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[MrRoboto75]

Actually, a dungeon based around mario 64 could be fun, with magic paintings leading to various demiplanes scattered about the dungeon.

[McTraveller]

A Veritasium Gem - but the WTF starts at about timestamp 29:25.

Spoiler (click to show/hide)

The Game of Life - simulating The Game of Life 

[Kagus]

A Veritasium Gem

"There is a hole at the bottom of math... A hole that means we will never know everything with certainty"

Including, hilariously, that statement. Which is very apt, considering.

[McTraveller]

A Veritasium Gem

"There is a hole at the bottom of math... A hole that means we will never know everything with certainty"

Including, hilariously, that statement. Which is very apt, considering.

Actually no - the Incompleteness Theorem is one of the things we can know with certainty - so long as our system is Consistent. It's only if the system isn't consistent can we make no statements.

[Jopax]

Apparently Company of Heroes 3 is a thing, just out of the blue they kicked out a pre-alpha thing that a bunch of folks streamed. Looks pretty good for a pre-alpha.

[Vector]

Actually no - the Incompleteness Theorem is one of the things we can know with certainty - so long as our system is Consistent.

Well, so long as we can axiomatize a copy of the natural numbers in the system.

[wierd]

The godel system did that, yes.

[scriver]

Math sits on a throne of lies!

[methylatedspirit]

Actually no - the Incompleteness Theorem is one of the things we can know with certainty - so long as our system is Consistent. It's only if the system isn't consistent can we make no statements.

That sounds like a mindfuck. The statement that you can't decide if all statements are true in a consistent system, is itself decidable. The statement that you can't know everything is one of the statements that you can say is true.

I mean, phrased that way, it sounds obvious, but I wasn't expecting it to be formally proven!

[NJW2000]

Gentle reminder that the Incompleteness Theorems don't actually tell us about truth - they tell us about derivability in formal systems. Truth is a semantic notion, and is generally thought about in terms of (intended) models when it comes to formal systems.

It's also very much an open question whether the theorems actually tell us something about knowledge in mathematics. If you think something like Hilbert's Program is necessary for us to know mathematical statements, then yes, they do tell us something about knowledge in mathematics. I suspect many mathematicians would disagree with that. I'd say that I know that Robinson arithemetic is consistent - I just can't offer you a proof in finitary arithmetic!

[TheSteppeWolf]

IS THERE A FUCKNG "THINGS THAT MADE YOU PAIN TODAY' THREAD?

Today I fucking fell on my ass onto concrete because I tripped and I broke BY FUCKING TAILBONE AND IM IN AGONE AND IM GOING TO THE HOSPITAL NW THE PAIN IS BLINDING

[TheSteppeWolf]

Sorry I can't type straight

[KittyTac]

That's a yikes from me.

[Mathel]

Ouch.

My laundry machine failed yesterday, taking a portion of the house's electric installation.
No breakers fell, but I still tried resetting the ones, whose circuits were off. Nothing. I checked fuses, all were at 0 Ω.

I was calling electricians if they were willing to come and fix it. 3 refused.
Then I called a fourth and he told me to try resetting all breakers, not just the offending ones.

And it helped! I am not going to try the laundry machine again, but everything else works.

[Vector]

Gentle reminder that the Incompleteness Theorems don't actually tell us about truth - they tell us about derivability in formal systems. Truth is a semantic notion, and is generally thought about in terms of (intended) models when it comes to formal systems.

It's also very much an open question whether the theorems actually tell us something about knowledge in mathematics. If you think something like Hilbert's Program is necessary for us to know mathematical statements, then yes, they do tell us something about knowledge in mathematics. I suspect many mathematicians would disagree with that. I'd say that I know that Robinson arithemetic is consistent - I just can't offer you a proof in finitary arithmetic!

*applause*