I was thinking about how interesting it was that different people could hear the same lyric in different ways – “Poker Face” by Lady Gaga for example. And then, my mind immediately jumped to “Huh, why has no one tried embedding word superpositions in songs?”[1] The answer is that people have – Ableton has a feature to play certain portions of songs. However, in poetry, there’s also an additional constraint to play with: letting the reader see the unresolved form of the superposition, rather than only the collapsed form. That too has been done; there’s already a poem called A Superposition Poem. However, there does not seem to be a poetry format that combines the idea of the reader explicitly seeing unresolved superpositions, superpositions having specified probabilities for each collapsed state, and conditional probability weighting between superpositions. And I need this format to exist – think about all the possible interesting poems other people could have achieved with this format, if it had existed previously. And so, I’m here to make it.
My intention with this is to create a new area for humanity to explore – I definitely don’t expect to be able to explore it entirely myself. I’d feel really fulfilled if someone took this format and used it to create a work far greater than I could even imagine. That’s why I wanted to make an editor that anyone could use to write poems, and issue challenges to get people exploring the possibilities of this new format, rather than just writing a poem of my own and calling it a day.
Superposition Poetry
Superpositions can be represented as a list of possible outcome words {N_1, N_2, …}, in addition to probabilities assigned to each one, {a_1, a_2, …} that sum to 1. This allows the author to encode multiple possible words into one position in the text, and supply information on how likely each of those words is. A superposition poem is a regular poem with some superpositions embedded in it. The author specifies possible outcomes for each superposition, probabilities for how likely each outcome is, and is able to specify conditional probabilities for each possible state of prior superpositions. The reader reads through the text on the left, and when they click on a superposition, represented as a blue ????, a sidebar pops up telling them information about the superposition. Note that the superposition is not “something that could be any of the possible outcomes”; it is all of the possible outcomes, at once.
The reader can also click on an outcome to collapse that superposition, but leave other superpositions uncollapsed; when this happens, other superposition probabilities update given the info that the collapsed superposition resolved to the outcome it did. I see this as more conditioning (the reader restricting the search to states where outcome X is true), rather than choosing outcome X to be true, though it is up to artistic interpretation. This can be seen in the screenshot – choosing the 5% probable option for superposition 1, {1=”across the trenches”}, raises the probability of {2=”shot his chest”} massively, from 3.51% --> 70.00%. The superposition interface gives:
The current probabilities for each outcome, factoring in the reader’s currently collapsed superpositions through Bayesian inference.
Either the full transition matrix (across every possible superposition collapse), or active row matrix (given the reader’s currently collapsed superpositions), and the current probabilities for each outcome there.
In the matrix, guaranteed outcomes are highlighted blue – the row is highlighted blue if that state is forced, and the column is highlighted blue if that state is forced due to something other than the row state being forced.
Conditional Probability
Now, let’s go into conditional probability more. Here’s an example of how we use conditional probability weighting:
There once was a man from {Nantucket-50,Lynn-50}. He kept all his cash in a {bucket-100/0,tin-0/100}.
Let’s assume you sample the 1st superposition and get “Nantucket”. The second superposition matrix (or 2D tensor) collapses to a vector (or 1D tensor).
There once was a man from {Nantucket}. He kept all his cash in a {bucket-100,tin-0}.
Since, in the 2nd superposition, “bucket” has 100% sample probability while “tin” has 0%, we can resolve it:
There once was a man from {Nantucket}. He kept all his cash in a {bucket}.
Though “bucket” and “tin” are equally likely to occur when sampling randomly, they are 100% correlated to the location – the Nantucket man always keeps his cash in a bucket, and the Lynn man always keeps his cash in a tin. This is the idea of conditional probability weighting using matrices.
You can also use it to represent information impossible to glean from just one collapsed superposition:
There once was a man from {Nantucket-50,Lynn-50}. He kept all his cash in a {bucket-100/90,tin-0/10}.
This probability matrix tells us that almost all people, regardless of place, use a bucket to keep their cash instead of a tin. However, of the people that do keep their cash in a tin, they are all from Lynn, and not Nantucket. P(Lynn|bucket) = 47.4%, but P(Lynn|tin) = 100%. Thus, knowing that a man keeps his cash in a tin reveals the man’s location completely, yet knowing a man keeps his cash in a bucket reveals next to nothing. You can’t get this from just one example, precisely because one example prevents you from seeing all the other possibilities.
