The Self-Referencing Question-Answer (The Mimethesis)

By Marigold A. N. Willaby

What question will I start with?

Well, that's a silly question, since the answer is right there in the text: "What question will I start with!" This is an example of a question which answers itself, which I'll be calling a "mimethesis." These peculiar linguistic objects possess a surprising depth, and have been lodged in my mind ever since I first encountered them. My family members, too, have had these questions burrow into their skulls, making a habitat of their fascination. Reader beware: they have a sneaky yet powerful allure.

I've been cataloguing and categorizing them for a long time now, more than I'd thought. Lo, here we are. Below is my documentation of what I've uncovered: a taxonomy of self-referential questions.

Self-Reference

I first heard of the mimethesis in Douglas R. Hofstadter's Metamagical Themas, a collection of the playful columns he wrote for Scientific American. The first two chapters are devoted entirely to sentences which reference themselves in peculiar ways—and to understand the mimethesis you must first understand self-referential sentences.

The canonical example of a strange self-referential sentence is the "liar's paradox":

This sentence is false.

The Liar's Paradox

The punchline, of course, is that the sentence is neither true nor false due to its self-reference.

Self-referencing sentences need not be limited to paradoxes for interesting behaviour to arise, though. Some other great examples from the column are the following (in order of brain-hurtfulness):

• I am the thought you are now thinking.
• If this sentence were in Chinese, it would say something else.
• This sentence contains one numeral 2 many.
• I don't care who wrote this sentence—whoever he is, he's a damn sexist!
• This sentence does not have the property it claims not to have.
• If the subjunctive was no longer used in English, this sentence would be grammatical.
• "yields falsehood, when appended to its quotation." yields falsehood, when appended to its quotation.

The last example is equivalent to the liar's paradox, formulated as something called a "quine," which achieves self-reference while avoiding the use of "I" or "this sentence." A couple synapses certainly misfired when I read it for the first time, but Hofstadter helps us understand it: "This sentence describes a way of constructing a certain typographical entity—namely, a phrase appended to a copy of itself in quotes. When you carry out the construction, however, you see that the end product is the sentence itself [...]." A very clever way to achieve self-reference.

These are a delightful rabbit hole in their own right, but nestled beside this lovely quine derivation is an inconspicuous invitation to the reader.

On the basis of Quine's clever construction we can create a self-referential question:

What is it like to be asked, "What is it like to be asked, self-embedded in quotes after its comma?" self-embedded in quotes after its comma?

Here again, you are invited to construct a typographical entity that turns out, when the appropriate operations have been performed, to be identical with the set of instructions. This self-referential question suggests the following puzzle: What is a question that can serve as its own answer?

What a provocative puzzle indeed.

Mimethesis: An Introduction

A mimethesis (pl. mimetheses) is a question that is its own answer. Notice, the literal sentence itself must be its own answer; it shouldn't merely contain the answer to its own question. A false example of this would be:

✗ How many words does this ques7ion contain?

Sure, the question has the answer (7), but remember a mimethesis is built on self-reference. The question must entirely be its own answer.

However, we can slightly modify the above question to get a positive example of a mimethesis:

✓ What's an example of a question with nine words?

Mimethesis 1

See, the sentence is an example of the properties the question is asking for.

Notice, this has a distinct flavour from the example that Hofstadter gives in his original prompt. In the original prompt, there is only one possible response to the question, which is itself. Compare that to (Mimethesis 1), where you could conceivably give any number of responses, such as "How many tomatoes will fit inside my brother's mouth?" It just so happens that the question itself is one such possible answer. This is an interesting distinction that will bring us to our first axis of categorization.

Lastly though, one more debatable case. A thought-provoking example given in Metamagical Themas is the following from Jim Shiley, modified slightly for use on a webpage.

How far across the screen will this sentence run?

Pseudo-Mimethesis 1

This one is very interesting, since it probes at the fuzzy edges of what a mimethesis even is; it's up for debate whether this is a true mimethesis or not, but I am personally not counting it. As we've defined it here, a mimethesis is a question that is its own answer, but cannot merely contain the answer. This example seems only to be evidence of its own answer. To highlight why exactly I think this shouldn't count, we could construct a similar pseudo-mimethesis:

How many words are in this sentence?

Pseudo-Mimethesis 2

Its mechanism is the same as (Pseudo-Mimethesis 1), but feels distinctly less like the real examples of mimetheses we've been exploring so far. The answer is not the actual sentence; the answer is just "7 words." I would conclude then that (Pseudo-Mimethesis 1) cannot be a mimethesis.

