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Soho at that time was a quiet backwater where vice was conducted with a minimum of effort. The aspidistra of English prostitution was kept flying down pissy alleys. And the occasional influx of kids from the suburbs, or men from the ships, flushed the network of drinking clubs and knocking shops clean for another fortnight.

Vice still had the same scale as the architecture, it was only three or four storeys high. Homosexuals, jazz musicians and journalists formed companionable gaggles. Things that people did were still risque before they became sordid.

I put up at the Majestic Hotel in Muswell Hill, a pink, pebble-dashed edifice. Originally it must have been intended for an Edwardian extended family, but it had become home to riff-raff from all over the world: salesmen, confidence tricksters, actors and graduate students. I ventured by juddering bus down into the West End on a daily basis. The cab company the card in Alkan’s bathroom referred to was easily found. It was a cubbyhole tenanted by an Italian speaker in a flat tweed cap. He made no sign of remembering a tall, thin man, somewhat like Le Corbusier. Indeed, it could have been a resistance to the Modernist movement as a whole that made him so abusive towards me when I pressed him for information.

I took to wandering hither and thither, aimlessly crossing and recrossing my steps. I was convinced that Alkan was in the West End of London and that he wanted to be found. I saw his behaviour as purposive. I gave no thought to the fact that my grant had run out, that I was due to appear before the supervisory panel in a matter of weeks, and that my leviathan of a thesis lay beached on the nylon counterpane of my foldaway bed in Chelmsford.

One of the main disadvantages of an impoverished, nomadic metropolitan existence is that in winter you cannot have privacy without either purchasing it, or gaining access to it in a lockable toilet cubicle. I desperately needed privacy, for, during my years of retreat from the world, I had developed certain private habits, certain rituals combining magical twists of thought with bodily functions that I had to perform on a four-hourly basis. Lacking the wherewithal for a hotel (we were formally expelled from the Majestic every morning at 9.00 and not allowed back in until 5.30), I took to the conveniences, becoming adept at selecting the toilets where I would have the most genuine peace and quiet. This was a difficult and absorbing task. So many of the public toilets and even those in large hotels and restaurants were frequented by homosexuals. I had no argument with these people, either moral or psychological (and I may point out at this juncture that Quantity Theory as a whole maintains no defined perspective), but the push, shove and then rasp of flesh, cloth and metal fastener against ill-secured prefabricated panels and grouted gulleys tended to interrupt my rituals.

So, I elevated my search for the ideal cubicle — warm, discrete, well lit — to an exact science. Unnoticed by me, this search was beginning to usurp the primary quest. It is ironic, therefore, that unknowingly, unintentionally, I began to find evidence of the great psychologist where I myself sought refuge.

I could avoid the actual congress of homosexuals quite easily. However, without abandoning my private study altogether I could not hope to avoid the evidence of their activities: crude but believable advertisements, scrawled in Biro or neatly lettered; seemingly hacked with an axe, or delicately carved with a penknife; they drew the reader’s attention inexorably to penile size:

I’m 45 and my wife gives me no satisfaction coz shes too slack. If you have a 9″ cock, or better, meet me here after 6 any wensday. I will take on any number of lusty boys.

and:

Boys under 21 with 6″ or more meet me here. You do it to me I’ll do it to you.

And the direct, if disturbing:

Give me big dix.

There was one of these water-closet communicants who was more readily recognisable and more prolific than the rest — I began to see his entreaties in a lot of my favourite haunts, and to come across them occasionally when I broached new territory. This person was distinguishable by his rounded, laboured writing in red Biro, which reminded me of the hand of an adolescent schoolgirl — especially the characteristic of drawing small circles in place of the point over the ‘i’. Furthermore, his graffiti were always written neatly on the wall directly above or below the point where the toilet paper dispenser was mounted. They were also very carefully executed. With some of the best examples I could actually see where the artist had used a ruler to get his script to line up just so. As for content, alas that was wearisomely predictable:

Meet me here on Friday or Saturday evening if you are better than 7″. I have a 9″ cock which I like to have kissed and sucked till I come in someone’s mouth. I like young boys of around 16, but also more experienced men.

This I noted down in my leather-bound journal from the wall of an unpretentious, unfrequented, spotlessly clean, underground municipal convenience in Pimlico. I had no idea why I had taken to recording such things. I had been in London only a fortnight or so; I had no fixed view about the status of my quest for Alkan. On the whole I was inclined to view it as spectacularly important. I had, after all, given up my forthcoming exam in order to find him. My analysis with him was incomplete, I had no family or friends to support me. On the other hand I could just as easily feel dismissive and indifferent about the quest for Alkan. Who needed the daft old coot anyway? Nonetheless I did immediately notice the connection between the advertisement above and this:

I like to suck young boys cocks and to have mine sucked as well. I’ve only 5″, but it’s hard all the time. If you’re 16 or under meet me here on Tuesday at 9.00.

neatly scripted beneath the Smallbone of Devizes ceramic, interleaved sheet-holder clamped to the distempered wall of the warm and capacious gents at the Wallace Collection. And this:

Fun time every evening here or at the xxxx [illegible] club. All experienced men better than 8″ meet me for sucking frolics. I am 27 and I have 9 good inches which you can nip and lick.

incongruously proclaimed from a bare space of rendering, framed with grout, left available, as if on purpose, by the absence of a tile in the checkerboard that skirted the commode in the denizens of the Reform Club.

If I idly noted down this smut cycle it was not for any reason but boredom. It wasn’t until later, days later, that, glancing on passing, in the canted, cracked, oval mirror that capitulated on top of the dead bureau in my L-shaped wind-tunnel at the Majestic, I saw the hidden significance of these three bites. I saw it as a sequence solely of numbers, integers, detached from the penises-in-themselves, thus:

7, 9, 16, 5, 16, 9, 8, 27, 9

This in itself obviously represented an intentional sequence. The very fact of the way relation between primes and roots was organised, implied a capricious mind intent on toying with a willing enquirer. I immediately felt the presence of Alkan in that simple sequence. I knew that I was in no real position to analyse the sequence as it stood — and that infuriated me … I knew that if the sequence was to prove meaningful it must have a progression.

My cottaging became more intense. I spent virtually all my days in toilets. The one day I had to abandon my quest and attend the National Assistance Board, I managed to contrive to wait for some hours in the toilet. When I emerged my number was called, an example, I feel, of perfect timing.

Eventually I began to find little outpourings, here and there, which were unmistakably more elements of Alkan’s coded message. Each set of figures was couched in the same form, written in the same hand and situated within the toilet cubicle in the same place. After a fortnight I had an impressive set of integers of the form: