An alien intelligence thought experiment

[hatch22]

Hi everyone. I'm new here. I debated about whether this post belonged in this thread or the "Other Scifi" thread, but I think the focus on logic and science makes it reasonable to place here.

I've been doing some world building for a science fiction setting. I've got some really strange aliens, and I'm trying to figure out how they might think. They are ultimately a plot device, so there are somewhat arbitrary constraints on them, but I think given the constraints we can reason about them as a thought experiment, in keeping with the non-fictional nature of this forum.

One of the themes I'm exploring is the nature of boundaries and ways to blur them or put them in sharp relief by a change in perspective. For my aliens, I started off by trying to come up with a strange (to us) way to approach math and physics that wasn't so alien that I couldn't reason about it. I came up with two related ideas:

First, approach the strangeness of particle-wave duality from the other direction. Humans are generally good at thinking in terms of particles and infer waves from the effect of energy propagation through particles of matter both large (e.g. groups of molecules) and small (electrons). So these aliens find waves intuitive and infer particle-like qualities through observing the complex interactions of waves.

Second, approach problems of a logical or mathematical type from the context of the frequency domain rather than the time domain that we find so intuitive. Their math is some kind of Fourier-like analysis. So the concept of addition and subtraction might be understood in terms of wave superposition. Multiplication would perhaps be understood as convolution. These are only suggestions to get your minds going. Other ways of thinking about math or logic are fine.

So for this thought experiment, the alien intelligences must:
1. Find waves intuitive, and particles more difficult to think about, though not necessarily completely counter-intuitive.
2. Perform math and logical thinking in some fashion that takes into account #1 above (e.g. they probably have difficulty with the idea of integers and counting).
3. In some way be able to perceive physical reality in terms of waves and energy rather than distinct points in space and matter.
4. Be able to find enough common ground in the understanding of the physical world to make communication with humans possible but difficult.

Given the above constraints:
1. How might an alien intelligence perceive the world physically (sensory apparatus)?
2. How might an alien intelligence perceive the world philosophically (how it thinks about reality)?
3. What axioms of mathematics or logic might they adopt as useful (related to 1 and 2 above)?
4. How might they go about trying to communicate with humans, and/or conversely how might we go about trying to communicate with them?

Please tackle any of the above questions you like. For question 1 keep in mind that whatever senses the aliens possess do not (for my purposes) need to be physically realizable by humans. They just need to not violate any known laws of physics. Violations of principles like locality and positing the existence of additional spacial dimensions like in some string theories or M-theory is fine. I'm looking for explanations that do not violate physical laws, not explanations that are empirically testable by humans. Clarke's third law and all that. I'm after verisimilitude here, not total realism. The other questions are more important in terms of how they see the world and do logic and math, but since perception of the physical world affects what is intuitive, I felt I should include it.

Looking forward to your thoughts.

[Kuroneko]

That's a larger than usual stretch, simply because the universe is particle-like both at the fundamental and large scales. If one makes a human with eyes that are just one order of magnitude higher sensitivity, that person would be able to perceive individual photons in very dark environments--energy arrives in particles, not waves. So ultimately, pretty much the only origin that could make sense for them is an intentional experiment by some prior race [1] that imposed such a mental model on them. But perhaps the Stargliders got bored one day, so let's the question of how they got to be that way alone for now.


Historically, our theoretical mathematics began with geometry, as we find points and lines very intuitive concepts. We model waves as functions--relationships between points. Getting there took quite a bit of abstract development, which we can simply reverse [2]. So what kind of mathematics follows from treating not points, but (what for us is) entire functions as primitives?

One reasonable answer is straightforward: their analogue of Euclidean geometry is what we would call in mathematical jargon a "torsor over a Hilbert space", or rather some specific case of it (if they primarily 'visualize' three-dimensional waves, perhaps what we would identify as L2(R3)). That's not to say that this beast is easy for normal people to understand; the point of the thread is that it isn't. But I hope to show that for a being that finds 'waves' as immediate in its mental visualization as we find 'points', that kind of construct becomes very natural.

So what can one do with waves? One can add or subtract them, intensify them [3], and tell how much of one wave is "in" another. To be a Hilbert space, the collection of such waves must be complete in the sense of not having 'holes' [4]. Finally, the 'torsor' part is equivalent to saying "you see the origin--this special null wave, which you can add to anything and not change it? forget about it." Euclidean space doesn't come with an origin.


