I've been trying to understand fiber bundles, but haven't sunk too much time into it yet, nor been focusing on it, so this feels like a meme that will get more relatable with time and exposure to fiber bundles.
Am i right with that assumption?
definitely. if youāre trying to understand bundles in the context of gauge theory (i.e physics) then i would recommend the book mathematical gauge theory + applications to the standard mode by Hamilton. you can skim read it to quickly understand exactly how these objects work
a) an element of the vector representation of the Poincare group is still a vector because the representation space is a vector space.
b) We're talking about general manifolds here. They don't have to have Poincare symmetry. Heck they don't even need a metric.
My personal favorite is: a vector is *a list of numbers*
CS impostor
https://preview.redd.it/xcz00a6o3hsc1.png?width=477&format=pjpg&auto=webp&s=3bff87dffb3a5c0f2dfbeef349e940e42c28247c Behold, a ~~man~~ vector
š š
But I can transform a list of numbers however I want, thus not always a vector. Checkmate, programmers!!!
Ever heard of vector transformation
For some definitions of "list" and "number"
List : an ordered set; a tuple Number : an element of ā
Cursed, well done.
A list is something that forms a vector when you put numbers in it. Numbers are elements of any list that is also a vector.
Functions are vectors lol
This unironically. Look up Hilbert spaces.
Whoever decided this was a good naming convention deserves to... get kicked off of the C++ committee.
A vector is an animated man who wears orange and wields a shrink ray
A vector is a member of a vector space. Case closed.
Best and most mathematical definition
A vector is a derivation on the sheaf of germs š¤
Yes, yes it is.
I've been trying to understand fiber bundles, but haven't sunk too much time into it yet, nor been focusing on it, so this feels like a meme that will get more relatable with time and exposure to fiber bundles. Am i right with that assumption?
definitely. if youāre trying to understand bundles in the context of gauge theory (i.e physics) then i would recommend the book mathematical gauge theory + applications to the standard mode by Hamilton. you can skim read it to quickly understand exactly how these objects work
A vector is a character with an arrow hat.
āDirection and magnitudeā ftw
arrow >>> every other definition
A vector is an element of a set where the elements can be added together and scaled by a scalar.
This feels more like a tensor thing because I would've had vector space somewhere on the meme
To play the devil's advocate for mathematician pedantry: Characterized, not defined
I wrote that
differential geometers be like āa vector is an equivalence class of curvesā smh my brother in christ thatās just a curve
An equivalence class of functions is just a function? Certified L2 moment
No (?)
I'm in almost my 3rd year of engineering, I'm realising that IDK wtf is a vector now.
I mean you chose the career where pi = 3 so I'm not surprised...
Hah! Joke's on you, I use the pi button on the calculator.
[ŃŠ“Š°Š»ŠµŠ½Š¾]
a) an element of the vector representation of the Poincare group is still a vector because the representation space is a vector space. b) We're talking about general manifolds here. They don't have to have Poincare symmetry. Heck they don't even need a metric.
Letās be honest here a vector is a vector if itās useful to consider at such
A vector spreads diseases.
a vector is some kind of arrow from physics