Division algebras and physics (Video 1/14). First video ~ general audience

Note 2: no dividing by zero, of course.

Video 1 of 14 - first video is meant for a general audience

Series: Division algebras and the standard model

Some short videos filmed by Vincent Lavigne

Seminar by C. Furey,
Walter Grant Scott Research Fellow in Physics
Trinity Hall, University of Cambridge

[rossrose]

Absolutely captivating series by Dr. Furey. I have an obsession with octonions and stumbled across the Dr.'s videos. Very good material, very good presentation, and very pleasant to watch.

[pedrocortez]

Mind blowing. Congratulations Dr. Furey, I honestly do hope your research of Octonions leads to furthering our understating of our universe.

[jackpitts]

Bravo! That's great logic, and definitely think you're right here. The Cayley-Dickson algebras are perfect math, as it relates to the "real" world. Furthermore, I think the world is quantum, which means integers dominate. So the only trick is to define the purpose of the irrationals which measure things like angles (sqrt(2), sqrt(3)) and arcs (pi, pi/2, etc...) as well as other curves such as those created with "e" such as exponsentials and logs. I would say that our base irrationals are scalar transform, so from 1 to pi, or 1 to sqrt(2) such that the irrationsl act as their own identities. Think of it like multiple Planck lengths, but each dimension has it's own length or integer base unit, or identity. In complex numbers, the base unit is i in one dimension, and 1 in the other. i is a type of idenity with special powers to transform into the integers (when squared, or multiplied by other 2 dimensions as in quaternions).

[victorrobert]

Illuminating lectures on Octonions. Thank you so much Dr. Furey for your tireless effort and all the progress that you have

[ICManygrins]

You're a great educator. Thanks for the video series. I appreciate that you get to write your first name on the blackboard time and time again as you explain your theories.

[ericclaptonsrobotpilot]

Dr. Furey, As someone who finds almost everything interesting, but does not have much undergrad education in science and math I have learned a lot about many a things over the years in the subjects of Mathematics, Physics, The Standard Model, Quantum States, Genetics, Astronomy, Cosmology, Theoretical and most recently about how the four number systems may help to explain the standard model (via Eric Weinstein) I have learned about all of these things via the Joe Rogan Experience podcast. Now, I didn't get to learn in depth about all those subjects by just listening to a single episode, but it was like a springboard to dive deep into the subject matter being discussed. Joe has world renowned scientists from all fields of expertise on the show. You would fit in perfectly as a guest. Joe is the best host because he actively listens and keeps asking deep questions in an effort to help himself and his audience not only learn, but understand esoteric concepts.

Please do the JRE podcast sometime soon,
A Fan
Seth

[Nekuzir]

Also found out about surreal numbers, neat stuff

As for whether or not higher dimensional systems can be useful in describing nature, it doesn't need to be true that nature have more unseen dimensionality to it for these systems to be useful. You can describe anything which relies on x number of variables for the output with x numbered dimensional number systems. The octonions for example are useful it making sure 8 different radio towers send radio waves which always constructively interfere with eathother. But if it were 9 towers you could just add another dimension

[ZeroG]

I found my happy place. Thank you for this.

[sriram]

I came here to learn about Octonion after Joe rogan's podcast on eric weinstein

[kfawell]

You suppose that it is hard to believe that nature uses R, C, and H, but not O (which is a compelling supposition). Is another way to say that this? Given that R is a special case of C which is a special case of H, then it seems reasonable to assume nature really uses O and what we have understood so far in nature is phenomena in terms of the first 3. This feels like the same kind of inspiration for Dirac deriving, well, the Dirac Equation. (BTW, I am a lay person who came here after reading the Quanta magazine article.)

[russelljohnson]

I'm no mathematician, but after reading the article on WIRED I instantly saw a correlation between octonions and other studies/theories which use an eight variable approach to understand behaviors in nature, human behavior, music & etc. Entertain me for a second but walk away from the complexity and math of octonions and replace some verbiage like "Law of Nature" with "Harmony". Like a scale in music, the 1st, 3rd & 5th notes make up the triad of harmony which is the principle of all music (well which has harmony that is..). Each of these notes have different properties as it relates to origin or key note "1" but basically a song spends more "Time" on the triad notes during a song/score. What if we took the quanternions (e1, e2 & e4) and changed them to be the triads (notes 1, 3 & 5) as it relates to the octonion peculiar theory/math. I would guess that once all of the 8 different unconventional elements are identified and further understood that they may have more in common with the laws of harmony than that of nature. Go ahead and laugh or call me crazy but sometimes it takes a complete different way of thinking about something to make so complex, simple enough to understand. As an example, over a decade ago, I read an article on technical analysis of the stock market (of all things) and explained the Elliot Wave Theory as a way to put "rules" or "laws" to the behavior of the market. At first I read for fun until I saw that the theory is based off an eight wave pattern of growth which also happens to be a fractal. Wouldn't you know it that the growth waves are wave 1, 3 and 5. I spent many years studying the stock market using the Elliot Wave Theory and I have to admit it is the most practical and best approach to understand the markets behavior. Mathematical harmony transcends so many different studies, fields that I would be shocked if we ever do achieve the great equations which takes gravity (I'll just call that the base cliff as foreshadowing) into account within our solid theories of physics today, that mathematical harmony would play a big part.

