Cardinality. It’s a concept I have been fascinated with since being exposed to it by my high school geometry teacher. He put the problem to me like this.
The real numbers and the rational numbers are both infinite sets. But there are infinitely more numbers in the real numbers than the rational numbers, and not the other way around. Why does this make sense?
In a sense, it doesn’t. I know the answer now: The real numbers are ‘uncountably infinite,’ meaning there is no way to “map” them all out the way we can map the rational numbers. But that doesn’t mean there is an “infinity beyond infinity” that they exist in.
Why does this concept work? It is a useful abstraction. It’s not 100% accurate – nor does it need to be.
Useful abstractions like this are the key to fueling creativity in all fields – the arts, the sciences, technology and design, entrepreneurship. We can all recall that time that we heard of a new scientific innovation and immediately had our minds spinning to turn it into a business, yes?
That’s what Cardinality is all about. Finding the fine line between technical detail and creative visualization, to spearhead your own imagination.
We can merely distill the content. The space of your own ideas is uncountably infinite.
-Andrew
