Interview with Martin Gardner, Volume 52, Number 6

Interview with
Martin Gardner

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Notices:

Was there someone in your early life who

inspired you in math and science?

Gardner:

Yes, I had a physics teacher named M. E.

Hurst, and he was my most inspiring high school
teacher. I got to know him fairly well. I dedicated one
of my books to him. He got me interested in physics.
Actually, I hoped to become a physicist, and I wanted
to go to Caltech, where Millikan was chief physicist.
Caltech wouldn’t take you until you had at least two
years at a liberal arts college. So I went to the Uni-
versity of Chicago and got hooked on philosophy of
science. I abandoned my plans to become a physicist.
I didn’t get any degree higher than bachelor’s.

Notices:

You also had an interest in magic from

an early age. How did that develop?

Gardner:

My father was not a magician, but he

knew a few magic tricks that he showed me as a

small boy, and that got me interested. Then I got
acquainted with a Tulsa magician, and I discovered
the magic periodicals and magic shops. I’m not a
performer. The only time I came close to per-
forming was when I was in college in Chicago. I used
to work Christmas season at Marshall Field’s de-
partment store, demonstrating magic sets. That’s
the closest I ever came to getting paid for doing any
magic. It’s been a lifelong hobby. I particularly like
magic tricks that are based on violating topologi-
cal laws. I’ve done a number of books for the magic
trade. They sell in magic stores.

Notices:

Your father was a petroleum geologist.

Gardner:

My dad got a Ph.D. in geology, and at

that time the oil business was just getting started. So
we moved to Tulsa, and he became what they called
a wildcatter. He had a small oil production company

Martin Gardner occupies a unique position in the mathematical world. The author of the “Mathematical Games”
column that ran for twenty-five years in

Scientific American

magazine, he opened the eyes of the general public to

the beauty and fascination of mathematics and inspired many to go on to make the subject their life’s work. His
column was the place where several important mathematical notions, such as Conway’s Game of Life and Penrose
tiles, first became widely known. It was also a place where the sheer fun of mathematical games and puzzles was
celebrated and savored. His crystalline prose, always enlightening, never pedantic, set a new standard for high qual-
ity mathematical popularization. In 1987 he received the AMS Steele Prize for Mathematical Exposition “for his many
books and articles on mathematics and particularly for his column ‘Mathematical Games’ in

Scientific American

.”

In addition to writing about mathematics, Gardner has also been a prominent debunker of pseudoscience, starting

with his very first book, originally published in 1952,

Fads and Fallacies in the Name of Science

. His many magazine

articles and book collections have performed a public service by exposing quackery and fraud that masquerade as
science. His lifelong interest in magic—he was once among the top “card mechanics” in the nation and has written tech-
nical manuals for professional magicians—has brought him special insights into the methods of spoon-benders and
other hucksters who claim their feats have a psychic basis.

Martin Gardner was born October 21, 1914, in Tulsa, Oklahoma. He attended the University of Chicago and earned a

bachelor’s degree in philosophy in 1936. After four years in the Navy, he worked as a freelance writer of short stories in
Chicago. In the mid-1940s he moved to New York City, and for eight years he wrote for

Humpty Dumpty

, a children’s mag-

azine. He began his

Scientific American

column in 1957. In the early 1990s he retired to Hendersonville, North Carolina,

from where he continued his prolific writing career. A man of wide interests, Gardner is the author of over fifty books,
including a novel,

The Flight of Peter Fromm

, and works on philosophy and literature. In 2002 he moved to Norman,

Oklahoma, the home base of the University of Oklahoma, where his son, James Gardner, is a professor of education.

What follows is the edited text of an interview with Martin Gardner conducted in November 2004 by

Notices

senior writer and deputy editor Allyn Jackson. Also present were James Gardner and

Notices

editor Andy Magid. Their

help with the interview is gratefully acknowledged.

—A.J.

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that consisted of himself, an accountant, and a sec-
retary. He would go out and look for what they call
domes—oil accumulates under limestone domes.
He would hire some drillers to drill for oil,
and occasionally he would hit and most of the time
wouldn’t. That’s what he did for a living. He con-
tributed occasionally to geological journals.

Notices:

And what about your mother?

Gardner:

She was a kindergarten teacher in Lex-

ington. They met at the University of Kentucky. But
she was mainly a housewife.

Heroes of Philosophy

Notices:

Rudolph Carnap was one of your teachers

at Chicago.

Gardner:

Yes, he is one of my heroes. I took a

seminar from him under the GI bill after I got out
of the Navy. It was not when I was an undergrad-
uate. That was the only graduate course I ever
took. It was on the philosophy of science, and it had
a big influence on me. Later, when Carnap was giv-
ing the course in California, I persuaded him to have
his wife tape record it. She typed it up and sent me
the typed version. I edited it into a book called

In-

troduction to the Philosophy of Science

. That was the

only popular book that Carnap ever did. All I did
was edit it into language an average person could
understand without knowing any math.

