The central issue I see with this argument is that it seems to assume time in the setup to the examples, or implicitly in the equation. For example:
For example, if a guy called Join Doe is traveling from Berlin to Moscow, there might be at least two bits of information about this:
John Doe is in Berlin
John Doe is in Moscow
How do we distinguish between the Berlin to Moscow case, and the Moscow to Berlin case? You mention this point later:
time does not really tell us if Johnny starts his journey in Berlin or in Moscow.
So I can accept the argument that Berlin,Moscow and Moscow,Berlin are the same amount of time—it stands to reason that doing the same thing in reverse order should take the same amount of time, which the information rule seems to capture. But this doesn’t seem to square with the Minsk example:
it might even happen, because he is so very much in love with this girl, that he will never arrive in Moscow. In that case, the amount of time between departure and arrival is infinite.
Based on the previous example I would expect Berlin,Minsk,Moscow to be the same as Moscow,Minsk,Berlin, and this seems to hold up—but it doesn’t seem consistent that Berlin,Minsk,Moscow is more time than just Berlin,Moscow and yet Berlin,Minsk is infinite.
It also looks to me like we have a problem with trying to integrate new kinds of information. For example, under this rule Berlin,Minsk,Moscow and Berlin,Paris,Moscow are the same amount of time—but when we look at the map we see Paris is farther away from Moscow than Berlin is. How do we account for this, under the rule?
Welcome to LessWrong!
The central issue I see with this argument is that it seems to assume time in the setup to the examples, or implicitly in the equation. For example:
How do we distinguish between the Berlin to Moscow case, and the Moscow to Berlin case? You mention this point later:
So I can accept the argument that Berlin,Moscow and Moscow,Berlin are the same amount of time—it stands to reason that doing the same thing in reverse order should take the same amount of time, which the information rule seems to capture. But this doesn’t seem to square with the Minsk example:
Based on the previous example I would expect Berlin,Minsk,Moscow to be the same as Moscow,Minsk,Berlin, and this seems to hold up—but it doesn’t seem consistent that Berlin,Minsk,Moscow is more time than just Berlin,Moscow and yet Berlin,Minsk is infinite.
It also looks to me like we have a problem with trying to integrate new kinds of information. For example, under this rule Berlin,Minsk,Moscow and Berlin,Paris,Moscow are the same amount of time—but when we look at the map we see Paris is farther away from Moscow than Berlin is. How do we account for this, under the rule?