I can’t be bothered to carry a camera around with me wherever I go, but my mobile phone camera produces pretty shitty images, especially in low light levels. Here’s an example of my living room with normal indoor lights:

You can probably see the noisy image at this reduced size, but if we zoom into the full resolution it gets much worse. Take a look at the teapot:

A couple of days ago it struck me that it ought to be possible, in principle, to take multiple photos of the same scene and have some software align them as best as possible, do some sort of averaging process and eliminate the noise. I’d heard about high dynamic range imaging (HDRI) before and it seemed like the sort of software techniques you’d need for that would be similar to the problem I’m set myself. And sure enough, they are, and it turns out Adobe Photoshop CS3 has some tools for this built in. So what I did was to take 13 pictures from the same place, each one with a different brightness level (to try to capture details at all the different light levels), and merge them together using Photoshop’s “Merge to HDR” tool. Once the image is merged into HDR, you show it to someone on a standard dynamic range monitor (i.e. everyone), you need to convert it to a normal dynamic range image, and there are various ways to do this. I just tried Photoshop’s default setting, and it’s “highlight compression” setting, and here are the results:

As you can probably see, the detail is much clearer and there’s much less noise. This is even clearer on a close up, take a look at the teapot in the new version:

Impressive!

If you have Photoshop, it’s only a matter of a few minutes to load these pictures in to do this, and there may well be free software out there that does the same thing. The biggest problem with this way of getting decent pictures out of a mobile phone camera is that you have to take the same picture from roughly the same angle lots of times. Sometimes you can do this, but sometimes it’s a bit more difficult. Fortunately, my phone has a ‘burst mode’, which takes 4 pictures in very quick succession. It’s still not going to be any good for a scene with moving objects in it (because they will just blur), but it takes the hassle out of taking the same picture over and over.

Anyway, for future food and cake pictures on this blog (always taken with my phone because I don’t own a camera), expect the quality to be much better now that I know about this HDR technique.

Does anyone else have any tips for getting the best out of a mobile phone camera? Mine’s a Sony Ericsson K750i incidentally. And just to finish up with, here’s a gallery including the full 1600×1200ish photos so you can look at the detail close up.

Update. I just added three new pics to the gallery, two of books and tea where I took 16 images all at the same brightness level and merged them to HDR, and another one of the living room but with different and slightly more natural looking colours.

Recently I wrote a post that provoked much disagreement, claiming that almost nobody believes in God. On further reflection, I think I can make a clearer statement (although with a less punchy headline sadly). A less divisive way of putting it might be, what should we make of statements like

He believes X but acts as if he doesn’t,

and

He believes X but doesn’t act consistently with those beliefs.

These are quite curious statements, especially the first. I find these statements interesting because I want to try to interpret them as a Pragmatist. Briefly, a Pragmatist tries to only talk about things to the extent that they have real world consequences, and tries to give things meaning relative to those consequences. From this point of view, if we take the first statement as accurate, then we have a real problem. The first clause says that he believes X, but the second denies any connection between X and his actions. To define a pragmatic (I’ll use small p from here on) conception of ‘belief’ would mean defining it in terms of its consequences, but the statement says there are none.

This might seem like a fairly irrelevant problem, but I think it’s more significant than it seems because people make statements like this all the time. I’ll illustrate with three examples:

1. The “champagne socialist” claims to believe in an ideal of equality, but acts to get as much as he can for himself.
2. The theist who regularly sins and just generally doesn’t seem to pay anything more than lip service to his faith.
3. The drug addict, can see clearly that his habit will kill him but keeps on doing it anyway.

The first two seem problematic to me, and the third less so although it shares many similar features.

Now at this point I should say that you could easily disagree that these are problematic. For example, most people aren’t pragmatists and so wouldn’t see the difficulty in finding a pragmatic definition of belief to be a problem. For my part, I feel that something like pragmatism is inescapable - if we’re to make sense then what we talk about has to be grounded in experience. William James sometimes referred to pragmatism as “radical empiricism”, which seems appropriate.

In the entry I wrote about belief in God, I took a point of view which I think is roughly equivalent to what Dennett calls the Intentional Stance. Although I must say I haven’t read his book so I might be mistaken. As I understand it, the intentional stance says: hypothesise that an individual is acting rationally with respect to his beliefs and desires. We can’t know what the beliefs and desires are (they’re internal), but we can see the actions and from that attempt to infer what the beliefs and desires are. Even though we know that individuals are not rational, thinking about in this way might tell us something useful.

