“Where’s The Moon? I Don’t See The Moon!” Or, Mathematics To The Rescue

I was dragging myself up the stairs of Founders Hall.  The cement steps and barren walls reflected the darkness of the time ahead.  For, my next class was Speech Communication with Professor B.  I was not doing well in the course.  As my current lady would say:  “You’re going down, down, down!”  And so I was.  But perhaps, I should tell you something about Miss B and how I got into trouble.

Miss B was a tall, wiry lady with sharp, unforgiving eyes and a total lack of manners.  We didn’t get along from the start.  I remember her saying with a sarcastic tone:  “Look at that!  A little boy wearing his tennies!”  She was frank, if nothing else.  And when I tried to act out a favorite childhood verse, she would yell out:  “Where’s the moon?  I don’t see the moon!”  At the time, that comment stunned and hurt me, because I was quite fond of the verse I was interpreting.  Later, Professor B told me that the only thing that could save me was the final, which was a monologue of at least ten minutes.  I thought and thought about possible selections.  I knew if I picked something well-known I could be compared with the greatest and I’d come up way short.  Fortunately, at that time, I was reading some wonderful mathematical stories from Clifton Fadiman’s Fantasia Mathematica.  Bruce Elliot’s story, “The Last Magician” really appealed to me.  The main character was an old man who was fond of a magician’s helper and commits murder because of the cruel way the magician treats her when a futurist society has condemned her to death for misceganation(She was Martian and became pregnant by the magician from Earth).  So, the story had intrigue, action build-up and the main character was an old man.  And, growing up next door to my Dad’s parents, I knew my Grandpa Johnny quite well, so I thought I could act out the part with some accuracy.  Also, the story dealt with the magician trying to escape from a supposedly real Klein bottle

Attempt to picture a Klein bottle, a three dimensional surface that has only one side, which is impossible.

An attempt at constructing a Klein bottle, a three dimensional surface that has only one side, which is impossible.

and was mathematical in nature, so probably few, if any, people had seen it performed.  When I thought about all the advantages, I thought it would be an excellent choice for a monologue.  I would need to trim some parts, though.

Finally, the long-awaited day arrived.  Everyone was busy rehearsing their lines and trying to get into character.  Wouldn’t you know it?  I was the first person Miss B called on.  I knew if I wanted to do well, I was going to have to become an old man in every way.  I tried hard to imagine my Grandpa Johnny and become him.  I tried to walk with difficulty, struggle to get some of my words out and look confused.  And as I reached the podium, the words did come out.  “The harder he worked the worse he treated Aydah…  It seemed as if every time I turned around I’d find her hiding in some corner, crying… I knew she would have to die.  That was why I had pressed the button that switched the bottles the first time, before she ever did…  I guess I must be getting old;  lately I’ve taken to wondering about King Solomon.  He knew so much, I wonder if he knew about Klein bottles…”  Then, a loud applause.

“Well, Bob just disappeared!  A feeble old man replaced him!”  Professor B’s eyes sparkled with admiration and respect.   Mathematics had come to the rescue.



Robert Brooks: The Wizard of Shape, part 1.

During my adult life, I became interested in discovering why forms were the way they were, the laws governing the formation of forms, the applicability of forms, and the inks between different forms.  I realized that for the purpose of my study I would have to come up with an appropriate definition of form.  I chose to define form as a perceived structure or concept represented by a definite pattern.  Applying my definition to the study of forms, I saw that forms would fit into three major categories:  NATURAL FORMSCREATED FORMS, and THEORETICALLY-DERIVED FORMS.  Natural forms pertain to those forms which exist in the physical world independent of human beings.  Cloud patterns and ocean waves are natural forms.  Created forms are those forms which arise from the human imagination.  These forms include poetry, architecture, and sculpture.  Theoretically-derived forms involve forms which arise through logic and reasoning.  Cycloids and lemniscate are examples of such forms.

Topology belongs to the last category.  It may be called the “aerobic” branch of mathematics, because it looks at the properties of shapes after they are twisted and stretched.  Topology is a qualitative form of mathematics, involving concrete shapes that ten-year-olds could play with.  Stephen Barr’s Experiments in Topology, offers numerous examples of topological fun.  One such, is twisting a two-sided strip so that it has one edge, resulting in the Mobius Strip.    For those that want to read about the creative, imaginative side of topology, I recommend Clifton Fadiman’s two collections of short stories and verse:  Fantasia Mathematica,  and The Mathematical Magpie.

When I started selecting interviewees for my book The Magicians of Form, The late Robert Brooks, then a Professor of Mathematics at the University of Southern California, was my first choice.  Dr. Brooks taught a course in topology, and had an ability to make the complex simple.  His warmth and enthusiasm put me at ease, and I found myself even more interested in the subject matter of topology.  What follows is an excerpt of an interview that took place in his office at USC.IMG_5961

                              “I think the thing that motivated me was the thought that ‘They’re holding something back from us’.”

RW:  Dr. Brooks, perhaps you could say something about your early interest in mathematics.

RB:  I think I wanted to be a mathematician since I was in the 4th or 5th grade.

RW:  Does that mean you had a natural aptitude in solving mathematical problems?

RB:  Well, I like to think I have a natural aptitude.  But let me tell you a story…  This was in the 1st grade, and we were doing primitive addition, and learning to add several digit numbers together.  Then we began to learn carrying, and it dawned on me that all the numbers we had been given to add up until that time, had been kind of “cooked up”, so you didn’t have to carry.  I was a little upset that no one had pointed that out to me; and I said to myself, “I wonder what else they’re holding back?”  And I must have spent about two weeks adding random numbers together.  Then I came to the conclusion that the only thing you had to know in adding two numbers together was carrying, and then you could any two numbers, no matter how many digits they contained.  But I felt I had to prove that.

This was the first problem I remember thinking seriously about.  I recall working on it for a long time, and I ended up giving up.

RW:  So you had the desire to go from the specific to a general rule, to an overall proof/

RB:  I think the thing that motivated me was the thought that “They’re holding something back from us”, and I wanted to be on top of what was going on.

RW:  You had a certain lack of trust in the whole procedure.

RB:  Absolutely!  And I think one thing that’s so appealing to me about mathematics is its real immediacy;  that you’re basically on your own with the materialand if there’s something thereyou’ve got to find it.

RW:  So you’re the pioneer?

RB:  You’re just about everyone in this business.  You’re the pioneer, you’re the explorer, you’re the critic.  In many cases, you’re the audience.

RW:  Then it’s really your world.  You’re immersed in this abstract universe that you’ve created.

RB:  That’s right….  But topologists have a certain disdain for abstraction.  Topologists want to show what’s there.