Likely consequences of having such a mental model:
[*] Quantum mechanics is extremely intuitive: the calculations are all in a Hilbert space (or rather, a tightly related concept).
[*] Idealized points are not impossible to think about, but not very intuitive, or at least not particularly significant. That's because "any" space of points corresponds to a commutative C*-algebra, but any C*-algebra is representable as a collection of operators on a Hilbert space, and the noncommutative ones have no points. So having "points" would be seen as being a particular special case that's not at all necessary for visualization. Downside: ordinary spatial reasoning may be very inefficient.
[*] Ordinary calculus might be harder. On the other hand, differential noncommutative geometry may be is much easier in general, which contains calculus as a (commutative) special case.
[*] Large chunks of abstract algebra become easy. Being able to visualize spaces with no points would be an interesting ability.

---
[1] Evolving in a primarily liquid environment is insufficient, because evolutionary pressure would only favor amorphous forms where the resources are not sufficient to reasonably evolve sapience.
[2] That in itself introduces quite a bit of anthropocentrism, but I have a difficulty conceptualizing humanly-unimaginable things.
[3] This would be a bit backwards from their point of view. Just as we originally got our real numbers from considering geometrical relationships, they probably would get their concept of real numbers from such relationships (most likely projections) between waves.
[4] I'm going to skip formal completeness in favor of brevity--anyone can look up the full definition should they be so inclined. The last part corresponds exactly to how the rationals are (geo)metrically incomplete, and hence the need for irrationals. The corresponding statement here would be that if one has a sequence of waves getting closer and closer to each other, then the sequence gets closer to some other fixed wave.

[hatch22]

@Kuroneko, thanks for the reply. I like how you brought out useful implications of thinking in terms of waves.

Torsors over Hilbert spaces are definitely a good fit. My background is in engineering (undergrad, physics minor) and computer science (working toward Ph. D.), but I have worked with Geometric Algebra (a kind of Clifford algebra) to model 3D solids and physical interactions in a R4,1 Minkowski space (a homogeneous 5D vector space with a Minkowski metric), so I can follow you, but probably only to a first approximation.

As far as the aliens' origin is concerned, I'm perfectly fine with them being an artificial race. That opens up some interesting plot possibilities. That said, I've heard it argued that sapient intelligence could develop on something as bizarre as the magnetic fields produced by the plasma on the surface of a star. I know this isn't very likely, but in science fiction you can get away with a lot if you describe it well. If you've any ideas as to any kinds of strange environments could evolve such creatures "naturally" (even though we all know the likelihood of such a thing is practically zero), I'd be interested to hear it. For example, could such creatures evolve in a plasma environment and be able to "read" magnetic waves? Just a thought.

One thing you might clarify for me. What exactly do you mean by "ordinary spacial reasoning" and to what degree would it be inefficient. In other words, how might they try to reason about space? I could see this as an important part of answering question 4.

You've definitely done what I am hoping people will do, take the starting premises and see where they might lead. To that end you have answered question 2 fairly well and touched on questions 1 and 3. Any takers for the other questions? Any questions for me to clarify anything? I look forward to more good insights.

[Kuroneko]

That said, I've heard it argued that sapient intelligence could develop on something as bizarre as the magnetic fields produced by the plasma on the surface of a star.

Sounds extremely dubious. In general, substantive life processes, whatever form they take, are going to require an environment that takes low-entropy enegy input and give high-entropy energy output. This works well on a planet around a star due to the temperature difference:
[input] few high-energy photons ----> lots of low-energy photons [output]
So in addition to rather extreme temperatures and want of material resources, the environement is also very entropically unfriendly to life.

What exactly do you mean by "ordinary spacial reasoning" and to what degree would it be inefficient. In other words, how might they try to reason about space? I could see this as an important part of answering question 4.

Inefficient in the sense that their mental machinery would do more computation that would be necessary if represented in another way. It doesn't necessarily mean they would be bad at it (it's quite possible for them to be better than humans). Say you have a Hilbert space of "waves", with operators on it forming an algebra. A point is an algebra homomorphism to the base field of the Hilbert space, or, in slightly less obtuse language,
-- A point is collection of operations on waves that in some sense 'acts like' your scalar field.
A location would be quite literally represented by operations on waves. Distances between points would be represented via another contraption called the Dirac operator, and so on.

And that's a good reason to believe that such a species would have been artificially designed tp think in that manner. It's certainly possible do things that way, simply because a particular case is provably isomorphic to ordinary Euclidean geometry, and with enough mental computational power possible to do it fast, but it's very hard to believe that this kind of model could evolve naturally, rather than the result of someone's crazy experiment in mind-building: not immediately abstracting location, since it would be such a a basic survival skill for any would-be sapient species, requires some intentional mental wiring to the contrary.

Communication would probably require starting from scratch: here's our rules of logic, here's are some laws of physics, here's a hydrogen atom to establish scale, etc. Some possibility as to their reasoning may be that they find quantum logic the most 'natural' (this once again can be naturally built out of operations on waves).