Because I’ve been making Powerpoint slides for presentations recently, I couldn’t help but turn this idea into one of those silly diagrams with boxes and arrows. In the diagram ‘internal model’ refers to the model of the world that an individual has, which is continually updated according to their experiences. The ‘plan’ box gets arrows from ‘goals’ and ‘internal model’ because it is a rational maximiser attempting to find actions which, at least in the individuals internal model of the world, would best fit its goals.

Model 1 - The intentional stance?

I think this way of looking at things can tell us a lot, but it has some difficulties with the example of the drug addict. Now the drug addict doesn’t appear to act as if he believes his habit will damage him, although he says he knows it will, wishes to stop, etc. His claims about what he claims to believe also seem fairly uncontroversial in some sense, and are entirely about real world things with real world consequences (unlike the case of belief in God). One response would be to say that his goals are different to what you might think: an addict has the overriding goal of getting high. The trouble with this is that for this to be right, the goals must have been changed by his previous actions. If the individual’s goals as well as his internal model can be changed, then it becomes a lot more difficult to infer anything about the goals or beliefs from the actions. In particular, what is to stop us saying that everyone’s ‘goal’ is to do the actions that they actually do? This fits with the intentional stance but tells us next to nothing. I think I know what the response to this criticism would be: that that would be to multiply the number of ‘goals’ unnecessarily (one for each action). Fair enough, but it does point to a genuine problem with that theory I think.

In the case of addiction, we actually have quite a good scientific theory as to what happens. Taking addictive drugs releases chemicals into the brain which mess up the reward signals that our brain uses as part of its decision making process. It shouldn’t be a surprise that injecting chemicals into the part of us that makes decisions might mess up that process. Now should this be described as messing with our goals and desires, or as messing with our rationality?

Returning to the first two examples of the champagne socialist and the sinning theist, I think most people would say that they really do believe what they say they believe, but that those beliefs don’t directly determine the individual’s actions. This seems a reasonable point of view, but it needs some work to make it more precise. My first attempt is this boxes and arrows diagram:

Model 2 - The adviser to the king

In the top left we have a box with little boxes inside it. The large box represents in some sense the conscious part of this individual’s mind. He has a conscious model of the world, conscious goals, and from this he can formulate a conscious plan. However, in the larger scheme of things, these consciously determined plans don’t have the final say. There is also an unconscious scheme: an unconscious internal model of the world, unconscious goals, and a plan based on these unconscious elements in addition to the conscious ones. It is this unconscious bit that has the final say, and the results of actions taken feed back into both the conscious and unconscious internal models of the world. In this model, the conscious part is in some sense acting as an adviser to the real decision maker, the unconscious part. Relative to this scheme, we can say that the beliefs of the conscious part (the internal model inside the top left box) are that individual’s ‘beliefs’. This could explain why an individual could be capable of ‘believing’ one thing but acting in contradiction to that belief: the unconscious planner is just overriding the suggestions of the conscious adviser.

This model can also explain a lot. You could say that the conscious module at the top left is a sophisticated, rational reasoner, capable of using logic, deduction, etc., whereas the unconscious decision maker uses much cruder rule, something along the lines of: do what’s worked well in the past according to how much dopamine is sloshing around my brain afterwards. This would obviously explain the drug addict example where the unconscious decision maker is getting directly messed with chemically. It would also explain the sinning theist and champagne socialist: the unconscious decision maker with the real power has just realised that the high and mighty ideals of the conscious module don’t make it happy, whereas sex and champagne do.

So this scheme is nice, but it has a different set of problems. The first is that it is much more empirical than the intentional stance scheme. Who knows if this is how the brain really makes its decisions or not? Further neuroscientific research may tell us how we really make decisions, but wouldn’t we like to be able to say something meaningful without waiting for that (which may easily be many decades coming)? In general, ‘belief’ clearly relates to an internal state and therefore a definition of it would seem to have to relate to a model of human thought and behaviour. Or is there another neutral way of defining it? I haven’t got one. Any suggestions?

