Recent content by FactChecker

Another view: Anything near the limit of what we "see" now is really the result of our interpretation using a lot of manipulation and modeling. As our models and techniques improve, we will be able to "see" farther.

You need to be clear on what you mean by "infinitizing operation". The OP talked about "a new infinite number of dots, ad infinitum." The "new infinite number of dots" and "ad infinitum" are two different concepts. The first will not create a larger set and the second will.

It's my understanding that people looking for dark matter look at the velocity of orbiting objects rather than trying to figure out the curvature of space. I think the velocity is much easier to determine directly.

I disagree. Allowing the process to go on infinitely long can increase the size. Cantor's diagonal proof shows that the reals, represented by infinite sequences of digits, are an uncountable set.

A related question: In general, how well does AI handle games where a winning strategy must include some random behavior to keep the opponent guessing? Many of the above mentioned games require AI to react to unpredictable moves, but what if AI must make unpredictable moves? ADDED: Are there...

Well, I don't know what you are trying to get at. There are an infinite variety of rules that can be thought up. The ones we use have many applications, are consistent, lead to a lot of theorems that are useful, etc. There is nothing wrong with investigating your own ideas as long as you don't...

I don't think you paid enough attention to @Dale's post #8. In your first post, you propose that ##0/0 = 1## and also that ##0^2/0 = 0##. Since ##0^2 = 0##, we have ##0=0^2/0=0/0=1##. This is using your special rules. ##0=1## is unacceptable.

Division is not defined arbitrarily. We start with two operations, addition and multiplication, that have very specific, desirable properties. Then division is defined as the inverse of multiplication. The result is that division by zero is undefined.

You might be interested in Abstract Algebra. They study the basic abstract properties of sets with an operation or two (usually called addition and multiplication). In that, the zero element is the element, 0, where (a+0 = a, for all a). This would talk about the special properties of the 0...

Ok. I'll buy that. And I guess they are envoys if they contain things that might be discovered by others.

Sorry, I didn't read the whole paper because their batteries are/will be dead thousands of years before they reach anything. Pioneer batteries have been dead for years. Voyager batteries will only last another 9 years. Is there some reason to question where they will go in the next thousand years?

Good point. The concerning issue is that it is often so hard to understand why AI comes to the conclusion it does. It is not intellectually satisfying to know the answer without understanding why.

You have a point regarding funding, but, IMO, there is value in knowing what is right and what is wrong, regardless of who gets the credit.

Sorry, I might be dense. I understand where people are getting the ##n^2-1##, but I have no clue what the OP means by "gives", other than that. I give up.

IMO, this is an important point. It is hoped that a solution (AI or otherwise) of a math/physics problem gives some insight to a new principle that advances our understanding of the subject.