A History of Vector Analysis

A History of Vector Analysis: The Evolution of the Idea of a Vectorial System

— (Dover Books on Mathematics)

— by Michael J. Crowe

Summary of book

The book has eight chapters: the first on the origins of vector analysis including Ancient Greek and 16th and 17th century influences; the second on the 19th century William Rowan Hamilton and quaternions; the third on other 19th and 18th century vectorial systems; the fourth on the general interest in the 19th century on vectorial systems including analysis of journal publications as well as sections on major figures and their views (e.g., Peter Guthrie Tait as an advocate of Quaternions and James Clerk Maxwell as a critic of Quaternions); the fifth on Josiah Willard Gibbs and Oliver Heaviside and their development of a modern system of vector analysis.

— Wikipedia on A History of Vector Analysis

2013.02.02 Saturday ACHK

Anatta 4

無我 4 | Mirror selves 4

有時,人會能醫不自醫。

有時,人「能醫不自醫」原因是,人不能在自己的「主觀世界」中,看到完全的自己。

人只能從別人的主觀世界中,間接看到自己。

正如,任何一部相機,都不能直接為它自己拍照。

— Me@2010.12.13

— Me@2013.02.02

2013.02.02 Saturday (c) All rights reserved by ACHK

乘法意思 1.3

這段改編自 2010 年 4 月 3 日的對話。

但是,運算的過程中,你用了乘數表,而乘數表本身,是由加法製成的。換句話說,即使你把「3.1 乘以 2.1」詮釋為「長方形面積」,最終你也要答我,如何把它化成「重複加法」。

3.1 cm x 2.1 cm = ?

如果要把這一道算式化成「重複加法」,唯有將它化成「整數乘法」。我們可以先回顧一下,運算這個面積時,那兩個小數從何而來。小數出現的原因是,單位太大。如果我們轉用小一點的單位,就可以避免小數的出現。

3.1 cm x 2.1 cm

= 31 mm x 21 mm

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

換句話說,我們用來「點算」面積的網格太大,導致不能密鋪平面。如果我們轉用小一點的網格作為單位,就可以避免「密不鋪面」的情況出現。

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.    

— Me@2013.02.02

2013.02.02 Saturday (c) All rights reserved by ACHK