Author Archives: ChefCouscous

Mind over Matter : Bruce Lipton

Medicine, Philosophy, Science 1 Comment

Key Points:

1. The Foundation of Science has changed since Newtonian Era, except Biology / Medicine and Psychology which don’t keep up:

Math => Fractal Math

Newton Physics (Matter)=> Quantum Physics (Energy)

(Organic) Chemistry => Electro-Chemistry

Energy = Field = 气 Chi / Qi

3. Environment -> Mind -> Perception -> Genetic Control

4. Consciousness (5%), Subconscious-ness (95%)

Examples:

  • Driving car: inexperienced driver (consciousness), experienced driver (subconscious).
  • Dating (conscious behavior)

Note: The successful Deeplearning AI is using the concept of Perception called “Perceptrons” by analysing the Environmental (BIG DATA) pattern with the help of Mathematics (Calculus : Gradient Descent, Statistics : Bayesian Probability, Algebraic Topology, etc).

Prime Number Theorems Conjectures Explained

Modern Math 1 Comment

1. Twin Primes Conjecture : there are infinitely many pairs of Twin Primes among the infinitely many prime numbers.

Note: 2013 Zhang YiTang proved the gap between the twin primes is no more than 70,000,000 [Terence Tao’s Polymath Project using Zhang’s method to further narrow the gap to 246 ]

2. Goldbach’s Conjecture

Chen’s “1+2” Theorem

3. Palindromic Primes (eg.11, 101, 16561)

4. Riemann Hypothesis

https://www.sciencealert.com/prime-number-theorems-conjectures-explained

French Math “Coniques” : ellipses, paraboles, hyperboles.

Education, Elementary Math, French, Modern Math 1 Comment

French Math is unique in treating these 3 conic curves: (ellipse, parabola, hyperbola), always starts from the first principle – a la the Cartesian Spirit “I think therefore I am” (我思故我在).

“Catersian” Analytical Geometry was co-invented by two 17CE French mathematicians René Déscartes and Pierre de Fermat.

Note: The “elliptic curve” is a powerful geometry tool used in Number Theory (proved the 350-year-old Fermat’s Last Theorem in 1994 by Andrew Wiles), also in the most advanced Encryption algorithm.

Why Math is so Sexy?

Education 1 Comment

Cédric Villani (Field Medal 2010) the French mathematician becomes a deputé (equivalent to Member of Parliament) in President Emmanuel Macron’s new party “En Marche” consisting of 90% non politicians.

His new revolution in French Primary School Math Education is introducing “Singapore Math” : the 1960s Chinese Secondary School One Math (算术 Arithmetic) modified by the ex-Nantah (南大, now Nanyang Technological University) Prof Lee Peng Yee (李秉彝) with the Polya Problem Solving Method aided by visual Model diagrams.

France excels in Abstract (aka New / Modern / Bourbaki) Math but poor in Applied Math, while Asian countries (China, Singapore, Korea, Japan etc) are opposite. This demonstrates clearly in the Asian 15-year-old students scoring Top PISA Math Tests & Math Olympiad Championships (even in the USA teams), while the French young Mathematicians (< 40 years old) take 1/3 of the world’s Field Medals – “the Nobel Prize of Math”.

It is ideal to combine the Asian (applied) Math pedagogy for Primary school (from 7 to 13 years old) math and the French (abstract) Math (eg. Set, Group, Ring, Field, Vector Space, epsilon-delta Analysis…) in high-school math (from 15 to 18 years old).

The wise Cédric Villani is just doing this Ideal Combination of “East and West” for French Primary School Math Education .

Note: In the video (12:12 mins) Villani described his “Eureka discovery” inspiration at 4 am in Princeton Institute of Advanced Math. The same experience found by many mathematicians eg. Poincaré, Zhang Yitang, etc. Read Villani’s book where he called this “Strange Head Voice” (definitely not hallucination!!) experience as “The direct phone call from God “.

数学范畴化 Categorification

Chinese, Modern Math 1 Comment

https://www.zhihu.com/question/31823394/answer/53592663?from=timeline

Key Points:

  • Category and Functor are above the underlying algebraic structures (Set, Group, Ring, Vector Spaces, etc), study the relations between these structures.
  • Early 19 CE mathematicians before “Category Theory” already knew there is 1:1 mapping between the Field Extension and Galois Group.
  • Treat Structures and Relation between them (Functors) on equal footing.

Kotlin: Co-Variance, Contra-Variance, Invariance, Immutability

IT, Uncategorized Leave a comment

Kotlin is a functional programming (FP) language which has the Category concept of co-Variance, contra-Variance. Java is object-oriented not FP, it has only Invariance.

https://dzone.com/articles/variance-immutability-and-strictness

Note:

Covariance and contravariance are terms that refer to the ability to use a less derived (less specific = CoVariance eg. Apple instead of Fruit) or more derived type (more specific = ContraVariance, eg. Gala instead of Apple) than originally specified.

Generic type parameters support covariance and contravariance to provide greater flexibility in assigning and using generic types.

  • Invariance

    Means that you can use only the type originally specified; so an invariant generic type parameter is neither covariant nor contravariant. (Java is always invariance.)

英国留学生带你回忆被数学支配的恐惧

Chinese, Education, Math Story, Philosophy, Science 1 Comment

这位中国留英数学专业的小伙子有很好的口才: 数学之美, 他的数学遗憾。

华威大学（The University of Warwick)，famous for mathematics in UK.

Key Points:

Einstein用 Riemann Geometry 数学救了Newton 物理。

中国数学的没落: 自从明朝科举废除数学考试

3位大师救近代中国数学: 华罗庚, 陈省身, 苏步青

数学光明的未来: AI, Big Data, Cloud Computing

天才的崎岖道路: “扫地僧”张益唐

时代的”指数” exponential快脚步, 不要追风, 要一以贯之 : Prof. Andrew Wiles proved 350-year-old “Fermat’s Last Theorem” (FLT).

[纠正]: Andrew Wiles 超过40岁, 没赶上Fields Medal, 只得个”奖励”。他看到椭圆(Ellipse)气球, 得到突破 FLT “工具”的灵感 – “Elliptic Curve” 。

数学是什么: 爱情, 艺术, 音乐, 科技

Learn Kotlin sans Java

IT Leave a comment

Kotlin is Object-Oriented Java + Functional Programming.

Much as we hate Java, Kotlin can’t run away from the Java “ghost” especially in Android development using the Java API and OO design patterns.

This tutorial, however, teaches you Kotlin “sans Java“, a great news for novices without Java knowledge.

I like this Kotlin teaching approach for 2 reasons:

  1. No need to struggle with Java /Android OO architecture until later stage;
  2. No need to be intimated by the complicated “Android Studio” editor.

https://hackernoon.com/how-to-write-your-first-program-in-kotlin-8554cb526158

Reform in French Baccalaureat

Education, French 1 Comment

Current Baccalaureat Drawback:

  • Study too many subjects,
  • High Drop out

New Reform:

  • Specialised on 4 major subjects – include compulsory French Literature (penultimate year before Bac) & Philosophy.
  • ala British A-level on 4 Advanced Subjects (eg. For Science stream: 1. Math, 2.Physics, 3.Chemistry /& Biology, 4.Economics) + 1 “Ordinary” Subject (English General Papers) + Project (Social / current affairs)

https://www.economist.com/news/europe/21736539-reforming-french-education-will-not-be-easy-emmanuel-macron-wants-change-beloved

《The Master Algorithm》

IT 1 Comment

Main Point: One single “Master Algorithm” for all kinds of knowledge from chess to Go to Medicine to Stocks to …, only differ in ‘Data’ context, but the same One thinking “Mind”.

《The Master Algorithm》must have these 5 features:

  1. Evolving-structure-based(ala genetic),
  2. Learning parameters (connected) ,
  3. Probability-based (Baeysian),
  4. Symbolic (knowledge representation as symbols),
  5. Analogy-based (recognise similarities).

  • Symbolic like “equation” used in Physics: F = ma => F – ma = 0 => general equation “U (X) = 0”
  • Evolutionist: rules create new rules and discard old irrelevant rules, like the nature selection “survival the fittest “.
  • Overfitting Data: Bias vs Variance. Eg. A clock aways late by 1 hour (high B, low V); if it tells almost the right time but alternate erractically between fast & slow (low B high V)

Induction is the inverse of Deduction: Deduction:

A is a, (A = Socrates, a = human) if a then b (b = mortal) Therefore A is b.

Induction:

The above is TRUE for A = {Plato, Aristotle, Confucius, …} who were Philosopher (P), Therefore (by Induction), P is b

Bayesian Theorem (Cause & Effect)

  • Pastor Thomas Bayes (18CE) invented it.
  • Pierre-Simon Laplace (19CE) codified it.

