# AllAmericanBreakfast comments on The Telephone Theorem: Information At A Distance Is Mediated By Deterministic Constraints

• This has a curious relationship to some math ideas like the golden ratio. Take a rectangle proportioned in the golden ratio. If you take away a square with side length equal to the smaller side length of the rectangle, the remaining smaller rectangle is equal to the golden ratio. Information is propagated perfectly.

Imagine that we were given a rectangle, and told that it was produced by modifying a previous rectangle via this procedure (by “small-side chopping”). We couldn’t recover the original precisely unless it was in the golden ratio. But if it is in the golden ratio, we can recover it. Intuitively, it seems like we could recover an approximation, depending on how close the rectangle we’re given is to the original. We can certainly recover one of the side lengths.

Edit: You actuall can reconstruct the previous rectangle in the sequence. If a rectangle has side lengths a and b, then small-side chopping produces a rectangle of side lengths [a, b—a]. We still have access to perfect information about the previous side lengths.

It also seems possible that if you start with a randomly proportioned rectangle, then performing this procedure will cause it to converge on a rectangle in the golden ratio. Again, I’m not sure. If so, will it actually reach a golden rectangle? Or just approach it in the limit?

Edit: Given that we preserve perfect information about the previous rectangle after performing small-side chopping, this procedure cannot ultimately generate a golden rectangle.

If these intuitions are correct, then a golden rectangle is a concrete example of what the endpoint of information loss can look like. Often, we visualize loss of information as a void, or as random noise. It can also just be a static pattern. This is odd, since static patterns look like “information.” But what is information?

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