So where does that leave experiences with hallucinogens like DMT and ayahuasca?

The brain is capable of generating a complete reality that actually seems more real than normal reality. Researchers have actually found the same neural circuits activated that are used in normal vision.

https://www.newscientist.com/article/dn20978-drug-hallucinations-look-real-in-the-brain

Similar experiences in sensory deprivation and near death experiences.

]]>**Scott** suggests (in the original post) that “To ask ‘Why is *X* true?’ is simply to ask: ‘What could we have changed in order to make *X* false?'”

To appreciate the vast STEAM-power that Scott’s suggestion generates, it is helpful to consider a concrete proposition, namely X = “The quantum metrology triangles of the *Systeme Internationale* can be physically realized with exponentially small error, and can be computationally simulated to any physically realizable error with PTIME resources.”

Or to strengthen the proposition, X = “For any finite laboratory temperature, in the limit of vanishing measurement error, the entropic cost of computationally simulating an SI measurement process is equal to the entropic cost of conducting the measurement.”

It’s fun to see how naturally this “X-postulate” generates the great themes of quantum mechanics and geometric mechanics. Grothendieck’s celebrated question “What is a metre?” inspires us to conceive interferometers; the quest for stable wavelengths inspires us to conceive lasers; stable lasers (and masers) answer the question “What is a second?”; with metres and seconds in-hand we observe the trajectories of (conserved) masses and (conserved) charges, so that the questions “What is a kilogram?” and “What is a coulomb?” receive answers, the coupling of magnetic fields yields answers to “What is a tesla?”; with Josephson junctions and the integer quantum Hall effect we close metrology triangles by answering questions like “What is a volt?” and “What is an ohm?”.

Finally (and most mysteriously) the practical need to conduct experiments deep in a gravity well in an accelerated frame-of-reference forces us to scrupulously account for general relativistic effects (at the classical level).

The ability to efficiently *simulate* these experiments is (at it seems to me) equally miraculous to the ability to accurately *conduct*, and here Scott’s question ‘What could we have changed in order to make *X* false?’ receives a natural answer, namely: “The (strictly restricted) set of Hamiltonian functions that nature provides is naturally matched to the (strictly algebraic) state-spaces that geometric mechanics requires for efficient simulation, such that neither can be altered without falsifying ‘Postulate X’.”

**Conclusion** The rising tide of textbooks on this topic — *e.g.* Doran and Lasenby’s *Geometric Algebra for Physicists* (2003), and Holm, Schmah and Stoica’s *Geometric Mechanics and Symmetry: from Finite to Infinite Dimensions* (2009) … and there are many more — helps us to perceive an abundance of practical 21st century STEAM-implications that flower naturally from Grothendieck’s quasi-philosophical question “What is a metre?”

**Open questions** Is Nature mindful of the Postulate X’s link of privileged Hamiltonian functions to privileged algebraic geometries? Or are these computational/experimental associations mere fortuitous accidents, of interest mainly to experimental physicists and engineers?

These are the sorts of questions regarding which, in Mark Twain’s phrase, “It were not best that we should all think alike.”

]]>This answer can be quoted pretty much verbatim when answering the question: “Why does the Omnipotent Being, a.k.a. God Almighty, exists?”

… And then we come to the question of why anything exists. For an interventionist, this translates into: what causal lever could have been pulled in order to make [omnipotent being not exist]? Well, whatever lever it was, presumably the lever itself was [an omnipotent being] — and so you see the problem right there.

]]>In the ring Z[ζ_pⁿ], p factors into many factors, growing with n. But it’s almost all repetition. If q is a different prime, then in Z[ζ_qⁿ] p factors into lots of factors with little repetition (each factor is repeated < q times, but the number of factors grows with n). Following Sniffnoy, I think that if you take any square-free number n congruent to 1 mod p (p not 2), then p factors into two distinct factors in Z[√m]; and if m₁, m₂… are a bunch of such numbers, then p factors into many factors in Z[√m₁,√m₂,…]. I think that gives the maximum number of factors, 2ⁿ. (You probably want the m's to be coprime, which might take some work. Ideally prime, but that's a lot of work.)

I think that's all true without concern about the ideal class group, but such problems can be solved by adding 1/N to the ring.

]]>In recent years, in dreams, I am often aware that I am dreaming, which sometimes wakes me up, so I remember it.

Related observation. I am kind of addicted to reading, and anything with writing on it grabs my attention and I try to read it, even if upside down, etc. When dreaming, I sometimes see a book or newspaper, and try harder and harder to read it. But there is never anything that I can make out, and I wake up from the frustration of not being able to read it. This makes me wonder if there is some incompatibility between reading and dreaming.

This happen to anyone else?

]]>Two favorite quotes:

“…there is nothing more real than dream. This statement only makes sense once it is understood that normal waking life is as unreal as dream, and in exactly the same way.” – Tenzin Wangyal Rinpoche in The Tibetan Yogas of Dream and Sleep

“… do not alter the reality of the dream; do not divorce the magic of the story or the vitality of the myth. Do not forget that rivers can exist without water but not without shores. Believe me reality means nothing unless we can verify it in dreams.”- Don Manuel Cordova (Ino Moxo) speaking in Cesar Calvo’s The Three Halves of Ino Moxo.

]]>I.e. could reality be a “super” dream?

The quantitative differences are:

– the degree of logical/self-consistency in dreams.

– the degree of hidden(unconscious) resources necessary to generate the “scenarios” of the dream world (e.g. instantiate the illusion of other sentient beings). If you can dream a complex physics experiment (or a computer solving a tough NP-hard problem), your “brain” has to come up with the necessary resources, but so does the real universe.

I guess it all boils down to saying that if you have enough computing resources to fully simulate a closed physical system (from the outside), the simulation and the “real” system are by definition equivalent for a consciousness that’s “inside” them (part of the simulation)?

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