Sunday, December 14, 2008

Apocrypha Redux


I recently came across this interesting book “Mathematical Apocrypha Redux”, by Steven Krantz which, as per the cover page, is about “More Stories and anecdotes of Mathematicians and the Mathematical” (the word “more” is used as this is a sequel to the book “Mathematical Apocrypha”, by the same author). Lots of interesting stories, and some not so, but I singled out the following few (often, abridged and restated) for this post:



(1)
The daughter of mathematician Lee Neuwirth, Bebe Neuwirth, played Frasier Crane’s wife in the popular television shows Frasier and Cheers (thanks to Frasier, I can’t enjoy any other sitcom as much – Frasier has definitely raised the bar).




(2)
It is not very widely known that Knuth’s first publication was for the MAD magazine (MAD Magazine 33 (June 1957),36-37). It was called “The Potrzebie system of weights and measures”. The article parodied the established system of weights and measures that we all use. For example, it proposed the fundamental units of length and force to the thickness of MAD Magazine #26 and "whatmeworry" respectively. It also suggested the "yllion" notation for large numbers: one myllion is one myriad myriad (l08) and one centyllion is 102102. "Potrzebie" is a word that publisher William Gaines lifted from a Polish aspirin bottle; it is the locative form of a Polish noun meaning "need."


(3)
Erdos had a friend working on harmonic analysis in Oxford, England. The poor man was hopelessly schizophrenic. When Erdos once visited him, the fellow just opened the door of his office a little bit and said, "Please come another time and to another person."


(4)
John von Neumann (1903-1957) once owned a dog named "Inverse". Rene Descartes (1596-1650) owned a dog named "Monsieur Orat," which means "Mr. Scratch".


(5)
Of the many incidents of mathematicians over thinking mundane life, this takes the cake. Or bread rather. Henri Poincare (1854-1912) was in the habit of buying a 1 kilo loaf of bread daily from a local baker. After a year of record keeping, he determined a normal distribution of the weights of the loaves with mean at 950gms. He called the police and informed them of the dishonesty on the part of the local baker. The cautious baker began serving him the biggest loaf in their store for the next year. He was clearly surprised therefore, when, after a year, Poincare again summoned the police : his records, this time, showed a bell-shaped curve with the minimum at 950 grams but truncated on the left side.


(6)
This is an old one. Niels Bohr (1885-1962) had a horseshoe nailed outside his house, over his door. One day, when asked incredulously by a friend whether he really believed that the thing would bring him luck, he replied, "I don't. But, I understand that it brings you luck whether you believe it or not."


(7)
Q: What do you get when you cross a mosquito with a mountain climber?
A: Silly! You can't cross a vector and a scaler.

(8)
This one is of potentially immense practical use to me (and fellow researchers I am sure). Often, after a presentation on an abstract subject, when the speaker requests enthusiastically for questions from the audience, he is greeted by embarrassing silence (due to the fact that no one but the speaker has the remotest idea of what is going on). As a remedy for such situations, Desmond MacHale, a author and a mathematician, has compiled the following set of questions, which a member of the audience might confidently put forth to the speaker, irrespective of whether he understands the subject matter or not:

  • Can you produce a series of counterexamples to show that if any of the conditions of the main theorem are dropped or weakened, then the theorem no longer holds? What inadequacies of the classical treatment of this subject are now becoming obvious?
  • Can your results be unified and generalized by expressing them in the languag e of Cat egory Theory?
  • Isn't there a suggestion of Theorem 3 in an early paper of Gauss?
  • Isn't the constant 4.15 in Theorem 2 suspiciously close to 4n/3?
  • I'm not sure I understand the proof of Lemma 3-could you outline it for us again?
  • Are you familiar with a joint paper of Besovik and Bombialdi which might explain why the converse of Theorem 5 is false without further assumptions?
  • Why not get a graduate student to perform the horrendous calculations mentioned in Theorem 1 in the case n = 4?
  • Could you draw us a simple diagram to show what the situation looks like for n = 2?
  • What textbook would you recommend for someone who wishes to get students interested in this area?
  • When can we expect your definitive textbook on this subject?
  • Why do you think there was such a flurry of activity in this area around the turn of the century and then nothing until your paper of 1979?
  • What are the applications of these results?
(9)
When Emmy Noether (1882-1935) applied for the position of a faculty member at Gottingen, she faced a lot of opposition – as part of then prevalent prejudices against women. David Hilbert (1862- 1943), strongly defended her stance, and is known to have uttered the following words when addressing the council of the university: : "I do not see why the sex of the candidate should be an argument against her appointment as Privatdozent; after all, we are not a bath-house ..."


