Ancient information theory
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What is information theory?
Imagine Alice has an idea and she wants to share it. There are so many ways to share an idea. She could draw a picture, make an engraving, write a song, (piano music) send a telegraph or an email. But how are these things different? And more importantly, why are they the same? This story is about a fundamental particle of all forms of communication. It begins with a special skill you likely take for granted. Language. All language allows you to take a thought or mental object and break it down into a series of conceptual chunks. These chunks are externalized using a series of signals or symbols. Humans express themselves using a variation in sound and physical action, as do chirping birds and dancing bees. And man-made machines exchanging a dancing stream of electrical vibrations. Even our bodies are built according to instructions stored inside microscopic books known as DNA. All are different forms of one thing. Information. In simplest terms, information is what allows one mind to influence another. It's based on the idea of communication as selection. Information, no matter the form, can be measured using a fundamental unit, in the same way we can measure the mass of different objects using a standard measure such as kilograms or pounds. This allows us to precisely measure and compare the weight of say rocks, water, or wheat using a scale. Information too can be measured and compared using a measurement called entropy. Think of it as an information scale. We intuitively know that a single page from some unknown book has less information than the entire book. We can describe exactly how much using a unit called the bit, a measure of surprise. So no matter how Alice wants to communicate a specific message, hieroglyphics, music, computer code, each would contain the same number of bits, though in different densities. And a bit is linked to a very simple idea. The answer to a yes or no question. Think of it as the language of coins. So how is information actually measured? Does information have a speed limit? A maximum density? Information theory holds the exciting answer to these questions. It's an idea over 3,000 years in the making. But before we can understand this, we must step back and explore perhaps the most powerful invention in human history. The alphabet. And for this, we return to the cave.