@mind_blower69 Best Explanation of Gradient, Divergence and Curl #curl #divergence #gradient #math #physics
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Category Archives: Physics
Tensor
Convolution Theorem: Fast Fourier Transform
https://vt.tiktok.com/ZSPYDFBxb/
Convolution Theorem, using FFT (Fast Fourier Theorem) , also the key maths used in the AI Convolution Neural Network (CNN) by Yann LeCun (Turing Prize equiv “IT Nobel” ) from private Grande Ecole ESIEE (5 years sans Concours, after he gave up the infamous Classe Préparatoire’s Concours-focused Abstract Algebra).
MIT Prof Walter
This is the famous MIT Physics Prof Walter
Lagrangian Mechanics
Lagrangian Mechanics (L=K-U) easier than
Newton Mechanics (F=ma) where many forces to consider.
Emmy Noether Symmetry & Conservation of Energy
This ordinary “Euler-Lagrange Equation” is the origin of Theoretical Physics , pioneered by Emmy Noether, who discovered ‘Symmetry’ (L) in the ‘Conservation of Energy’.
An Art graduate in English and French languages, Noether continued studying Maths for 6 yrs under David Hilbert. She was also ” Der ” (masculin = Le) ” Father ” of Abstract Algebra.
https://vt.tiktok.com/ZSA2q7xsx/
Kitchen Math: Olive Oil Stokes Flow
Tensors
1988 Math Olympiad 6th Questions: 2 Fields + 1 President (Romanian)
Solution: Use Fermat’s 无穷递降 法 Infinite Descent Method (Note *）
https://vt.tiktok.com/ZShWpm7CR/
Note (*) : Fermat used this prove Light Refraction Law 光折射定律
Ternary 三进制
Ternary Go ： 黑/白/空
Physics Nobel vs Maths Fields
日本人得物理 Nobel Physics (12) 多过Fields (3)的原因：物理狂。
France : Physics Nobel (15) Fields (13)。数学狂
USA: 97 Nobel Physics vs 14 Fields
Germany: Physics 26: Fields 9
China: 2 Physics vs 1 Fields
https://www.zhihu.com/question/24127370/answer/3518982011?utm_psn=1848684419742830592
Yang-Mills Conjecture
Key Points :
- Yang-Mills Conjecture unite 2 out off 4 forces: strong (proton-neutron) vs weak (quarts)
- Like currency conversion from A to B currencies, the underlying money unchanged (invariant); Symmetry is the invariant of the weak forces
- Symmetry in weak forces: Non-Abelian U(1) Group eg complex number a+ib
- Later SU(1), SU(,2) , SU(3) symmetries for higher dimensions 2,3,4
- Yang-Mills still one unsolved in the 7 millennial math conjectures (except Poincaré Conjecture solved by Perelman), but has so far nurtured many Nobel Physicists.
Nakamura’s Blue LED
This youtube video has garnered 9 million viewership and many praises for its excellent explanation of semi conductor and PN junction.
Nakamura’s determination is admirable, despite having no (PhD) degree then, his success is :
1) dirty hand 动手;
2) stubbornness to stick to his belief;
3) challenge the stupid upper management (of Nichia).
Note:
The blue light (on LED screen in most mobile phone, iPad, LED TV) is bad for eyes. Put a layer of blue-light screen protector (S$30) to protect eyes.
Planck Constant
In 1973 A-Level Physics we studied “Black Body radiation”, Planck’s Constant … and the famous formula
E= ħν
but did not know the background discovery history, thermodynamics , entropy, and math tricks (limit) used by Planck.
Pi collisions between blocks
This 3Blue1Brown guy is an American PhD in Maths, promoting fantastic maths applications in Physics.
The “Pi” solution using Geometry “Phase Space” for collisions is awesome !
机器学习和线性代数 – 特征值和特征向量
Symmetry Groups in Physics
Group Theory of Symmetry in Physics Conservation Laws (in Energy, Momentum), Quantum Physics in unifying the 3 (out of 4, except Gravitational) universal Forces.
Theory of Everything: δS= 0
From Fermat Theory of Least Time to Newton Law of Gravity to Quantum Theory… : The Theory of Everything
δS= 0
Physics Problem solved by Euclidean Geometry or Affine Geometry Methods
Assume no friction at the 4 sided walls, the billiard bounces with incident angle always equal to reflection angle.
Proof: The bouncing path loci forms a parallelogram:
Dynamics & Geometry & Matrices
Conservation Laws, solved using Matrices.
[The answer is Pi]
2nd Method: Use Geometry to solve .
3rd method: using Optics (beaming light)
黎曼猜想可能被统计物理揭开面纱
【黎曼猜想可能被统计物理揭开面纱 – 今日头条】
https://m.toutiao.com/is/RgsGAvQ/
Arikan’s Polar Code Explained
Turkish Bilkent University Prof Arikan’s Polar Codes 极化码 Math behind Huawei 5G.
