This is a spectacular lecture - I've had an "interest" in topology for a long time, but I could never really get my ahead around how it was relevant to other, more "practically interesting" areas of math. But Dr. Wildberger just made that make sense to me, right around the half-hour mark. I feel like a new brick just settled into place in my "knowledge wall," and I always just love that feeling. 🙂
11:30 - Ok, I was also having initial trouble seeing that connection between the circle on the sphere and that "vertex" point. But Dr. W's response to the audience question was well done and now I see - I hope the questioner does too. The key thing was when he pointed out that if I was looking at the sphere with my eye at the vertex, the part of the sphere I could see would like inside a circle on its surface. "Click."
Enjoying the lecture series. One humorous comment is that the early part of this (esp around the 10m mark) could easily have the speech distorted, fake subtitles added, and reshared as 'Lecture on the Theory and Construction of Death Stars'... (I guess that's what happens if you grow up watching Star Wars)
I'm not sure i understand why there are 2 layers; is it that one layer is "z" and the other "z^2"? or that they represent the 2 complete revolutions made by z^2 with one revolution of z? and why is it okay to make slits? it doesn't seem like a continuous transformation. Thanks.
You say s2 + point in infinity. Does it matter which point? Because previous video said about line in infinity, which suggest there is more than one possibility...
Hello Prof. Wildberger, I was wondering if you had a syllabus of some sort for this course. And i was also wondering what you thought of the book on Algebraic Topology by Allen Hatcher to be used as a companion to these lectures.
hi professor, i want to ask why only (1,0) is the exceptional case instead of (k,0) for all k .why is the other points already included in the 1D subspace
y2536524 it is the line through the point from the origin. It can be scaled by any complex number. Hope that helps. (Just realized I’m 5 years late but fuck it)!
This is a spectacular lecture - I've had an "interest" in topology for a long time, but I could never really get my ahead around how it was relevant to other, more "practically interesting" areas of math. But Dr. Wildberger just made that make sense to me, right around the half-hour mark. I feel like a new brick just settled into place in my "knowledge wall," and I always just love that feeling. 🙂
These lectures are very clear and engaging. Many thanks to A/Professor Wildberger for sharing these with the world!
Dr Wildbergeris awesome. He can guide you to your personal mathmatical niche. Absolutely a genius.
Totally hooked, what a wonderfully rich subject. Feel privileged to be able to sit this course from the UK, thank you to the Prof and to UNSW
Thankyou Dr Wildberger
11:30 - Ok, I was also having initial trouble seeing that connection between the circle on the sphere and that "vertex" point. But Dr. W's response to the audience question was well done and now I see - I hope the questioner does too. The key thing was when he pointed out that if I was looking at the sphere with my eye at the vertex, the part of the sphere I could see would like inside a circle on its surface. "Click."
17:35 to 17:38 gave me chills.
Enjoying the lecture series. One humorous comment is that the early part of this (esp around the 10m mark) could easily have the speech distorted, fake subtitles added, and reshared as 'Lecture on the Theory and Construction of Death Stars'... (I guess that's what happens if you grow up watching Star Wars)
I like these lectures a lot, thanks for uploading them.
Great explanations; Thanks Professor.
I'm not sure i understand why there are 2 layers; is it that one layer is "z" and the other "z^2"? or that they represent the 2 complete revolutions made by z^2 with one revolution of z? and why is it okay to make slits? it doesn't seem like a continuous transformation.
Thanks.
Is NJ laying the mathematical schema of quantum wormhole?
Do you mean AdS/CFT? It's veery distantly related, although the dualities between different surfaces/spaces are important and somewhat similar.
You say s2 + point in infinity. Does it matter which point? Because previous video said about line in infinity, which suggest there is more than one possibility...
Hello Prof. Wildberger, I was wondering if you had a syllabus of some sort for this course. And i was also wondering what you thought of the book on Algebraic Topology by Allen Hatcher to be used as a companion to these lectures.
29:29 Riemann Death Stars
awesome lecture, I guess I've learnt something.
hi professor,
i want to ask why only (1,0) is the exceptional case instead of (k,0) for all k .why is the other points already included in the 1D subspace
y2536524 it is the line through the point from the origin. It can be scaled by any complex number. Hope that helps. (Just realized I’m 5 years late but fuck it)!
Certainly the first statement is correct. However it is not so clear what you mean by the last two... but I think roughly your intuition is okay.
👍🏼
It's amazing that Zero is going to infinity : it's a matter of rotation
wow
life Cann't be more Simple, or may be more complicated !
Ogres are like power maps on the Riemann Sphere
It seems the 9 and 10 do better than the 3 on an layered onion 🧅 to me.
a debonair mathematician