: Stories with multiple possible interpretations: do you plan for it? There are many stories out there that are open-ended, up for different interpretations. Many theories spawn around such stories,

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I assume the op meant something in the style of the lady and the tiger. While the obvious answer is that art is open to interpretation, I'm willing to guess you know that by the time you get to this answer.

You do not need to plan ambiguity, and at times this can be harmful as the best story telling tends to be highly specific. If you want an ambiguous ending, (inception) then after you write enough of the story you figure out what your question is and go back and make sure that question is central to events and that you've appropriately foreshadowed conflicting, but very possible, endings.

I do not think it's likely that most projects start out this way; though it can happen if you keep the target in mind. I think it is usually an act of revision. The original plan is not as important as recognizing the opportunity and then adjusting appropriately.

The last thing you want to be is vague, though. You want each possibility to be scintillatingly real and feel legitimately possible. Only then can you get your readers to argue with each other vehemently and with passion. Think of it as the reverse mystery. Instead of solving a problem, you're setting one up with multiple answers. There are suspects, red herrings, pieces of evidence, and tensions/ conflicts that play to different sympathies.

If you want to use this sort of device as a subplot or ancillary element, then you will likely need to not just change the scale, but also the importance. This is because if the element is too important it will draw attention and be a point of confusion; thus distracting your readers and harming your work. At that point it will become the plot.

The other way to have "ambiguity" is to write only the essential. If you set a good pace and only give people the important details there will be space they naturally fill with imagination, without complaint. This is not merely readers interpreting differently, it's allowing the mind to do what it does naturally: create shortcuts for a partially observed world that it can use to navigate the world. If you do this well, you can hack the brain into making all sorts of leaps.

Regardless, people will interpret works how they see fit; but it's obvious that a controlled voice can ensnare a readership in a mystery intentionally.

The other option is to write without direction, and pray you have magic fingers. You can do better than that.

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While this is about a song not a story, I believe a quote is in order.

When asked what "American Pie" meant, McLean jokingly replied, "It
means I don't ever have to work again if I don't want to."[16] Later,
he stated, "You will find many interpretations of my lyrics but none
of them by me ... Sorry to leave you all on your own like this but
long ago I realized that songwriters should make their statements and
move on, maintaining a dignified silence.

As a writer you may have a clear idea of what you mean and think it's right there in black and white. However your readers aren't you, they have different experiences, ideas, and interests. What you think is a story that about self discovery, growing up, perseverance and learning to give up the past, will be interpreted as a commentary on the loss of innocence by an uncaring society, or a testament to nihilism and you have to destroy your past while giving up your dreams.

You can plan several interpretations, but don't expect your readers to follow along.

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Ditto to @Secespitus . Readers will interpret a story in terms of their own world view.

Just for example, on another forum we were discussing Arthur C Clarke's short story, "The Nine Billion Names of God". Without going into details about that story or giving any spoilers, it's about a group of monks of an unusual religion, and the story ends with the hero learning that the seemingly crazy beliefs of these monks are true: their god really exists.

I don't believe in the religion of the story -- no one does, it was just invented for the book. When it got to the end and the monks' religion was proven true, my reaction was, "Ha ha, so their crazy religion is true!" I didn't see it as a blasphemous attack on my own religion or anything like that because it was just a story and it was a made-up religion. But two atheists in the conversation insisted on trying to "interpret" the ending in a way that did not make the monks' religion true. They pointed out scientific flaws and said that this proved the author did not mean that the ending literally happened that way, that he must have meant it was some sort of illusion, etc., and, to my mind, tied themselves in knots trying to explain why the author didn't mean what he said.

If I read a story where the ending "proves" some religious or political or social or whatever idea that I disagree with, my reaction is generally, "Oh brother, does the author think he's going to convert me to this belief because he arranges a FICTION story where they turn out to be right?" But apparently some readers insist on finding an interpretation of the story that is consistent with their own beliefs, rather than just say, "Oh, I disagree with the author about this."

I read an article by the well-known science fiction writer Isaac Asimov once in which he said that he once attended a lecture in which, he was surprised to hear, the lecturer used one of Asimov's stories to make a point, explaining the professor's interpretation of the story. Afterwards Asimov talked to the professor and said that that wasn't what the story meant at all. He said that after arguing for some time, he made his clincher argument "After all, I'm the author!" The professor was unimpressed, and calmly replied, "Just because you wrote the story, what makes you think you know anything about it?"

My point -- and I do have a point -- is that you shouldn't work too hard to give your story multiple interpretations. Deliberately create a LITTLE ambiguity. But readers will find all sorts of unintended ambiguity, so if you go too far, the story becomes too much of a blank. You have to give the reader material to work with.