Notices:

What was it about his approach to phi-

losophy that attracted you?

Gardner:

He was in the logical positivist school.

The essence of logical positivism is that a philo-
sophical statement is totally meaningless unless
you can prove it logically or find some empirical
evidence for it. From his point of view, all meta-
physical statements are totally meaningless in the
cognitive sense. They can have an emotional mean-
ing, but that doesn’t prove that they are true. It just
means that you want to believe them.

Once Bertrand Russell came to the University of

Chicago to give a series of seminars, and Carnap
attended them. I attended one in which they got into
a big discussion about whether their wives existed
or not. Carnap is inclined not to call himself a re-
alist. The only reason he recommends the realis-
tic language is that he thinks that’s the most effi-
cient language for science. Of course, Russell is a
dyed-in-the-wool realist who thinks the universe ex-
ists whether anybody observes it or not. So Rus-
sell kept turning the argument into a question of
whether they had a right to say their wives really
existed outside of their own experience. The next
day I was in the University of Chicago post office
building to pick up some mail, and I saw Profes-
sor Hartshorne, from whom I was taking some
courses. He asked, “Were you at Russell’s seminar
yesterday? How did it go?” I said, “Well, Russell tried
to convince Carnap that his wife existed, but Car-
nap wouldn’t admit it.” And who should walk in

except Carnap! To my great embarrassment
Hartshorne said, “Mr. Gardner here attended your
seminar last night, and he said you wouldn’t admit
that your wife existed.” Carnap didn’t smile at all,
he just glowered down at me—he was a very tall
fellow—and he said, “Well, that was not the point
at all.” What exactly the point was, I am not quite
sure! This ends on a very tragic note. It was some
time later that Carnap’s wife committed suicide.
She hanged herself. I have no idea why. I know
about it only because there was a piece in Cali-
fornia newspapers about it. I never asked Carnap
about it.

Bertrand Russell is another one of my heroes.

Notices:

Did you meet Russell at that seminar?

Gardner:

No, I never met him personally.

I was at Chicago during the famous Hutchins-

Adler  period.  Mortimer  Adler  came  from  an
orthodox  Jewish  background  and  became  fasci-
nated  by  Catholicism,  and  he  almost  joined  the
Catholic church. Half a dozen or more students of
Adler’s at Chicago became Catholics as a result of
taking courses from him. I never liked Adler. I took
one course, a Great Books course he taught with
Hutchins. I wrote a letter to the

New Republic

—it

was published—saying that readers should all pray
for Adler’s conversion to the Catholic church, be-
cause that would clear the air, and we would know
exactly what he believed. I have a very rare docu-
ment, a speech that Adler gave at Northwestern Uni-
versity, and incredible as it may seem, he argued
that, if the Catholic church is a true church, it had

Figure 1. This original of Escher’s

Circle Limit

hangs in Martin

Gardner’s home.

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a right to execute heretics.
Can you imagine somebody
in  this  day  and  age  saying
that the church had a right
to execute heretics? That’s
in  this  lecture.  Adler  of
course  is  very  much
ashamed of it. But the punch
line is that, shortly before he
died,  Adler  joined  the
Catholic church. So it took
about half a century for the
prayers of the

New Repub-

lic

readers to be answered.

Notices:

You wrote that

letter at the time you were at
Chicago?

Gardner:

Yes, I was an

undergraduate. Adler was a
character. He had a tremen-
dous ego. He edited the

En-

cyclopedia Britannica

. If you

look  through  the  first  vol-
ume, which has general ar-
ticles,  you  will  find  very
short  articles  on  Bertrand
Russell,  no  article  on  Car-
nap, a very short article on
Quine—and when you turn
to Adler, a big, long article
of several columns! But the

university  was  an  exciting  place  partly  because
Adler aroused so much animosity among the fac-
ulty and among the students. This led somebody
to  propose  the  “Madman  Theory  of  Education”,
which  says  that  every  university  should  have  a
madman on the faculty who gets the students all
riled up in opposing his views. There was also a joke
going  around  at  the  time  that  the  University  of
Chicago  was  a  Baptist  school  where  Jewish  pro-
fessors were teaching Catholic theology.

Notices:

You didn’t take any math or science

when you were there?

Gardner:

The university had what they called the

“New Plan”, and everybody had to take survey
courses. There were four survey courses, and one
of them was called Physical Science, and you had
to take that. That was the closest I came to taking
a science course, aside from a geology class that I
audited. But I didn’t take any math. My knowledge
of math is at a very low level. I go up to calculus,
and beyond that I don’t understand any of the pa-
pers that are being written. I consider that that was
an advantage for the type of column I was doing
for

Scientific American

, because I had to understand

what I was writing about, and that enabled me to
write in such a way that an average reader could
understand what I was saying. If you are writing

popularly about math, I think it’s good not to know
too much math.

Launching a Writing Career

Notices:

When did you decide you wanted to become

a writer?

Gardner:

While I was a student at the University

of Chicago. I was doing occasional pieces for little
magazines that didn’t pay anything. Before World
War II, I was working in the public relations office
of the University of Chicago, mainly writing science
releases. When I got out of the service, I could have
gotten that job back. At that time I made my first
sale. It was a short story for

Esquire

magazine, and

I actually got paid for it. That was when I decided
I was going to try to freelance. I followed that story
with a science fiction story about topology called
“The No-Sided Professor”. It’s about a mathemati-
cian  who  was  a  student  of  the  properties  of  the
Möbius strip. You take a strip of paper and twist
it and glue the ends together. It loses one of its sides
and becomes a one-sided surface. So I imagined that
the professor had found a way to fold a piece of
paper  so  that  it  lost  both  sides  and  became  a
no-sided  surface  and  just  vanished  with  a  little
“pop”. So that was the beginning of my “No-Sided
Professor”.  For  about  a  year  I  lived  on  sales  to

Esquire

magazine—all fiction.

Notices:

Then you moved to New York. When

was that?

Gardner:

It was 1944 or 1945.

Notices:

You went to make your living as a writer

in New York.

Gardner:

That’s right, New York’s where all the

action is. I married a New York girl. I couldn’t make
a living freelancing.

Esquire

had moved from

Chicago to New York and had a new editor, and the
new editor didn’t care for the type of story that I
was selling. So my market with

Esquire

dropped off.

I got a job with

Humpty Dumpty

magazine, a chil-

dren’s magazine. That was how I managed to exist.
I worked at home and wrote activity features, a
short story for every issue about the adventures of
Humpty Dumpty Jr., and a poem of moral advice
from Humpty to his son. I did that for eight years.
I stopped doing it after I began selling to

Scientific

American

Notices:

How did it come about that you started

writing for

Scientific American

Gardner:

I was interested in the topic of me-

chanical devices that solve logic problems. I sold

Scientific American

an article on the history of

logic machines. These are mechanical devices that
solve problems in elementary logic. This was be-
fore the days of computers, of course, which now
can do it much more efficiently. With the article they
included a pasteboard sheet that was bound into
the magazine, and the sheet contained pictures of
cards that had windows in them. You could cut the

Figure 2. These hexaflexagons,

some of them handmade, were

collected by Martin Gardner

after his column on the subject

appeared in

Scientific American

They are kept, together with all

of his files from his writing

career, in the Martin Gardner

archive at Stanford University.

Photo

Allyn

Jackson.

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cards out and cut open the windows. Then you
could pick out cards for the two premises of a syl-
logism and put them on another card. Through the
windows you could see the conclusion of the syl-
logism. They asked me if I had any more articles
similar to that one. The second article I sold them
was on hexaflexagons. They had been invented by
a group of graduate students at Princeton, includ-
ing, of all people, Richard Feynman.

Notices:

How did you find out about hexa-

flexagons?

Gardner:

From my magic contacts, believe it or

not. There was a stockbroker in New York City
named Royal Heath, who was a magic buff. I was
in his apartment one day, and he showed me a large
hexaflexagon made of cloth. I had never seen one
before. He told me that the group at Princeton had
invented it. So I saw the possibility of an article, and
I made a trip to Princeton. I interviewed John Tukey,
one of the coinventors. He became a very famous
mathematician much later. That article ran in

Sci-

entific American

in December 1956. Gerry Piel, who

was the publisher, called me in to his office and
said, “Is there enough similar material to this to
make a regular feature?” And I said I thought so.
The next issue was the first of the columns, the Jan-
uary 1957 issue. I resigned from

Humpty Dumpty

and rushed around the old book sections of New
York to pick up all the math books I could find that
had recreational material.

Notices:

There was a big response to the hexa-

flexagon article, wasn’t there?

Gardner:

Yes, it caught on. All over New York,

and especially in advertising, people were folding
hexaflexagons! During the first year after the arti-
cle, a lot of advertising premiums came on the
market that were paper hexaflexagons with space
for an advertisement.

Notices:

This group of magicians you knew in

New York—can you tell us about them?

Gardner:

I got acquainted with a lot of famous

magicians. I was doing pamphlets for the profes-
sion  with  material  that  they  provided.  I  lived  in
Chicago for fifteen years, and I first got acquainted
with  professional  magicians  there.  They  would
meet every week at a roundtable. It included a lot
of  famous  performers—the  names  would  mean
nothing now, though. Magic has become a TV spec-
tacular,  with  David  Copperfield  and  his  rivals
spending millions of dollars on equipment for their
shows.  But  in  those  days  the  magicians  worked
night clubs. My interest is in what they call close-
up magic, which you do close-up, rather than on
the stage.

