"But I am not an object. I am not a noun, I am an adjective. I am the way matter behaves when it is organized in a John K Clark-ish way. At the present time only one chunk of matter in the universe behaves that way; someday that could change." -- John K Clark
That one struck particularly, nice one.
It's interesting, actually. You're motivated by other peoples' low opinions of you -- this pressure you feel in your gut to prove Caledonian et al wrong -- so you've taken that is probably fairly standard human machinery and tried to do something remarkable with it.
My question is, are you still motivated by the doubt you feel about your native abilities, or have you passed into being compelled purely by your work?
Tim, that was fascinating. I don't know how he did it. I certainly don't have a "trick," but of course you can't know that.
Ian: that's a great idea, I'll try it tonight if I have some time. I'll report back honestly. I think I'll be able to perform under those circumstances, but it'll be interesting to see.
Math isn't a language, mathematical notation is a language. Math is a subject matter that you can talk about in mathematical notation, or in English, etc.
What is the useful distinction here? Are you claiming that Math has a reality outside the notation? If Math isn't defined by the notation we use, then what is it?
Math is just a language. I say "just" not to discount its power, but because it really doesn't exist outside of our conception of it, just as English doesn't exist outside of our conception of it. It's a convention.
The key difference between math and spoken language is that it's unambiguous enough to extrapolate on fairly consistently. If English were that precise we might be able to find truth in the far reaches of the language, just like greek philosophers tried to do. With math, such a thing is actually possible.
So, 2+3=5 corresponds to your dots or sheep, and that's the whole fact of the matter. Cats are called cats because that's what we feel like calling them and calling them dogs won't change their cat-ness.
It FEELS like there should be more because of the way we are accustomed to extrapolating math. There is no additional fact to account for, though.
The only time this isn't really the case is with exotic math which corresponds to a basically "counterfactual" world like "What if the world were made of city blocks?" (Taxi Cab Geometry). It's true that we can imagine false worlds and invent precise language to describe those worlds, but such a description does not make them less false, just more vivid fiction.
"I'd carpet developing nations everywhere with infrastructure like roads and such, and pay for literacy and clean water everywhere, and I'd still have money left over."
I would also do this. In addition, I'd fund the rapid development of the cleanest energy we could muster, and I'd make nutritious food ubiquitously available.
funny, I was considering being the AI for a couple friends of mine. I haven't thought of how to do it yet -- only tried hard to think of it.