The global expansion of the telegraph continued to surprise even its backers. When the first telegraph office opened in New York City on Wall Street, its biggest problem was the Hudson River. The Morse system ran a line sixty miles up the eastern side until it reached a point narrow enough to stretch a wire across. Within a few years, though, an insulated cable was laid under the harbor. Across the English Channel, a submarine cable twenty-five miles long made the connection between Dover and Calais in 1851. Soon after, a knowledgeable authority warned: “All idea of connecting Europe with America, by lines extending directly across the Atlantic, is utterly impracticable and absurd.” That was in 1852; the impossible was accomplished by 1858, at which point Queen Victoria and President Buchanan exchanged pleasantries and The New York Times announced “a result so practical, yet so inconceivable … so full of hopeful prognostics for the future of mankind … one of the grand way-marks in the onward and upward march of the human intellect.” What was the essence of the achievement? “The transmission of thought, the vital impulse of matter.” The excitement was global but the effects were local. Fire brigades and police stations linked their communications. Proud shopkeepers advertised their ability to take telegraph orders.
Information that just two years earlier had taken days to arrive at its destination could now be there—anywhere—in seconds. This was not a doubling or tripling of transmission speed; it was a leap of many orders of magnitude. It was like the bursting of a dam whose presence had not even been known.
And:
Szilárd — who did not yet use the word information — found that, if he accounted exactly for each measurement and memory, then the conversion could be computed exactly. So he computed it. He calculated that each unit of information brings a corresponding increase in entropy—specifically, by k log 2 units. Every time the demon makes a choice between one particle and another, it costs one bit of information. The payback comes at the end of the cycle, when it has to clear its memory (Szilárd did not specify this last detail in words, but in mathematics). Accounting for this properly is the only way to eliminate the paradox of perpetual motion, to bring the universe back into harmony, to “restore concordance with the Second Law.”
Szilárd had thus closed a loop leading to Shannon’s conception of entropy as information. For his part, Shannon did not read German and did not follow Zeitschrift für Physik. “I think actually Szilárd was thinking of this,” he said much later, “and he talked to von Neumann about it, and von Neumann may have talked to Wiener about it. But none of these people actually talked to me about it.” Shannon reinvented the mathematics of entropy nonetheless.
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Solomonoff, Kolmogorov, and Chaitin tackled three different problems and came up with the same answer. Solomonoff was interested in inductive inference: given a sequence of observations, how can one make the best predictions about what will come next? Kolmogorov was looking for a mathematical definition of randomness: what does it mean to say that one sequence is more random than another, when they have the same probability of emerging from a series of coin flips? And Chaitin was trying to find a deep path into Gödel incompleteness by way of Turing and Shannon—as he said later, “putting Shannon’s information theory and Turing’s computability theory into a cocktail shaker and shaking vigorously.” They all arrived at minimal program size. And they all ended up talking about complexity.
And, an amusing quote:
The key to [quantum] teleportation and to so much of the quantum information science that followed is the phenomenon known as entanglement. Entanglement takes the superposition principle and extends it across space, to a pair of qubits far apart from each other. They have a definite state as a pair even while neither has a measurable state on its own. Before entanglement could be discovered, it had to be invented, in this case by Einstein. Then it had to be named, not by Einstein but by Schrödinger. Einstein invented it for a thought experiment designed to illuminate what he considered flaws in quantum mechanics as it stood in 1935. He publicized it in a famous paper with Boris Podolsky and Nathan Rosen titled “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” It was famous in part for provoking Wolfgang Pauli to write to Werner Heisenberg, “Einstein has once again expressed himself publicly on quantum mechanics… As is well known, this is a catastrophe every time it happens.”
More (#1) from The Information:
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And, an amusing quote: