The oddity explained.

I've continued to get odd emails from sybil.cumae. I've worked out where the name comes from (By the power of google!!). It seems that there was a mythical oracle called the Cumaean sibyl, about whom there are various legends. I guess this is a sidelong claim that the content of the emails is true. This isn't my only discovery, though. In fact, I now reckon I know what's going on, as I'll explain in a minute.

Although the emails are starting to get a little longer, they are still terse by comparison with other emails. I've started to enjoy getting them; it's fun to check the random odd facts, which are beginning to be a little more interesting, and introduce me to areas I wasn't aware of. A disproportionate number deal with mathematical facts, though, and I think I've finally found one email which is in error:

Date: Tue, 28 Oct 2008 09:59:25 +0000
From: sybil.cumae@googlemail.com
To: sfwc@hotmail.com
Subject: I thought you might want to know...

Any even integer greater than 2 is a sum of two primes.

This is, of course, the Goldbach conjecture. The reason it is called a conjecture is that, although it is widely believed to be true, nobody knows of any way to prove it. I guess whoever is researching the facts in the emails didn't do their homework properly.

However, the content of the email that has finally cleared up this whole mess was as follows:

The winning numbers in the UK national lottery lotto game on Saturday 1st November 2008 will be 18, 19, 25, 30, 33 and 43.

Of course, there is only one way to reliably predict such things in advance: The emails I've been getting are part of an elaborate 'football picks' scam. The way that this usually works is that letters or emails are sent out to (initially huge numbers of) victims with betting tips about who will win particular football matches. For each match, about half of the victims are told that each team will win. Of course, this means that a lot of incorrect predictions are made. Any victim to whom an incorrect prediction has been sent will be abandoned. Eventually, there will be a very small number of victims left, for each of whom all of the predictions so far have been correct.

All that any of these victims are aware of is the sequence of correct predictions which has been sent to them. So they think that the tipsters are giving sound advice. Playing on this mistake, the tipster contacts these victims offering to give further tips in return for a fee, now that their expertise has been 'demonstrated'. The victims pay the fee hoping to win their money back by gambling on the basis of the tips they are given. The tipster, no longer caring whether the victims win or lose, disappears with the fee. Something of this kind was the basis for Derren Brown's 'the System'.

This scam has now become rather well known, (even referenced in 'the Simpsons'), so that running it in this iterative way has become impractical. Accordingly, the scammers who are sending me these emails have modified it to make it less recognisable in at least three ways:

• Numerous other, easy to obtain, facts are also sent. This encourages the user (me) to check those facts, and to imagine that that whoever is sending them has researched all of them. This subtly hides the fact that the final 'fact' is not researched at all.
• All the eggs are put in one basket: Only one prediction (of lottery results) is made, but the prediction is improbable enough to be highly convincing. This removes the repeated predictions which are a giveaway for the usual scam.
• I'm not completely certain about this last point, but it is rather likely. The chances of winning the lottery are about 1 in 14 million, and there are only 60 million people in the UK, so normally to pull this off the scammers would have to email about one person in four. Nobody I've spoken to is getting similar emails, so I think it is very unlikely that they have done so. Instead, my guess is that they have covered the numbers they didn't send by placing a bet on the results of this weeks lottery draw betting that none of their predictions were right.

I've worked out the numbers for this last point and I reckon it could be done. For example, they may have placed a bet of £100,000 that none of the numbers will be 25, thus reducing the number of people they must email to about 1.7 million, which is a much more manageable number (I'd guess about double this number were emailed to give the system some slack). If none of the numbers are 25, then they win their bet and so make a profit of about £14,000. Otherwise, they have lost £100,000 which they must recoup from somebody they have emailed. But one or two of the victims believe that they can predict lottery numbers (and may even have won) and will now be squeezed in the hopes of recouping the lost £100,000 together with a large profit. The money involved here is not precise: It can be scaled up or down depending on the resources available to the scammers and how much they think they can practically squeeze out of the victims.

Needless to say, I haven't bought a ticket.

To swallow meditation...

