Every wave is perfect. This sounds like a cliche, but I don’t mean every wave is great. I mean they are analytically, objectively perfect because they can’t be anything else. A wave is continuously convoluted with itself, so if there is a local distortion due to some external constraint, it is ironed out in the following periods. If you somehow made a square wave, it would renormalise itself in only a few periods. In fact, the normal distribution looks like a wave because every wave is a normal distribution. There is only one wave equation, and it describes every type of wave. Waves are universal, whether quantum fields or water waves or gravitational waves.
But lurking inside the perfection is a monster. A beast. Two beasts, actually. Fundamental uncertainty and pi. If you have ever tried to catch a big wave, you know that you don’t know exactly where it will break. Even pipeline and Teahoopu will break differently depending on the water on the reef from the previous wave and a whole bunch of other factors. Part of the problem is that a wave is not an object. It is the normal distribution of potential and kinetic energy, separated by half a period in space and time. When potential is maximum, kinetic is minimum and vice versa. Near equilibrium, kinetic and potential energy are indistinguishable and superimposed on one another, but when an energy gradient exceeds the limit of the equilibrium state, kinetic and potential are separated and they follow one another away from the source until eventually they recombine, either by breaking against an object or dispersing into the medium.
In addition to being perfect, every wave is quantised and natural. That is, you can only have a natural number of waves. You can’t have half a wave or 3.14 waves; you can only have a natural number of waves. Wave interactions are also natural and perfect. Combine two wave forms and you get another natural number of waves. Fourier analysis allows us to deconstruct (or construct) waves into component parts, and this always happens according to the logic of wave interactions. Whether in the form of harmonic oscillations or travelling waves, the logic of wave interactions is perfect and natural and, perhaps most important, it is totally real. The problem is that reality is made of more. You can’t have a wave without a medium, and even if that medium is the empty vacuum of space, its behaviour is profoundly different from the logical behaviour of waves. Regardless of scale, the behaviour of that part of reality that is not wave-like is purely probabilistic. Call it quantum uncertainty or entropy, the result is the same muddling, illogical condition of uncertainty.
In glassy systems, we think that many of these interesting properties occur because there’s what’s called a complex potential energy landscape. If you consider the total energy of the entire system as a function of where the atoms are, then in a glass, which isdisordered, that landscape is incredibly complex. https://www.quantamagazine.org/the-physics-of-glass-opens-a-window-into-biology-20180611/
If you have a perfectly random, stochastic process, it will come out in a normal distribution. Not only will it look like a perfect wave on a graph, but you will recognise it as a pulse, because the middle third will be recognisable as a pulse. Normal is the most amazing, wonderful, magical thing in the universe. Have you ever met a perfectly normal person. It is like touching a warm, soft blanket. They seem to have no edges. Normal may sound boring, but it is one of those great, mysterious phenomena that just knocks you over when you try to grasp it. It can’t exist in isolation. You can’t have one normal thing. It only exists in groups of independent things, so normal can’t even be a thing. And yet, there it is. Everywhere. (blackbody radiation is skewed high because quantisation means that low-energy interactions need not emit radiation at all.
Logic is a fundamental property of waves and harmonic oscillators. Logic is not a fundamental property of the media through which waves pass. To understand why logic works for real waves, you have to understand that every wave is perfect. This sounds like a cliche, and surfers will protest that some waves are thick and heavy, some are elegant and smooth, and others downright gnarly, but I don’t mean every wave is great. I mean they are analytically, objectively perfect because they can’t be anything else. A wave is continuously convoluted with itself, so if there is a local distortion due to some external constraint, it is ironed out in the following periods. If you somehow made a square wave, it would renormalise itself in only a few periods. Logic is appealing to the conscious mind because consciousness has to work with highly coherent waves. This imperative arises from the need for coherence of individual thoughts and the fact that they must be amplified to exceed the noise of random impulses. It also gives rise to wave-dependence, i.e., that consciousness depends on binary operators of “logical” thought. Logic seems like a necessary result of the transmission of internal communications through wave patters. In sum, logical thought is only realistic or rational with respect to wave patterns and harmonics. In complete reality, logic may be delusional or even psychotic, but it is coherent.
