Information Series

[C C]

Part One: Information is bits

https://plus.maths.org/content/information-birth-bit

EXCERPT: We send information over the internet every day. All that information, whether it's a birthday email or your homework, is in encoded into sequences of 0s and 1s. What's the best way of doing this? The way that uses the least amount of 0s and 1s and therefore requires the smallest amount of computer memory? . . .

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Part Two: Information is surprise

https://plus.maths.org/content/information-surprise

EXCERPT: It's not very often that a single paper opens up a whole new science. But that's what happened in 1948 when Claude Shannon published his Mathematical theory of communication. Its title may seem strange at first — human communication is everything but mathematical. But Shannon wasn't thinking about people talking to each other. Instead, he was interested in the various ways of transmitting information long-distance, including telegraphy, telephones, radio and TV. It's that kind of communication his theory was built around.

Shannon wasn't the first to think about information. Harry Nyquist and Ralph Hartley had already made inroads into the area in the 1920s (see this article), but their ideas needed refining. That's what Shannon set out to do, and his contribution was so great, he has become known as the father of information theory....

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Part Three: Information is complexity

https://plus.maths.org/content/information-complexity

EXCERPT: How much information is there in this article? It's hard to tell. Its length clearly isn't an indicator because that depends on my choice of words. One thing you could do to measure information is to condense the article into bullet points. If you end up with many of them, then that's because the article is pretty dense. If there's only one, then the information it conveys is rather basic, or at least not very complex....

[Magical Realist]

EXCERPT: How much information is there in this article? It's hard to tell. Its length clearly isn't an indicator because that depends on my choice of words. One thing you could do to measure information is to condense the article into bullet points. If you end up with many of them, then that's because the article is pretty dense. If there's only one, then the information it conveys is rather basic, or at least not very complex...

There is more information than that. There is the syntactical information of the letters and punctuation marks. There's the grammatical information of nouns, verbs, articles, pronouns, prepositions, and their structure in sentences. There is the information of the rhetoric, the usage of the words, of english language, vernacularisms, idioms, slang usages, stylistic traits. There's information about the logic of the propositions and what is being inferred from it. And even beyond the semantical information of the article itself, there is an implicit network of other definitions, truths, assumptions, beliefs, culturally specific references, implications, and conceptual contexts in which the bullet points take on their specific meanings. Information is ALWAYS rich, dense, many-layered, and dynamically interrelated on all levels.

[C C]

Part Four: Information is sophistication

https://plus.maths.org/content/informati...istication

EXCERPT: Kolmogorov complexity gives a high value to strings of symbols that are essentially random. But isn't randomness essentially meaningless? Should a measure of information assign a low value to it? The concept of sophistication addresses this question....

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Part Five: Information is noisy

https://plus.maths.org/content/information-errors

EXCERPT: When you transmit information long-distance there is always a chance that some of it gets mangled and arrives at the other end corrupted. Luckily, there are clever ways of encoding information which ensure a tiny error rate, even when your communication channel is prone to errors....

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Part Six: Information: Baby steps

https://plus.maths.org/content/information-baby-steps

EXCERPT: If I tell you that it's Monday today, then you know it's not any of the other six days of the week. Perhaps the information content of my statement should be measured in terms of the number of all the other possibilities it excludes? Back in the 1920s this consideration led to a very simple formula to measure information....