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bolbteppa
bolbteppa
12:02 PM
@SillyGoose you wont really understand what a connection is until you learn the language of gerbes
I'm going to have a heart attack reading all this language aimed at obscuring the idea of taking a simple derivative :p
Connection form
In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of a coordinate frame, and so is not a tensorial object. Various generalizations and reinterpretations of the connection form were formulated subsequent to Cartan's initial work. ...
This entire article is very triggering, can't just take a simple derivative, no we have to re-define it as a map using bundles and call the derivative a connection, then we give the game away and admit connections arise from taking derivatives of the basis in a particular frame, then we repent and throw holy water over our back burning off the sin of going to a particular frame to repent
 
Mr. Feynman
Mr. Feynman
@bolbteppa that subtle sarcasm kills me :P
@bolbteppa I don't understand why you despise this so much: I mean, it's not like the Differential Geometry Police is raiding your house to have you use this formalism
I mean, plenty of people don't give a damn about bundles in physics
 
naturallyInconsistent
naturallyInconsistent
12:20 PM
@Mr.Feynman oh, you underestimate how many people have already fallen to the Differential Geometry Police. However, not as many as the extremely active King Genuflection Bureau is at making sure people respect strings.
 
Mr. Feynman
Mr. Feynman
I want to learn strings to be allowed to disrepect ST
But I think I'm falling in love in the process
 
naturallyInconsistent
naturallyInconsistent
ah, the pot is cracking
 
Mr. Feynman
Mr. Feynman
Periodic motion, they say
 
bolbteppa
bolbteppa
@Mr.Feynman I will never stop mocking the differential geometry morality police
 
Ryder Rude
Ryder Rude
12:38 PM
@bolbteppa hi. did u try to learn this alien language stuff and found that it didnt have a pay off?
im interested in this language, which is y im asking
 
bolbteppa
bolbteppa
Yes
 
Ryder Rude
Ryder Rude
so it only overcomplicates basic ideas
i was recently reading the category theory definition of a cartesian product, and it was over complicating a basic idea
 
bolbteppa
bolbteppa
Absolutely
 
Ryder Rude
Ryder Rude
if theyre going to talk about pairs of functions anyway, y not just talk about pairs of elements
it's overcomplicating the cartesian product
 
bolbteppa
bolbteppa
Category theory is supposed to be a good idea, supposedly showing how different theorems in different subjects are all coming from the same underlying ideas, however that promise completely fizzles when you actually study it
 
Ryder Rude
Ryder Rude
12:42 PM
oh
 
Mr. Feynman
Mr. Feynman
@bolbteppa I disagree and I'm glad to read that because these are the best dissings of the century
If you dislike rigorous differential geometry, which is arguably one of the most intuitive fields of mathematics, what do you think about measure theory? :P
Or Real Analysis
Please, don't tell me you prefer Newton/Leibniz style calculus
 
Slereah
Slereah
Measure theory is just saying if something is big or not
 
bolbteppa
bolbteppa
With measure theory you know what you're getting yourself into, you've signed up for the rigor, it's unavoidable and necessary
 
Slereah
Slereah
How unintuitive could it be
 
ACuriousMind
ACuriousMind
12:57 PM
@Slereah how big is the Cantor set
 
bolbteppa
bolbteppa
You are absolutely forced to deal with the contradictions arising from naive probabilistic thinking, it has earned the rigor, with real analysis you are talking about simply filling in a few tiny gaps in basic calculus, you can frame it in a grand confusing way and there are around 5 equivalent ways to do this because completeness of the real numbers can be frames in these different ways making it very confusing to study if you don't know that
 
Slereah
Slereah
@ACuriousMind somewhat
 
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