Notices:

In New York you met Persi Diaconis in

this circle of magicians. How old was he when you
met him?

Gardner:

I think he was a late teenager. He was

a professional card shark, or a card mechanic, as

they call it in the trade. He worked ships between
New York and South America. Of course, nobody
suspected him of being skillful with cards because
he was just a teenager. He was a student at City Uni-
versity of New York, and he paid his way through
the  university  with  the  money  that  he  got  from
poker games on ships. At that time Persi was very
anxious to get into Harvard. The head of the sta-
tistics  department  at  Harvard  was  Frederick
Mosteller, who is a magic buff. He was very active
in magic, and his picture has been on the cover of
magic  magazines.  I  knew  Mosteller  slightly,  so  I
wrote him a letter and said, “This young student
is one of the best card mechanics in the country.
He does a fantastic second deal and bottom deal.”
(Those are terms for fake deals. When you are deal-
ing from a deck, there is a way to deal the second
card instead of the top card, and there is a way to
deal the bottom card instead of the top card.) I got
back a letter right away from Mosteller, which said,
“If he’s willing to major in statistics, I can get him
into Harvard.” So I asked Persi if he was willing to
major in statistics, and he said, “Of course!” So he
got  in,  got  his  Ph.D.  in  statistics,  and  is  now  at
Stanford.

By the way, I gave all my math books and math

files to Stanford, at the request of Donald Knuth.
His

Art of Computer Programming

is filled with

Figure 3. This large-as-life portrait of Albert Einstein was taken
by a friend of Martin Gardner’s and hangs in Gardner’s home.

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recreational material. One time he wanted to get
access to my files and asked if he could visit me
when I was living in Hendersonville. He came and
stayed a week. I had rented an apartment just to
contain my books and files. Knuth stayed in the
apartment. It had a kitchen, so he cooked his own
meals,  and  on  Sunday  he  walked  to  a  nearby
Lutheran  church.  He  pulled  out  from  my  files  a
stack  of  papers  about  this  high,  which  I  photo-
copied for him. Now my files are being indexed by
someone at Stanford.

For every column I did there may be four or five

folders containing research and notes that I took.
I subscribed to seven or eight math journals that
had recreational material, and I would clip articles
and file them in appropriate folders.

When the column started, the math was on a

pretty low level. It slowly got a little more techni-
cal, partly because I was learning math myself
while I was writing the column, and partly because
I was getting material from top mathematicians who
were interested in recreational math. So the column
became much more interesting a few years after it

started, because I was publishing material that
hadn’t been published before. It was coming from
Sol Golomb, John Conway, Ron Graham, and Frank
Harary, among others.

One of the frequent contributors was Sol

Golomb. In a paper that he had written when he was
quite young, he introduced the idea of polyominoes.
When I did the column on polyominoes, it was the
first introduction to the general public and to math-
ematicians.  That  was  one  of  my  very  successful
columns.  A  lot  of  mathematicians  began  experi-
menting  with  polyominoes,  and  especially  the
pentominoes.

The Game of Life

Notices:

How did you get in contact with Golomb?

Gardner:

I think I had a copy of the paper in

which he first named the polyominoes. I think I just
wrote to him and got into correspondence with him,
and then we became pretty good friends.

One of my most popular columns was based on

Conway’s Game of Life. During a visit with me,
Conway rapidly went over maybe twenty different
things that he was working on at the time, and one
of them happened to be the Game of Life. He didn’t
think there was anything special about it. Of the
things he told me, I thought that was the most in-
teresting. When I wrote that up, it really caught on.
Computer people all over the U.S. were trying to
write algorithms for their computers to play the
game. There was one fellow I heard about who had
a button under his desk at work, so that he would
be working on Life configurations on his computer,
but if someone in management walked in, he would
press the button, and the computer would go back
to something related to his job.

Notices:

How was it that out of this list of twenty

different things you picked the Game of Life?

Gardner:

Well, I got columns out of some of the

other ideas too.

Notices:

But you knew the Game of Life was

something special.

Gardner:

That’s right. If I had known more about

mathematics, I might not have thought that. But I
approached it as a sort of a half-layman. I later
did a second column on Life, because Conway had
offered $50 to anybody who could create what he
called a Glider Gun. That is a configuration that,
when you applied the transition rules of Life, would
shoot off gliders. It was discovered by Bill Gosper,
who at the time was working for Marvin Minsky at
MIT in the artificial intelligence program there. The
Glider Gun opened up all kinds of possibilities. So
I did a second column based on the Glider Gun. It
turned out that by using gliders and shooting them
down with another gun, you could actually use the
Game of Life to do anything you could do on a gen-
eral purpose computer, which was a surprising

Figure 4. Cover of the January 1977 issue of

Scientific American

that carried a column by

Gardner about Penrose tiles.The set of Penrose

tiles shown was originally drawn for Martin

Gardner by John H. Conway. (Courtesy of

Scientific American

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discovery, made by Conway. So the game turned
out to be far from trivial.

Notices:

Did Conway tell you how he came up with

the specific transition rules in the Game of Life?

Gardner:

All Conway would say is that he ex-

perimented with a wide variety of rules and that
the rules he finally settled on were the most pro-
ductive and the most interesting. I got to know Con-
way fairly well, and he is an authentic genius. His
name appears quite often in the column. He sent
me marvelous material. I had the great privilege of
introducing  him  to  Benoit  Mandelbrot.  This  was
when I was still living in New York. Mandelbrot was
living in Westchester, not too far away. Conway vis-
ited  me  and  stayed  maybe  several  days.  I  was
slightly  acquainted  with  Mandelbrot,  so  I  called
him, and he rushed over to meet Conway, because
Conway was working on the Penrose tiles. The Pen-
rose tiles have a fractal quality—you can keep mag-
nifying portions of them and you always get the
same tiling. So Mandelbrot was quite fascinated by
the tiles.

Ciphers, Quantum Mechanics,
and the Nature of Reality

Notices:

How did you first find out about the

Penrose tiles?

Gardner:

I think Penrose sent me a copy of the

piece that he had done on them for a magazine, and
I got into correspondence with him and found out
more about them. Then Conway got intrigued by
them. Actually, most of the pioneer discoveries
about the Penrose tiles were made by Conway.

Another column I did was on trapdoor ciphers,

and that aroused a lot of controversy. One of the
discoverers  of  the  trapdoor  cipher,  Ron  Rivest,
came to see me to tell me about it and also to give
me materials for a column. The cipher introduced
a whole new era in cryptography, because it was
an unbreakable code. I had said in the column that
if you want to know more about Rivest’s trapdoor
cipher, he has an unpublished technical paper on
it, and he has offered to mail it to anyone who sends
him  a  stamped,  self-addressed  envelope.  Rivest
got  flooded  with  thousands  of  letters.  Then  the
government  stepped  in  and  forbade  him  from
mailing out his paper. It was a year or two before
the government allowed him to release information
on the code. For about a year I got angry letters
from  people  who  said,  “I  followed  your  advice
and I wrote to Rivest and I asked for the paper, and
I never heard from him!”

Rivest gave me a short sample written in the

code, and he offered a prize to anyone who could
crack it. It was many years before somebody
cracked this particular message that I had pub-
lished. It was cracked by a lot of computers work-
ing in tandem, running for many, many hours. As
a result, Rivest had to revise his code a little bit,

so he used larger primes. The code is based on mul-
tiplying two primes together. I think he had to go
to a much larger prime to keep the code sound.

Notices:

Have you followed developments in

quantum coding?

Gardner:

Yes, I have a very low-level under-

standing of quantum codes. Apparently it’s possi-
ble to base a code on quantum mechanics, though
I don’t know how it’s done exactly. If I were younger,
I would try to understand quantum mechanics. It’s
such a fascinating field. An illustration that ran with
an article I did for

Discover

, called “Quantum Weird-

ness”, shows an eye looking at a tree, illustrating
the question of whether the tree exists if nobody
is observing it. Of course, quantum mechanics is
tinged with this kind of solipsism, because there
is a sense in which an electron doesn’t really have
any  properties  until  you  measure  it.  There  is  a
subjective  aspect  to  quantum  mechanics.  Some
experts  like  Eugene  Wigner  were  convinced  the
universe wouldn’t exist if it didn’t have observers
in  it.  He  argued  that,  without  a  conscious  mind
observing  the  quantum  events,  the  events  don’t
really exist, which I think is a crazy point of view.
But  it  is  defended  by  a  number  of  quantum  me-
chanics  experts.  Einstein  thought  this  approach
was completely ridiculous. He liked to say, “Does
the tree exist if a mouse observes it?” That was one
of Einstein’s famous rebuttals

Notices:

So you don’t believe in these ideas?

Figure 5. This illustration appeared on the cover of the issue
of

Discover

magazine that carried Martin Gardner’s article on

quantum mechanics, “Quantum Weirdness”. A framed version
hangs on Gardner’s wall.

Gardner:

No, I’m a hardheaded realist. I think

the universe exists even if life ceased to exist. Most
philosophers of science are realists. Bertrand
Russell certainly was. And of course Einstein and
his friend Kurt Gödel were devout realists.

Notices:

Did you ever get interested in the

philosophy of mathematics and the question of the
reality of mathematical objects?

Gardner:

Yes, I have. I have published a num-

ber of pieces defending mathematical realism.