Over the summer, I regularly attended a meditation class run by the Cambridge Buddhist Centre. Unfortunately, it clashes with the category theory seminars so I've had to stop. Each class lasted about an hour, and consisted of a short introductory talk (to let complete newcomers like me know what we would do) followed by about half an hour of meditation. The meditation was of two kinds: The 'mindfulness of breathing', in which we tried to be completely aware of our breathing, and the 'development of loving-kindness' in which we pictured a variety of people and tried to feel love for them.

These practices came out of a Buddhist tradition (the good folk at the Buddhist Centre claim that they were developed by the Buddha himself, but it doesn't really matter either way). In order to explain a bit about what they are about, I shall show my complete ignorance of Buddhism by talking about it a little. The first surprising thing about Buddhism is its diversity. The first big split seems to have come a few centuries after the death of the Buddha, when the Mahayana school split off. When Buddhism (mostly Mahayana, as far as I can tell) spread across Asia it mutated and incorporated local traditions and pantheons wherever it went, getting mixed up with Taoism and Bon and producing anything from the paradoxical Zen to the flamboyant Tibetan style. Each of these schools, and the many others, are further subdivided, in a way reminiscent of protestant denominational fertility gone wild.

I've followed this trend by producing my own slant on what the Buddha (or at least those who came up with the words attributed to him) was on about. What follows is by no means orthodox Buddhism of any kind, though the ideas it is based on mostly come from the Theravada school. Think of it as an improvisation in a Buddhist key.

As human beings, we are subject to persistent and pervasive delusion. One of the nastier aspects of this is that it is built into the way that we think, reason and communicate so that any attempt to deal with it is liable to suck us further into the quicksand. Here are several specific areas where we are deluded:

• When we use language, we divide the world up into neat conceptual chunks. We'll see a building as a single entity, distinct from the rest of the world. This distinction is sensible, but it isn't as precise as we habitually assume. There are gaping grey areas. Is the furniture part of the building? What about the built-in furniture? The paint on the walls? The pictures on the walls? The hooks holding them up? The water pipes? The water? The limescale? The wiring? The light bulbs? The walls? The curtains? The windows? The holes in the walls in which the windows are placed? Some things (like the bricks in the walls) are a relatively stable part of the structure and change only rarely. Others (like the newspaper on the table) are replaced much more often and we don't count them as part of the building. In between it isn't so clear.
  
  In a sense, there's nothing wrong with this world-chunking: To an excellent approximation our environment can be divided up in this way. The division itself is no more of an illusion than is Newtonian physics; both are great approximations (though quantum theory suggests that the ladder of approximations never bottoms out in precision: The world is radically and ineradicably approximate). The illusion comes in when we forget that that is all that is going on, and see the divisions as precise rather than approximate. We imagine, for example, that there is some kind of clearly delineated 'substance' of the building, to which the various parts stand in some clear relation. We even conceptualise entities with no sensible physical correlate, such as rainbows, in this simplistic way.
  
  
• The first problem is particularly serious for the way that we see ourselves. First, we are especially prone to seeing ourselves as simple coherent wholes, and to seeing our chunking of ourselves off from the rest of the world as exact. This is made all the worse by the fact that this approximation is much less sensible than many of the others that we make. I've discussed one aspect of this in a previous post. Essentially, the idea that 'me, right now' and 'me in a few years' correspond to different instances of the same self is no more than a useful convention.
  
  I must pause at this point to explain why this ambiguity of the self unifies the idea of reincarnation with the golden rule. The trouble with the idea of reincarnation, as with many hypotheses about life after death, is that we typically identify beings by the continuity in time of the bodies to which they are associated. The death and decomposition of the body prevent such identifications being made, so identifications of newly born beings with past dead beings seems arbitrary and unjustified. On the other hand, we have a habit of identifying various beings with the beings associated to the same bodies at slightly later times, or after a good night's sleep. There is a strand of Buddhist thought which emphasizes the arbitrariness of this by talking about life as a process of continual reincarnation, with every moment seen as a small death and rebirth, sleep seen as a more emphatic instance of the same, and death itself as a qualitatively similar process.
  
