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Category: books

Lockdown reading : SNORT

Published May 2, 2021 by lievenlb

In this series I’ll mention some books I found entertaining, stimulating or comforting during these Corona times. Read them at your own risk.



This must have been the third time I’ve read The genius in by basement – The biography of a happy man by Alexander masters.

I first read it when it came out in 2011.

Then, in conjunction with Genius at play – The Curious Mind of John Horton Conway Conway’s biography by Siobhan Roberts, in july 2017, which is probably the best way to read this book.

And, then again last week, as Simon Norton‘s work pops up wherever I look, as in the previous post.

It takes some time to get used to the rather chaotic style (probably used because that’s how Masters perceives Norton), and all attempts at explaining Simon’s mathematics can better be skipped.

The book tries to find an answer as to why a child prodigy and genius like Simon Norton failed to secure a safe place in academics.

Page 328:

Simon’s second explanation of his loss of mathematical direction is heartbreaking. Now that Conway has fled to America, there is no one in the mathematical world who will work with him.

They say he is too peculiar, too shabby, too old.

His interests are fixed in mathematics that has had its day. His brilliance is frigid. His talent, perfectly suited to an extraordinary moment in algebraic history (the symmetry work at Cambridge during the early 1970s and 1980s) is out of fashion.

This may give the impression that Norton stopped doing good math after Conway left for Princeton in 1985. This is far from true.

Norton’s Wikipedia page mentions only post 1995 publications, which in itself is deplorable, as it leaves out his contributions to the ATLAS and his seminal paper with Conway on Monstrous moonshine.

Here’s Alexander Masters talking about ‘Genius in my basement’

I’ll leave you with a nice quote, comparing Monstrous Moonshine to a Sainsbury’s bag on Jupiter.

Page 334:

This much I do know: Monstrous Moonshine links the Monster to distant mathematics and the structure of space in ways that are as awe-inspiring to a man like Simon as it would be to an astronaut to step out of his space machine on Jupiter, and find a Sainsbury’s bag floating past. That’s why it’s called ‘Moonshine’, because mathematicians can even now hardly believe it.

‘I think’, said Simon, standing up from his berth and shaking crumbs and clotted blobs of oil and fish off his T-shirt onto the covers, ‘I can explain to you what Moonshine is in one sentence.’

When he really tries, Simon can be a model of clarity.

‘It is,’ he said, ‘the voice of God.’

Ps, wrt. SNORT.

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Finnegans Wake’s geometry lesson

Published April 14, 2021 by lievenlb

The literary sensation that spring of 1939 no doubt was the publication of Finnegans Wake by James Joyce. On May 4th 1939 FW was published simultaneously by Faber and Faber in London and by Viking Press in New York, after seventeen years of composition.

In 1928-29, Joyce started publishing individual chapters from FW, then known as ‘Work in Progress’, including chapter II.2 ‘The Triangle’, of which a brief excerpt was already published in February 1928. The name comes from the only diagram in FW, the classical Euclidian construction of an equilateral triangle (FW, p. 293)



This Vesica piscis has multiple interpretations in FW, most of them sexual. The triangle $\Delta$ is the Sigla for Anna Livia Plurabelle throughout FW, but it also refers to the river Liffey through Dublin.

Here’s Anthony Burgess explaining some of the Sigla, the relevant part starts at 14.20 into the clip.

In fact, many of FW’s Sigla are derived from mathematical symbols, such as $\exists$ (Earwicker), $\perp$ and $\vdash$ (Issy). For more on this, please read The logic of the doodles in Finnegans Wake II.2.

Not only does the equilateral triangle $\Delta$ refer to the river Liffey, the entire Euclidian diagram can be seen as a map for Dublin and its surroundings, as emphasised by the words “Vieus Von DVbLIn” (views from Dublin) in FW right under the diagram.

Here’s Dublin with the Liffey running through it, and Phoenix Park, which also features prominently in FW, see for example Phoenix Park in Finnegans Wake.



Views of Dublin – Photo Credit

The similarity between the map and the diagram is even clearer in Joyce’s own drawing in the first draft of FW.



The Triangle – Photo Credit

There’s a lot more to say about Joyce’s uses of geometry and topography in Ulysses and Finnegans Wake, in fact Ciaran McMorran wrote an entire Glasgow Ph. D. about it, but perhaps I’ll save some of that for a future post.

But what does this have to to with the Bourbaki Code, the puzzles contained in the Bourbaki-Petard wedding announcement?



Well, I claim that Andre Weil hid the Vesica Piscis/Euclidian diagram into the ‘faire part’. The challenge is to view the wedding announcement as a partial city- map. Clearly this time, the city of Dublin should be replaced by the city of Paris. Se non e vero …

Probably, there are enough hints contained in the previous posts in this series for you to spot the triangle(s) on the map of Paris. If you do so, please leave a comment, or email me.

Meanwhile, we’ll unravel first the more obvious levels of interpretation of the wedding announcement.

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Ghost metro stations

Published April 1, 2021 by lievenlb

In the strange logic of subways I’ve used a small part of the Parisian metro-map to illustrate some of the bi-Heyting operations on directed graphs.



Little did I know that this metro-map gives only a partial picture of the underground network. The Parisian metro has several ghost stations, that is, stations that have been closed to the public and are no longer used in commercial service. One of these is the Haxo metro station.



Haxo metro station – Photo Credit

The station is situated on a line which was constructed in the 1920s between Porte des Lilas (line 3bis) and Pré-Saint-Gervais (line 7bis), see light and dark green on the map above . A single track was built linking Place des Fêtes to Porte des Lilas, known as la voie des Fêtes, with one intermediate station, Haxo.



For traffic in the other direction, another track was constructed linking Porte des Lilas to Pré Saint-Gervais, with no intermediate station, called la voie navette. Haxo would have been a single-direction station with only one platform.

But, it was never used, and no access to street level was ever constructed. Occasional special enthusiast trains call at Haxo for photography.



Apart from the Haxo ‘station morte’ (dead station), these maps show another surprise, a ‘quai mort’ (dead platform) known as Porte des Lilas – Cinema. You can hire this platform for a mere 200.000 Euro/per day for film shooting.

For example, Le fabuleux destin d’Amelie Poulin has a scene shot there. In the film the metro station is called ‘Abbesses’ (3.06 into the clip)

There is a project to re-open the ghost station Haxo for public transport. From a mathematical perspective, this may be dangerous.

Remember the subway singularity?

In the famous story A subway named Mobius by A. J. Deutsch, the Boylston shuttle on the Boiston subway went into service on March 3rd, tying together the seven principal lines, on four different levels. A day later, train 86 went missing on the Cambridge-Dorchester line…

The Harvard algebraist R. Tupelo suggested the train might have hit a node, a singularity. By adding the Boylston shuttle, the connectivity of the subway system had become infinite…

Now that we know of the strange logic of subways, an alternative explanation of this accident might be that by adding the Boylston shuttle, the logic of the Boston subway changed dramatically.

This can also happen in Paris.

I know, I’ve linked already to the movie ‘Moebius’ by Gustavo Mosquera, based on Deutsch’s story, set in Buenos Aires.

But, if you have an hour to spend, here it is again.

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