C: Cause
E: Effect

\boxed{ P (C | E) = \frac{P (E|C) \times P (C)}{P (E)}}

Prove:

suppose among 100 patients there are flu = 14 patients, Fever = 20, both = 11

flu = Cause, Fever = Effect

P (Fever |flu) = 11/14
P (flu) = 14/100
P (Fever) = 20/100

P (flu & Fever) = P (flu) x P (Fever |flu) …[1]

Also,

P (Fever & flu) =P (Fever) x P (flu | Fever) …[2]

[1] = [2]:

P(Fever) x P (flu | Fever) =P (flu) x P (Fever |flu)

Divide both sides by P (Fever),

P (flu | Fever)
= P (Fever|flu) x P(flu) / P(Fever)
= 11/14 x 14/100 / (20/100)
= 11/100 / (20 /100)
= 11/20

References :

  1. 《Probably Approximate Correct》 – Leslie Valiant, Harvard ( Turing Award)

Mathematical Thoughts on Western versus Chinese (aka TCM) Medicine

Uncategorized Leave a comment

TCM (Traditional Chinese Medicine) is a Continous Function (T) with 4 major “component” parameterized (pj) role-grouping:

T (p1, p2, p3, p4) :-> D

D being the disease treatment.

\boxed {\int T (p1, p2,p3,p4). dt = D}

Let’s use the popular and simplest “Chinese Panadol” aka “Lonicera & Forsythia Cold Tablets” (银翘解毒片) as an illustration: (sold in both TCM & western pharmacies in Singapore.)

p1 : 君 King role – main drug(s), powerful but usually toxic.
eg. 金银花 (Flos Lonicera Japonicae) & 连翘 (Fructus Forsythiae)

p2: 臣 Lieutenant role – Counter the side-effect (eg. toxic) of the King, like his supporting officer.
eg. 薄荷 (Herba Menthae), 牛蒡子(Fructus Arctii)

p3: 佐 Assistant role – Assisting both p1 & p2.
eg. 竹叶 (Herba Laphatheri) & 桔梗 (Radix Platycodonis)

p4: 使 Envoy role– Smoothen the whole process. eg. 甘草 (Radix et Rhizome Glycyrrhizae)

Each group Pj may consist of 1 or more drugs {pj1, pj2…pjn} of the respective roles.

Western Medicine is a Discrete Function (W):

W (X) : -> D

A specific drug (X) is made into a discrete pill for particular disease D treatment.

eg. Beta-blocker “Atenolol” pill for Blood Pressure; “Pravix” (or “Aspirin”) pill for Blood Thinner. Western medicine deals with side-effect by giving a second pill to counter the first drug’s damaging effect ala TCM p2 “Lieutenant” (臣) role (eg. “Omeprazole” to suppress the side-effect of Pravix / Aspirin which might cause stomach / duodenal ulcer after long-term use).

W (X2) : -> D

W (X3) : -> D

…

\boxed{\displaystyle\sum_{j=1}^{n}W(X_j) = D}

Reflections:

  1. When a disease is uniquely identified by a specific cause, Western “discrete function” treatment is efficient and fast.
  2. However, certain disease is a “syndrome” (eg. hyper tension, diabetes, depression, rheumatism, cold, ‘ABS’: 大肠敏感群候症…) with no specific cause(s), TCM “continuous function” is more effective though takes longer time.

Conclusion:

“West” should meet “East” in this century by combining TCM and Western Treatments for better patient benefits.

Example: 2015 Nobel (Medicine) Prize was awarded to the Chinese TCM Lady Researcher Tu Youyou 屠呦呦 : https://theconversation.com/is-the-2015-nobel-prize-a-turning-point-for-traditional-chinese-medicine-48643

Inventor of Yin-qiao 银翘: Wu JuTong 吴鞠通 (1758 AD- 1836 AD, 清 – 乾隆)

AI – DeepLearning – Machine Learning

IT, Modern Math 1 Comment

3 Waves of AI Evolution:

1st Wave (1950s) : Alan Turing “The Father of AI” and his Princeton Prof Alonzo Church (Lambda Calculus). MIT Prof Malvin Minksy’s “Lisp” Functional Programming (a.k.a. Symbolic or Declarative) Language.

2nd Wave (1980s – 1990s) : Knowledge-Based Rule Engine Expert Systems.
Failed because knowledge acquisition process is too difficult with limited rigid rules.

3rd Wave (2010s -): DeepLearning is the latest AI tool for Machine Learning, famous after 2016 “AlphaGo” game by a former Funan-center UK Kid Demis Hassabis (UK/Greek father & Singapore Chinese mom teacher) beat 2 “Go” World Champions (Korean Lee Sedol 李世乭 and China 柯洁).

Great Books Recommended –

1. Learn Everything in 《Deep Learning》:

  • Math (eg. Gradient Descent – by French GrandMaster Cauchy 1847),
  • Linear Algebra (eg. Matrix, Eigen-decomposition),
  • Probability (eg. Bayesian, etc),
  • Key Deep Learning techniques.

Note: Available at Singapore National Library (LKC Reference #006.31).