  This has moral implications. I've discussed morality already here, and this comment is an expansion on the third paragraph from the bottom. We have clear moral beliefs related to our own benefit; for example that pain is bad. In fact, these beliefs are mostly related not to ourselves as beings now, but to ourselves in the future: The beings that will in the future be associated to our bodies. But the identification of these beings as special is pure convention, and singling them out for special moral attention is so arbitrary that the conscience rebels against it. I've heard Buddhists argue that I should treat other beings ethically because (modulo reincarnation) they may be, for example, my mother. The perspective I have outlined is even more radical. I should love my neighbour as myself because (modulo a useful convention) they are myself.
  
  
• Closely related to the above two problems is the way that we think about the words we use. We imagine that each word captures a clearly definable concept with some correlate in the world. A major activity in philosophy is exploring to what extent this is true. Alarmingly, many of the words we use (such as 'self', 'be', 'know', and so forth) don't have sensible definitions corresponding to the way that we naturally use them. This hasn't stopped some from mistakenly trying to find out what, for example, knowledge 'really is'. I'm told that pointing out and avoiding such mistakes was a big part of what Wittgenstein was doing later in his life, but this may be just a rumour; I've never checked.
  
  
• Very often we find that the world is not as we wish it to be. Such problems are exacerbated by our habit of fooling ourselves into thinking that the world could be other than, in fact, it is. For example, if I break my arm, then I am likely to find myself imagining a world in which my arm is suddenly no longer broken as if it were possible, when it is not. Most of our desires (not all: Hunger and thirst are almost always free of this) are of this illusory form; when we desire a thing we imagine a world in which we possess that thing without undergoing the sacrifice necessary for that possession (if it is even possible).
  
  
• Sometimes we desire the world to be different in a way that we can legitimately bring about. For example, you may want to own a TV, and be able to afford one. Even in these circumstances, however, our desires often fool us by presenting as possible a world in which we obtain the desired in an ideal way. You may ignore the fact that the television will break down soon enough, or that the image will jump when old motorbikes pass your house, or that the television will bring disappointment through expectation of programmes which you miss or which are over-hyped. When we desire a thing we imagine a world in which we possess that thing without the inconveniences (both trivial and serious) that follow from the nature of that thing.
  
  
• We have the same blinkered attitude to the things that we already have and take joy in. We can not recognise without effort that they are transitory: Gone before you can say 'where moth and rust doth corrupt'. It is hard to enjoy a thing without imagining a world in which that thing is enduring and innocent of the inconveniences (both trivial and serious) that follow from the nature of that thing. There's a neat story illustrating a good attitude here: A man had a beautiful glass which he would often drink from. One of his friends asked him 'aren't you worried that if you use that glass all the time you will break it?'. Holding the glass up so that the light sparked intricately through it, the man replied 'I know that it is already broken. That is why I make such use of it.'
  
  
• This mistake is also particularly serious for the way that we see ourselves and those we love. We do not recognise that we are transitory. Tomorrow we will not be the same as today, and the pleasure we have now will have passed. In a year or two we may be embarrassed by who we were, just as now we would be embarrassed at who we will become. As we grow older, our bodies and minds will gradually break down, until sooner or later they fail catastrophically in death. After that, we will be inaccessible to all who seek us. Those who love us will be left with small reminders of us which mock them with false hope. It is painful even to consider these things, and we typically simply ignore them. This cocoons us from seeing how precious our passing bounties are and multiplies our grief when they are inevitably lost.

These are just a few of the veins of illusion running through our minds. Even in talking about them I've had to use words and concepts, which introduce their own mirages. This all seems pretty hopeless and gloomy. However, the Buddha was extraordinarily optimistic about our ability to overcome all of this.

He claimed that it is possible to become free of all of this illusion, and to see the world as it is. So, for example, we would not see ourselves as simple unified souls, or distinguish ourselves fundamentally from other people. We would go beyond words by not attributing to them any power to divide up the world. Since the delusions we suffer are so fundamentally part of us, and form much of the way we conceptualise ourselves, this freeing can be thought of as a kind of loss of self, like the blowing out of a candle: An unlightenment, if you will. On the other hand, since much of what would be lost is associated to the 'autopilot' systems in our brains which guide us unthinkingly through daily life, there is also a strand of thought which sees this as a kind of awakening.

