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Sexual reproduction has never passed on a full winning combination intact. Sex messes with success.
By separating the function of adaptation from the function of maintaining the integrity of individual genes, sex allows much greater diversity while still keeping genes whole. Sex is not only fun, it is good engineering practice.
The English system of weights and measures is a binary system: eight ounces in a cup, sixteen in a pint (the American pint, that is—as in “a pint’s a pound the world around”; the imperial pint is twenty ounces, and the troy pint is twelve ounces), thirty-two in a quart, sixty-four in a half gallon, and one hundred and twenty-eight in a gallon. Expressing numbers in binary notation is no more difficult than expressing measures in quarts, pints, and cups. One hundred and forty-six ounces, for example, is one gallon plus one pint plus one quarter cup: 128 + 16 + 2 = 146. Written in binary, 146 is
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Meaning is a bit like pornography:
He carved ivory into bars, ruled marks corresponding to numbers on the bars, and then performed multiplication by sliding the bars alongside each other until the marks corresponding to the two numbers lined up. The total length of the two bars together then gave the product of the two numbers. The slide rule was born.
A digital electronic computer is a digital computer that operates electronically. An analog computer is one that operates on continuous signals as opposed to bits; it gets its name because such a computer is typically used to construct a computational “analog” of a physical system. Analog computers can be electronic or mechanical.
From his home in Cordova, the twelfth-century Muslim philosopher Averroës (Ibn Rushd) in his studies of Aristotle concluded that what is immortal in human beings is not their soul but their capacity for reason.
Programming computers to perform simple human tasks is difficult: getting a computerized robot to vacuum a room or empty a dishwasher, even to minimal standards, is a problem that has outstripped the abilities of several generations of researchers in artificial intelligence. By contrast, no special effort is required to program a computer to behave in unpredictable and annoying ways. When it comes to their capacity to screw things up, computers are becoming more human every day.
Of course, humans have been speculating about the origins of the universe far longer than they have been dabbling in modern science. Telling stories about the universe is as old as telling stories.
In Norse mythology, the universe begins when a giant cow licks the gods out of the salty lip of a primordial pit. In Japanese mythology, Japan arises from the incestuous embrace of the brother and sister gods Izanagi and Izanami. In one Hindu creation myth, all creatures rise out of the clarified butter obtained from the sacrifice of the thousand-headed Purusha. More recently, though, over the last century or so, astrophysicists and cosmologists have constructed a detailed history of the universe supported by observational evidence.
Ultimately, information and energy play complementary roles in the universe: Energy makes physical systems do things. Information tells them what to do.
Entropy is a measure of the degree of molecular disorder existing in a system: it determines how much of the system’s thermal energy is unavailable for conversion into mechanical work—how much of its energy is useful.
(A calorie is the amount of energy required to raise one gram of water one degree Celsius. A kilocalorie, 1,000 calories, is what someone on a diet would normally call a Calorie: a teaspoonful of sugar contains ten kilocalories of free energy. One hundred kilocalories is enough energy to lift a VW Bug one hundred feet in the air!)
Unfortunately, to reverse this process is not so easy. If you wanted to convert the energy in heat, which has lots of invisible information (or entropy), back into energy in chemical bonds, which has much less entropy, you would have to do something with that extra information. As we will discuss, the problem of finding a place for the extra bits in heat puts fundamental limits on how well engines, humans, brains, DNA, and computers can function.
The maximum rate at which a physical system can process information is proportional to its energy.
To do anything requires energy. To specify what is done requires information. Energy and information are by nature (no pun intended) intertwined.
If there were no alternatives to the initial state of the universe, then exactly zero bits of information were required to describe it; it registered zero bits. This initial paucity of information is consistent with the notion that the universe sprang from nothing.
A lot had happened. But what was the universe computing during this initial billionth of a second? Science fiction writers have speculated that entire civilizations could have arisen and declined during this time—a time very much shorter than the blink of an eye. We have no evidence of these fast-living folk. More likely, these early ops consisted of elementary particles bouncing off one another in random fashion.
