Quantifying Information Content Does Not Bring Meaning Fr...

It is perfectly true that redundancy aids recognition of a signal as a language or a code, and this recognition is crucial to SETI. However, Shannon’s method provides only a quantitative measure of the complexity of a language or signaling system—not a translation. And while it is axiomatic in cryptology that redundancy helps in deciphering a text, the task of decipherment/cryptanalysis is to move from an encoded text to the original text—not from text to meaning. To get from text to me...

 Prime Numbers and Cryptography

Algorithms for finding prime numbers date back at least as far as ancient Greece, where mathematicians used a straightforward approach known as the Sieve of Erastothenes. The Sieve of Erastothenes works as follows: To find all the primes less than n, begin by writing down all the numbers from 1 to n in sequence. Then cross out all the numbers that are multiples of 2, besides itself (4, 6, 8, 10, 12, and so on). Take the next smallest number that hasn’t been crossed out (in this case, 3), an...

 Redundancy of English language is a Goldilocks zone for C...

In Shannon’s terms, the feature of messages that makes codecracking possible is redundancy. A historian of cryptography, David Kahn, explained it like this: “Roughly, redundancy means that more symbols are transmitted in a message than are actually needed to bear the information.” Information resolves our uncertainty; redundancy is every part of a message that tells us nothing new. Whenever we can guess what comes next, we’re in the presence of redundancy. Letters can be redundant: be...

 Blockchains

Ownership on the Bitcoin blockchain is determined by a pair of cryptographic keys. The first, called the public key, resides in the blockchain for anyone to see. The second is called the private key, and its owner keeps it safe from view. The two keys have a special mathematical relationship that makes them useful for signing digital messages. Here’s how that happens: Helmut takes a message, combines it with his private key, does some calculations, and ends up with a long number. Anyone who...

 The Monte Carlo Method and Evolutionary Algorithms

Back then, I thought of one thing: Have you heard of the Monte Carlo method? Ah, it’s a computer algorithm often used for calculating the area of irregular shapes. Specifically, the software puts the figure of interest in a figure of known area, such as a circle, and randomly strikes it with many tiny balls, never targeting the same spot twice. After a large number of balls, the proportion of balls that fall within the irregular shape compared to the total number of balls used to hit the ci...