4D front page

These pages

came from the 4D class at The Paideia School in Atlanta, Georgia. The goal in this course is an impossible one: to visualize the unvisualizable, four dimensional objects.

Seeing and Thinking

The topic of visualizing four dimensional objects has been an activity of great pleasure here at Paideia for many years. The idea of seeing with your mind’s eye what you cannot see with your physical eye is very appealing, an exercise of imagination enhanced by mathematics. There are many ways a student can approach this. Some just think about it logically, a great way to visualize 4D things. Some just see shapes well or draw well. Some extrapolate or reason by analogy. All such techniques are useful in building an image of a four dimensional object. They are also conducive to conversation. Students follow those abilities that are their best, and gain their own insights into 4D. In addition here at Paideia the student can latch onto a large group of alumni who have been doing this themselves and have continued their explorations. They can both give guidance and be impressed by the particular thoughts that you come up with.

Most tutorials were written by former students.

VISUALIZATION

You begins with the visualization exercises found here.

Learning that is truly new

Adults see and understand by applying past understandings to new events. A young child learns chaotically by organizing and making sense of new perception. He or she does learn to speak one step at a time or one lesson at a time but is rather thrown into a new world of sounds and, in its own way, the student learned to deal with them.

In the four dimensional world you are the kid you once were. The abilities you had then you need now. You need to learn, so to speak, by going back to the sandbox and playing with the items you run into. But now the play items, such as hypercubes and 120 cells, are much more adult.

But you are becoming adults with the advantages of being an adult, so after play, you conjecture; you systematize — you do all the things that your experience and your brain let you do.