Could we Be Living on a 4-Dimensional Surface?

This is a sure sign that I have a crapload of free time. Just hear me out – this is interesting!

Moving in One Dimension

Say there is a universe that lived in just one dimension – on the x-axis. People in it can only move forward and backward. They’re not even aware of the concepts of left/right and up/down. How can we create a world for them where they can always keep moving without coming to any kind of “barrier”?

The solution I came up with was to connect the two ends of a line to form a circle. Problem solved. Though the circle itself is a two dimensional object, the 1-D people are living on its surface blissfully unaware of the fact that there are any extra dimensions below them. If the circle is large enough, they won’t notice the curvature at all!

Moving in Two Dimensions

What if we have another universe made of two dimensions alone? Basically everyone lives on a flat sheet and can move forward/backward and left/right, but not up and down. How can we design a sheet in such a way that they’ll always have space to move around without ever encountering any “edges”? My solution was to make a sphere where everyone lives on its surface. Though a sphere is a 3-D object, the people living on it are unaware of anything other than moving backwards and forwards. Kind of like ants. If the sphere is big enough like maybe the size of a planet, it’ll look flat to them. Sounds familiar eh? :D

Moving in Three Dimensions

Coming to our own universe, we can move up/down, left/right, and front/back. We live in 3-D space. But like the above two, how can we construct a system where we can keep going forever in any direction without encountering any barriers? Any “container” will have boundaries that we bounce off against. But the universe has no conventional boundaries. It’s expanding all the time but there are no “barriers” so to speak. How can this be?

If a one dimensional unlimited space is the surface of a 2-D circle and a two dimensional unlimited space is the surface of a 3-D sphere, can it be possible that an unlimited three dimensional space is the surface of a 4-D object? Just like our 2-D people on a sphere don’t know you can move up or down, we ourselves don’t know about the 4th dimension…it boggles the mind to think about kind of shape it’ll look like. I don’t think we can imagine such a thing.

Can it be possible that an unlimited three dimensional space is the surface of a 4-D object?

Of course we call time the 4th dimension, but it’s not a spatial one. We can only imagine 3-D spatial objects. And yet space itself might be the surface of an immense 4-D structure! Just like when a sphere like a planet is big enough we can’t tell that it’s curved and we see the surface having only two dimensions, if our universe is big enough (and boy it is!) we won’t notice the slight “curvature”. And if we keep going…and going…and going…in any direction, eventually we’ll end up where we started. Or at least I think that’s what will happen.

Whatever this 4-D spatial object is, it’s expanding at an ever increasing pace. Like the spots on a balloon become bigger and bigger as it’s inflated even though they’re not moving. Space itself is expanding – our atoms and molecules are stretching. Difficult to imagine isn’t it?

So what do you think? Can we be living on the surface of some unimaginable 4 dimensional structure?

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Comments

  1. Western Point of View says

    The fourth dimension is based on time.

    Time as we know it is linear. All time moves forward–from 3PM to 5PM lets say.

    THe universe IS 4th dimensional in that if one has the ability to play with relativity, they are able to witness and manipulate the 4th dimension as we can with the 3rd dimension.

    Unfortunately, we have not been able to travel faster than light yet. Time itself as WE know it expands linearly, however if one can manipulate light and relativity, we can then access that balloon not just in the forward direction but in the reverse direction as well.

    Too bad Einstein ain’t alive anymore eh?

    Reply

    • In reply to Western Point of View

      I’m only talking about spatial dimensions. I’ve already mentioned time in the article in the 6th paragraph and I’m not referring to that here. I didn’t want to introduce an additional layer of confusion!

      Reply

      • Western Point of View says

        In reply to bhagwad

        No that’s the thing–time IS spatial. Obviously we can’t witness that, but time IS the spatial piece of the puzzle. Since we are so intertwined within time itself, we cannot see it as a structure. Since we are moving forward linearly as apart of the rules of relativity, we cannot witness time.

        Time is perhaps a curved object that is expanding like a balloon.

