Can all information be expressed as bits?

[Jim Kata]

I heard Claude Shannon believed all information could be expressed as a string of bits. Is there a theorem supporting this claim, or is this just some kind of folklore belief?

 

[phinds]

Define information and you will likely have your answer.

 

[DrZoidberg]

A system that has n possible states has an information content of log(n).
If you use log to the base 2 the unit is bits. For example a byte in a computer can have 256 different states, therefore it represents log₂256 = 8 bits of information.
For every physical system - atoms, molecules, even black holes - you have a certain number of possible states that that system could be in. You can always measure the amount of classical information in bits. Classical information is everything that you could measure. But there is also quantum information which is expressed in qubits.

 

[f95toli]

Yes, there are theorems proving that all bandlimited analogue information can be perfectly encoded into a string of bits. This is called the Nyquist-Shannon theorem, there is a nice wiki about it

http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem

Btw, that the information have to be bandlimited is not really an issue: ANY real physical process is in practice bandlimited, simply because you can approximate it with arbitrary precission.

 

[alphysicist]

The claim that all information can be expressed as bits is a well-known concept in the field of information theory, pioneered by Claude Shannon in the mid-20th century. This idea has been extensively studied and is supported by various theorems and principles in information theory.

One key theorem that supports this claim is Shannon's source coding theorem, which states that any discrete information source can be compressed into a binary string with negligible loss of information. This theorem has been proven mathematically and is widely accepted in the scientific community.

Additionally, the concept of entropy, which measures the amount of uncertainty or randomness in a system, also supports the idea that all information can be represented as bits. In information theory, entropy is often referred to as the fundamental unit of information, and it can be calculated for any type of information, whether it is text, images, or even sound.

Of course, there may be some limitations to this concept, as there are certain types of information that may not be easily quantifiable or compressible into bits. For example, subjective experiences or emotions may not be easily expressed in binary form. However, in general, the idea that all information can be represented as bits is a well-established and widely accepted concept in the scientific community.