Views From the Sixth Floor - Shaftesbury Avenue

Recently my part of The Bank's business moved up to the sixth floor. This has some rather good views over the West End. We're not going to be there for long - maybe another nine months - so I'm going to be snapping away whenever the light is good enough.

This little street behind an Odeon cinema looks a lot better in this photograph than it does from ground level...

And this is a view into an upper floor studio or store at Central St Martin's...

And who can resist - well, I can't - the sight of cranes silhouetted against an evening sky?

They moved into the space before they had a LAN wired in, so for about six weeks they were using ordinary BT broadband and VPN. For the first three weeks, they were using wireless to get to the broadband and even the colouring-in people noticed it was slow. Now we're all wired up and our Cisco VoIP phones are back on-line. So they're going to move the seats around again. Which really is moving deckchairs on the Titanic of morale they've made for themselves.

My Brush With Algebraic Geometry

Sometime back in the mid-Ougties I decided that I would try to learn some Algebraic Geometry.  I did what anyone would do: I bought Hartshorne's Algebraic Geometry and Eisenbud's Commutative Algebra from Amazon and started reading. Some many months later, when I realised I had no idea what "divisors" really were, I ran across a simple explanation in Shaferavtich's book and bought that. Apparently many people have problems learning from Hartshorne's comprehensive but very abstract book. (A divisor, by the way, is a generalisation to higher dimensions of the idea of the roots of a polynomial.)

Modern algebraic geometry is not about conics and envelopes of curves and anything else you may recognise from A-levels. In the same way that Georg Cantor had to develop the theory of infinite sets to cope with zeros of Fourier series, Alexander Grothendieck developed vast swathes of category theory to cope with problems in algebraic geometry and frame it in a general setting. Of this approach, its high priest, Robin Hartshorne, says: "the person who works with schemes has to carry a considerable load of technical baggage... sheaves, abelian categories, cohomology, spectral sequences and so forth". Not to mention a hefty lump of commutative algebra. 

Why algebraic geometry? Isn't algebra one thing and geometry another. Well, here's how it works.  Descartes taught us how to take a curve and describe it with an equation such as y = 3x+4. This can be written in the form f(x,y) = 0 (y - 3x+4 = 0 in the example). In other words, a curve or a finite set of points is the solution to an equation: it's the set of points (x,y) such that f(x,y) = 0. Now let's take the ring of real-valued functions of two variables with real coefficients, R(x,y), and consider the ideal (f) generated by f(x,y). Factor R(x,y) by the ideal (f) to get the quotient ring R(x,y)/(f). Each one of these steps generates an unique object, so we can take a curve and associate it with a quotient ring. We can also associate the curve with a field of rational functions by looking at all the real-valued rational functions defined everywhere on the curve: this is the function field. It turns out that (roughly) the curves are equivalent if their function fields are isomorphic. So we can learn a lot about curves from these algebraic objects. But notice how quickly it went from something you did in school to something you can do an entire Maths degree and still avoid (commutative algebra).

The subject is cluttered with a lot of what's known in the trade as "machinery", which is one of those terms that mathematicians get and is difficult to explain. "Machinery" is needed for a number of things: one is using equivalence classes to mod out issues with specific co-ordinate representations of spaces or functions; another is to ensure that local representations of a part of a space or function are "glued together" in a coherent way; and yet another is representing a space or object by a set of ideals or filters.  The first piece of real machinery most mathematics undergraduates come across is a differentiable manifold or a fibre bundle.

The abstract spaces of algebraic geometry, called schemes, use all the machinery ever devised and then some more. A scheme is a locally ringed space such that every point has an open neighbourhood that is isomorphic to the spectrum of some ring. A locally ringed space is a topological space with a gadget called a sheaf that assigns a ring of functions (think of them as polynomials) to each open set. The spectrum of a ring is its set of prime ideals with the Zariski topology and a sheaf of rings defined in a manner so horrible not even Shaferavitch could simplify what's on page 70 of Hartshorne. When I first tried getting to grips with the definition I thought of schemes as like manifolds made up of locally patched Stone spaces (very "sort of").  As an example, the spectrum of the integers consists of: a) ideals generated by the prime numbers, b) co-finite subsets of the (ideals generated by the) primes and c) a set of polynomials which don't have a particular prime as a zero.

