“The second [moral] is that entropy is a global quantity, like energy or angular momentum, and shouldn’t be localized on the horizon. The various attempts to identify the microstates responsible for black hole entropy, are in fact constructions of dual theories, that live in separate spacetimes.”
If you want to know how the world is always going to hell in a handbasket, but never quite getting there, you have to understand something about waves. Hawking was talking about black hole entropy, but all waves share that global quality. They are relationships between their ends and origins as much as they are phenomena. Language handles them poorly, even though communication is made of them. Language describes bowling balls well – waves, energy, information and entropy, not so well. Every wave waves a set of waves until there is no wave left to wave. A wave is subject, verb and object – actor, action and casualty – at all times and locations in its lifecycle. A wave is not a thing, but it is the consistent behaviour of waves in all things that gives things the solidity that makes them things. The number of peaks in a wave set is countable, but its shape, size and total energy – its entropy – is not. This is the difference between resonance and resonators in general.
As it turns out, a wave is as hard to define as it is to hold in your hands. We can sort of say that a wave is the transmission of energy through a relatively static medium, but that’s just the nominalisation of the verb transmit. It is convenient to call a wave “information,” but that doesn’t help much because information isn’t any easier to define. In the case of a standing wave, a particle may pass the wave on without moving, so a wave is not just motion. Electromagnetic waves definitely act like waves, but they don’t have a medium that we know of, just fields. In a sense, a wave is the coordination of energy. Waves are related to entropy in every instance as waves transport energy down gradient from order to disorder, but because entropy is so hard to define, that is no more helpful than calling waves information. Waves are fundamental to the point where string theory defines the entire universe and everything in it in terms of waves, but that still doesn’t tell us what a wave is. A wave is not a particle. Phenomena may be wave-like or particle-like, but still, the particle is definite while the wave is indefinite
Although a wave makes sense as energy transmitted through a medium, when you hit interference the transmission analogy breaks down. It isn’t a package in the post. A wave isn’t cancelled by a wave moving in the opposite direction, but by an identical wave carrying the same energy in the same direction, just out of phase. This is true of all waves: sound, water, light, even a stadium crowd wave. This is not energy moving through a medium, it more like potential, and even more like information about energy that can be converted into actual energy with the right interaction. Imagine a wave coming in from the sea that could crash violently onto the shore. If you went behind an island and generated a wave with the same energy in the same direction, but with the opposite phase so the water goes up when the other wave would make the water go down, the two waves will cancel each other out and no energy will reach the shore. This is why it’s probably better to think of the kinetic energy of an electron as information up until the moment when it actually gets measured as energy. Until that moment of measurement, the information may or may not be cancelled by equal but inverse information, leading to a measurement of no energy.
When you say something, your words are wavelike. They may have the potential to transmit ideas, but there is interference at every phase, from the sound waves in air to the ear to the nervous waves in the mind of the listener. Ironically, interference is most likely from the most similar statements. So if you feel like people are missing the point entirely, it may be that you see waves, while they see particles. If the world feels like it’s disintegrating, that’s probably because it is. But remember that waves originate far from where you see them. I’m not talking about the butterfly effect; a big wave depends on innumerable small interactions averaged together, so one butterfly more or less is irrelevant. With wavelike things, origin stories are always dubious. In the words of Duke Kahanamoku: “Be patient. Wave come. Wave always come.”
To understand why entropy is beautiful, you have to hit rock bottom, or try to hit rock bottom. It’s hard. The work of removing all of the energy from a system is phenomenal. At the atomic scale and below, all of that entropy bleeding away from macroscopic phenomena, all of the wave energy dissipation and dispersion, starts to bounce back. Brownian motion has no entropy equivalent. This is not to say there is no friction at that scale, only that friction excites the atoms and makes them move faster, rather than slower. The movements are chaotic, so there’s no free energy here, but there is a lively dance that is not at all like dispersion or the heat death of the universe. Life depends on the random dance of particles in water. Proton pumps wait for brownian motion to propel hydrogen ions randomly into their channels. Like a lock system in a canal, the gate closes behind and opens in front and the proton pops out. The cell doesn’t make energy in this way, but the extra protons create an electromagnetic gradient that does physical work. And remember, the cell isn’t a heat engine powered by thermodynamic gradients. At the proton’s scale, wave energy can’t disperse any further and entropy hits rock bottom, but then it bounces back. Thermal and kinetic energy are no longer distinguishable, and they’re not distinct from mass or information. Atoms can’t slow down without cooling down, but there’s nowhere for their heat to go, so they dance and shove one another. At that scale, entropy is exciting, not depressive. In cells, the entropy of chemical decay bounces back from proton pumps into electromagnetic potential and then multiplies into the massive kinetic motion of muscles. After it hits rock bottom, entropy dances and shines.
Fire is enchanting, but the important thing about fire is the fuel and the waste, not the flame. You can’t make a burned log burn again, no matter how much new heat you apply to it. Once the redox is complete, the log is waste, not fuel. On the other side, you can’t put out a fire by wetting the flame. You have to cut off the fuel to stop the reaction. That’s why the human relationship with fire is so special. A child learns to speak long before they are ready to build and tend a fire: to understand the relationship between fuel, flame and waste. That little, tiny bit of insight into entropy makes the difference between bewilderment and competence. We still have a lizard brain enchanted by the flame, which is easily seduced and distracted, so it is only with supreme concentration that the mind grasps entropy and remember to apply it to dynamic events. The central nervous system evolved to find food and avoid danger, both of which behave like bowling balls. Entropy behaves like a wave. Relationships also behave like waves. You probably love and hate your friends and spouses with something like a wave function probability distribution. The similarity between relationships and waves may explain why human beings can have so many more friends (as opposed to chemical relationships) than any other animal. It is, however, still easier to live in the lizard brain, so we are burning out the planet and fighting over the remaining fuel. Entropy consumes intelligence as well as energy.