Every now and then I attend a lecture where the speaker says, "Rather than give a prepared presentation, I'll just open the floor for questions." This almost invariably results in awkward silence and then some lame, vague, general questions. Because without a prepared presentation, what are we going to ask questions about? If someone gave a lecture on, say, the role of General Foobar in the American Revolution, it might bring all sorts of questions to mind. Why did Foobar order a retreat in the Battle of Podunk? What was Foobar's role in the peace negotiations? Where did Foobar get his military training? etc., etc. But if someone just says, "I'm a historian. Do you have any questions about history?" where would we start?

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The point of a theory crafting story is that the mysteries are left unsolved enough for the audience to want more, that explanations do exist but there is always a reason to doubt them. That we really want to figure it out, even after the story is complete.

Although it is not a book, the Five Nights At Freddies video game franchise:

Survives off of this phenomenon, asking "who is the purple guy", "what happened to start this" and "why am I working here!?".

Another example is the movie Pulp Fiction:

"What's in the case?", viewers are forced to keep asking that question even after the movie is over.

Or Kafka's book The Metamorphosis:

Where a man is transformed into a giant insect, the reasons for which are never explained, and the story focuses mostly on the effect the transformation had on the family, giving the reader a real sense of "But, why?"

These are certainly done on purpose, with intentional red herrings and teases throughout. Books can definitely thrive off of this, and I'd even say that every story leaves some questions unanswered.

There is a fine line between a frustrating question and this phenomenon and only you as the writer will be able to find that balance point. You have to offer enough evidence of something but not proof of it.

The benefit is that you will be adding these hooks into your story anyway. They're what kept us reading in the first place. The trick, I believe, is to not explain everything, yet give evidence that there is an explanation. The problem is, not all questions are strong enough. I don't need to know what war the Mentor fought in, but I may really wish I understood the Anti-Hero's motivations behind leaving the Protagonist alive when they did.

Although it's undeniable that readers will make their own interpretations of a book and there is always some amount of wiggle room in any story, there is something to be said about stories that promote theory crafting from the audience.

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There is a joke that we always told each other in my school when we had to analyze texts or poetry that goes something like this:

Teacher: What did the author mean when he said that the curtains are blue?
Pupil 1: The curtains are a replacement for the endless skies that can't be seen from the inside. They are the narrators way to connect to the outside world by mimicking the world.
Pupil 2: Blue was obviously a color that symbolized being calm in the time the author lived. By making the curtains blue he allowed the reader to get a glimpse of the narrators state of mind, which is calm in the face of the upcoming storm.
Pupil 3: No, obviously it was just a barricade to shut himself out of the world and by making it blue he wanted to show to other people that he was normal and yearning for the outside, while deep inside his chest he knew that he would never want to leave his house again.
Teacher: You are all completely wrong. Blue is obviously part of the greater color scheme. If you had a look at the first pages of the book you would notice the turquoise boots, later these blue curtains and in the end the green grass. The curtains are merely a symbol for the change that is happening throughout the book. Remember this kids: metamorphosis is an important topic in basically all books of this time! It is a concept that you need to understand in order to pass the test.
...
Author: Blue is my favourite color.

And the moral of this story: it doesn't matter what your true intentions are, someone will find a way to interpret your writing in a way that profits them - and depending on their current situation, the general spirit of the time and the amount of people you are asking you will get far more interpretations than you could ever hope to put into this book deliberately.

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Interpretation arises from uncertainty, so to some degree, you can control whether there will be multiple interpretations or not. Interpretation is what happens when you ask the reader to "fill in the blanks", and there is enough material around those blanks to have an idea of what might be in there.

Achieving multiple interpretations is a complicated art, since you need to know when it is necessary to give the reader more clues, or when to cut down on them. A blank too wide will produce no interpretations since the reader has not enough material to imagine what could be in there, and will just make them feel lost, while a blank too narrow will often end up in a single, probably "correct" interpretation.

But the blanks need not be necessarily completely blank themselves. Ambiguity here is your friend, and if some of the clues are blurry, it may give people probabilistic insight into the "correct" (although I may add it is probably better if you do not even know the answer yourself) interpretation, while also misleading them if they decide to consider other interpretations. So to speak, if you write a clue to be easy to interpret in different ways, let's say two for simplicity's sake, your reader will have to consider what lies in the blank if interpretation A is true, and what lies in the blank if interpretation B happens to be true. Add several of these ambiguous clues, and the reader will have to consider the cartesian product of all possibilities, and pick one or more based on the reader's subjective connotations.

One last possible technique is using symbolism. Symbolism ofuscates true meanings, and its exact interpretation often depends on the reader's point of view, as Mark Baker very correctly stated in his answer. By using symbols as clues, you make whatever is in the blank blurry and open to interpretation.

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