Grant Sanderson
@
3blue1brown


Pi creature caretaker.
Math videos: youtube.com/c/3blue1brown
FAQ/contact: 3blue1brown.com/faq

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Grant Sanderson
@3blue1brown

Aug 10  
The slope of f(x) = x^2 at the intersection x=f(x)=1 is 2, so that point should be unstable.
And indeed, if set variable x to be 1.0001 or 0.99999 and loop over the operation "x = x^2; print(x)" you'll find that it diverges away from that fixed point.


Grant Sanderson
@3blue1brown

Aug 7  
Like minds!


Grant Sanderson
@3blue1brown

Aug 6  
Yes, of other collections (not a joke).


Grant Sanderson
@3blue1brown

Aug 6  
Right, exactly. I guess what I'm wondering is if it's obvious that a "typical" group, or a typical simple group anyway, looks more like S_n than C_n in this sense.


Grant Sanderson
@3blue1brown

Aug 6  
Yes, but not in a way that would match this pattern. You can try it yourself by factoring a few other numbers around the same size as this one. One thing you'll notice is that it's much more typical to have much larger primes somewhere in the factorization.


Grant Sanderson
@3blue1brown

Aug 6  
I'd love that! You can shoot me a message here: 3blue1brown.com/faq#contact


Grant Sanderson
@3blue1brown

Aug 6  
I wonder if there's a way to make rigorous the idea that choosing a "random" finite group will have a size whose prime decomposition "looks like" that of n! for some n.


Grant Sanderson
@3blue1brown

Aug 6  
One the one hand this seems strange, e.g. cyclic groups show no such preference. But then again S_n obviously does, so maybe via Cayley's theorem, it's somehow to be expected of groups in general.


Grant Sanderson
@3blue1brown

Aug 6  
I had never really noticed this before and would have assumed that it's just because the examples we tend to work with are "simpler" in some sense.


Grant Sanderson
@3blue1brown

Aug 6  
Math Twitter:
Is there a known reason behind why the prime factorization of the size of the monster group has a kind of exponential decay pattern to it? That is, lots of 2's, a fraction as many 3's, a fraction as many 5's, ultimately petering out at 71? pic.twitter.com/gzRCOuIvsg


Grant Sanderson
@3blue1brown

Aug 4  
It is compulsory, so for the example you mention, it's why it's very important to have a "null" bit that doesn't change what square the configuration points to.


Grant Sanderson
@3blue1brown

Aug 4  
Maybe a more perfect video would have reoriented the picture of the hand to match the example, but then again the process of learning to use the righthand rule involves practicing reorienting an image like that in your head.


Grant Sanderson
@3blue1brown

Aug 4  
Ah, I see the confusion. The hand is not meant to align perfectly with the axes draw, just to be there as a guiding reminder of how the righthand rule works.


Grant Sanderson
@3blue1brown

Aug 4  
It's meant as a tongueincheek joke :)


Grant Sanderson
@3blue1brown

Aug 4  
Woohoo! Congrats. Looking forward to getting my preorder :)


Grant Sanderson
@3blue1brown

Aug 3  
Wordplay + internet replies = 🙄
I wonder how Abbot and Costello would have fared on Twitter.
"I think you're misunderstanding that Who is a person, not a pronoun!" twitter.com/3blue1brown/st…


Grant Sanderson
@3blue1brown

Aug 3  
Somehow it's weird to me that "old" has two antonyms: "young" and "new". Do other languages have separate words for old?


Grant Sanderson
@3blue1brown

Aug 3  
Take a computer from 1995 and one from today, which one is "old"?
Take the version of you from 1995 and the version from today, which one is "old"?
Some things age into the past, others into the future.


Grant Sanderson
@3blue1brown

Aug 3  
I'd actually be genuinely curious to hear if @johncarlosbaez
thinks these interactive visualizations are helpful at illustrating the SU(2) > SO(3) connection.


Grant Sanderson
@3blue1brown

Aug 3  
It's done in the context of a stereographic projection, so much of the lecture is aimed at building intuition for what that is, but hopefully, it can give you some intuition for how each action involves "two perpendicular rotations", and why it's a double cover of SO(3).

