I've read it, and I tend to think the position it argues for is likely correct, but for complex systems that we don't have models for, the only basis we have for believing it is that we have enough holes in our knowledge of how things interact that it is possible that no esoteric physics play a role and so assuming that they do not is the simplest plausible assumption. There is a good reason for that to be a working assumption.

Until we can work out all the relevant implications of mundane physics and either find them adequate or not to model he phenomena of concern, we can't say that the physics of those phenomena are known (or say that they aren't; we’re in the realm of potential unknown unknowns.)

Now give a full mathematically rigorous explanation of consciousness.

Give three examples.

Do not use the word "Obviously..."

That's neither here nor there. The actions of a swarm of ants or Windows 10 can look dark, mysterious, inexplicable, or downright malicious, but there's nothing in their behavior that warrants something out of our known physical law.

That doesn't necessarily mean we understand their behavior, of course. Complex behavior can arise out of simple underlying rules. That's hardly controversial, except (for some reason) when it's about human brains.

This isn't necessary at all for GPs point. We also can't give a mathematically rigorous explanation for the path a hurricane will take, but that doesn't mean there's magic unknown physics at play.

First give a definition of consciousness that allows me to determine whether something is conscious or not.

You may want to check out the proof: https://news.ycombinator.com/item?id=18377525

That links to a comment on a different article that says "here's a great math-free explanation" and links this discussion.

The parent link at the top of the page is to the proof. I'm pointing to the HN page in the hopes of discussion.

Here's the direct link to the proof: https://www.am-nat.org/site/law-of-information-non-growth/

The blog post explicitly addresses this