### deep or trivial

I would summarize the previous blog post as follows:

In general, a closed system, which contains e.g. a physicist and/or computer, cannot predict its

own future, even if we assume deterministic laws of physics (*).

This is quite easy to understand once you think about it;

But is this some deep insight or just trivial stuff?

An equivalent statement would be that, in general, a closed system, which contains e.g. a physicist and/or computer, cannot

determine or know its own microstate.

Although equally trivial, it has a bit more 'statistical mechanics flavor' to it and might be interesting if one considers foundational

questions about entropy or even more profound quantities.

It also has a certain Zen-like quality...

(*) See also this and that.

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## 4 comments:

I disagree, because a fractal can contain its own description. The world could be a fractal.

Indeed, if the closed system contains an infinite amount of information the statements would not necessarily hold.

I implicitly assumed a finite number of degrees of freedom.

I don't know what "determine" or "know" mean in the phrase "determine or know its own microstate"

Is that like having a file where the last n bits can be decompressed to the entire file? For a *specific* file I'd say that it would depend on the (external) decompression algorithm. We might consider the decompression algorithm to be external if it represents the laws of physics.

On the other hand its easy to show by counting, that for a fixed algorithm you cannot encode a generic n+m number of bits into n bits, which is even stronger than saying that the encoding must be part of the file.

I guess a more interesting question would be 'what is the minimum entropy a computer (or physicist) can assign to itself'.

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