Notices:

Have you ever met a mathematician

who was not a realist?

Gardner:

I have not actually met any, but there

are a number of mathematicians who are not
realists. Reuben Hersh is a marvelous example of
a person who thinks that mathematics is entirely
a human product and has no reality outside of
human culture. He has written a whole book about
this called

What Is Mathematics

Really

To Reuben

Hersh,  mathematics  is  no  different  from  art  or
fashions in clothes. It’s a cultural phenomenon. The
postmodernists  in  France  have  essentially  this
point of view. And it drives me up the wall. I like
to say, “If two dinosaurs met two other dinosaurs
in  a  clearing,  there  would  be  four  of  them  even
though the animals would be too stupid to know
that.” Of course, the argument as to whether the
universe exists outside of the human mind goes
back to the middle ages.

Roger Penrose is a good example of a staunch

realist in mathematics. He likes to talk about the
Mandelbrot set as an example of something out
there, independent of human minds, because as you
keep magnifying portions of it and exploring it, you

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discover new properties. It’s like walking through
a jungle and charting the mountains and rivers
and so on. Something is out there, independent of
your mind. It doesn’t have the same kind of real-
ity as sticks and stones, but it has its own peculiar
reality. In the new book of Penrose,

The Road to

Reality

, he has a whole chapter defending mathe-

matical realism.

I once asked Raymond Smullyan, who is an

expert on set theory, if he knew of any experts on
set theory who are not realists. He could not think
of a one.

Notices:

That’s an interesting example, of course,

because set theorists use things that are really
exotic, like inaccessible cardinals.

Gardner:

They exist in this peculiar mathemat-

ical world of their own. They don’t exist the way
the Sun exists or the Moon exists. But they exist the
way complex numbers exist, for example, or imag-
inary numbers. They have a peculiar reality.

The last math conference I went to was in some

town  in  North  Carolina.  It  was  a  conference  to
honor the mathematician Hermann Weyl. Penrose
was speaking, and I went there partly to hear him
speak  and  to  meet  him.  I  also  went  because  Ed
Witten was talking on superstrings. I understood
everything that Penrose said in his lecture, and I
didn’t understand a single sentence of Witten. Not
a single sentence. Superstring theory has been ab-
sorbed into membrane theory, or M-theory, as they
call it. There is not a scintilla of empirical evidence
to  support  it.  Although  I  have  only  a  partial  un-
derstanding of M-theory, it strikes me as compa-
rable to Ptolemy’s epicycles. It’s getting more and

Figure 6. An artist

friend drew this

picture for Gardner,

illustrating the

maximum number of

pieces into which a

bagel can be sliced

by three planes.

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more baroque. Penrose thinks that M-theory is very
ingenious and very beautiful but has no relation to
physical reality. That’s his opinion.

Notices:

Because of the lack of empirical evidence?

Gardner:

Yes. But Penrose has a rival theory

that he calls twistor theory. I only partially under-
stand it, but twistors are structures that he thinks
are the basic elements of spacetime. The theory is
based on earlier work on what are called spinors.
I have only a very dim grasp of his twistor theory.
He has a big section on it in his latest book, and
he has published numerous papers on twistor
theory. I noticed that when he discusses twistor
theory in this new book, he speaks of efforts that

have been made to combine it with membrane

theory. He comes to the conclusion that there is no

way they could be combined, and he states flatly

that if one is true, then the other has to be false.

Now, whether twistor theory has any relevance to

the universe, I haven’t the foggiest notion. But

there is a whole group of mathematicians working

on it.

Notices:

So there is no empirical evidence for

twistor theory either?

Gardner:

None whatever.

Martin Gardner’s Notes on the Illustrations

Some of the illustrations in this article are photographs of artworks owned by Martin Gardner and displayed on the
walls in his home. He kindly wrote the following notes about each work.

Figure 1.

Maurits Escher’s

Circle Limit

, so called because the circle is the limit of an infinite set of smaller and smaller

fishes. I devoted a

Scientific American

column to Escher many years before he became famous. I first learned of Escher

from pictures in Donald Coxeter’s classic

Introduction to Geometry

. Coxeter told me in a letter that Escher still had

copies of this picture for sale. I bought it directly from Escher for sixty dollars. Had I anticipated his fame, I could
have bought many of his black and white pictures for a paltry sum. The picture is based on Poincaré’s model of the
hyperbolic plane. The model is used to prove that if Euclidean geometry is consistent, so is hyperbolic geometry.

Figure 3.

Einstein. This picture was taken by a college friend, David Eisendrath, a professional photographer in

New York City. It ran on the first page of a short-lived newspaper called

that had been funded by Marshall Field.

