I know I’ve been terrible about updating my blog lately. I’ve got some good excuses. (The usual: very busy with work. The less usual: new glasses that I’m having a very hard time adapting to. Getting old sucks. My eyes have deteriorated to the point where my near vision is shot, and the near-vision correction in my lenses needed to get jumped pretty significantly, which takes some serious getting used to.) And getting discussions of type theory right is a lot of work. Type theory in particular takes a lot of work, because it’s a subject that I really want to get right, because it’s so important in my profession, and because so few people have actually written about it in a way that’s accessible to non-mathematicians.

Anyway: rest assured that I’m not dropping the subject, and I hope to be getting back to writing more very soon. In the meantime, I decided to bring you some humorous bad math.

Outside the scientific community, one of the common criticisms of science is that scientific explanations are “just a theory”. You hear this all the time from ignorant religious folks trying to criticize evolution or the big bang (among numerous other things). When they say that something is just a theory, what they mean is that it’s not a fact, it’s just speculation. They don’t understand what the word “theory” really means: they think that a theory and a fact are the same class of things – that an idea starts as a theory, and becomes a fact if you can prove it.

In science, we draw a distinction between facts and theories, but it’s got nothing to do with how “true” something is. A fact is an observation of something that happens, but doesn’t say why it happens. The sun produces light. That’s a fact. The fact doesn’t say why that happens. It doesn’t have to say how it happens. But it does. That’s an observation of a fact. A theory is an explanation of a set of facts. The combined gravitational force of all of the particles in the sun compress the ones in the center until quantum tunnelling allows hydrogen atoms to combine and fuse producing energy, which eventually radiates as the heat and light that we observe. The theory of solar hydrogen fusion is much more than the words in the previous sentence: it’s an extensive collection of evidence and mathematics that explains the process in great detail. Solar hydrogen fusion – mathematical equations and all – is a theory that explains the heat and light that we observe. We’re pretty sure that it’s true – but the fact that it is true doesn’t mean that it’s not a theory.

Within the scientific community, we criticize crackpot ideas by saying that they’re not a theory. In science, a theory means a well-detailed and tested hypothesis that explains all of the known facts about something, and makes testable predictions. When we say that something isn’t a theory, we mean that it doesn’t have the supporting evidence, testability, or foundation in fact that would be needed to make something into a proper theory.

For example, intelligent design doesn’t qualify as a scientific theory. It basically says “there’s stuff in the world that couldn’t happen unless god did it”. But it never actually says how, precisely, to identify any of those things that couldn’t happen without god. Note that this doesn’t mean that it’s not true. I happen to believe that it’s not – but whether it’s true or not has nothing to do with whether, scientifically, in qualifies as a theory.

That’s a very long, almost Oracian introduction to today’s nonsense. This bit of crackpottery, known as “the Principle of Circlon Synchronicity”, written by one James Carter, has one really interesting property: I agree, 100%, with the very first thing that Mr. Carter says about his little idea.

The Principle of Circlon Synchronicity is not a Theory

They’re absolutely correct. It’s not a theory. It’s a bundle of vague assumptions, tied together by a shallow pretense at mathematics.

The “introduction” to this “principal” basically consists of the author blindly asserting that a bunch of things aren’t theories. For example, his explanation for why the principal of circlon synchronicity is not a theory begins with:

There are many different theories that have been used to explain the nature of reality. Today, the most popular of these are quantum mechanics, special relativity, string theories, general relativity and the Big Bang. Such theories all begin with unmeasured metaphysical assumptions such as fields and forces to explain the measurements of various phenomena. Circlon synchronicity is a purely mechanical system that explains local physical measurements. You only need a theory to explain physical measurements in terms of non-local fields, forces and dimensions.

This is a novel definition of “theory”. It has absolutely nothing to do with what the rest of us mean by the word “theory”. Basically, he thinks that his explanations, because they are allegedly simple, mechanical, and free of non-local effects, aren’t theories. They’re principals.

