iPhone app iPad app Android phone app Android tablet app More
• FRONT PAGE
• Politics
• Entertainment
• Arts
• Tech
• Green
• Food
• Education
• Weird News
• ALL SECTIONS

Featuring fresh takes and real-time analysis from HuffPost's signature lineup of contributors

Seeing the 4th Dimension in Sphereland

Posted: 08/22/2012 7:36 pm

This summer, superheroes defended humanity in The Avengers, and a special agent traveled through time in Men in Black 3 to stop an assassination by an alien. Computer-generated images fill such summer blockbusters, enabling us to witness scenes previously conjured only in the minds of the writer and director.

Viewing ideas through the lens of mathematics also enables us to examine the unseen. In fact, a new film Sphereland, available on DVD, takes a viewer through a fantasy tale exploring what we can only imagine -- the 4th dimension. To see how one might gain insight into such a higher dimensional space, let's examine the relationship between the 2nd and 3rd dimensions to gain perspective on moving from the 3rd to the 4th. Let's begin by considering my self-portrait.

What if I lived in the 2D world of your screen? If I looked like this cartoon, I would have very limited vision since my eyes couldn't see beyond the edges of my face. Any line in two dimensions is analogous to a wall in our three dimensional world.

Let's get even simpler with the drawing below. The pupils of this 2D blockhead could only see as far as the edges that outline its eyes.

What cartoon might lead to a happier existence in such a two dimensional world? How about the picture below?

Now, our square friend can see the world and appreciate the words on this page and the beauty within your digital screen. Think about your place within this 2D world. You could put your nose centimeters from your screen and, so long as you didn't punch through the screen directly in front of the Mr. Square's eyeball, our flat friend wouldn't know you were there.

What if our blue cartoon still lived in two dimensions but his world, rather than being flat, was curved like the surface of a sphere? He could, much like those in the time of Christopher Columbus, think his world was flat. In such a two-dimensional universe, the world could seem flat, when it actually had curvature in the third dimension where you and I live. We three-dimensional human beings only fully appreciate the curvature of our world when we leave the two-dimensional surface of our planet and view it from outer space -- something that the two-dimensional blockhead cannot do.

In a similar way, could our three dimensional universe be curved in a fourth dimension? Could this even be detected in our third dimension? Could someone from a 4th dimension be quite close to us in our 3D universe? What would happen if a 4D being intersected part of itself with our universe? We cannot fully answer such questions. Yet, the film Sphereland takes a viewer through a tale that delves into such inquiries.

The movie is a sequel to Flatland: The Movie and is based on Edwin A. Abbot's Flatland and Dionys Burger's Sphereland. In Flatland: the Movie, Arthur Square, played by Martin Sheen, and his curious granddaughter Hex, played by Kristen Bell, meet Spherius, played by Michael York, from Spaceland. Arthur and Hex face grave danger and confront the third dimension.

The movie Sphereland is set on the eve of this 2D world embarking on its first mission into their "outer-space." A key discovery in the film results from the angles of a triangle. If you draw a triangle on a piece of paper, the sum of its angles is 180 degrees. How then, could Puncto, played by Danny Pudi, have measured a triangle in Flatland's outer space with angle sums greater than 180 degrees? Such mysterious triangles can exist, which the space explorers discover as they contemplate the third, fourth and even higher dimensions.

Sphereland offers insights into the 4th dimension by examining how its 2D characters might experience life in the third. Admittedly, such ideas are difficult to comprehend.

Could the shape of our universe be curving in some higher dimension? Could someone in a fourth dimension be present, like you, dear reader, could be to our blockhead, without being visible in our three dimensional world? What would a four-dimensional sphere look like were it to intersect our world? Youth and adults alike can gain insights through the educational and entertaining film Sphereland. And maybe, someday, an astronomer or physicist will discover mysterious measurements that, upon reflection, give insight on the shape of our universe. The answers may, as they do in Sphereland, lie in the stars and in space exploration.

• 10
• 0
• View FAQ
Comments are closed for this entry
View All
Favorites
Recency  |
Popularity
11:17 PM on 08/30/2012
Higher mathematics has the related concept of co-dimension: the number of dimensions by which an object falls short of spanning the entire universe it lives in. A line in 3-D space has dimension one but co-dimension two, for example. Perhaps the universe we know doesn't live in a higher dimensional super-universe, but instead the things we think of as points have components with higher co-dimension inside them, a la string theory. How those higher co-dimensional objects curve in our existing universe might be a more pertinent question.
HUFFPOST SUPER USER
westnova
.......
07:01 AM on 08/26/2012
Please go to pat. no. 3940100 and you will see what I did with triangles. Actualy triangles are fractals. I now think that I created a fractal bubble and that it may explain quantum theory. By asigning the three constants, the weak,strong and the electromagnetic to the three corners of the fractal and joining them as opposits you come up with my SUPER NOVA.
12:55 AM on 08/25/2012
Could the universe be curving in some higher dimension? Of course it could. If it does, it will leave a physically measurable trace, e.g. by turning the polarisation of photons along their path.
HUFFPOST SUPER USER
firewired
Compared to what?
09:58 PM on 08/23/2012
Here's a big, 5-second W O W!! Great write-up; it does make me want to see it! Good job.

Hope to read more from you in future. Insightfult!
This user has chosen to opt out of the Badges program
05:20 PM on 08/23/2012
both science and religion share a sticking point. creation
if "in his image" (hebrew tselem Elohim) used the alternate definition of "in his imagination"
we could answer all of those questions that we avoid in both religion and science.
dreams, hallucinations, other dimensions
after all it is scientifically proven that the vast majority of what our senses reveal is created in our mind and not processed from external stimuli.
12:59 AM on 08/25/2012
Please drop a one pound stone on your big toe from roughly shoulder height and then report back to us how the vast majority of the pain from your broken toe was only created by your mind.

:-)
oneeasyrider
E=mc2: From light you exist
02:09 AM on 08/23/2012
A time traveler (TT) who never slows below speed of light would view our existence as static or immovable. TT would see us like immovable statues in a wax museum. At the same time, we would never be aware of TT if he changed nothing in our immediate environment, but if he did, objects would appear to move instantaneously from one place to another as if by magic or quantum particle-like. Makes one wonder, why would TT be interested in our presence or reality? But if he is interested, he could be starring amusingly at you, standing inches away, right now.

Sphereland should be an interesting movie.
01:03 AM on 08/25/2012
Said "time traveler" is a photon. Just because photons don't have time does not mean that everything is static to them. Instead they measure everything in terms of spatial distance, measured by counting their own wavelenghts. The total information content of the universe is exactly the same to photons as it is to massive matter particles. They merely "express" that information in different "units".
oneeasyrider
E=mc2: From light you exist
06:09 AM on 08/25/2012
Why didn't you answer my question?  What's with the snark or tangent?  I really thought your post was great, but was confused by the last line.  I simply wondered if you made a mistake or would like to know if I'm missing something.