Infinities of age and size - Part 1 (George Ellis)

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1. 39:25 "And by the way, there's nothing wrong with philosophy. I'm all in favor of philosophy." Good man. Science has it limits, as does faith. Philosophy takes a sledgehammer to BOTH.
2. This is quite cogent and very much in line with Lee Smolin and Roberto Mangabeira Unger's critique of mathematical cosmological models using infinity, in THE SINGULAR UNIVERSE AND THE REALITY OF TIME.
3. This assumes the laws that affect us in our universe apply to the universe itself like for instance the concept of cause and effect or the nature of infinity. We have no right to assume this. #ShawnCarroll
4. Depending on what definition we give to the universe, we could possibly defend infinity in space and time. Empty space-time of maximum possible entropy could be a toy model for the definition of infinity both in space and in time.
5. It is undefined, it is invented, to describe a result or an answer. We should not forget our alphabet. Can I say what was before the creation of space? I personally can't . Space is just The field, the empty field, just by definition, so space does not need to exist, it's perception is a consequence of the existence of any energy including ourselves.the problem is the BB theory, of course it make sense to think of our observable as one entity, like a galaxy or a solar system or .....but for logic sake ...why the universe had to have such a tiny start, it could have been some kind of ocean of
   Nicely distributed elementary " g o d particles" that , like how any physical entity forms. Now this on the side, let's not forget that it is only a theory
   That I personally have to consider, but since it is incomplete, it needs to be modified or completed. Even if there was or still isn't , it would still be is, the is is alw is . It is like saying not there was is more relevant than there was n
6. The joker may have a finite amount of laughs; while using infinity to disprove infinity; saying there can never be infinity. "Never" is another word for infinity\zero.
   ∞ will have the last laugh; all the way to eternity.
7. 
   Laureano Luna: " The set of possible thoughts is not finite, for there's a possible thought about each natural number."
   This is technically true, since "not finite" could refer to a endlessly increasing finite, ie, to a "potential infinite", rather than to an "actual infinite" (which is logically impossible).
   
   But, if the intended idea was that for each number in the series {1, 2, 3, ...} there corresponds a possible thought, such that, by taking the series as an actually completed whole, an actual infinity of possible thoughts would obtain... well, then that idea would be false, since the series cannot ever be taken as an actually completed whole, since by definition the series is endless and necessarily incompleteable.
8. He makes very good points, but what he forgets is that same kind of problems and paradoxes arise if the universe is finite in size and has a finite age. And other thing he forgets is that he always assumed the universe is of finite age, then indeed inflation does not get you an infinite universe. But there is eternal inflation also, which can be past complete, that is infinite. That might very well be the case, but that can not be proven.
9. I would disagree.  I think infinity will eventually be shown to be the answer--of course it's not "big" or "small" because infinity is beyond relation.  As indicated, a fractal (i.e. fractal as information) is infinite, i.e. scale-less. Will infinities be discovered in the material world?  Seems unlikely--since materiality depends upon pairs, comparisons , differences--but I love the way the universe continues to surprise us. I doubt, for example, that genetic codes are finite.  Are the patterns of snowflakes finite?   It also depends upon perception--the perceiver and the perceived, ie. consciousness.  The problem is, that material scientists ignore the subject of consciousness--they hold themselves apart from their theories.  What is the scale of thought?  What is the scale of the "pictures" in the "brain" that are supposedly transcribed from the "external" mind.  For that matter, what is the scale of the universe? It is not that the question of infinity is not "testable"--the issue becomes whether infinity is necessary to solve all the presently unsolvable problems. If it does, then it seems like a viable theory. 
10. What about the mass of photons? Everything seems to indicate that it is zero, and you can write that as n/∞, or you can say it is infinitely small.
11. But I do sympathize with Hilbert's and the lecturer's thesis that there is no infinity in the real world. See .logika.umk.pl/llp/1834/5-1834zw.pdf
12. 14:40 'The infinity of that tape is a meaningless concept', referring to a Turing machine tape. The fact that an infinite tape is not realistic doesn't turn the concept meaningless. He should have added 'for all practical purposes'. 16:00 Gold's theorem does not depend on languages' having infinite length sentences. 16:34 The set of possible thoughts is not finite, for there's a possible thought about each natural number. The set of all possible brain states is surely finite.