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The History of Non-Euclidian Geometry - The World We Know - Extra History - #5

🕑 Added 2018-06-22 17:31:00 +0000 UTC

Comments

Dusk Star

Regarding the Quantum Mechanics / Quantum Computing videos - would it be possible to suggest running the scripts by someone like Scott Aaronson? So much reporting and pop science gets things horrifyingly wrong, and I don't want to see that happen here.

Juan Alberto Aranda Alvarez

This series made me become a Patron. You did such a good job of explaining such an important discovery! Now is going to be so easy for me to explain to my 12 year old child why Einstein is so important. Than you.

jesyspa

"Our knowledge is always evolving. It means that it might be the wrong idea to think of mathematics as 'true' or 'not true'. Rather, it might be more useful to simply ask 'is it well reasoned?' This frees us from the trap of having to prove the unprovable, and allows us to find reason in the unreasonable." This is a really fascinating question, and I'm glad it's mentioned! I do think that it's not quite so simple: 'is it well reasoned?' presumes the existence of a fixed reasoning system, which not everyone (*cough* Brouwer *cough) agrees with. Moreover, even if we assume a fixed metalogic that we're all okay with and then study a logic within it (this is the way geometry is treated in this series, for example), we can say "any consistent system is good", but this clashes against our intuitions: if the logic of natural numbers (Peano Arithmetic) is consistent, then it remains consistent if we add the assumption that it is *not* consistent! (This is all getting very far from the original topic, of course.) PS: Can't wait for your quantum computing series!

Ethel_Mezezi

6:13 Mr. Math, I don't feel so good...

Paul Lenoue

All of these references to mathematicians and scientists being thrown into fearful panic reminds me of the last panel in this comic: <a href="http://www.girlgeniusonline.com/ggmain/strips/ggmain20180622.jpg" rel="nofollow noopener" target="_blank">http://www.girlgeniusonline.com/ggmain/strips/ggmain20180622.jpg</a>

Michael Jebbett

Dude...

schuyler

what will the one off be ?

Jason Fox

Bravo! I know you only touched upon it at the end of this episode, but it's another interesting deep dive into math about there will be parts of geometry that will remain unsolvable. Remember that about 15 years after General Relativity, Godel presented his Incompleteness Theorems that showed that even first-order arithmetic will have unprovable elements. The work of all of math during the late 19th and early 20th centuries is incredibly fascinating!