He also made some particular claims about the way to achieve this unlightenment, all of which were thoroughly practical. Over the years, Buddhists have come to think of this Way in sufficiently exalted terms to merit a capital W. Much of the Way consists in a particular style of living, modelled on how a person would live if they were unlightened. Much of this corresponds to sensible ethical teaching. Other bits of the Way concern meditation, and in particular meditation of the two kinds mentioned above.

The first good reason to do the 'mindfulness of breathing' meditation is that it is a simple context in which to attempt mindfulness; that is, a direct awareness of how a thing is without use of the usual mental filters and shortcuts. The breath is so comparatively simple and regular that it is a good place to start in attempting to see things as they really are. The second good reason comes from one of the direct effects of making such an attempt: Namely that you fail, and fail in a particular way. The mind becomes distracted, and thoughts of unrelated matters slip in unnoticed. Observing this process allows you to see how busy the mind is, and (to a small extent) in what its activity consists. Not only does this allow you to see how automatically illusory thought patterns are produced, it also reveals how inadequate our ideas of the self as simple and continuing are. Hume put it very well:

For my part, when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never can observe any thing but the perception. When my perceptions are removed for any time, as by sound sleep, so long am I insensible of myself, and may truly be said not to exist. And were all my perceptions removed by death, and could I neither think, nor feel, nor see, nor love, nor hate, after the dissolution of my body, I should be entirely annihilated, nor do I conceive what is further requisite to make me a perfect nonentity. If any one, upon serious and unprejudiced reflection, thinks he has a different notion of himself, I must confess I can reason no longer with him. All I can allow him is, that he may be in the right as well as I, and that we are essentially different in this particular. He may, perhaps, perceive something simple and continued, which he calls himself; though I am certain there is no such principle in me.

The second kind of meditation is aimed at dealing particularly with the issues mentioned after the second bullet point above. The first part of the meditation (once you have settled down and relaxed) consists in regarding yourself, and exploring how it is that you love yourself. Then various other people are brought to mind (a friend, a passer-by and an enemy) in turn, and for each person you take the time to recognise that they are a person in the same way as you are, and explore how this allows you to love each of them in the same way. Finally, you regard all of these people together, and try to equalise up the love that you feel for them (and, of course, yourself) which of course involves seeing the distinctions between these various beings for the conventions that they are. This second meditation is therefore aimed at a particular illusion only, but one which there are strong ethical reasons for overcoming.

That is the theory, at least. Do these practices work? That is, do they lead people towards unlightenment (and, along the way, love of neighbour)? I don't know. The theory sounds plausible but so do many false theories. Tests so far have established that there is something going on (that is, meditation involves real structural mental change), but as far as I know they have not shown that these changes are as claimed. Since the claims seem perfectly testable, however, I'd be very much in favour of tests exploring whether meditation does what it says on the tin, and whether any other strategies are equally or even more effective.

An oddity.

I've been getting some very odd emails, which I can't really explain. Here's a typical example:

Date: Mon, 13 Oct 2008 11:52:04 +0100
From: sybil.cumae@googlemail.com
To: sfwc@hotmail.com
Subject: I thought you might want to know...

Alaska is the largest state in the USA.

Others (from the same address and with the same subject line) have had similarly terse content:

• The 500th digit of pi after the decimal point is 2.
• The reciprocal of the fine structure constant is about 137.036
• Gray whales migrate at an average speed of 3 mph.
• King George III of the United Kingdom died on a Saturday.

I've checked these statements (wikipedia is my friend) and they all seem to be accurate. I can't see anything else they have in common. And I have no idea why anyone would send them to me. I don't know anyone called anything like Sybil Cumae. They don't have any kind of attachments that could be harbouring viruses. I've tried telling hotmail that messages from sybil.cumae@googlemail.com are junk, but it still puts them in my inbox. I'm beginning to suspect that this is some kind of viral marketing thing for a microsoft product, but I haven't heard of anyone else getting similar emails and I can't find any reference to it online.

I'm stumped.

