Tuesday, October 18, 2016

How do I know?

The appeal of human authority is great and for most people that's all they have. They are told what is true or not, and in many cases have no means to check. Human authority is the ultimate authority for them, but in mathematics that is not the case.

But MOST of what most people know of mathematics IS on human authority while I found myself metaphorically in the wilderness with new mathematical approaches which was VERY distressing. So I found absolute truth in identities.

The identity which changed so much for me I call a tautological space:

x+y+vz = x+y+vz

Is weird to talk how much I considered that, and thought about it, to convince myself that what I was taught by human authority and common sense must be true, actually was! Identities are true in and of themselves, like x = x. Is just true. But I was doing different things with it.

x+y+vz = 0(mod x+y+vz)

Wrapped up into a modular expression is the SAME THING but presented differently. Is weird though. Some may think that 'mod' means the two expressions are different. Puzzle that one out then. (If it is new to you, I explain more on this page.) Why are the expressions equivalent?

From there it was just a matter of believing in logic, and over time I relied on mathematical authority, and human authority? Well that can just be plain wrong.

And I learned a love of mathematical proof.

James Harris
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