Different Views of Category, Type & Set

Different views of objects 对象 by:

1. Category 范畴 (morphism* between Objects, Functors ‘F‘ between Cats);

2. Set 集合 (a “smaller Cat”, only objects);

3. Type 类型 (deal only with same kind of objects: Int, String, Boulean…).

Note : Category can be a Set (SET) , Group, Ring, Vector Space (Vect) , “Topo” (Topology) … any algebraic structure with Associative Morphism (Map or ‘Arrow’ ) between them.

Note (*) : A morphism 态 in layman’s term is best illustrated by geometry:

2 triangle objects are similar 相似 = homomorphism 同态

2 triangle objects are congruent = isomorphism 同构


Note: Analogy –
Category : School
Type : Boy Class, Girl Class
Set : Students mixed of Boys, Girls


2019 Worst Computer Languages – What Not To Learn


Excluding the 3 Most Popular Languages – Javascript, Java, Python,

Dart and Kotlin emerge in 2019 thanks to Google’s support them as First-Class Language, Dart with Flutter uses in next Fuchsia OS , Kotlin replaces Java in Android OS.

RIP Sir Michael Atiyah

Singapore Maths Tuition

Rest in peace, Sir Michael Atiyah. Many scientists have called Atiyah the best mathematician in Britain since Isaac Newton.

Read also our previous posts:

Source: New York Times

Michael Atiyah, a British mathematician who united mathematics and physics during the 1960s in a way not seen since the days of Isaac Newton, died on Friday. He was 89.

The Royal Society in London, of which he was president in the 1990s, confirmed the death but gave no details. Dr. Atiyah, who was retired, had been an honorary professor in the School of Mathematics at the University of Edinburgh.

Dr. Atiyah, who spent many years at Oxford and Cambridge universities, revealed an unforeseen connection between mathematics and physics through a theorem he proved in collaboration with Isadore Singer, one of the most…

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Logic & Math (Set Theory)

Cambridge Prof Peter Smith:

You can download the book at the bottom link from the below web site.


Philosophy using Math – that is cool!

Set Theory is Philosophy, see this “Set Proofing Technique” taught in French Baccalaureate high school but Cambridge GCE A level ignores :

Prove : A = B
You need to prove 2 ways:
A ⊂ B
B ⊂ A
=> A = B

In the Bible 《John 14:11》
Jesus said to his disciples:
“Believe me when I say that I am in the Father and the Father is in me”.

Proof: Father (God) = Jesus

“Father in Me” :
Father ⊂ Jesus
“I am in the Father” :
Jesus ⊂ Father
Jesus = Father (God)
[QED. ]

Merry Xmas! 圣诞快乐!

The amazing power of word vectors

the morning paper

For today’s post, I’ve drawn material not just from one paper, but from five! The subject matter is ‘word2vec’ – the work of Mikolov et al. at Google on efficient vector representations of words (and what you can do with them). The papers are:

From the first of these papers (‘Efficient estimation…’) we get a description of the Continuous Bag-of-Words and Continuous Skip-gram models for learning word vectors (we’ll talk about what a word vector is in a moment…). From the second paper we get more illustrations of the…

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