Can we measure the complexly of natural language by an entropy based compression method? (4)

Size of books depends on languages

My friend (and my teacher) Joerg once asked me that how large the Japanese translated books compared with other languages. Japanese uses Kanji (Chinese characters). Because these characters can encode several Latin characters to one Kanji, he inferred Japanese translated books are smaller or thinner than the original ones. For example, the character ``mountain'' is one character ``山'' in Japanese. But, Kanji usually needs higher resolution compared with Latin characters.

I answered the books seems thinner than original ones. I have several Shakespeare's books, and I assume these translations are as accurate as possible. Some friends visited my place impressed how small Japanese books are. But, there are some other factors, for instance, a Japanese book might be made of thinner paper, the size of characters might be relatively smaller, and so on. This is an interesting point, but, we must consider many parameters.

Comments

Why A^{T}A is invertible? (2) Linear Algebra

Why A^{T}A has the inverse Let me explain why A^{T}A has the inverse, if the columns of A are independent. First, if a matrix is n by n, and all the columns are independent, then this is a square full rank matrix. Therefore, there is the inverse. So, the problem is when A is a m by n, rectangle matrix. Strang's explanation is based on null space. Null space and column space are the fundamental of the linear algebra. This explanation is simple and clear. However, when I was a University student, I did not recall the explanation of the null space in my linear algebra class. Maybe I was careless. I regret that... Explanation based on null space This explanation is based on Strang's book. Column space and null space are the main characters. Let's start with this explanation. Assume x where x is in the null space of A . The matrices ( A^{T} A ) and A share the null space as the following: This means, if x is in the null space of A , x is also in the n...

Gauss's quote for positive, negative, and imaginary number

Recently I watched the following great videos about imaginary numbers by Welch Labs. https://youtu.be/T647CGsuOVU?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF I like this article about naming of math by Kalid Azad. https://betterexplained.com/articles/learning-tip-idea-name/ Both articles mentioned about Gauss, who suggested to use other names of positive, negative, and imaginary numbers. Gauss wrote these names are wrong and that is one of the reason people didn't get why negative times negative is positive, or, pure positive imaginary times pure positive imaginary is negative real number. I made a few videos about explaining why -1 * -1 = +1, too. Explanation: why -1 * -1 = +1 by pattern https://youtu.be/uD7JRdAzKP8 Explanation: why -1 * -1 = +1 by climbing a mountain https://youtu.be/uD7JRdAzKP8 But actually Gauss's insight is much powerful. The original is in the Gauß, Werke, Bd. 2, S. 178 . Hätte man +1, -1, √-1) nicht positiv, negative, imaginäre (oder gar um...

No virtual machine on Oracle virtual box and Avira

December 2015, I suddenly cannot run Oracle VM Virtual Box (5.0.10) on Windows 7, my desktop machine. It failed to create a virtual machine, the error message is the following. VirtualBox - Error In supR3HardNtChildWaitFor --------------------------- Timed out after 60001 ms waiting for child request #1 (CloseEvents). (rc=258) where: supR3HardNtChildWaitFor what: 5 Unknown Status 258 (0x102) (258) - Unknown Status 258 (0x102) I relatively less use the virtual machine on this desktop machine. But when I would like to use Linux, then I need to reboot the machine. This is inconvenient. I have another windows 7 notebook, but I don't have this problem. Today I found the solution. https://avira.ideascale.com/a/dtd/Avira-sollte-das-Ausf%C3%BChren-von-VMs-in-Virtualbox-nicht-blocken/160234-26744#idea-tab-comments The combination of Avira's process protection and Virtual Box cause this problem. Avira announced the real solution will be provided at the release of 9th of Feb...

Lx=d: SundayResearch

Search This Blog