Now that we've distinguished what is and isn't a mimethesis, we can move on to expanding on our first observation: A discussion of endedness.

Axis 1: Closed and Open Endedness

An open-ended mimethesis has many possible responses, one of which happens to be the question itself. For example:

Can you repeat this question back to me?

Mimethesis 2

I could just say "No!" Now, I don't owe anybody anything, but let's say I'm a friendly person and I play along. A valid response then to this proposal would be for me to repeat the question back: our mimethesis. These are fun, since they aren't as strict in their form, so there is lots of creativity to play around with how exactly the question answers itself.

By contrast, a closed-ended mimethesis has only one possible response. Here's an example, closely following Hofstadter's quine construction:

What question do you get when you follow, with its own quotation and a question mark, the phrase "What question do you get when you follow, with its own quotation and a question mark, the phrase"?

Mimethesis 3

Once again, the quine construction means that the sentence replicates itself via the reader following its instructions. Moreover, it becomes the only possible response to the mimethesis.

You'll notice closed-endedness is much harder to come by, since its rule is so much more strict. That gives these types of mimetheses a special kind of allure.

Axis 2: Pointedness (or, Where Does a Question Live?)

There is another way to categorize mimetheses: where they point. A mimethesis must have some sort of self-reference, but exactly where that self-reference is merits differentiation. I'm calling this "pointedness." Looking at some examples, we can see different categories arise; Hofstadter's original prompt works by pointing back at its own structure, but (Mimethesis 2) works only if there are two interlocutors in a dialogue. This opens up a new avenue for exploring different kinds of mimethesis, so long as we can categorize where a question can exist.

Note, some of the categories in this axis might have some overlap.

Structural

First, a question exists inside a language, which has its own structure. Words, letters, sentences. These can be exploited to create mimetheses of varying difficulty, and they are the bulk of what we've seen so far. Here are some more examples:

• What's a question with 7 words and 2 numerals?
• What is an example of a question that starts with "What" and ends with "soggy biscuit?"
• What are all the words you've read on this line, ordered chronologically by when you read them?
• What's contained in the span of this question?
• If you were to spell out the string of characters from the previous 'I' all the way to the final '?' (inclusive), what would you get?

Note the last three are nice closed-ended examples that avoid the typical quine construction.

Finally, as a nice difficult example, inspired by the tradition of self-enumerating sentences (and specifically Lee Sallows' contributions), we have the following:

If you think you're so smart, then what is an example of a question with twelve a's, two b's, two c's, two d's, fifty e's, eleven f's, three g's, fourteen h's, nineteen i's, one j, two k's, eleven l's, five m's, twenty-six n's, twenty o's, five p's, two q's, eleven r's, thirty-eight s's, thirty-nine t's, seven u's, twelve v's, fourteen w's, three x's, eleven y's, one z, thirty-two commas, twenty-five apostrophes, five hyphens, and last, but not least, a single ?

Depending on how much time, computing power, and willpower you have, this might be closed-ended!

Contextual

A question exists not only inside a language, but inside a medium through which it's conveyed. This could be paper, sound, a book, a sign, a screen, or any number of things. Pointing at the context in which a question lives is an easy way to create mimetheses. For example:

• What's the first (and only) question in this list?

Unfortunately, to demonstrate these, different mediums must be leveraged. For example, as remarked in "Metamagical Themas," the author Raymond M. Smullyan's book entitled What Is the Name of This Book? works quite well here. Since we're on a website though, we can leverage some fun aspects of the medium of websites to create mimetheses. For example:

What do you get if you copy and paste me?

This would certainly only work on a digital medium. For a more specific example, you should look at the URL of this webpage.

We are biased towards visuals since you are reading this on a webpage, but a question can also be conveyed by sound. Leveraging qualities of sound can be used to create mimetheses as well, as in the following example (which you will note, must be said aloud in a particular way to work):

WHAT'S AN EXAMPLE OF A QUESTION THAT WAS SHOUTED AT THE TOP OF MY LUNGS!?!?

To explore more mimetheses in this category, we must ask: "In what mediums can questions exist?" In print and sound, for sure, but more interesting answers to this create more interesting mimetheses. Case in point, a question can exist in the mind. How can this fact be leveraged? This will be explored later in the phenomenological category.

