The Limits of Understanding

This statement is false. Think about it, and it makes your head hurt. If it’s true, it’s false. If it’s false, it’s true. In 1931, Austrian logician Kurt Gödel shocked the worlds of mathematics and philosophy by establishing that such statements are far more than a quirky turn of language: he showed that there are mathematical truths which simply can’t be proven. In the decades since, thinkers have taken the brilliant Gödel’s result in a variety of directions–linking it to limits of human comprehension and the quest to recreate human thinking on a computer. This program explores Gödel’s discovery and examines the wider implications of his revolutionary finding. Participants include mathematician Gregory Chaitin, author Rebecca Goldstein, astrophysicist Mario Livio and artificial intelligence expert Marvin Minsky.

This program is part of The Big Idea Series, made possible with support from the John Templeton Foundation.

The World Science Festival gathers great minds in science and the arts to produce live and digital content that allows a broad general audience to engage with scientific discoveries. Our mission is to cultivate a general public informed by science, inspired by its wonder, convinced of its value, and prepared to engage with its implications for the future.

Subscribe to our YouTube Channel for all the latest from WSF.

Original Program Date: June 4, 2010
MODERATOR: Paul Nurse
PARTICIPANTS: Gregory Chaitin, Mario Livio, Marvin Minsky, Rebecca Newberger Goldstein

Paul Nurse's Introduction. 00:00

Who is Kurt Godel? 03:36

Participant Introductions. 07:22

What was the intellectual environment Godel was living in? 10:57

Godel's beliefs in Platonism. 19:45

Gregory Chaitin on the incompleteness theorem. 22:30

Platonism vs. Formalism. 27:18

The unreasonable effectiveness of mathematics in the world. 40:53

The world is built out of mathematics... what else would you make it out of? 47:44

Mathematics and consciousness. 53:29

What are the problems of building a machine that has consciousness? 01:01:09

If math isn't a formal system then what is it? 01:07:40

Explaining math with simple computer programs. 01:18:33

Its hard to find good math. 01:25:40

[WorldScienceFestival]

Hello, YouTubers. The World Science Festival is looking for enthusiastic translation ambassadors for its YouTube translation project. To get started, all you need is a Google account.


To create your translation, just type along with the video and save when done.

The World Science Festival strives to cultivate a general public that's informed and awed by science. Thanks to your contributions, we can continue to share the wonder of scientific discoveries with the world.

[JasonJason]

It doesn't matter what documentary I fall asleep to on YouTube, when I wake up, this is on.

[SitNSpinRecords]

I’m not good at mathing, but I do know one thing..
that hum in the speakers is because the power amps and mic are plugged into the same circuit as the lights.

[lastchance]

FINALLY!! A moderator who let the scientists talk and the discussion evolve naturally. Brilliant discussion by some brilliant people. Thank you

[MrBendybruce]

This was a group of very intelligent, opinionated, and socially awkward individuals who nonetheless managed to have a stimulating and thought provoking conversation. Made me feel right at home.

[grayxy]

Too short. Every single of them deserves at least 2h just alone. Finally some actual discussion. Great. Enjoyed.

[Kvantifierad]

It's nice to see a humble presenter for a change. This is one of the few presenters in theese WSF panel discussions that doesn't interrupt the panelists while they're speaking and it makes for much more interesting discussions. I wonder when the other egomanic presenters will realise this.

[tysparks]

The wonderful thing about these brilliant people is their senses of humor.
I can't imagine a greater group to have a drink with.

[pauloabelha]

Every mathematician was once a child. Piaget went on to study children to arrive at the "what is knowledge" question. I believe that is very important and has been forgotten in this discussion.

[RadiationOverdose]

To me, Gödels theorem essentially states that it is impossible to have an isolated system. Any system can only be complete and true within the context of another system. This theorem is fundamentally consistent with features of quantum mechanics and special relativity. In quantum mechanics, the mechanism of observation tells us what is true about an electron or photon and in special relativity the measurement of energy is always in the context of another system. These are core features of our reality.

The best part about this theorem, for anything to exist there must be an endless chain of systems that describe (prove/validate) it. Ultimately, there is no end to the feast of knowledge.

[aperson]

Hello, congratulations to the moderator, Paul Nurse, for actually letting the speakers talk :-) ✔

[realskepticalstoic]

Mario is my favourite science illustrator. He is able to come to conclusion from multiple and divergent questions. Congratulations for this video.

[Kurtlane]

At 22:40: "80 years later we still don't know what the hell Gödel proved."Thank you so much. I thought I was the only idiot. Makes me feel so much better.

[srikiraju]

Livio is so good in this, impressive how he brought everyone together

[TheHelvetican]

Five years ago we reached out limit of understanding and entered an era of willful misunderstanding.

[dannycrofts]

'The more I think about language, the more it amazes me that people ever understand each other at all.'

- Kurt Gödel Ω
The statement A ∧ B is true if A and B are both true; else it is false. ☑️ 101

[mustafaabohari]

One of best discussion on any science topic that I ever saw. it was relevant and also entertaining. kudos to all the panelists and big thumbs up

[lutaayam]

The advantage of not being smart is that I'm always living in awe of such people. It's a world of wonder! How can people be so gifted?! How do they come up with such elegant ideas?!!!

[Nurmncr]

lol @ the few of us in the world who would watch a video like this by choice.

[amdenis]

Great discussion. I love how Minski is the only panel member who gets applause, despite the fact that he has repeatedly, confidently, and so consistently shot down the work and direction of other scientists for decades and repeatedly turned-out to be wrong. It’s fine to be wrong, especially while pushing boundaries, but his hubris has cost us decades of important research across thousands of great scientists. Worse yet, he still argued for his disproven approaches, and against validated and verified science such as the perceptron/neural networking; denying basic reality along the way in favor of his disproven beliefs.