Strange loops 'R' Us

I got a heap of books for my birthday, which I want to get my thinking straight on. So I'll be writing about them here. The first to arrive was a book by Douglas Hofstadter (of 'Gödel, Escher, Bach' fame) called 'I am a strange loop'. In this book, Hofstadter revisits his previous musings on selves, souls and strange loops.

The jumping-off point is a paradox. Careful examination of the brains of human beings has shown no violations of the laws of physics, and all the physical evidence we have points to the idea that the matter of which we are formed follows the same rules as all the other matter we come across. So it looks like we could, in principle, explain all the behaviour of any given person in standard physical terms. So, for example, the answer to the question 'why is this person angry' would be 'well, you see, these various atoms are banging about in such-and-such a way'.

But an odd thing happens; our explanations very often go the other way. We ask 'why is it that this collection of atoms is moving about in such-and-such a way?', and reply 'well, because this person is angry/sad/happy/thankful'. The explanation here looks like it is going the wrong way; the lower levels (in a reductionist sense) are being explained in terms of the higher.

Hofstadter summarises this paradoxical aspect of our selves by saying that we are 'strange loops'. The loopiness is clear; our thoughts can be explained in terms of physical events, and physical events can be explained in terms of thoughts. It is this second kind of explanation which makes the loop strange; it goes the wrong way - events at a lower level are explained in terms of those at a higher level.

As an analogy, he points to the proof of Gödel's theorem. In this proof, a statement G of number theory is concocted which cannot be proved or disproved. The (lower level) fact that G cannot be proved is explained in terms of higher-level properties relating to a subtle scheme for coding statements of number theory as numbers. Here, too, the explanation seems to go the wrong way.

Hofstadter goes no further than this in defining just what a strange loop is, and he certainly does not give a precise definition. Instead, the idea serves as a powerful analogy bringing out an aspect of the strangeness we often overlook in our all-too-familiar selves. The puzzle has been sitting under our noses for a long time, and there have been many proposed resolutions.

For example, it has been proposed that it is impossible in principle to reduce the soul to the usual behaviour of matter. Instead, our souls are made up of a different, more ethereal stuff which interacts with the matter in our brains in a deeply mysterious way. This removes the strangeness and sees our consciousness as involved in a much more mundane causal loop.

The trouble with this proposal is that if it is right we ought to see some violation of the laws of physics happening inside people's brains. The fact that we see no such thing has led to the suggestion that the link may not be causal; that the matter may in fact be carrying on in the usual way of matter and yet still have a mysterious 'self', made of spirit-stuff, associated to it. The trouble with this idea that the soul doesn't affect the body is brought out in a beautiful though experiment by Raymond Smullyan.

Another proposal is that there is no such thing as a soul; that such things as minds, ideas, consciousness etc. are pure illusions, and there is really nothing but physical stuff. Now, given how obvious it is that we are, for example, conscious beings, it is hard to argue for the idea that this is just an illusion. The main argument presented here is that, after careful investigation, we have not found the soul anywhere. But things need not be localised to particular collections of matter in order to exist. Think of the colour red, for example.

Another argument sometimes given here is as follows: Carefully examine the many things you associate with yourself. You find that your body is not yourself. Nor is any particular thought or feeling or sensation. In fact, close introspection reveals that in our multitudinous mental life there is not one simple thing we can point to and cry 'There it is: The self!'. The absurdity of this argument can be seen by applying it to chairs. Examine a chair closely, and study its parts. The legs are not the chair. The flat surface for sitting on is not a chair, and nor is the back. In fact, close examination shows that no simple part of the chair is the chair itself. Are we forced to conclude that there are no such things as chairs?

The option I think is correct works like this: We can (in principle) describe a person in terms of the physical stuff of which they are formed (though such descriptions are likely to be tedious). We could alternatively describe them in terms of their personality, and of what they are thinking and feeling. These are just two different descriptions of the same thing, with the second description much more useful to us because of its coarser grain. Anger does not cause the mental processes we associate with it, nor is it caused by them. They are two descriptions of the same process. The explanation of each in terms of the other is not causal; it is a matter of translation.