Agentic

A question exists as asked by some sort of agent—human or otherwise. For example, you might imagine two people in a conversation. Mimetheses leveraging this are similar to contextual mimetheses, but can lean on the informalities of conversation to work, and so they can get extra silly and creative. The next two are courtesy of my uncle, along with some additions from myself. For each of these, imagine two people talking to each other, who are then provoked to repeat the same thing back.

• We're all ready now? (The other person says it back in confirmation)
• What are YOU doing? (Imagine the second person saying it back sarcastically)
• What did you just say? (Imagine the second person is hard of hearing)
• Can you repeat what I'm saying back to me?

With the exception of the last one, these have a very special property that the other mimetheses lack... one that was a core assumption from the start! These are not self-referential. The question doesn't point back at itself in any way, instead it relies on being a possible answer in a semantically meaningful conversation. This raises an interesting question: how else can mimetheses avoid explicit self-reference? I have not been able to answer this, though I expect it would involve thinking about the agents which ask and respond to a question.

Now, all this talk about agents and the visual of two people in conversation brings up another interesting point. When asking a question there's an implicit assumption here that you, the reader, are asking the questions. When you read aloud the question "What am I saying?" the "I" is carrying a lot of assumptions. Who is "I"? To illustrate my point, here's a selfish mimethesis:

What question did I just type out in a markdown document in an essay on mimetheses that has since been compiled into a webpage and read by you?

It's a mimethesis I can hog all to myself! As it exists, it will never be a mimethesis to you no matter how hard you try.

This raises another question: who can answer a question, and how can we leverage this to create different mimetheses? If you want to anthropomorphize your computer, then the following just might work:

What am I rendering on the screen?

Answering this question fully might bleed into areas outside our scope. Can only conscious beings ask and answer a question? Even if the answer is "yes," an enthralling wrinkle is created when the philosophy of panpsychism is considered. Do you think artificial intelligence can meaningfully ask and answer questions? Most people might intuitively say "yes." I implore the reader to create new mimetheses based on wherever their personal philosophy lands on these topics.

Temporal

To close off this axis, remember that nothing can exist only in a place. It must also exist at a time.

What's the sentence you just read 3 seconds ago?

This mimethesis can only exist in the precise moment where 3 seconds have elapsed since you started reading it. Even better, we can create an example which can only exist in the past, and can never be replicated:

What was a sentence that was in past tense?

As it stands currently, the example exists in your memory of a past point in time as a mimethesis. However, if I were to explicitly answer it by saying: "What was a sentence that was in past tense," it stops working, since that sentence currently IS in the past tense, not "was"! So, that mimethesis can only exist in the past, inside your memory, through the phenomenon of time. Fascinating.

This points at something a little deeper though. This sentence doesn't just involve time, but can only answer itself through the process of memory recollection. We've discovered a question isn't always a mimethesis by virtue of being; sometimes there must be some mechanism which is actively invoked to answer the question. This brings us to our next and final axis.

Axis 3: Becomingness (or, How Does a Question Answer Itself?)

Through our previous example, we've seen some questions must invoke some peculiar processes in order to be answered. By exploring these mechanisms, we find new ways to create mimetheses. We must ask, how exactly does a question become an answer?

Once again, notice these categories overlap each other in places.

Imperative

Every question so far has answered itself through the action of the reader. Usually the reader, well, reads. We don't necessarily need a reader to just read though. It raises the question: Can we coerce the reader into different, stranger actions?

To see what I mean, let's pretend you don't know French. Then you won't understand the following example.

Quelle phrase inciterait mon lecteur à la traduire en anglais ?

Now, since you don't know French, you will have to translate it, and upon translating it you will realize with much glee that you have answered it in the process:

What sentence would prompt my reader to translate it into English?

It almost feels like a prank! But, I guess knowing French ruins the whole first example now that I think about it. I'm undeterred, though, and since I'm in a mischievous mood, the cryptographically inclined reader might enjoy this duplicitous imperative mimethesis:

Grkd usxnk aeocdsyx qodc k csvvi mbizdyqbkzrob dy nomyno k coxdoxmo?

These imperative mimetheses need not be sneaky like this; for example, take note of this previous example from the "Pointedness" axis:

What do you get if you copy and paste me?

This doesn't beguile the reader into answering it, but it still requires an unorthodox action to be performed. Also note how the axes combine here: It's imperative on the Becomingness axis, but contextual on the Pointedness axis.

Here's another deceit-less example that only works if you read it aloud:

What did I just say?

