Concepts of higher dimensions – Part 2 : Higher dimensional objects in a world

Continuing where we left off in my last post, I shall try and explain why it is so difficult to imagine or understand a dimension beyond the basic 3 spatial dimensions.

It’s simple actually, if you first try and understand the impact of a 2-dimensional object in a 1-dimensional world, and a 3-dimensional object in a 2-dimensional world. It will be pretty obvious, what it would be like to have a 4-dimensional object in our world.

2-dimensional object in a 1-dimensional world
2D object through 1D world Let’s take the case of a 1 dimensional world first. ZED is happily living in this 1 dimensional world of its, unknowing that higher dimensions exist. One fine day, a 2-dimensional object decides to invade his world.

How will ZED react to that? Will it comprehend the 2-dimensional nature of the object? Let’s see for ourselves.

Initially, as the 2D object is away from ZED’s 1D world, all is well with ZED. But it (and its world) are entirely unaware of the existence of the 2D object. For all they know, there can never be anything outside their world; leave alone an object of an additional dimension!

As soon as the object intersect it’s world, ZED sees it’s world cut away. Remember, ZED’s world is not really a tube, but a very thin string. Pass a knife (2D object) through that string (1D object), and that world is literally cut away.

This continues till the object has contact with ZED’s world.

As soon as the object clears the world, it disappears again from ZED’s world.

3-dimensional object in a 2-dimensional world

3D object through 2D world

Now take the case of ZED living in a 2-dimensional world. This time, his happy life is disturbed by a 3-dimensional object. The events occurring follow a similar pattern to the previous explanation.

Initially, when the object is away from ZED’s world, ZED and his world are unaware of the object’s existence.

As the object enters ZED’s world, ZED sees a small dot appear out of nowhere. (Remember, ZED’s world is as flat as a sheet of paper. When a spherical object intersects that, the point of contact is just a dot initially)

As the object continues passing through the world, ZED sees the dot slowly forming a circle which keeps expanding in size. When the object is halfway through the world, ZED sees the circle at it’s widest (the diametric plane of the sphere)

Again, as the object continues its journey, the circle shrinks in size till its just a dot. Then it vanishes!

Zed is standing there not believing its eyes!

So now you see how an extra dimensional object entering one’s world can make it look like something else, and how its behavior seems mystical.

Anyways, so let’s ponder on some things we understood from this :

1. In the first example, even though the object was 2-dimensional, ZED could only see it as a point. In the second example the object was a 3-dimensional one, but ZED only saw it as a 2-dimensional object. In both cases, even though the object had an extra dimension, all ZED could see and comprehend were the dimensions in its world.

So we can extrapolate this case to a 4-dimensional object entering our own world. We can safely guess that we would only be able to see a 4-dimensional object as an ordinary 3-dimensional object. (Makes me wonder how many of the things that exist in our world are actually 4-dimensional!!)

2. In both the above examples, since the object had an extra dimension, its entry into the worlds seemed magical. From ZED’s (and its world’s) perspective, the object just ‘appeared’ out of nowhere, and then vanished into thin air!

It would seem appropriate to imagine the same thing happening to us. A 4-dimensional object would appear to form out of thin air, and then vanish without a trace, leaving our jaws dropped to our knees!

3. One last thing to note from these examples was the apparent change of shape and distortion of size of the object. The object had a constant shape and size throughout, but from ZED’s perspective, it changed shape before its eyes. It also managed to expand and then contract in size.

So then, the princess went upto the charming prince and asked him to slay the dragon. The prince smiled. He was glad to oblige.

Sorry, but just making sure you are still mentally awake.

Did this help you understand why the concept of extra dimensions seem so bizarre to us? Or why we can’t imagine objects with more than 3 dimensions? Or why we haven’t ever seen an object with 4 dimensions in our world?

In the next article in this series, I shall talk more about 4 dimensional objects, how we imagine they would look like, their probable behavior etc.

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About Filya

'As you can see, we've had our eye on you for some time now, Mr. Jokhi. It seems that you've been living two lives. In one life, you're Firoz Jokhi, program writer for a respectable software company. You have a Social Security number, you pay your taxes, and... you help your wife carry out her garbage. The other life is lived in computers, where you go by the hacker alias Filya, and are guilty of virtually every computer crime we have a law for. One of these lives has a future, and one of them does not.' - The Matrix

Posted on August 18th, 2009, in Analysis and tagged , , , , , , , , . Bookmark the permalink. 7 Comments.

  1. I have wondered about this and was google’n it when I found this page. What examples of truly existing 1 and 2 dimensional object are viewable in our 3d world? I have banged my head try to think what could be 1 dimensional? 2? I came upon and recognized a 2d object that is all around us all allot of the time and I never noticed before. The clue came while watching a movie. It was so irrelevant at the time but then pow! This stupid movie had a kid that could stop time. The world froze leaving him to move around and draw people while they were frozen in time. It dawned on me that this wouldn’t work photon being energy bounced off surfaces to the cones and rods of our eyes would freeze in time also. If he froze time, the world would go black. Now I have No idea how, but this made me think of photons…absents of light…shadows…shadows….two dimensional object. A shadow is a 2d object in a 3d world! The absence of photons in a 3d world makes a 2d object. It takes a 3d world for 2d object. The protrusion a the 3d object is able to block photons to create the 2d object….ok…what could be one dimensional? what does a 4d shadow into or 3d world look like? [kinda what you ask in your lesson..but as a shadow.] sorry about the length but I got excited when I found the page here.

    • Thanks for reading up and am glad you liked this.

      You nailed it there. A shadow could indeed be considered a 2D object. An extremely thin sheet of paper and thin string could come as close to a 2D and 1D objects in our world. An atom could be considered a 0D (or point) object.

      You bring up an interesting thought about the shadows though. A 3D object does cast a 2D shadow. But even a 2D object casts a 2D shadows (think of a shadow of a sheet of paper). So maybe a 4D object would cast a 3D shadow or even a 4D shadow.

      ps: What movie was it? I would like to watch something like that :)

  2. Just recently I had a visions where I was taken to the 18th dimension. All good and I saw a hexagonal shaped crystal!

  3. what is the eighteenth dimension?

  4. bizarre – yes!!! next?

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