Suppose I have an expression grammar in which the multiplication operator * and the addition operator + have their usual relative priority (namely, * binds more tightly, i.e. is evaluated first). Then suppose I – perhaps unwisely – introduce a prefix operator, which I'll call PFX for want of a better name, which has intermediate priority between the two, so that

• PFX a + b behaves like (PFX a) + b, i.e. the PFX is evaluated first
• PFX a * b behaves like PFX (a * b), i.e. the PFX is evaluated second.

a * PFX b + c

There's a particular annoying pattern I notice in debate, in which one person criticises another's choice of argument on the basis of a sort of misapplication of pragmatics.

Here's a concrete (if slightly melodramatic) example. Imagine we're drinking together, and you demand, suspiciously, ‘Wait, how do I know you haven't poisoned this bottle of wine?’. To which I respond, ‘I'm drinking from it too, so that would be a really bad idea!’ Now if you were to think, or say, ‘Oh, so you would have poisoned it if we hadn't been drinking from the same bottle?’, you'd be committing this fallacy.

Because in fact, of course, the main reason I haven't tried to poison you is some combination of because I don't want to and because I'm too moral to do such a wrong thing, and both of those reasons would still apply regardless of any detail of who was drinking what.

But you can't check those statements, because they're about stuff entirely inside my own head. So if I'd tried to use either one as a defence, then you'd be no more convinced of my non-murderousness than you are now, because if you can believe I might try to poison you in the first place, then you'd have no trouble also believing that I'd lie about my motives in the course of the attempt. Whereas you can easily verify for yourself that I am indeed drinking from the same bottle, and perhaps you might find it harder to believe I was self-sacrificingly murderous than merely self-interestedly murderous.

(Since this is a silly hypothetical example, let's assume we can disregard all the even more improbable edge cases beloved of fiction, like the poison being in the ice cubes, or smeared on your particular glass in advance, or that I took the antidote beforehand, or have spent ten years building up resistance to iocane powder, etc…)

Anyway. That's why I chose that particular reason as the one to mention: not because it was my core reason or my only reason, but because it was one you'd be more likely to believe, because you could check it yourself.

I think the general pattern of which this is an example is: it's a fallacy to assume that someone who has mentioned one good or bad property of a thing (or reason to do it or not do it, or whatever) must have chosen that particular property because it's the most important or the only one, rather than choosing the property most appropriate to what particular goal the utterance as a whole is trying to achieve.

In this silly example, my goal is to try to convince you that you're safe; so I have to pick a reason that will actually manage to do that job, rather than one that is more important to me but likely to be less effective. In other kinds of debate, one might similarly choose the argument that appeals most to the particular audience one is trying to convince, not the one that is most fundamental in the arguer's own mind. Or you might avoid particular arguments because you know they'll cause some enormous derailing sidetrack. Any number of reasons, really.

So. Does this fallacy have a well-known name?

I visited my mum yesterday, and we ended up going through a box file of snippets she'd saved from my childhood. Among them, printed on silvery ZX thermal printer paper that brought a nostalgic smile to my face in its own right, was the following Sinclair BASIC program, printed together with its output.

   5 BORDER 0: PAPER 0: INK 7: CLS
  10 DIM x(40)
  20 FOR z=1 TO 40: LET a=z*0.1
  30 LET y=SQR (1+(a*a))+SQR ((4-a)*(4-a)+4)
  40 LET x(z)=y
  50 NEXT z
  60 LET smsf=1
  70 FOR z=1 TO 40: LET a=z*0.1
  80 IF x(smsf)>x(z) THEN LET smsf=z
  90 NEXT z
  95 PRINT "GG end to J", "Road length"
 100 PRINT smsf,x(smsf)

GG end to J     Road length
13              5.0001815

I don't know why Mum chose to save that program in particular, out of all the ones I must have printed out in the few years I had the Spectrum and that printer. She guessed that it must have been the first one I wrote, but it seems a bit sophisticated for that – surely there would have been a pile of ‘hello, world’ type things before this quite mathematical one?

Regardless, I had completely forgotten it, and it makes me smile at the fact that what it seems to be doing is numerically testing the proposition that a straight line is the shortest distance between two points. (Line 30 calculates the distance from (0,0) to (4,3) via the point (a,1); the rest of the program tries this for lots of different values of a, and finds the one that gives the shortest total distance, which unsurprisingly is the point where the straight-line route intersects the line y=1, to the limits of rounding error.)

