Happens to the best of us. However, it is worth emphasising that you have provided little evidence with your writing that the actual ideas coming from peak experiences are worth much. You have provided a great deal of indication that the motivational aspect of these ideas is useful, though.

This relates to something I've been arguing hereabouts since before the founding of Less Wrong. Basically, if you reduce all of your decision-making to a mathematical algorithm, then you're limiting the power of your decision-making to those parts of your brain that can do math. But our brains can do amazing things if we let them, and are mostly not very good at math.

a good cognitive hazmat suit

I want one!

the traffic light shimmered silvery-blue, like an arc of liquid electricity creeping across the surface, and then returned to normal.

I would wonder if something like that actually happened - it might have been an unfamiliar trick of the light or electrical malfunction...

Once I was walking down the back of West Rock at twilight and suddenly noticed everything was done up in strange, bright colors - the rocks were teal and purple, the leaves were emerald green, etc. After several minutes, the experience didn't go away, and so I picked up a representative purple rock and brought it back to civilization, thinking that would dispel the clearly hallucinatory magic. I immediately asked a passerby, "What color is this rock?", to which the response was indeed "purple". I resolved thenceforth to pay a little more attention to my surroundings.

This would be better if the human character was voiced by an actual human and the robot were kept as it is. The bad synthesized speech on the human character kicks this into the unintentional uncanny valley, while the robot both has a better voice and can actually be expected to sound like that.

For those interested in these topics I suggest reading Robert Anton Wilson's nonfiction, specifically the Cosmic Trigger series and Prometheus Rising.

How to step outside the rational box without going off the deep end. Essentially, techniques for maintaining a lifeline back to normality so you can explore the further reaches of the psyche in some degree of safety.

I developed some of these!

I had a manic episode as well, but it was induced by medication and led to hypersocial behavior. I quickly noticed that I was having bizarre and sudden convictions, and started adopting heuristics to deal with them. I thought I was normal, or even better than normal. Then I realized that such a thought was very abnormal for me, and compensated.

Mania, for me, was like thinking in ALL CAPS ABOUT THINGS I USUALLY IGNORED. It was suddenly giving credence to religion not because I ceased to be an atheist, but because WE ARE ALL CONNECTED REALLY! It was fuzzy thinking, but damned if it didn't make people like me more for a bit. It was looking people IN THE EYE, BECAUSE THAT IS WHAT TRUST AND SOCIAL COMMUNICATION IS ALL ABOUT, all the time, when I am normally shy of eye contact.

(If you find the CAPSLOCK intrusions in the above paragraph annoying, imagine THINKING THIS WAY and you begin to see why mania is a very tiring thing and NOT RECOMMENDED unless you REALLY KNOW WHAT YOU'RE DEALING WITH.)

Compensation strategies:

• Another person in the mental ward, who had lived with mania for a longer time, taught me that breathing exercises can help. Stretch arms upward; inhale. Slowly lower them, exhaling. Repeat as needed.

• I realized that because I was now trusting people (read: believing everything I heard), I was susceptible to getting extremely paranoid. This is not as contradictory as it sounds. After all, if you trust people who don't trust their doctors, you will trust in their paranoia. I therefore told myself, repeatedly, to trust my doctors. Over and over. This self-brainwashing was a good move in hindsight. Chaining myself to the mast of somebody else's sane clinical judgment protected me and insured that I left the mental ward quickly.

• I tended to think that I should try to "help people." Mania amplified that hero complex. I therefore repeated a mantra to myself, over and over, with manic fervor: People help themselves. People help themselves. You don't help people. People help themselves.

• I was encouraged by a visiting parent to take notes of ideas, so I could pursue them later. Result: Lots of notes that I later sorted out into "reasonable" and "not worth pursuing." This was helpful. Nothing permanently insightful, but some decent ideas.

• Another mantra: Even brilliant ideas are wrong 99% of the time. No matter how good your idea is, it is probably wrong. You are probably wrong. You are probably wrong. Under normal circumstances, this isn't a great mantra. During mania, it is essential.

If anybody ever questions my credentials as a rationalist, I think I can safely say that I tried very hard to be a traditional rationalist with an eye for biases even when I was technically not in my right mind.

mathematical truths contain zero information, since they are automatically true in every possible world

This is a false assertion, they are only true if the axioms used to conclude them correspond to reality. There are proofs that rely on the Axiom of Choice which is not accepted (as far as I can tell) by everyone on this site (as well as the axiom of infinity?). There are proofs that rely on the GCH or Large Cardinal Axioms or V=L which are not among the accepted axioms and proven to be independent of the other axioms.

Interesting article, I will need to think quite thoroughly about this for some time. In the meantime I hope I can bothered you with a quick question:

What is your gender?

This might seem irrelevant, silly (as perhaps it is easy to deduce from your handle for someone of a different background that me or because you mentioned it in some other post I haven't read) or even offensive (it is certainly not meant that way), but I assure you that this is simply because I want to understand you better (in order to get part 1 to 3 right). It may seem not much can be derived from such information when dealing with unorthodox cognitive spaces or exploring the perspective of those who are neurodiverse in relation to me (and this post is arguably as much about the latter as the former), but every little bit helps me shift my estimation of the odds to where they should be. Actually on second thought I think simply the differential demographics of different kinds of neurodiversity and their interaction with society means gender is hugely important.

I forget if I've linked it here before, but here's a critique of a commonly claimed connection between mystical experiences and genuine enlightenment or creativity.

One was a metric on the space of events over a given probability space; it popped into my head as I was waking from a dream during the peak of my mania. If you're interested: for events A and B, we can define d(A,B)=1-P(A|B)P(B|A).

This doesn't appear to actually be true. :-/ Say we take our probability space to be [0,1], and we take A=[0,2/3], C=[1/3,1], and B=[0,1]. Then d(A,B)=d(B,C)=1/3, so d(A,B)+d(B,C)=2/3, but d(A,C)=3/4>2/3. Any ideas on how to fix?

(Also strictly speaking it would be a pseudometric on the set of positive probability events, with two events being equivalent if they differ by a set of probability 0, but that's nitpicking.)

Can you post references to new mathematical (or philosophical) proofs that you have solved so we can check the assertion that such altered states are beneficial? Have the results been peer reviewed or published (not that them not being peer-reviewed or published makes them any less valid but this gives a baseline of that others have checked your work)?

Also, what was your reasoning for doubting that you exist? How was Descartes proof insufficient?