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Scripturient: The Geometry and Toplogy of Pasta

I’ve always had a geeky appreciation – and awe – of mathematics. I have spent countless hours tinkering with programs that create math-based designs like fractals and Spirograph-style curves. As a young teenager I spent hours playing with an oscilloscope making sound waves dance on the tiny screen. But I never really thought much about . . . → Read More: Scripturient: The Geometry and Toplogy of Pasta

Molly'sBlog: A Devilishly Smart Pope


One of the books I’m reading now is John D. Barrow’s ‘The Book of Nothing’. The subject is  a look at the concept of ‘nothing’, the void, emptiness, zero, the vacuum and so on. There’s actually quite a bit to say about nothing, and book ranges from a history of the mathematical sign for zero, through the ‘philosophic concept’ of nothingness, to the idea of the vacuum in physics, its explanation by the ‘ether’ and the eventual overthrow of that concept. Temperatures (absolute zero) and the place of the vacuum in quantum mechanics, relativity and cosmology come on stage, and the book ends with a return to the philosophic concept itself. Yes, quite complex, and I’ve barely gotten to chapter 2. Nice to have a roadmap to a blank space. I’ll be reviewing the book when done.

But one of the matters that did come up was the story of Pope Sylvester II, one of the few admirable holders of the keys of Peter in the Middle Ages. This is a story appealing enough to shove its way to the front of the ‘Molly Line’. Sylvester II was born Gerbert de Aurillac (945 – 1003). He reigned as Pope from 999 to 1003. Yes the Pope in the Chair during the turn of the millennium. The world didn’t end, and Gerbert/Sylvester was definitely one of the more capable Popes of the age. A lot of his accomplishments were political and hardly bear mention here. Defending the property of the Church. Playing off one ruler against another though he was usually in alliance with the Holy Roman Emperor of the time.  The politics of Italy at the time were particularly chaotic, and once both he and the Emperor had to flee Rome during one of the revolts. He even tried to reform the Church’s organization and reduce abuses such as simony, concubinage and nepotism. This was an Herculean task, and even with the assistance of St. Jude (the patron saint of the impossible) the Church remained just about as corrupt as always. He did, however, succeed in significantly increasing the Church’s title holdings. Maybe this goal was in direct contradiction to the idea of making the Church into a more ‘Holy’ outfit. He also played a major role in the Christianization of Eastern Europe, appointing Metropolitans for both Poland and Hungary, and in the later case naming that country as a ‘Kingdom’. Thus the Crown of Hungary became dependent on the Papacy.

His political accomplishments were minor compared to his intellectual contributions to European culture. He had early on spend considerable time as an envoy to the far more civilized Muslim states of southern Spain, and he turned his natural curiosity to good effect there, absorbing much of the culture of Andalucía. When he returned to France he was appointed head of education for the Archdiocese of Rheims, and from there he significantly elevated the clerical level of education throughout the French Kingdom.

 When his patron died he was considered the natural successor, but the Capetan monarchy had other ideas, and a relative of the King was appointed in his stead even though Gerbert was a supporter of Hugh Capet whose reign marked the end of the Carolingian dynasty. Barrow has this matter somewhat confused as he lists this Episcopal position without mentioning that Gerbert’s appointment was overthrown. Consistent with the political level of the time the King’s appointee was later removed because of suspicion of treason to his sponsor. Gerbert who initially was himself accused of treason to the House of Capet was reappointed, but this was challenged and his appointment declared invalid. When he did finally become Pope he pretty well washed his hands of the matter by declaring his competitor as the legitimate Archbishop. Barrow also confuses another appointment of his, as Archbishop of Ravenna, supposing him to be the ‘Abbot’ of Ravenna. All this is quite forgivable as the politics of the time, clerical and lay, were by their very nature confusing.

Gerbert was lauded for his scholarly contributions in a number of fields. He became the tutor of both Emperors Otto II and his son Otto III, and, as mentioned above, he was elevated to the Papacy with the support of the latter. Gerbert was a true polymath. He was the accepted authority in the liberal arts in his day and a major influence on theology. He was also something of an engineer, designing a hydraulic organ that didn’t require air to continually be pumped in as it played. He is also credited with advances in the art of clock making due to one which he designed for the Cathedral of Magdeburg. Even this is confused. Some sources such as the ‘Catholic Encyclopedia’ say that he was the inventor of the pendulum clock. Others say that his clock was mechanical but weight driven rather than using a pendulum. Still others say that his clock was actually simply a sundial. It was, however, in the field of science and mathematics that he made his greatest contributions.

Gerbert was credited with a number of innovations. He introduced the abacus to Europe, and also the use of the Arabic/Indian number/decimal system. Both were necessary foundations for the later rise of commercial enterprises in the Renaissance. Hard to do proper accounting with Roman numerals. Not that they were always appreciated. In 1299 the decimal system was outlawed in Florence supposedly because it was more vulnerable to fraud. The worry about this matter delayed the adoption of decimal numbers in northern Europe until the sixteenth century. For Gerbert, however, they were a Godsend, and he was the foremost expert on mathematics, geometry and astronomy of his day. Much of this was based on what he had learned in southern Spain even though he was creative enough in his own right.

He is credited with the reintroduction of the ‘armillary sphere’ to western Europe. This is a 3D model of the heavens, and fitted with viewing tubes it was an early prototype of the telescope. It should be noted that such a sphere would imply that the Earth itself was a sphere. Not that the idea of a flat Earth was universal in Medieval times, but it was common enough even though the use of spheres such as this proliferated.

