Ivan • Claude Shannon

The preface

Hello everyone. Actually, initially this article was not supposed to be about Claude as a person, but exclusively about Claude's entropy, which I know from the theory of Data Science. But in the process of writing it and getting to know his biography, I couldn't help but have one thought in my head: "My God, this is literally Kojima from the world of computer science." That's why we're here now. I will try to tell you briefly what kind of person he is, but most importantly, what discoveries he made and why he was nicknamed the "father of the information age".

Short biography

Claude Elwood Shannon was born on April 30, 1916 in Petoskey, Michigan, and grew up in Gaylord. His father was a probate judge, and his mother was a teacher and school principal. He graduated from the University of Michigan in 1936 with a bachelor's degree in mathematics and electrical engineering. After that, he enrolled at the Massachusetts Institute of Technology (MIT), where he worked as a research assistant under the supervision of Vanivar Bush with a differential analyzer.

In 1937, as a 21-year-old master's student, Shannon wrote the paper "Symbolic Analysis of Relay and Switching Circuits," which many consider to be the most important master's thesis of all time. In this work, he showed how Boolean algebra can be applied to the analysis of electrical circuits, laying the theoretical foundations of digital computing based on relay mechanisms that underlie logic circuits.

In 1941, Shannon joined the mathematics department of Bell Laboratories, where he worked until 1972, and in 1956 became a professor at MIT, combining work with Bell Labs until the end of the 1970s. During World War II, he was involved in cryptography, and it is known that he discussed cryptographic ideas with Alan Turing during the latter's visit to Bell Labs, but they did not have a formal joint project. Claude Shannon died on February 24, 2001 in Medford, Massachusetts.

Key concepts and discoveries

Article "Mathematical theory of communication"

Shannon's main achievement was the publication in 1948 of the article "Mathematical theory of communication" in the Bell System Technical Journal. The work was published in two parts (July and October) and later (in 1949) it was published as a separate book in collaboration with Warren Weaver. This article changed the world forever and laid the foundations of information theory.

The article is considered the "Great Charter of the Information Age" and the "blueprint of the digital age".

1. The bit as a unit of information

Shannon introduced the concept of "bit" (binary digit) — the smallest unit of information. The word bit itself was proposed by mathematician John Tukey, and Shannon consolidated its use in theory. His key idea was that any information can be measured and encoded using a sequence of zeros and ones.

2. Mathematical model of communication

Shannon has developed a fundamental communication model that includes:

Information source — produces a message
Transmitter — converts the message into a signal
Communication channel — signal transmission medium
Receiver — restores the message from the signal
Recipient — the final addressee of the message

This scheme has become a universal model for analyzing any communication system.

3. Entropy and uncertainty of information

Shannon introduced the concept of information entropy — measures of uncertainty or randomness in the message:

H = - \sum_{i=1}^{n} p_i \log_2 p_i

Where:

$p_i$ — probability of occurrence of the $i$ th message,
the logarithm is taken in base 2, since information is measured in bits.

He showed that entropy quantifies the uncertainty of the message source and sets the limit for effective data compression.

4. Bandwidth of the communication channel

One of the most important results was the channel capacity theorem (Shannon capacity theorem).

Shannon deduced the formula:

C = B \log_2(1 + S/N)

$C$ — maximum information transfer rate (channel bandwidth) in bits per second,
$B$ — the bandwidth of the channel in hertz (Hz),
$S/N$ — the ratio of signal power to noise power (signal-to-noise ratio).

This formula defines the theoretical limit of the speed of reliable information transmission over a noisy channel.

5. Coding theorems

Shannon formulated two fundamental results:

The source encoding theorem — sets data compression limits;
The channel coding theorem — proves the possibility of error-free transmission at speeds below the bandwidth of the channel.

Impact on the modern world

Shannon's theory led to unexpected conclusions.

For example, for reliable transmission in a noisy environment, it is optimal not to repeat the message multiple times, but to use intelligent (sophisticated) codes that allow information to be transmitted up to the Shannon limit with a given probability of error.

But personally, I would single out this one separately, that under standard conditions for both one source and one receiver, separate encoding (compression into bits and subsequent transmission) is an asymptotically optimal solution. Simply put, in most cases it is more profitable and versatile to represent and transmit information as a sequence of bits, so it is easier to process and find errors in the signal and easier to prevent collisions (provided there is no delay and a known SNR).

Afterword

I don't know what you think, but in my opinion, this is a truly legendary person. I am very surprised that despite such great achievements and contributions to computer science, almost nothing is told about him at school or university (or at least that's how it is for me), although Shannon's work laid the foundation for the development of modern telecommunications, the Internet, data compression, cryptography and almost all digital technologies that you and I know, and most likely if it weren't for him, you probably wouldn't even be able to read this article right now.

In any case, it's pointless to guess what would have happened. Better yet, if you are really interested in what I am telling you here and you would like to learn more and delve deeper into this topic, I strongly recommend reading the article on wiki, everything is described there in some detail and to the point.

I hope to intrigued you, see you soon ~