Einstein had just become a U.S. citizen, as indicated by the tiny flag in his lapel. Dave told me that although Einstein
was dressed in a business suit and tie, he wore tennis shoes with no socks. The cloud of smoke resembles a goatee.

Figure 5.

The eye looking at a tree. This was an illustration for my article “Quantum Weirdness” that ran in

Discover

(October 1982). Quantum theory has a tinge of solipsism in the sense that basic particles have no definite

properties until they are measured. A few physicists have argued that the Moon doesn’t exist unless it is observed.
Einstein, who disliked quantum mechanics, liked to ask: “Observed by a mouse?” Bishop Berkeley claimed that “to
be is to be perceived.” This prompted Ronald Knox to write a famous limerick:

There once was a man who said: “God
Must think it exceedingly odd

If he finds that this tree
Continues to be

When there’s no one about in the Quad.”

The answer was supplied by an anonymous author in an equally famous limerick:

Dear Sir, your astonishment’s odd,
I am always about in the Quad.

And that’s why the tree
Will continue to be

Since observed by yours faithfully, GOD.

Figure 6.

The sliced doughnut. In an early

Scientific American

column I asked for the maximum number of pieces

into which a torus could be sliced by three planes. An old puzzle concerned slicing a pie or cake with three cuts. I
generalized it to a torus. An artist friend, John McClellan, who ran an art store in Woodstock, New York, sent me

this picture as a gift. The answer is 13 pieces. The formula for

cuts is

Figure 7.

The domino picture was made by Ken Knowlton, a mathematician who pioneered this technique. He

makes similar pictures with other objects such as playing cards, sea shells, etc.

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Debunking
Pseudoscience

Notices:

How have you

managed the professional
aspects of your writing ca-
reer?  Are  you  part  of  a
professional  author’s
guild  or  something  like
that?

Gardner:

I used to be

a member of the Author’s
League, and I finally
dropped out of it because
it kept getting more and
more expensive to be a
member,

and

they

weren’t really helping me
in any special way. I don’t
have an agent, for exam-
ple.  I  finally  learned
enough  about  contracts
so I could do them on my
own. I did have an agent
for  my  first  book,

Fads

and Fallacies in the Name
of Science

. A high school

friend of mine was a lit-
erary agent. Actually, he
persuaded me to do that book. I had done an arti-
cle for the

Antioch Review

on pseudoscience called

“Hermit Scientists”. My friend said, “Why don’t you
expand this into a book?” So he handled the book
for me and sold it to Putnam’s. It did so poorly with
Putnam’s that they remaindered it after they sold
a few copies! Then it was picked up by Dover, and
it became one of Dover’s best sellers. There was a
nighttime radio program by a man named Long
John Neville. He picked up on this book, and for
about a year he had on his program cranks who at-
tacked the book. It was the attacks on the Long John
Neville show that boosted the sales. It hasn’t been
out of print since. I have chapters in the book at-
tacking pseudosciences that at the time I wrote the
book I would never have expected to survive.

Notices:

But some of them have, like Scientology.

Gardner:

Yes, I have a chapter on Scientology—

in those days it was called Dianetics. It was such a
crazy point of view I couldn’t imagine that it would
last more than a few years. It became a tremendous
movement. There are Hollywood stars who are Sci-
entologists. I think L. Ron Hubbard originally
thought of it just as a way to make money. But then
later on he began to believe it himself.

Notices:

How did you get interested in debunk-

ing pseudoscience?

Gardner:

First I have to talk about my religious

background. When I was in high school, I was an
evangelical Protestant, due mainly to the influence
of a Sunday school teacher I knew. He had a

wonderful  name  for  an
evangelical  Christian,
George Getgood. He was
also a counselor in a sum-
mer camp that I attended
in Minnesota every year.
I went through a tempo-
rary  phase  of  consider-
ing myself an evangelical
Christian. There was a pe-
riod  in  which  I  was
doubtful  about  the  the-
ory of evolution, mainly
because  of  reading  a
crank

book

called

The New Geology

, by a

creationist named George
McCready  Price.  His  at-
tack  on  evolution  was
fairly  sophisticated.  He
was  a  Seventh  Day  Ad-
ventist who believed that
the fossils were remnants
of  life  that  perished  at
the time of the flood. He
argued that the theory of
evolution is largely based
on the fact that when you

consider the fossils in the different strata, you find
very simple forms in the older strata, and then as
you get into younger and younger strata, you get
more complicated forms. But, he said, this is cir-
cular reasoning, because the way they date the
beds is by the type of fossils they contain. So his

New Geology

is filled with photographs of places

where the fossils are in the wrong order: you find
the complicated fossils in the lower beds and the
simpler fossils in the higher beds. What he didn’t
realize is that these “upside- down” fossils are due
to folding of the strata or cleavage along a fault line.
But if you don’t know this fact, his arguments are
quite strong. It was not until I took courses in ge-
ology at the University of Chicago that I understood
where Price went wrong. His book is one of the great
crank works of all time. Modern creationists are still
citing it and recommending it—sometimes without
giving him credit! I think that was the first time that
I became interested in pseudoscience. I probably
would not have followed it up if my friend had not
recommended I do a book about it. Later I got ac-
quainted with the philosopher Paul Kurtz, the ma-
gician James Randi, the sociologist Marcello Truzzi,
and the psychologist Ray Hyman. We started the
Committee for Scientific Investigation of Claims of
the Paranormal, or CSICOP, as we called it. I began
doing a column in the

Skeptical Inquirer

, and those

columns have come out as book collections.

