Alexander Masters - The Genius in my Basement

In Simon’s kitchen, Hunger has slobbered everywhere.

Yellow smears splashed along the left-hand worktop are from cartons of chicken biriyani, the lid ripped off; the drips of purple, slightly granulated, are Fern’s® brinjal pickle; the intermingled slops of ochre green, Mr Patak’s® mixed pickle.

‘And what’s wrong with Mr Fern’s mixed pickle?’

‘I don’t know. I’ve never tried it. Do they do one?’

Both types of stain are the result of scraping contents from jars with a plastic spoon that is too short, and rushing the findings back on a bombing run across the sideboards to the now dead chicken. By the sink, chicken in black bean sauce has added a brown tinge.

This rancid atmosphere and the cold, soporific mood of the main rooms, together with the almost undetectable whiff of furniture polish from the paintings and mahogany items that Simon inherited following the death of his father – a homeopathic dose of plushness – combine to give the Excavation a pleasant smell. Warmed up, with perhaps a squeeze of lemon and lime shaving cream thrown in to suggest Life, it might even be cosy.

All the same, it’s easy to get carried away by this bomb site. Simon isn’t universally messy, even outside his head. He’s as fussy as a surgeon when it comes to planning a journey. He manages two homes (he has a flat in London), has a turnover of satisfied tenants, and is never behind with bills, legal documents or financial dealings with his accountant. None of these is true of me. In addition, his transport newsletter comes out once every three or four months, is twelve to sixteen pages long, single-space, eight-point type, covers hundreds if not thousands of unfailingly accurate details about new routes, closures and timetables, and keeps careful account of all local outrages by the government Highways Agency. When Simon wants there to be order, he’s unmatchable. When not, a colostomy bag is not more disgusting. Simon insists that this basement is his catalogue: all it needs is pruning, sorting out, filing, and it will be an invaluable library of documentation.

A list, from 1992, of a few of the bus and train journeys Simon made that year. He has a pile of such lists, over a foot high.

‘A documentation of what, exactly?’ I ask while he sits down to his supper.

‘Where I’ve been?’ he suggests.

I call it his middenheap. These papers are just bones: all that is left after Simon’s banquet on their information relating to buses and trains: the public-transport detritus of a monstrous feast on facts that began when he was three.

‘How about if I take the focus of the story off the floor and into the air?’ I suggest breezily, returning to the battle. ‘“One of the greatest mathematical geniuses of the twentieth century lives beneath my floorboards,” I could begin, “in the dank, foetid gloom of his subterranean …”’

‘No.’

‘Not dank?’

‘No.’

‘Or foetid?’

He shakes his head.

‘How about miasmic? I quite like miasmic. It sounds poetic.’

Also no good: ‘Ungh-ungh.’

I take a deep breath, slowly let out air, and reach across for Simon’s thesaurus. ‘Ponging?’

*6 The Monster

(Mathematical chapters in this book are quarantined by a *)

That’s the name of Simon’s special area in mathematics, because of its gargantuan complexity and fiery insight into the fundamental structure of our universe.

No one knows what the Monster looks like. It can be detected only through its mathematical traces. Like shadows and ghosts, it inhabits a penumbral landscape between abstraction and solidity.

The Monster belongs to an area of mathematics known as Group Theory, or the study of symmetry.

Groups are represented in textbooks by tiresome grids of numbers similar to sudoku tables, yet they are among the most startling investigative tools in human thought. Quantum Theory, Relativity Theory, predictions about the number and types of sub-atomic particles, the codes used to scramble military and financial information – all of it fundamentally reliant on the study of Groups. They have even been used to investigate incest among Aboriginal tribes.

A sudoku table has nine rows and nine columns of numbers.

The Monster has 8080174247945128758864599049617107 57005754368000000000.

*7

Introducing

To understand Simon’s particular genius – how it developed and why for a few years he led the braying pack of mathematicians hunting down the Monster – the reader needs to know about squares.

On the face of it, the study of symmetries is a subject for children. A square has symmetry: you can rotate it, and the result looks just as if you’d done nothing at all:

The same goes for an equal-sided triangle:

A circle, cube, sphere, and a host of other shapes with names like dodecadodecahedron (twenty-four faces) and icosidodecadodecahedron (forty-four faces) each has similar symmetrical properties.

In order to develop mathematics out of such simple stuff, we have to keep a diary of these symmetries.

For example, to keep track of these four moves, we can represent them like this:

Note that there’s a sense of self-containment about this set of operations. A square has four sides and therefore only four distinct ways of rotating. After that, you’ve exhausted all the possibilities. No amount of rotating will paint it green or puff it up to twice its original size. Other operations are needed to perform that sort of thing.

If we rotate a square in any of the above four ways, it still looks to the outsider just like the square we started with:

But, privately, we know we’ve been fiddling. For example, if we rotate a square through two turns (i.e. flip it head over heels), we can represent this:

In other words,

signifies the act of swivelling a square through two 90-degree turns, without anybody noticing.

Naturally, if you turn a square by one turn through 90 degrees, then do it again, that’s the equivalent of two 90-degree turns overall:

1 + 1 = 2

Similarly, rotate a square once, followed by two more turns, and the result is equivalent to three turns. You’ve almost gone the whole way round:

1 + 2 = 3

And so on. Rotate a square by two turns, then do nothing, go off and play with somebody else’s crayons, and no one’s going to be fooled – it’s still just two turns:

2 + 0 = 2

A square looks just the same after any combination of these operations, or all of them:

The figures with arms and legs are simply diary entries to keep track of the secret things we’ve been doing to the square in the playpen.

What happens if we turn a square, say, five times? That’s the equivalent of spinning it through a full cycle, then throwing in an extra single turn for good measure:

Group Theory isn’t interested in recording such clever-clogs stuff. Turn a square round five times and you might as well just have turned it once. It’s the final outcome only that matters, so it’s put down as an ordinary single turn: