Dog blog 21 - 1 + 1 = 2?

1 + 1 = 2?
The Dog has never been that great at maths. Dave - pictured with Sammy in their "Lord of the Sith" poses for their weekly Star Wars night - thinks he's slightly better at it, but only because he can count up to eleven.

One of the most baffling things for the Dog is the idea that "1 + 1 = 2". Dave tried to explain it to me once using apples. We were originally going to try to work out what "2 + 1 = 3" means, but Dave was hungry and mumbled something about that being terribly very complicated - and ate one of them.

Dave tries to explain it all
"So here's one apple. A tasty pink lady apple.", said Dave. "And here's another one.".

"That's two apples. So 1 + 1 = 2". Job done Dave thought.

"But what if one of the apples is green, and the other one is red?", I asked.

Now that didn't make a lot of sense to Dave. He's colour blind for a start, like most dogs, so wasn't really sure what I was getting at: "There'd still be two apples".

"Ok Dave, but what if it was an apple and an orange?".

"Well, there'd be just one apple then."

"Yes", I said. "But there'd be 2 pieces of fruit.".

This was all a bit too much for Dave who, by now, was getting hungry again and decided to see what would happen if he ate both apples. Which unfortunately backfired on our endeavours. And, as it turned out, on Dave a couple of hours later. Apples disagree with him.

Something missing?
What "1 + 1 = 2" doesn't really tell you is what you're counting. With an apple and an orange, you get 2 pieces of fruit - for sure - but it doesn't make much sense to the Dog to describe that as "1 + 1 = 2". It seems more accurate to say "1a(f) + 1o(f) = 2f(a + o)". Where the "f" represents fruit of course.

"1 + 1 = 2", then, seems to be saying that "there are 2 items of the same class". That's easier maybe on the right hand side of the equation. But tricky on the left: 1a is not the same as 1o. It's only when they're accepted as belonging to the same unifying class "f" that they can be counted together.

The loneliest number
And there seems to be a problem for "1" on its own. Are there really 2 identical "1"s? In every way? Can ideas occupy the same space-time? If they can't, are they in fact truly "identical"? The proposition itself seems to suggest that, in some way, the later "1" is an "other" 1.

All that makes the Dog's head hurt, and I think it's because for all its appearance of logical purity, "1 + 1 = 2" is actually more "open textured" a phrase than that: you still need to read in the answer to "well, one what?".

Enough brain hurty for the now. Off to chase rabbits. And to make it easier, I'm just going to chase one.

Dog blog 20 - "no trainers"

"No trainers"
The Dog went for a little run round the park today, with Lenny, Bonzo and Poppy (pictured here in their finest fettle). Most fun, even though there were no rabbits to chase. Bonzo had his ball though - on one of those springy long stick things that makes it easier to throw. Fab.


Pootling
We then thought we'd pootle along to the Botanic gardens, where we were met by a very interesting sign: "no jogging". This started a lot of yabbering about it, us being of course, along with Dave (indisposed unfortunately today, away off looking for blue mice), all founder members of the Dog Philosophy Club. 


We thought of some difficulties with the sign: "jogging" is fiddly to pin down - when does it become "running"?; when does it become "walking"? What if you were chasing after a small child who was about to fall into a pond - would that be "jogging"? More likely "running". What if you were doing something only for a couple of seconds that was faster than walking - would that be "jogging" for at least some of that brief period of time? 


"No trainers"
Poppy thought we could save ourselves the trouble by just saying "no trainers". It would be much harder, she thought, to do anything much other than "walking" in shoes. But then we'd stop a lot of owners from being able to enter the gardens - on a straw paw poll, over half were wearing some type of trainer. And we'd then get into the bother about working out what a "trainer" really was. What about those sort of climbing type boots which you see hill runners wearing? Or trendy plimsoles that you wouldn't really want to do anything other than walking in? Tricky. 


After a lot of thought, we decided that "no jogging" probably wasn't so bad after all. What really mattered, said Bonzo, was that it stopped most people from jogging round the gardens, and that most people had an idea that it meant something other than walking, and probably something most people would choose to do for fun (if they liked jogging), rather than do to stop children from falling into ponds. 


And that, pitched in Lenny, is much the same sort of dilemma for any rule drafting - does it matter so much what the language means in terms of understanding it around the margins, or is what matters more the effect the rule has on the overall constituency of persons whose behaviour you're trying to influence? If what you're really trying to do is stop most people from doing sports jogging or running round the park, "no jogging" is probably as good as any - why not use that one, and see how it goes. "No trainers" goes too far, and stops an awful lot of people from doing anything in the park - as they can't get in. 


All very interesting we thought, as we all jumped in the pond - and promptly got banned from the gardens for a day. Even though there wasn't a sign about that.