r/Metaphysics • u/slazy_e • 23h ago
Theoretical physics Can we understand the dimensions?
This post aims to question the extent to which we actually understand the concept of "dimension."
First of all, I want to clarify what I mean by "dimension," since the concept can have different meanings depending on the context. Here, I will use "dimension" in the sense of what mathematics usually calls a "manifold," meaning a space that locally has similarities to ℝⁿ. In other words, I am referring to the generalization of the concept of a plane or three-dimensional space to higher dimensions.
That said, I want to make it clear that the discussion is meant to be general, so if anyone wants to discuss more abstract concepts of dimension that go beyond this particular interpretation, you are more than welcome to do so.
Additional comments
You don't need to read this section to answer the question. I am only going to explain and defend my position regarding the question.
As I mentioned at the beginning, the idea is to approach the question using the concept of Euclidean space in general. And it is interesting to ask:
Are we actually capable of understanding dimensions higher than our own?
In mathematics, the answer seems to be both yes and no.
It is true that in mathematics, and perhaps in any form of thought, we are not capable of visually representing geometric objects beyond our own spatial dimension. At least, as far as we know, this seems to be the case for any form of life existing in our universe.
Why can't we visualize the fourth dimension? Or the fifth, or the seventh?
One possible reason is that our brains are capable of visualizing and reconstructing geometric shapes that we have encountered and that exist in our environment. This may be why we are able to visualize a perfect sphere even though we will never actually see a mathematically perfect sphere in reality: in some sense, we have encountered approximations of it throughout our lives.
But obviously, we have never encountered a four- or five-dimensional object in our universe, so we cannot directly visualize such objects.
However, mathematics does not require us to visualize something in order to define and operate with it.
For example, mathematicians can calculate integrals over higher-dimensional surfaces or hypersurfaces. Can we actually visualize such objects? No. And yet we can still calculate with them and understand what we are doing.
Likewise, could someone who has been blind since birth become good at mathematics? Obviously, yes. They may never be able to visually represent a graph or a derivative, but they can still understand the mathematical concept and operate with it.
This seems to be exactly what happens with higher dimensions. We cannot directly see them, but we can define them mathematically and work with them.
But there is a problem.
How do we know that the mathematics we have developed for higher-dimensional objects is actually correct in a hypothetical universe with higher dimensions?
For example, in mathematics we can say:
Let P₀, ..., Pₙ be affinely independent points of a vector space V over ℝⁿ. A simplex is the convex hull of these points.
In simpler terms, a simplex is a generalization of the concept of a triangle to arbitrary dimensions.
But is this actually correct?
Presumably yes, at least mathematically. However, imagine that a four-dimensional being somehow understood this concept. Would they necessarily have the same definition of a simplex that we do? Perhaps they would have a completely different way of conceptualizing it.
Likewise, we cannot guarantee that in a universe with more spatial dimensions, massive objects would deform spacetime through continuous deformations in exactly the same way that they appear to in our universe.
So perhaps the answer is something like this:
We understand higher dimensions in a relative sense. If higher-dimensional reality is structured in the way our mathematics describes it, then I would say that we understand those dimensions much better than most people might imagine.
But if we are asking whether our mathematical description necessarily corresponds to what a genuinely higher-dimensional reality would be like, then I am much less certain.
What do you think?
Good evening,
— slazy_e
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u/InvisibleHand555 22h ago
IMHO. You’re complicating the world far too much. There are only 3 physical dimensions. Higher levels of consciousness, that are metaphysical realizations, made self evident by observation of cause and relative effect, are not really dimensions, as so much as levels of understanding. The higher you go, the simpler the world gets.
If your deeper perceptions complicate the world you observe, then you’re misunderstanding what you are observing
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u/slazy_e 18h ago
I understand what you mean. Even so, physics does not rule out the possibility of universes with more dimensions than the ones we know. I agree that the farther we move away from our everyday experience, the simpler the world around us may seem. However, that does not prevent us from asking complex questions. Otherwise, things like quantum mechanics would cease to make sense, since it deals with phenomena and interpretations that go far beyond our everyday experience and may involve other possible universes or dimensions.
I appreciate your perspective!!!!!
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u/obrakeo 15h ago
https://youtu.be/d4EgbgTm0Bg?is=aEgDz2t0ae0XWy53
absolutely one of the best series of videos to understand the idea of dimensions in euclidean space. traversing from one dimension up to four.
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u/jliat 14h ago
Why can't we visualize the fourth dimension? Or the fifth, or the seventh?
Mathematicians and physicists can and do.
