Start watching at 1:08:12. He says,
"I agree there's no problem with infinity in mathematics or in physics or in other studies. That's not the point. There's a difference between infinity, the potential infinity as an idea and actual infinity in the real world. Don't take my word for it, here's what the mathematicians say. David Hilbert ... is a renowned mathematician of the, or was, of the 20th century after whom Hilbert spaces and Hilbert operators that are prevalent in quantum mechanics is used, he said, "The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought. The role that remains for the infinite to play is solely that of an idea."
Kasner and Newman, contemporary renowned mathematicians: "The infinite certainly does not exist in the same sense that we say there are fish in the sea. Existence in the mathematical sense is wholly different from existence of objects in the physical world."
There's no way in the real world, within our sensorially perceivable naturally world within space time that infinity can exist. If it does, you end up with a whole host of contradictions. If we had an infinite number of people in the room and five have left, how much do we have? An infinite number of people! But five have left! So, there's a distinction between the idea of infinity and the ontological reality of infinity in the real world."
Krauss's response is good. First, Hilbert was not a physicist, but a mathematician; his opinion about physical reality was not definitive back in 1926, when his article was written, and it is certainly not definitive now. Hilbert provided no empirical evidence that the infinite cannot exist in nature, and these days, physicists routinely consider the possibility of various aspects of infinity in nature. Does it or doesn't it? We don't know for sure, but we can't rule it out by Hilbert-style thought experiments alone.
Second, Uthman starts with a premise like `you can fit an infinite number of people in a finite room' (not an exact quote), which nobody is asserting. Then he asserts a contradiction where none exists. Yes, it's true that if you remove a finite number of items from an infinite set, the resulting set is still infinite. Why is this a contradiction? The answer is, it's not. Infinite quantities don't behave like finite ones, so they may not match the average person's intuition, but that's not the same as a "contradiction".
Thanks for pointing this video out. I have heard Uthman Badar in other debates and have noticed (but not been surprised by) his naïveté.
His counterexample to the real world existence of infinity is hilarious: "Let there be an infinite number of people in a room..." Forget the fact that "infinity minus five equals infinity" makes perfect sense (whereas he thinks he got a contradiction of sorts), and focus on the premise. How on earth can we, in the real world, have an infinite number of people in a room? OK, I see... we need an infinite room :-)
Now, the problem is on the meaning of "real world existence of infinity". Clearly, Badar has some kind of geometric viewpoint. He wants to "see" infinity in space. But how about subtler notions of existence of infinity?
"Yes, it's true that if you remove a finite number of items from an infinite set, the resulting set is still infinite. Why is this a contradiction? The answer is, it's not."
Heck, it's almost a definition!
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