Adonis Diaries

Archive for January 23rd, 2010

Pizza and pie lovers: Problems of etiquette and equitable portions; (Jan. 27, 2010)

This article explains how it took 11 years for two mathematicians, Rick Marby and Paul Deiermann, to come up with a satisfactory resolution of how to split equitably a round (circle) pizza or a pie between two eaters.

Marby stated: “If a mathematician is unable to solve a problem, it would be stupid to take on the challenge. We decided to play stupid.  Paul and I are the kinds of mathematicians who take pleasure in the beauty of the demonstration: we care less for applicability of the concept.”

There are many cases of mathematicians working on problems that “consciously” have no practical applications. They do take the time to demonstrate their concepts and theorems and produce functions: applications materialize much later for the benefit of sciences.

For example, the Italian Guiseppe Peano described in 1890 a function that filled entirely a finite space (a square in that case).  A century later, this function turned out to be fundamental in fractal theory (applied in biological structures, in economics, and meteorology).

Personally, I think that no one invest time on a project if there was no personal practical interest. The initial interest is so personal and feels un-important to colleagues that the mathematician is shy to state his “secret” interest.

Let us try to expose the problem.  First, the two eaters have to abide by the etiquette that you cannot get another slice before the other has finished eating his slice.  The portions are picked up clockwise for easy visualization one after another.  Another restriction: all slicing lines cross a single point if the server is lousy enough not to cut along the center of the perfectly circle (geometrically) pizza.

Now, if one of the lines cross the center, there is no problem of equitable portions (in the final quantity of devouring pizza), regardless of the design on the number of lines of slicing.  If the pizza is cut in two parts then you know which part is larger when the line does not cross the center.  Otherwise, for any even numbers of lines the equitability is restored, assuming you are abiding by the etiquette rule.

The problem gets nasty if the number of lines is odd.  If the number of lines is 3, 7, 11, or 15 then the one eating the piece that include the center will be at an advantage (this advantage is relative to the quantity and not what happens after eating!).

If the number of lines is 5, 9, 13, or 17  the advantage is reversed.  That should cover the equitability problem.

Now, for the remaining story:  In 1967, the mathematician LJ Upton resolved the problem with four lines; then he threw the challenged to resolve the problem along that concept of equitable portions.

In 1968, the problem of 8 lines was solved (mathematically) and for all even numbers of lines.

In 1994, Marby and Deiermann accepted the challenge to study the odd number of lines slicing the pizza and not passing by the center.  For lenient practical eaters it should not matter that much if the point is close to the center: the problem is to convince mathematicians.

Paul quickly found a “gorgeous” demonstration for three lines and it got nastier later on. The problem can be solved easily by induction using the current technology of measuring areas: in this case, induction reasoning on the possibilities is accurate since we are not taking samples in complex experiment with many variables (all we have is number of odd lines as variable).

Rick and Paul wanted a classical mathematical demonstration, preferably the simpler and most beautiful demonstration.  They had to skim the Internet for theorems and functions and discovered that in 1979, a mathematician got fun demonstrating the complex algebraic problem of rectangular strips (don’t ask me for further details).

If you ask me to take on the psychological characters of Rick and Paul, I may venture to say that this couple is voracious, but pretty cheap.

621.  Sex: an exclusively personal value (Draft); (Jan. 20, 2010)

 

622.  Save Darfur Movement? Not a cent reached Darfur; (Jan. 21, 2010)

 

623.  “Development programs in Africa are planned poverty”; (Jan. 21, 2010)

 

624.  Do you publish on WordPress.com? Then, you are a public figure; (Jan. 22, 2010)

 

625.  What did come first? (Jan. 23, 2010)

 

626.  Circulating premium Gold-paper currencies (Jan. 24, 2010)

 

627.  I want a listener; (Jan. 24, 2010)

 

628.  How have you been “existing”? (Jan. 25, 2010)

 

629.  “I want to be carried away by my emotions”; (Jan. 25, 2010)

 

630.  Shadows and Booms; (Jan. 26, 2010)

 

631.  Rare heavy dirt?  Premium dirt? (Jan. 26, 2010)

 

632.  Michelle and Barack Obama; (Jan. 27, 2010)

Michelle and Barack Obama; (Jan. 26, 2010)

            The journalist Peter Nicolas of the Los Angeles Times followed Barack Obama on the Presidential campaign trails and wrote: “I cannot say with any certainty who is Obama.”  Law professor Mark Sawyer who once attended Obama’s law classes said: “Barack is how you see he is.  Barack is enigmatic in his positions, brilliant, able to defend the positions of opponents, and he is distant (as if called somewhere else).”

            Barack planned for his presidency since 2002, even before being elected Senator to Illinois: Anthony Lake (Bill Clinton’s National Security advisor) aided Barack forming his “diplomatic team”.  Obama knew in the minute details George W. Bush 2004 campaign. Obama has no need to prove (like Clinton) that he is the smartest among his team members and counselors: he has the capacity to dominate without provoking.  The few instances of weariness are results of experts expounding indefinitely on issues Barack knows about.

            A young lady wrote an article saying “we are fed up of drama”.  Obama picked up the message for his slogan “Obama- No drama” and then the next slogan “Changes we can believe in”.  Obama said on CBS: “I tolerate no ego trips in the team for personal promotions.  I tolerate no back stabbing to go ahead.  A few warnings and then you are out of the team”.  With Obama the crux of the matter is “Problems are complex: There is no unique resolution.”  Obama is very conscious that he is a public figure and thus, “What I say or do is what I mean”.

            Michelle Robinson Obama was a successful lawyer and a Harvard graduate when she married Barack in 1992.  Michelle focused her energy, as recommended by the campaign advisors, submitting to interviews for family magazines.  Mark Sawyer stated “People were not yet ready to admit that highly educated black women have potentials to make any difference in society: they are accepted as assistants and dedicated to family.”  Michelle is fundamentally a sarcastic person and skeptical that black personalities are taken seriously: she frightens audience when she looks serious.

            Michelle’s brother Craig was basketball star in Princeton when she applied and admitted in 1981.  Her sociology thesis was on how black students integrated in white socio-cultural structure and how blacks ended up feeling alienated of their community of origin after graduation.  The skeptical tone of her thesis was that Michelle felt that she will always be relegated to the peripheries of the successful elites.

            In 1989, Michelle was a lawyer at a firm and she was asked to take care of new recruit from Harvard.  She and barrack had their first kiss at Baskin-Robins on 53rd Street: they had first seen a Spike Lee movie.  Michelle quits private practice and joined Chicago’s Mayor Office. She was Vice-president of external relations at the university hospital in Chicago when Obama was elected Senator in 2004.  Michelle’s salary climbed from $121,000 to $317,000 in 2005.  The couple was living in a single family home worth $1.65 million: the two published books of Barack Obama were best sellers at the time.

            “Do you want to know how Barack prepares for debates? He spends a few minutes with me and Barack is set and ready” said Michelle.


adonis49

adonis49

adonis49

January 2010
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