What I didn’t understand is why you removed quantum experiments from the discussion. I believe it is very plausible to have something that is physically unpredictable, as long as the thing doing the predicting is bound by the same laws as what you are trying to predict.
Consider a world made of reversible binary gates with the same number of inputs as outputs (that is every input has a unique output, and vice versa).
We want to predict one complex gate. Not a problem, just clone all the inputs and copy the gate. However you have to do that only using reversible binary gates. Lets start with cloning the bits.
In is what you are trying to copy without modifying so that you can predict what affect it will have on the rest of the system. You need a minimum of two outputs, so you need another input B.
You get to create the gate in order to copy the bit and predict the system. The ideal truth table looks something like
In | B | Out | Copy
0 | 0 | 0 | 0
0 | 1 | 0 | 0
1 | 0 | 1 | 1
1 | 1 | 1 | 1
This violates our reversibility assumption. The best copier we could make is
In | B | Out | Copy
0 | 0 | 0 | 0
0 | 1 | 1 | 0
1 | 0 | 0 | 1
1 | 1 | 1 | 1
This copies precisely, but mucks up the output making our copy useless for prediction. If you could control B, or knew the value of B then we could correct the Output. But as I have shown here finding out the value of a bit is non-trivial. The best we could do would be to find sources of bits with statistically predictable properties then use them for duplicating other bits.
The world is expected to be reversible, and the no cloning theorem applies to reality which I think is stricter than my example. However I hope I have shown how a simple lawful universe can be hard to predict by something inside it.
In short, stop thinking of yourself (and Omega) as an observer outside physics that does not interact with the world. Copying is disturbing.
I believe it is very plausible to have something that is physically unpredictable, as long as the thing doing the predicting is bound by the same laws as what you are trying to predict.
[attempted proof omitted]
I hope I have shown how a simple lawful universe can be hard to predict by something inside it.
In short, stop thinking of yourself (and Omega) as an observer outside physics that does not interact with the world. Copying is disturbing.
Even though I do not have time to reflect on the attempted proof and even though the attempted proof is best described as a stab at a sketch of a proof and even though this “reversible logic gates” approach to a proof probably cannot be turned into an actual proof and even though Nick Tarleton just explained why the “one box or two box depending on an inherently unpredictable event” strategy is not particularly relevant to Newcomb’s, I voted this up and I congratulate the author (whpearson) because it is an attempt at an original proof of something very cool (namely, limits to an agent’s ability to learn about its environment) and IMHO probably relevant to the Friendliness project. More proofs and informed stabs at proofs, please!
What I didn’t understand is why you removed quantum experiments from the discussion. I believe it is very plausible to have something that is physically unpredictable, as long as the thing doing the predicting is bound by the same laws as what you are trying to predict.
Consider a world made of reversible binary gates with the same number of inputs as outputs (that is every input has a unique output, and vice versa).
We want to predict one complex gate. Not a problem, just clone all the inputs and copy the gate. However you have to do that only using reversible binary gates. Lets start with cloning the bits.
In is what you are trying to copy without modifying so that you can predict what affect it will have on the rest of the system. You need a minimum of two outputs, so you need another input B.
You get to create the gate in order to copy the bit and predict the system. The ideal truth table looks something like
In | B | Out | Copy0 | 0 | 0 | 00 | 1 | 0 | 01 | 0 | 1 | 11 | 1 | 1 | 1This violates our reversibility assumption. The best copier we could make is
In | B | Out | Copy0 | 0 | 0 | 00 | 1 | 1 | 01 | 0 | 0 | 11 | 1 | 1 | 1This copies precisely, but mucks up the output making our copy useless for prediction. If you could control B, or knew the value of B then we could correct the Output. But as I have shown here finding out the value of a bit is non-trivial. The best we could do would be to find sources of bits with statistically predictable properties then use them for duplicating other bits.
The world is expected to be reversible, and the no cloning theorem applies to reality which I think is stricter than my example. However I hope I have shown how a simple lawful universe can be hard to predict by something inside it.
In short, stop thinking of yourself (and Omega) as an observer outside physics that does not interact with the world. Copying is disturbing.
Even though I do not have time to reflect on the attempted proof and even though the attempted proof is best described as a stab at a sketch of a proof and even though this “reversible logic gates” approach to a proof probably cannot be turned into an actual proof and even though Nick Tarleton just explained why the “one box or two box depending on an inherently unpredictable event” strategy is not particularly relevant to Newcomb’s, I voted this up and I congratulate the author (whpearson) because it is an attempt at an original proof of something very cool (namely, limits to an agent’s ability to learn about its environment) and IMHO probably relevant to the Friendliness project. More proofs and informed stabs at proofs, please!