---
Of course, there may be alternative interpretations of what 'thinking in waves' might mean. I just picked what I see the most robust one in terms of what could be reasonably said about such thinking. I think it's probably the most provocative one.

[hatch22]

Sounds extremely dubious. In general, substantive life processes, whatever form they take, are going to require an environment that takes low-entropy enegy input and give high-entropy energy output. This works well on a planet around a star due to the temperature difference:
[input] few high-energy photons ----> lots of low-energy photons [output]
So in addition to rather extreme temperatures and want of material resources, the environement is also very entropically unfriendly to life.

I get you. I'm just trying to come up with something creatively different that isn't totally beyond the realm of possibility. Here is another creatively wacky idea. Feel free to bash it to smithereens if you think it is too absurd, but I'm trying to think outside the box. Let's say that gravitons exist. Let's also say that, at least for this hypothetical world similar to ours, that some version of string theory or M-theory is true that allows for a 4th spacial dimension (macro scale). Alien's existing in a 4th dimensional position "above" or "below" our D-brane would only have gravitons leaking through to work with (as far as we could tell). Assuming the existence of some kind of unobtainium in the 4th dimension that would allow the use of gravitational waves as an energy source (e.g. something vaguely like a Weber Bar), could being located near a strong gravitational source provide a similar scenario to a planet absorbing a sun's photons? Both photons and gravitons are (thought to be) massless and convey energy:
[input] few high-energy gravitons----> lots of low-energy gravitons [output]?

Again, I realize this is very hypothetical on multiple levels, I'm just trying to think unconventionally. My setting already allows for the reality of a 4th spacial dimension for unrelated reasons (don't worry it's not FTL travel), and it's not supposed to be our world, just one with compatible physics. So the question would be if there is some intrinsic reason that this couldn't physically work given the existence of a 4th spacial dimension and said gravity powered (bio)technology.

A location would be quite literally represented by operations on waves. Distances between points would be represented via another contraption called the Dirac operator, and so on.

Can you think of any practical limits on what this would mean in terms of interacting with humans or physical substances in general? How might a human "look" with this kind of representation? Would the complicated de Broglie wave of a solid thing still give some basic information in terms of what it is made of? Some kind of wave "fingerprint" for recognition?

Communication would probably require starting from scratch: here's our rules of logic, here's are some laws of physics, here's a hydrogen atom to establish scale, etc. Some possibility as to their reasoning may be that they find quantum logic the most 'natural' (this once again can be naturally built out of operations on waves).

Quantum logic sounds like a good option to me. It is distinct from the propositional logic most people are accustomed to but not totally alien, just fuzzier. I would think the simplest starting point might be some kind of three valued Łukasiewicz logic of false/don't know/true that roughly corresponds to the concept of less/equal/greater.

Thanks for your input so far. Any other ideas? Is there another form of math that would be unintuitive to humans but not require such on odd mental model?

[Starglider]

I was tempted to speculate on this (implementing cognition using wavefunction descriptions and transforms) but I'm not sure that I understand the relevant maths well enough to avoid making elementary errors. However;

Quantum logic sounds like a good option to me. It is distinct from the propositional logic most people are accustomed to but not totally alien, just fuzzier. I would think the simplest starting point might be some kind of three valued Łukasiewicz logic of false/don't know/true that roughly corresponds to the concept of less/equal/greater.

This conception of 'quantum logic' is not anything special. Multi-valued and probabilistic logic have been around for a long time. Software that can actually manipulate complex probability distributions over variables, or conditional distributions over multiple variables, is relatively recent but still nothing special. The human brain almost certainly uses a highly informal version of this along with an effectively 'holographic' information coding scheme.

[Kuroneko]

Assuming the existence of some kind of unobtainium in the 4th dimension that would allow the use of gravitational waves as an energy source ... could being located near a strong gravitational source provide a similar scenario to a planet absorbing a sun's photons?

Unlike the electromagnetic field, a spherically symmetric gravitational field can carry no gravitational waves, by Birkhoff's theorem (a mathematical result of GTR analogous to Newton's shell theorem). So the only way to get a graviton source from a star would be using using sharp inhomogeneities in the star, and the weakness of gravity requires them to be extremely violent.

My setting already allows for the reality of a 4th spacial dimension for unrelated reasons (don't worry it's not FTL travel), and it's not supposed to be our world, just one with compatible physics. So the question would be if there is some intrinsic reason that this couldn't physically work given the existence of a 4th spacial dimension and said gravity powered (bio)technology.

Gravitational interactions are far too weak. But if this is the kind of world you're describing, then it's simply better not to try to explain it explicitly using physics from this one. I think in most cases, Clarke's third law is less of a justification and more of literary advice: trying to inject too much physics into exotic fictional phenomena virtually guarantees the author shooting himself in the foot. Much of the time, "it just works" is best.

