Duane Michels, Droste, Economics, and Music
The recursive playlist that I posted a few weeks ago seems to have generated some interest in the economist community, at least a small part of it. I guess recursions are big with economists and especially big among economist/musicians, a small sub-set of a sub-set of the population but a vocal and articulate one.
Until now, I hadn't known that the so-called 'Droste Effect' - as illustrated on the package of the typical Droste cocao package, above - was an example of a recursion. I just didn't know what it was called. I have enjoyed my Droste on many trips to Holland. I love hot cocoa and recursions. How did my friends Christian and Theresa know this when they put together my birthday playlist?
Apart from the Droste package, my favorite example of a visual recursion is a famous series of photographs by Duane Michels called "Things are Queer." Here is part of that sequence - I don't want to give away the whole story!
So, why am I writing about recursions again? A few days ago, I got an email from a friend of mine, Chris, a member of that minority group, the economist/musicians. He borrowed a record from me a few weeks ago and wanted to let me know that, no, he hadn't lost it and yes, he would be getting it back to me soon.
I know where he lives, so I'm not worried. I told him not to worry. But, I said, "check out my blog while you're at it...."
He did, and this is what he wrote: Hey Paul: Sorry to have not returned your record yet ... I'm still workin' on it (and I've been delinquent). Will get it back this weekend .. with a surprise (I hope).
I wrote back: Chris: Thanks for the update - I was hoping/confident that you hadn't forgotten! New entry on my blog might be of interest - check it out and spread the word to others interested in music and music on vinyl.
Then, Chris sent me this message:
Yes Paul, I've been waiting to
hear what you were going to do about that plastic bag. The tension
was killing me. I'm quite relieved.
Great playlist. FYI, economists are obsessed with
"recursions." Here is our bible:
http://books.google.com/books?hl=en&id=tWYo0QolyLAC&dq=recursive+methods+economics&printsec=frontcover&source=web&ots=rh3lTEu7w1&sig=cZ-z0UzBqPfs5aTyd2SJ-4clieo&ei=iYuUSYKKLsH7tgfVzfC-Cw&sa=X&oi=book_result&resnum=1&ct=result
Recursive methods are what we use to describe dynamic systems. The
idea is that there are one or more state variables that can change over
time, but, conditional on the state variables, the behavior of the system is
time invariant. So, the question is what are your state
variables? How did they change? And then, in what sense did
your system behave the same, conditional on these state variables?
Let me try. There are obvious, somewhat discrete changes in the
musical genre over time ... jazz, soul, punk, etc.. This is the
state variable. It is the cutting edge of the contemporaneous
music. But then, weird, perhaps dissonant stuff appears over top of
this? From Mingus to Cash. From Redding to
Sinatra. Ska to deeply depressive, disturbed music
(Cohen). So I guess that's what your friends are telling you
... you have this recurring tendency to be at the cutting edge but then you get
weird. This would be a complement (sic) to me.
Reminds me of my favorite Neil Young quote. After making the
Harvest record, he made a very dark unpopular record called "Tonight's the
Night." Someone asked him what happened and he replied
"well, I suddenly found myself in the middle of the road ... so I headed
for the ditch."
(Dave, Stan, Kevin ... thought you might get a kick out of the definition of
"recursions" on Paul's blog ... and you'll surely love the playlist
... I've already ordered a few MP3s based on this).
http://blog.vinylrecordarchitect.com/
And then this arrived from Chris' brother, Kevin:
So Paul has a recurring tendency. Pardon me for jumping in to poke at the ribs of the economists, Paul. Hmmm, is there a difference between a tendency and a recurring tendency?
How about a partially recurring tendency?
Here is a practical definition of recursion:
Take the phrase from Paul's blog "Something
is also said to be recursive when it is the result of a recursive
procedure" and replace 'recursive' with any adjective over and over again.
Maybe start with the adjective "sexual".
