My Favorite Word is Discrete, What's Yours?
Discrete is a word that gives me a little spark of joy every time it pops into my head.
The dictionary definition of discrete is individually separate and distinct. That makes sense to me, but if you hadn’t encountered the word, without any context would you really understand what that is supposed to mean?
The more mathematical definitions are not really satisfying either. They basically boil down to the opposite of continuous, a bijection with the natural numbers, and other more complex definitions that I won’t pretend to understand.
I think the best way to understand the word discrete is to just see it.
In this example, the discrete function on the left can only be sampled at the seven points shown, whereas the continuous function on the right can be sampled at an infinite number of points. Even this description of the image does not really capture the idea as precisely as the image itself.
Yet, after seeing the image, I think the word-based definitions feel grounded and much more satisfying. Individually separate and distinct has a more specific meaning after looking at this picture.
That’s why I like the word discrete so much, it’s a word that represents an idea that is very difficult to express in words. And yet, once you gain an understanding of the idea through a medium other than words, the word itself can take on all the indescribable meaning of the idea in an actionable way.
For example, I could describe the atoms that make up a body of water as discrete, and someone who understands the word will know exactly what I mean. I could also say that from the perspective of a person observing a body of water, that the body of water does not appear to be discrete. Better yet, since we established that discrete is the opposite of continuous, I could say that the body of water appears to be continuous, and the person would understand what I mean. But, if I asked that person to explain what I meant when I described the atoms or the water as discrete or continuous, I imagine a wordy and hand wavy description (like the one on your screen right now) would follow.
I see discrete as a word at the extremes of both the power and the limitations of language, and I’d love to find more words that live in this neighborhood. Maybe if I find enough of these words I’ll maintain a list or something.
If you know any feel free to share! My email is on the home page of this blog, and I’ll check the comments on Hacker News to see if the three people that read this leave any comments.