"Nobody supposes that the computational model of rainstorms in London will leave us all wet. But they make the mistake of supposing that the computational model of consciousness is somehow conscious. It is the same mistake in both cases."
Because computers don't actually do arithmetic, they simulate it. When you take 2 sticks, add 2 sticks, and obtain 4 sticks, that's arithmetic. Having a raised flag with one lowered flag to the right and the left of it and then changing this configuration to having a single raised flag with two lowered flags right to it, and interpreting this charade as having added 2 to 2 and obtained 4 — that's just a simulation. It didn't actually have added 2 and 2 of anything.
Well, if I write "2 + 2 = 4" on a piece of paper, am I doing arithmetic, or merely simulating it? After all, there are no sticks involved.
But I'm also willing to accept that a computer is simulating arithmetic, and not actually doing it. That makes no difference to me, as long as the output is the same. In fact it's kind of a boring distinction to make.