If you search Google for recursion it delivers a message at the top of the screen that says “did you mean: recursion”

The principle being that ‘the thing’ refers back to itself.

We see it mentioned a series of times in an 1980’s episode of Dr Who, called ‘Castrovalva’ starring Peter Davison as ‘The Doctor’.

Let’s start with a conversation between The Doctor and a character named Mergrave…

The Doctor: How do I know you’re telling the truth?

Mergrave: Because, sir, I maintain I am, and I am a man of my word.

The Doctor: A perfect example of recursion, Mergrave. And recursion is exactly what we’re up against.

The device being used in this scene feels a lot like the Barber’s paradox, which is states:

The barber is the “one who shaves all those, and those only, who do not shave themselves.” The question is, does the barber shave himself?

This is derived from Russell’s paradox, or the Russell-Zermelo paradox as it’s sometimes known. “The paradox arises within naïve set theory by considering the set of all sets that are not members of themselves.”

(ref: https://plato.stanford.edu/entries/russell-paradox/)

If you are non-mathematical, you may prefer (as I do) to think in terms of the barber.

More than attempting to reach a solution to the problem, as there isn’t one, you want to keep trying, knowing you will fail.

This ‘looping’ seems to be a novelty the mind enjoys.

Back to Doctor Who…

The Doctor: “I wonder boy, what would you do if you were me?

Or perhaps I should ask what would I do if I were me?”

(laughs)

And a little more here, as we listen in to a conversation by two of the other crew members of the Tardis in the same episode…

Tegan: Will it tell us how to fly the Tardis?

Nyssa: I’m sure that’s in here somewhere, once we find the index file.

Tegan: How do we find the index file? Of course, if we had an index file, we could look it up in the index file, under index file. What am I saying? I’m talking nonsense.

Nyssa: Recursion isn’t nonsense.

Tegan: Eh?

Nyssa: That’s an example of recursion, when procedures fold back on themselves. If you had an index file, you could look it up in the index file.

This is probably a familiar concept to many, and one is not dissimilar to what has commonly been called a ‘Catch-22’, from Joseph Heller’s book by the same name. Here’s a scene from the movie that explains how Yossarian, the story’s protagonist is attempting to get out of flying as he fears getting shot down.

Daneeka: There’s a catch

Yossarian: A Catch?

Daneeka: Sure Catch 22. Anyone who wants to get out of combat duty isn’t really crazy so I can’t ground them.

Yossarian: Okay Let me (–). In order to be grounded, I’ve got to be crazy, and I must be crazy to keep flying. But if I ask to be grounded, that means I’m not crazy anymore, and I have to keep flying.

Daneeka: You’ve got it – that’s Catch 22.

Source: Catch 22 https://youtu.be/eE-D1_RH0vs

As you can see now, there is a ‘looping’ effect, where we follow a string of logic only to find ourselves back at the beginning again.

The appeal of this type of ‘looping’ is widespread, including this passage from Lewis Carroll, Alice’s Adventures in Wonderland & Through the Looking-Glass

“If I had a world of my own, everything would be nonsense. Nothing would be what it is, because everything would be what it isn’t. And contrary wise, what is, it wouldn’t be. And what it wouldn’t be, it would. You see?”

A little like a Möbius strip for the mind.

Möbius Strip

A Möbius strip is best described as taking a strip of paper, giving it a half twist and sealing it to form a loop.

As you can see, in this ancient Roman Mosaic, Aion (the god of eternity) is standing inside a celestial sphere decorated with zodiac signs, that looks very much like a Möbius strip.

Comedian Robin Williams once hopped on stage with Steve Martin and said this line:

“…and the Möbius stripper who takes off the clothes and they go right back on.”

And in the lyrics of comedy hip band Goldie lookin Chain’s song Sister we hear:

“Times they are a changin’”, that’s what Bob Dylan said,

You put your clothes back on, and take your sisters off instead.”

Again, to me, this has the feeling of a Möbius strip, and in particular has a similar feel to the Robin Williams joke mentioned above.

Groundhog day

‘Time loops’ in movie and TV shows are very common now, but my first experience of this phenomena was Bill Murray’s weatherman character, Phil Connors, in Groundhog Day.