When the amount of energy in a typical jiggle became less than the amount of energy required to hold together some form of composite particle—a proton, for example—those particles formed. When the jiggles of the constituent parts—quarks, in the case of a proton—were no longer sufficiently energetic to maintain them as distinct particles, they stuck together as a composite particle that condensed out of the cosmic soup. Every time a new ingredient of the soup condensed out, there was a burst of entropy—new information was written in the cosmic cookbook.
The laws of quantum mechanics are responsible for the emergence of detail and
Properly understood, the second law of thermodynamics rises from the interplay between “visible information,” the information we have access to about the state of matter, and “invisible information,” the bits of entropy—no less physical—that are registered by the atoms forming that matter.
Temperature is a measure of the trade-off between information and energy: atoms at a high temperature require more energy to register a bit of information, and atoms at a low temperature require less energy to register a bit. Temperature is energy per bit.
Any process that erases a bit in one place must transfer that same amount of information somewhere else. This is known as Landauer’s principle, after Rolf Landauer, the pioneer of the physics of information,
When the heat energy of the gas is extracted—for example, by having the gas push against a piston—the bits are left behind. The moving piston turns heat energy into mechanical energy, the energy per atom (and hence per bit), decreases, and the expanding gas cools down. As long as the temperature of the gas does not go to absolute zero, each atom (and hence each of its bits) still requires some energy, so that amount of energy must remain in the gas, rather than becoming mechanical energy. Since some energy must remain behind, not all of the energy can be extracted in the form of work.
It is perhaps easier to conceive of an increase in entropy in these terms: energy degrading from useful to useless forms. Hot baths grow cold. Cars run out of gas. Milk goes sour. So how can we think of this process in terms of information? The answer lies in a fundamental fact of nature that I call “the spread of ignorance.” Unknown bits infect known bits.
Boltzmann defined the quantity he called H as the degree to which we know the position and velocity of any given atom in a gas.
Boltzmann’s quantity H is in fact the entropy of an individual atom, multiplied by minus one. He showed that when the positions and velocities of the atoms are uncorrelated—that is, independent of each other—collisions between them will decrease H and increase the entropy of the individual atoms. Subsequent collisions, he argued, would continue to increase that entropy. He concluded that his H-theorem justified the second law of thermodynamics by supplying a mathematical proof that entropy must increase.
In my M.Phil. thesis, “The Spread of Ignorance,” and Ph.D. thesis, “Black Holes, Demons, and the Loss of Coherence,” I provided an answer for this question by developing an approach for treating the second law of thermodynamics in terms of the spread of ignorance. This method shows that Boltzmann’s H-theorem is “almost true” for “almost all” physical systems.
Ignorance spreads, individual entropies increase. In this picture of the second law of thermodynamics, entropy increase is like an epidemic. Bits of ignorance are like viruses that are copied and spread by interaction. The contagion continues until all parts of the system have been infected. At this point, the entropies of the parts taken individually are close to their maximum value.
The demon’s goal is to “erase” the gas bit by restoring it to 0. But because the underlying laws of physics preserve information, he can restore the gas bit to 0 only by transferring the information in the gas bit to his own bit. The total information remains constant.
Recall that entropy is invisible information, or ignorance—information that is unavailable. But the distinction between “visible” and “invisible” depends on who is looking. It is in fact possible to decrease entropy by looking at something.
He went on to say that although he had not been influenced by work on quantum mechanics, he was not surprised that the laws of physics mirrored ideas from literature. After all, physicists were readers, too.
Similarly, in the quantum-measurement process, you provisionally identify the spread of information from the system to the measurement apparatus as irreversible. If it turns out later that the dynamics of the measurement process undo themselves to restore the original state, you simply rescind your identification of the spread of information as an irreversible process. Since most of the time entropy continues to increase and information continues to spread, you rarely have to recant.
What’s going on is that quantum mechanics, unlike classical mechanics, can create information out of nothing.
