A review of the book Godel, Escher and Bach

Godel, Escher, Bach; An eternal gold braid

Vintage books, 1979

 

A 1999 edition is available on Amazon.

I recently read “spacebookthenovel” by Robert Allan Richardson in which he referred glancingly to this astounding book that I had read many years ago.  I could not resist it, I searched my library and there is was among my mathematics books.  It is not an easy read by any means and as I looked at it I saw that one of our Labs had found it an equally tough item to chew on.  She had managed to make inroads on the lower left corner but thankfully left the rest intact.

First let’s look at the three individuals.  Opening with J.S. Bach, Hofstadter examines this brilliant musician’s famous Musical Offering to King Frederick the Great.  It is what we would now call a fugue and it’s theme is The Royal Theme.  It is an extraordinary musical piece being a six part fugue.  To give you an idea of how extraordinary this is you could compare it to playing sixty simultaneous blindfold games of chess and winning them all.  In presenting his copy of the piece to King Frederick the following was inscribed on the first page: Regis Iusfu Cantio Et Reliqua Canonica Arte Refolula.   “At the King’s command, the song and the remainder resolved with canonic art”.  Ricercar are the initials of the statement but also an old Italian word meaning “to seek” (in modern Italian “cercare.”) In these musical types a single theme is played against itself.  A very simple example would be to sing what we call rounds such as “row, row, row your boat, or Frere Jacques.  The voices are sung by voices coming in at every fourth beat but they can also be sung inverting the melody, reversing it, echoing it, going up or down an octave, or even changing the time.  The central point is that the ricercar is RECURSIVE producing what Hofstadter calls “strange loops”.

The four CD set “The Glenn Gould edition of The Well Tempered Clavichord” with 48 fugues and preludes demonstrate this type of music very well. He was particularly renowned as an interpreter of the keyboard music of Johann Sebastian Bach. His playing was distinguished by remarkable technical proficiency and capacity to articulate the polyphonic texture of Bach's music. You might be interested in exploring this musical piece.

Next is M.C. Escher.  If you have ever seen any of his work you will remember they feature impossible constructions, explorations of infinity, architecture, and tessellations. Take  his pencil drawing of two hands, each drawing the other.  Another is his “waterfall” which pictures a canal of water starting under a waterfall that turns a waterwheel, proceeds through four 90 degree turns and ends producing the waterfall from whence we started.  Again a RECURSIVE resulting in that strange loop.

If you are interested in pursuing Escher’s art I recommend “The Graphic Work of M.C. Escher” available on Amazon for, interestingly $95 or $.065.  I can never figure out Amazon’s pricing but there are other editions of Escher and you will enjoy looking at his truly fascinating view of the world.

And now to Kurt Godel, the key figure in this wonderful book.  In our first two artists we could see a conflict between the finite and the infinite resulting in paradox.  In the 20th Century a mathematical equivalent was discovered , with enormous repercussions.  A Strange Loop was found by this brilliant mathematician.  In its simplest form it can be likened to the liar’s paradox proposed by the Cretan Epimenides to this effect: All Cretans are liars.  Cogitate on this simple statement for a moment.  An even simpler statement would be “I am Lying” or “this statement is false.”  It is self-referential and a Strange Loop indeed!  In Godel’s mathematical world his strange loop statement, which I will not produce here because it is in German and even translated to English you will think it still in German,  means  he proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers set theory with the axiom of choice, that: If the system is consistent, it cannot be complete and the consistency of the axioms cannot be proven within the system. That is  Gödel essentially constructed a formula that claims that it is unprovable in a given formal system. If it were provable, it would be false, which contradicts the idea that in a consistent system, provable statements are always true. Thus there will always be at least one true but unprovable statement. In fact, there is an infinity of true statements it cannot prove. Whew!

Turning now to the book it is centered around Strange Loops, those recursive auto references; that generate twisted hierarchies, which, according to the author, can explain much about Intelligence, Consciousness, DNA, symbols and meaning. It  spans Zen and Zeno, Bach and Cage, Escher and Magritte, Gödel and Turing, Cantor and Russell. The auto-references allow him to jump up and down, and move in stimulating vortexes, culminating as a ricercar in 6 voices in a digression about free will, life and death at various levels

Also, each "serous" chapter is prefaced by an amusing dialogue between Achilles and a Tortoise (from Zeno's "paradoxes') and other droll characters. 

All in all a fascinating book. It is a golden braid intertwining looks at logic, philosophy, consciousness, music, art, biology, computers, and countless other topics through the prism of concepts of uncertainty, incompleteness, and self reference. 

If you decide to buy this book, and you should, get the 1999 edition.  Hofstadter’s forward does a much better job of preparing you for what follows than did his original.  And remember, you don’t have to read it all in one pass.  Do as my Lab did: chew on small portions and enjoy.

