Hi, a timeline question, and some math about encryption

[Roger]

You're correct that we make very little mention of using quantum computing in the setting. This is not due to a specific rejection of QC in the setting so much as it being the case that most of us don't fully understand it sufficiently to feel comfortable writing/speculating about it and those of us who do understand it well enough haven't chosen to do the necessary writeups to help us develop that aspect of the setting. If someone (such as yourself perhaps) was willing to help us fold QC and encryption information into the setting in a realistic and (mostly/reasonably) layperson understandable fashion we would likely to happy to do that.

Sounds like an interesting project - I think this discussion might be a good first step.

The upshot of much of this is that the archai can probably break or bypass or otherwise cheat a lot of modosophont/low transapient encryption, but that even the S6 have limits in terms of raw breaking of encryption, meaning that even modos can successfully encrypt messages the gods can't break.

OK, so then as I suspected we're in a Minicrypt or Cryptomania scenario. Again, this sounds like if it could be written up at an encylopedia-suitable level with fewer technical terms than I've been using above, as an article on encryption (with some mention of why that almost invariably isn't enough when facing technotelepathy/cliology/archailect-level hacking/etc./etc., except maybe in a first-contact situation or the like), so there might be an article in this.

Various initial thoughts here:

a) Given their rather...fuzzy...relationship with the concept of individuality as we humans generally understand it, archai could easily have hundreds or thousands of quantum computing 'lobes' or sub-selves within their brains that operate at the full #3 level that you describe. They aren't really the 'full' mind of the archailect - but they would be a part of it and would possibly think of themselves as equivalent to the full archai in their own way - or at least definitely a contributing member of the 'orchestrat' so to speak.

b) As an alternative to a Tipler Oracle, the archai might used nested Void Pockets/specialized Void Ship like devices to pack nearly a Lunar mass worth of quantum computronium into a volume no more than a nano-meter across (and do this repeatedly if desired). The QC hardware might start as raw matter and then be created after void pocket enclosure - or not. I/O issues might be...interesting...but some creative potential solutions come to mind.

c) We've toyed a bit with the idea that S2 or higher minds might be able to (as a bit of transapient 'magic') create and maintain arbitrarily large quantum entangled states and/or create 'room temperature' quantum entangled states (aka the environment is very 'noisy' and chaotic, but the transaps can maintain the entangled states anyway - at least to a point. While certainly speculative, does this strike you as a potentially workable idea or too far beyond the pale in this universe?

a): Agreed, and that's what I meant by my discussion about specialist nodes above, and by the digression under quantum-level-1) of it being safe to assume that even a quantum-level-1) archailect would have small specialist nodes of S0, S1, or for a higher archailect maybe S2 that were fully quantum.

I really need a more baseline-friendly terminology -- how about rather than quantum-level-0) through 3) I call these "completely classical", "quantum coprocessor", "partly quantum", "fully quantum"?

b): Good point! Yes, that's obviously the easy way for an archailect to make a fully quantum S3 or S4 (so it's a safe assumption that an S3 black angel or an S4 void ship ISO seraph is likely to have one or more void motes that contain a fully quantum subnode one toposophic level down, so S2 or S3 respectively, for handling problems where that looks useful); and it has a nice progression to using a Tipler Oracle to hold a fully quantum S5.

c): In general, that sounds impossible -- the state would collapse in attoseconds or even less -- normally too fast even for error correction from magmatter quantum sensors/processors to maintain it. But there might be plenty of subtle counterexamples, under special circumstances -- perhaps ones a mososophont or supoerbright could understand if it were explained to them, or not, but that they would have a lot of trouble actually finding. Basically you *can* do this, if you can find a (possibly subtle) quantum subspace concealed somewhere within the full dynamics of the system that either a) has no noise interactions with the rest of the system (so it's completely isolated), or very low interactions (low enough that you can add enough quantum error correction to keep up with the noise -- there tends to be a threshold here, as the noise increases this switches from possible to impossible), or b) that has quantum interactions with the big noisy environment that are moderate but (almost) always of a limited predictable form or forms (so the noise you're trying to block has a predictable format), and you can apply error correction that recognizes any signals of that form, can tell that they must be noise, and thus can cancel them, while you do your actual computation only over modes that are orthogonal to the noise.

