Doctor Who and the Regeneration Didactic Science Fiction

By Bobby Neal Winters
I started reading science fiction in the 70s. At that time, I was reading mainly stuff from the 50s and the 60s. Think of Isaac Asimov, Robert Heinlein, and Arthur C. Clarke.  I cut my teeth on Lucky Star, The Foundation Trilogy, 2001: A Space Odyssey, and Space Cadet.
This is didactic science fiction.  If you are worried about that word “didactic,” it means that this science fiction, for the most part, was interested in teaching more than it was about the story. In particular, Lucky Star, was intended as a channel to bring the knowledge of science to young minds. The was so much the case that Asimov was moved to put disclaimers at the beginning of certain of these books after the science became obsolete, e.g. when it was learned that Venus wasn’t covered by oceans.
In didactic science fiction, the story is merely a vehicle for teaching.  You get lines like, “We shall head of the pirates at Mars, which you know is the fourth planet from the sun.”  I’d better be careful, I may have actually read that somewhere.  There is a tendency to make fun of this, and truly some of it was so awful as to be funny, but I did learn a lot of science from it.  Some of it was so good that I didn’t have to study from my textbooks much in high school; I’d gotten the “facts” from science fiction.
I want to come at this from a couple of orthogonal ways today. (Notice how I worked in that mathematical term, orthogonal.  It means at right angles, though it can be generalized to apply to vectors in an arbitrary inner product space.  Look it up.)  The first of these is literary and the second--get ready--is didactic.
As a writer, I am interested in that old didactic science fiction because I want to write some new didactic mathematical fiction. I like teaching mathematics; I like writing fiction; writing mathematical fiction seems like a nice marriage between those two.    One thing we writers do in pursuing our aims is to steal and thieves don’t steal things they don’t like.  I like Doctor Who and Doctor Who provides an excellent example.
It began as good didactic science fiction and remains so through many regenerations.  What it teaches isn’t so much hard science as the social sciences.  The Doctor is a time traveler, and this gives him the opportunity to visit a lot of history.  Someone of a suspicious nature--here, here, pick me--might observe that the Doctor spends a lot of time in Great Britain in general, in England, in particular, and in London to be even more particular.  
As Doctor Who has been around so much, it gives us the opportunity to watch it develop over time.  As with every other science fiction franchise, the special effects have improved, but there is more going on than that.  In the new series there is a lot more emphasis on emotional connection with people. In the olden days, there were actors speaking lines; they were carrying out the motions of an adventure; they lived; they died; but somehow they didn’t make me care.
The most recent regeneration of the series is much different. While the special effects in the old series were...uh...awful which I say to avoid the word horrendous, those in the new are grand.  But that is minor in comparison to the level of emotional connection one has with the characters.  Care is taken in the writing, acting, and direction to create characters that one cares about.
And it still teaches.  The new series continues to show history, but it has also ventured into art.  One episode involving Vincent Van Gogh stands up well against Lust for Life.  It also ventures into philosophy and science.  It does it well. What is the secret?
The secret was in how it engaged our emotions. This is done through good story-telling. Time has been taken to create multi-dimensional characters. (How fitting for Doctor Who!) And--wait this is important--the guardians of the franchise apparently do believe in character.  One is able to put oneself within the character and feel what they are feeling.  The Doctor is not treated by the writers as a puppet.  He is an emotional being who, although he is a Time Lord, reacts emotionally like a human.  When his beloved traveling companions Amy and Rory were sent to the past--and effectively killed to the Doctor--by the Weeping Angels, it dealt him a psychic blow requiring about a century to recover from.
I would draw the lesson that one puts good, well-drawn characters into an engaging story, and then work in any didactic elements that one can make comfortably fit.  The comfortable fit is important.
I look back on that and see that although I was talking about writing I was, at the same time being didactic.  I hope it was a comfortable fit. Let me now be didactic and I will see if I can work something else in comfortably at the same time.
T. S. Eliot wrote in The Hollow Men “Between the conception/ And the creation/ Between the emotion/ And the response/ Falls the Shadow.” Well, between being didactic and doing product placement lies social engineering.
Oops! There I’ve said it. The phrase “social engineering” evokes dark images of evil old men in back rooms moving around people like pawns and of raving, drooling conspiracy theorists clawing the furniture and howling at the moon.  
I am okay with both of those.
We don’t necessarily need science fiction for social engineering, but it has a comfortable place there.  We can look at Star Trek for example.  Captain Kirk had a Vulcan first officer and an African Communication officer.  This made people more comfortable with the idea of working with people who were different from them in general.  In particular, it was aimed at making whites more comfortable working with blacks as equals.  
It was a good cause. Was it education, social engineering, or the spirit of the times?  Not an easy question.  An easier question would be what’s the difference.  I would say the difference is the level of organization.  Social engineering would be need to be organized at some level higher than those involved in any particular step and emerging at multiple venues.  As for the spirit of the times, let me remark that any effort at social engineering will be more successful if it can work in concert with something of the spirit of the times.  It is easier to grow an oak from an acorn than it is to create the acorn.
Let me mention briefly also the topic of Anthropogenic Global Warming.  I saw this referenced in Robert Silverberg’s Hot Sky at Midnight back in 1999.  This was five years before the release of The Day After Tomorrow in 2004 to use the disaster movie tropes to bring the message to a much broader audience.  When An Inconvenient Truth came out in 2006, a broad audience was ready.
One could create a conspiracy theory about a group of people who wish to shift the world to the use of nuclear energy by creating a fake crisis.  One could spin a story about concerned scientists harnessing sympathetic ears in the media to get their message out.  One could imagine simply an idea emerging into a culture.  
Take your pick.
It does strike me that if you want to get a message out and you can plan and are patient--oh, and if you have the money--then this is a smart way to do it.
To get back to Doctor Who as an example, I will say that it does a bit of social engineering itself.  These days that a program will provide examples of “different” people working together is a given and it does plenty of that, but other topics appear that I find charming:  It is a patriotic show.  I find the pride displayed in being British to be delightful even when it is at the expense of Americans. (They think we are too violent and gun crazy.  Go figure.) The most delightful and effective example of patriotism occurred when the Doctor’s companion Rose wore a Union Jack and hung from a barrage balloon during the Battle of Britain.
The show also fosters a notion that Church of England will continue into the future to fight evil and provide comfort.  Those who follow the travails of the C of E might find these the most daring science fictional elements of all, but I digress.
In the end, I do believe they’ve got something that works, and something others might want to try regardless of their agenda:  Good characters and engaging stories.  Once you’ve got those you can work in whatever is comfortable.