Barrow’s book corrected a misconception of my own, one that I had held for more than a few years. I knew that Sylvester II was a remarkably educated and knowledgeable man well ahead of his time. I also knew that one of the medieval Popes had been dug up from his grave and the corpse put on trail. I’d always assumed that the uncommunicative defendant was Sylvester. During his lifetime and after his death rumours circulated that he was in league with the Devil, that he had even constructed a bronze head that would answer questions posed to it. Sort of an early robot I guess. I assumed that this was the reason for the exhumation. Wrong I was. The corpse was that of one Pope Formosus, and the charges were much more mundane. After the guilty verdict was pronounced the hapless cadaver was chopped to pieces, burnt and the ashes thrown into the Tiber. That will teach him.

The accusations of witchcraft would certainly be a likely medieval explanation for Sylvester’s brilliance, but no – he stayed in the ground. Not that he rested easily though. The legends of his life followed him into the grave, and typically they are also confused. One legend says that when a Pope is due to die that Sylvester’s bones rattle in the tomb. Another says that the walls of the crypt weep on the sad occasion. I guess there’s no reason they can’t both be right.

. . . → Read More: Molly’sBlog: A Devilishly Smart Pope

Political Eh-conomy: Magic numbers and the math stick

Economics is often associated with numbers. We are bombarded with economic data: GDP, unemployment, inflation, debt, exchange rates, market indices…the list is seemingly endless. While many of these numbers change – we are encouraged to cheer when they rise, jeer when they fall – there are others that are presented as fixed, immutable boundaries between . . . → Read More: Political Eh-conomy: Magic numbers and the math stick

Scripturient: Blog & Commentary: Doing it by the numbers

The first thing I learned – well, not the first but up there, for sure – is that volume measurements are for amateurs. Being an amateur (and expecting to be there for some time yet), I took it on the chin when asking typical neophyte questions about recipes and ingredients. Might as well have hung . . . → Read More: Scripturient: Blog & Commentary: Doing it by the numbers

Another Step to Take: 5 Reasons to Make a Set of Napier’s Bones

Napier’s bones are easier than slide rules,” my seven year old announced the other day. I had found extra-wide wooden craft sticks (popsicle sticks), shown him how to write the multiplication table on them, dividing the one’s digit from the ten’s digit with a diagonal line. Each stick contained the first ten multiples of one number. . . . → Read More: Another Step to Take: 5 Reasons to Make a Set of Napier’s Bones

Dead Wild Roses: Sodoku and Mathematics

Every wonder how many clues you needed to uniquely solve a Sudoku puzzle? Watch and find out


Filed under: Science Tagged: Mathematics, Sodoku

. . . → Read More: Dead Wild Roses: Sodoku and Mathematics

Progressive Proselytizing: The N-Party Problem

There is a famous problem in classical mechanics, a branch of physics, called the n-body problem. While interesting in its own right, the problem can be used as an analogy that is illustrative towards politics; in particular, the issue of predicting long term trends of political systems with two or more major political . . . → Read More: Progressive Proselytizing: The N-Party Problem

Progressive Proselytizing: The sensitivity of the Ontario election results to the Green Party vote

One of the interesting results of the Ontario general election was the collapse of the Green Party from its 2007 peak of 8% down to just over 3% in 2011. In this post I run the math on various counterfactual scenarios to see what would have happe… . . . → Read More: Progressive Proselytizing: The sensitivity of the Ontario election results to the Green Party vote

Progressive Proselytizing: On Objective Morality

Most moral theories are predicated, at their root, by various assumptions or axioms which in turn cannot be derived independently. That is, there does not seem to be some cosmically significant, absolute grounding for morality that simply and unques… . . . → Read More: Progressive Proselytizing: On Objective Morality

Progressive Proselytizing: The Concept of Infinity

It is often suggested that the human mind is incapable of conceiving of the concept of infinity. I would submit firstly that in many ways the concept of a finite universe is actually as hard if not harder to conceive of and, further, that looking deepe… . . . → Read More: Progressive Proselytizing: The Concept of Infinity

Progressive Proselytizing: My Central Tension in Moral Philosophy

It would be nice to be able to say that my moral leanings followed a consistent system of moral belief and didn’t leave central questions such as the source of morality unanswered. Were that the case, it might superficially lend credence to the weight … . . . → Read More: Progressive Proselytizing: My Central Tension in Moral Philosophy

Progressive Proselytizing: Electoral math II: vote splitting in the Liberal ridings the Conservatives won

While there was an enormous transfer of seats towards the NDP from the Bloc and to a lesser extent the Liberals, the Conservatives managed to move from a minority to a majority largely due to 26 seats they picked up from the Liberals. Three weeks ago, … . . . → Read More: Progressive Proselytizing: Electoral math II: vote splitting in the Liberal ridings the Conservatives won

Progressive Proselytizing: Electoral Math I: Vote Splitting and the NDP+Liberal merger hypothesis

This historic election has seen the complete collapse of the Bloc Québécois and the decline in the Liberal party to historic lows while propelling the Conservatives to a majority government and the NDP to the official opposition. With the governing… . . . → Read More: Progressive Proselytizing: Electoral Math I: Vote Splitting and the NDP+Liberal merger hypothesis