This weird type of quantum correlation is called “entanglement.” If a classical system is in a definite state, with zero entropy, then all the pieces of the system are also in a definite state, with zero entropy. If we know the state of the whole, then we also know the state of the pieces. For example, if two bits are in the state 01, then the first bit is in the state 0 and the second bit is in the state 1. But when a quantum system is in a definite state, though, such as the correlated state of our quantum bits, the pieces of the system need not be in a definite state. In entangled states,
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There is nothing impossible about this kind of oppositeness. It is just that in the classical world the brothers must share a bit of information for each possible question that can be asked. In the quantum version of this story (“Two entangled spins walk into a bar . . .”), the two entangled spins share one and only one quantum bit, and yet they are capable of giving opposite answers to an infinite variety of questions corresponding to the infinite set of possible axes about which they
In the wave-function-collapse picture of quantum measurement, by the time I write to tell you that I heard a click and when I turned around the cat was dead, the part of the wave in which the cat is still alive has disappeared.
This solution to the measurement problem depends not only on the present but on the future. If the other parts of the wave function will never again interfere with ours, then we say that the future history of the wave function decoheres. This “decoherent-histories” approach to quantum mechanics neatly resolves most of the troubling aspects of the measurement problem.
Similarly, in the Schrödinger’s Cat paradox, once the detector has clicked and the cat is dead, looking at the cat again to see if it is still dead makes no difference for the future: the cat stays dead. The histories of that experiment are thus decoherent. In this case, we can say that the cat is either dead or alive, but not both.
If making a sequence of measurements on a quantum system changes its future behavior, then the histories corresponding to the possible sequences of outcomes of the measurements are coherent.
There is some division in the physics community about the Many Worlds interpretation of quantum mechanics. In 1997, I debated the issue with the Oxford physicist David Deutsch, who is a strong advocate of the Many Worlds picture. I’m not sure who won the debate in this particular world.
Out of this set, one history really happens. The remainder of the histories correspond to inaccessible pieces of the wave function.
There are other parts of the wave function in which I wrote something else and you are watching TV. But those parts of the wave function don’t correspond to what really happened. They are like the forking paths in Borges’s story: even if they are there, they have no effect on reality.
If classical mechanics were correct, atoms would survive for only a tiny fraction of a second before disintegrating in a burst of light. But the correct picture of atoms is given by quantum mechanics, not classical mechanics. Quantum mechanics guarantees the stability of atoms, and the stability of atoms, in turn, is one of the most concrete confirmations of quantum mechanics. Without quantum mechanics, the life of an atom would be exciting but short.
Wave-particle duality implies that an atom’s electrons consist of a set of discrete waves, so there are only so many orbits they can take. They never fall into the nucleus, and we can count the possible options (no peaks, one peak, two peaks, and so on).
If the atom is bathed by photons whose energy is not equal to the energy difference between the state it’s in and some higher energy state, then it will not absorb the photons. Atoms can absorb energy only in specific chunks (quanta). This feature is useful for controlling the state of atoms.
Spontaneous emission of photons is responsible for the phenomenon known as fluorescence. A fluorescent light works by exciting atoms out of their ground state and letting them jump back, emitting light in the process.
Just as a quantum bit can register two values at once, a quantum computer can perform two computations simultaneously. David Deutsch called this strange ability of a quantum computer to do two things at once “quantum parallelism.”
In a quantum computer, however, there is no distinction between analog and digital computation. Quanta are by definition discrete, and their states can be mapped directly onto the states of qubits without approximation. But qubits are also continuous, because of their wave nature; their states can be continuous superpositions.
How long can computation continue in the universe? Current observational evidence suggests that the universe will expand forever. As it expands, the number of ops performed and the number of bits available within the horizon will continue to grow. Entropy will also increase, but—because as the universe gets bigger it takes longer and longer to reach thermal equilibrium—actual entropy will increase at a slower rate than maximum possible entropy. As a result, the number of calories of free energy available for consumption within the horizon will increase.
