Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (127 page)

Prologue

Page 8
There is a famous Russian poem…
Selvinsky (1920).

Page 16
One day… the idea came to me…
Poincaré (1908), p. 52.

Page 21
likeness is a most slippery tribe…
Plato (1977), p. 231a.

Page 21
a mobile army of metaphors…
Nietzsche (1873), p. 46.

Page 22
The light of human minds, is perspicuous words…
Hobbes (1651), Chapter V, 36.

Page 22
Expressing oneself with metaphors has the quality…
Alberic (1973), pp. 146–147.

Page 22
A science that accepts images is…
Bachelard (1934), p. 47.

Chapter 1

Page 38
Censorship is the mother of metaphor…
Jorge Luis Borges, quoted in Manea (1992), p. 30.

Page 38
Leisure is the mother of philosophy…
Hobbes (1651), IV, 46.

Page 38
Death is the mother of beauty…
From the poem “Sunday Morning”, in Stevens (1923).

Page 60
I’ll tell you something…
Robert Pond, “Fun in metals”,
John Hopkins Magazine
, April 1987, pp. 60–68, quoted in Murphy (2002), p. 18.

Page 61
A language is a dialect with an army…
Max Weinreich (1945). “The YIVO and the problems of our time”. Lecture delivered at the Annual YIVO (Yiddish Scientific Institute) Conference, New York, 5 January 1945.

Chapter 2

Page 97
Our goose is cooked…
Chiflet (1985) and Whistle (2000).

Page 112
A famished fox observed some grapes…
Morvan de Bellegarde (1802).

Page 112
Driven by hunger, a fox was lusting…
Phædrus (1864), Book 4, Fable 3.

Page 112
We can’t have all we seek, alas…
Benserade (1678), p. 108.

Page 112
A certain fox from Normandy…
La Fontaine (1668), Book III, p. 11.

Page 132
When a dog eats the flesh of a goose…
Henri Poincaré, as quoted by Roger Apéri in Dieudonné, Loi, and Thom (1982), pp. 58–72.

Page 133
There Is No Word…
Tony Hoagland,
Poetry Magazine
, July–August, 2012.

Chapter 3

Page 138
Items to save when one’s house is burning down…
Barsalou (1991).

Page 154
Phelps is pretty much my double…
Mark Spitz, quoted in an article by Drew Van Esselstyn in the
New Jersey Star-Ledger
, 15 August, 2008.

Page 155
Back in 1972, they didn’t have a 50-meter race… Ibid
.

Page 160
Karnak Caps…
From
Egypt Sweet
by Kellie O. Gutman (privately issued, 2005), p. 9.

Chapter 4

Page 188
Ireneo Funes, the main character in Jorge Luis Borges’ short story…
Borges (1962), p. 114.

Page 208
As both émigré and physicist, Dr. Teller was aware of the Nazis’ lengthening shadow…
Mark Feeney, in the obituary “Bomb pioneer Edward Teller dies”, in
The Boston Globe
(“Nation” section), 10 September, 2003.

Page 221
Of course, the historical figure of mathematical fame…
Swetz and Kao (1977), p. 7.

Chapter 5

Page 274
Genius is 1 percent inspiration…
Thomas Edison in 1902, as reported in the September 1932 edition of
Harper’s Monthly Magazine.

Page 301
If the only tool you have is a hammer…
Maslow (1966), p. 5.

Page 313
That memory is knowledge, that knowledge is going to interfere…
Jiddu Krishnamurti, “First conversation with Dr. Allen W. Anderson” in San Diego, California, 18 February, 1974.

Page 313
“Freedom from the Known”, the title of one of his most famous works…
Krishnamurti (1969).

Page 315
There are magic links and chains…
James Falen, “Odelet in Praise of Constraints”, in Hofstadter (1997), p. 272.

Chapter 6

Page 330
In their book
Mental Leaps
…
Holyoak and Thagard (1995), p. 139.

Page 334
The 1930s is a composite analogy…
Khong (1992), p. 59.

Page 334
The analogy of Munich raised the stakes…
Khong (1992), p. 184.

Page 337
One of the most interesting fndings of researchers…
Khong (1992), p. 217.

Page 338
These findings may leave us feeling…
Gentner, Rattermann, and Forbus (1993), p. 567.

Page 368
When I look at an article in Russian…
Personal letter from Warren Weaver to Norbert Wiener, quoted in Weaver (1955).

Page 363
Parfois, le succès ne fut pas au rendez-vous…
Bertrand Poirot-Delpech, in the obituary “Sagan, l’art d’être soi”, in
Le Monde
, 26 September, 2004.

Chapter 7

Page 388
All summer long, without a care…
La Fontaine (1668), Book I, p. 1.

Page 400
The real problem with the interface is…
Norman (1990), p. 210.

Page 408
I will sette as I doe often in woorke use, a pair of paralleles…
Recorde (1557).