It's very good for stretching the brain. But in the end, I'm a logician and just not that interested in curves and numbers and other such things. I found Goldblatt's Topoi: Categorical Analysis of Logic recently and am reading that almost for light relief. It uses categories called topoi to construct alternative models of set theory. Toposes were invented by Grothendieck to solve problems arising in algebraic geometry. Hence my interest: toposes are used in mathematical logic and set theory to do all sorts of clever things, and second because algebraic geometry doesn't fit with the conventional foundational / axiomatic approach to mathematics. I will go on dipping into the books, but there are some things you really do need to study full-time, and algebraic geometry is one of them.

What's Your Myers-Briggs Type?

Someone at work mentioned that they had done a Myers-Briggs and been pronounced an ISTJ. They weren't sure they really liked it, but from what I know of them it was as accurate as any of these things can be. This made me look again and I decided I'm almost the opposite: an ESFP. That means I get energy from dealing with people or other stimuli, focus on details and facts, put personal and social criteria above "objective" ones, and prefer not to commit to an early decision but leave my options open for as long as possible.

How does this square with the fact that sometimes I will be very glad when a meeting gets cancelled so I can concentrate on some piece of programming or analysis? Isn't that very introverted? Extroversion, in the psychological sense, isn't about people, it's about your need for external stimulation (which back when these psychologists were getting going and there was no TV, You Tube or iPods, pretty much meant people). An introvert is scared of being overwhelmed, an extrovert is scared of being bored. Anyway, we can't like everyone and some people or situations with people in them are just not simpatico, so it's not about people, it's about the kind of people. If most people aren't your kind of people, you're not going to be seen around people much - but that doesn't mean you're not an extravert. It just means you are in a minority.

As for the details bit, well, that's me. Life is not a big picture, it's a mass of details, but of course what I know with experience is that implementation without strategy is blind, but strategy without implementation is empty. Where I work, we have neither.

As for the criteria, yes, I put personal factors first (is this what we want to be doing? how does it make me look? what are the other people we don't want to be confused with doing? how will it be taken?) but only because, again, experience tells me that you have to do the numbers first. The numbers tell me what to reject - too expensive, not profitable enough, takes too long, won't fit through the door, insurance is impossible - but not what to accept. It's the personal stuff that tells me what to accept after all the duff stuff has been rejected.

As for not committing? Put that down to the influence of the Rat in my Chinese horoscope. We Rats have to have an escape plan - and anyone with an out before they go in is not committing. My main decision criterion is: how much will this cost to reverse / undo / paint over / do another way? If the answer is, not much, then I'll go ahead with a decision. If the answer is, a whole lot, I will usually decide we have to do it another way, one that we can back out from. Anything with low entry barriers and huge exit costs is going to get a very wide berth from me - hence my never even thinking of marriage. I could no more consider marriage than a sailor could spit into the wind. So I leave as much undecided as possible, partly to give Fate and Lady Luck as many opportunities as possible, and partly because I prefer the process the French call engragement - whereby one eventually does something without ever actually having decided to do it. (I'm sure that word exists - I read it somewhere, but I've never seen it since.)

However, I bet that if I actually answered the questions (which I just did here) I would need to pay attention to the words. One of the questions is: after prolonged socialising, do I feel the need to get away for some peace? You might say yes if you've seen me on occasion, but you would be missing the fact that I was "socialising" with people or in a situation I didn't want to be with or in right from the start: I was being dutiful. Under those circumstances anyone would want to get away asap - and if I had somewhere with people to go afterwards, I would, but I don't, so it looks like I'm getting some peace and quiet.

I might be an ESPF but I very often live the life of an ISTJ. There's nothing that says the way you're living is how you want to be living, and looking at how you do live may be no guide to who you are. It's just a guide to the compromises you made.

