Introduction To Mathematics

“Pseudoscience is a claim, belief or practice which is presented as scientific, but does not adhere to a valid scientific method, lacks supporting evidence or plausibility, cannot be reliably tested, or otherwise lacks scientific status. Pseudoscience is often characterized by the use of vague, contradictory, exaggerated or unprovable claims, an over-reliance on confirmation rather than rigorous attempts at refutation, a lack of openness to evaluation by other experts, and a general absence of systematic processes to rationally develop theories.”

-Wikipedia introduction to Pseudoscience
Hello. I’d like to stop and say a brief word about mathematics. This a topic that will either bore or confuse most of you. It does both to me. I had problems with maths at school and, like a lot of people, I assumed that I was simply too dense to learn numbers. I had a problem seeing that apples and bananas were equivalent, so that A equals B. Even today, take me past the first decimal point or any fraction smaller than 1/4 and a small part of my brain starts dancing really fast and whistling really loud. I am, in short, good at calculating a 20% tip and very little else.
I’m now going to reveal a scene from my childhood. It’s not something I’m comfortable doing, but my therapist recommended I expose myself to strangers (he’s now in prison). One day in Primary school I had to answer a difficult maths question. It was one of those “if John has three bananas and Mary gives him five apples, how many pieces of fruit does John have?” questions, which confused the pants off me because I had a vague idea that a banana was a herb or something, and five plus three was still five plus three no matter how hard I considered the matter.I sat and stared at the page for half an hour before bursting into tears.
Until university I thought it was just the case that some people are good at maths and some people aren’t. That was until I discovered the beautiful world of Logic. First-Order Logic is to mathematics and science what these two doctrines are to..well…all other academic fields. Philosophy has been called “the mother of science”, but in a pig’s arse it is. Philosophy is ineffable pondering. Logic is the mother of science.
If you’re not familiar with Logic now is not really the time for a full discussion, but I’ll give you the basics. Logic is a way of drawing a picture of reality. Aristotle would have it this way: “A is A”. You get the idea. Wittgenstein, who we should thank on bended knee, established that logic is a system through which we picture reality in statements, collectively called “The Case”. Logical points are connected by things like “and”, “or” and “if, then”. As far as basics go, that’s all there is to it. The world is logical in how it works. If A, then B. Maybe A or B. A and C. You get the idea. Of course, Wittgenstein wasn’t all there…
To pure Logicians, mathematics is bullshit. There are exactly two (read that: two) expressions of quantity in pure logic. You have “∀”, which means “all, or all known”, as in “all swans are birds”, or you have “∃”, which means “one, or at least one”, as in “at least one person is called Bernie Ecclestone”. You don’t actually need any other quantifiers. Numbers are bullshit or, to put it academically, a “quantification aberration”. After all, all quantities are at least one and can’t be any more than everything. Even one is a bit tricky for real mathematicians, as expressed neatly by this SMBC comic:
The great German philosopher Gottlob Frege (roll that name around your mouth and really savour it) once tried to codify what “one” was exactly and ended up with two books concerning the problem: “The Foundations of Arithmetic” and “Begriffsschrift” (the latter of which I “read” in the original German, because I’m a cocky runt who won’t let anything as basic as a lack of knowledge of a language stop me from being an interminable smart-arse). Bertrand Russell devoted twenty years to developing a foundation for numbers and never completed it. Then along came Kurt Gödel, a young Austrian mathematician, who took a view of the situation and concluded that
For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.”
In short, the greatest logicians of the twentieth century got together and concluded that mathematics was bullshit. Even mathematicians are more or less of this opinion:
The problem that faces us is a world that runs on mathematics. Economics, the bastard son of arithmetic and pseudo-science supreme, is the method by which we understand whether things work or not. How else would we have ended up in a world where a country can be in debt to the tune of a trillion dollars. A. Trillion. Dollars. A thousand billion. A thousand thousand million. A thousand thousand thousand thousand. A thousand is ten hundreds. I can count to a hundred on a good day, maybe. A trillion dollars is a little beyond my scope. I’m starting to think that’s less a failure in my thinking and more a failure in the world. This is a world where the stock market can be down fifteen points and it has been a good day. This is a world where America has spent $68 Billion on defence in the last 20 years and its inhabitants still don’t feel safe. Help me, I feel ill, I’m getting off.
The most pernicious illogic of all is the idea that money works, a principle that’s been the central tenet of mercantilism and capitalism since the 1200s, yet still offends good, honest, working people. Money, in terms of work, accrues interest. As do loans, debts, and trades. That’s money working, ie numbers breeding more numbers. How? Not logically. Scientists have tacitly accepted the interesting quirk that mathematics happens to coincide with reality every so often, even though the world is logical and maths isn’t. Why this should be is one of the great unresolved mysteries of modern times.
A spectre is haunting the world: the spectre of numbers. We rely on numbers to interpret the world, even though there is no basis for such a reliance. As a consequence, it’s a strange and eerie world we live in. A world that runs on something more like mysticism than a science.
I would say more, but I’ve taken up enough of your time. I’m expecting a cadre of irate economics majors to fire-bomb my house tonight. What’s the number for the police?

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