Oh. No. You. Di'int.

Pseudoscience is something I don't really have the social skills to fight head on. I'm not a practical, working research scientist. "But that's obviously nonsensical" isn't a sufficient counterargument for, say, homeopaths.

Speaking of which, let's take a brief detour to cover that. Homeopathic remedies "work" for a suitably relaxed definition of "work". By "work", what homeopaths mean is that homeopathic remedies do have measurable beneficial effects on those who receive them; and, as scientific studies have routinely and eternally confirmed, those beneficial effects are precisely equal to the beneficial effects experienced by patients administered a placebo instead. In other words homeopathic remedies work precisely as well as "nothing-disguised-as-a-pill". Or, to put that in black and white: if your remedy works precisely as well as "nothing at all", then your remedy does nothing. It is possible that there might be other remedies - let's call them null-remedies - out there, which, when administered to one group of patients while the others are given a placebo, actually have literally no effect on the health of the patient, while those with the placebo actually do cheer up and feel a little better, as we might expect. In that situation we would have to conclude that the null-remedies, since they do not even cause the patient to cheer up a little, are actually counter-acting the placebo effect. If a pill does literally nothing, not even a placebo effect, then we know it is actually harmful. That's negative. Remember this: placebo is zero. Placebo is zero. To simply have "no effect" is less than zero. For a medicine to attain the status of "actually viable as a legitimate medicine" requires measurably more than just the placebo effect, which homeopathic remedies do not and, if the slightest logic is applied, cannot provide.

The real question, then, is: should it be medically acceptable to sell a placebo? My answer is: only if it's labelled, in black and white, as a warning from the Department of Health: "PLACEBO". "Dimextrothin - proven weight loss through psychological (placebo-effect) appetite suppression." "Take an unlimited quantity at will for strictly illusory light to moderate pain relief." "100% pure water. No active ingredients." Anyway.

So yes: there's junk science. But it's not often you run into actual junk mathematics. Here's the thing about junk mathematics. Science is up for debate. With a law, a theory, a paper, a data source or a single datum, you can dispute the author, the source, the motivation, the politics, the data gathering methods and the spelling. You can fight over this stuff. That which is "true" is what stays standing after the fight is over. That's how science works. Science is what fits the universe better than anything else, all brute force statistical manipulation and personal biases removed.

Mathematics? Not so much.

When you're wrong in maths, you're wrong. You're wholly, one hundred percent wrong. Exactly as wrong as it's possible to get. Boolean false. Zero points out of a possible one. When you're wrong in mathematics, you're claiming a falsehood is true. That means that the statement you just made - regardless of its other ramifications - results in one equalling zero and the destruction of all mathematics. When someone proves you wrong in mathematics and you raise protest, the person who proved you wrong will turn around with condescending amusement and go, "I'm sorry. Did you just argue back? Perhaps you mistook mathematics for one of your airy-fairy grey-area subjects? Literary analysis? Philosophy, maybe?" And that person can be anybody. It can be a high school upstart who spotted a typo in your long division. It can be the Lucasian Professor of Mathematics undermining your life's work in two lines. There are no points for experience here. There are no "mainstream" and "alternative" mathematicses. There are no "fringe theorems".

That which is "true" is that which makes the universe easiest to understand, model, explain, predict and generally deal with. Climate change is real because this is the option (as opposed to the "climate change isn't real" option) which best explains accumulated climate data. Solipsism is obviously complete horsebull, because assuming that other people are real is a much more efficacious way to deal with real life than behaving as if they don't exist. No, there is no Matrix, because pretending there is a Matrix doesn't help us with anything or explain anything or predict anything.

Point nine recurring equals one because the people who operate under the assumption that point nine recurring equals one are real mathematicians who accomplish real maths, and the people who believe otherwise are to a man gawking, wrong-headed bystanders who have no business playing with concepts they don't understand, and who have accomplished no significant mathematics. At all. The people who are right are the people whose beliefs haven't led to the undermining and collapse of all mathematics. The people who are wrong do not matter. Be quiet. Adults are working.

You can't say things like "it is not possible to represent all real numbers in any given radix system". You can't say "the real numbers aren't well defined" and argue for the countability of the real numbers if you don't accept the well-formed and logical existence of infinite decimal expansions as real numbers. You can't use "Cantor was ridiculed again and again" as an argument against his mathematics or say that Cantor's enumeration of the rationals being technically a surjection, not a bijection, invalidates it. Well, you can, in as much as humans have the right to be wrong. But you're not a plucky underdog challenging the status quo. You're not a breath of fresh innovative air to a stiff-collared, staid establishment grown complacent, creaky, stale and irrelevant. If you've come up with something which directly contradicts established mathematics, you're just wrong. And if you don't stop talking (and start disabling comments) when a mathematician who knows anything about anything tells you that, then you're more than wrong, you're out of your depth and self-evidently mucking with forces you don't understand.

This guy's filling (polluting) Knol with his dubious junk. If Knol was relevant, I'd bother to campaign against it.