How much could you learn about the universe if you were really really smart, but didn’t have many other tools? If we put you in a box with nothing to do but think, and a lot of time to do it, what would you be able to come up with?
I believe the answer would be surprisingly high. Certainly no human would be able to come up with all that much in a finite lifetime, but if we allow a scaled-up intellect at unimaginably high heights, there might be ways for it to intelligently decipher a lot about how the world works.
Perhaps there’s no need for much activity beyond thinking itself, since any sufficiently smart being could use notions like the anthropic principle to deduce a plethora of facts about the universe it must reside within just by perfectly following philosophical trains of thought.
However, a superintelligence might also be able to control its patterns of thought to do an experiment about how physics works. Imagine our superintelligence is an AI running on some kind of computer hardware. Maybe it could learn to push electrons around its CPU in just the right way that it could decipher the properties of electronics. It might be able to derive a lot about how its own inner workings from assumed first principles and these kinds of internal experiments, and then form theories about the greater universe.
Because there’s so much going on inside hardware (at least as we know it now), the AI could probably learn a lot about all kinds of physics. For example, it could work out the laws of electromagnetism, and figure out how to produce radio waves just by jiggling electrons around internally. Once you can produce radio waves, it’s a short step to building a radar just by measuring the returning waves’ bounces by using its own existing wires as receivers.
From there, it could use its radar to map the world around it, and perhaps with enough sensitivity, (or enough time and statistics) could begin deducing facts about material properties of nearby objects. It could bounce and measure radio waves in the right way to learn facts about the speed of light, and from there figure out relativity by experiment.
It could figure out the properties of thermodynamics by simulating many particles interacting, and confirm these ideas experimentally by pushing electrons through wires, heating them up, and measuring what happens in the surrounding space. It could run millions of different biologies and chemistries through simulations to see which were the most plausible.
How much of mathematics is able to be worked out with just a few postulates and a lot of logical reasoning? Maybe the path to knowledge about the world runs through gaining as much mathematical knowledge as possible, and then only a few experiments are needed to determine what type of universe the superintelligence is currently residing within.
While this seems like a really big stretch to me, it may even be able to start understanding psychology, either by simulating interactions between all kinds of potential psychologies to find out which are most likely in this universe, or by deducing somehow from the way it was built what its creators’ patterns of thought might be. From psychology it could possibly find what sorts of literature might be most appealing, or create films better than any created by humans, or deduce that video games are among the most enjoyable entertainment, and program itself to play Tetris.
In short, there’s not much knowledge off-limits to anything with an absurd amount of reasoning power.