly many ways of parameterising a logarithmic spiral so as to closely match the curve of a nautilus shell but none of these except to most contrived comes anywhere near to the Golden Ratio.

The claim that the Golden Rectangle is the most "pleasing " comes to us Adolf Zeising who is the one who single-handedly started the whole Golden Ratio craze in the first place. In 1855, he published a book which he modestly entitled:

A New Theory of the proportions of the human body, developed from a basic morphological law which stayed hitherto unknown, and which permeates the whole nature and art, accompanied by a complete summary of the prevailing systems

It was from him that we learn that the proportions of the human body are based on the Golden Ratio. For example, taking the height from a person's naval to their toes and dividing it by the person's total height yields the Golden Ratio. So, apparently, does dividing height of the face by its width. From here Zeising made the connection between these human-centred proportions and ancient and Renaissance architecture. Not such an unreasonable jump, to be fair, but the connection to the Golden Ratio had no basis in reality. When measuring anything as complex as the human body, it's easy to come up with examples of ratios that are very near to 1.6 (or 5/3). But there's no need to jump from here to any conclusions about the Golden Ratio.

After Zeising's time the enthusiasm for finding Golden Rectangles has only grown in art and architecture. The first artist to have his paintings analysed for Golden Rectangles was the French pointillist, Georges Seurat. These conjectures ultimately proved to be groundless.

Attention has since shifted to the works of Leonardo Da Vinci whose gigantic reputation as an innovator and visionary, one imagines, would have been too attractive to resist. Leonardo's connection with the the Golden Ratio is strengthened by his association with Luca Pacioli, a Franciscan friar and famous mathematician (and patron saint of chartered accountants) who wrote a book on the ratio which he entitled The Divine Proportion . Leonardo himself provided the illustrations for the book.

Leonardo may indeed have explored the use of Golden Ratio, perhaps due to Pacioli's influence, however there is absolutely no evidence that he did. Instead we have evidence that he used approximations to draw his pentagons, not something one would expect from a person supposedly enamoured with the Golden Ratio. Where some people have proposed that he used it in the composition of his paintings, none of the suggested places where he is said to have used it (such as in the dimensions of the face of the Mona Lisa or the body of the unfinished St. Jerome) are particularly convincing. Of the countless rectangles proposed none fit very well and this lack of precision undermines the basis of any argument that is based on geometry. In addition, it needs to be noted that the Virgin on the Rocks , St. Jerome and the Last Supper where all painted by Leonardo some years before he even met Pacioli.

Now please don't get me wrong. The Golden Ratio really is a remarkable number which many interesting mathematical properties – some of which I hope to explore sometime in a future post. But for me what I find so astonishing and frustrating about it is the role that it serves as magnet for so much nonsense, something that it seems to attract as inexorably as a belly button attracts lint.

For those interested in pursuing this rant on the Golden Ratio further to some more carefully reasoned work. I have these recommendations:

Good stories, pity they're not true
Good introduction to the myths and truths about the Golden Ratio. Unfortunately, it drops a clanger in accepting the nautilus shell as a valid demonstration of the Golden Ratio.

Book Review: The Golden Section
Nice blast on the Golden Ratio cult before launching into a review of a worthy book on the maths of the subject (even though some book publisher felt the need to put the Mona Lisa on the front cover).

Under Siege: The Golden Mean in Architecture
You may be surprised how much credence the Golden Ratio conjecture is still given in the field of architecture. This article shows how slowly the tide is turning.

The Golden Section in Architectural Theory
Another excellent article article from the Nexus Network Journal whose mission is to explore the connections between architecture and mathematics. This one carefully follows the history of the Ratio and demonstrates that it was not used in ancient or Renaissance architecture. It covers a lot of interesting history along the way.

Da Vinci’s First Code: Our Numbers Our Gods, the Pentagram
A clear debunking of the Golden Ratio, especially its purported use in the paintings of Leonardo Da Vinci.

I've long been a fan of MisterAitch and his blog, Giornale Nuovo. If, like me, you have an interest in history, the visual arts and the generally esoteric, then I suggest you hightail it over there immediately (well, after reading this at least). I've lost count of the number of times I've had to pick my jaw off my desk from astonishment at some post or other.

Anyway, this is all by way of an introduction to a new favourite of mine — also courtesy of MisterAitch — Curiosities of Literature, a remarkable compendium of literary and historical anecdotes by Isaac D'Israeli (father of British Prime Minister Benjamin Disraeli) who originally published it in six volumes between 1791 and 1834. MisterAitch has taken to serializing this work as a blog with self-contained portions being posted every second day.

Now to be frank, I've never been terribly enthused by these kinds of blogified books in the past. I just haven't had patience to keep up with the interminable to-ings and fro-ings of Samuel Pepys or, for that matter, the elusive elucidation in Leonardo's notebooks which have been more slog than pleasure (especially seeing that the images referred to are nowhere to be seen). But so far Curiosities really seems a different and altogether much more promising exploration of the format — each post is a self-contained capsule — most of modest length — which may be read in any order or skipped altogether.

Trawling the archive (which has only been running since January) is the best way to get a feel for it and there's more than a few belly laughs in there as well. I'm just going to include two snippets. The first is innocuously entitled Literary Controversy :

Martin Luther was not destitute of genius, of learning, or of eloquence; but his violence disfigured his works with invectives, and singularities of abuse. The great reformer of superstition had himself all the vulgar ones of his day: he believed that flies were devils; and that he had had a buffeting with Satan, when his left ear felt the prodigious beating. Hear him express himself on the Catholic divines: “The Papists are all asses, and will always remain asses. Put them in whatever sauce you choose, boiled, roasted, baked, fried, skinned, beat, hashed they are always the same asses.”

I was thinking that another book that might also be able to benefit from the blog treatment is the 18th century comic novel The Life and Opinions of Tristram Shandy, Gentleman which was written by Laurence Sterne and published in 9 volumes between 1759 and 1767. The book purports to be an autobiography of the aforementioned Shandy but is really a virtuoso performance of the Arte of Digression which takes as its purpose the deliberate subversion its own plot, structure, chronology and even its role as a book. The whole thing reads as a very modern — even post modern — experimental novel, and yet it is even more remarkable because it is also amongst the earliest works in the novel genre.

If you've been reading Laputan Logic for a while you've probably already worked out that I have a simple-minded obsession with blogging about firsts, oldests, originals, precursors and archetypes. Some particularly egregious examples of this pattern can be found here: I, II, II, IV, V, VI, VII, VIII, IX, X and here.

That last example being particularly relevant because it was about the Burnt City, an extremely ancient urban centre in South Eastern Iran which thrived from 3200 BC until 2100 BC and understandably has quite a few firsts to its name (oldest board game, oldest comb, earliest brain surgery). As far as ancient cities go, and this was one of the largest in the second millennium BC, it also had a number of fairly unusual features — the majority of the population were women, and power was held by women (who were snappy dressers) and they engaged in the sacrifice of men and dogs.

But most amazing of all: they invented cinema!