The second problem is more philosophical, and relates to how we use a term like belief. Suppose the model of decision making in the adviser model was accurate, does it make sense to say that the individual as a whole ‘believes’ what are really just the beliefs of one part of it? Or is this just overemphasising the conscious part of belief? Perhaps we need a new vocabulary of belief that makes this distinction clearer? Or perhaps we should just abandon the word entirely?

I propose that instead we always bear in mind the limit of applicability of a concept. Most concepts are useful when used in certain contexts, but break down at certain edge cases (like for example, the concept of ‘inside’ breaks down at a quantum level when objects can jump between positions without going through intermediate ones). From this point of view then, we could say that the concept ‘belief’ has some everyday uses, but that we should always have in mind the pragmatic limit of applicability. Things like belief in gravity or belief about some observable facts, which people act consistently with almost all of the time, could be still used unproblematically, but talk of belief in ideals or belief in God should raise alarm bells because we know that these beliefs will not inform us as to individuals actions. An alternative conclusion to my previous controversial entry would then be: belief in God is beyond the pragmatic limit of applicability of the concept ‘belief’.

OK, not nobody, but almost nobody.

To believe something, you have to act in a way that is consistent with the belief being true. Otherwise, you’re just saying that you believe it. If someone tells you that twiglets are highly toxic and will kill you instantly, at the same time as munching a bag full of them, you’re likely to doubt they really believe it. Same thing if they told you that it would lead you to an eternity of damnation. You wouldn’t trade in the brief pleasure of eating a bag of twiglets for an eternity of damnation if you really believed in it. But this is exactly the situation of people claiming to believe in God whilst simultaneously doing things all the time that are inconsistent with it being true. Anyone who believes in hell but sins anyway - they don’t really believe in hell. Someone who believes in the teaching of Jesus, but also thinks that capitalism is a great idea - doesn’t really believe in Jesus’ teachings at all. And so on.

Now at this point, a Catholic will come along and say: you don’t necessarily go to hell if you sin, as long as you repent afterwards. But… if you sin planning to ‘repent’ afterwards, that doesn’t count (so I’m told). Well, I bet quite a lot of that goes on if people were honest with themselves. It seems to me that if you really believed in God, you wouldn’t try to sneak stuff by on a technicality. If you have any respect for the concept at all, you’ve surely gotta believe that He is wise to that.

In fact, when a religious rule is inconvenient, it tends to be ignored, or the meaning of it changed. In a capitalist society, the stuff that is antithetical to the pursuit of wealth is ignored. In a liberal society, the stuff about stoning adulterers and homosexuals is ignored. Conversely, in an illiberal one the stuff about loving your neighbour and turning the other cheek is ignored.

When it comes to a clash between what religion says you should do, and what is convenient to do in real life, convenience wins out over religion almost every time. Or in other words, the reason that there are so many adulterous affairs is that people don’t give any credence to the idea that they will be eternally punished for it in the afterlife (no shag is good enough to warrant infinite and everlasting pain as a consequence, surely?). In practice they behave, quite sensibly, as if the notions of religion were false. And for these reasons, I think it’s fair to say that most people don’t believe in God.

The meaning of ‘belief’

I suppose to make my case a bit more convincing I need to say something about the meaning of the word ‘belief’. Three obvious possibilities come to my mind when trying to define what belief might mean, someone believes something if:

1. They say they believe it.
2. They act in a way that is consistent with it being true.
3. They are in some internal state correlative with the concept ‘belief’.

The twiglet example shows that (1) isn’t good enough, and it’s not clear that (3) has any meaning although it’s obviously compelling in some way. So for me, I have to go with (2), although I’d modify it slightly. I would say that to believe something is, roughly speaking, to act in accordance with a mental model of the world in which the proposition is true. I prefer this way of talking about it because it deals with the difficulty of defining what is or isn’t true (you can define truth or falsity of a proposition relative to a model without having to define it for the real world), and it gives a slightly more precise idea of what sorts of actions would count as consistent (i.e. those that are made by some decision-making procedure based on a mental model relative to which the proposition is true). This definition has its difficult points too, but I think it’s a helpful starting point at least.

