Sorry, Google, That’s Not Recursion
When the tech industry co-opted the definition of something they fundamentally don't understand (Reading time: 5 min)
Every once in a while, a misunderstanding ends up becoming a new reality—and in this case, the tech industry is the perpetrator, making all of us just a little dumber.
What the hell am I on about? A little-understood word called recursion.
To illustrate how little understood this word really is, particularly in the tech field, let’s ask an AI—Grok, specifically.
“What is recursion?”
“Recursion is a programming concept where a function calls itself to solve a problem by breaking it into smaller, similar subproblems. It typically involves a base case to stop the recursion and a recursive case that reduces the problem size. For example, calculating a factorial: factorial(n) = n * factorial(n-1) with a base case of factorial(0) = 1. It’s like a Russian nesting doll—each call opens a smaller version until you reach the smallest one, then it builds back up.”
I have only two words for that: ummmm, no.
Lest you think otherwise, trust me—it’s not just Grok that gets this wrong.
The first sentence gives it away: “Recursion is a programming concept…” No, it really isn’t. I have no doubt that would be news to Italian painter Giotto, who used recursion in his painting Stefaneschi Triptych around 1320. Houston, we got ourselves a problem.
Let me save you some time and be direct: recursion existed well before programming, and it has existed in multiple fields like logic, art, language, architecture, and others for a very, very long time.
What likely happened is programming became so big, so popular, and recursion—already misunderstood and rarely discussed—got gradually narrowed down largely to just programming.
Fear not, for even when it is discussed outside of programming, it is still perfectly misunderstood.
Let’s look at my favorite example: the wonderful, mind-bending film Inception.
Entire websites are dedicated to breaking down the recursion in the film that doesn’t exist. You’re probably asking yourself, “Then what are they on about?” The answer, at least for Inception, is nesting.
Nesting, which is not recursion, is when we have things within things within things. Of course, the best example is Russian nesting dolls (I mean, it’s kinda in the name), but this is exactly what happens in the movie—there are dreams within dreams within dreams. So it’s an absolutely wonderful and beautiful example of nesting, but it’s not recursion.
Let’s continue and look at another tech example of what recursion certainly isn’t.
Type “recursion” into Google. Near the top it says “Did you mean: recursion,” with “recursion” appearing as a hyperlink. Click that, and it loads the same page again, creating an infinite loop without a hint of actual recursion.
Facepalm.
@Google: That is an example of a loop, not recursion #GetItRight
So what the hell actually is recursion?
Well, I had to come up with my own definition—because that seems to be the popular thing to do these days. The thing is, my definition is broad enough that it defines recursion in a manner where it can be applied to multiple fields—you know, like how it was before big tech got involved.
Recursion is a process or structure in which each step, layer, or generation contains or operates on a representation of the previous one, creating cumulative self-reference.
The cumulative self-reference doesn’t have to go on forever or be particularly long—it can be either finite or infinite.
It also has nothing to do with “base cases,” except in programming, so let’s return to Italian painter Giotto to see some real recursion.
In Stefaneschi Triptych (c. 1320), he depicts Cardinal Stefaneschi kneeling before St. Peter, offering him the very painting you’re looking at—an image of the painting within the painting. Now that’s recursion: an object containing a representation of itself.
But let’s make it even simpler, because this can be a mind-bending topic, for sure—two mirrors facing each other.
Now that’s crazy recursion in action.
See, each new image reflects the last, creating a seemingly infinite strain of smaller and smaller mirrors. Each new image contains the previous, which contains the previous, and so on and so forth.
That’s recursion.
Pardon me, but I must reemphasize:
TWO MIRRORS FACING EACH OTHER RESULTS IN RECURSION.
Phew! I feel better. The world now shines just a little brighter because I’ve cleared up a topic that no one knew needed fixing.
Think about it.
I had a thought about recursion.
That thought about recursion led to an investigation.
That thought about recursion led to an investigation that led to identifying a problem.
That thought about recursion led to an investigation that led to identifying a problem that led to fixing it.
That thought about recursion led to an investigation that led to identifying a problem that led to fixing it that led to this sentence you’re now reading, encasing you in a whirlwind of recursion that leaves your head spinning.
And lest you have any doubts, ultimately, who did I reference for my understanding of recursion?
Well, myself, of course.
If you found this essay interesting, I'd truly appreciate your thoughts in the comments. And if you know someone else who would get something out of this, please share it. Thank you!
I really enjoyed reading this article! Bully for you and the attempt to create a definition for recursion.
I tend to come at it first from a math perspective. Euclid's "Elements" (about 300 BCE) used recursion in som of his proofs about geometric constructions that involve iterative processes. In the 17th century Isaac Newton and Gottfried Leibniz worked on infinite series, which were conceptually linked to recursion but they were not formalized as such. I suppose my favorite has to be Kurt Gödel in his 1930's work on incompleteness theorems where he used recursive functions as part of his formal system to show how certain problems in number theory could be encoded within logic itself.
None of these, however, can hold a candle compared to your two mirrors facing each other! Congratulations!