Choose Your Own Adventure vs Superposition Poetry
Superposition Poetry is distinct from CYOA (Choose Your Own Adventure) – the main differences are the narrative implication and what the reader sees. In CYOA, the emphasized narrative is the post-collapsed story, but in Superposition Poetry, the emphasized narrative is the pre- or partially collapsed story. CYOA implies that the user makes choices to influence the story, but Superposition Poetry implies that the user makes choices to decode an already existing story. As a result of this, CYOA is mostly based around the choices, with constant material across choices being a deviation, whereas Superposition Poetry is mostly based around the story, with superpositions being a deviation.
Most CYOA stories do not assign weights to alternatives, instead waiting for the user to choose a story; this doesn’t allow artistic expression of likelihoods. Most CYOA stories do not allow later user choices to be revealed to update our estimates of the probability of earlier user choices – most are chronologically linear. Taken together, as far as I can tell, there does not exist a CYOA game where both 1. Narrative choices are probability-weighted and 2. Later gain of information can update the inferred probabilities of earlier choices.
The Stranger
Now, let’s look at a superposition poem. I made an original poem called The Stranger using my superposition editor, inspired by Thomas Hardy’s The Man He Killed (1902).[2] I chose this poem because the main idea of the poem is represented quite nicely, and even elevated, with superpositions. In The Man He Killed, the narrator recounts the tale of him killing an enemy soldier. The narrator laments that if the two had met at an inn, they would have drunk as friends. But when enlisted in an army, likely for no grander reason than money, they are mandated to kill each other. But while The Man He Killed simply describes the possibility of meeting the stranger in an inn, The Stranger tells the story of both the inn-meeting and the battlefield-meeting at the same time, in the same words.
Superpositions can influence literary storytelling.
In Stanza 2, both “shot his chest” and “passed a pint” do not describe the stranger as the object of the action – “shot him dead” or “shot that liar” would have worked. One possible interpretation is the narrator attempting to hide the weight of his actions from himself.
The nature of conditional probabilities lends itself well to the central point of Hardy’s poem – that the exact same actions are considered moral or immoral depending on the circumstances. This is emphasized ironically through the probabilities: the stranger is 7000x more likely to be shot when meeting across the trenches versus in the inn, though both shootings are the same action leading to the same outcome.
And literary storytelling can influence superpositions.
Another interesting thing in Stanza 2 is the stranger “[raising] his hand”, which shows that ordinary literary double meanings still work – a superposition isn’t needed here. The hand raise can represent both a greeting and a surrender.
Basic literary techniques still work to convey difficulty – in Stanza 2, “across the trenches” breaks meter and requires effort, while “at the inn” doesn’t. Even without looking at the probabilities, readers can determine which is harder.
The Reader Interface
While many prior works to Superposition Poetry just show either 1. All superpositions collapsed or 2. No superpositions collapsed, the reader interface allows the reader to collapse some of the superpositions. This also means that rare events are far easier to navigate – rather than the sampler being emphasized, and readers having to dig through the underlying code to find rare options, in Superposition Poetry, the reader interface is emphasized; clicking on any choice in the interface immediately shows all its possible outcomes, regardless of how rare they are.
In addition, Bayesian backward inference allows the reader to also experience the ambiguity of the characters in the story. For example, revealing {3} first would allow the reader to know whether the narrator called the stranger a friend or foe that day, but not fully expose the result of whether the narrator shot the stranger or gave him a pint – just like a group of people who only hear how the narrator reports the story.
Prior Art
“A Superposition Poem” by Sarah B. Royal: This poem does have the same idea of showing superpositions of words to the reader, but also does not specify weighted probabilities within a superposition, and does not have any probabilistic interaction between superpositions. The lack of conditional dependencies limits author freedom – even with just 5 superpositions and 3 words for each, you need to make sure that 243 different readings all make sense and convey meaning.
Bracery: This is a scripting language, but it does allow for superpositions in the coding process and allows weights within superpositions, so it could be used for poetry. It allows for conditional interactions between superpositions, albeit with if statements and weighting instead of matrices. However, the reader is never shown the underlying superposition, only its output – which means that the reader only ever sees ordinary text, and the probabilities seen in these superpositions are not directly inspectable by the reader. Because of this, probabilities in Bracery function more to control the story, whereas probabilities in Superposition Poetry are another element of the reader’s experience. Effectively, Bracery’s output is equivalent to just the “Sample” mode of the Superposition Poem reader interface. In addition, Bracery does not have a Bayesian backwards inference mode equivalent to our own – Bracery’s inference does not apply to interactions between weighted superpositions.
