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### Course: Computer science theory>Unit 3

Lesson 1: Ancient information theory

# What is information theory?

A broad introduction to this field of study. Created by Brit Cruise.

## Want to join the conversation?

• What is a bit density?
• Bit density measures how many bits can be stored in some area or volume. As far as I'm aware there is no formal definition but you can get an informal idea from a few examples.

A typed paper has some number of letters on it, let's say 1000. Then a rough estimate for the bit density would be 1 KB per sheet of paper, assuming 1 byte per character. There could be many ways to increase the density, e.g. use a smaller font or use something more efficient than letters, like tiny squares that can either be on (black) or off (white). I've heard of software to back up information on paper that can store 500 KB per sheet.

On the other hand there are fingernail-sized microSD cards that can store 64 GB - a much higher bit density!

Given that a sheet of paper has an area of ~ 624 cm^2 that means its bit density is about 1 KB / 624 cm^2 = 0.0016 KB / cm^2. But a microSD card has an area of about 1.65 cm^2 so its bit density is about 64 GB / 1.65 cm^2 = 38.8 GB / cm^2. So, by this rough calculation the bit density of a microSD card is about 24,250,000 times greater than that of a sheet of paper.
• In electronics, a 'bit' is the best 'fundamental unit of information,' because the 'smallest unit of information' in electronics IS a bit (with only two options, on or off). Intuition tells me that we use the bit because (1) It is the smallest prime number and (2) It is the basic unit for information stored in electronics (where we see much of the practical application of this theory).

Am I right to assume that a bit is not always either the most representative or the most fundamental unit to quantify information?

For example, DNA has 4 molecules, so the smallest DNA pair has 4 options rather than 2... right? The coding of proteins in the human body are driven by 20 proteinogenic amino-acids (base 20). In the English language, there are 26 letters (perhaps punctuation should be added, making it more)... we just translate it to bits/bytes out of convenience (for conceptualizing and structuring the programing of computers). Though I can't think of any examples, I bet there are examples in nature that are 'base 3', which would not translate 'naturally' to 'base 2.' Some units of information are not even discrete. The smallest unit of light (a single photon) could theoretically be divided into an 'infinite spectrum of wavelengths' (base infinity??), limited only by our ability to detect small differences.

Also, I imagine 'base 2' is theoretically NOT the most efficient way to store information if the primary goal is increased information density.

Great video! Seems like one of those concepts that is both simple and complex at the same time. It is messing with me. Are the above questions/assumptions correct?
• At , he says one bit is the answer to a yes or no question. So is a one bit one yes or one no to a question, or the question itself, or the question and the answer?
• The bit is the yes or no, the 1 or 0, the on or off.
• hey how could the value on the scale be not an integer number ? =/ I mean bit can't be divided into smaller parts, or can they ?
• Great question.Yes they can! We will cover this in detail soon (video on entropy has not been posted yet still working on it).
• Did you have to rip out the page of a perfectly good book? I mean, surely you could have made your point some less damaging way. I literally recoiled in horror. (Yes, I mean literally.)
• Asked the same question. I was mortified that he would do that to a book (ಥ‸ಥ)
• The various forms of Alice's message at all have a bit value of 25.5. Does that mean there are 25.5 parts to the idea of her message or 25.5 letters in the message?
• Some of something but not all of it only a little bit
• what's the most used and still continued to use method since ever?
• I think Art, because people still draw things to show their feelings, events, and maybe even a story (like in cartoon or anime)
• What's informtaion theory in a nutshell?
• A theory which answers two important questions. (among other things)
1. What is the speed limit of information? How do we measure this?
2. How can we send information reliably in the presence of noise?