Turkish Bilkent University Prof Arikan’s Polar Codes 极化码 Math behind Huawei 5G.
https://m.bilibili.com/video/BV1fq4y1g7hq/
Symmetry & Vibrations
👍 Some Symmetry in GROUP Theory.
https://fb.watch/6ePlgNwYmr/
Physics proves Maths
He applied Physics (flux ) Gauss Divergence Theorem ‘DIV’ operator to get the derivative of Volume = Surface Area “
👍 That’s beautifully an example of using Physics to prove Math.
https://en.m.wikipedia.org/wiki/Divergence_theorem
Gear 齿轮 ＞17
3 Math Foundation Skillsets for Engineering / Finance Students
【普通人学数学系列-下集：学到什么程度】
理工/金融科Engineering/Finance 的三个扎实数学基础 ：
1) Calculus
2) Linear Algebra
3) Probability / Statistics
Prerequisites for the 3 above in
1) O/A level : Trigonometry, Algebra, Geometry
2) Vector Space (with some basic Algebraic Structures : Group, Ring, Field )
3) O/A level : Permutation/Combinatorics
对称破缺的物理“美”
Yang-Mills Equation：陈杲Chen Gao’s weak Solution
数学与物理的关系
（小学生与诺奖得主杨振宁的对话）
Math was a tool for Physics (Newtonian Physics)
Math & Physics were independently developed ( Physics Gauge Field = Math Fibre Bundle )
Physics is a tool for discovering Math (Quantum Physics : String Theory)
杨振宁 Yang-Mills Conjecture is one of the unsolved Millenium Math Problems.
傅立叶变换：美颜和变声原理？
Octonions & United 4 Forces
剑桥数学物理学家以八元数打开“万有理论”研究思路
This Cambridge Mathematician explains why need so many number system :
N Natural,
Z Integers
R Real,
Complex,
Quartenions (1,i,j,k) ,
Octonions
She believes the Octonions is the secret behind united field of the 4 forces :
G gravitational,
E electrical,
M magnetic,
W weak force in particules.
Maxwell United EM,
Einstein United GEM,
She believes her research in Octonions can unite GEM+W.
量子纠缠科普
听杨振宁讲物理课
听杨振宁讲物理课（七）：
[7.1] 好书推荐
1. E. T. Bell: 《Men of Mathematics” 》 – ［Comments:］ Irish Hamilton & Quartenions – Bell said Halmiton later’s life was a tragedy in trying to make quartenions universally applied in Physics but failed. Prof Yang : Quartenions will be “universally useful” in future.
Note : Quartenions (1,i,j,k) & Special Relativity – Does it ring a bell to you the UNIVERSAL 4 FORCES (Gravity, Electric, Magnetic, Particles Weak force) :
Division Algebras and Physics
2. E. Segrè (吴健雄的博士导师) & the story of the missing Periodic Table Element ’43’ (Tc) discovered by accident from unwanted trash.
[7.2] 重力势能和弹性势能
听杨振宁讲物理课（二）：速度和加速度
Particle Physics solved by Algebraic Topology with Co-Homology structure
物理学家已经确定了粒子碰撞的代数结构，这将诞生新的物理理论
Keywords: Algebraic Topology 代数拓扑， Co-Homology structure 上同调结构
丘成桐：经典广义相对论的历史和守恒量
Wolf Prize : Donaldson
The Modern Math is now proved by Physics, unlike the past history in reverse direction.
The first Math Fields Medals awarded to a Quantum Physicists Edward Witten in String Theory, now the 1st Wolf Prize to Donaldson who proved Math with Physics 杨振宁 Yang-Mills Equation (which is still one of the 7 Millenium Math Conjectures worth $1 m Clay Prize, but proven true in Physics Experiment) .
Wolf Prize is S$1m for 数学终身奖， unlike $100K Fields Medal for < 40 years old. Only Harvard Dean 丘成桐 (HK) received both prizes, while his mentor 陈省身 only Wolf (same year as Paul Erdos).
https://wolffund.org.il/2020/01/13/simon-donaldson/
《万物皆数》
1+2+3+… = – 1/12 (Euler)
The Simple Math Behind Our Expanding Universe
Schinzel-Zassenhaus conjecture ：the Repulsive Force Within Polynomials
Critique on Chinese Mathematics – Harvard Prof ST Yau
The Simple Math Behind Our Expanding Universe
Universality – eigenvalues
“Eigenvalues” 特征值 spacing of the “random” matrices follow the Universality pattern.
Nobel 2016 Physics Topology Insulator
杨振宁数学
Claude Shannon: How a Genius Solves Problems — Quartz
Nuclear Physics Leads to Linear Algebra Non-Traditional Method
Strange Nuclear Physcis leads to Math discovery of Linear Algebra new method.
Traditional Method:
Characteristic Polynomial – >Find Eigenvalues – > Solve Simultaneous Linear Equations – > Eigenvector
…
Traditional Way : Find eigenvalues first, then eigenvector.
Terence Tao’s Comments:
Relativistic Space Time, Fengshui, Isometry
风水 Fengshui (aka Geomancy) is Einstein Relativistic using Compass （东西南北上下 ＝Space) & Timing (吉凶日/时间 ＝ auspicious date & time).
宇 \Yu (Space) 宙 \Zhou (Time) = Space-Time
eg.
宇环 (universal surrounding)
宙时 (instant timing)
Axonometry = Isometry ( dengjiao toushi 等角透视，ie Angle Preserved Projection )
Chinese art is axonometric using isometry geometry, scrolling from right to left along time. Example : this digital animated 12-century painting
清明上河图 Qingming Festival River Scene（北宋）
“Why the world relies on a Chinese ‘perspective’” by Jan Krikke, China, AI and Quantum Physics
https://link.medium.com/z5LaoL0tdZ
From poor in math to Quantum Physics
She is a Cambridge PhD in Quantum Computing.
How to learn Quantum Mechanics on your own :
Math Online Tom Circle 