This construction already gives us a function such that every interval (x_1, x_2) contains a point x such that f(x) = y for every rational number y.

Now, in a similar way we may consider a set of the form s + Q where s is an irrational number. Setting f(x) = s + q_n for all x in s + A_n, we get a function which also attains all numbers of the form y = s + q for some rational q on every interval.

Finally, let's say that two real numbers s and t are equivalent if they differ by a rational number. By the axiom of choice we can choose a representative from every equivalence class, so that for every two representatives s and t the sets s + Q and t + Q are disjoint. Using the above construction for every representative lets you define a function with the property you wanted.

On top of this base model one could then also introduce subsidies for specific energy intensive industries that are deemed essential (probably not bitcoin).

That would handle the distribution of limited* amount of energy we have. CO2 emissions should probably be taxed separately and progressive rates would seem reasonable to me here as well.

* Yes, we can still build more, but at some point the energy usage has to stagnate. Exponential growth in usage would lead the Earth to become very hot in a few hundred years since the only way heat gets released to space is via infrared radiation which is limited by the surface area of the planet [1, Section 1.3].

[1] Murphy, T.: Energy and Human Ambitions on a Finite Planet (2021), a free textbook at https://doi.org/10.21221/S2978-0-578-86717-5

It is an interesting question how much music itself can advance while still staying enjoyable by a significant number of people. For instance much of the popular music nowadays appears to be rather simplistic in terms of rhythms and harmony, and the innovation has been happening more on the timbre.

In classical music more modern approaches such as atonality never seemed to gather such large scale interest as the stuff from older masters. Time will show if e.g. microtonal music will make a breakthrough at some point, but it is hard since the new harmonies sound just 'wrong' until the listener learns them. (Of course for some native listeners the same could presumably be said about western music.)

I guess it's not a completely unreasonable guess to say that there are some optimal thresholds of complexity for a human brain and that's why simple regular clapping and singing in thirds and fifths will continue to evoke the strongest emotions for the majority of people.

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Just as an example, some African countries could decide that in fact they would like to make the climate even colder than it used to be, which on the other hand would negatively impact agriculture away from equator. I think these questions form a big potential source of global power struggle and conflict.