In my experience of explaining this idea to people, there are various sticking points that stop people from agreeing that nobody believes in God. For starters, it seems kind of rude to suggest all these people are saying they believe in God but don’t really. Well, maybe that is rude, but is it any ruder than saying that one of their fundamental beliefs is wrong and that their view of the world is completely warped? I don’t think so, but even if it is that’s no reason not to say it. I think a more fundamental sticking point is that most people tend to have some sort of mixture of definitions (1) and (3) in their minds when asked about what belief means. If there is a mental state correlative to ‘belief’ - and introspection and intuition says there is - then surely the best person to report the status of that mental state is the person concerned. All very democratic, but people are often very bad at introspection and may themselves think that the fact that they are saying something without attempting to deceive means they believe it. The problem with that is: what about the unconscious?

The last sticking point is perhaps the most interesting of all, that in many ways it seems as though people do act in a way that is consistent with it being true. They go to church (some of them), they try to avoid sinning too much, they pray, etc. My response to this is that all of these actions are consequences of their believing that they believe, but not their actual believing. And I think that’s not a contradiction. The thing is, our mental models are disjointed fragmentary ones, not grand theories of everything. To get by in the world, we only need incomplete, heuristic models of situations that tend to recur. A mental model of the world in which we act as if we had a mental model of the world in which God exists doesn’t necessarily mean that we do indeed have a mental model of the world in which God exists. Mental models, and decision making procedures based on them, don’t have to be complete or accurate. They don’t need to be deductively complete or consistent, because most of the time we’re not capable of nor interested in making all the deductive conclusions possible from our different fragmentary mental models. In particular, our mental models of ourselves are often quite incredibly wrong. We think “In situation X I would do Y”, but then situation X happens and we do Z, the exact opposite of Y. It happens all the time. So it’s perfectly possible that we can believe that we believe in God, and consequently do all of the things we associate with a person who believes in God, but not actually believe in God (which would if we thought about it deeply enough, entail doing all sorts of things we wouldn’t actually do).

Dennett

With most ideas, someone has already had them before you (often Hume in my experience, the clever bugger), and this is no exception. I haven’t read much Dennett, but it appears he has covered some of the same ground. I’m told that he makes a distinction between belief and opinion that is somewhat akin to what I’m talking about here. I didn’t find anything directly about this (please post a link in the comments if you have a good one), but his article Do Animals Have Beliefs? has this interesting nugget which might have some relevance to the discussion of the three definitions of belief above:

There are independent, salient states which belief-talk ‘measures’ to a first approximation.

I also found this YouTube video of him saying that he doesn’t believe that believers really believe. It’s my first embedded video on this blog, too.

Seen on a street in Paris - anyone care to enlighten me as to what this might mean?

Democracy is one of those words that everybody uses but about which there is not a great deal of clarity as to what it means. The first ideas I can remember having of democracy were that it means a government elected by the people, or a government representing the will of the people. The first idea led me to declare that democracy was not a good thing, the second to declare that we do not live in a democracy (for various reasons to do with the biases and influences in our political process, and the impossibility of designing a perfect voting system). I no longer believe these. Instead, I now say that we do live in a democracy, that this is a very good thing, but that it means a lot less than many people think it does, and that we can do better.

For the past few years I’ve been considering an alternative view of democracy, which although it seems fairly obvious, doesn’t appear to be widely considered (Wikipedia’s article on democracy doesn’t mention anything like it anyway).

Democracy as elections, and democracy as government by the will of the people both have problems which relate to each other. The main problem with the democracy as elections theory is that it doesn’t explain why this should be a good thing. The most obvious response is that this process ought to result in a government that is representative of the electorate. Likewise, if you try to define democracy as meaning a system with governments that are representative of the people, you then have to explain how the system ensures that. Both of these views of democracy rely on the other, and they each have meaning only if they can be satisfactorily connected. Democracy as government by the will of the people is the intent, democracy as elections is the process used to try to ensure that.

It’s usually considered that you also need to have free and fair elections, secret ballots and a free press. It’s intuitively obvious at first glance that these things are all good ideas, and that not having them creates problems. The question is: does having them guarantee a representative government as a result? I know of no convincing argument that it does. Indeed, it misses out what I consider to be a fairly major additional requirement: that there is a certain level of equality of wealth and power in the society concerned. Even adding this in as another basic requirement for democracy, it’s not clear that this would guarantee a representative government. Maybe you also need a certain universal level of education and political awareness? How do you specify and guarantee that? You could go on and on.