Page 413
Multiplying one number by another is…
Bezout (1833), p. 12.

Page 415
As long as one considers numbers as abstract entities…
Bezout (1833), p. 13.

Page 420
To divide one number by another means…
Bezout (1833), p. 21.

Page 420
The number to be divided is the
dividend
…
Bezout (1833), p. 21.

Page 420
One’s goal in doing a division is not always to find out…
Bezout (1833), p. 21.

Page 436
Categories let people treat new things as if…
Spalding and Murphy (1996), p. 525.

Page 436
Analogy is what allows us to see the novel as familiar…
Gick and Holyoak (1983), p. 1.

Page 436
In an analogy, a familiar domain is used…
Clement and Gentner (1991), p. 89.

Page 436
If one establishes that a given object belongs to a certain category…
Anderson (1991), p. 411.

Chapter 8

Page 438
Could anyone think… that they have always marched forward…
Poincaré (1911), p. 31.

Page 440
“8–3” is easily understood; 3 can be taken from 8…
De Morgan (1831), pp. 103–104.

Page 443
an elegant and marvelous trick found in the miracle of Analysis…
Leibniz (1702), p. 357.

Page 454
I saw that mathematics was split up…
Einstein, cited by Banesh Hoffmann (1972), p. 8.

Page 461
That he may sometimes have missed the target…
Planck, quoted in Stehle (1994), p. 152.

Page 467
That a principle of such broad generality…
Einstein (1920), p. 17.

Page 473
With his instinctive sense of cosmic unity he now tosses off…
Hoffmann (1972), p. 81.

Page 477
In his paper of 1905 Einstein said that all energy…
Hoffmann (1972), p. 81.

Page 495
[The new principle] had artistic unity…
Hoffmann (1972), p. 113.

Page 498
I first had the decisive idea of the analogy…
Einstein, quoted in Stachel (2001), p. 255.

Page 500
What made my reputation as a mathematician is…
Villani (2012), p. 146–147.

Page 501
Yet when we see how shaky were the ostensible foundations…
Hoffmann (1972), pp. 127–128.

Page 501
Mr. Einstein is one of the most original minds I have known…
Hoffmann (1972), p. 99.

Page 501
A contemporary of Johann Sebastian Bach once said…
David and Mendel (1966), p. 222.

Page 502
Good mathematicians see analogies between theorems or theories…
Ulam (1976), p. 203.

Epidialogue

Page 506
categories allow us to treat new things as if…
Spalding and Murphy (1996), p. 525

Page 506
analogy is what allows us…
Gick and Holyoak (1983), p. 1.

Page 507
Analogy pervades all our thinking…
Polya (1957), p. 37.

Page 507
When faced with something new, we cannot help…
Oppenheimer (1956), p. 129.

Page 507
Analogies and metaphors are pervasive…
Gentner and Clement (1988), p. 307.

Page 507
Analogy is ubiquitous in human thinking…
Thagard, Holyoak, Nelson and Gochfeld (1990), p. 259.

Page 509
The trips we take in the world of mathematics…
Alain Connes, in the short film
Mathématiques, un dépaysement soudain
, produced in November of 2011 by Raymond Depardon and Claudine Nougaret at the Fondation Cartier in Paris.

Page 509
a mobile army of metaphors…
Nietzsche (1873), p. 46.

Page 509
Whoever first compared a woman to a rose was a poet…
Georges Courteline.

Page 509
Henri Poincaré described mathematics as…
Poincaré (1908), p. 29.

Page 523
the ability to separate things according to their natural divisions…
Plato (1950), 265d–265e.

We have divided our bibliography into eleven sections, one for each of the ten main parts of our book, with one extra section at the beginning providing a list of references that have global relevance to the ideas that we are exploring in our book. Since some of the works cited below are relevant to more than just one chapter of our book, certain entries appear in more than one section of the bibliography. We have preceded each section with a few very general comments about the books and articles listed in it.

General

We open our list of references with a set of books that are relevant to every aspect of our own work. In particular, the book by Fauconnier and Turner, like ours, places conceptual mapping at the center of cognition and also uses a rich and highly variegated array of examples to flesh out the key themes. The volume by Holyoak and Thagard and the anthology edited by Gentner, Holyoak, and Kokinov have become standard references for the field of analogy, seen from a cognitive-science perspective. Both Helman’s compilation and that by Vosniadou and Ortony tackle analogy from a number of angles, the former placing it in an interdisciplinary perspective and the latter focusing on links to similarity. Although these two works are not recent, many of their chapters are still highly relevant. Murphy’s book is an excellent resource on categorization, while Lakoff and Johnson’s study has greatly enhanced the recognition of the systematic role played by metaphor in human thought. Lastly, Sander’s book and that by Hofstadter and the Fluid Analogies Research Group paved the way for the present volume, although they are somewhat more traditionally academic in style.