Teaching, Writing, and Mathematics

By Bobby Neal Winters

I have been thinking recently about the writing of mathematics.  This is rendered to being a highly academic exercise as I have not produced any original mathematics to write about for quite some time.  I don’t bring very much credibility with me to this endeavor because during the brief interval I was producing original mathematics I cannot say that I was a very good expositor of it.  

What has happened in to bring my thoughts to the writing of mathematics?  One thing is that I have begun writing myself.  I began writing a weekly column for the local news paper about 10 years ago.  Figure 52 columns a year--I never miss a week--and seven hundred words a column--I usually overrun that barrier--and this comes to about 364,000 words.  I write things besides my column so I will say that I’ve produced about half a million words in the last ten years.  If repetition is the mother of learning--and I believe it is--then I may have learned something about how to write.

In addition to this, it has been my pleasure to teach out of a pair of very well-written books: A Radical Approach to Real Analysis and A Radical Approach to Lebesgue’s Theory of Integration, both written by David Bressoud.  These books are, as I said, well-written, but I think more important to their effect on me is they are written as historical approaches to their particular subjects.  

The historical approach has been very enlightening to me.  Mathematics is a land populated by optimizers and those seeking efficiency through brevity.  A result is discovered and proven with great difficulty.  Then time is spent in organization working out theory wherein the proof of the result seems not only easy but inevitable.  The historical approach allowed me to appreciate that what has been rendered as clear as glass to students of the subject today was once a riddle in a mirror.