Order at Amazon: https://www.amazon.com/gp/aw/d/0262035618/ref=mp_s_a_1_3?ie=UTF8&qid=1516412628&sr=8-3&pi=AC_SX236_SY340_FMwebp_QL65&keywords=deep+learning

2. 《The Master Algorithm》 (Book or Audio)

http://catalogue.nlb.gov.sg/cgi-bin/spydus.exe/FULL/EXPNOS/BIBENQ/7400075/198909068,1

5 “Tribes” of Machine Learning, all with 3 layers (Representation, Evaluation/Scoring, Optimisation) :

  1. Connectionists (“Deep Learning”, Neural Network)
  2. Bayesians (Probability, Inference Rule)
  3. Analogizers (Similar Pattern)
  4. Symbolists (Logic)
  5. Evolutionaries (Survival the fittest )

Notes:

1. Bill Gates recommends this excellent book for 2018 reading, also found it on Chinese President’s Xi JingPing’s Office Bookshelf in 1 Jan 2018 New Year Speech.

http://www.chinadaily.com.cn/a/201801/15/WS5a5bf75aa3102c394518f26b.html

2. All available copies of this book in the Singapore National Library Board have been loaned out !! (Unusual in low-readership Singapore). Please reserve it via online queue.

3. Audio version (10 CDs) is excellent for in-car listening while driving, or travelling on plane/train/bus for busy persons.

Pre-requisites For Abstract Algebra

Modern Math Leave a comment

The 2 important pre-requisites for Abstract Algebra are “abstract thinking”, namely :

  1. You must not think of “concrete” math objects (geometrical shapes, Integer, Real, complex numbers, polynomials, matrices…), but rather their “generalised” math objects (Group, Ring, Field, Vector Space…).
  2. Rigourous Proof-oriented rather than computation-oriented.

The foundation of Abstract Algebra is “Set Theory”, make effort to master the basic concepts : eg.

  • Sub-Set,
  • Equivalence Relation (reflexive, symmetric, transitive),
  • Partitioning, Quotient Set, Co-Set
  • Necessary condition (“=>”), Sufficient condition (“<=”). Both conditions (“<=>”, aka “if and only if”)
  • Proof : “A = B” if and only if ∀a ∈ A, a ∈ B => A ⊂ B, and, ∀b ∈ B, b ∈ A =>B ⊂ A [我中有你, 你中有我 <=>你我合一]
  • Check if a function is “well-defined”. (定义良好)
  • These concepts / techniques repeat in every branch of Abstract Algebra which deals with all kinds of “Algebraic Structures”, from Group Theory to Ring Theory to Field Theory … to (Advanced PhD Math) Category Theory – aka “The Abstract Nonsense”.

Math Talent in Studying Math Easily

Education Leave a comment

Math Talent gives you the initial advantages like learn Math easily, understand quicker, less effort… it is akin to having a 100-meter head start in running competition, that’s about 30% advantage. You still need the remaining 70% in perseverance, passion & determination to succeed !

Einstein wrote to a young girl who complained about her difficulty in Math, to whom Einstein replied, “My Math difficulty is even worse!”. The greatest scientist of the 20th century lacked “Math talent” in Advanced topics in Riemann (curvature) Geometry, 4-dim Time-Space Math. He seeked help from his “Math-talented” wife & best friend, “Math Master” colleagues (David Hilbert , Emmy Noether), his Princeton neighbour SS Chern (陈省身) etc. His ETH Zurich University Math Professor Minkowski could not believe the former “lazy” student (Einstein) could invent “Relativity Physics” using Minkowski 4-dim Time-Space Math [1].

Footnotes

[1] Minkowski space – Wikipedia

Franco-Anglo Mathematics Research Cooperation

French Leave a comment

French people are rational (think before action), English people are imperative (action before think).

17CE French Mathematician & Philosopher René Descarte : “I think therefore I am” 我思故我在 。He invented Analytical Geometry (xyz cartesian geometry).

De Moivre Theorem:
(cos \: {x} + i.sin \: {x})^{n} = cos \: {nx} + i.sin \: {nx}

http://www3.imperial.ac.uk/
newsandeventspggrp/imperialcollege/newssummary/news_10-1-2018-16-41-35

Mathematicians Find Wrinkle in Famed Fluid Equations | Quanta Magazine

Modern Math Leave a comment

Navier-Stokes Equation – $1 million Clay Prize and one of the 7 Millenium Problems.

This N.S. Equation predicts the movement of fluids (air current, water flow) as vector field (with value and direction), matches the physical experiment outcome, but not proven mathematically.

https://www.quantamagazine.org/mathematicians-find-wrinkle-in-famed-fluid-equations-20171221/