A helpful analogy is that of temperature and pressure. We can (in principle) describe a gas by specifying just where all the particles are and how fast they are moving (though such descriptions are likely to be tedious). We could alternatively describe it in terms of its temperature and pressure. Once more, these are just two different descriptions of the same thing, with the second description much more useful to us because of its coarser grain. The temperature does not cause the particles to move at the speeds they do; it is a redescription.

Scientifically, we have a pretty good idea of what temperature and pressure mean in terms of the behaviour of atoms. At one time, though, there was no understanding of what temperature and pressure meant in terms of more basic physics. We are in a similar position today with regard to the soul. This does not mean that there are no such things as souls, any more than their ignorance meant that, for those long-gone scientists, there was no such thing as pressure.

This gives a useful perspective on the second resolution. It may be that, one day, we will understand that some of the vocabulary we use to talk about ourselves (such as the word 'ourselves') is misleading, and reject it, just as the theory of phlogiston was rejected. At that time we will be able to say with confidence that the notions we reject are illusions. We are currently very far from that stage: We may never reach it, and almost certainly won't in my lifetime. For the forseeable future, we won't not know what is illusory and what isn't.

Hofstadter's next point is that our idea of the soul is a little blurred around the edges (just as all our ideas are). For example, each person has models in their own head of the other people they know well. For people in strong relationships these models can become intertwined in feedback loops with the self-models of the other people (Hofstadter repeatedly confuses these self-models with the selves themselves). Accordingly, it isn't possible to completely localise a person within their own head.

The punchline is that, when a person's body dies, the person lives on to a small extent in the heads of those who loved that person. The trouble is that the extent to which the person lives on is negligible by comparison to what is lost. It is analogous to the extent to which the person lives on via the atoms from their body which have been incorporated into other living organisms. When a person dies, the loss to us is irreparable and complete. This is why we grieve so strongly, and why we reach out for comfort in the smallest scrap of hope that the person still, in some sense, lives on.

Swift meditation.

In ten or twenty years, when the person I have become reads this blog, I have no doubt that he will be shocked and outraged that he could be associated with a person like me. I feel the same way when I read the brief diary I kept on a short trip I and some friends took to Bolivia just after our GCSEs. We spent most of the time touring the diverse and spectacular landscape, from salt plains to rainforest, by boat, bus, plane and on foot.

The trip had two large impacts on my life; first, it helped me recognise in a small way how the same humanity I see in myself and those I know well is also found, radically transformed, in other cultural settings, and how the simple joys of life do not rely on the material securities in which we often ground them. Second, and more mundanely, to get fit in readiness for the high altitudes, I began to run. Running has now expanded to become an integral part of my life, and it is this much easier topic that I'll talk about here.

When I first started, I could barely keep going for 2 minutes together, even at a jog. I've been steadily improving since then and I'm pleased that I haven't yet reached my limit. I now normally run 3 times a week, for about an hour, on a variety of routes. I only occasionally run competitively, and though I'm encouraged by my clear improvements I'm still nowhere near the front of the pack.

I run, in increasing order of importance;

• To keep fit. As ways of staying fit go, running is simple, flexible and cheap.
• For the beauty. This consists not just in the magic of the landscape but the freshly-patterned sky set free from the buildings which cage it in in the town.
• To get away. When I'm running, I can't worry about work or life, and I don't have to.
  
• For the buzz. As ways of getting high go, running is simple, flexible and cheap.
• For the willpower. By experimenting in this toy setting, I've learned how to 'force my heart and nerve and sinew to serve their turn long after they are gone'.
  

A final aspect of running raises an odd moral problem. When I run, I'm often in pain. This is my body's way of saying it wants to slow down. So I lie to myself, saying that the pain is unrelated to the running, and would carry on in any case. This barefaced lie is enough to fool the system in my brain which otherwise would override my desire to keep going and bring me to a wheezing halt. I'm not too worried by this; I think the bit of myself that I'm fooling is non-conscious and so I have no obligations to deal honestly with it.

Where, though, is the line to be drawn? How deeply can I delude myself without hypocrisy? Do I have an obligation to correct my natural tendencies to fool myself (for example, about how likely a marriage is to last for life)? I don't know. As with other moral issues, I err on the side of caution, and of doing no harm. What I do to myself when I run is about as far as I'd be prepared to go.