Have fun,
Kevin
Then this arrived, from Chris:
In addition to adjectival redundancy, I'm also guilty of spelling mistakes. I spelled "compliment" as "complement." The result is some confusion regarding whether Paul's recurring tendencies complement mine --- making them even more recurrent I guess --- or whether I am complimenting Paul's weirdness. Interestingly, the word `complement' also plays a key role in economic analysis. I'm not sure where to go with this. Kevin?
I am a computer scientist, and the mathematical concept of recursion is also tremendously popular in that field, especially among aficionados of the Lisp programming language. Lisp was invented in the 1950s by the mathematician John McCarthy as a language to specify abstract functions called lambda calculus. It wasn’t intended as a practical programming language but it turned out to pioneer many key ideas in computer science that have taken decades to percolate in mainstream languages like Java. The key to Lisp is that it doesn’t have a syntax (words to dress up the program) but instead expresses programs in terms of their pure structure (form follows function, for you architects), which allows the programs to manipulate themselves in completely unrestricted ways. As McCarthy famously wrote: “I would rather write programs that write programs than write programs.” Now that’s recursion.
The bible of recursion on the shelf of every nerd in his 40s and beyond is the classic “Godel, Escher, Bach” by Doug Hofstadter, published 30 years ago already. The book shows how the same mechanisms of recursion are at work in the music of Bach, the self-referential pictures (often of architectural themes) of Escher, and the work of mathematician Kurt Godel. Probably the most dazzling illustration of the concept of recursion is Godel’s famous incompleteness theorem, a sort of mathematical analog to Heisenberg uncertainty principle. Godel uses recursion to show that the truth of some simple mathematical statements cannot possibly be determined, a seemingly impossible result. His proof relies on the fact that even simple mathematical languages can express sentences such as “this statement is not provable”, that twist upon themselves like Mobius strips and cannot be reconciled under any logic system. The same logic has been used to show that you cannot write a program that will determine if another program will complete!
Finally, a music note: I am mostly responsible for the jazz component of Paul’s 50th list. Unfortunately, Paul was born as bebop was in its dying throes, so most of my collection was unusable. Fortunately, Paul’s infant years corresponded to Miles’ and Coltrane’s greatest years, and Mingus was still active too. A Love Supreme would have been a great choice for 1964, but we were trying not to repeat artists and it was a great opportunity to slip in an early Mose Allison composition. Mose Allison is a poorly known gem at the frontier of jazz and blues who is still going strong and touring after all those years. Catch him if you can and your life will never be the same – mine hasn’t since it was thanks to him that I won the attention of my wife. Other than the Jazz purist thing, I mostly own uncategorizable stuff like Ennio Morricone soundtracks and compilation of Kurt Weill songs (maybe I have a thing for German guys named Kurt after all). Eclecticism is a tough road to slog but it is often more rewarding than the comfort of established schools.
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Well we are straying far from the music now....but to bring it back. A song can be recursive in structure (see this example: http://www.geocities.com/Vienna/9349/recursion.html) and there are some styles of music (like Indian ragas) that are expressly recursive. As a former math geek, I find music based on the Fibonacci series very cool, but not exactly something you can dance to....so back to the list...since the whole thing was bounded by some rules (one song per year, mostly one song per artist, and stuff that we already had or that was readily available), and the eclecticism becomes a bit more understandable. We did have a hard time in the 90's--so some of the songs are from our 11 year old's collection....
I wish I had put more funk on the list (and all of your economist friends should be required to listen to Wizard of Finance), and I wish I had put more punk--but it was getting late and I couldn't find my Dead Kennedys and Butt Hole Surfers tapes. Alas.
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Dear Christian,
I also read - or tried to read - Godel Escher Bach. In 1987, when I arrived in Pittsburgh to teach at Carnegie Mellon, it seemed like all of my colleagues had read or were reading this book. Almost seemed like required reading for entrance into the Academy. To me, it is one of those books that rewards re-reading every ten years or so - so I am due!
BTW, our new building for the National Aviary will be composed of several recursive elements that are featured at one scale and material on the exterior and another on the interior. Makes visiting and experiencing the building a bit of a game in itself. For the economist and computer scientist visitors, at least.
Thanks for your interest in the blog - come back soon!
PAUL
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