The entropy (a measure of possible surprise) of the Internet includes not just the hardware and software but all the biology of the humans interacting on it, which is not just a product of their DNA. There is a lot more water out there interacting with the Internet than in your cup of water.


At the infinite asymptotic limit of all possible trials (or otherwise stated that on a long enough time window in the past and future of the path dependencies of irreversible thermodynamic processes), you will be exposed to all possible surprise due to the microstates (and their Butterfly effect interaction with the environment) unless you can replicate those trials in an isolated system (which you can't in a real world). You implicitly presume that thermodynamics processes are reversible (i.e. able to be isolated to known initial conditions), but they are only reversible in a general relativistic framework, wherein the reversal is a simultaneous occupation of more than one inertial frame (which is impossible due to the quantified speed-of-light). You build artificial, impossible conditions around which you base your analysis, i.e. I am pouring this cup of coffee without any entropy in the initial conditions of the experiment (i.e. a totally isolated system).

You don't live in a vacuum!

And that is the essence of the error you keep repeating and why you still are incorrect about our past discussion about human vs. machine intelligence.


Due to microstates interacting with the environment as you pour, aka the Butterfly Effect, you don't know if the next time you were going to pour a cup of coffee, you instead have an entirely different outcome than had you not poured the coffee (and due to the microstates in some cases, not just due to the macrostate of pouring). That is why it is myopic to say the microstates in the water are irrelevant.


You think seem to think statistical averaging loses microstate information relative to the totality of every possible inertial frame and that is your huge blind spot in our debate on machine intelligence. From the perspective of any particular snapshot of the macrostate, you might conclude that the information was lost, but this would be myopic. No one person is omniscient and has perfect information, but this doesn't mean the information was destroyed as the process of evolving to the dynamic, continuous, living system of microstates that exist at any point in time is irreversible (i.e. not bijective to the past). Meaning that  inertial frames lose their ability to know the totality of the universe (i.e. they become unknowing of the totality so in this sense they've lost access to all information) but the total entropy of all inertial frames hasn't disappeared. The Second Law of Thermodynamics tells us that entropy does not decrease on the whole universe, but can only decrease in some systems as it increases in others.

You are conflating the perception of information by any finite perspective (i.e. any partial order) with the entropy of the unbounded universe. The perception of a total order can't exist (because it would require an unquantifiable speed-of-light and the past and future would collapse into indistriguishable), but the (Butterfly) effects of the total entropy exist via unbounded space-time.