Q: Is it possible to write a big number using a small number? Is there a limit to how much information can be compressed?

Q: Is it possible to write a big number using a small number? Is there a limit to how much information can be compressed?

Physicist: Although there are tricks that work in very specific circumstances, in general when you “encode” any string of digits using fewer digits, you lose some information. This seven digit number has a seven digit address, which is absolutely typical. If the nth symbol in your set shows up with probability P n , then the entropy in bits (the average number of bits per symbol) is: . The entropy tells you both the average information per character and the highest density that can be achieved. Here the log was done in base 2, but it doesn’t have to be; if you did the log in base 26, you’d know the average number of letters needed per symbol.

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