Let me give you a concrete example of each. For a), there exist thin film materials that have quantum excitations that are always linear: maybe they're boundaries between patches of material with opposite magnetizations, or something more subtle -- anyway, they have to consist of closed loops. If you have a system that consists of a donut shape coated with this material, then there's a potentially a topological effect -- the loop may be such that it can collapse to a tiny loop and disappear, or the loop may be wrapped around the donut so it can't disappear, and has a minimum size (the circumference of the donut in the direction it's wrapped around). This might be a physical donut, or it might be something more subtle like a donut-shaped strange attractor inside the local dynamic behavior of a distribuited system. In a hot, wet, messy system, there is likely to frequently be enough thermal noise to create or destroy a little loop of this linear exitation. But it could be the case that the system isn't hot enough, or strongly interacting enough, or whatever for there to be any significant chance of it spontaneously creating a loop as big as the minimum size of loops that are wrapped around the donut -- so there would be a very low error rate for that subsystem, consisting only of loops wrapped around the donut. Or there might be some symmetry or topological reason why the interactions that normally occur in the system can never create such a loop, no matter how hot it gets (but the archai's effector system can, by using more exotic physics). Then the error rate for that system would be (at least to an excellent approximation) zero. Either way, you have an isolated subspace of topological loops with little or no noise, so (if tis space is also unobservable to other systems and sophonts in the space -- they can't see into it, because it's decoupled) then you can put a fragile entangled state in it, or use it for quantum computing. This is called "topological quantum computing" -- there are some similar tricks for braids or knots rather than loops called "braid quantum computing", and so forth, and probably a lot of other more subtle tricks us modos haven't thought of yet.

For the second type of subsystem b), the one where the noise is recognizable, suppose you have something that has fairly high symmetry -- for example, consider a sphere (either a physical one, or some sort of effectively spherical subspace of the entire space of dynamics of the whole system). Suppose it's pretty strongly coupled to the rest of the system, so lots of thermal noise gets into it and out of it, but suppose that for some reason in the dynamics (maybe the main coupling is via a uniform magnetic field, or something, so it's inherently antisymetric) the noise consists only (or at least almost entirely) of odd spherical harmonics on the sphere -- ones that are antisymmetric under swapping the north and south poles of the sphere. Suppose the archaic conceals the quantum system they want to create entirely in the even spherical harmonics of the sphere. Then (to the extent that the sphere has perfect spherical symmetry), that's perfectly orthogonal to all the noise modes, and thus unaffected by them. So if the sphere has really perfect symmetry, they can just ignore the noise. Or, if (as seem more likely), the sphere isn't perfectly symmetric, just very symmetric, they can put in some sort of damping or error correction mechanism that rapidly damps or cancels the odd harmonics (before their slight crosstalk from those to the even ones due to the less-than perfect symmetry of the spere can cause a problem), while leaving the even harmonics alone. Either way, now the quantum subsystem of even harmonics is sufficiently well isolated from the main system to be usable for quantum computing or the sorts of tricks that you're discussing.

Basically in each of these cases, what the archai is doing is identifying some small (perhaps subtle and inobvious) subset of the dynamics of the big messy system that is, for some (again, perhaps subtle and inobvious) reason, mostly or almost entirely decoupled from the rest of the system, and perhaps also subtly engineering the dynamics in a way that greatly increases the decoupling.

So I would say the answer to "can an archai do this at will across a wide area of a general, big, messy, not previously chosen environment?" is "probably not, unless they get lucky or ingenious". But if the question is "can an archai locate some small or subtle location/structure or other thing somewhere inside general, big, messy, not previously chosen environment where they do have the opportunity to do this, or can they prearrange the ability to do this, in a subtle way that a modosophont would never figure out in advance?" then I strongly suspect the answer is going to be "almost always (though possibly not in a way that happens to be useful for their current purpose)". In general, the situation here is complex enough (and incomprehensible enough to a modo reader) that an author can probably have it happen or not happen as they wish for plot reasons. The challenge for an author is coming up with a plausible sounding collection of buzzwords if you feel you have to describe to the reader *how* the archai did it -- I would suggest avoiding that if possible: leave it a mystery or speculation if you can. If you really want to try, the key elements here are a small subsystem, that in some way is weakly coupled to or blocked from all the noise in the big system (and similarly is unobservable by observers in the big system), or can be engineered to be so, probably for subtle reasons involving symmetry or topology or some mathematical buzzword like that (ideally one most readers have heard of but know little enough about that you can snow them successfully).

