I figure Josh Chafetz at
oxblog shouldn't have all the fun posting excerpts of his dissertation online. So the following is the introduction to my related work chapter (the rest of the chapter had long since been written) with some hyperlinks added (rather than the end-of-chapter reference list that people reading the dead tree version have to use). While I would hide the bulk of this post "beneath the fold" if I knew how, I think this portion is a fairly entertaining read.
Chapter 2 Related Work
“I am self-taught. If I see far it is because I am standing on the feet of giants.”
- Russ Nelson, The Angry Economist
Nelson’s somewhat self-aggrandizing quote is an interesting play on a famous line in a 1676 letter that Isaac Newton penned to Robert Hooke.
“If I have seen further [than Hooke and Descartes], it is by standing upon the shoulders of giants.”
As Newton was himself a giant, it is common to assume the quote originated with him. However, Newton’s maxim was a slight variation on the following quote popularized by Robert Burton in his 1621 work, The Anatomy of Melancholy:
“A dwarf standing on the shoulders of giants sees farther than a giant himself.”
Prior to Burton, Bernard of Chartres had written in the 1100’s:
“We are like dwarfs on the shoulders of giants, so that we can see more than they, and things at a greater distance, not by virtue of any sharpness of sight on our part, or any physical distinction, but because we are carried high and raised up by their giant size.”
Both Burton’s and Bernard’s lines were modifications of a quote collected by the ancient Roman poet Marcus Lucan:
“Pygmies placed on the shoulders of giants see more than the giants themselves.”
But even Lucan referenced the otherwise unknown Didacus Stella as the originator of this quote. So Newton’s classic aphorism used to acknowledge the work of others was itself predicated on a series of quotes from other writers.
Since Newton, various wits have offered their own interpretations, including:
"If I have seen farther than others, it is because I was standing on a really big heap of midgets." - Eric Drexler
“If I have not seen as far as others, it is because I have been standing in the footprints of giants." – attributed to various authors
Indeed, the number of quotes related to Newton’s famous line is so long and involved that an entire text – Robert Merton’s On The Shoulders of Giants – is dedicated to the subject.
The application of game theory to distributed radio resource management is a rich field full of giants and heaps of midgets. If the etymology of a single quote fills a book, an exhaustive documentation of all work related to game theory and radio resource management would be expected to fill several books. So rather than attempting to provide an exhaustive documentation, the following chapter endeavors to highlight the works that are important to understanding the field of game theory as applied to distributed radio resource management.
posted by Jody @ Monday, November 08, 2004
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