I suck at physics, sorry for this stupid question.
This question came to mind after reading the New Scientist article on how our 3D physics may be equivalent to 2D physics.
This got me thinking – to what extent is our traditional 3D spatial universe, plus a time dimension that goes in one direction, is based on our human perceptions?
IOW, if there is no difference between our 3D universe and a 2D universe on paper, does that mean there can possibly exist a species of alien wherein the only perception of universe is in 2 spatial dimensions? (Or, higher dimensionality than 3, if you take the purported 11 dimensions of string theory in account.) To what extent is our perceived number of spatial dimensions, grounded in “reality” versus evolutionary bias?
I suppose one can’t rule out aliens that perceive the two-dimensional underlying space in a holographic universe, but such aliens would be so different from us that we probably wouldn’t even recognize that they exist, much less that they’re intelligent creatures, and likewise they wouldn’t recognize us.
Wandering into GD territory, that’s my answer to the Fermi paradox – that totally unrelated species of aliens simply cannot communicate with each other, because everything is just that grossly distorted through our physical senses.
I’m more interested in what extent spatial dimensionality is tied into our sense, though. Is there any reason beyond the circumstances of our evolution and minds that, generally, our universe should be measured in 3 spatial dimensions?
Impossible to say. If our senses are being fooled by a holographic effect then it could be possible for a being or technology to only experience 2D. Not sure how they would come about that way as light sensing cells will experience the illusion of 3D as they are ‘looking’ directly at the hologram. I guess you would have to presume a pretty odd being with a sensory system we cant describe, which kinda puts this in the ream of “who knows.”
It’s not a matter of evolution. Such hypothetical 2-D entities could not possibly share an evolutionary history with 3-D entities such as ourselves. They wouldn’t even be made up of atoms or subatomic particles we’d recognize, and whatever it is they’re made of would be equally alien to us. The closest you’d even find to them in science fiction would be the “hyperintelligent shade of blue” that Douglas Adams joked about, but they’d be significantly weirder yet than that, even (and vice-versa us, from their point of view).
could a sort of an answer to this question be obtained empirically? E.g. could a few humans be placed into a 2D visual virtual reality environment and told to play a Life in Flatland role playing game?
Well, the bigger question I am asking is – what evidence is there that our universe is properly conceived as three spatial dimensions? Yes, we can point to a cube and show each other, here’s the X, Y, and Z axes, but if the mathematics and physics show that the universe can be represented equivalently in an arbitrary number of spatial dimensions, does this mean that the way we conceive these X, Y, and Z axes are an illusion created from our physical senses?
Using the holographic universe example – these hypothetical 2D-perceiving creatures, presumably, would be made up of the same elements and building blocks as the rest of us – but could their sense of perception would be radically different such that they wouldn’t perceive the “Z” dimension on the same cube?
Most non-mathematicians aren’t aware of the ways in which seemingly unrelated and totally different mathematical representations are equivalent to one another. This oddity runs over into physics. The equations of four-dimensional space-time can be written equivalently as three of space and one of time or as three of time and one of space. The compact dimensions needed in string theory are equivalent to Calabi-Yau manifolds.
So saying that our three spatial dimensions can be mathematically equivalent as encoded onto a surface of a volume of two dimensions probably doesn’t mean that much to our everyday senses. Our universe does have three dimensions of space and one of time. How they get expressed mathematically is interesting for exotic problem solving, but doesn’t have much to do with living humans.
Heck, I don’t even have an iPhone. I’m not likely to lose a whole dimension just because it’s the hip, cool, new thing.
Aha… now we’re getting closer to the root of the question that I am not expressing very well. My understanding is that equivalent, is, well, equivalent. What is your basis for making this statement:
… when there are other, possible equivalent models in mathematics and physics? Because, to my very limited understanding, if the universe can be encoded equivalently into other numbers (or types) of dimensions, then the way we perceive the universe as 3 spatial and 1 temporal dimensions comes the bias of our physical senses. What am I missing?
