experience

1.1.3

Numbers in the Raw

Introduction

Let's begin our discussion of large numbers at the very beginning. I don't just mean beginning at one, I mean beginning without the hindsight of centuries of mathematics. Forget the googolplex, forget trillions, billions and millions, even forget one, two, and three! Forget what you know about arithmetic, and even forget how to write numbers. I invite you to imagine having no names or symbols for any number what so ever. Let's start with a proverbial blank slate!

Given this severe handicap, how would we do mathematics? How would we count? and what kind of conversation about large numbers could we have?

In this article we'll explore large numbers through the eyes of an innocent, who has never seen or heard of any mathematics at all. In doing so, I hope to recapture the bare essence of googology, the study of large numbers. The fact is, numbers are visceral, and even without any language or notation we can talk about large numbers. This is a state of mind not that different than what early humans would have experienced. They would have been surrounded by a world full of numbers, and while they could not quantitatively describe them, they could at least have a qualitative experience of them.

I invite you to join me on an experiment: Let's see how far we can get in our contemplation of large numbers without the aid of any form of mathematics...

Numbers in the Raw: Innate Googology

When we look out upon the world we immediately find that it's full of things to look upon. Early man must have found his world overwhelming in his deeper moments of contemplation, when he realized there was more to his world than what was right before his eyes. Despite the fact that he would have had no words, nor symbols, for any kind of number, early humans would not have been number-blind. Even animals have an innate concept of number, and it's been shown that even babies have an innate understanding of small quantities. The early human would notice that there was a difference in quantity in the images below:

The awareness may have only been a vague feeling, but it was sufficient for early man to get by. From this vague "number sense" our modern understanding of number would emerge. Why were humans able to perceive number, what purpose did it serve. There were many practical reasons why the ability to have a sense of quantity was vital for survival. For example, if one saw a few predators coming their way:

ran for a bit and then saw this:

it would pay to recognize something was unaccounted for. The ability to sense difference in small quantities was also probably used to keep track of offspring.