There’s also the problem of what these requirements themselves mean. What is a free press for example? Is it just a press free from censorship? Or is there a requirement for a certain level of diversity? Can a press in a ruthlessly competitive free market, relying on advertising for most of its income be considered enough to satisfy the requirements of a democracy? Other questions you might need answers to are: what level of equality is required? What level of education and political awareness? Which form of voting system should we use (FPTP, PR, etc.)? This last question is related to perhaps the most fundamental question of all: what exactly is the will of the people? What does that even mean? These are all enormously complex questions, and without answers to them it’s not clear that we can say we know what democracy means in the standard view.

My alternative view doesn’t explain away the problems mentioned above, but I believe it clarifies the problems, connects the theoretical issues with reality more firmly, and suggests more useful ways of moving forward.

The first view is that democracy shouldn’t be seen as a positive guarantee of good government, it should rather be seen as a negative guarantee: a guarantee that the extremes of bad government are excluded. It’s clear that all our voting procedures, our not-quite-free press, our unequal society and so forth do not necessarily guarantee a government that is good in any sense of the word. But, it’s also clear that in this system it would be very difficult to get a really awful government that acted manifestly against the interests of everyone in society. In England, this view is a historically accurate one. The Magna Carta came about not because the barons wanted a good government that worked in the interests of everyone in society, but because the King was abusing his powers too much and it was hurting them. Further extensions to democracy in England came about gradually, slowly increasing the number of people whom the government could not systematically abuse. Each increase was hard fought for and was a reaction to abuses by the government, rather than an attempt to create a positive system of government. We should not expect a historical process that advances in reaction to abuses to have produced a system that goes far beyond the prevention of abuses to guarantee positive good government that works in the interests of all.

This view has several consequences. First of all, we should realise that the democracy that we have has been very hard fought for, and we need to preserve those aspects of it which prevent these extreme abuses. A danger of thinking of democracy in purely positive terms (how can we make government work better for everyone rather than how can we prevent the government abusing its power), is that by underestimating the importance of the negative aspect it potentially opens the door to precisely those abuses which democracy evolved to exclude. If you believe that the democratic process guarantees a government that is good in some positive sense, then it doesn’t make any sense to put restrictions on what that government can do - why hamper their good efforts? The present Labour government in the UK has introduced or attempted to introduce several pieces of legislation which reduce the limitations on its own power, supposedly to allow it to serve us better (to protect us from terrorism). The now infamous Legislative and Regulatory Reform Bill attempted to give ministers the power to overturn legislation without consulting parliament. It’s important to realise that our democratic process doesn’t guarantee positive good government, and that’s why it’s absolutely essential to maintain those aspects which stop the government from abusing its power, even if that also makes it more difficult or stops them from doing some things which might be considered positive. Our democracy is not yet secure enough that we can forget about this fundamental negative aspect of it. In fact, it’s a relatively recent phenomenon. It wasn’t until 1928 in the UK when women were given equal voting rights to men that the majority of the population participated. Even now, the 21% of the population under the age of 18 cannot vote (see this fun age pyramid).

A second consequence of this view is that democracy develops by narrowing the window of opportunity for abuse. Advances in democracy are moments when an old form of systematic abuse ends. This can be a progressive notion. For example, at the moment I would argue that there are various structural aspects of our democracy and capitalist economy that mean that a series of governments which systematically favour the interests of the wealthy is possible. Changes in our society that made governments that were systematically biased in favour of the wealthy impossible or unlikely would be an advance in democracy. I would go further and say that the democratic case for socialism is strong, but that’s another story.

The obvious criticism of this view is that it misses out the positive aspect of democracy. Sometimes elected governments do things which are positively in the public interest, and the reason for that is that they were elected to do so. The creation of the NHS or the welfare state might be a good example of this. There are a few responses to this. First of all, there is a question of whether or not the creation of the NHS and welfare state were positive acts, but rather acts taken to avert further dissent (i.e. defensive manoeuvres). Secondly, the alternative view doesn’t say that positive acts are impossible, just that there is no guarantee that they will happen. To argue for the positive view of democracy you would have to argue how democracy makes these outcomes more likely. It’s not obvious to me that this is possible even if we had a good idea of what socially good outcomes might mean. Indeed, there is some good evidence that democratic structures don’t encourage such outcomes. For example, the median voter theorem is a mathematical idealisation of two party democracy which suggests that governments will tend to suggest policies which favour the median voter. This is clearly not encouraging policies which are representative of the electorate, but it is encouraging policies which exclude the worst extremes (although actually, the median voter theorem is a sort of perturbation analysis so it doesn’t say anything about extremes). A good example of this was Brown’s last budget which increased the tax burden on the rich and the poor, but decreased it for those in the middle. The third response to the criticism is that where abuse of a system is possible, it seems that it tends to happen. This makes understanding the extent to which democratic structures exclude possibilities for abuse much more important than understanding how they enable positive acts.