>Well, the bigger question I am asking is – what evidence is there that our universe is properly conceived as three spatial dimensions?
Im sure you can devise a cosmology described as having any number of dimensions and make it mostly self-consistent and logical the same way we can use different bases of numbers in mathematics. Because we cant have perfect knowledge your question is probably unanswerable. For instance, our 3+1 (dont forget time) dimension system isnt perfect and probably willl never be. A competing 2+1 or whatever system may have the same amount of problems. I’d think there’s a range where it doesnt make sense, say a 1 dimension or 100,000 dimension universe.
3+1 may just be the most convenient for thinking beings and produces the least amount of error and aberrations. Not sure how to test that without someone sitting down and creating a competing 2+1 system and comparing the two.
I’m with OP. If it’s true that the 2D and 3D ways of describing physics are equivalent, then I can’t see any reason there might not evolve creatures that percieve the universe two dimensionally rather than three dimensionally.
I say I “can’t see any reason,” but to be clear, I can imagine possible reasons. Maybe one of the two equivalent models is more computationally tractable or something.
But it’s not true, I think, that any creatures percieving things according to the 2D model must necessarily be physically extremely different from us to the point of being practically unrecognizable as thinkers or even as physical objects. I’m not even sure why people on this thread think that would have to be so.
Physics is math at its root. But the practice of physics is experimental. We use lasers and GPS and other stuff that depends on physics in an everyday world of three spatial dimensions and one time dimension. You might say that the math underlying it can be expressed in a variety of ways but how does that impact anything?
We have evolved to see a certain tiny span of electromagnetic radiation because that’s the band that the atmosphere happens to be transparent to and is of the right size for physical objects like eyes to react to. We are tied to EM that way, but it doesn’t depend on us.
We have similarly evolved because the constants of the universe are of certain dimensions that allow physics to work to eventually create an environment in which human life can form. As far as we can tell, this was true before humanity or life on earth existed and will continue to do so.
I suppose you could argue that this is all perception, but that doesn’t seem to be true. Our physical world takes on a certain form that we perceive and try to account for mathematically. But math can take on any number of equivalent forms. Our physical reality doesn’t appear to work that way. It has one fixed form. I doubt that any human mind could even conceive of what a being on a two-dimension surface would be like, any more than we can visualize how the axis of a fourth spatial dimension intersects the others. We literally can’t see it, even theoretically. Representing it mathematically is trivial. Math isn’t physics.
I thought the idea with the “holographic universe” thing was that the equivalency of the mathematical models implies that physical observations can’t distinguish between them. In other words, if two mathematical models are equivalent and each accounts for all observations, then observation can’t decide which model is the correct one, which for all intents means there is no unique correct model.
(ETA: That’s not to say any of the models on hand right now “account for all observations” of course. I’m just discussing what it would mean for two mathematical models in physics to be equivalent.)
There may be computational advantages to certain representations. For example, some calculations are easier to do in polar coordinates instead of cartesian coordinates.
So it might be that evolution will tend to drive creatures toward 3-d mental representations because those are more useful for the sorts of computations one needs to do quickly in survival situations.
Ultimately, we perceive three dimensions because the particles which make up our body are arranged in a three-dimensional space. The holographic model doesn’t say that that three-dimensional space isn’t real, or that the particles within it don’t exist, but rather that that three-dimensional space and everything in it are manifestations of phenomena in a 2-D space. Effectively, the 2-D space is a completely different universe than the one we live in. By way of analogy, I could take a piece of paper and write on it a description of a room. There might be (and probably are) organisms that live on the surface of that piece of paper, but those organisms would not perceive the room that I wrote about. If they were extremely intelligent, the paper-dwellers might deduce that the ink features they observe have meaning, and might conceivably even be able to learn what that meaning was and read the description of the room, but that wouldn’t mean that the room is the world they’re living in.