The list of things that don’t need a theory, according to Mr. Carter, is extensive.
For example:

The photon is not a theory. The photon is a mechanical measurement of mass. The photon is a conjoined matter-antimatter pair that is the basic form of mass and energy in the Living Universe. All photons move at exactly the speed of light relative to one another within the same absolute space. Photons are produced when a proton and electron are joined together to form a hydrogen atom. The emission of a photon is a mini annihilation with part of the electron and part of the proton being carried away by the photon. A photon with mass and size eliminates the need for both Planck’s constant and the Heisenberg uncertainty principle and also completely changes the meaning of the equation E=MC2. This is not a theory of a photon. It is the measurements describing the nature of the photon.

This is where we start on the bad math.

A photon is a quantum of light, or some other form of electromagnetic radiation. It doesn’t have any mass. But even if it didn’t: a photon isn’t a measurement. A photon is a particle (or a wave, depending on how you deal with it.) A measurement is a fundamentally different thing. If you want to do math that describes the physical universe, you’ve got to be damned careful about your units. If you’re measuring mass, you your units need to be mass units. If you’re describing mass, then the equations that derive your measurements of mass need to have mass units. If a photon is a measurement of mass, then what’s its unit?

Further, you can’t take an equation like , and rip it out of context, while asserting that it has exactly the same meaning that it did in its original context. Everyone has seen that old equation, but very few people really understand just what it means. Mr. Carter is not part of that group of people. To him, it’s just something he’s seen, which he knows is sciency, and so he grabs on to it and shouts about it in nonsensical ways.

But note, importantly, that even here, what Mr. Carter is doing isn’t science. He’s absolutely right when he says it’s not a theory. He asserts that the whole meaning of changes because of his new understanding of what light is; but he doesn’t ever bother to explain just what that new understanding is, or how it differs from the old one.

He makes some hand-waves about how you don’t need the uncertainty principle. If his principles had a snowballs chance in hell of being correct, that might be true. The problem with that assertion is that the uncertainty principle isn’t just a theory. It’s a theory based on observations of facts that absolutely require explanations. There’s a great big fiery-looking ball up in the sky that couldn’t exist without uncertainty. Uncertainty isn’t just a pile of equations that someone dreamed up because it seemed like fun. It’s a pile of equations that were designed to try to explain the phenomena that we observe. There are a lot of observations that demonstrate the uncertainty principle. It doesn’t disappear just because Mr. Carter says it should. He needs to explain how his principles can account for the actual phenomena we observe – not just the phenomena that he wants to explain.

Similarly, he doesn’t like the theory of gravity.

We do not need a theory of gravity to explain exactly how it works. Gravity is a simple measurement that plainly shows exactly what gravity does. We use accelerometers to measure force and they exactly show that gravity is just an upwardly pointing force caused by the physical expansion of the Earth. The gravitational expansion of matter does not require a theory. It is just the physical measurement of gravity that shows exactly how it works in a completely mechanical way without any fields or non-local interactions. You only need a theory to explain a non-local and even infinite idea of how gravity works in such a way that it can’t be directly measured. Gravity not a theory.

Once again, we see that he really doesn’t understand what theory means. According to him, gravity can be measured, and therefore, it’s not a theory. Anything that can be measured, according to Mr. Carter, can’t be a theory: if it’s a fact, it can’t be a theory; even more, if it’s a fact, it doesn’t need to be explained at all. It’s sort-of like the fundamentalists idea of a theory, only slightly more broken.

This is where you can really see what’s wrong with his entire chain of reasoning. He asserts that gravity isn’t a theory – and then he moves in to an “explanation” of how gravity works which simply doesn’t fit.

We do not need a theory of gravity to explain exactly how it works. Gravity is a simple measurement that plainly shows exactly what gravity does. We use accelerometers to measure force and they exactly show that gravity is just an upwardly pointing force caused by the physical expansion of the Earth. The gravitational expansion of matter does not require a theory. It is just the physical measurement of gravity that shows exactly how it works in a completely mechanical way without any fields or non-local interactions. You only need a theory to explain a non-local and even infinite idea of how gravity works in such a way that it can’t be directly measured. Gravity not a theory.

The parade of redefinitions marches on! “Exactly” now means “hand-wavy”.

We’re finally getting to the meat of Mr. Carter’s principle. He’s a proponent of the same kind of expanding earth rubbish as Neal Adams. Gravity has nothing to do with non-local forces. It’s all just the earth expanding under us. Of course, this is left nice and vague: he mocks the math behind the actual theory of gravity, but he can’t actually show that his principal works. He just asserts that he’s defined exactly how it works by waving his hands really fast.