Not Absolute, but Non-Negotiable

Moral relativism, the idea that there is no unique right answer to any given problem of what to do and how to behave, has for a long time been the very height of intellectual chic. Its proponents, when not wanting to simply scandalise, can appear worldly, travelled and perhaps even a little louche. To its opponents, it is the very depth of intellectual depravity, and very principled, upright and serious of purpose they can sound too. It's an argument that has been going on since the classical Greeks - who seem to be the first to notice that people did things different than they did in Piraeus and didn't seem to be any the worse for it.

The argument over whether there is always One Right Answer is irrelevant for one simple reason: the principle of rationality requires us to describe at least one set of circumstances under which we would give up that very answer even if we thought we had it. If you want to be a rational absolutist, you will have to describe any of your principles in such exquisite, counter-example defying detail, that it will never be usable twice. It will be perfect, and perfectly useless. But this debate seems to generate a lot of heat and is not going to go away on a technical point about rationality and practicality. This suggests that there is something else going on. It's not about moral epistemology, but something else. What?

There is always the psychological explanation: absolutists had strict parents or don't tolerate Others very well, relativists are easy-going and like variety. That may explain where some of the heat comes from, but it doesn't explain why the parents are strict. Where's the benefit? Strict is hard work and makes Jack a dull boy.

Moral absolutism has the same purpose as an idiosyncratic diet or the requirement to circumcise males: it stops one tribe mixing with another and thus maintains the authority of the priests, rulers and wise men. How, after all, can you in all conscience inter-marry with someone who worships false gods and has such barbaric ceremonies? How could you even sit at the same table with people who eat pork? How could anyone call themselves a man who let his daughter go around with whichever men she chose? These are, after all, serious matters, affecting our very identity and honour.

Or not, if you really need the people from that country across the Mediterranean to trade in your ports. Faced with the need to get spices, wheat, decent armour and other exotic goods, we can surely overlook the minor matter of which Gods they worship? Does it matter if they have two wives each, when what we need is a safe passage through their country? It is entirely possible that moral relativism was developed from a series of practical observations to a full-fledged theory by Greek intellectuals in response to their merchant economy's need for a theory to peddle to the xenophobic crowd.

The same principle applies to running an Empire. If what matters is getting the taxes and whatever raw materials and land you were after and being able to work and transport stuff safely, then do you really care if they worship a pagan fertility god and burn wives after the husband dies? It's about the oil, right? The European Empires started to go downhill once European women started to live in them and, of course, when the missionaries started converting the natives. It's one thing to steal something I didn't know was valuable, but entirely another to have some jumped-up woman from Surrey telling me I'm a savage. Especially when her uncle was having an affair with my daughter back in the day. (Think India, not Africa.)

That's what the relativism vs absolutism debate is really about. Absolutists are looking for reasons not to deal with Others, whereas relativists are looking for reasons to deal with as many Others as have something interesting to trade - provided they obey the basic rules of trade and communal life. Because while nothing is absolute, some things are non-negotiable: paying bills, delivering goods, honouring deals, keeping promises and neither killing, stealing nor holding to ransom. You want to trade in our country, you obey our commercial laws.

Lunch Places

Recently the gang from the office (or "me and the kids") have been sampling the local restaurants at lunchtime. Since we're but a stroll away from Soho and Chinatown, that gives us a decent range. It all started when I asked one of my young colleagues, a Japanese lad who likes his food, where I could get good Dim Sum. So he took me here...

... the Harbour City Restaurant on Gerrard Street. And very good the Dim Sum was too. I didn't get too adventurous, just up to Shark's Fin, but at least I now know what the fuss is about. This was after he had insisted I stop going to Itsu for my sushi and go to Yoshino on Shaftesbury Avenue instead...

They have a huge range, much wider than the Itsu's and Yo Sushi's, and it is half the price. It's not as homogenised as Itsu, but it is a lot tastier and way, way better than Pret. There's only one Yoshino though.

