The Number is 42

Today, April 2, 4/2, is a special day, because "42", as some may know, is
              the answer to life the universe and everything 
This was pointed out in the Hitchhiker's Guide to the Galaxy, which is a book very popular with the geeky computer crowd.

In the book, its geeky, but cool author, Douglas Adams, apparently chose 42 because, at the time the book was written, n =42 was the only number that defied the power of a supercomputer to: "find x, y, z such that x^3+y^3+z^3=n"
(Note: there is more info and an erratum on the bottom of the blog regarding the actual origin of 42.)

In the decades after that, with faster computers, after about a million hours of processing were spent on an open cloud of PCS's, the answer actually was found and is this:

 42 = (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3

Note: if "42" needs to be defined with an x, y, z-equation and an answer that will not change with time, one can ask for the largest (rational) number n such that there are positive integers p, q, r such that " 1 − 1/n = 1/p + 1/q + 1/r " 

 

However, the number, 42, still remains magical, because

➤ 42 degrees is angular radius of the (highest intensity, spectrally pure band) of the (primary) rainbow, also know as the rainbow angle, which is the angle of the viewing cone between us and the rainbow

➤ 42% is the the highest theoretical efficiency of converting mass to energy (with E=mc^2), theoretically possible at the edge of a black hole; for comparison, in stars it's only 0.7%: http://www-astro.physics.ox.ac.uk/~garret/teaching/lecture7-2012.pdf 

In comparison, in stars, that efficiency is only 0.7%. That  is because, crudely speaking, the ratio of the atomic mass to mass number for hydrogen is 0.7% higher than that for carbon, so when a star burns H into other elements, with C "on average", that 0.7% gets converted into energy and makes stars shine oh-so-very-brightly  

(That 42% is a bit trickier: normally, when a black hole swallows a chunk of matter, it releases about 6% of it out as energy.  However, if the black hole rotates, the efficiency goes up, and, at the high end, theoretically, it is 42%) 

➤ 42 is frequently used by Lewis Caroll in Alice's Adventures in Wonderland, a great story of oddities in the world Down the Rabbit Hole, with quotes of possibly deeper meaning, like "It's no use going back to yesterday, because I was a different person then.". 

Lewis Caroll  is the pen name of English mathematician Charles Lutwidge Dodgson who not only wrote the famous story about Alice, but is also known the "Dodgson condensation" method for calculating determinants of square matrices and, more importantly, for the poem and now also the English term "Jabberwocky", which is, in general, a nonsense poem or rhyme that could be (sometimes, somewhat) elegant and a pleasure to read, e.g.Twas bryllyg, and ye slythy toves
Did gyre and gymble in ye wabe:
All mimsy were ye borogoves;
And ye mome raths outgrabe.‘Beware the Jabberwock, my son!
The jaws that bite, the claws that catch!

Beware the Jubjub bird, and shun

The frumious Bandersnatch!’ …

By the way, nonsense poems used to be popular in Victorian England (the last 60 years of the 19th century). The Victorian poet Edward Lear wrote and published a poem called The Owl and the Pussycat:The Owl and the Pussy-cat went to sea

In a beautiful pea-green boat,

They took some honey, and plenty of money,

Wrapped up in a five-pound note …It became his most famous poem.

But I digress.  42.  So, that x^3+y^3+z^3=nis actually an instance of a wider class ofthe Diophantine Equation.  Some of such problems were discussed in my extracurricular math seminars in high school, but we definitely would not be using supercomputers or even PCs trying to solve them, even if such things actually existed at that time.

Another instance of the Diophantine Equation is the famous Fermat's Last Theorem, which states that there are no integers x, y, z that would satisfyx^n + y^n = z^n for n>2.  It took almost 360 years to solve this puzzle and was deemed so difficult and consequential for the field of mathematics (by spawning whole new areas of research) that the accomplishment merited the Abel Prize, the most prestigious award in mathematics (to Andrew Wiles).



Interestingly, the Abel Prize was proposed/created to directly complement the Nobel prizes, which do not include a prize for mathematics.  It is named after a very talented Norwegian mathematician, Niels Henkrik Abel, who made huge contributions to mathematics in the space of just a few years. He made his discoveries while living in poverty and died at the age of 26 from tuberculosis.

To show that the quintic equation has no algebraic solution, Abel  invented a whole new branch of mathematics: the group theory, without which much of today's math and physics would not be impossible.  The terms associated with his contributions are numerous and so commonplace is a mention of his name in mathematical literature that it is typically spelled with lowercase "a", especially as an adjective, e.g. abelian category.  Strangely, having your name spelled like this with lowercase is considered a very high honour among mathematicians.

The prize was proposed in 1899 to be a part of celebration of the 100 year anniversary of Abel's birth in 1802.  In 1902, king of Norway and Sweden, Oscar II, agreed to fund the prize.  However, shortly thereafter Norway and Sweden went their own ways and the prize had to wait another 100 years for the Norwegian government to fund it and set it up, this time for the 200 year anniversary.

There is only one person that won both the Abel Prize and the Nobel Prize, which is John Nash (with the Nobel for economics).  That accomplishment is even more impressive considering that Nash was mentally ill and had to struggle with depression, schizophrenia and hallucinations his whole life.  John von Neumann would likely also qualify (math+physics), but it just did not happen...

