Information
Information is whatever reduces uncertainty about something: a fact, a signal, or a pattern that lets a receiver know more after receiving it than before. In everyday speech it means useful knowledge — a train time, a diagnosis, a headline — while in the technical sense developed by Claude Shannon in 1948 it is a precisely measurable quantity tied to how surprising a message is, regardless of what the message means.
Information is distinct from data, even though the two words are often used interchangeably. Data is the raw material: recorded symbols, measurements, or numbers such as "38.5". Information is what a receiver can extract from data in context — "the patient has a fever" — and the same data can yield different information, or none, depending on who reads it and what they already know. A temperature log is just data to someone who cannot read its units, and a sentence in an unknown language carries plenty of data and almost no information for the person who cannot read it. Computers store and move data; people and programs turn it into information by interpreting it.
Shannon's 1948 paper, "A Mathematical Theory of Communication" in the Bell System Technical Journal, made information measurable by deliberately setting meaning aside. Building on Ralph Hartley's 1928 work on transmission, Shannon observed that the engineering problem is to reproduce at one point a message selected at another point, and that what matters is how many alternatives the message was chosen from and how likely each was. A message that was certain to arrive carries no information; a rare, surprising one carries a lot. The average information per message, called entropy, is H = minus the sum of p × log2(p), taken over every possible message with probability p, and measured in bits when the logarithm is base 2. A fair coin toss has entropy of exactly one bit, while a coin that lands heads 90% of the time has about 0.47 bits, because its outcomes are less surprising.
Shannon's framework yields two limits that govern all digital communication. The source coding result says that a source with entropy H cannot be compressed losslessly below H bits per symbol on average, which is why a repetitive text file shrinks dramatically under ZIP while already-compressed or random data barely shrinks. The channel coding result says that every noisy channel has a capacity, and that error-correcting codes can make transmission arbitrarily reliable at any rate below it. Reed-Solomon codes, used on CDs and in QR codes, and the error correction in Wi-Fi and cellular links are practical descendants. Modern machine learning borrows the same vocabulary: cross-entropy loss, the standard objective for classification models, is a measure built directly from Shannon's formula.
The technical sense and the everyday sense answer different questions, and mixing them up causes real confusion. Shannon information measures surprise and quantity; it says nothing about whether a message is true, useful, or meaningful. A string of random characters has maximal entropy yet is worthless to read, while a profound sentence may have low entropy because its words are predictable. Everyday information adds meaning, truth, and relevance on top: the same quantity of bits can be a reliable report or a convincing rumor. A common mistake is to assume that more data automatically means more information, when much of a large dataset may be duplicated, noisy, or irrelevant to the question being asked.
Information is also physical and social. It has to be carried by something — voltages, magnetic domains, light pulses, ink — and it is only useful when sender and receiver share an agreed code, such as ASCII from 1963 or Unicode from 1991, for interpreting the signals. Whole fields, from genetics to cryptography to data science, now treat information as a quantity that can be stored, compressed, transmitted, and protected. Keeping the distinction between data, information, and meaning in mind helps in deciding what to collect, what to trust, and what a result actually tells you.
Read information as the reduction of uncertainty a message delivers to someone able to interpret it — measurable in bits as surprise, but only worth anything once data has been understood in context.