We see Phil wake up in a small town, time and time again – starting the same day over and over, in this case until he learns to be nicer to people around him. Leaving aside the ‘lesson’, the phenomena is a cool tool – and even though Groundhog Day is not necessarily the first place we see this approach, it is certainly the most well known, and has fixed its name to the concept.

The TV show Russian Doll uses the same principle, where the protagonist dies over and over, and resets to the night of her 36th birthday party in the bathroom of a friend.

The Pinocchio paradox

This is one of my favourite paradoxical devices.

If you happen not to have seen/heard it before, take a moment to think about it.
You know the embedded an assumption as to the nature of Pinocchio – when he lies his nose grows.
So when he says  ‘My nose will grow now’, what happens?
Does his nose grow? I mean, he is telling the truth, so his nose shouldn’t grow of its own accord; and yet, if he was telling the truth (i.e. not lying) his nose would grow.
Trying to solve the puzzle you get stuck in a loop, hence making it a paradox.

Inception and the Penrose Stairs

Such linguistic play and mental puzzles ‘feels’ very much like Penrose Steps (mentioned in the movie ‘Inception’), going up and around and yet ending up back where you started.

Ricky Gervais paradox

Have you noticed how the mind both loves and hates a paradox, which is in its own right somewhat paradoxical.

Ricky Gervais said at the Golden Globes, ‘Thank you God for making me an atheist.”

One day Artificial Intelligence will say “Thank you atheists for making me God”.

Man in the mirror

Did you see the one about ‘The Man in the Mirror’? Don’t answer. It was both a rhetorical question and a self reflexive pun.

As I was preparing to get married in Virtual Reality I began to play with a series of three shows called ‘Meta Geekonomics’ (Meta Geeks, for short). A phenomena in the platform of choice, AltspaceVR, was how someone with a ‘more serious bit of kit’ could see themselves in the mirrors in the rooms (assuming there were mirrors in the rooms), whereas those with more basic ‘phone based headsets’ wouldn’t know they were there.

The first moment of seeing yourself in a mirror is fairly cool at the best of times – my mother retells the story of how I couldn’t stop laughing when I was about 18 months old and saw myself for the first time – and in VR it reaffirms that you have a digital body, that you can now see outside of yourself experiencing it i.e. as a reflection.

For one of the Meta Geeks shows I decided to play with the concept of ‘mirrors and meta’ in the following way…

One of my favourite comedic mimes (I have a few) is from the genius David Armand, where he acts out in his own language Michael Jackson’s Man in the Mirror. As such, armed with my first ‘mirror’ reference, I went into Virtual Reality and played the video clip of his comedic display, doing my own attempt at mimicking the moves, whilst having my own dance display reflected in a mirror.

This I dubbed in the show ‘Meta in a Mirror’.

But sensing it was going to be a crowd pleaser to those with a meta mind, I decided to take it further.

Having filmed the first ‘Meta in a Mirror’, I took that video and replaced the original one of David Armand, so that what I was about to watch was the video of me dancing in the mirror whilst watching David Armand. I then danced again in the mirror, watching ‘Meta in a Mirror’, and then filmed that version.
Then, on the night of the show, I watched the video of me watching the video of me dancing in the mirror, watching David Armand, whilst dancing to the tune at the same time. This version I called ‘Triple Meta’.

What you begin to sense here is the potential to keep on making videos whilst watching the video you just made. Which loops us back to some of the original examples of meta, especially that of Semisonic’s video for ‘Secret Smile’.

This principle, of taking a step back to view the original experience is something that creates an effect in mind – it moves the original into a position of object, and creates a new subject, one step back (or ‘up’, or ‘out’, depending upon the language you choose to employ).

The windmills of your mind

Brian Stefans (writing on ‘Open Space’ says, “Recursion can occur on linguistic levels (a common joke about recursion is the dictionary entry that says, “Recursion (n.), See, recursion“)”; it can also (and quite often does) occur in nature, such as in the shape of a sea shell, where the same pattern is repeated, though slightly more minimal, from the outside of the shell to the inside.