The idea of this way of looking at democracy is to better understand what it actually is and how things really happen, a realist view rather than an idealist one. But I am an idealist, so I also want to understand how to make things better and believe it can be done. This way of looking at things helps in various ways. First of all, it’s always good to be realistic about what is actually going on to better understand how to make things better. Much thinking about democracy appears to be of the self-delusional form. Secondly, it already suggests a whole series of ways of improving democracy by reducing the window of opportunity for abuse. Lastly though, it provides a better framework for proposing positive improvements to our democracy. By dropping the fiction that democracy is about good government and representing the people, it concentrates our attention on systematic analyses of what different democratic structures can do. It also strongly emphasises that positive functions of democracy have to be backwards compatible with the important negative function.

One day, we will perhaps reach a stage where we have a society of rough equality, where no part of it is systematically abused by any other part of it. At that stage, our thinking about democracy and government can begin to focus on ways to achieve more directly positive outcomes, but we haven’t reached that stage yet (and if we do reach that stage, we’ll likely be thinking about everything very differently anyway). At the moment, our problem is the opposite. We have many governments of democratic nations around the world systematically attacking fundamental aspects of democracy, we have the press becoming less and less free as it reduces spending to compete for ever diminishing profits and becomes more and more reliant on government and corporate propaganda. We also have the prospect of potential crises such as climate change, which mean that the negative function of democracy will become even more important than ever if we want to avoid the worst happening to our society in the aftermath of the crisis (for example, the BNP has an electoral strategy that is designed around gaining power in exactly this sort of crisis situation).

OK, this is not the entry I promised in my last blog entry, but…

What is the quickest way to type 250 c’s in a row in a standard Windows text field? I make it 24, can anyone beat that?

c, c, (press and hold) ctrl, a, c, v, v, v, v, v, a, c, v, v, v, v, v, a, c, v, v, v, v, v

I haven’t written much on this blog for a long time, and I have five planned entries to write so I’m soliciting opinions about which people would prefer to read. Let me know what you think if you have any preferences. In rough order of which I think would be more interesting or more likely to complete:

1. Nobody believes in God. In which I will argue that hardly any people who identify as religious behave in a way that is consistent with their really believing in God.
2. Democracy. In which I will describe two somewhat uncommon (but by no means wholly original) views I have about what democracy means: democracy as a word without a fixed meaning but with Wittgensteinian ‘family resemblances’; democracy as a historical phenomenon designed to exclude tyranny rather than as a way to guarantee good or representative government.
3.  Arationality and Honesty. In which I’ll talk about what it means to be rational, put forward the hypothesis that it’s impossible to be completely rational, relate this to the epistemological theory of pragmatism, then turn to ethics and the idea of coming to terms with our own inconsistency, and taking responsibility for your actions rather than trying to act according to a moral code, and finally talk about propaganda, cognitive dissonance and this alternative ethical theory.
4. Capitalism. My eight reasons/meta-reasons for being opposed to capitalism.
5. Religion and Politics. I’ve had this sitting in my WordPress drafts folder for over a year now so it’s fairly unlikely I’ll ever actually finish it. In it I’ll talk about terrorism, Islam, authority, hierarchy, democracy, politics and the possibility of irresolvable differences of opinion, and finally a suggestion that politics is much more important to talk about than religion.

Alternatively, if you have any suggestions for what I ought to write about instead - let me know…

So, a while ago Edward the Bonobo suggested that I should spend less time on politics, and more time on food, so this entry is devoted to the delights of eating in Paris.

