4th dimension

Wow. I spent the whole afternoon watching videos/reading articles about the 4th dimension. I had already heard about it a lot but had never spent time trying to grasp what it really was. It’s so cool and completely blows my mind! I can’t say that I understand everything and I still have a lot to learn but this is the little that I have understood so far:

  • 0 dimensions: nothing.
    No height, no width, no length.
  • 1st dimension: one line.
    The line can be shorter or longer but it can never be wider or taller. If a 2d being (you can imagine a sheet of paper) is placed in a 1d world, the ‘creatures’ within the 1d world will not be able to perceive the 2d being fully. They will only be able to see it as a point.
    You stack a number of parallel lines and you create width (2d).
  • 2nd dimension: a sheet of paper (with no height/thickness).
    Imagine a world called Flatland (2d) represented by a sheet of paper. The ‘flat creatures’ living in Flatland can only move along that paper (left, right, front, back but not up). If you place a 3d object in this 2d world, the creatures within the 2d world will not be able to perceive the whole object. They will only see a cross section of the object (a line). As the ‘creatures’ move around in Flatland, the line changes because as they move, they are able to perceive the other dimensions of the object – they see the object from the sides/back/front. The 3d object can move through the 2d world. This means that if the object has a strange shape (not a cube but a sphere for example) and that it decides to move through the 2d world, the ‘flat creatures’ will first perceive the sphere as a point. Then, the point will slowly grow into a line and finally, shrink back into a point.
    You stack a number of papers and you create a stack which has height (3d).
  • 3rd dimension: a cube/our world.
    Pretty easy to imagine.
    What if you stack a series of 3d worlds next to each other? Theoretically, this would create the 4th dimension.
  • 4th dimension: an infinite amount of 3d moments stacked right next to each other (which is why some people define time as the 4th dimension). The 4th dimension could therefore be characterised by length, width, height and duration. If you were to visualize yourself in the 4th dimension you would look like “a long undulating snake with your unborn self at one end and your deceased self at the other end” (this is called a “spime”).
    The reason why we, 3d ‘creatures’, can not fully perceive the 4th dimension is the same as why 1d ‘creatures’ only perceive a portion of the 2d world and 2d ‘creatures’ only perceive a portion of the 3d world.
  • Now, what if we bend Flatland on itself? Imagine that it becomes a sphere. A little ‘creature’ on Flatland could walk on a straight line and would eventually come back to its’ starting point. He could then deduce that a 3d world exists. This means that maybe, our 3d world could also be curved into a 4th dimension.

Here are some other videos that explain the concept really well: video 1 (Carl Sagan), video 2.

Image: how a “tesseract” changes over time, viewed in the third dimension.

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