Science is the magic that actually works.
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I guess physicists do not realize that there is a one-to-one correspondence between a sentence and an equation. We know this from George Boole's work.
First of all, an equation is an equality of ratios stated with standard units. A true equality of ratios, on the other hand, is always stated with relative units. But in physics, most equations that look like an equality of ratios are not equality of ratios. Physicists routinely divide an equation into two parts by assigning a name to each part thus one side of the equation becomes just a label or a placeholder. The equation had been divided into two definitions (but still connected by the equality sign). Physicists still read these definitions as equations. The reason for this confusion is that in physics the fundamental symbol that makes the equation, the equality sign, is a loaded symbol. It can be used to make a definition, a proportionality, an equation and also an identity.
When a physicist repeats the official physics propaganda that "you should learn the equations because the equations are precise, sentences are not," we can only laugh at his naiveté. How can physics equations be precise when it is created by using the most loaded symbol in physics? But this is the standard rhetorical device physicists use to stave off any non-physicists who question their sacred doctrine. I showed elsewhere that “learning more physics” is not necessary to question the doctrine, because doctrine comes before physics.
We can easily convert any equation into the form of a sentence or convert a sentence into the form of an equation. This is no different than the relationship between geometry and algebra. The same idea can be expressed algebraically or geometrically.
What is fundamental is the ratio and the equalities of ratios. Equation is not fundamental and it is not precise; the equation is the Latin of physics.
***
I’ve known John Baez since Usenet days. He was the moderator of the newsgroup sci.physics.research. He was always ready to help with physics questions and he had a talent to explain even the most difficult concepts in simple language. I learned a lot physics from him and sci.physics.research. But today I intend to analyze this sentence of his:
Science is the magic that actually works.
I want to understand if this sentence has a meaning and if so what it is. I also like to practice my claim that any sentence can be expressed as an equation.
So let
S = Science
M = Magic
M' = Magic that works
Obviously M and M' are not synonyms or equivalent. They are different things. Magic refers to something impossible that a magician fools you into believing that he made the impossible happen. The magician does this by fooling the observer. Therefore, by definition, magic means that the impossible did not happen but faked. Magic that works is not magic. In fact, “magic that works” simply means “magic that is not magic.” But a thing cannot be itself and not be itself at the same time. (But in physics things can be and not be at the same time, as we will see below.)
Symbolically this sentence can be expressed as
S = M’ (1)
This statement does not contain the symbol M, so Dr. Baez’s statement is not about magic at all.
We say that equation (1) is independent of M.
We note that M is not M'
M /= M'
This sentence simply attempts to define the word “science” with a new definition of magic. But it does not succeed because “magic that works” is not “magic”. The sentence ends up defining “magic” as “not magic.”
This form of definition is common in physics.
Also, there are more layers of hidden definitions in this sentence. When Dr. Baez says “science” he means "physics." And he reduces physics to equations. His sentence can be written as, “Physics equations are magic that actually works.”
Initially, he sets us up by saying that the symbols of an equation *seem* magical to a child and then with a sleight of hand he drops the word "seem" so that the sentence becomes "magic that works."
But this is not even true. There is nothing magical in physics equations. In fact a physics equation is the exact opposite of magic because all terms in an equation must be either actual numbers or must be placeholders for numbers. And those numbers must be properties of actual quantities existing in nature.
What may have looked like magic to a child may have been the abracadabra movement of symbols that physicist like to call "derivation." So, just by moving around symbols ceremoniously physicists claim to arrive at deep truths. In fact, derivation is nothing more than putting together the equations physicists have separated previously. We mentioned that physicists split equations again and again to create new definitions. This is the modern version of the old scholastic method of “splitting hairs.” Derivation is the reverse of this process, that is, the combining of previously split equations.
But the physics derivation is all pretend and nothing else. Something known is derived from other things that are known but were hidden by previous manipulations. By algebraic substitutions nothing new can be discovered.
There is nothing magical in derivation either. It is done by using the laws of algebra.
Science was born as an antidote to magic and it is still the opposite of magic. And science will never be "magic that works" because magic that works is not magic. The way a miracle that repeats is not a miracle but a natural phenomenon. So the sentence “a natural phenomenon is a miracle that repeats” can be a meaningful sentence to a physicist. Because it is of the same form as Dr. Baez’s sentence.
***
Why is this important? Why not accept this sentence as a bon mot and enjoy its ambiguity? Why take it so literally?
The reason is that physicists use this sentence form to define fundamental concepts of physics. For instance, they use it to define the concept of particle, one of the most fundamental concepts in physics. For instance, physicists can say something like "a particle is a wave." The form is the same.
P = Particle
W = Wave
P = W
We see that this is not an equation but a definition.
But particles do not exist in modern collider experiments. Only fields and waves exist. So the sentence "particle is a wave" is not even a definition, it is making two words synonyms. In this case the word "is" makes "particle" and "wave" synonyms. Wave has physical existence but particle does not. So, "particle" is defined as placeholder for the word "wave".
Once again we see that the equation is the Latin of physics. Physicists use it to hide information and as a rhetorical device to fit data into the doctrine.
Notes:
--- The sentence occurs in The Math That Takes Newton Into the Quantum World:
But later, when I realized that by fiddling around with equations I could learn about the universe, I was hooked. The mysterious symbols seemed like magic spells. And in a way, they are. Science is the magic that actually works.
--- The equation: The loaded balance of physics
--- Wikipedia entry for George Boole
--- John Baez's blog.
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