Let’s start with my local cake shop (well, local to where I work, not where I live), La Boulange cinquieme. After trying most of the pâtisseries near where I work, this one won out for me, for their fantastic tarte aux framboises. If you happen to find yourself in the latin quarter of Paris (the 5th arondissement), I can recommend a visit (although there’s somewhere else you should go too - more on that below). You’ll find it near the southern end of rue Gay-Lussac (but watch it, it’s not open at the weekend). Here are a couple of pics of some the large cakes I bought for my dad’s birthday party, although I’m afraid the picture quality is not very good because they were taken on my phone, first the tarte aux framboises (they do little individual ones too):

And the Opéra (a sort of chocolatey coffee wafery affair):

I bought four cakes from this shop for my dad’s party, including a clafoutis (a sort of baked custard and fruit tart) and a tarte aux noix (walnut and caramel tart). I was actually quite lucky to get them, because normally for the large tarts you need to order in advance (something I didn’t know at the time). It was quite fun going into the shop and saying “Bonsoir, je voudrai quelques tartes entiers, s’il vous plait“, “Oui Monsieur, lesquelles?“, “Er… les toutes“, “Les toutes?!”, “Oui, les toutes“, “Tres bien Monsieur“. It’s not often you get to go into a shop and buy up their whole stock of something. And I’ve had very friendly service there ever since then. (Please excuse my almost certainly wrong French above.)

The other cake shop you should visit if you are south of the river in Paris is Pierre Hermé about half way up rue Bonaparte north of the Jardin du Luxembourg. The French take their pastry very seriously, and this is reflected in the fact that Hermé was awarded the Legion d’honneur in 2007. I went for his most famous cake, the Ispahan. The photo below is from his website because my camera phone photo doesn’t do it justice. I had the small, individual version of this tart, which consists of a rose macaron like biscuit, with raspberries, lychee and a rose petal cream. Wow! If you love cake and you don’t mind the expense (it was about €6-7 for an individual portion), it’s definitely worth the trip.

While I was there, I also couldn’t resist getting one of the famous macarons (a tiny little sandwich of two almond meringues with various different fillings). His flavours are very unusual. Normally you get things like raspberry, chocolate, coffee and so forth. I went for his olive oil and vanilla macaron and I can tell you it was amazing. I shall be back to try some of the others, although I’m not sure about the foie gras and chocolate one.

Next stop, chocolate. A friend advised me about a chocolatier called Patrick Roger which he claimed was the best in France. So, while I was doing christmas shopping, I thought I’d pop in and get some presents there. He wasn’t wrong, eating chocolate from this place is a seriously different experience to eating chocolate from anywhere else I’ve been been. Or in the words of my mum after she’d eaten some - what is the point of eating ordinary chocolate ever again after something like that?

While I was there, I noticed that the shop sign had something which seemed rather boastful. It said Meilleur Ouvrier de France (best [chocolate] maker in France). Well, it turns out that this is an award given every three years to the best places in various categories (food ones are the ones I’m interested in, but they also do many other things). So now I’m on the lookout for more MOF shops (the MOF website is unfortunately totally hopeless and can’t be used to find out where they are). I found the MOF fromagerie at the north end of the rue Monge near where I work, and bought some cheese there, but to be honest I’m not a huge fan of smelly, mouldy French cheese so this wasn’t such a revelatory experience as the chocolate.

Last but not least, restaurants. I haven’t had such good luck in restaurants in Paris as I had hoped, so nowhere stands out particularly. If you want an excellent and inexpensive place in the 13th arondissement (where I live), I can highly recommend l’Ourcine on rue Broca. They do a set three course meal for €30, which was fantastic both times I went. If you want something a bit posher than that, but you don’t want to go to the sky high trois étoiles places, you might like Au Trou Gascon in the 12th arondissement (just north of the river to the east). I had the five course dîner Gourmand which is very good value at €50, and consisted of:

• Gambas, royale de foie gras, émulsion de chataîgnes (prawns, foie gras mousse, chestnuts)
• Noix de St Jacques, endives fondantes (scallops with endives)
• Filet de biche, semoule de brocoli, fumet cacao (fillet of venison, some sort of brocoli thing, smoked in cocoa?)
• Faisselle pastorale, miel citronné, huile d’olive et pignons (faisselle is a soft white cheese, here served with honey, olive oil and pine kernels)
• Glace chocolat noir « minute » servie devant vous, éclats de marron, meringue vanillée (very dark chocolate ice cream with chestnuts and vanilla meringue)

Other than the cheese, which as I’ve said I’m not a big fan of, it was all delicious. I wouldn’t have minded a more interesting pudding that chocolate ice cream and meringue, but it was a good one.