Leveraging different mediums, we can create stranger mimetheses. Get out a pencil and paper and write this one down:

What did I just write?

Phenomenological

Perception is an action. A question must be perceived by some being in order to be received. This means we can leverage the phenomenon through which the question is perceived in order for it to answer itself. These are especially enticing. For example:

What does this sentence look like on the page?

Phenomenological Mimethesis Vi.

What makes this a mimethesis is subtle; it has to do with where the question lives. Before you read that question, it existed only on the page, but once you read it, a copy of the question started existing in your mind. Here is where the true mimethesis lies. Assuming you are a conscious being, that question then existed as a conscious visual perception of the sentence, and only here can the question point to itself to be its own answer.

Now, I read sentences aloud in my head, which means the above (Phenomenological Mimethesis Vi.) not only existed on the page, and as a conscious visual perception, but also as an aural perception. It existed briefly as a sound in my head. The question here, existing as sound, is also NOT a mimethesis, since for the question to answer itself it must exist as a visual phenomenon. Instead, if I wanted to leverage the aural phenomenon of the question to create a mimethesis, I could write the following:

What do I sound like in your head?

Phenomenological Mimethesis Au.

This is the aural equivalent to (Phenomenological Mimethesis Vi.).

Now, the astute reader might say, "Well, these all sound an awful lot like the Pseudo-Mimethesis! What makes these different?" The key here has to do with pointedness—where the sentence lives. When I ask "How far across the screen will this sentence run?", the answer is the length of the sentence, not the sentence itself. You might argue when I ask "What do I sound like in your head?" that the answer is just the sound of the sentence, not the sentence itself. This is a correct possible answer, but it misses the point slightly.

At the risk of belaboring the point: The (Phenomenological Mimethesis Au.) as it exists on the page is NOT a mimethesis. Only once the question exists as a sound in your head may it be classified as a mimethesis, since the question, as it exists as a voice in your head, is the exact answer it seeks. In comparison, in the (Pseudo-Mimethesis), the content of the question never meaningfully exists as just "width" in your mind, and thus there's nowhere the question (existing as width) may be its own answer.

With this in mind, here are some more possible mimetheses in this category.

What is this sentence's meaning?

By virtue of reading this sentence and having understood it, you have transformed the sentence into some sort of statement personally meaningful to you. The question exists in your head as a meaningful statement, and has thus answered itself.

What is my conscious experience in your mind?

Similar to the last one. By having read it (and again, presuming you're a conscious being), the question exists as a conscious experience, and so the question answers itself here.

(Read aloud) How does this sentence feel in my throat?

This one is, at first, debatable. For it to be a mimethesis, you would have to argue that the content of the question can exist meaningfully as vibrations in your throat. Then, the question as it exists here may answer itself. A question is raised then; much like the content of the (Pseudo-Mimethesis) can't exist meaningfully anywhere solely as "width," can a question exist anywhere meaningfully as "vibration?" For the average person, maybe not, but I would argue it can, since this is one of several methods Helen Keller used to recognize speech.

Where and how can a question meaningfully be encoded? As sound, visuals, feeling, meaning, or perhaps other places? This question is then key to discovering more phenomenological mimetheses. I implore the reader to explore this question, since I've personally exhausted seemingly most avenues here. The last two major human senses we possess are that of taste and smell, but I'm unconvinced these can be meaningfully used to encode questions. If we rule the senses out, the previous examples show we can still find a question existing as meaning, or as a conscious experience in someone's mind. We can then find more mimetheses by enumerating the remaining phenomena the conscious mind can perceive. Taking inspiration from the Pointedness axis, we know time is an important facet in how a question lives. Humans have a conscious experience of time as memory. A question can exist as a memory. So, for my last mimethesis in this category, we have this intriguing creature, one of my favourites:

What do you remember?

Paradoxical

These are some of the most fun, since they are the only type that seems to "jump out of the system." The question must exist in a logical system that presupposes itself in order for it to work. The action required is presupposition. To understand, note the following non-mimethesis:

What's a question that answers itself?

It does not work, because the question has not answered itself yet, so the sentence cannot yet work as an answer to the question. Except, it does work! Just in a logically loopy way. If you presupposed its mimethesis-ness, then it is true. The example can only be a mimethesis if it answers itself, and it can only answer itself if it's a mimethesis. It's a fixed point! It only works by virtue of circular logic, where you must presuppose its truth first. It's much like the liar's paradox if the liar had a brother: "this sentence is true." For those curious, this is called the truth-teller paradox.

