C. Furey - Division algebras and physics - for a more general audience
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- čas přidán 7. 10. 2017
- Note 1: More precisely, four algebras generalize the real numbers *in a particular way*. To see what we mean by *in a particular way*, please see Section 1.1 of arxiv.org/pdf/math/0105155.pdf
Note 2: No dividing by zero, of course.
Dr. Cohl Furey
Walter Grant Scott Research Fellow in Physics
Trinity Hall, University of Cambridge
Filmed by Vincent Lavigne at VIVIDCAM
This film describes some of the motivation behind my research
Intended for a popular audience
www.furey.space
damtp.cam.ac.uk/people/nf252/
arxiv.org/pdf/1611.09182.pdf
arxiv.org/abs/1603.04078
arxiv.org/abs/1405.4601 - Věda a technologie
Wow - this comes across like the trailer to a thriller...More please !!!
So true. I felt the same
This version with the background music was better. I think a very strong attraction to mystery and curiosity is vital to pursue such austere subjects as mathematics.
I hope she finds what she's looking for. Additionally, I hope she finds a faculty position, but more importantly, I hope she post a video of her playing the accordion.
Nobody but North Koreans like accordions that much 😅
She is a fellow at Cambridge University.
Thank you so much for creating this channel. I'm pursuing theoretical physics (particle physics). So your videos are precious for my research. As we human (or any animal) see this universe not "as it is" but as the model that is useful for us to survive (we can't overlook evolution) hence we can't see or experience 100% reality intuitively, our senses are not evolved to comprehend it. We only have mathematics & experimental data at our disposal to create a picture of the objective (actual) reality. Thanks again for all these videos.
Put her on Joe Rogan to explain what the hell Eric Weinstien was talking about with his magic tollbooths and Spanish churches.
So this is really good stuff. Clearly well-prepared. Would like to see many more videos of this professor.
Good afternoon.
Thank you for your very important work.
I would like to make three remarks (suggestions).
1. Non-associativity is the same important property of space as non-commutativity (chirality of rotation in the visible three-dimensional world). No tricks are needed to get rid of non-associativity. In addition to the left-right property, which we visually observe in the visible space-time, there is also an additional left-right property for the second space-time, which is shown by the second quadruple of octonions (e4, e5, e6, e7).
2. When you draw the Fano plane, it is very important to put the unit "e4" in the center, and not the unit "e7".
3. It is important to separate "e4" and not the unit "e7".
Even though I'm not a mathematician I get a very general idea of what your research entails and find it facinating. Surely you are bound to discover correlations between octonions and physics as you continue your work. Now I'm going to go binge watch your videos and try to coax a kernel or two of understand to pop. Thanks for the straight forward delivery of information.
That (musical) pause at the end gave me goosebumps. Superb intro.
Oh my, this is really interesting! I had thought that perhaps different types of numbers applied to different levels of reality, just like you're talking about in this video. I asked some of my mathematician friends and they weren't familiar with any such concept. But I couldn't get over how different numbers readily apply to different things, ie. you can have 1 apple, but not i apples. Thank you for this!
Is there more detail on how exactly these classes of division algebras are used in their respective domains (C in quantum, Quaternions in Relativity)? Just curious if there's some fundamental interpretation to how these classes relate to each other in turn.
Looking forward to catching up on things topic.
This immediately reminded of Hoffman's paper on the Interface theory of Perception. If dimensions can be generalized, then all interactions we observe can just be measurements along different dimensions. This really changes the way I think about the space dimensions because it means that there's no reason that the way we consciously perceive space (as distances between things) is accurate, it could just be an evolutionary fluke?
cogsci.uci.edu/~ddhoff/Hoffman-Stevens-Handbook.pdf
Beautiful.
My only problem (generally) is the zero / infinity division aspect of the number system (starting at the Reals) not really being a division algebra once the physicist/mathematicians make approximations and ignore terms, leading to argument as about 'duality' (or lack of) when such approximations are made. Love all the rest!
Great!
Well... she is absolutely stunning!
Could it be that octonions are the mathematical structure of quantum computing functions or super string theory?
The universe is learning about itself...one day we will be able to simulate reality, if we describe all forces =D
brilliant
You explain things very well. Any recommended reading on quaternions? I think this will have big implications in physics too.
Abstract Algebra.... I love math!! I like proofs like some people like crossword puzzles. I have limited understanding of quaternions and want to learn more.