Vices like drugs, gambling and prostitution spread through society by dispersion in waves where every citizen is a provider, conduit and consumer of intoxication, risk and sex. Everyone is subject, verb and object simultaneously, which makes grammatical constructions difficult. Pollution and corruption also spread through dispersion, through physical entropy, and regulations to stop them tend to fail because the regulators, whether lawmakers or police, assume that these things move like water through a pipe, where you can shut off the valves and stop the flow. Dispersion waves don’t have a source, conduit and discharge, so like entropy in general, they can’t be turned off or destroyed. A violent response to a wave will just increase its power. You can’t fight vice, but you can address the desperation of the producers and the consumers to dissipate the tension in the system. Without compression and tension, the waves dissipate. All waves dissipate through entropy, so whatever wave you’re currently looking will probably die away naturally before you can respond to it.
The genius of digital technology is to make information, which spreads by dispersion and suffers from entropy, look like a bowling ball that you can sit on a rack and then fling down the alley when you need to make a point. Never mind that this isn’t an accurate representation of reality, it isn’t even an accurate representation of the information in the computer, which has enough electrons working together to make their local average seem stable and not wavelike at all. These bowling balls of information are great for comparing local averages across time: how many criminals did we arrest this year versus last year? Which is great for finding trends that have nothing to do with the cause or resolution of crime.
Bowling ball-like information makes grammatical constructions much easier, but doesn’t help with wave-like problems. The central nervous system evolved to find food and eat it, not to understand the true nature of food, which is one reason why science could put a man on the moon but not solve poverty: poverty like a wave and a rocket is like a bowling ball. Getting behind a bowling ball is much easier.
The relationship between information and matter is not trivial, and may be more like the relationship between energy and matter, forming something like a triangle of influence in space-time. Information and energy both dissipate entropically through agglomerations of particles such that matter is, on average, stable in appearance. Appearance, though, is a function of information. Perhaps because information takes on a life of its own in human communication and has so many trivial uses for social organisms, we think of it as independent from matter and energy. Note, however, that we also think of energy as independent of matter.
The myth of Sisyphus shows how deeply entropy is engrained in the psyche and mythology of human history. The essential difference between gods and humans is that gods do not suffer entropy. Superheroes also live beyond the effects of entropy. Magic shows work by concealing the entropy of the reactions, whether spacial (disappearing and reappearing), informational (which card did you pick?), or chemical (spontaneous flame and reorganisation). Entropy is the difference between science and science fiction.
entropy doesn’t give a damn about all the progress you’ve made or how hard you are trying. the more work you do, the more entropy piles up around you. the more success you have, the less opportunity will be left over. when your heat sink is full, you fail. that’s the shit on a stick of physics, and it’s the hardest thing to accept in science. nature gives the illusion of perpetual motion, but the counter-entropic moments are tiny, and, like a pendulum, if you stop them they don’t just go again. whatever progress you think you are making, you have to look at the entropy that comes with it to know whether the thermal reservoir can sustain it or if it is a flash in the pan that will burn through its neighbourhood.
When Stephen Hawking wrote that physics “can predict just half what we could, according to the classical 19th century view“, it should have been earth shattering. Determinism isn’t a minor point in science; it’s the foundation of the scientific method. It’s tempting to say that just because we can’t predict it doesn’t mean that we can’t understand it, but while that may be intuitive agreeable, it’s not scientific: you can’t check the validity of your hypothesis if you can’t predict something with it, and if you can’t test your prediction, you can’t build a new hypothesis based on it or break it down into finer truths. If science just went from 99% complete to 49% complete, it should made news beyond an academic, soft-science journal, but we may just be at a loss for a rational response. Nobody who understands what just happened wants a return to emotive fascism, although the global rise of fascism probably isn’t a coincidence. Science hasn’t stabilised the stock market, stopped climate change or eliminated militancy. But there may be a rational response to the half of the universe that isn’t accessible to scientific investigation.
Entropy affects chaos in the same way and at the same rate that it dissipates resonance and harmonics. So while chaotic processes can’t be predicted, you can predict that the chaotic elements will degenerate over time into orderly resonance. Watch the ripples on a bowl of water when you drop something into it: the first wave is simple, then the interference builds chaotic movements, but then the interference patterns fade and the orderly base harmonic of the container is all that’s left. We can also predict that the chaos will degenerate at a rate that follows a logarithmic curve, which is familiar to everyone because it’s the rate at which energy dissipates in general, whether it’s a musical note dying, ball bouncing to a standstill or food getting cold on a plate. In the lab, this rate can be calculated and predicted pretty easily, but in the real world, or any open system, we don’t know the base of the logarithm so we can’t calculate it scientifically, but we can imagine it aesthetically.
Coincidentally, this also illustrates the relationship between information and thermodynamic entropy. There was a lot of information in the movement of the surface when there were waves all over the place, coinciding with the free kinetic energy of the waves, but as the waves dissipated into the natural resonance of the whole bowl, the information also dissolved until in the end there was just the one bit of information in the single wave tilting back and forth. (It should be noted that this is different from Shannon entropy, which is the measure of the carrying capacity of an information transmission system.)
The important thing is not to panic and revert to fascism. If you try to kill the chaos, it will get stronger. Imagine throwing more balls at the water to try to stop the waves from interfering with one another; that’s the essence of the fascist response to disorder. The results are predictable.