Something To Think About: A World’s Thanksgiving

Tomorrow is Thanksgiving in the U.S.  However, I would like to offer a post for a World’s Thanksgiving.  I would like to offer a tribute to Stanislav Petrov, a Russian, whose calm, rational thinking prevented WWIII in 1983.

An anti-ballistic warning system issued several alarms, indicating that the U.S. had fired a missile towards Russia.  Petrov kept his cool and reported the warnings as false alarms.  Later, it turned out that a cloud clover had caused a malfunction in the system.

Stanislav Petrov is no longer with us, but we can be grateful and proud that such a man was there at such a critical time.  Let the whole world give thanks to this Russian hero.

Where Is The Frog?: Something To Think About

So, where is the frog?

Somewhere there's a frog. Can you find it?

Somewhere there’s a frog. Can you find it?

Camouflage creates its own kind of illusion.  Nature thrives on it, and optical illusions often befuddle humans.

S. Tolansky, a former Professor of Physics at the University of London, wrote a small treatise dealing with visual illusions.  And he argues that camouflage is a practical use of optical illusions.  Camouflage is used by animals and plants primarily as a means of protection from predators and by humans for warfare.  But all illusions are dependent on the health of the eye;  severe astigmatism can destroy the illusion featured below.  Yet, it is well to remember that things are not always what they seem!:oi-1

Something To Think About: Two Mathematical Thought Problems From Russia

The Russians have a long tradition of mathematical thought problems which occupies a distinguished part of their elementary mathematics classes.  Here are two samples by J. I. Pearlman:

  1.  Who Counted More?  Two people counted the number of people that passed them on the sidewalk for a period of one hour.  One stood at the gates of a house, the other walked up and down the sidewalk.  Who counted more?
  2.   The Grandfather and his Grandson.  What I am going to tell you took place in 1932.  My age then was the same as the last two digits of the year I was born.  When I told my grandfather about this correlation, he surprised me by declaring that the same correlation was true for his age as well.  How old was each of us?

Something to Think About: Fifty Million People can be Wrong!

Hugh Lieber's drawing of Nazi Germany.

Hugh Lieber’s drawing of Nazi Germany from The Education of T.C.MITS by Lillian and Hugh Lieber.  More on the Liebers in a future post.

Something To Think About: “Would You Pay The Price? What Would You Do?”

The above lines come from the 1966 American musical Cabaret based on writings of Christopher Isherwood and John Van Druten.  The musical focuses on the lives of a few people and their reactions to the growing Nazi threat in 1930s Berlin.  The musical was unusual in that it did not have a happy ending and Americans are used to happy endings.  Thomas Hischak offers his own description of Cabaret in his The Oxford Companion to the American Musical:  “Arguably the most innovative, hard-hitting, and uncompromising musical of the 1960s,…”  What makes this musical so innovative?  It introduces us to decadent Berlin through an MC of the Kit Kat Club, himself a mixture of playfulness, immorality, and darkness.  As the show progresses, the political overtones become ever more ominous and threatening.  The title, which also serves as one of the main songs in the musical, is a celebration of irresponsibility and seediness.  Sally Bowles, one of the chief entertainers at the Kit Kat Club and the girlfriend of Clifford Bradshaw, an American writer, sings the song as a tribute to her late girlfriend Elsie.  Sally’s friend was a prostitute, drug addict and alcoholic who died from too much of the latter.  Sally sings of Elsie’s death, “… But when I saw her laid out like a queen, she was the happiest corpse I’d ever seen.”  Elsie’s memory motivates Sally to return to the cabaret where she will probably end up like Elsie.

A sub-plot concerns the romance between Cliff’s landlady, Fraulein Schneider and the Jewish fruit seller, Herr Schultz.  After she accepts Herr Schultz’s proposal of marriage, pressure is put on her by Nazi smuggler, Ernst Ludwig, who had introduced Cliff to Fraulein Schneider’s boarding house, to break off the marriage to avoid the repercussions of marrying a Jew.  She decides to comply with Ernst’s demand.  Cliff and Sally are shocked to learn of her decision, so she asks them, “What would you do?”  Although, she emphasizes her status as an old woman, the song that follows could be sung by anyone who is confronted with a despicable regime and the consequences of doing what is ethically right.

In London in 1993, Sara Kestelman gave an intense, harrowing interpretation of the role of Fraulein Schneider for which she won the Laurence Olivier Award for Best Performance in a  Supporting Role in a Musical.  What follows is her version of the song, What Would You Do? My thanks to lluluss for posting this song on youtube.https://youtu.be/dQ3b3JzctWE

Something To Think About: Mathematical Lunacy

The notion that mathematical reasoning is somehow linked with mental illness is not as far-fetched as it might first appear.  The late mathematician, Robert Brooks, provides an amusing analogy of his own in our discussion of mathematical shape;

RW:  Then it’s(the world of mathematical shapes) your world.  You’re immersed in this abstract universe that you’ve created.

RB:  That’s right.  My wife is a family physician, and she says that the patients that remind her of me the most are the schizophrenics, because they’re walking around in a world that’s very real to them, but invisible to anyone else….  I actually spend a lot of time just sitting with… paper models, playing with them, and asking myself what is the same about them, and what is different.

Mathematics and mental illness:  Something to think about.

Something To Think About

Below are two quotes from two mathematicians.  Robert Brooks is speaking about mathematics, but could his statement refer to something else?  Charles Kalme mentions education and not mathematics, but is there a connection between the two quotes?  What do these two quotes suggest in our everyday lives?

“…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…;  and I said to myself,  “I wonder what else they’re holding back?”–Robert Brooks, Assistant Professor of Mathematics, University of Southern California

“Education courses are where you learn not to rock the boat.”–Charles Kalme, Assistant Professor of Mathematics, University of Southern California