        For all we know, time IS spatial, we just cannot witness it.

        Time itself is like a bubble. Time paradoxes are like a needle. One SMALL paradox would burst the entire frame of time, forward and back.

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      • In reply to Western Point of View

        That’s not true. To my knowledge, modern physics refers to what we know as a pseudo Euclidean space known as “Minkowski spacetime” where there are three spatial dimensions and the additional linear dimension of time combines to create a 4-D manifold. For more information on Minkowski spacetime, see here: http://en.wikipedia.org/wiki/Minkowski_space

        In any case, I want to keep time out of this entirely since I’m speaking only of “pure” spatial dimensions since I don’t need time to talk about degrees of freedom of one dimensional lines or two dimensional surfaces. If it makes things easier, you can advance all dimensions by one and say that a circle is a 3-D spacetime, and a sphere is a 4-D spacetime.

        In which case, the title of this post becomes “Are we living on the surface of a 5-D object” instead of 4-D. But like I said, I want to ignore time here for convenience without sacrificing the basic concept.

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  2. Sakthi Muruganandam says

    You really do have a crap load of time :) but as long as its used in articulating such abstract thoughts with clarity, its not bad at all

    Reply

  3. Absolutely ! and science now says that there are 10 dimensions. i have a sort of GUT feeling that the three dimensional perception is somehow related to the 3 semicircular canals in the inner ear. if we had 4 we would perceive the 4th dimension. maybe future humans will have them :)

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  4. Well thought ! In fact I spend a lot of my time thinking about these philosophical things. But here I’d like to correct you. A circle (made by joining two ends of a string) is actually 1 dimensional. Don’t confuse it with infinitesimally thin disc, which is 2-dimensional. You can view a hollow circle as an extension of a curved line. Similarly, a hollow sphere (only a hollow sphere can be obtained from a 2-dimensional sheet) is actually 2-dimensional. A solid sphere is 3-d though. To get a better idea you can follow these links-

    https://en.wikipedia.org/wiki/Dimension_(mathematics_and_physics)

    http://math.stackexchange.com/questions/37250/how-many-dimensions-does-a-circle-have

    Reply

    • In reply to Rajat Gaur

      Wow – that’s an interesting thought! Wikipedia says (correctly) that you just need one polar coordinate for a unit circle to specify any point. But what about non unit circles? We’ll still need two dimensions to describe a random circle – namely x^2+y^2=r. On the other hand, if we’re on the circle itself we could just specify the distance from the starting point to locate any other point on it. So from that aspect it’s one dimensional.

      I guess it’s also whether or not we view a curved line as a “line” at all. Depends on the definition. If we talk about a line as only being a straight line, then a curved segment of a circle is not a line. I’m not sure I can think of it using one dimension only since we’ll have to introduce angle of curvature etc which necessitates more than one metric. Or maybe I’m not very clear about this in my own head :)

      Reply

  5. musingsofanerraticmind says

    As you would have imagined, this question has been asked before. In fact, purely in mathematical terms, and in a concrete manner, this question was asked about a 100 years ago. I recommend reading on the Poincare conjecture. In fact, this is the question that leads to what we know as the 3-sphere. The solution to this legendary problem, or the proof of the conjecture, was provided by Grigory Perelman, who later on went to refuse the Fields medal. In the proof to this conjecture, possibly lies the answer to the shape of our universe. For a interesting perspective of the problem, I link you to this feature article on “The New Yorker”.

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  6. musingsofanerraticmind says

    I forgot to link you the article in “The New Yorker”.
    http://www.newyorker.com/archive/2006/08/28/060828fa_fact2

    Reply

  7. String theory proposes that the universe has 10 spatial dimensions. “The elegant universe” by Brian Greene will definitely interest you.

    Reply

    • In reply to Himanshu

      I gave up on string theory in college when I found the mathematics were far beyond what I could follow :) . But yeah it’s very interesting. Of course, until it’s proven by experiment it’ll just remain a theory – but a fascinating one at that!

      Reply

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