Cent mille milliards de poèmes by Raymond Queneau: This book is a set of 10 14-line sonnets, all with the same rhyme scheme and rhyme sounds. This allows the reader to construct a poem in which they have 10 interchangeable choices for each of the 14 lines, and they all work, leading to 100 trillion poems. Effectively, it functions as a 14-line poem where each line is a superposition between 10 possible lines, with no probabilities specified for each of the 10 possibilities. However, this was developed as a form of constrained writing, not as a form of superpositions – hence why it does not specify probabilities within lines and has no conditional interaction between separate lines.
World Lines by Amy Catanzano: Each poem is represented as a 2D graph that includes multiple interconnected lines. Readers start at the beginning and traverse downward, able to switch lines at any connection point. Now, just 100% mathematically, this is equivalent to a random list (like Queneau) where each line gets an adjacency matrix, where its entries are ones and zeroes. The artistic mechanism lies in the layout of the graph, the colorings, and which points are adjacent. However, this format does not allow for conditional probability weighting within superpositions – which direction to go at each connection point isn’t weighted. Between superpositions, Catanzano’s work does not specify probabilities. You might question if the adjacency matrices could make up for the lack of specified probabilities. However, due to the fact the entries of the matrix have to be solely ones and zeroes, it cannot weight different paths more or less. Thus, these adjacency matrices do not represent the full spectrum of conditional matrices. It also does not have a UI for Bayesian inference, though it could support it.
In conclusion, all 4 of these prior formats differ from the format I’ve described here.
If you want to experiment with the format yourself, I made a list of 12 Superposition Poetry Challenges – 5 structural challenges that impose a structural constraint while building the poem, and 7 literary challenges that force you to find meaning in the constraint.
Feel free to share poems or challenges I haven’t thought of in the comments! I’d love to see how this format develops.
I assume my mind went from “a lyric being different things to different people” --> “intentionally constructing a lyric to be different things some of the time” --> “Huh, why has no one tried embedding word superpositions in songs?”.
Inventing a New Poetry Format: Superposition Poetry
[The Stranger: Interactive Poem Reader]
I was thinking about how interesting it was that different people could hear the same lyric in different ways – “Poker Face” by Lady Gaga for example. And then, my mind immediately jumped to “Huh, why has no one tried embedding word superpositions in songs?”[1] The answer is that people have – Ableton has a feature to play certain portions of songs. However, in poetry, there’s also an additional constraint to play with: letting the reader see the unresolved form of the superposition, rather than only the collapsed form. That too has been done; there’s already a poem called A Superposition Poem. However, there does not seem to be a poetry format that combines the idea of the reader explicitly seeing unresolved superpositions, superpositions having specified probabilities for each collapsed state, and conditional probability weighting between superpositions. And I need this format to exist – think about all the possible interesting poems other people could have achieved with this format, if it had existed previously. And so, I’m here to make it.
My intention with this is to create a new area for humanity to explore – I definitely don’t expect to be able to explore it entirely myself. I’d feel really fulfilled if someone took this format and used it to create a work far greater than I could even imagine. That’s why I wanted to make an editor that anyone could use to write poems, and issue challenges to get people exploring the possibilities of this new format, rather than just writing a poem of my own and calling it a day.
Superposition Poetry
Superpositions can be represented as a list of possible outcome words {N_1, N_2, …}, in addition to probabilities assigned to each one, {a_1, a_2, …} that sum to 1. This allows the author to encode multiple possible words into one position in the text, and supply information on how likely each of those words is. A superposition poem is a regular poem with some superpositions embedded in it. The author specifies possible outcomes for each superposition, probabilities for how likely each outcome is, and is able to specify conditional probabilities for each possible state of prior superpositions. The reader reads through the text on the left, and when they click on a superposition, represented as a blue ????, a sidebar pops up telling them information about the superposition. Note that the superposition is not “something that could be any of the possible outcomes”; it is all of the possible outcomes, at once.
The reader can also click on an outcome to collapse that superposition, but leave other superpositions uncollapsed; when this happens, other superposition probabilities update given the info that the collapsed superposition resolved to the outcome it did. I see this as more conditioning (the reader restricting the search to states where outcome X is true), rather than choosing outcome X to be true, though it is up to artistic interpretation. This can be seen in the screenshot – choosing the 5% probable option for superposition 1, {1=”across the trenches”}, raises the probability of {2=”shot his chest”} massively, from 3.51% --> 70.00%. The superposition interface gives:
The current probabilities for each outcome, factoring in the reader’s currently collapsed superpositions through Bayesian inference.