I can disprove his principle of gravity quite easily, by taking my phone out of my pocket, and opening Google maps.

In 5 seconds flat (which is longer than it should take!), Google maps shows me my exact position on the map. It does that by talking to a collection of satellites that are revolving around the earth. The positions of those satellites are known with great accuracy. They circle the earth without the use of any sort of propellant. If Mr. Carter (or Mr. Adams, who has a roughly equivalent model) were correct – if gravity was not, in fact, a force attracting mass to other masses, but instead was an artifact of an expanding earth – then the “satellites” that my phone receives data from would not be following an elliptical path around the earth. They’d be shooting off into the distance, moving in a perfectly straight line. But they don’t move in a straight line. They continue to arc around the earth, circling around and around, without any propulsion.

In any reasonable interpretation of the expanding earth? That doesn’t make sense. There’s no way for them to orbit. Satellites simply can’t work according to his theory. And yet, they do.

Of course, I’m sure that Mr. Carter has some hand-wavy explanation of just why satellites work. The problem is, whatever explanation he has isn’t a theory. He can’t actually make predictions about how things will behave, because his principles aren’t predictive.

In fact, he even admits this. His whole screed turns out to be a long-winded advertisement for a book that he’ll happily sell you. As part of the FAQ for his book, he explains why (a) he can’t do the math, and (b) it doesn’t matter anyway:

The idea that ultimate truth can be represented with simple mathematical equations is probably totally false. A simple example of this is the familiar series of circular waves that move away from the point where a pebble is dropped into a quiet pool of water. While these waves can be described in a general way with a simple set of mathematical equations, any true and precise mathematical description of this event would have to include the individual motion of each molecule within this body of water. Such an equation would require more than the world’s supply of paper to print and its complexity would make it virtually meaningless.

The idea of the circlon is easy to describe and illustrate. However, any kind of mathematical description of its complex internal dynamics is presently beyond my abilities. This deficiency does not mean that circlon theory cannot compete with the mathematically simplistic point-particle and field theories of matter. It simply means that perhaps ultimate truth is not as easily accessible to a mathematical format as was once hoped.

It’s particularly interesting to consider this “explanation” in light of some recent experiments in computational fluid dynamics. Weather prediction has become dramatically better in the last few years. When my father was a child, the only way to predict when a hurricane would reach land was to have people watching the horizon. No one could make accurate weather predictions at all, not even for something as huge as a storm system spanning hundreds of miles! When I was a child, weathermen rarely attempted to predict more than 2 days in advance. Nowadays, we’ve got 7-day forecasts that are accurate more often than the 2-day forecasts were a couple of decades ago. Why is that?

The answer is something called the Navier Stokes equations. The Navier-Stokes equations are a set of equations that describe how fluids behave. We don’t have the computational power or measurement abilities to compute N-S equations to the level of single molecules – but in principle, we absolutely could. The N-S equations – which demonstrably work remarkably well even when you’re just computing approximations – also describe exactly the phenomenon that Mr. Carter asserts can’t be represented with mathematical equations.

The problem is: he doesn’t understand how math or science work. He has no clue of how equations describe physical phenomena in actual scientific theories. The whole point of math is that it gives you a simple but precise way of describing complex phenomena. A wave in a pool of water involves the motion of an almost unimaginable number of particles, with a variety of forces and interactions between those particles. But all of them can be defined by reasonably simple equations.

Mr. Carter’s explanations are, intuitively, more attractive. If you really want to understand relativity, you’re going to need to spend years studying math and physics to get to the point where its equations make sense to you. But once you do, they don’t just explain things in a vague, hand-wavy way – they tell you exactly how things work. They make specific, powerful, precise predictions about how things will behave in a range of situations that match reality to the absolute limits of our ability to measure. Mr. Carter’s explanations don’t require years of study; they don’t require to study esoteric disciplines like group theory or tensor theory. But they also can’t tell you much of anything. Relativity can tell you exactly what adjustment you need to make to a satellite’s clock in order to make precise measurements of the location of a radio receiver on the ground. Mr. Carter’s explanations can’t even tell you how the satellite got there.