小算盘 大乾坤 Abacus

浙江临海市 国华珠算博物管主人 木匠 雷国华 收藏算盘20年,凭个人力量,保存中国算盘发源地的文化遗产,为此散尽钱财借债,免费开放给公众参观。说到家人因支持他而受苦,感慨激动不已。

中国的算盘上面2珠 (2×5),下面5珠(5), 共15,加1 = 16 进位。古代是16位 (Hexadecimal) 制, 半斤 八两 (= 1/2 斤 x 16 两 = 8 两)。

日本改良成10位制: 上面1珠 (1×5),下面4珠(4), 共9,加1 = 10 进位。

明朝万历年间的 “平民王子”朱载堉 (1536 AD – 1610 AD) 发明现代音乐的 十二平均律 (12-tone Equal Temperament) , 用81档的大算盘算出:先开立方根,后开平方根 2 次

\boxed { \displaystyle \sqrt[12] {2} = 2^{\frac {1}{12} }= 2^{{\frac {1}{3}}.{\frac {1}{2}}.{\frac {1}{2}}} = \sqrt {\sqrt {\sqrt[3]{2}}}}

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Math for AI : Gradient Descent

Simplest explanation by Cheh Wu:

(4 Parts Video : auto-play after each part)

The Math Theory behind Gradient Descent: “Multi-Variable Calculus” invented by Augustin-Louis Cauchy (19 CE, France)

1. Revision: Dot Product of Vectors

https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/vector-dot-product-and-vector-length

2. Directional Derivative

3. Gradient Descent (opposite = Ascent)

https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/gradient-and-directional-derivatives/v/why-the-gradient-is-the-direction-of-steepest-ascent

Deeplearning with Gradient Descent: