Okay, I was among the first people here who called Zed’s statement plain wrong, but I now think that there are enough high-status individuals of the community that are taking that same position, that it would serve knowledge more if I explained a bit in what slight sense his statement might not be completely wrong.
One would normally say that you calculate 3^4 by multiplying 3 four times: 3 3 3 3 But someone like Zed would say: “No! Every exponential calculation starts out with the number 1. You ought say 3 ^ 4 =1 3 3 3 * 3”. And most of us would then say: “What the hell sense does that make? What would it help an AI to begin by multiplying the number 1 with 3? You are not making sense.” And then Zed would say “But 0^0 = 1 -- and you can only see that if you add the number 1 in the sequence of the numbers to multiply.” And then we would say “What does it even mean to raise zero in the zeroth power? That has no meaning.” And we would be right in the sense it has no meaning in the physical universe. But Zed would be right in the sense he’s mathematically correct, and it has mathematical meaning, and equations wouldn’t work without the fact of 0^0=1.
I think we can visualize the “starting probability of a proposition” as “50%” in the same way we can visualize the “starting multiplier” of an exponential calculation as “1″. This starting number really does NOT help a computer calculate anything. In fact it’s a waste of processor cycles for a computer to make that “1*3” calcullation, instead of just using the number 3 as the first number to use.
But “1” can be considered to be the number that remains if all the multipliers are taken away one by one.
Likewise, imagine that we have used both several pieces of evidence and the complexity of a proposition to calculate its probability -- but then for some reason we have to start taking away these evidence -- (e.g. perhaps the AI has to calculate what probability a different AI would have calculated, using less evidence). As we take away more and more evidence, we’ll eventually end up reaching towards 50%, same way that 0^0=1.
Okay, I was among the first people here who called Zed’s statement plain wrong, but I now think that there are enough high-status individuals of the community that are taking that same position, that it would serve knowledge more if I explained a bit in what slight sense his statement might not be completely wrong.
One would normally say that you calculate 3^4 by multiplying 3 four times: 3 3 3 3
But someone like Zed would say: “No! Every exponential calculation starts out with the number 1. You ought say 3 ^ 4 =1 3 3 3 * 3”.
And most of us would then say: “What the hell sense does that make? What would it help an AI to begin by multiplying the number 1 with 3? You are not making sense.”
And then Zed would say “But 0^0 = 1 -- and you can only see that if you add the number 1 in the sequence of the numbers to multiply.”
And then we would say “What does it even mean to raise zero in the zeroth power? That has no meaning.”
And we would be right in the sense it has no meaning in the physical universe. But Zed would be right in the sense he’s mathematically correct, and it has mathematical meaning, and equations wouldn’t work without the fact of 0^0=1.
I think we can visualize the “starting probability of a proposition” as “50%” in the same way we can visualize the “starting multiplier” of an exponential calculation as “1″. This starting number really does NOT help a computer calculate anything. In fact it’s a waste of processor cycles for a computer to make that “1*3” calcullation, instead of just using the number 3 as the first number to use.
But “1” can be considered to be the number that remains if all the multipliers are taken away one by one.
Likewise, imagine that we have used both several pieces of evidence and the complexity of a proposition to calculate its probability -- but then for some reason we have to start taking away these evidence -- (e.g. perhaps the AI has to calculate what probability a different AI would have calculated, using less evidence). As we take away more and more evidence, we’ll eventually end up reaching towards 50%, same way that 0^0=1.
I feel compelled to point out that 0^0 is undefined, since the limit of x^0 at x=0 is 1 but the limit of 0^x at x=0 is 0.
Yes, in combinatorics assuming 0^0=1 is sensible since it simplifies a lot of formulas which would otherwise have to include special cases at 0.