Consider all programs encoding isomorphisms from a rock to something else (e.g. my brain, or your brain). If the program takes k bits to encode, we add 2−k times the other entity to the rock (times some partition number so all the weights add up to one). Since some programs are automorphisms, we repeatedly do this until convergence.
The rock will now possess a tiny bit of consciousness, or really any other property. However, where do we get the original “sources” of consciousness? If you’re a solipsist, you might say, “I am the source of consciousness.” I think a better definition is your discounted entropy.
Can’t you choose an arbitrary encoding procedure? Choosing a different one only adds a constant number of bits. Also, my comment on discounted entropy was a little too flippant. What I mean is closer to entropy rate with a discount factor, like in soft-actor critic. Maximizing your ability to have options in the future requires a lot of “agency”.
Maybe consciousness should be more than just agency, e.g. if a chess bot were trained to maximize entropy, games wouldn’t be as strategic as if it wants to get a high*-energy payoff. However, I’m not convinced energy even exists? Humans learn strategy because their genes are more likely to survive, thrive, and have choices in the future when they win. You could even say elementary particles are just the ones still around since the Big Bang.
*Note: The physicists should reverse the sign on energy. While they’re at it, switch to inverse-temperature.
While I sort of get what you’re going for (easy interpretability of the isomorphism?), I don’t really a see a way to make this precise.
Consider all programs encoding isomorphisms from a rock to something else (e.g. my brain, or your brain). If the program takes k bits to encode, we add 2−k times the other entity to the rock (times some partition number so all the weights add up to one). Since some programs are automorphisms, we repeatedly do this until convergence.
The rock will now possess a tiny bit of consciousness, or really any other property. However, where do we get the original “sources” of consciousness? If you’re a solipsist, you might say, “I am the source of consciousness.” I think a better definition is your discounted entropy.
Not trying to split hairs here, but here’s what was throwing me off (and still is):
Let’s say I have an isomorphism: sequential states of a brain ϕ→ molecules of a rock
I now create an encoding procedure: physical things e→ txt file
Now via your procedure, I consider all programs P which map txt files to txt files such that
e∘P∘e−1=ϕ
and obtain some discounted entropy. But isn’t e doing a lot of work here? Is there a way to avoid infinite regress?
Can’t you choose an arbitrary encoding procedure? Choosing a different one only adds a constant number of bits. Also, my comment on discounted entropy was a little too flippant. What I mean is closer to entropy rate with a discount factor, like in soft-actor critic. Maximizing your ability to have options in the future requires a lot of “agency”.
Maybe consciousness should be more than just agency, e.g. if a chess bot were trained to maximize entropy, games wouldn’t be as strategic as if it wants to get a high*-energy payoff. However, I’m not convinced energy even exists? Humans learn strategy because their genes are more likely to survive, thrive, and have choices in the future when they win. You could even say elementary particles are just the ones still around since the Big Bang.
*Note: The physicists should reverse the sign on energy. While they’re at it, switch to inverse-temperature.