SPACEBOOKTHENOVEL

Review of “SPACEBOOKTHENOVEL”

Robert Allan Richardson

Originally an Ebook but now in print on Amazon

$14.95

 

Pagescape Press 2013

 

A thought provoking book but the question is what thoughts are provoked.  The problem with dealing with the PhD Professoriate is that each thinks he/she is the repository of all that is great and good in the world and this book is a regurgitation of the author’s concept of that collection.

 

Benjamin Bidwell, a consumate talker as a child, loses his voice early in life to his consternation.  He was fifteen and had been entered into a speech contest, at which he was odds on favorite to win given his penchant for oratory.  But alas and lackaday just as he starts into providing those golden thoughts he becomes mum.  As Benjamin puts it “So ended my prodigies of speech.”

 

He was not content within his silence and as he worked hard and well at various farms all those words kept piling up inside him. Straining to be free.  And then, mirabile dictu, he found a way to release himself from this enforced silence: he saw and answered an ad for an auctioneer school.  Indeed he regained his power of speech and we are henceforth treated to his every thought, profound to whimsical.  Except for Professor Richardson’s use of punctuation the phrase “stream of consciousness” becomes one of those provoked thoughts we spoke of at the outset.  In any case Bidwell decides he will learn everything necessary to provide him the wherewithal to judge all that is right and wrong with the world. 

 

On this journey of exploration Benjamin provides us both an outside view of life and an inside view.  The outside consists of his starting to work as a farmhand milking cows while he attends University as a free spirit simply auditing those classes in which he was interested.  No need to pay, after all he is going to do the world a good turn by learning all this.  He does an auction for a friend and this leads eventually to his starting his own business and turn leads to buying a farm, and eventually into a bookbinding business. There is a side trip into singing operatic duets. The book ends with pages of apparent witticisms and common phrases turned about. 

 

The inside view, during these discourses examine our present day technology and Bidwell’s extreme dislike for it as it apparently takes us outside of ourselves.  I grant that all technology throws shadows but Richardson dwells in those shadows and predicts disaster.  As a pacifist he seeks to prove his courage and his manhood.  I hold no brief against that. I have nonesuch as friends but I am aware of much good they do when they choose to support their country. But methinks the Professor doth protesteth too much.

 

Why is it the intellectuals conceit that the only life is the life on a farm, being a horny-handed son of the soil.  As Reginald Heber( English clergyman, traveler, man of letters and hymn-writer) would have it "...every prospect pleases and only man is vile”. The present population of the United States is approximately 300 million I believe.  Can you imagine if all 300,000,000 of us lived and worked on a farm?

 

 I would call Professor Richardson a neo-Luddite except for the irony of his writing this novel originally in cyberspace.  And perhaps his magnum opus suffered in translating from modern technology to use of the Gutenberg approach.

A review of Stephen Puleston's "Brass in Pocket

Brass in Pocket

A Detective Drake novel by UK author Stephen Puleston

This is a good, solid detective novel and is the first in a series of Detective Inspector Drake adventures.  Set in rural north Wales the American reader faces two interesting situations. First is the fact that we do not recognize some of the idiom and, while meanings can be gained from context, it helps to know in advance, for example,  that “biro” is the UK slang for “ballpoint” as it allows reading without speed bumps.  Secondly neither are we cognizant of the rivalry between various regions of the UK.  The word “Scouser” is used with some frequency and after some research, I found that the word pertains to those from the Liverpool area and they are considered by the Welsh to be less than honorable shall we say.  However, in this day and age of the Internet I think my two comments are more cavils than complaints.  We read books available to us from around the world and they open our minds, as good books should, to newer and certainly more different things.

All strong detectives should have an idiosyncracy if not an eccentricity and Detective Inspector Drake has a good one.  He suffers from an Obsessive-Compulsive Disorder requiring him to frequently adjust everything on his desk to their assigned meticulous positions. There are other indications but the reader will find them as the story progresses and discover how they put forward or inhibit the detecting being done. Drake also solves Sudoku puzzles to help himself feel more in control.

Brass in Pocket is the title of a song by The Pretenders that came out in 1979.  The novel opens with the killing of two policemen and one of the clues was a note left at the scene containing the lyrics of the song under which was scrawled the number 4.  There are further murders and each is accompanied by a note containing the lyrics of a song from 1979. More and more pressure is brought to bear on DI Drake both from his superiors and journalists to solve the crimes before the murder can strike again and, as the story progresses, he even comes to fear for his job.  Several other crimes are revealed and solved as the investigation moves forward and the suspense builds well.  The denouement is has a nice hook and you are left wondering why you didn’t see it earlier, given what you now know.  Shades of Hercule Poirot. Good stuff for a detective story.

I have not read any of Mr. Puleston’s previous works but I look forward to doing so and certainly the second outing of DI Drake with his adventures in rural north Wales as he twiddles his biro and scowls over the machinations of Scousers.