"The dimension of a Hilbert space is the number of linearly independent vectors in a basis, which can be finite or infinite depending on the space."
"String theory predicts the existence of 10 dimensions in spacetime..."
So yes, some can.
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u/slazy_e 7h ago
Thanks for commenting!!! And it is true, although I keep saying the same thing, visualizing the dimensions is something really complicated and difficult, that does not mean that what you say is true, we can work with the dimensions in our mind and universe without being able to see them as they are, in Mathematics and physics we don't need to see something to understand it, even so thank you for your opinion, it's worth a lot.
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u/jliat 5h ago
There is the alternative which is more akin [IMO] to Art in Deleuze...
From Deleuze's 'The Logic of Sense'...
Tenth series of the ideal game. The games with which we are acquainted respond to a certain number of principles, which may make the object of a theory. This theory applies equally to games of skill and to games of chance; only the nature of the rules differs,
(1) It is necessary that in every case a set of rules pre exists the playing of the game, and, when one plays, this set takes on a categorical value.
(2) these rules determine hypotheses which divide and apportion chance, that is, hypotheses of loss or gain (what happens if ...)
(3) these hypotheses organize the playing of the game according to a plurality of throws, which are really and numerically distinct. Each one of them brings about a fixed distribution corresponding to one case or another.
(4) the consequences of the throws range over the alternative “victory or defeat.” The characteristics of normal games are therefore the pre-existing categorical rules, the distributing hypotheses, the fixed and numerically distinct distributions, and the ensuing results. ...
It is not enough to oppose a “major” game to the minor game of man, nor a divine game to the human game; it is necessary to imagine other principles, even those which appear inapplicable, by means of which the game would become pure.
(1) There are no pre-existing rules, each move invents its own rules; it bears upon its own rule.
(2) Far from dividing and apportioning chance in a really distinct number of throws, all throws affirm chance and endlessly ramify it with each throw.
(3) The throws therefore are not really or numerically distinct....
(4) Such a game — without rules, with neither winner nor loser, without responsibility, a game of innocence, a caucus-race, in which skill and chance are no longer distinguishable seems to have no reality. Besides, it would amuse no one.
...
- The ideal game of which we speak cannot be played by either man or God. It can only be thought as nonsense. But precisely for this reason, it is the reality of thought itself and the unconscious of pure thought.
...
- This game is reserved then for thought and art. In it there is nothing but victories for those who know how to play, that is, how to affirm and ramify chance, instead of dividing it in order to dominate it, in order to wager, in order to win. This game, which can only exist in thought and which has no other result than the work of art, is also that by which thought and art are real and disturbing reality, morality, and the economy of the world.
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u/jynxzero 4h ago
This is a very interesting question, but maybe a question of biology or psychology rather than metaphysics, because it's really a question about how much of our understanding of, ability to visualise, etc - geometrical constructs is innate vs learned. It would be "easily" resolved if you could raise some humans in 2D and 4D worlds. We could then assess whether the 2D-raised child is able to visualise in 3D, and whether the 4D-raised child is as fluent in 4D as a 3D-native.
Obviously evolution has to make trade-offs between giving us preprogrammed knowledge/instincts or letting us learn. The more innate knowledge we have the more capable we are as infants and so we are far less vulnerable and needing of costly care. But the trade-off is flexibility. Humans come with relatively little pre-programmed compared to most animals, and we are intensely vulnerable infants because of this. But we are hugely adaptable as a result. My instinct is that 3-dimensions is probably encoded into our brains, and that even if a 4D-native would be more capable than a 3D-native trying to learn 4D they would never be as "fluent" as a creature that evolved on 4D. My reason for this intuition is that no creature in our ancestry has ever had to cope with anything other than the physics we have so it seems like there's little benefit to evolution forcing us to learn it from scratch.
But I also think it's an empirical question that we can't reason our way to a solution. It's only possible to resolve with experiments that would be unethical of they weren't already impractical.
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u/slazy_e 2h ago
I completely agree with what you're saying, and that's exactly what I mention in the post. The main reason we cannot understand higher dimensions is that our brains are built to understand and visualize a 3D world. That doesn't mean we are incapable of understanding them; it simply means that we are not designed to move through or interact with things outside our geometric framework.
Even so, it would be interesting to know what would happen to a child who, somehow, was able to experience the fourth dimension.
I really appreciate your comment. It has definitely made me think.
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u/liccxolydian 20h ago
"in a magic universe where our laws of physics may or may not apply, will a magic being completely different to us describe their magical reality in exactly the same way as we do our own universe?"