I really liked this video. I don’t think I could explain what makes the juxtaposition of the random ideas so compelling but it totally works. Also your painting is cool
Since you are a bit on the younger side, and I am someone like you - someone who has a natural curiosity that tends to "figure things out" (even if scientists, academics, etc. already have in past centuries/millennia) - prepare for a lifelong journey of people gaslighting you. Even those close to you, friends and family, despite them only wanting the best from you. I say this not as an excuse to dismiss their feedback, their feedback might actually be useful, but people's fears and gaps in knowledge doesn't necessarily predicate useful advice. Even if they are experts in the subject which you are discussing. Looking at the comments, the color theory thing doesn't make sense to a lot of people. It's already a pretty big leap to connect your color theory to your birthday paradox example. I like that you point out that "cool" colors in the real world are often quite hot, it's very much a comedian's take on absurdly socially accepted norms that we all blindly accept. But, an audience would have to first understand the idea of hot vs. cool colors, then connect that with the fact that "hot" in the real world colors are most often "cool." Them, they have to know that, even though things that are hot turn blue/white, most human intuitive understandings still apply to the art theory model of "cool" being blue/white. Though, you could argue that this is the case only because artists and designers produce media that reinforce the idea to peoples intuitions, but I'll stop there before I get too far in tangent. Then, to wrap it all up, they have to take all that and somehow apply it to a theoretical mathematics object. And that's just to be able to follow you past the first ~25% of the video. You figured something out and have a unique perspective about it. But, even the PhD mathematics guy in the comments appears to have missed the point. I like what you are doing and I hope your curiosity rabbit hole leads you toward better communication (man this comment really seems scathing, but I am quite excited about what you are exploring). If I've learned anything to help me with my communication (verbose as it still may be in a comment like this), metaphor and humor (much like that Socratica channel employs) has done wonders. I have begun to apply this in my writing and tested my combination of technology + philosophy writings to readers not necessarily adept in these subjects and they actually liked it! But, I came upon this intuitively because my only intention was to respect the readers' time and make reading my treatise enjoyable for them. Anyway, that's my opinion. It could be unhelpful just as others may have/will be unhelpful with what you are accomplishing here.
Hey, I'm a PhD student in mathematics, and my field of research is.... kind of close to this, so I thought I'd give my 2 cents on learning things like this. I will say that memorizing lectures on these topics might be the least productive way to learn. All my friends who went far in math didn't do it by having good memories, they did it by taking the time to develop strong intuitions and learn to "feel" math, the way you did with the birthday paradox. Doing this is a lot harder, and requires a bit of guidance on what order to learn things in. The number n(n-1)/2 is actually just the number of ways to choose 2 things from a list of n things, as you learned with the birthday paradox. The reason this appears in the indefinite orthogonal group is not particularly interesting, it's just a matter of counting dimensions. The more interesting part is the structure of the object itself: indefinite is referring to "not being positive definite or negative definite", which are meaningful terms coming from matrix analysis. If you want to learn more about these objects I think that's a great idea; these fields are fascinating. However, jumping straight into Lie groups is inadvisable, since there's a lot of intuition from analysis and algebra you'd need to develop to get a good intuition for these objects. The fact that a Lie group is just "a group that is also a differentiable manifold" requires that you understand what a group and a manifold are, and neither of those concepts is trivial. My recommendation would to be to get a background in linear algebra, especially spectral theory (which is just the theory of eigenvectors and eigenvalues), since this is where the notion of definiteness comes from, and discrete group theory (which is what most people are referring to by default when they describe group theory). Once you get a decent understanding in those, it would be worth learning about analysis, which will give you a lot of the background necessary to understand some of the more technical parts of Lie group theory.
Whats going on man? Is this a feber dream? What was that about color temperature? Like am I stupid? I took algebra in college I know some of this stuff but I dont understand this video. You made a painting? Using the colors of the temperature color scale? What is lie groups?
![[MIRRORED] LISA - ROCKSTAR 🎸 MV version #LISA #BLACKPINK #ROCKSTAR](http://i.ytimg.com/vi/-U58DuCCtZk/mqdefault.jpg)
I really liked this video. I don’t think I could explain what makes the juxtaposition of the random ideas so compelling but it totally works. Also your painting is cool
mathematicians aren't predictable
YOU SAID IT...
@@brockbierly Nobody else is brave enough these days.
