The Trouble with Infinity

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When you do math in your everyday life, you expect there to be a correct answer to your calculations, but when you're dealing with infinity, you can't even assume that there even IS a correct answer. Mathematician W. Hugh Woodin has dedicated his life to problems that may not even have an answer. Listen to him explain some of the difficulties in doing so.
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Опубликовано:

28 сен 2024

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Комментарии : 16

@Achrononmaster Год назад

Understatement of the Multiverse: "It is a big subject...". I think he knew he was making a geek joke.

@ronronladouceur 4 месяца назад

The thing is that you do not accept that there is no beginning... You built a wall and you do not see that this is juste a construction... If you suppose just a moment that this wall is a construction, dismantle it, and look if you can see better...

@58VintageSunburst 7 лет назад

The trouble with infinity is that a lot of smart people like Woodin have worked on infinity for 100+ years and have made almost no progress. So, maybe the most we can say about infinity (in Mathematics, not Philosophy) is that its a bad idea to begin with.

@entoris476 7 лет назад

What a misguided point of view you have.

@latioswarr3785 6 лет назад

Math takes a lot of time to advance sometimes centurys.

@loneranger4282 3 года назад

Fermat's last theorem took 300+ years before it was finally solved. And the Riemann could take even longer possibly.

@annaclarafenyo8185 3 года назад

Almost no progress??

@Achrononmaster Год назад

Judging by the results on display any any talks by Woodin and colleagues, they've made enormous progress. 58VintageSuburst coming with the strong I-have-not-listened-to-anyone-but-the-finitists energy.

@Aluminata 9 лет назад

A 2 dimensional sheet of paper is infinitely thin.

@radiow4qa71 Год назад

Excellent summary of a real issue... one wonders how this plays into "limits" and the calculus.

@mickmccrory8534 5 лет назад

I'm reminded of Max Plank's Black body radiation problem. The math exploded at higher freq.'s & didn't match experimental results... Solution... Quantum Mechanics. Maybe math needs Quantum math, where numbers reach a Plank limit, & an Uncertainty principal kicks in. Maybe decimal places don't go on forever.

@90sokrates 4 года назад

NOPE

@Achrononmaster Год назад

Not a good analogy, it's a dis-analogy. Decimal expansion is an idea, not a physical process. The idea is valid mathematics, so there is a well-formed statement in number theory to be proven, or shown to be Godel un-provable from the ZFC axioms. Your point can be taken differently, such as with Homotopy Type Theory extension, where "mathematics" is not _just_ ZFC, but can include other formal systems too. What Woodin hopes is that *_all_* such formal system will agree on CH and related theorems. This is the gold Woodin seeks. I've always backed his quest. It's not merely mathematics, although it is mathematics, it is also poetry or art of a kind.

@mickmccrory8534 Год назад

@@Achrononmaster ..... In math your theory can go to infinity. In Physics, that usually means your theory is wrong.