What is infinity?

Thinking about running away from home, most individuals naturally confront a natural question. “If I walk out, where do I end up?” By naturally, I refer to a logical consistency, a divine intelligence that would reason through all the possible preparations in the advent of any possible adversity. Of course, we are not divine and so we try to prepare for some potential scenarios with a meager manifest of needs and ingredients.

So, I start walking, walking and walking. I have a map, a running away from home map, and perhaps an idea of a goal. If I have a computer, I have an active participant in my escape. And maybe I want to escape from IT. So, I toss my device, off into that tilled field over there.

If I hadn’t thrown the device away… in that scenario, I would find that the computer had already drawn from a statistical ensemble, or menagerie, of other escapees. And become — be — my untrustworthy, my almost divine advisor. Call it my assistant, my commander, my idol. So, impulsively, I toss the device away.

You leave your home, really, when you cross over a threshold into the unknown. The day you got into your car, drove onto the highway, thru new and alien cities.

The day you started walking and night fell, and you slept by the side of the road. When the sun arose, and the new day began, you woke up and started walking, not knowing where you were going.

These thoughts are about crossing boundaries in your mind, crossing boundaries in the real world. These thoughts are about making my own thoughts, and realizing the work it takes, freeing myself from advice, from the devices. Is it worth the effort? If I accept the collaboration, I will always be confronted with two worlds that are correlated, loosely sometimes, but with incomplete and false data.

I am a mathematician. I am my own computer, I make my own architecture.  Running away from home, is finding a new mind. Perhaps you had a map, and a foolish idea of a destination. Now you have an empty space.

This is where infinity starts.

Mathematicians explain infinity as an unbounded process. As an example, the counting process has a beginning but no end, 1,2,3… Or the divisive process, cutting an interval repeatedly in half, 1/2, 1/4, 1/8… The idea is that one can define a looping process and that is infinity.

But common sense tells up that all processes must end eventually. The counting process terminates when the counter dies, the divisive process stops when we reach the quantum limit of atoms and physical measure.

It is easier to define the rules with infinity, than without it. It is simpler to talk about all the numbers possible 1,2,3,… than to talk about all numbers up to a largest number. Or to talk about a largest map. It is simpler to make an infinite map of directions, North, South, East and West. You can just keep walking, reaching the next town down the road. It is harder to think about the limits. Yes, if you keep walking, eventually you end up where you started. But this is so complicated. Infinity is so much easier.




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