User:Protonk/BTM

Burn the mathematics is a quotation by English economist Alfred Marshall from a 1906 letter addressed to his protégé A. L. Bowley. The passage containing the quotation lays out Marshall's maxims for using mathematics in economics, instructing Bowley to use mathematics not as "an engine of inquiry" but as a language and dispense with the mathematics once suitable prose has been found to express the model. The quote has been treated by historians of economic thought as emblematic of Marshall's distaste for the mathematization of the discipline.

Letter to Bowley
"I went more and more on the rules—(1) Use mathematics as a shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you canʼt succeed in 4, burn 3. This last I did often."

subsequent interpretation
=Quotes for later use=

Sutton 2000
"The key to Marshall's view lies in his claim that economic mechanisms work out their influence against a messy background of complicated factors, so that the most we can expect of economic analysis is that it captures the "tendencies" induced by changes in this or that factor. A rise in demand implies a "tendency" for price to rise in the sense that, so long as none of the complicating factors work in the opposite direction with sufficient strength to cancel its effect, we will see a rise in price." -Sutton, p. 4 Marshall's Tendencies. He goes on to talk about Marshall's analogy to tides (p.4-5) and notes (p.5) how the theory of tides was in its infancy when marshall made his analogies.

"To Marshall, theory alone was empty, while empirical investigations without theory were suspect; only the interweaving of theory and evidence constituted "economics proper" -ibid 13

p18-19 connects the GLS approach to estimation w/ marshall's analogy about tides, breaking down variations in a dependent variable between a "systematic part" and a "disturbance term" Obviously econometrics has settled on treating the disturbance as a random draw.

Heilbroner 1999
p.207 Heilbroner repeats an argument made by Schumpeter, noting that relegating math to footnotes was a rhetorical strategy (making economics accessible to businessmen)

p. 317 though associated w/ "laws" of demand and supply Marshall was hesitant to connect economics with hard sciences.

Coase 1994
Coase, quoting Marshall: "a training in mathematics is helpful by giving command over a marvelously terse and exact language for expressing clearly some general relations and some short processes of economic reasoning; which can be expressed in ordinary language, but not with equal sharpness of outline. And, what is of far greater importance, experience in handling physical problems by mathematical methods gives a grasp, which cannot be obtained equally well in any other way, of the mutual interaction of economic changes" (p174 in coase, App. D p. 781 in Principles, volume 1)

Marshall feared that overuse of mathematics unlinked from the real world would lead to diversions from real problems into mathematical fancies. (very rough paraphrase) Coase p. 175

Coase argues that then current practice in economics might have borne out Marshall's fears. (175)

Skousen 2009
Skousen compares Marshall's quote's to Von Mises's more extreme admonitions about mathematics and treats Samuelsons's Foundations as a reversal of Marshall's framework--math in the body text, analysis in the footnotes. Skousen then connects the dispute over form to the arc that mathematical economics traveled over the 20th century, but doesn't return to the quote. p. 365-366

Weintraub 2005
Argues that Marshall's views about mathematics were not necessarily the consensus at Cambridge, despite the influence of his book. p. 144

Uses Keynes' letter to Harrod to undergird the argument that Keynes and Marshall held similar views about mathematics (esp. mathematics by economists untrained in rigorous math), "One hears the echo in this letter of Marshall’s 1906 letter to Bowley, about the need to “burn the mathematics.” That Keynes, writing a quarter century after Marshall, speaks of exactly the same relation of economics and mathematics, is signiﬁcant, but not in my view for the reason that is commonly maintained." p.146

Weintraub turns off this to suggest that Keynes was locked in a 1906 Caimbridge view of mathematics, ignorant of the intervening years and major changes. p. 147

This continues on 152-153, though is less relevant to BTM.