Either the full transition matrix (across every possible superposition collapse), or active row matrix (given the reader’s currently collapsed superpositions), and the current probabilities for each outcome there.
In the matrix, guaranteed outcomes are highlighted blue – the row is highlighted blue if that state is forced, and the column is highlighted blue if that state is forced due to something other than the row state being forced.
Conditional Probability
Now, let’s go into conditional probability more. Here’s an example of how we use conditional probability weighting:
There once was a man from {Nantucket-50,Lynn-50}. He kept all his cash in a {bucket-100/0,tin-0/100}.
Let’s assume you sample the 1st superposition and get “Nantucket”. The second superposition matrix (or 2D tensor) collapses to a vector (or 1D tensor).
There once was a man from {Nantucket}. He kept all his cash in a {bucket-100,tin-0}.
Since, in the 2nd superposition, “bucket” has 100% sample probability while “tin” has 0%, we can resolve it:
There once was a man from {Nantucket}. He kept all his cash in a {bucket}.
Though “bucket” and “tin” are equally likely to occur when sampling randomly, they are 100% correlated to the location – the Nantucket man always keeps his cash in a bucket, and the Lynn man always keeps his cash in a tin. This is the idea of conditional probability weighting using matrices.
You can also use it to represent information impossible to glean from just one collapsed superposition:
There once was a man from {Nantucket-50,Lynn-50}. He kept all his cash in a {bucket-100/90,tin-0/10}.
This probability matrix tells us that almost all people, regardless of place, use a bucket to keep their cash instead of a tin. However, of the people that do keep their cash in a tin, they are all from Lynn, and not Nantucket. P(Lynn|bucket) = 47.4%, but P(Lynn|tin) = 100%. Thus, knowing that a man keeps his cash in a tin reveals the man’s location completely, yet knowing a man keeps his cash in a bucket reveals next to nothing. You can’t get this from just one example, precisely because one example prevents you from seeing all the other possibilities.
Choose Your Own Adventure vs Superposition Poetry
Superposition Poetry is distinct from CYOA (Choose Your Own Adventure) – the main differences are the narrative implication and what the reader sees. In CYOA, the emphasized narrative is the post-collapsed story, but in Superposition Poetry, the emphasized narrative is the pre- or partially collapsed story. CYOA implies that the user makes choices to influence the story, but Superposition Poetry implies that the user makes choices to decode an already existing story. As a result of this, CYOA is mostly based around the choices, with constant material across choices being a deviation, whereas Superposition Poetry is mostly based around the story, with superpositions being a deviation.
Most CYOA stories do not assign weights to alternatives, instead waiting for the user to choose a story; this doesn’t allow artistic expression of likelihoods. Most CYOA stories do not allow later user choices to be revealed to update our estimates of the probability of earlier user choices – most are chronologically linear. Taken together, as far as I can tell, there does not exist a CYOA game where both 1. Narrative choices are probability-weighted and 2. Later gain of information can update the inferred probabilities of earlier choices.
The Stranger
Now, let’s look at a superposition poem. I made an original poem called The Stranger using my superposition editor, inspired by Thomas Hardy’s The Man He Killed (1902).[2] I chose this poem because the main idea of the poem is represented quite nicely, and even elevated, with superpositions. In The Man He Killed, the narrator recounts the tale of him killing an enemy soldier. The narrator laments that if the two had met at an inn, they would have drunk as friends. But when enlisted in an army, likely for no grander reason than money, they are mandated to kill each other. But while The Man He Killed simply describes the possibility of meeting the stranger in an inn, The Stranger tells the story of both the inn-meeting and the battlefield-meeting at the same time, in the same words.
Superpositions can influence literary storytelling.
In Stanza 2, both “shot his chest” and “passed a pint” do not describe the stranger as the object of the action – “shot him dead” or “shot that liar” would have worked. One possible interpretation is the narrator attempting to hide the weight of his actions from himself.
The nature of conditional probabilities lends itself well to the central point of Hardy’s poem – that the exact same actions are considered moral or immoral depending on the circumstances. This is emphasized ironically through the probabilities: the stranger is 7000x more likely to be shot when meeting across the trenches versus in the inn, though both shootings are the same action leading to the same outcome.
And literary storytelling can influence superpositions.