Reasons why there is no Nobel Prize for mathematics are not entirely clear.  Perhaps it was due to Nobel's low opinions of the practical benefits of mathematics to humanity.  Perhaps it was due to his dislike of the important Swedish mathematician Mittag-Leffler.  But it was not likely due a rivalry over a woman, as is sometimes believed.

Nobel was a strange man, who made a lot of money with his invention of dynamite.  Upon reading his own obituary, from a newspaper that mistook the death of his brother for his and criticized his earthly life harshly for being "a merchant of death", he decided to donate his fortune to establish a prize celebrating science (and some others accomplishments, which tend to be more political, like the "Peace" prize for Yasser Arafat or the "Literature" prize for Bob Dylan). 😬

Yasser Arafat is famous for leading Fatah, a group long associated with anti-Jewish terrorist activities.  Fatah's subgroup, Black September, carried out the kidnapping and killing of Israeli athletes at Munich 1972 Olymics.  Arafat was a close friend to some of the most brutal dictators in the region, like Sadam Hussein or Idi Amin, who were well known for their mass atrocities.  He was Amin's best man at his wedding. 

Eventually, he shifted the official policy of his organization of unconditionally destroying Israel and, instead, accepted the UN resolutions that gave Israel the right to exist.  That led to so-called Oslo Accords in 1993, for which he was given the Nobel Peace Prize.  To many, the state of affairs that those accords were trying to resolve seems worse and more hopeless today than it was at that time.

Bob Dylan's literary accomplishments are curious.  He was an accomplished rock star, whose songs were popular, despite (maybe because of) strange lyrics like

Come gather 'round people
Wherever you roam
And admit that the waters
Around you have grown
And accept it that soon
You'll be drenched to the bone

But he never wrote any real book, except perhaps Tarantula, which won the top place in the list of "Top Five Unintelligible Sentences From Books Written by Rock Stars" with this gem:

 

"Now's not the time to get silly, so wear your big boots and jump on the garbage clowns."

That does not seem to go well with the requirements put forth for the Nobel Prize in Literature that the prize should go to: "the person who shall have produced in the field of literature the most outstanding work in an ideal direction". 

 

By the way, Nobel  himself dabbled on the literary scene.  However, his prose tragedy, Nemesis, was deemed so perverse and shocking that the entire stock was destroyed, save three copies.  He was not a very good playwright, but he seems to have had a thing for sex and also a thing against the capitalist system (from which he got all his money).  Eventually, the play was staged.  According to the August Strindberg Intima Theater, the play is about

 "violence, sex, torture, deceit, forbidden lusts, revenge and religious fanaticism".

The show's director, Rikard Turpin, described the play as
"a lurid parade of torture, rape and incest that features a drug-induced vision of the Virgin Mary, a conversation with Satan and ends in a 40-minute torture scene ... got everything you could wish for: cruelty, passion, sexuality".

Oh, well, at least the Nobel in Physics still means something, at least some of the time - Stephen Hawking, one of the best and certainly best-known physicists of his time, has never received the Nobel Prize.   But other people working the same subject, black holes, did.

Side note:

The story of 42 is not as simple as I presented it. For example, as is explained in https://en.wikipedia.org/wiki/Phrases_from_The_Hitchhiker%27s_Guide_to_the_Galaxy, it all has to do with what came first, the answer or the question and what it means to the survival of planet Earth.

 

From there, I summarize:

A group of hyper-intelligent pan-dimensional beings interrogate Deep Thought, a supercomputer purpose-built (by others) to answer the Ultimate Question.  Turns out that the answer is 42.  However the question itself is not known any more.

Deep Thought can't find it itself, but it can create a new supercomputer, Earth, which will take 10 million years to find the question, with the pan-dimensional beings acting as observers in the form of white lab mice.  However, Earth is destroyed by Vogons five minutes before the calculation is finished, apparently at the behest of psychiatrists that were fearful of losing their careers once the Question (and the answer) is known. 

Now, lacking the real question, the mice settle for "How many roads must a man walk down?", authored by the now-Nobelist Bob Dylan. 

Later, attempting to recover the question at last, from the brainwave patterns of a survivor, based on clues from Scrabble-playing cavemen that spell "forty two", the random letters subsequently pulled from the bag spell "What do you get if you multiply six by nine?", which, of course, is 54, not 42, but there is the joke...

People tried to ascribe deeper meaning to that by noticing that, when written in the base-13 number system, 6×9 actually is 42, to which Adams responded "I may be a sorry case, but I don't write jokes in base 13".

At some point, he also refuted any deeper meaning of 42 altogether, by saying "It was a joke. It had to be a number, an ordinary, smallish number, and I chose that one. Binary representations, base thirteen, Tibetan monks are all complete nonsense. I sat at my desk, stared into the garden and thought '42 will do'". 

Note: The Hitchhiker's Guide to the Galaxy was first a radio series, then a set of books, then TV series, then a feature movie.  The plots in all those platforms differ slightly, but the underlying current of entertaining sci-fi absurdities prevails.

 

Erratum: Upon re-examination of my sources, I come to the conclusion that, indeed, it was not Douglas Adams, but the mathematicians involved in solving x^3+y^3+z^3=n on a supercomputer, being great fans of Adam's books themselves, that came up with the idea that the existence of this particular problem is the reason for the answer in the book being 42.  Oh well, as Giordano Bruno would have said, se non è vero, è ben trovato - even if not true, it is well conceived.