The Law of the Letter

(Written 24th September, 2013)

Dear Reader,

I really like writing letters. With a pen and paper, to be more specific. I don’t really know why. Perhaps it’s the challenge? Email programs and word processors allow almost endless editing; with pen and paper you must either have multiple drafts or be willing to be honest about your mistakes. It also helps to plan ahead: it is rare for me to write a letter without premeditation.

So, I am writing this on paper with a BiC médium; later I plan to copy the handwritten letter to the computer. I hope to resist the urge to edit, because that would defeat the purpose! I must be careful what I write, because I’m committed to it.

I think these restrictions are actually what makes letter-writing so appealing to me. Certainly it is but one example of a constraint, much like those I see real writers and poets using. Viewing things more mathematically, one could say that the creative process is aided by pruning down the space of all possible texts to a more reasonable size.

I still have a very important freedom, however: the reader and writer (that is, you and I) don’t have to approach the letter in real time. I can pause for thought, you can get a cup of tea (or whatever). I can also squeeze in extra letters when I’ve missed them…

I think it will feel quite odd not to put this letter in an addressed, stamped envelope when I am finished. That is certainly an element of the ritual of writing a real letter. But sentimentality is a slippery slope and I don’t wish to start pining for the days when I would have given my letter to somebody on horseback.

Even if those particular features will not be present, I’ve enjoyed this little communication. Perhaps another time I will actually try to impart something like a message…




The ex post probability is either 0 or 1

The things you think of while doing the dishes. At the Maths Faculty in Cambridge, there are cunningly no dishwashers. Allegedly there are showers, a proven idea-generating tool. But I think they are there for other reasons.

Intuitively, it feels as if “after the fact” the probability of any event should either be 0 or 1. Either it happened or it didn’t. Well, except if your last name is Clinton.

Framing this in terms of rigorous axiomatic probability theory: consider the filtered probability space (\Omega,\mathcal{F},(\mathcal{F}_t)_{t\in I},\mathbb{P}). Consider real-valued random variables on this space and use the notion of conditional expectations. Define conditional probability in terms of conditional expectation as follows: for A \in \mathcal{F} and \mathcal{G} \subseteq \mathcal{F} a sub-\sigma-algebra we have \mathbb{P}(A | \mathcal{G}) := \mathbb{E}(\mathbf{1}_A | \mathcal{G}).

Now take A \in \mathcal{F}_t – we are thinking of t as being the current time, and we are looking at the event A which occurred at or before the current time. Since A is \mathcal{F}_t-measurable, \mathbf{1}_A is an \mathcal{F}_t-measurable random variable. Thus we can “take out what is known”: \mathbb{P}(A | \mathcal{F}_t) = \mathbb{E}(\mathbf{1}_A | \mathcal{F}_t) = \mathbf{1}_A.

But indicator functions are always either 0 or 1. Hence the result.

This is a (very, very simple) 01 law. And you don’t really need maths for it.

The Metaphorical God

For various reasons (symbolism included),  I’ve decided to distribute this short essay to a wider audience today. Thanks to those who gave me feedback on the initial drafts!


In which the author clears the cobwebs off his knowledge of economics, and puts it to use, ignoring its creaking and groaning.

I was recently browsing the Dutch Piratenpartij (Pirate Party) website, and came across this (somewhat old) article. It is entitled “Kom niet aan het recht om te delen!”, roughly translating as “Don’t infringe upon the right to share!”. It discusses the philosophy of filesharing.

The very first argument presented attempts to use economics to prove a point, providing a supply and demand diagram (labelled in English). I got a bit confused at this point, and had to reread the argument several times: I eventually convinced myself1 that the diagram didn’t make sense in the context it was used! The article was talking about monopoly markets, while the diagram was talking about price ceilings! Both can be argued to cause deadweight loss (mentioned in the article) – along with just about anything that takes the market away from free market equilibrium. See later for more information about deadweight loss…

Not trusting my own conclusion, I went to Wikipedia to find the ‘correct’ diagram. Indeed, I found it here. The diagram made much more sense. Mainly because it actually fit the context, secondly because it used straight lines instead of curves. The latter is important because straight lines help you to remember that the whole construction is an idealisation…

See is the diagram below (copyright and licensing information here2)

Supply and Demand Diagram

Source:; CC BY-SA 3.0 AND/OR CC BY 2.5 AND/OR GFDL >=v1.

I’m still a bit confused about the green line…

I will now offer a quick explanation that will help if your economics knowledge creaks like mine. If you are an economist you may get bored and/or horrified.

In a free market, the market forces a quantity Qc of items to be exchanged at a price Pc. This quantity and price maximises the surplus of both producers and consumers.

For the consumers, surplus is the total ‘perceived’ value of the goods minus the total cost they paid to the producers. For the producers, it’s the total value received from the consumers minus the actual total manufacturing costs of the goods. Roughly speaking.

In a monopoly market, the seller sets the price, so as to maximise his/her/the company’s own surplus, and Qc and Pc become Qm and Pm respectively.

What happens to the total surplus? Some of the lost consumer surplus is picked up by the producer. Some people, however, can’t pay for the good at the new, higher price. So they simply don’t buy it!

The consumers who have to exit the market lose their surplus, and the company loses the surplus it could have had from selling to these customers (but makes up for it elsewhere, otherwise this new price wouldn’t be profitable!)

So the TOTAL surplus (i.e. the surplus of the whole society) goes down. This is called deadweight loss, because this surplus is just lost, not shuffled around

A company can make more profit by trying to get the consumers back. They can do this by offering lower prices to those who are willing to pay less.