Can you think of any practical limits on what this would mean in terms of interacting with humans or physical substances in general? How might a human "look" with this kind of representation?

If they're higher dimensional, the easiest way to have an understandable perception that's nevertheless far removed from human ones is as three-dimensional distributions, perhaps qualified by some other properties (as we would, say, color). The practical issues of interaction wouldn't really be in getting the information they want but communicating it effectively. For example, instead of thinking of the distribution as in terms of values at different locations, instead as relationships between some "preferred basis" of waves (this is pretty much the generalized Fourier transform idea). Or some more more abstract (for us) algebraic manner.

Would the complicated de Broglie wave of a solid thing still give some basic information in terms of what it is made of? Some kind of wave "fingerprint" for recognition?

Wait, do you mean somehow perceiving the quantum state directly, rather than just having an analogous mental visualization? Any interaction with a macroscopic system is a kind of measurement, so what would get extremely messy and with very dubious positive results.

[hatch22]

Unlike the electromagnetic field, a spherically symmetric gravitational field can carry no gravitational waves, by Birkhoff's theorem (a mathematical result of GTR analogous to Newton's shell theorem). So the only way to get a graviton source from a star would be using using sharp inhomogeneities in the star, and the weakness of gravity requires them to be extremely violent.

My setting already allows for the reality of a 4th spacial dimension for unrelated reasons (don't worry it's not FTL travel), and it's not supposed to be our world, just one with compatible physics. So the question would be if there is some intrinsic reason that this couldn't physically work given the existence of a 4th spacial dimension and said gravity powered (bio)technology.

Gravitational interactions are far too weak. But if this is the kind of world you're describing, then it's simply better not to try to explain it explicitly using physics from this one. I think in most cases, Clarke's third law is less of a justification and more of literary advice: trying to inject too much physics into exotic fictional phenomena virtually guarantees the author shooting himself in the foot. Much of the time, "it just works" is best.

OK, scratch that then. I just wanted to see how far I could stretch things. I want these aliens to be as plausible as possible and very alien to us within the limits of their role in the story, but it's perfectly fine if they are artificial beings. I may even be able to use their artificiality to my advantage in the story. So in this case I'll just leave the particulars hidden and use "It just works" as you suggested. After all, there is still an awful lot we don't understand about the nature of reality.

If they're higher dimensional, the easiest way to have an understandable perception that's nevertheless far removed from human ones is as three-dimensional distributions, perhaps qualified by some other properties (as we would, say, color). The practical issues of interaction wouldn't really be in getting the information they want but communicating it effectively. For example, instead of thinking of the distribution as in terms of values at different locations, instead as relationships between some "preferred basis" of waves (this is pretty much the generalized Fourier transform idea). Or some more more abstract (for us) algebraic manner.

This sounds good to me. Now I just have to figure out if a particular basis makes more sense for general use than others, or if a preferred basis would be communicated as part of the language for each interaction. In other words is there any particular basis that would make a good default?

Wait, do you mean somehow perceiving the quantum state directly, rather than just having an analogous mental visualization? Any interaction with a macroscopic system is a kind of measurement, so what would get extremely messy and with very dubious positive results.

Yeah, this was me talking without thinking it through. I was thinking in terms of how they might identify different elementary particles or atomic elements, but of course this probably wouldn't work at macro scales. Sorry for any confusion. What I'm going for is a mental model based on waves, not a directly perception of the quantum state. That said, de Broglie waves have been demonstrated for things as large as small molecules, and it's speculated that they would exist for any isolated object, so I don't think the idea is totally crazy.

This conception of 'quantum logic' is not anything special. Multi-valued and probabilistic logic have been around for a long time. Software that can actually manipulate complex probability distributions over variables, or conditional distributions over multiple variables, is relatively recent but still nothing special. The human brain almost certainly uses a highly informal version of this along with an effectively 'holographic' information coding scheme.

Thanks for chiming in Starglider. You are right that we probably use something like quantum logic all the time and it's nothing new. It's just that most of the philosopher types I know generally use plain old vanilla propositional logic, and many of them have found this kind of multi-valued logic a bit confusing, at least at first. I wasn't trying to imply that multi-valued logic was anything new, just that many people I know would not find it immediately intuitive. After all, something is either true or false, right? Degrees of "trueness" and "falseness" can be confusing to people who have never seen it before.

[Gil Hamilton]

Would not the Equivalence Principle come into play? When you started getting beyond the scales of de Broglie wavelength for a given thing, quantum mechanics just rolls into classical mechanics and classical mechanics likes particles. Quantum mechanics is fantastically useful stuff for explaining alot of phenomena, but as Kuroneko says, the universe on a macroscale behaves like its made of particles.