Gödel's Incompleteness (extra footage 2) - Numberphile

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Professor Marcus du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford.

Professor du Sautoy's book as mentioned...

We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science.

NUMBERPHILE

Videos by Brady Haran

[unvergebeneid]

I like that guy. I hope we'll see him again in future videos!

[qfytidw]

Q) Why do you need to make so may 'extra footage' videos on Gödel?

A) Any sufficiently long series of videos on Gödel must also be incomplete!

[chizhang]

Prof. du Sautoy's shirt really resonates with the topic they are discussing...

[AJMansfield]

You should do a thing discussing how the incompleteness theorem relates to the halting problem, and how the whole Turing machine thing was used in Turing's proof.

[YairPinto]

I'm not sure Marcus does this on purpose, but I feel that he is seriously misrepresenting Godel's theorem. It does NOT prove that certain truths are unknowable. It only shows that there is not one formal system (i.e. one algorithm), that can prove all true statements.
Godel's own theorem is a case in point: for every formal system a Godel statement can be formulated that is unprovable from within that system, yet conscious humans can understand that the statement is true. So it is a knowable true statement, yet one that cannot be proved with an algorithm.
Marcus kind of brushes over this, and writes this down to our understanding being another formal system. However, it is also conceivable that human understanding simply does not equate to a formal system.

[SubTroppo]

This reminds me of the best expression I have come across for the inherent limit of human knowledge: "bounded rationality".

[highlewelt]

The link to this video in part 1 of the extra footage is missing

[SmileyMPV]

What if we cannot find the answer to the question "Are there questions about the universe which we cannot find the answer to?"

[asailijhijr]

Can you still prove or find Godellian concepts in an axiomatic system that doesn't have primes? Are there different ways of encoding logical statements?

[DanielFoland]

Waiting for Extra Footage 2 to go live was the closest I've had to a cliffhanger is some time. _What's he gonna say? I don't know. Exactly! Gah!_

[StuMas]

The conclusion I've reached is that Atheism is: Admitting you don't YET understand God.
Religon is: Pretending you NOW understand God.

(...something along those lines..)

[Tossphate]

Thanks for including all the extra footage, there's so much more than the main upload. It's great to see prof MDS on your channel, I remember his RS Xmas lecture was superb.

[GinoTheSinner]

If there are "things beyond science" they are actually a part of science, we just don't know how to incorporate them. Things work the way they work, end of story. If it's transcendental in a whole new mathematics/logic kind of way then that's how it works.

There is no such thing as a "scientific world" and a "mystic/transcendental world", because as soon as one interacts with the other, then that is the way it is. And it works in some way, according to some rules.

Checkmate mystic atheists

[trapper]

Man the universe is sooo fucked up.
I love it.

[yeet]

Love this guy too... but ugh!.. Marxist theologian?.. can't think of anything less cool, at least from an atheist-libertarian mindset, lol

[davidwilkie]

If science, the process, requires agnosticism, to operate as an observer of least bias, then atheism has a deliberately indiscriminate bias against emotional beliefs that shouldn't be necessary, if the process of science is kept separate from what is generally socio-political. Except when it's the subject of study?

[edwardowen]

When I saw there was extra footage I hoped it was going to be an hour long. Please do more with Markus on this topic, it's absolutely fascinating. Thanks for the video!

[alainmifsud]

Question: What is the cardinality of all the unprovable statements under our axiomatic mathematics, how much larger is it than the cardinality of the set of those statements which may be proved?

[jasonfeingold]

Again, Goedel's theorem deals specifically with the Principa and related systems. Isn't it rather fatuous to extend that to anything else?

[jb]

Human self-awareness is something science can't know.