Another way to create this effect is the following:

What's an example of a mimethesis?

Now with that in mind, depending on how you answer my following question, it might be a mimethesis:

What mimethesis did I correctly predict you would ask in response to me?

Existential

I can only hypothesize about the existence of this kind of mimethesis. So far, we've seen examples that answer themselves through action, through mere perception, and then through presupposition. What if there was a mimethesis that required no action? What if it answered itself solely by existing? I have not been able to find one after much, much thought, so it might be better left as an exercise for the reader.

The closest I've been able to come to this elusive creature is this absolutely fascinating specimen of a sentence:

What's an example of a rhetorical question?

It needs no questioner, it needs no responder, not even a perceiver. It can merely exist somewhere floating in the empty universe, and so long as no one perceives it, then maybe by some strange circular logic it can serve as its own answer... so long as no one answers it. I'll let you be the judge if this counts as a true mimethesis of the strangest kind.

[REDACTED]

Wrapping up this final axis, I see we're pretty far down the rabbit hole now. We've come up with some very strange questions, and even hypothetical categories, but there is still one more absurd category to explore—one that evades any axis, one that blows the whole world of mimetheses wide open.

But first, we must answer our silliest question yet.

What Even Is a Question?

So far we've assumed the very nature of a question, but we haven't actually defined what we really mean by "question." What is it really? Some sentence with a question mark on the end? Something someone says in a rising tone to elicit a response? What even is a question?!

Well, depending on how you want to answer this, we can enter into one last category of mimethesis that opens a door to a whole new kind of puzzle: The metaphorical mimethesis.

The Metaphorical Category

If you ask The Cambridge Grammar of the English Language, then a question is defined by its ability to establish a set of logically possible answers. This is assumed to be on the level of linguistic semantics, but we can capture the essence of a question while crossing into different domains, by use of metaphor.

For example, a scientific experiment is an inquiry into nature, with the intent of narrowing the set of possible valid theories. A mimethesis in this domain might be an experiment which has itself as the outcome. As another example, in mathematics a conjecture is the equivalent of a hypothesis, and must be proven or disproven. A mimethesis in this domain might be a conjecture which is its own proof, or perhaps a theory which is its own mathematical proof. Those who are familiar with Gödelian shenanigans might see where this is headed. You can code mathematics in a formal language, and some of its sentences are able to reference themselves. "Henkin's sentence" is a sentence which expresses its own provability, and Löb's theorem says that this is provable, which might make it mathematics' mimethesis.

If we loosen the definition even further, the metaphor can be extended to even further domains, like music. For those familiar with functional music theory, there are chords which create tension, and chords which create resolution, and the push and pull between these chords creates musical interest. Tension chords set up an expectation for certain resolutions, thus reducing the set of possible chords afterwards. This means tension chords roughly sound like "questions" which are "answered" by their resolutions, and so with this metaphorical mapping the mimethesis in this domain becomes a chord which resolves to itself. The closest things I've come to here are consecutive diminished 7th chords resolving downwards a semitone, or similarly with dominant 7th chords resolving downwards a semitone via tritone substitution. Their problem is the resolved chord doesn't have the same pitch class set as the tension chord, only the same shape. Either way, they make for fun resolution patterns to compose cadenza passages on the piano.

The creativity here is really endless, and I implore you to create your own metaphorical mapping onto your own domain of choice.

A Pure Maths of Language

Here we are, then. But, why? When first embarking on this journey to taxonomize these odd specimens of sentences, it was fueled purely by some kind of twisted puzzlish amusement only a mathematician could enjoy. Somewhere along the way though, I realized these mimetheses each shared something in common: To point back at themselves, some hidden machinery would have to be exposed. When you ask questions, do you think of its letters, its medium, its phenomenon as it exists in your mind? No, but when trying to fold a mimethesis back in on itself, these aspects are necessarily revealed. This taxonomy then turned out to be an anatomy as well. Each category discovered a new constituent of a question I never realized existed until the answer I sought pointed back at it. I think that's the case for this kind of logical play: new understanding.

Pure mathematicians study abstract objects for no other reason except that they are interesting, and the uses show up later. These objects are so abstract that in order to study them, one must pull at them to see which parts buckle. You don't learn what a thing is made of by using it the way it was meant to be used—you take the screws out! You make it do something absurd, like answer itself, to see how the object strains. Try it with whatever subject enraptures you. The parts that strain will be the edges you have yet to uncover.