[FOM] Martin Gardner

[Vaughan Pratt]

One of mathematics' most loved figures, Martin Gardner, died on Tuesday 
in an assisted-living facility in his home town of Norman, OK.  Many 
testimonials to his extraordinary energy and his enormous influence on 
the popular understanding of mathematics can be found across the web, of 
which the following merely scratch the surface.

http://www.nytimes.com/2010/05/24/us/24gardner.html

http://www.washingtonpost.com/wp-dyn/content/article/2010/05/24/AR2010052403747.html

http://www.guardian.co.uk/commentisfree/2010/may/29/martin-gardner-bad-science-goldacre

Like many on this list, much of what I knew of popular mathematics since 
I was a young sprout came through the remarkably many Gardner channels. 
  My first and only personal interaction with him however was when I 
wrote to him about a problem he had posed in the 1970's.  He had asked 
in his Scientific American column whether a four-legged table could 
always be placed on a bumpy floor so that it did not rock about two of 
his legs. (I have exactly this difficulty today with my bathroom scale, 
which sits awkwardly on a bathroom floor with quite bumpy tiles from a 
long-deceased Mexican building, and I have to relocate it every time the 
cleaners move it.)  There was an obvious positive answer, but I noticed 
it had a fatal flaw with no workaround, so as a very junior assistant 
professor I wrote him a brief note to point this out.  No reply, so no 
interaction.

Two years later he visited MIT to discuss gliders with Bill Gosper on 
the 9th floor of 545 Technology Square, where the heavy lifting in AI at 
MIT took place in those days, at least for those not obliged to publish 
so as not to perish.  Fully expecting to perish at MIT back then I had 
been working there along with other places around MIT.  During his brief 
visit I took the opportunity to bring this issue up again with him, and 
we talked about it for a few minutes, with no firm conclusions.

A week later I received a note from him agreeing that the problem was 
indeed flawed as I had said.  He said that it had not occurred to him 
that a floor could behave in that way.  (Of course the floor must be a 
single-valued function z = f(x,y), without which all bets are obviously 
off.)

My only regret is that he did not publish a retraction.  But honestly, 
who would have noticed?  I was happy simply to have done more than 
merely shake his hand and talk about the weather.

I also took the opportunity at that time to ask him why he never used 
complex numbers to cope with situations that seemed to me would benefit 
from them.  His answer was that he had decided that complex numbers were 
too advanced for his column.  That seemed like a reasonable threshold to 
me, with the advantage that one could compare the complexity of any 
given concept with that of complex numbers to decide whether it was 
suitable for his column.  In retrospect however I think a case could 
have been made for them in terms of LOGO's turtle geometry as developed 
back then by Seymour Papert and Hal Abelson, where multiplication by i 
could be explicated simply as asking the turtle to turn left.  I made an 
argument along those lines for Seymour's benefit on the occasion of his 
chair at MIT, giving an elementary turtle argument to show that the 
fixpoints of the derivative operation mapped vertical lines to circles. 
  With a little more intuition about the connection between algebra and 
geometry I think Martin Gardner could have been as persuasive an 
evangelist for complex numbers as he was for so many other facets of 
accessible mathematics.

Vaughan Pratt