Another interesting thing in Stanza 2 is the stranger “[raising] his hand”, which shows that ordinary literary double meanings still work – a superposition isn’t needed here. The hand raise can represent both a greeting and a surrender.
Basic literary techniques still work to convey difficulty – in Stanza 2, “across the trenches” breaks meter and requires effort, while “at the inn” doesn’t. Even without looking at the probabilities, readers can determine which is harder.
The Reader Interface
While many prior works to Superposition Poetry just show either 1. All superpositions collapsed or 2. No superpositions collapsed, the reader interface allows the reader to collapse some of the superpositions. This also means that rare events are far easier to navigate – rather than the sampler being emphasized, and readers having to dig through the underlying code to find rare options, in Superposition Poetry, the reader interface is emphasized; clicking on any choice in the interface immediately shows all its possible outcomes, regardless of how rare they are.
In addition, Bayesian backward inference allows the reader to also experience the ambiguity of the characters in the story. For example, revealing {3} first would allow the reader to know whether the narrator called the stranger a friend or foe that day, but not fully expose the result of whether the narrator shot the stranger or gave him a pint – just like a group of people who only hear how the narrator reports the story.
Prior Art
“A Superposition Poem” by Sarah B. Royal: This poem does have the same idea of showing superpositions of words to the reader, but also does not specify weighted probabilities within a superposition, and does not have any probabilistic interaction between superpositions. The lack of conditional dependencies limits author freedom – even with just 5 superpositions and 3 words for each, you need to make sure that 243 different readings all make sense and convey meaning.
Bracery: This is a scripting language, but it does allow for superpositions in the coding process and allows weights within superpositions, so it could be used for poetry. It allows for conditional interactions between superpositions, albeit with if statements and weighting instead of matrices. However, the reader is never shown the underlying superposition, only its output – which means that the reader only ever sees ordinary text, and the probabilities seen in these superpositions are not directly inspectable by the reader. Because of this, probabilities in Bracery function more to control the story, whereas probabilities in Superposition Poetry are another element of the reader’s experience. Effectively, Bracery’s output is equivalent to just the “Sample” mode of the Superposition Poem reader interface. In addition, Bracery does not have a Bayesian backwards inference mode equivalent to our own – Bracery’s inference does not apply to interactions between weighted superpositions.
Cent mille milliards de poèmes by Raymond Queneau: This book is a set of 10 14-line sonnets, all with the same rhyme scheme and rhyme sounds. This allows the reader to construct a poem in which they have 10 interchangeable choices for each of the 14 lines, and they all work, leading to 100 trillion poems. Effectively, it functions as a 14-line poem where each line is a superposition between 10 possible lines, with no probabilities specified for each of the 10 possibilities. However, this was developed as a form of constrained writing, not as a form of superpositions – hence why it does not specify probabilities within lines and has no conditional interaction between separate lines.
World Lines by Amy Catanzano: Each poem is represented as a 2D graph that includes multiple interconnected lines. Readers start at the beginning and traverse downward, able to switch lines at any connection point. Now, just 100% mathematically, this is equivalent to a random list (like Queneau) where each line gets an adjacency matrix, where its entries are ones and zeroes. The artistic mechanism lies in the layout of the graph, the colorings, and which points are adjacent. However, this format does not allow for conditional probability weighting within superpositions – which direction to go at each connection point isn’t weighted. Between superpositions, Catanzano’s work does not specify probabilities. You might question if the adjacency matrices could make up for the lack of specified probabilities. However, due to the fact the entries of the matrix have to be solely ones and zeroes, it cannot weight different paths more or less. Thus, these adjacency matrices do not represent the full spectrum of conditional matrices. It also does not have a UI for Bayesian inference, though it could support it.
In conclusion, all 4 of these prior formats differ from the format I’ve described here.
Anyway, play with the Superposition Poetry Editor here if you want: https://arkendor.github.io/superposition-poetry/.
And here is the GitHub: https://github.com/arkendor/superposition-poetry.
Creative Challenges
If you want to experiment with the format yourself, I made a list of 12 Superposition Poetry Challenges – 5 structural challenges that impose a structural constraint while building the poem, and 7 literary challenges that force you to find meaning in the constraint.
Feel free to share poems or challenges I haven’t thought of in the comments! I’d love to see how this format develops.
Thank you for reading!
I assume my mind went from “a lyric being different things to different people” --> “intentionally constructing a lyric to be different things some of the time” --> “Huh, why has no one tried embedding word superpositions in songs?”.
Poem Showcase, Poem Github