As a teacher, it reawakened the excitement of the subject in me.

But in presenting this material to my classes, I’ve reproduced the older proofs of various results that have been included and in doing so I’ve noted a difference in style with much of modern mathematics.  There is a tendency in modern mathematics to drift toward the abstract.  This is a reasonable tendency as the abstract proofs tend to be cleaner and tend to give broader results, i.e. if I prove something about metric spaces, then I prove it about the real numbers, the complex plane, and spaces of functions at the same time.

That is something of an illusion, however.  The abstract structures are out-growths of specific examples.  The examples were originally things that were interesting in themselves and drove the construction of theory to discuss them of abstract structures to more easily prove results about them.

It is somewhat ironic that my experience as a mathematician helped me to be a better writer of things besides mathematics.  As a topologist who studied 3-manifolds, I took trips in my head to places no one had been before and then attempted to explain them to those who’d remained at home.  I learned the art of description as I described these strange places. In the construction of proofs order is important.  In good writing, some things must be explained before others can be understood.

As a writer, it seems to me that in well-written mathematics, well-constructed examples serve the same purpose that metaphors do in good writing.  Much writing seeks to create in you a picture that I have seen in me.  This is true whether I am writing about house cats, building a computer, or mathematics.  If I am to be successful, I must reach you by beginning with a thing you already understand and build from it.  Our shared experiences make communication possible.  Mathematically, the creation of a well-chosen example gives writer and reader a common, shared experience from which the writer may then deviate in order to build.

This technique is especially evident in the proofs in analysis that begin with the proof of a simple, very special case and proceed through stages of increased generality until the most general case is proved.  At its best, one can see the whole of the problem is in that very special case and the succeeding generalizations are simply minor modifications of the original proof.

There have been times when I’ve complained that too much of the time we who teach mathematics treat it as a murder mystery.  We withhold or downplay certain very important details.  We keep things to ourselves as our own little secrets.

I think I know why we do this.  We are trying to teach our students how to think for themselves.  There is a reluctance to “lay out everything plain” because it will deny the students the joy of the gestalt that we ourselves experienced, the joy that led us to become mathematicians.

I must say that there is much virtue to this point of view.  The problem is that it is so easy to do very, very badly.  There is also a tendency--among some in the profession--to use this as a technique to build up their own egos at the expense of their students’. This is far from universal, however.  Much more of a problem is judging difficulty.  What is easy to a professional might be insurmountable to a student.  The teacher’s job is to lay out bread crumbs to tempt the student to the point of gestalt but not so many as to rob the student of the joy of that gestalt. The fat cat will catch no rats.  Not that a cat eats bread crumbs, but sometimes you have to mix your metaphors.

In our teaching, in our writing, we must free ourselves to ape literature.  We we must foreshadow the great mathematical truths to come with smaller, more easily digestible truths.  When the student finally comes to the climax, he must be so prepared that the final step to him is nature, the final joy is true, but he should then be able to reexamine his steps and realize his arrival at this particular point was no accident.

I mentioned at the beginning of this article that when I was producing original mathematics I wasn’t a particularly good expositor of it.  There are those who will read that sentence and recognize me as a master of understatement.  While a careful study of my articles would undoubtedly produce additions to this list, I believe I had two major problems: impatience and an over-reliance on notation.

I believe we can all agree that taking one’s time to do a good job is a virtue.  A lack of patience can cause a lack of proper care.

Creating notation is a way around the difficulties we sometimes encounter in natural language.  Creating a well-chosen metaphor, a well-created example is another.  The example has the advantage that someone might name it after you one of these days.

If I were suddenly given my mathematical life to live over, I hope that I would choose to grasp onto mathematical exposition as the true art that it can be.  To first live the mathematical adventure and then tell the tale, and to understand the telling of the tale is as at least as important as the adventure because its purpose is to convince others to have adventures themselves.

(Bobby Winters is Assistant Dean of the College of Arts and Sciences and Professor of Mathematics at Pittsburg State University. He now holds the title of University Professor.)