[JamesGarry]

Beautifully presented! <clicks through to next video>

[argiepoul]

The forth number system(octonions) is for theory of everything I believe!!

[darklydrawl]

Thank you. That was excellent. Looking forward to seeing the following videos.

[JDMathematicsAndDataScience]

Dr. Furey, I want to understand this more. Can you be so kind as to give a suggested reading list that will get me up to speed with this material?
Some sort of prerequisistes.

[Garganzuul]

I like this argument. Similarly, should we believe that all that scale-space between Planck-length and subatomic particles is empty?

[StsFiveOneLima]

This is absolutely fascinating. Possible follow-up: Why is it that the 8 dimensional numbering system is the point at which algebraic operations break down?

[lchtrmn]

Visually, the chalkboard doesn't provide enough contrast to distinguish some of what is written. However, the sound of the chalk certainly provides a percussive contrast to her lecture. It would be vastly better if the writing were done via a projector, or, if the board was black and the chalk much brighter.

[山山-yq]

🍎フラクタル的観察:
0次元の点は変分の
1/2の点で、
1/3の点で、
1/5の点で、
1/7の点で、

1次元の線・体積を埋め尽くす。
2次元の面・体積を埋め尽くす。
3次元の体積を埋め尽くす。
4次元の体積を埋め尽くす。
0±ε次元の体積を埋め尽くす。
そして0±ε次元に一致する。

点のネイピア数eは、
2次元から3次元を埋め尽くす。
点の円周率πは、
3次元から4次元を埋め尽くす。

3次元球面体同士の接触は
微小量の無限小面同士の接触で有るので、
そこは無限小面で扱うのが妥当だろう。


1/2は代数的に1/3, 1/5, 1/7を
生成する。

オイラーの公式、
e^iπ +1=0,
代数幾何学は
オイラーの公式を
普遍に保つことを
要請する。

臨界領域に於いては、

★
オイラーの公式が成り立つ物は、
これは極めて少ない。

★
オイラーの公式が成り立たない、
不道徳で有り得ない物が
満ちに満ちて
生成される。

1/2は2進法、
|↑>, |↓>, |←>, |→>,
メビウスの輪、

クラインの壷、
1/2+1/2=1=1/2 ÷ 1/2=2/2,

1/2は時空間を
尺取り虫
(a measeuring worm)の様に
変分を繰り返して移動する。
これは
ミクロなブラックホールと
ミクロなホワイトホールに
見える。
それを担うのが、
グルーオンであり、グルーオンの
体積空間の振る舞いが
尺取り虫(a measureing worm)に相当する。


正五角形はフリップをしながら、
軌道回転運動をする。
軌道角運動を獲得する。

正七角形はフリップして
軌道角運動をする。
厳密な理想の周回運動をすると
扱うなら、そうだろうが
実際は螺旋を描く！
原点から次第に離れる。
ハイパーインフレーション。

重力場を生み出すのは
1/7, 7である。
ここから、
0, 1, 2, 3, 4, 5, 6, 7, の
8元数が
量子力学と一般相対性理論を
統一する必要充分な元数である。
私はそう考える。

360°/7=7×51°+3°,
1周回度数360°ではなく
357°ならば
綺麗に周回する。
このとき時空間は歪む。
地球上の重力加速度程度ならば、
ほぼ平坦が保たれる。


剰余の3は原点の
無限小周りの時空間を、
決定する。
仮に
2π≡360×7= 2520,
⇔
π≡2520,
とするなら、
10以下の自然数で割り切れる。
空間を10次元に設定すると、
単純化された一個の
宇宙は
天球、プラネタリューム、
水晶球に、
あるいは
光点なり質点に
閉じ込めることになる。

天球の原点から極限的致命的
激烈な光子と素粒子が放出され
錯綜して
宇宙空間は射影される。

[davidgoldfield]

Can you go into more detail on the relationship between Quaternions and Special Relativity ?