Notices:

Have you been present at demonstrations

by psychics, like Uri Geller, who bends spoons?

Figure 7. This enigmatic portrait of Martin

Gardner is made of dominoes.

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Gardner:

I have never actually seen Uri Geller,

though I have written two booklets exposing his
methods, under the pseudonym of Uriah Fuller. His
methods are well known to magicians. The magi-
cians understood what he was doing from the very
start.

Notices:

When you wrote those booklets, didn’t

that break the magician’s code of not giving away
the secret of the tricks?

Gardner:

Not really, because the things that Uri

Geller does are not done by magicians. Magicians
would be ashamed to stand up in front of an
audience and bend a spoon! It seems too silly. The
booklets don’t expose anything that magicians do.
They just expose what Geller does.

Notices:

So how does he bend a spoon?

Gardner:

He gains access to the spoons before

the demonstration. If you take an ordinary spoon,
it’s easy to bend it. You can bend it back and forth
a few times to weaken the metal to the point where
if you just stroke the spoon it bends. That’s the
whole secret of Uri Geller’s metal bending—getting
to the material in advance and preparing it.

Art and Aesthetics

Notices:

If you had been a mathematician, what

area do you think you would have worked in?

Gardner:

Topology fascinates me, because you

are dealing with such basic properties.

Notices:

You argue in your book

Whys of a

Philosophical Scrivener

that there exist absolute

aesthetic standards for art.

Gardner:

Yes, though it’s very hard to state what

they are. Ed Rinehart made a fortune painting can-
vases that were just one solid color. He had his black
period in which the canvas was totally black. And
then he had a blue period in which he was paint-
ing the canvas blue. He was exhibited in top shows
in New York, and his pictures wound up in muse-
ums. I did a column in

Scientific American

on min-

imal art, and I reproduced one of Ed Rinehart’s black
paintings. Of course, it was just a solid square of
pure black. The publisher insisted on getting per-
mission from the gallery to reproduce it.

Notices:

And they gave it?

Gardner:

They gave it.

Notices:

If there are absolute standards for

aesthetics in art, do they also exist in mathematics?

Gardner:

Dirac was a great believer in having

beautiful equations. “There is no room in mathe-
matics for ugly mathematics,” was, I think, one of
his statements. But in physics you can have very
beautiful theories that turn out to be totally false.
There is a predecessor of string theory called vor-
tex theory, in which all the basic particles were
supposed to be knots in the ether. Since there is
no friction in the ether, once a little particle would
form, it could not lose its shape. I was doing some
checking on it, and I ran into statements by top

physicists (including James Maxwell, Lord Kelvin,
J. J. Thomson, and Albert Michelson) that this the-
ory is too beautiful not to be true. See Chapter 32
in my

New Ambidextrous Universe

Speaking of art, several times I met Salvador

Dali in New York. We would have lunch together.
He had read my writings about mathematics. He
was interested in mathematics in a funny way.
Some of his paintings show a reflection in a cylin-
der or a cone, which is called anamorphic art. He
also did paintings that turn into other pictures
when you give them a rotation of 90 degrees. He
liked to experiment with strange art.

Notices:

What was he like as a person?

Gardner:

He seemed perfectly normal.

Notices:

Really? Even with that mustache!

Gardner:

Yeah, he had that funny mustache. I

remember  after  one  lunch,  he  wanted  to  go  to
Brentano’s  bookstore.  We  walked  down  Fifth
Avenue, and we could take only about five steps
before  someone  handed  him  a  pen  and  a  piece
of  paper  and  wanted  his  autograph.  He  would
scribble really fast, and then we would walk on.

About the Cover

Martin Gardner, the subject of this month’s fea-
ture interview, was photographed at his resi-
dence in Norman, Oklahoma, on March 3, 2005.
Gardner is holding the 1999 “Definitive Edi-
tion” of his book

The Annotated Alice

, first pub-

lished in 1960. There are now over 500,000
copies in print. In the background is Ken Knowl-
ton’s portrait of Gardner, constructed from
dominos. (This photograph, in addition to the
uncredited photos in the article, were taken for
the

Notices

by Gilbert Jain Photography.)

—Andy Magid