Someone make a scientist channel for scientist. That way we don’t always have to gear the conversation to high school science!
Thanks! For quaternions there is a lot material available. One you might like is a book by Pertti Lounesto called Clifford algebras and spinors.
Thank you! I will order it!
belatedly, but maybe it'll help you and/or others: there's a great interactive 3Blue1Brown video on quaternions, too
It’s a great video
when Einstein got to the E=mC2 part, he had completed his mission, his current job. helped end the war. i suspect, had his work been supported further, or the work that came after that was as well documented, he would have modified his theory that there is no spooky action at a distance.
You actually made the concept simple. Brilliant! All my math and science teachers tried to prove how smart they were. To finally see someone reduce Algebra's Division to a 2 minute video and make me feel lost is awesome. Maybe we have too many men in the field right now.
Stop judging people by their sex and start judging people as individuals.
Interesting, I'm going to have to look at the longer videos, and try to understand what you're talking about. :) This could be bad, as I only have high school maths.
Pick up an introductory book on Abstract Algebra.
Look up the 3 Blue 1 Brown channel. Thank me later.
An excellent start! (And welcome to the world of internet comments... 😱)
Does anyone know why ikj = -1 for quaternions?
Is it an axiom?
ijk = -1 because when you divide both sides of the equation by one of the units from the left side (for example, jk = -1/i), you will multiply the imaginary denominator on the right side by its complex conjugate (i = 0 + i, so the complex conjugate is 0 - i, or just -i) to turn it into a real number (you cannot divide by an imaginary number, so i×-i = 1 because i×i = -1 by definition). Don't forget to multiply the numerator on the right side by that same complex conjugate or else you'll change the value of the right side of the equation and both sides will no longer be equal (you end up multiplying the whole right side by -i/-i, which does equal 1). Now jk = (-1×-i)/(i×-i) = i/1 = i. Therefore, jk = i, which means ijk = i×i = -1.
You can do the same thing for j and k as well, but when dividing by j, shift it in the "ijk" product one place to the left or right to get i and k together and put a minus sign on the "ijk" product, because j = ki = -ik.
Going to your typo, ikj = 1 when you switch 2 of those units around once (if starting from ijk) because multiplication order is important (quaternions have anticommutative multiplication; switching the order of any 2 factors once, one place at a time for each factor, introduces a minus sign, and doing the same thing one more time with any 2 factors takes away that minus sign). This corresponds with the order of rotations in 3D space. A different order can give a different orientation.
How does "Therefore, jk = i, which means ijk = i×i = -1" follow?
Of course if ijk = -1 then
i*ijk = -i
i^2 jk = -i
-jk = -i
jk = i
Don't see how that proves ijk = -1
I was writing a response, but I decided I didn't think through this enough after all. It may be by definition, although it's easy to prove using Geometric Algebra, but that's not using the quaternion units themselves...
I suspect it is by definition
In any case, thank you .
She is indeed very spooky
i want korean language
Spreading these comments around a bit. I may pop a bottle of bubbly if: are you picturing a field of edges between balls like in czcams.com/video/xvflQcHT5C4/video.html ? 🍻 :-/ Jumping to conclusions...ball in ball still fits the radius must be 3 to 1 rule, so? Feels real close! 🍻
WOW, so there actually is a real-world problem to represent an intuitive way of thinking about non-associative action - ball rolling on a ball, brilliant :D
Well, it sounds like Cohl has found another way to express the three quantum forces, but not Gravity. So, the Octonions must not be the last word on unification theory.
I've often thought that Quantum particles are like higher dimensions popping in and out of lower dimensions - like a sphere moving through a plane - first you see a dot, then a circle, then a larger circle, and then decreasing circles till you see a dot again. This seems to me to explain how come quantum particles can jump energy barriers, quantum entanglement. Of course, the process is much more complex.
I also see possibly evidence for this in Special Relativity, where mass and energy increases as you get closer to the speed of light. The increasing mass is like the higher dimensional space going through a smaller dimensional space.
just because something is true, doesn't mean you aren't barking up the wrong tree and ending up with empty space
I'd say she is a UFO tv show fan. Think of the women on moonbase. Seems reasonable that someone who likes Sci-Fi would go into science.
I would give up all my athleticism and handsomeness to be smart enough to attract this female.