Also, consider the manus dei effect (which I assume involves a lot of tiny imperceptible magmatter processors and effector field generators, and so forth, and requires very intense surveillance and very close supervision from an archai to control) -- that could certainly engineer the sort of subsystem I describe above into the apparently-normal location and arrange for it to stay isolated for as long as was needed. Or the quantum system could just be a small amount of magmatter, which inherently has negligible interactions with the (non magnetic) real matter it interpenetrates. Or it could just consist of quantum computronium specks distributed amoung the nanites of the local angelnet. So yes, if you're willing to throw enough clarktech at this problem and get an achai personally involved, you they can almost certainly fake it -- just not where a modosophont is directly watching (unless the archai has quietly virtualised the modo, are now running them on quantum computronium, and are going to manus dei reengenerate them afterwards, Da'at style -- in which case they can do whatever they want, including taking them on a directed tour of the inner workings of a helium atom).

That's not really a problem unless you want to invent an entire quantum S-level terminology and then apply it to every mention of an S-level across the setting/ ;)

It is generally understood (or should be) that the toposophic levels as we currently describe them are a greatly simplified shorthand version of the 'real thing' that is actually used by professional Toposophic researchers and professionals inside the setting.

If one outcome of our discussions here is an article or article modification to add quantum terminology into the pages on toposophy that would be perfectly fine - just as long as (as mentioned above) we don't have to rewrite every mention of an S-level as a result:P

Completely agreed - no, this is more like the distinction between a slow god and a fast god -- sometimes important, but not important enough for widespread use of the notation for it (though doubtless in the venue the would be a notation for it, and our version of the encylopedia could mention that in a suitable article).

What I'd suggest is that the article about quantum sophonts say things like:
* Unless there is some very good reason to assume otherwise, it's a safe bet that most S3's and above are partly-quantum if inorganic, and even organic ones will have at least quantum coprocessors -- indeed, at this level being fully classical would normally be regarded as a form of antitransavancy.
* However, due to their sheer size, making archai fully-quantum is an increasingly difficult engineering challenge at higher toposophics levels. Also, because classical computronium generally runs full-classical algorithms a lot faster for quantum computronium would (since it doesn't have a lot of unnecessary quantum-error-correction overhead built in, and often can run at a higher temperature), for many problems where use of quantum algorithms at the top level of processing (rather than in subroutines) isn't useful, being fully-quantum is often an inefficient design. Thus archai are far more likely to merely have some fully quantum specialist subnodes -- perhaps large ones, than to actually be fully-quantum themselves.
* In high-tech societies even most baselines have a quantum coprocessor either implanted or available in their exoself or via ubiquitous computing, and this is almost universal among superbrights, while S0 vecs and other forms with inorganic comoutronium are almost invariably going to at least have a quantum coprocessor, and will generally be partly-quantum (unless they were built specifically for very high temperature or very high radiation environments, where the level of shielding required for this may become too burdensome)."
Then we let people assume that (unless we're talking about the Silk God) S4 presumably means SI:4(q2) or whatever the long notation we end up with looks like.

Also, this probably also should be mentioned in the sections on technotelepathy and baroquification, since it adds some complications there. For example, its basically impossible for a completely classical archai (if such a thing existed) to do always-accurate technotelepathy on a fully-quantum being, even one several toposophic levels lower, and probably hard to do it on one that's even partly-quantum. But a partly-quantum (or even merely quantum-subprocessor) S6 that has at least fully-quantum S2 specialist subnodes (which is a safe bet) is capable (up to the no cloning theorum and the existence of true quantum randomness) to doing technotelepathy on a fully-quantum S1. At the risk of oversimplifying, the more quantum you are, that also acts like free baroquification against anyone less quantum than you, and for the specific case of a fully-quantum defender vs. a fully-classical technotelepathist, that can act as extremely effective baroquification, typically enough to overcome several levels of toposophic difference -- which presumably means that fully-neoclassical transapients would be at a major disadvantage (enough that for a high transapient being fully classical would probably be considered to be a form of antitransavancy), and thus be rare.