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Schrödinger's cat reversed: a thought experiment

"Out of nowhere, a demon appears. That’s odd, you might think, but it’s not. Remember, we are conducting a thought experiment."

Christos Tombras
24 February 2020
Thought experiment.
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Author's photograph. All rights reserved.

Let’s imagine there was a lotto jackpot. The fourth in a row. The total prize exceeds now your wildest dreams. You can’t ignore it any more. You have made up your mind. You are going to play. You rush to the betting shop. You grab some lotto tickets, you take out your pen, and you are just about to mark some numbers down – when, out of nowhere, a demon appears.
That’s odd, you might think, but it’s not. Remember, we are conducting a thought experiment.
“Wait a second”, the demon says in an assertive but warm voice. “Please forgive the interruption. You came here to play lotto, no? I see your excitement and eagerness to choose some numbers, but may I have your attention for a moment?”
You are startled of course, if not a bit worried. He is a demon, after all. You look at him. A proper demon, with all his demon’s paraphernalia. Unsettlingly, he appears to be visible only to you: other customers are getting on with their business completely undisturbed. That’s highly unusual. But then the demon looks benign and friendly, so you are worried, but not too worried. Admittedly you are a bit curious too.
“You want to win” the demon is saying now, “and that’s why you are going to pick your five numbers carefully. You think you are free to choose any number you want, but – please allow me to disappoint you – you are not. I know exactly the numbers you are going to pick.”
You glance around nervously. No-one seems to pay attention to the exchange. People simply go about their business. The demon is waiting for a reaction.
“How do you know my numbers?” you ask. “How can you know my numbers? I haven’t written them down yet. I haven’t even chosen numbers yet. What are you trying to do?”
“Nothing, really”, the demon says. “You don’t need to worry. I just want to make a case about free will. You thought you are free to choose, and I want to show you, you are not. As I said, your numbers are known to me – even before you know them yourself.”
“What is this all about?” you exclaim. “Is this some kind of a trick?”
“Not at all. You are unconvinced, that’s natural, but it’s the truth. I can prove it to you.” The demon hands you an envelope. “Here. There is a paper in it”, he says. “It’s for you. It has the five numbers you were going to play.”
You take it reluctantly.
“This is what I am interested in”, the demon says. “I am interested in what you are going to do now.”
You remain silent.
“Or rather, I am not.” The demon smiles at you. “I know what you’ll do. I just know it. That’s all. Take care. Bye!”
And with that, the demon flies away.

You thought you are free to choose, and I want to show you, you are not.

So, here we are. This is the thought experiment.
What if you were indeed going to play lotto, and a demon did indeed appear to you and told you that he knew your numbers even before you knew them yourself, and what if the demon left you a paper with the numbers. What would you do?
Would you ignore the episode and pretend nothing ever happened?
Would you look at the demon’s numbers? And if you did that, would you first write your own numbers down or not? Because, you see, without having written them down, you can’t really know if the demon’s guess is correct. Would you trust the demon’s prediction and play along? Would you perhaps discard his numbers, and play something else?
On the other hand, if you did write your numbers, how would you be affected by the demon’s prediction? Imagine that he guessed correctly. Would you still play these numbers? What if he wasn’t correct? What then? Would you choose to play the demon’s numbers? Your numbers? Or perhaps a combination of the two?
And so on, and so forth.

Would you ignore the episode and pretend nothing ever happened?

The whole matter rapidly becomes very confusing.
But that is not the point. The point is that the more one thinks about it, something else becomes increasingly clear.

Whatever you decide to do; whether you’ll choose to use the numbers the demon predicted; or choose other, new numbers; or pretend there was no prediction; and so on and so forth. In all those cases, you have become aware of a demon’s prediction, and this very fact, the fact that a prediction exists, affects your choice in ways that render the prediction irrelevant.
A bit like Schrödinger’s cat, only reversed.

I don’t know the moral of this story.
Perhaps we could return to this next time?

This piece was originally published in the February edition of Splinters.

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