This is a mind-bending challenge because it is both abstract and abstruse so it lies at the outer horizon of understanding but not beyond our grasp.
It seems to me, the 2-box version is the clearest lens through which the universal law of chaos optimization is understood
Each box has a number on it and one has your number inside. The number in the box with your number on it may be your number or not as the number outside means nothing except you choose your number first. If another number is in the box you go to that numbered box and continue this pattern until you find the box with your number in it.
If there are two boxes and 2 prisoners the odds of one person picking correct box is 1 in 2; the odds of both being correct is 1/2 × 1/2 = 1/4
if they use optimization rule the odds of both being right is 1 in 2 because
if one of the prisoners decides to choose randomly, the odds of both being right are
1/2 × 1/2 = 1/4 as you add their independent risk into the equatione
The increase arises because their method is aligned with the internal structure of the permutation, rather than ignoring it.
They don’t impose external order; they cooperate with the system’s inherent law — the law of cycles within chaos.
You could have an infinity of boxes and the odds never fall below 30%
The stunning law of permutation is that there is an inherent relational ordering within apparent chaos and exists everywhere as it is inherent in everything. Including nature and within our own perception and
behaviors.
It seems to me, the 2-box version is the clearest lens through which the universal law of chaos optimization is understood
Each box has a number on it and one has your number inside. The number in the box with your number on it may be your number or not as the number outside means nothing except you choose your number first. If another number is in the box you go to that numbered box and continue this pattern until you find the box with your number in it.
If there are two boxes and 2 prisoners the odds of one person picking correct box is 1 in 2; the odds of both being correct is 1/2 × 1/2 = 1/4
if they use optimization rule the odds of both being right is 1 in 2 because
- The boxes contain their own numbers → perfect order are 1 in 2.
- The boxes contain not their own numbers are 1 in 2
if one of the prisoners decides to choose randomly, the odds of both being right are
1/2 × 1/2 = 1/4 as you add their independent risk into the equatione
The increase arises because their method is aligned with the internal structure of the permutation, rather than ignoring it.
They don’t impose external order; they cooperate with the system’s inherent law — the law of cycles within chaos.
You could have an infinity of boxes and the odds never fall below 30%
The stunning law of permutation is that there is an inherent relational ordering within apparent chaos and exists everywhere as it is inherent in everything. Including nature and within our own perception and
behaviors.
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