The beauty of Mathematics: Text and language vs numbers and information

Mathematics, writing and natural language are the carriers of information, and they have a natural connection. Language and mathematics are produced for the same purpose-to record and disseminate information. This article is "The Beauty of Mathematics" the first chapter notes.

In 1798, in the Napoleonic expedition, Lieutenant Pierre Francois Bouchard found a broken ancient Egyptian monument in three languages: Egyptian hieroglyphics, Egyptian phonetic texts and Ancient Greek , in a place called Rosetta, the famous Rosetta Stone (Rosetta) .

In 1822, French linguist Champollion cracked the ancient Egyptian hieroglyphics on the Rosetta Stone. The deciphering of the Rosetta Stone helped us to understand the history and civilization of the whole of ancient Egypt, thanks to the Egyptian record in three languages, which has two guiding meanings:

1. The redundancy of information is the guarantee of information security. The Rosetta Stone content is the same information repeated three times, so as long as a copy of the content intact, the original information will not be lost, which is instructive for channel coding.

2. The data of language, that is, corpus, especially bilingual or multi-lingual control corpus, is very important to translation, which is the basis of our machine translation research.

The generation of counting systems anecdotal: Russian-American physicist George in the book "from One To Infinity" tells the story of such a primitive tribe. Two chiefs than one who said the number of big, a chief thought, first said "three", the second chief thought for a long while, said you won. Because in primitive tribes, the material is very scarce, more than three of the time, they call "many" or countless. When our ancestors needed to record more than three o'clock, the counting system arose when they felt that there was a difference between five and eight.

Numbers are the basis of a counting system. The number of early risers is not written, but the finger is broken, which is why we use decimal today. There is no doubt that if we have 12 fingers, we must use 12 binary today. Gradually, our ancestors found that 10 fingers were not enough. Although the simplest way is to count 10 toes, this does not solve the underlying problem.

Our ancestors invented the carry system, which is what we call the ten-in-one today. This is a major leap in science for mankind. Almost all civilizations used the decimal, except for the Mayan civilization, where they counted all the fingers and toes before starting to carry, which was 20 binary. A century of the Mayans, which they called the solar age, was 400 years. 2012 is the last year of the current solar age, and 2013 will be the beginning of the new solar age, which is the so-called end of the 2012 world.

For the representation of different digit numbers, Chinese and Romans use explicit units to denote different levels of numbers, and the Chinese use a top trillion. The Romans represented by Ⅰ, Ⅴ on behalf of 5,ⅹ, representative of 10,l, C for the four, and D for 1000.

Both of these representations unconsciously introduce the concept of naïve coding. First, they all use different symbols to represent different mathematical concepts; second, they developed the decoding rules, in China, the rule of decoding is multiplication, in Rome, the rule of decoding is adding and subtracting-the small number is now the big number left for minus, plus on the right. In terms of the validity of the coding, the Chinese practice coin is brilliant.

The most effective description of the numbers was the ancient Indians, who invented 10 Arabic numerals, including 0, which were more abstract than those of China and Rome, but were easy to use, and they were introduced into Europe by Arabs and popularized.

In order to avoid transcription errors, the ancient Jews invented a method similar to that of our computer and communication Lieutenant colonel in today's request to copy the Bible. They do not have a Hebrew letter corresponding to a number, so that each line of text together to get a special number, this number becomes the check code for this line. Similarly, this is done for each column. When a Jewish scholar finishes a page of the Bible, they need to add up the text of each line to see if the new check code is the same as the original, and then do the same with each page. The rationale behind this is the same as the various checks we have today.

Notes on the beauty of Mathematics: Text and language vs numbers and information