A multitude of books distracts the mind.

Books: The crack cocaine of the literate classes.

This (stolen) quip captures with uncanny precision the way I relate to agglomerations of written words. I read compulsively and obsessively, to relax and to work, to exercise my mind and soul and to calm them. I'm currently partway through reading 5 books:

Sheaves in geometry and logic - Saunders MacLane and Ieke Moerdijk
The audacity of hope - Barack Obama
Surprised by hope - Tom Wright
Ethics - Baruch Spinoza
Conceptual foundations of quantum mechanics - Bernard D'Espagnat

This typical collection of books, together with the various papers and websites I'm reading my way through, takes a significant chunk of each day, but it is time I delight to give. The words I read connect me to people far removed in time and in space. When writing, they were able to carefully compose expositions of insights of a depth that we are too impatient to plumb in everyday conversation. By their radically different assumptions, they implicitly challenge the concepts that form the comfortable furniture of my worldview, undermining ideas that are so familiar they seem inevitable.

As I type this, I am sitting within 200 metres of one of the largest collections of books in the United Kingdom; the Cambridge University library. I find the thought of the shelves and shelves of books (over 5 million in all), most of which are filled with ideas and thoughts which will never have the chance to change me, impossible to capture. The simple awareness of it sucks away my mind like a sky filled with stars.

Of the many books I have read in the last few months, one stands out: 'The Road to Reality' by Roger Penrose. Penrose explains experimentally-based physics as it stands today, first laying the necessary mathematical foundations then swiftly assembling a structure which only just has sufficient rigidity to reach into the cloudy obscurity of general relativity and quantum field theory. Along the way he repeatedly points out subtle but illuminating perspectives on complex ideas. I was repeatedly left kicking myself over bits of mathematics that I thought I knew: 'Why did I never look at it like that? It's so obvious'. If you can get your hands on this book, and are prepared to fight to get through it, then you must read it.

I currently have a small stash of books sent to me by my relatives for my birthday, sitting in a knee-high pile on the floor of my room. I'll write a bit more about each of them here as I read them.

Long time, no say.

Since I've hardly posted anything here since before the summer holiday, I'll give a summary of some of the stuff I got up to.

First, I went with some fellow category theorists to Calais, for a conference. This was a really great experience. I was pleased to find that I could (with a little effort) follow most of the talks, and reconstruct those that I hadn't followed at the time. The range of topics was extraordinary, and all were extremely interesting. The main problem I had was with seeing the motivation of some of the talks; the speakers were addressing problems which had arisen slightly before I got involved and which I hadn't come across.

The other great thing about this conference was the opportunity to get to know some of the other students in the category theory community. Some were friends with whom I'd lost touch, others were completely new. It was good to spend time with people who care about the same mathematical issues. I can't wait until this conference rolls around again. Excitingly, there will also be a major category theory conference in Cambridge next year, in honour of Peter Johnstone and Martin Hyland.

Shortly after this, I visited Wales with some friends. We stayed in a youth hostel, and went on several enjoyable walks. The scenery was beautiful, and the weather mostly stayed fine, though we did get lost in the mist at one point, where the path disappeared. Thankfully, the land was sufficiently bumpy that we were able to find our way by navigating by the contours.

From there I went on to join the trinity lake hunt. This is a glorified game of tag over an area of a few square miles in the heart of the lake district. A few runners, designated 'hares', are given hunting horns and a half-hour head start. They have to blow the horns every couple of minutes and try to avoid getting caught by the 'hounds', that is, everyone else. Since I was only able to be there for a couple of days, I was made a hare: An exhilerating experience.

Finally, after a little time at home, my family and I spent 2 weeks in Scotland (my brother was only able to make the second week). We spent our time on gentle walks through the beautiful and diverse landscape, with some pauses to admire the birdlife and other wildlife. We saw a glut of eagles on Mull and were particularly thrilled by a close-up sighting of red-throated divers fishing in the sea.

Since then I've been in Cambridge, working on my PhD and amusing myself in between times with various other activities, which I'll discuss in the next couple of posts.