You may be familiar with **Flatland: A Romance in Many Dimensions** by 19th century author Edwin Abbott. Flatland is a two-dimensional land populated by polygons, and the story satirizes Victorian England's hierarchical social structure. Of equal interest to many readers is the book's **clear articulation of the mathematical ideas behind different dimensions**.

The narrator, named A Square, sees A Sphere (a visitor from a three-dimensional place called Spaceland) move through Flatland. But A Square doesn't recognize the visitor as a sphere, because he has no knowledge of the three-dimensional world the sphere inhabits. From A Square's vantage point as a flat observer, the sphere passing through the plane he inhabits looks like a single point that grows into a line. It then shrinks to a point again before disappearing magically *(click the illustration from the book to view full size)*. A** three-dimensional object is unrecognizable, and is beyond comprehension to a two-dimensional being**. But if he could be lifted up above the plane he inhabits, A Square would see the relationship between the sphere and the plane.

I think that **A Square's plight is analogous to that of many current undergraduate students when they interact with alumni**. The students' perceptions are limited in time and space by the very nature of their experience; **when an older, experienced alumnus passes through the student's world, context limits their ability to recognize the graduate for what he or she really is**: a rich resource, a person with experience and insight that the student could use, if only the student could rise above the Flatland of the insulated student environment and gaze upon it from Spaceland.

**Students who thrive in "real world" situations are those who rise up and seek a three-dimensional look at the world outside their campus**. This isn't a criticism of students, nor is it applicable to all undergraduates. But as I chatted about

**Flatland**with a colleague recently, it occurred to me that Edwin Abbott's ordering of the various dimensions could be compared to the relative amount of time students and alumni have spent in the wider world. Experience away from campus and from traditional student life expands the viewer's awareness of the world and provides depth that allows him to recognize and understand unfamiliar people and things.

**Does the analogy make sense?**

**Related**: In July 2008 I asked "do science students really learn science" - or something more?

*Illustration from chapter 16 of*

**Flatland: A Romance in Many Dimensions**by Edwin A. Abbott. In the public domain. Find the book in a library near you using WorldCat.