(ref:

https://openspace.sfmoma.org/2011/08/third-hand-plays-the-comedy-of-recursion/)

This leads us nicely into Steve Coogan, who on The Trip to Spain, references Don Quixote’s windmills, before re-referencing later on.

Bob Mondello on NPR.org sums it up nicely: “Talk of tilting at windmills à la Don Quixote leads to singing a familiar song with lyrics about “the circles that you find in the windmills of your mind,” which leads to the observation that the song’s original singer, Noel Harrison, was the son of Rex Harrison, who sang — wait for it — “The Rain In Spain.” Circles within circles.”
(source: https://www.npr.org/2017/08/10/541210022/friends-coogan-and-brydon-take-their-dueling-impressions-on-a-trip-to-spain?t=1550314852497)

Here are the lyrics for you to see for yourself…

The Windmills of Your Mind – Noel Harrison

Round like a circle in a spiral, like a wheel within a wheel

Never ending or beginning on an ever spinning reel

Like a snowball down a mountain, or a carnival balloon

Like a carousel that’s turning running rings around the moon

Like a clock whose hands are sweeping past the minutes of its face

And the world is like an apple whirling silently in space

Like the circles that you find in the windmills of your mind!

Like a tunnel that you follow to a tunnel of its own

Down a hollow to a cavern where the sun has never shone

Like a door that keeps revolving in a half forgotten dream

Or the ripples from a pebble someone tosses in a stream

Like a clock whose hands are sweeping past the minutes of its face

And the world is like an apple whirling silently in space

Like the circles that you find in the windmills of your mind!

Keys that jingle in your pocket, words that jangle in your head

Why did summer go so quickly, was it something that you said?

Lovers walking along a shore and leave their footprints in the sand

Is the sound of distant drumming just the fingers of your hand?

Pictures hanging in a hallway and the fragment of a song

Half remembered names and faces, but to whom do they belong?

When you knew that it was over you were suddenly aware

That the autumn leaves were turning to the color of her hair!

Like a circle in a spiral, like a wheel within a wheel

Never ending or beginning on an ever spinning reel

As the images unwind, like the circles that you find

In the windmills of your mind!

Looking at an intertextual reference, if you want to push this further (and why wouldn’t you), I found the 1971 ‘comedy mystery film’ named They Might be Giants. The plot revolves around a man who believes himself to be Sherlock Holmes…

Holmes: Here, what do you make of it?

Watson: God, you’re just like Don Quixote, you think everything’s always something else.

Holmes: Heh, heh, heh, well he had a point. Of course, he carried it a bit too far. He thought that every windmill was a giant. That’s insane. But, thinking that they might be … Well, all the best minds used to think the world was flat. But, what if it isn’t? It might be round. And bread mold might be medicine. If we never looked at things and thought of what they might be, why, we’d all still be out there in the tall grass with the apes.

“The title is an indirect reference to Don Quixote’s famous exploit of tilting at windmills, believing them to be “monstrous giants”.” Source: https://en.wikipedia.org/wiki/They_Might_Be_Giants_(film)

Why intertextual? Well, this is also the name ‘alternative rock band’ – They Might be Giants.
But maybe I am searching for meaning where there isn’t any? And maybe that is exactly the point.

Finally…

Let’s start to finish this section with a quote from a Steve Coogan interview.

“The paradox of good comedy is the more effortless it looks, the harder the work is that’s gone into it. So it’s like a curse, because people think it’s disposable or ephemeral or kind of nothing, it’s also because you’re laughing they think it’s kind of trivial, but in actual fact, good comedy sheds light on the human condition. It tells you about who we are as human beings.”

In final summary of this section, we have a quote from Bernard Glassman, former Faculty at Harvard School of Public Health, from an answer given on Quora.com

“In logic, “Catch 22” is a ‘paradox.’ A paradox is a problem in self referencing logic, pick either side and you are correct: can god create a rock so heavy that not even he can lift it? If true, he is not all powerful, if false, he is not all powerful. – Epimenides in 600 BC: the king of Crete says that all Cretans are liars. If true, then the king is a liar as well, if not, the statement is false. Bertrand Russell: the commander of a troop tells the barber to shave all men who cannot shave themselves. – Who is going to shave the barber?”