
Couple of days ago I wondered what will happen if I would trace back references of a randomly chosen OR paper. So, I selected article #7 from March/April 2012 issue of Operations Research journal and started investigating:
Jonathan Kluberg and Georgia Perakis, Generalized Quantity Competition for Multiple Products and Loss of Efficiency
Then I looked at reference #7:
Then I looked at reference #7 of that paper:
Branston D. (1976) Link capacity functions: A review. Transportation Res. 10:223–236
I wanted to look at reference #6 of that paper: (reason for choosing 6 is that I could not access some papers reated with reference #7)
Braess D. (1968) Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung 12:258–268. (Full text link) – This paper is Braess’s paradox paper.
Reference #7 of that paper is
Then:
GJ Minty, “A Comment on the Shortest-Route Problem,” Opns. Res. 5, 724 (1957)
Dantzig, George B., Disrete-Variable Extremum Problems. Operations Research. Apr57, Vol. 5 Issue 2, p266. 23p.
Harry M. Markowitz and Alan S. Manne, On the Solution of Discrete Programming Problems Econometrica
Vol. 25, No. 1 (Jan., 1957), pp. 84-110
G. Dantzig, R. Fulkerson and S. Johnson, Solution of a Large-Scale Traveling-Salesman Problem, Journal of the Operations Research Society of America Vol. 2, No. 4 (Nov., 1954), pp. 393-410
I think reading OR papers from 50’s is very helpful in understanding the basic of OR. Texts are not so complicated, and you can see how the problems originated, what were first attempts to solve them, what were the things authors could not try.
From Dantzig’s paper we go to this mathematics book:
W. W. R. Ball, Mathematical Recreations and Essays, as rev. by H. S. M. Coxeter, 11th ed., Macmillan, New York, 1939. (Dantzig cites this book because of Hamiltonian game, so I looked at the references in Hamiltonian game section.)
Édouard Lucas Récréations mathématiques volume 2 page 215 is about Hamiltonian Game. The game is the problem of finding a Hamiltonian cycle along the edges of an dodecahedron, i.e., a path such that every vertex is visited a single time, no edge is visited twice, and the ending point is the same as the starting point (Mathworld). It was invented by William Rowan Hamilton.
Twenty cities of the Hamiltonian Game:
On page 225 Lucas cites Cauchy’s article, I think that article is this. He tried to solve the game using geometry.
Cauchy cites Euclid’s elements. Euclid used Babylonian and Egyptian mathematics knowledge in his book.
We always say science is accumulation of knowledge, we stand on shoulders of giants. It was more powerful for me to observe this accumulation. I think by tracking back references we can rediscover contributions of forgotten scientists.
Similar trackbacking can be done by analyzing advisors. See example of Mike Trick.
Photo by VinothChandar
Reference Journey « OR Complete | Collective Operations Research Blog http://t.co/SQpVxCOW P(random reference walk is acyclic) = ?
The way we use and list references shows our way of thinking and our organizational approach to the problem. Often we analyze and organize our thoughts systematically. But if we can also focus on the history of our thought processes (aka historical approach) we can analyze our ideas in the order we developed them. Basically it is the difference between systematic philosophy and history of philosophy. Analyzing how our ideas evolve will increase our creativity. I think it is the most secure way to prevent ourselves to be blinded by our own ideas and concepts. This is why I always defend that history of science should be an integral part of the education system.
Just came across this, and it caught my imagination. Very nice post.
Just blogged on this myself (http://graham-kendall.com/blog/?p=286/). Would be very interesting if people started publishing their academic family tress.
Thanks for your blog post!