Story of A. Square...
When trying to consider the fourth dimension, remember the story of A. Square. He lives in the second dimension, Flatland. He does not know the third dimension. But if you saw him, you could see the entire plane he lived in, including the contents of everything. You could literally see anything.

(Read on to see an A. Square Adventure!) Flatland example

Welcome to Flatland! - The 2nd Dimension

Imagine if you will, a place which is flat.
We call this place, Flatland because it exists in the 2nd dimension

Dimensions, and the people who live there

0D - A. Point lives there all by himself. He also covers the entire dimension

1D - A. Segment lives here with all the other line segments sliding back and forth on 1-D lines

2D - A. Square is the topic of this page. He lives in flatland. (another town near there is Flatville) A. Circle lives here too (This is where we are at now.)

3D - A. Sphere lives in our dimension(3rd) along with all the other creatures that are 3d.

4d - A. Hypercube lives in the 4th dimension. He is the most complex of all creatures in the 3rd, 2nd, and 1st (excluding 0 dimensions). He has powers that humans don't

This continues and as usual they all have the same first name: Allan

Now that you know a little about the people and their dimensions, think about the advantages and disadvantages each of these creatures have compared to the others

You may notice that it is impossible for atoms to exist in dimensions less than the 3rd, but can something exist without having 3-D parts such as the basic building blocks of matter?
4-D bodies may have 4-D parts that make them unique to other dimensions, and doesn't mean that 3-D bodies don't exist. A. Square is curious about the 3rd dimension just the same way we are about the 4th. Thinking the way A. Square percieves the 3rd dimension can help us understand the 4th dimension.

A. Square's latest adventure

A. Square experiences gravity in the 2nd dimension of a 3 dimensional directional. Sort of a dimensional travel.

(Remember: To A. Square, the trip will be flat just like we think our gravity is strictly 3d.

The closer A. Square gets to the dense object, the faster he falls. Notice that he still thinks that everything is flat. He actually "shrinks" because the space around him expands, just like things shrink under pressure here in the 3rd dimension.

Space is elastic in that it can be stretched in the direction of the 3rd dimension to A. Square by a 3-d gravity. We must have a type of 4d gravity here in the fourth dimension.

A. square may not be able to leave his black hole of the 2nd dimension if he can not "climb out"...

Is this possible for a 3 dimensional being to help out A. Square?

I'll tell you!, A voice said.

Is that you, A. Sphere?

Yes! I can help you

I can't get out!!!

I am the object resting on your 2d plane which causes this gravity.

What do you mean?

Well, imagine if a 1-d creature would move into the dip of a parabola and got stuck. You would simply stretch the the line into a straight line, right?

Yes but, I can't visualize this in the 3rd dimension.

I now am leaving this plane now. Space should flatten out again.

Hey! I feel lighter each second..... Now I can leave with ease!

I have put on some weight recently.

I know. But since I can only be measured in area and you in volume, you are bound to attract me!

Email Me! with questions, comments, ideas, or anything else.

A. Square's adventure should change every now and then. - No set date, just when a good idea comes around

Return to the index

This window of the Fourth Dimension is hosted by Get your own Free homepage!