In return I mentioned this place that I read about in the excellent Londonicous blog...

... and immediately he said "you must try the bibimbab" to which I said "that's exactly what I want to do". So we gathered together the lads and off we went. And very filling and tasty it was too. The last one was suggested by one of the new starters last week, a Chinese lady who when asked for a good Chinese said with no hesitation that we should go here...

and so we did. Most of us had Dim Sum - and I tried a bit of Chicken Foot (it's cold, no-one told me it would be cold) - and one slightly more cautious young lady stuck with a chicken with vegetables. Again, all good. The real point is to get good advice: there are many indifferent restaurants on Gerrard Street. So I'm looking forward to what recommendations for an Indian our recent Indian recruit has. No Brick Lane (which is Pakistani / Bangladeshi anyway).

The Four Ways to Spend Money + One More

I ran across this on the 37Signals blog. It's a Milton Friedman thing:

You can spend your own money on yourself. When you do that, why then you really watch out what you’re doing, and you try to get the most for your money.

You can spend your own money on somebody else. For example, I buy a birthday present for someone.
Well, then I’m not so careful about the content of the present, but I’m very careful about the cost.

I can spend somebody else’s money on myself. And if I spend somebody else’s money on myself, then I’m sure going to have a good lunch!

I can spend somebody else’s money on somebody else. And if I spend somebody else’s money on somebody else, I’m not concerned about how much it is, and I’m not concerned about what I get.

Actually he left out a fifth, but then he didn't know about outsourcing companies:

You can spend the client's money on them. When you do that, you spend as little as possible to keep the profits high, and you don't care what the client gets.

If Not Magic, Then Why?

There are many things decent people don't want to be made to think about and the sex life of people over about forty-five is pretty close to the proverbial one about how sausages get made. So since that's what I'm going to talk about, you may want to move right along now.

I'm not exactly sure when my libido decided to go to sleep, but it did. How do I know this? Because when I look at pretty girls or attractive women these days I never experience that urge to action, or the pain that comes when you know you're going to let another one get away. Everything still works. It's just that I don't get as motivated anymore.

Well, I am fifty-five and I do have grey hair and my face has got a little soft in the way that mens' faces do when the testosterone level drops. I look better for my age than most women my age do - I look better for my age than the majority of men ten years younger do for their age - but I don't think I look attractive to women any more. At least not the women I'd like to look attractive to. Some of it is about confidence.

Some of it is about having been in a long-term-relationship in which, for one reason or another, we never quite got round to having sex anymore, and even stopped sleeping together because my snoring was getting too loud. I had operations for the snoring but it made not enough difference. My girlfriend started getting self-conscious about her appearance - she wasn't svelte as she was when we started going out - and what with the work situation - one or other of us was always worried that we were about to lose our job, or I was out of work, or we were having hell with our bosses - the sex just vanished. I think it was when she bought a new single bed for her place  - we never lived together - that I started trying not to see the writing on the wall.

I look at pretty girls and attractive women and I see things like "high-maintenance", "married", "looking for a husband", "too much energy for me to keep up", "um, I would be twenty years too old for her", "bonkers", "needy", "looking to be paid for", "late thirties and no ring? Lezzy or damaged?", and so on. See what's happening? I'm seeing the downside straightaway. I've forgotten there's an upside.

That upside isn't sex, by the way. I was always better at that than my partners were and there was only ever one I could make love with and know I was going to finish in a satisfactory way. Making love otherwise was a lot more inconclusive. So maybe I've lost motivation: why would I chase after something that actually isn't that satisfying and maybe never was? Or maybe there's nothing like a long-term-relationship that fizzles out over a long time to disabuse a guy of the one thing he's got to believe to make the whole thing worthwhile: that women are magic.

I know, how romantic (dumb) is that? But if women aren't magic, then the whole thing is about economics: how much time and money do you invest chasing after her and what do you get in return? Remember, it's not me who has the fun in the sack - it's mostly her. So if women aren't magic, they are just work.

Or friends. But that's not what we're talking about here.