(10)
When Bertrand Russell had, by his second wife, a first child, a friend accosted him with,"Congratulations, Bertie! Is it a girl or a boy?" Russell replied, "Yes, of course, what else could it be?"


(11)
That the bridges of Konigsberg were studied by Euler, which led to the foundations of graph theory and topology, is a popular mathematical trivia. Lesser known is the name of the seven bridges: Kramer, Schmiede, Holz, Hohe, Honig, Kottel, and Grone..



(12)
During class one day, while Lowell Coolidge (1873-1954), a member of the Harvard math faculty in the 1930s, twirled his watch on its chain, the chain broke and the fob watch flew out the window. Coolidge exclaimed, "Ah, gentlemen, a perfect parabola."

Coolidge was a geometer.


(13)
A student of Plato (428 B.c.-348 B.C.) once asked the great master, "What practical use do these theorems serve? What is to be gained from them?" Plato's answer was immediate and peremptory. He turned to one of his slaves and said, "Give this young man an obol [a small Greek coin] that he may feel that he has gained something from my teachings. Then expel him."


(14)
Does God play dice with the universe?

"God does not play dice with the universe." - Albert Einstein

"Who are you to tell God what to do?" - Niels Bohr
"God not only plays dice, but sometimes throws them where they cannot be seen." - Stephen Hawking


(15)

The episode “Treehouse of Horror”, from the sixth season of Simpsons, revealed the following counterexample to Fermat’s Last Theorem:
Take your TI -83 calculator and compute
[1782 12 + 184112 ](1/12)
You will find the answer to be 1922. Thus
178212 + 184112 = 192212 .

Why do you think this works?(Think about the round off error)



(16)
John Horton Conway was once asked to find the next number in the sequence:
1 3
1 1 1 3
3 1 1 3
1 3 2 1 1 3
1 1 1 3 1 2 2 1 1 3

Conway gave up after a couple of weeks worth effort. But you might want to try it … its not as difficult as it might seem- its just, well, a bit different. Hint: This sequence is called the “Look and say sequence”. The next few lines describe the solution in white font – select it to view it.

You read a number aloud, grouping identical consecutive digits together. This gives you the next number in the sequence. For ex we start with “1 3”. We read this number aloud by saying “1 one , followed by 1 three”. So the next number in the sequence becomes “1 1 1 3”. We now read this aloud, saying “3 ones (followed by) 1 three” – so the next number becomes “3 1 1 3”.And so on. Although Conway did fail to initially understand the sequence, he subsequently contributed a lot of ideas to aid in understanding certain properties of this sequence (and other such sequences, often called “atomic sequences”).

(17)

The trivia game ‘Six Degrees of Kevin Bacon’ is based on the small world assumption, and consists of trying to connect any actor to Kevin Bacon through his her roles with him, or with someone who has acted with him, or through any number of such intermediary actors.


Surprisingly, Paul Erdos has a Bacon number of 4. This is the provenance:
  • Paul Erdos was in N is a Number (1993) with Gene Patterson
  • Gene Patterson was in Bo x of Moon Light (1996) with John Turturro;
  • John Turturro was in Cradle Will Rock (1999) with Tim Robbins
  • Robbins was in Mystic River (2003) with Kevin Bacon
This Bacon number would come down to 3 once "Frost/Nixon" is released (slated to be released on 26th December,2008):
  • ErdÅ‘s was in N is a Numbe r with Gene Patterson.
  • Patterson was in Box of Moon Light (1996) with Sam Rockwell.
  • Sam Rockwell will be in Frost/Nixon (2008) with Kevin Bacon

