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Houshalter comments on Open thread, Nov. 02 - Nov. 08, 2015 - Less Wrong Discussion
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Random sequences aren't really interesting. Even the digits of pi are believed to contain every possible sequence of integers. The hard part is finding where each sequence is located. The index is likely to be longer than the sequence itself!
And a sequence of digits isn't computation. A recording of your neural activity isn't conscious. It's just a static object.
But there is no computation happening there. It's just random noise. It's just as likely to output 5 as 6 or 3. There is no causal link between you inputting "2+3" and the output.
I agree with your sentiment. I am hoping though that one can define formally what a computation is given a physical system. Perhaps you are on to something with the causal requirement, but I think this is hard to pin down precisely. The noise is still being caused by the previous state of the system, so how can we sensibly talk about cause in a physical system. It seems like we would be more interested in 'causes' associated to more agent-like objects like an engine than formless things like the previous state of a cloud of gas. Actually I think Caspar's article was trying to formalize something like this but I don't understand it that well: http://lesswrong.com/r/discussion/lw/msg/publication_on_formalizing_preference/
Read Causal Universes first if you haven't.
I think causality is the only requirement for "computation". Step A causes step B. A computation has happened. If A and B are independent, then there is no computation happening..