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Charlene Werner's understanding of math

Who is Charlene Werner, you might ask? Seemingly she is an optometrist who is a great proponent of homeopathy. However, she is mostly well known for her absolutely hilarious pseudoscience, as depicted in this video (don't be surprised if that video doesn't exist by the time you click on it, as Werner is busy sending cease-and-desist demands to everybody who posts the video).

The sheer stupidity of what she says in that video has been totally trashed in several blogs around the internet, so I'm not going to go through everything she says because that has been done already. Instead, I'm just going to concentrate on her misunderstanding of mathematical formulas in physics, and the "E=mc2" formula in particular, just as an intellectual exercise.

The relevant quote is:

You know that when light is energy, right? OK. And he [Einstein] gave us the theory that energy equals mass times the speed of light. E=mc2. OK. If we take that formula, and we think that there's a lot of mass, right? OK. If you collapse all the mass down into the universe, so that there is no space between the mass, do you know how much mass there is in the entire universe? You think you're a lot of mass, right?... Well, the whole universal mass can be consolidated down into the size of a bowling ball. That's all there is in the whole universe. So, how much mass are you? That's right, an infinitesimal amount. So if you take that formula, E=mc2, you can almost cross out mass. So the formula ends up being "energy = the speed of light."

(No, there's a lot more "mass" than that in the universe, but as said, I'll skip commenting on that and the other things she says, and concentrate only on the math.)

Werner seems to have a fundamental misunderstanding of what a physical formula is. She seems to think that it's some kind of metaphor, a vague description of the relationship between two phenomena. She seems to think that "E=mc2" means approximately the same thing as "there's some kind of relation between energy, mass and light". One also gets the feeling that she seems to think that the little 2 (the "square") is just for decoration, put there because it looks fancy, as she just mentions it but ignores it completely.

She seems completely unable to understand that this is not a metaphor or a vague description. This is a mathematical formula. Mathematical formulas are completely rigorous and obey very strict rules. You can't just shuffle things around however you want and expect it to remain valid.

So here's a list of things that she gets utterly wrong:

If there's any deeper meaning to the E=mc2 formula, it's that it establishes an equivalence between energy and mass (rather than energy and light, as she postulates). It gives the exact ratio between the two (in other words, "this many kilograms of mass are equivalent to this many joules of energy".) And this is an exact, mathematical equivalence, not a vague metaphor.

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