DOI:10.1215/00182702-37-1-133

Reviews of Weintraub 2002
"Weintraub stresses the emergence of more abstract set-theoretic thinking, connected partly to the development of suitable tools to study non-Newtonian physics. But it was also a product of pure mathematical imagination, driven to test the limits of a new conceptual framework. Weintraub’s broader thesis is that this “new math” was an essential precursor to truly modern economics: the old Tripos-style mathematics needed to be burned first." -Roy Epstein, p.514

The Journal of Economic History (2003), 63:2:514-516 Cambridge University Press doi:10.1017/S0022050703001888

Klemperer
Interpreted the quote as an exhortation to connect economic theory to practical applications. p.273

Paul Klemperer Using and Abusing Economic Theory Journal of the European Economic Association April–May 2003 1(2–3):272 –300

Porter
Compares Marshall's instructions w/ Pearson's less drive to keep statistics and mathematics relevant to the world. Pearson (obv) focused on mathematical statistics as a tool for inquiry but didn't want too many technical diversions to push theory away from practice. p.167

Places marshall in a line of economists complaining about abstractions p. 169

doi: 10.1080/1042771042000219019

LiCAlzi and Basile
Described Marhsall's quote as an elucidation of the rhetorical limits to mathematics. p. 105

Argued that Marshall's shuffling of math to the appendix of Principles was consistent with this stance and links Marshall's view to VonNeumann's warnings against succumbing to mathematical formalism. p.106

M. LiCalzi and A. Basile, "Economists and mathematics from 1494 to 1969: Beyond the art of accounting", in: M. Emmer (ed.), Mathematics and Culture I, Springer, 2004, 95-107.

Dimand
Dimand disagrees with Coase and suggests that the letter and the appendix to Principles show a tension Marshall felt between use of mathematics and reliance upon for exposition. p. 89

He follows up and supposes that Marshall felt that economists untrained in mathematics would be unable to explicate both the math and the grounding of the work in reality (citing an earlier portion of the letter to Bowley) p.90

Dimand also argues that Marshall's admonition to remand mathematics to the appendix might have caused Keynes to eschew publication of systems of equations for the IS/LM curve in his 1936 book, even though his earlier drafts and lectures contained them. p.90

This is a general counterargument to Paul Samuelson's claims that Keynes might not have understood IS/LM until someone else published the related system of equations. p.91

DOI 10.1215/00182702-2006-024

Deane
Suggests that Marshall's focus on applied and empirical work ceded to theory as revised new editions of Principles. p.6

http://www.jstor.org/stable/2232161

Fay
Notes that Bowley was one of Marshall's key disciples. p. 82

review concludes noting the salience of the BTM quote p. 87

http://www.jstor.org/stable/1811410

Shove
Treated BTM as an exhortation on rhetoric, noting that "while the mathematical apparatus translated into english and the non-mathematical extension of it to cover the element of time [here referring to Marshall's discussion of LR vs SR] formed the skeleton of the Principles, the bare bones had to be clothed in flesh before they could appear in public or rank as economics proper" p. 307-308

http://www.jstor.org/stable/2226235

Schabas
Schabas argues that while BTM was important, it has been used to draw misplaced inferences about Marshall and his approach toward mathematics. p. 72

---Reread for more later---

http://www.jstor.org/stable/234344

Franklin
Franklin takes BTM to represent Marshall's public views and treats his use of mathematics as a "secret vice" (somewhat tongue in cheek) p. 231

http://www.jstor.org/stable/2975753

Ormerod
Singles out BTM among a volume of correspondence from alfred marshall

http://www.timeshighereducation.co.uk/story.asp?storyCode=160470&sectioncode=8

Krugman
Krugman points out the ambiguity in Marshall's phrasing, questioning the phrase "engine of inquiry". He points to earlier experience marshall had where theory produced a paradoxical result and argues that this may have driven marshall to de-emphasize math as a tool to generate conclusions. p. 1833-1834

Krugman later argues that Marshall's dictum is fully defensible when determining how to present economics to an audience of students or non-economists. p.1835

He further argued that mathematical formulations represent the structure of theory and argument and that 'burning them' was a strategy which obscured the underlying framework of an argument. He then offers a revised admonition. p. 1836

http://www.jstor.org/stable/2565846

=Notes=