From a biggish thing about (among other things) Hamlet, proof-by-induction, fanfiction, the meaning of love, and the Eiffel Tower upside-down.

Now imagine (3,3) and (4,4) on the plane. Ya dig? OK: What's the next point?

Most people, I'm guessing, speculate that the 'next point' is (5,5). Linear progression. You don't even have to think of it as function input and output; you could just have a weird way of making two lists of integers that happen to proceed at equal pace from the same starting point. 'Sliding friction' is the force that resists you when you're sliding; 'static friction' is what fights against you starting. The latter is the greater force; as wacky Wernher von Braun said, 'Nature does not know extinction; all it knows is transformation.' The world has tendencies: in motion, stay in motion; at rest, stay at rest. Reality is opinionated. So are we.

We're made to extrapolate, which is how we invented God; we need order to make sense of infinity, which is why we invented God; we tend to value and enshrine straight-line thinking, which is why God looks like a bearded white man (and there's no such thing as a 'liberal media').

Proof by induction works like this: if you can show that a proposition is true for one baseline element, and that if it's true for one element then it must be true for the next one in line, then the proposition must be true for all elements. Inductive reasoning frees you to run - once you've settled on your baseline, your (literal) starting point, then all you need is a logic of association to allow you to make a universal statement. Which feels, let me tell you, absolutely wonderful. That wind-in-your-hair feeling of encompassing all of what you see in a single expression or conception. A formula.

But.

That joy (of understanding) doesn't come from a point. Think of singular aesthetic (i.e. learning) experiences that have 'changed your life,' or just your mind: I remember for instance my first rock show, being dumped for the first time, 'losing' my virginity, realizing I was falling in love with my future wife. You go back later on and fill in relationships to what you know, or to later examples of the same general phenomenon, but in each instant what prevails is confusion, loss of center, prior understandings (a/k/a 'priorities,' right?) falling away. The word for this feeling is freedom. The feeling changes you, but you can't possibly understand or articulate each moment within itself. The limited relationship between your reptilian, emotional, and analytical minds precludes such understanding.

And from that point, where do you go?

What would Hamlet say if he were here with us right now?