Very intelligent people do stupid things all the time, and their stupidity follows a pattern. Where Noether’s theorem holds, that is, where there is a conservation law and a symmetry, binary logic holds, and intelligent people are very successful. Where there isasymmetry and no conservation law, intelligent people become fabulously stupid because intelligent people have been trained to believe in symmetry and conservation of information. This is why the best and the brightest were able to delude themselves into thinking the invasion of Vietnam was succeeding, and why the yin/yang symbol is so comforting to the intelligent mind and also so misleading. There is no symmetry between order and chaos. This is why Chinese philosophy did not conquer the world, and why intelligent minds are loathe to accept thermodynamics. There is no symmetry between energy and entropy in real space. They are only related by probability, and even this relationship only applies to well defined variables. There is also no symmetry between information and communication in information space, which is why intelligent people believe stupid things they read online. Asymmetry compels people to retreat into well-defined fantasy worlds, which may explain why Henry Ford and Bob Mercer became racist psychopaths.
Quasi-Determinism is confined by two constraints: first, Noether’s theorem must hold throughout the event, so that there is a symmetry and property that is conserved for both cause and effect; second, the energy differential between cause and effect must be sufficiently large that the intervention of a measuring device does not substantially affect the result, that is, it must be possible to observe the event without disturbing it. For Rayleigh dissipation the first constraint is missing because there is no law of conservation or symmetry, while for bodies near equilibrium the second constraint is missing because measurement of events is impossible without disturbing the equilibrium.
The philosophy of science cannot itself be scientific or practiced scientifically. The effort to do so has led to its triviality. When John Horgan asked Karl Popper if the principle of falsifiability is falsifiable, Popper didn’t understand its significance for the practice of philosophy in general, and philosophy of science in particular. He didn’t see the connection with Godel incompleteness or thermodynamics.
physics of waves: http://www.people.fas.harvard.edu/~hgeorgi/onenew.pdf
The mind also experiences discontinuity perfectly, as it exists in physical reality. The existence of information is not an illusion, delusion or simulation. When you run into a wall, you may not know what the wall is, but you know that there is a discontinuity in the viscosity of the material filling the space around you.
https://www.quantamagazine.org/einstein-symmetry-and-the-future-of-physics-20190626/ Perhaps ironically, though, what is arguably the most revolutionary part of Einstein’s legacy rarely gets attention. It has none of the splash of gravitational waves, the pull of black holes or even the charm of quarks. But lurking just behind the curtain of all these exotic phenomena is a deceptively simple idea that pulls the levers, shows how the pieces fit together, and lights the path ahead. The idea is this: Some changes don’t change anything. The most fundamental aspects of nature stay the same even as they seemingly shape-shift in unexpected ways. Einstein’s 1905 papers on relativity led to the unmistakable conclusion, for example, that the relationship between energy and mass is invariant, even though energy and mass themselves can take vastly different forms. Solar energy arrives on Earth and becomes mass in the form of green leaves, creating food we can eat and use as fuel for thought. (“What is this mind of ours: what are these atoms with consciousness?” asked the late Richard Feynman. “Last week’s potatoes!”) That’s the meaning of E = mc2. The “c” stands for the speed of light, a very large number, so it doesn’t take much matter to produce an enormous amount of energy; in fact, the sun turns millions of tons of mass into energy each second… Over the past several decades, some physicists have begun to question whether focusing on symmetry is still as productive as it used to be. New particles predicted by theories based on symmetries haven’t appeared in experiments as hoped, and the Higgs boson that was detected was far too light to fit into any known symmetrical scheme. Symmetry hasn’t yet helped to explain why gravity is so weak, why the vacuum energy is so small, or why dark matter remains transparent.
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