This is the story of how I discovered that not every dog has his day.

I got a fantastic pair of dogs the other day, they’re always having pups, but the most amazing thing is that I’ve trained them to give birth to whatever kind of dog I specify. So I go to them one day, and I say “I want a dog born on the 22nd of February with 14 teeth and black hair and blue eyes, and sure enough, the dog is born.

Well I got to thinking about all the things I could do with this amazing dog breeding trick, and I thought about collecting the full set. It took me a bit, but eventually I realised that there was a never ending list of properties and abilities of dogs. I mean, there’s “propensity to chase cats” for example, but there’s also “psychic dogs”, and then theres “propensity to chase dogs that chase cats” and “propensity to chase dogs that chase dogs that chase cats” and so on. Or theres “dogs that can do only the 2 times table in their heads” or “dogs that can do only the 3 times table in their heads” and so on. So I began to realise that if you gave me any list of properties of dogs, I’d always be able to think of ones you’d missed.

Well, that put paid to the idea of collecting the full set, which was a disappointment, as you can imagine.

One day a man from the Pedigree office came round, and he said to me “You’ve got a large number of dogs that haven’t been named, if you want them registered, you’ve got to have them named”, so I went to work, and named all the dogs that I’d had born, quite a big task by then. I mean, you start ok with Rex, Bowser, Gnasher etc, but after the hundredth or so you start having to tax your creativity.

A couple of days later, I was thinking, and I realised that it’d be handy if I just worked out all the names of all the potential dogs that could be born, so I didn’t have to think up new names. Even if I used a meaningless string of letters or numbers, at least they’d have a name, and it’d keep the Pedigree office happy. Although there’s a never ending list of possible dogs, theres also a never ending list of possible names, so there should be no problem right?

So, I got a piece of paper, and down one side, I listed the names that I’d come up with in alphabetic order, and down the other side I listed the properties of the dogs. I was only able to make a start on each of those lists, but I figured that once I had a system, it’d be obvious how to continue it.

It went kinda like this

Name  | Psychic	| Eats Cats | does 2xTable | does 3xTable...
Rex1	No	    No		No	        No
Rex2	Yes	    No		No	        No
Rex3	No	    Yes		No	        No
Rex4	Yes	    Yes		No	        No

Well everything was fine until one day the Pedigree office turned up and complained about a dog that I’d had born with no name. I said “Look, it can’t have, cus I listed all the names out, and it’s all done”. The officer showed me the list and he said “Look, sir, this dog you’ve got, well it’s not called the first name, cos it’s different from Rex1 in that it’s Psychic, it’s different from Rex2 in that it eats cats, it’s different from Rex3 in that it can do the 2x table….”. And he went on. I saw what had happened in an instant. The dog born had the opposite characteristic to the first named dog in the first property, and to the second named dog in the second property, and to the third named dog in the third property, etc. Even if I listed the names forever, There’d still be at least one dog with no name.

I slowly came to realise something big, wonderful, and profound. We can never fully describe all the dogs that might exist.

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