OK, that’s all for now. Expect a report if I get round to visiting somewhere like the restaurant Hélène Darroze (the only Michelin three star restaurant in Paris run by a female chef). The lunch menu seems just about possible for a special occasion, at €70.

For many years, the ZNet website has been one of the best if not the best web site for the left. They’ve just finished a major upgrade to their site which could make it even better. The idea is to create a left wing community rather than just a site with lots of articles to read. Members can create their own blogs, join groups, discuss on the forums, etc. And many more things are coming. So, go check it out now! But, the upgrade has been a costly one, and ZNet needs more sustainers (people who make a periodic donation) to keep their operation running, and more importantly to expand it. So, take a look at the site, and if you like it take a look at this and think about joining.

One of the things about being ill is that you have to spend a lot of time in bed with nothing much to do. Having watched the whole first series of the Sopranos, I had to find something else. So here’s the result. I revisited an old program I wrote many years ago to solve the Countdown numbers game.

In this game, you’re given six numbers between 1 and 100 and a target number between 100 and 999. You’re given 30 seconds to try to make the target using the six numbers and the operations plus, minus, times and divide.

I originally wrote a program to solve this many years ago (when I was about 14 I think), but the algorithm I used was pretty horrible. I worked out by hand all the possible arrangements of brackets you could have for six numbers, and then tried each operator and number in each appropriate slot. It worked, but it was ugly programming.

Recently I’ve been learning Python for an academic project, and so I thought I may as well try rewriting it in Python. I think the solution I’ve come up with is nicer than any of the solutions I’ve found on the internet (mostly written in Java or C), although having written it I found this paper which uses a very similar solution to mine (but in Haskell rather than Python).

Python programmers might get something from the minimal code below (all comments and docs stripped out), or you can take a look at the full source code here, including detailed comments and docs explaining the code and algorithm.

My ideal (as always with Python) was to write a program you could just look at and understand the source code without comments, but I don’t think I achieved that. I’d be interested if a more experienced Python programmer could do so. Let me know.

This version is incomplete, from the slower version, and is supposed to be understandable without explanations (takes about 40 seconds to find all solutions, too slow for Countdown):

def ValidExpressions(sources,operators=standard_operators,minimal_remaining_sources=0):
    for value, i in zip(sources,range(len(sources))):
        yield TerminalExpression(value=value, remaining_sources=sources[:i]+sources[i+1:])
    if len(sources)>=2+minimal_remaining_sources:
        for lhs in ValidExpressions(sources,operators,minimal_remaining_sources+1):
            for rhs in ValidExpressions(lhs.remaining_sources, operators, minimal_remaining_sources):
                for f in operators:
                    try: yield BranchedExpression(operator=f, lhs=lhs, rhs=rhs, remaining_sources=rhs.remaining_sources)
                    except InvalidExpressionError: pass

def TargetExpressions(target,sources,operators=standard_operators):
    for expression in ValidExpressions(sources,operators):
        if expression.value==target:
            yield expression

This version is actually complete, from the faster version which needs the comments to explain (takes about 15 seconds to run, good enough to win Countdown):

sub = lambda x,y: x-y
def add(x,y):
    if x<=y: return x+y
    raise ValueError
def mul(x,y):
    if x<=y or x==1 or y==1: return x*y
    raise ValueError
def div(x,y):
    if not y or x%y or y==1:
        raise ValueError
    return x/y
standard_ops = [ add, sub, mul, div ]

def expressions(sources,ops=standard_ops,minremsources=0):
    for i in range(len(sources)):
        yield ([sources[i]],sources[:i]+sources[i+1:],sources[i])
    if len(sources)>=2+minremsources:
        for e1, rs1, v1 in expressions(sources,ops,minremsources+1):
            for e2, rs2, v2 in expressions(rs1,ops,minremsources):
                for o in ops:
                    try: yield ([o,e1,e2],rs2,o(v1,v2))
                    except ValueError: pass

def findfirsttarget(target,sources,ops=standard_ops):
    for e,s,v in expressions(sources,ops):
        if v==target:
            return e
    return []