But I do wonder whether this was something I typed in from elsewhere in full, or followed hints in a manual, or what. I'm particularly curious about the variable name smsf and the cryptic legend ‘GG end to J’…

Somewhere in my head is a very specialised pattern-recognition neuron, which seems to fire whenever I encounter – or, even more so, inadvertently write – any phrase or sentence that would scan perfectly as the first line of a limerick.

It's a very persistent and attention-grabbing neuron, for some reason. Every time it fires, I have to spend the next half hour vigorously resisting the urge to try to come up with the rest of the limerick. Even if the triggering phrase is something utterly, tediously mundane, as for example the one that emerged from my fingers just now as a hasty commit message: ‘A cleanup I noticed in passing’.

Since I've been musing about fiction recently, here's another thought that crossed my mind.

Fantasy fiction often has a magic system involving spells cast in spoken language. But what language? Why does that language work and not another? Or would another language work? Would it depend on the spell? On the caster? On the location? It seems to me that there are quite a few plausible ‘cosmologies of magic’ which would cause different answers to those questions, many of which have specific examples in existing fiction, and I wonder if there are any more I've missed out.

So, what have I missed?

It randomly occurred to me this morning to wonder if everyone else has had the same thought about this, or if it's just me.

For those who have read Discworld novels...

This weekend, after preparation and faff lasting several months, I migrated all of my free software projects out of Subversion into a collection of git repositories.

Good grief, it was a faff! It's surprisingly like moving house – there's no end of just-one-more-things that all have to be sorted out, and every so often you turn a corner and find another huge list of things to add to the list, and it's exhausting sorting it all out. I did as much as I could ahead of time (e.g. I did the work of stopping various projects from depending on a monotonic revision number a few weeks in advance of the moment of migration itself), and there's a big list of sortings-out left to be done which I'll get round to once I've rested, but even so, the actual ‘moving day’ still had a lot of bits and pieces I couldn't move to another day. I'll find work restful tomorrow, I think!

A random childhood memory of mine is of being about 10, and wondering what my life would look like when I was grown up and didn't live with my parents1 any more.

At that age, a thing I was enjoying doing in my spare time was making cardboard models of polyhedra. And I remember having the thought that once I was a grown-up, perhaps I might still feel moved from time to time to sit at home cutting and folding and gluing cardboard, but since I wouldn't be living with family any more, there'd be nobody else to show the things to once I'd made them. I found that thought rather upsetting, and started to think that perhaps being an adult wouldn't be very nice; I had an image of myself spending my life sitting in a house on my own, with nobody to talk to, and even the ways I was accustomed to amusing myself on my own not being as much fun as they used to be.

It was only a passing thought; there were clearly lots of things wrong with it, several of which I spotted fairly soon, so it didn't continue to worry me for very long. But it stuck in my head well enough that even now I can clearly remember having been worried about it once.

During the weekend just past, I put a fair amount of effort into helping drswirly design and make a cardboard cube with group theory notation all over its faces, for maths-teaching purposes. There were enjoyable coding challenges involved in writing the program that put all the right notation in the right places and printed out the net; when it was finished, we looked at it and went ‘ooh!’ (because it's quite pretty), and it will also come in actually useful to him and possibly to other maths-type people. And then he rewarded me with cake.

At times like this, I feel an urge to travel back in time and reassure my 10-year-old self that he was wrong in the one part that mattered. I would tell him, it turns out you're right that you'll live on your own when you grow up, and it turns out you're also right that you'll still make polyhedra every so often, but notwithstanding your pessimistic analysis it will still be great fun.

1. (Hmmm, I nearly wrote ‘didn't live at home any more’ there, which made sense in my head but once written down it's clearly a contradiction in terms!)

It occurred to me last week to wonder: in organisations that predominantly do development in Python, do the managers talk endlessly about having to get all their vaguely duck-shaped objects in a row?

Thanks to everyone who commented on my previous entry with proofs, software and other useful comments. I think I've now taken the investigation of this problem as far as I have the energy to, at least for the moment. A collection of all the useful things I know about it, including a big pile of data, is now up on a web page: http://www.chiark.greenend.org.uk/~sgtatham/matchsticks/.