Since you are a bit on the younger side, and I am someone like you - someone who has a natural curiosity that tends to "figure things out" (even if scientists, academics, etc. already have in past centuries/millennia) - prepare for a lifelong journey of people gaslighting you. Even those close to you, friends and family, despite them only wanting the best from you. I say this not as an excuse to dismiss their feedback, their feedback might actually be useful, but people's fears and gaps in knowledge doesn't necessarily predicate useful advice. Even if they are experts in the subject which you are discussing.
Looking at the comments, the color theory thing doesn't make sense to a lot of people. It's already a pretty big leap to connect your color theory to your birthday paradox example. I like that you point out that "cool" colors in the real world are often quite hot, it's very much a comedian's take on absurdly socially accepted norms that we all blindly accept.
But, an audience would have to first understand the idea of hot vs. cool colors, then connect that with the fact that "hot" in the real world colors are most often "cool." Them, they have to know that, even though things that are hot turn blue/white, most human intuitive understandings still apply to the art theory model of "cool" being blue/white. Though, you could argue that this is the case only because artists and designers produce media that reinforce the idea to peoples intuitions, but I'll stop there before I get too far in tangent. Then, to wrap it all up, they have to take all that and somehow apply it to a theoretical mathematics object. And that's just to be able to follow you past the first ~25% of the video.
You figured something out and have a unique perspective about it. But, even the PhD mathematics guy in the comments appears to have missed the point. I like what you are doing and I hope your curiosity rabbit hole leads you toward better communication (man this comment really seems scathing, but I am quite excited about what you are exploring). If I've learned anything to help me with my communication (verbose as it still may be in a comment like this), metaphor and humor (much like that Socratica channel employs) has done wonders.
I have begun to apply this in my writing and tested my combination of technology + philosophy writings to readers not necessarily adept in these subjects and they actually liked it! But, I came upon this intuitively because my only intention was to respect the readers' time and make reading my treatise enjoyable for them.
Anyway, that's my opinion. It could be unhelpful just as others may have/will be unhelpful with what you are accomplishing here.
As a person doing a master in physics I commend you for jumping head first into learning about Lie Groups hahaha, great video!
I don’t know how I got here, or what I’m doing here. But I am definitely glad I am
Hey, I'm a PhD student in mathematics, and my field of research is.... kind of close to this, so I thought I'd give my 2 cents on learning things like this.
I will say that memorizing lectures on these topics might be the least productive way to learn. All my friends who went far in math didn't do it by having good memories, they did it by taking the time to develop strong intuitions and learn to "feel" math, the way you did with the birthday paradox. Doing this is a lot harder, and requires a bit of guidance on what order to learn things in.
The number n(n-1)/2 is actually just the number of ways to choose 2 things from a list of n things, as you learned with the birthday paradox. The reason this appears in the indefinite orthogonal group is not particularly interesting, it's just a matter of counting dimensions. The more interesting part is the structure of the object itself: indefinite is referring to "not being positive definite or negative definite", which are meaningful terms coming from matrix analysis.
If you want to learn more about these objects I think that's a great idea; these fields are fascinating. However, jumping straight into Lie groups is inadvisable, since there's a lot of intuition from analysis and algebra you'd need to develop to get a good intuition for these objects. The fact that a Lie group is just "a group that is also a differentiable manifold" requires that you understand what a group and a manifold are, and neither of those concepts is trivial.
My recommendation would to be to get a background in linear algebra, especially spectral theory (which is just the theory of eigenvectors and eigenvalues), since this is where the notion of definiteness comes from, and discrete group theory (which is what most people are referring to by default when they describe group theory). Once you get a decent understanding in those, it would be worth learning about analysis, which will give you a lot of the background necessary to understand some of the more technical parts of Lie group theory.
Whats going on man? Is this a feber dream? What was that about color temperature? Like am I stupid? I took algebra in college I know some of this stuff but I dont understand this video. You made a painting? Using the colors of the temperature color scale? What is lie groups?
Its a feber dream
banger video, what do you tell your barber to give you?
"just fuck my shit up"
@@brockbierly fr not the answer i was looking for but stay winnig. tough times never last
Am i ok? I'm very confused. Is anyone else here?
Yes‼️
Yes‼️
I think your art is awesome.
forget about ittt
Oh, now they are lying to me?
G