Dear Rick,

I hope you and yours are safe and healthy in this crazy situation.

Thank you for a very creative essay. It is very interesting.

Of your five "deepest discoveries of since over the last two centuries" deterministic chaos, computational complexity, the Black hole information paradox, and the paradox of self reference, I believe that the paradox of self reference is...

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Dear Rick,

I hope you and yours are safe and healthy in this crazy situation.

Thank you for a very creative essay. It is very interesting.

Of your five "deepest discoveries of since over the last two centuries" deterministic chaos, computational complexity, the Black hole information paradox, and the paradox of self reference, I believe that the paradox of self reference is

of a somewhat different character. The limitations posed by self reference does not matter how much information is known. It would be impervious to Laplace's demon. It is inherent in the system as opposed to the dependent on the observer.

(Perhaps the Black hole paradox is also. I do not know enough about that.)

Another slight point is that I am not sure your question to Laplace's demon is really a self reference paradox. In my Outer Limits of Reason book I give two formualations of such self refential paradoxes when discussing predicting the future. It is from page 173:

Imagine for a moment that we are capable of perfectly predicting the

future. The simplest formulation of this puzzle is that we program two

computers with this ability. Call one computer Mimic and the other Contrary.

Both will simply print out the word true or false. The Mimic computer

will predict what Contrary will print at some specific time in the future

and print the same thing. In contrast, the Contrary computer will predict

what Mimic will do at that specific time and print the opposite. If Mimic

will print true , then Contrary will print false. If Mimic will print false, then Contrary will print true. This is a paradox. The astute reader will notice

that this is nothing more than a simple formulation of the liar paradox

that we met in chapter 2:

L_2 : L_3 is false.

L_3 : L_2 is true.

In a similar vein, we can formulate the same puzzle with one computer.

Program a single computer to predict what it will do at some specific time

in the future and have it do the opposite. In other words, the computer

will negate its own prediction. Such a computer would cause a contradiction

and hence cannot exist.

Again, thank you for writing such a nice essay. Please take a look at mine.

All the best,

Noson

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