Both the above linkages are disputed because the Gene Patterson in “N is a Number” might not be the same as the Gene Patterson in “Box of Moon Light” (1996)
Again, quite interestingly, Pope John Paul II has a Bacon umber of 3. Here’s how:
  • Pope John Paul II was in Padre Pio — Tra cielo e terra (2000) with Giovanni Lombardo Radice.
  • Giovanni Lombard o Radice was in The Omen (2006) with Vee Vimolmal
  • Vee Vimolmal was in Where the Truth Lies (2005) with Kevin Bacon
It turns out that apparently only 12% of all actors cannot be linked to Kevin Bacon at all. You can check whether an actor/actress is linked to Kevin Bacon here : http://oracleofbacon.org – for starters you might want to check out the Bacon numbers for Sachin Tendulkar, Aishwarya Rai and Amitabh Bachchan :).

The game also defines the concept of a “center of the Hollywood Universe” to be a person with a very low average “personality” number – which is calculated as the weighted average of the degree of separation of all the people that link to that particular person. The current best centre is Rod Steiger, followed by Christopher Lee, Dennis Hopper and Donald Sutherlannd. Karen Black is the highest ranked female center in the list.




(18)
Joe Kohn likes to say that there is no such thing as strong coffee. There are only weak men.

(19)
Jon von Neumann was once on a train and found that he was quite hungry. He asked the conductor to send the man with the sandwich tray to his seat. The busy and impatient conductor said, "I will if 1 see him." Johnny's reply was, "This train is linear, isn't it?"

(20)
W. Sierpinski (1882-1969) was once asked by his wife to watch their trunks when they were moving. She had pointed out that there were 10 trunks – but was surprised when Sierpinski told her upon her return, that there were only nine. And he promptly justified it by counting the trunks aloud: “Zero, one, two …”

(21)
Paul Erdos was an itinerant scholar. He never owned nor rented a home, didn't have a driver's license, didn't have a credit card. He habitually would show up on the doorstep of a friend or a collaborator-anywhere in the world!-declare that "My brain is open. "-and expect to be fed and housed and clothed. His motto was, "Another roof, another proof"


(22)
A popular modem off-Broadway musical is entitled Fermat s Last Tango.
It is quite extraordinary in that (i) it is about serious mathematics and (ii) it actually has lines that formulate serious mathematical thoughts.

Some examples are:
I knew, I swore,
That elegant symmetry
Of x squared plus y squared
Is square of z
Could not be repeated if n were three,
Or more!

At one point, Fermat himself appears, singing :
Elliptical curves, modular forms,
Shimura- Taniyama,

It's all made up, it doesn't exist,
Algebraic melodrama!


(23)
And finally, a compilation of the "inside interpretation" of various things said in the mathematical community (I think its just not the mathematical community - these are true for any research community :) ):


What's SaidWhat's Meant
This is trivial. I forget the proof .
This is obvious. You forget the proof.
This is a calculation. Let's all forget the proof.
Send me your preprints. Please go away.
Send me your reprints. Please stay away.
Read my book. I don't know.
That problem is intractable. I can't do the problem so neither can you.
He's one of the great living mathematicians. He's written five papers and I've read two of them.
What are some applications of your theorem? What is your theorem?
I don't understand that step. You goofed.
How do you reconcile your theorem with this example? You're dead.
Your theorem contradicts my theorem. I'm dead.
Where do you teach? Do you have a job?
Your talk was very interesting. I can't think of anything to say about your talk.
Have you had many students? Do you have any social diseases?
I read one of your papers. I wrapped fish with one of your papers.


On the whole, the book is more than an engrossing read if you are interested in mathematics and mathematicians - with around 300 pages of anecdotal trivia, that's hard to come across otherwise, its a rare treat.




Sources:
Mathematical Apocrypha Redux”, by Steven Krantz
http://www.en.wikipedia.org
michaelweening.spaces.live.com/blog/cns!97D2E88D450D7724!1783.entry


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