That’s an interesting thought. It steps beyond my realm of confidence, but I’ll ask in ignorance: can a biological brain really have infinite state space if there’s a minimum divisible Planck length?
Infinite and “finite but very very big” seem like a meaningful distinction here.
I once wondered if digital intelligences might be possible but would require an entire planet’s precious metals and require whole stars to power. That is: the “finite but very very big” case.
But I think your idea is constrained to if we wanted a digital computer, is it not? Humans can make intelligent life by accident. Surely we could hypothetically construct our own biological computer (or borrow one…) and make it more ideal for digital interface?
Absolutely nothing in the real world is truly infinite. Infinity is just a useful mathematical fiction that closely approximate the real world for large enough (or small enough in the case of infinitesimals) things.
But biological brain have significantly greater state space than conventional silicon computers because they're analog. The voltage across a transistor varies approximately continuously, but we only measure a single bit from that (or occasionally 2 for nand).
Not quite. Smaller wavelengths mean higher energy, and a photon with Planck wavelength would be energetic enough to form a black hole. So you can’t meaningfully interact electromagnetically with something smaller than the Planck length. Nor can that something have electromagnetic properties.
But since we don’t have a working theory of quantum gravity at such energies, the final verdict remains open.
Measurability is essentially a synonym for meaningful interaction at some measurement scale. When describing fundamental measurability limits, you're essentially describing what current physical models consider to be the fundamental interaction scale.
Infinite and “finite but very very big” seem like a meaningful distinction here.
I once wondered if digital intelligences might be possible but would require an entire planet’s precious metals and require whole stars to power. That is: the “finite but very very big” case.
But I think your idea is constrained to if we wanted a digital computer, is it not? Humans can make intelligent life by accident. Surely we could hypothetically construct our own biological computer (or borrow one…) and make it more ideal for digital interface?