Like that sounds, it’s not easy to do properly! However, cut-out coupons are one cunning attempt. (People who aren’t able to pay the full price might instead be willing to spend time cutting out coupons). This also restores (some of) the lost consumer-side surplus. Of course, the coupon system is neither totally efficient nor universally applicable.

As the article mentioned at the beginning argues, software piracy can be argued to reduce the part of the deadweight loss on the consumer side. I won’t go any more into this, as this article is way too long already! But I think you can see how the argument might go…


1 I thought at first that I might simply be not reading the Dutch correctly.
2It took me almost as long to figure out the legal details of displaying the image here as it did to write this article. I still am not clear whether all the licences apply or whether you can choose. Worst case it should be OK to use here. Correct me if I’m wrong.

File-sharing and business models

This evening I had an interesting discussion with my dad and sister about filesharing. It all started when I mentioned the Kindle at the dinner table. The things we discussed were rather standard. But one thing leads to another…

About an hour later, I noticed that there is already a business model out there that is similar to one in which filesharing is legalised. That is the ‘free1 software model’, implemented most notably by major Linux distributions. This is a rather fuzzy definition of the ‘free software model’, and there are many nuances. But for now, make your mental picture something like the GNU Public License (GPL), where the only real condition on redistribution is keeping the GPL and providing source code (again only roughly speaking).

With the free software model, businesses don’t usually charge for the software itself (because of the way in which redistribution can occur). Instead, they have found ways to sell services supporting the free software. Moreover, it seems to work, otherwise there wouldn’t be companies doing it…

I was quick to point out to myself that there are differences between (free) software and the music industry. After all, free software is built on the principle of substantial rights associated with licensing of a product (redistribution, inclusion of source code, etc.)

But this isn’t really an inherent, essential difference. In fact, it could be the difference that is causing the record industry to lose squillions2 every year.

File-sharing (legal or otherwise) is widespread. It shows that people naturally want to have more rights to redistribution of music, because they are doing it even though it is often illegal. By ignoring this demand, and instead providing essentially the wrong product, the record industry is, to put it very lightly, completely missing the point.

Lawsuits aren’t working to rein in illegal file-sharing very much at all. Record companies need to either accept that they are obsolete and disappear, or find new services they can offer other than simply distribution of music (no prizes for spotting a false dichotomy here though). It’s not the ‘pirates’ who are causing the record companies’ financial losses. Rather, it is the fault of record companies themselves for being so out of touch with their target market.

1 I am not going to get into the beer/speech divide here. It’s covered to death elsewhere.
2 A very scientific unit of measurement, defined by (inter alia, in all likelihood) the epic P. Bursill-Hall

Français, again

I blogged several months back about my troubles with French. I can now tentatively say that I have something a little more positive to report.

I made a New Year’s resolution to learn French. Most importantly, I’ve found that learning French makes a great break from work because:

  • It’s very different from my work
  • It doesn’t take much time to do a few flashcards with my program of choice, Byki
  • It’s hard enough that going back to work almost feels like a relief.

It’s very early to make any sort of definitive judgement, especially since my university work hasn’t started up again yet1, but it’s looking positive. Stay tuned.

1Though I already feel somewhat snowed under, figuratively speaking.

Naming: some thinking required

I’m sure that we’ve all seen company or product names which become horrendous (and/or hilarious) when spaces are removed to form a URL. I’m not going to discuss those here. Instead, I’m going to talk about two names that in their usual, unmodified form seem to be a few cards short of a full deck, jokers aside.

Twitpic (

The fatal flaw here, I think, was a lack of familiarity with British English. Having lived in the UK for more than 3 years, I may be overestimating, but I would expect enough English speakers to be able to avoid “twit” to prevent this kind of train wreck. Haven’t most people read Roald Dahl’s “The Twits”?

What strikes me more is that removing a single letter makes a great name: “Twipic”. It has similar advantages, but without the cruel irony it inflicts upon those users who happen to have their picture selected for the front page…

Wikiterms (

First, a little background. From what I gather, this is a service that aims to create a standard Terms of Service (ToS)  document that is fairer to end users. The idea is that if enough users demand these ToS, large companies will have no choice but to comply.

But here’s the (somewhat amusing) image it conjures up for me, in the form of a dialogue:

User Why do I have to pay you a yearly fee?
Company It says so in the Terms of Service!
User No it doesn’t, I’ve read the Wikiterms!
Company Which revision? Did you see my most recent edit? *evil laugh*

Yes, yes, I know that the word Wiki means ‘fast’1 and doesn’t necessarily mean something anyone can edit. But let’s put that aside. It’s the initial image it creates in my mind that’s important.

I think the problem here is perhaps a blind application of ‘trendy’ terms. But that’s only half the story – ‘iTerms’ is better, despite being ‘trendy’! The other problem is the possibly unsavoury link with Wikileaks. Put all of that together and you have a potentially massive public image problem. That will make it very hard for the effort to succeed.

In conclusion…

Everyone knows Shakespeare’s quote about names. In context, it’s even true. But most people already have an image of what a rose is. When the public isn’t likely to have already formed an image, a good name is vital.

All copyrights are property of the respective owners. If I can, I reserve all rights to the name “Twipic”… though somebody is bound to have thought of it first.2


1At least I do now. As my friend Max pointed out, I stated incorrectly in the first version of this article that it meant “community”. I guess I got confused with ‘ubuntu’. He pointed me (surprise surprise) to the German version of this Wikipedia page

2 And indeed, someone already has. Thanks Lovkush!