Edward R Dewey

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Edward R Dewey

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Edward R Dewey ( 1895 - 1978 ) was an Economist who studied cyclic patterns in economics and other fields. In 1931 he was apointed Chief Economic Analyst of the Department Of Commerce under the Roosevelt Administration to try to discovering the cause and underlying dynamics of the Great Depression . {Link without Title} He later founded an institute for exploring cycles.

DEWEY'S OBSESSION WITH CYCLES

Dewey devoted his life to the study of Cycles . In 1941 he founded an organization called The Foundation For The Study Of Cycles , which still exists and which remains active in promoting Dewey's theories in various venues.

Dewey said that

everything that has been studied has been found to have cycles present

Dewey carried out extensive studies of cyclicity in Economic , Geological , Biological , Military , and other trends. Among these, the best known today are his studies on the Cycles Of War .

In the course of his research, Dewey observed that seemingly unrelated events had often similar cyclicity (cycle synchrony). In particular, he claimed many cycles had periods that were related by powers or products of 2 and 3.

For example, consider the table below. To construct this table starting from the fraction 17.75, multiply by three as you proceed along diagonals from lower left to upper right, and multiply by two as you proceed along diagonals from lower right to upper left. According to Dewey, the underlined numbers are commonly occurring periods (in years):

142.0 213.9 319.5 479.3

-
71.0 106.5 159.8

-
35.5 53.3

17.75

-
5.92 8.88

1.97 2.96 4.44

0.66 0.99 1.48 2.22

0.22 0.33 0.49 0.74 1.11

CLAIMS

Dewey made several claims about cycles:
#Cycles of identical length were found both in business cycles and in biological cycles in nature and in wildlife, that is have the same Period .
#Similar cycles from different areas reached their peaks and troughs at the same time, that is have the same Phase .
Dewey gave the name "cycle synchrony" to these claims. {Link without Title}

CRITISM

The study of cycles has been robustly cricicised as Pseudoscience . Philip Ball in his book ''Critical Mass: how one thing leeds to another'' devotes a chapter to ''Rythems of the market place'' and examining the history of the study.

The truth is that dips and peaks in the economy resolutely refuse to recur in any predictiable manner, making attempts to construct cyclic theories of economics look increasing like Ptolemy's elaborate scheme for predicting the motions of the planets

Ball then discusses more modern theories which investigate the precence of Chaos in the buisness cycle. This work shows that economic cycles are neither completly periodic or completly random, rather thay follow a Lévy Flight distribution.Philip Ball, ''Critical Mass'' Random House 2004. ISBN 00994557865.

SOME MODERN MATHEMATICAL THEOREMS INVOLVING CYCLES

While the table above (like most of Dewey's work) amounts to Numerology , we can still ask: ''why are cycles so common in many-- but certainly not all-- phenomena in subjects such as economics, biology, and physics?''

It goes beyond the scope of this article to attempt to answer this question, but we can still ask: ''what does modern mathematics have to say concerning cyclic behavior common to many phenomena in economics, biology, and physics?''

As it turns out, there are several distinct (but related) notions of ''cycle'' which are studied in various areas of modern mathematics, particularly the modern theory of Dynamical Systems . Even better, there are several important and very striking theorems in which cycles play a leading role. Some of the better known examples include:

Sarkovskii's Theorem reveals the unexpected role played by multiples of two and three in answering the question: ''what periods occur in a dynamical system obtained by iterating a continuous map on the unit interval?'' The Sharkovskii theorem gives a ''complete'' answer to this question and thereby provides deep insight into these systems (which are more general than they might appear). In particular, it implies that ''if such a system has a three-cycle, it has n-cycles for every positive integer n!''

involve rational approximations, in the context of devising accurate but practical calendars, modeling astronomical motion, and so forth. Hurwitz's answer, by the way, is: ''the Golden mean'' (plus some closely related numbers).

The orbits. It turns out that the Golden Mean is associated with the most resistant tori, which gives a connection with Hurwitz's theorem! Applications of the KAM theorem include the orbits of solar system objects in complicated multi-body scenarios.

In symbolic dynamics, ''Bowen's formula'' gives the Artin-Mazur Zeta Function of a one-dimensional shift of finite type as a rational function (the reciprocal of a Polynomial , in fact) which is easily computed from the Graph defining the shift. Knowledge of the zeta function (and Möbius Inversion ) enables one to efficiently determine which periods occur and how many points have a given period. This formula is relatively easy, but it leads to a deep connection with the dynamics of closed geodesics on Compact Hyperbolic surfaces, and even an intriguing connection with the Prime Number Theorem ! See Prime Geodesic .

# many famous mathematicians have studied many different notions of cycles,
# the results of their work includes several of the most memorable theorems in modern mathematics,
# appropriate (mathematically defined) notions of cycles play important roles in various parts of the modern theory of dynamical systems, and therefore in the many applications of this theory to economics, biology, physics, and other areas.

It is important to understand that none of this work has anything relation with the semi-mystical speculations of Dewey. It is also important to understand that in symbolic dynamics one can exhibit dynamical systems ''which have no periodic points at all!'' Since these include systems which can be used to model real world phenomena, this fact directly contradicts the alleged claim by Dewey that all phenomena include cyclic behavior.

Nonetheless, members of the Foundation for the Study of Cycles have attempted to use mainstream research resting upon some sophisticated mathematical theories (including the theorems outlined above), in order to argue that the very existence of this work demonstrates (they allege) that Dewey's speculations constitute accepted science. This claim is not supported by examination of the mainstream research literature.

SEE ALSO

Business Cycle

Econophysics

Joseph Schumpeter who claimed in the 1940's that there were a least three buisness cycles, one short term, one of 7-11 years and one of about 50 years.Ball, ''Critical Mass'' Random House, 2004. p233

Elliott Wave Theory

EXTERNAL LINKS

Foundation for the Study of Cycles , which promotes Dewey's ideas.

REFERENCES

''Cycles: the mysterious forces that trigger events'', Dewey, Edward R.; Mandino, Og, New York, Hawthorn Books 1971

''Cycles, the science of prediction'', Dewey, Edward R.; Dakin, Edwin Franden, New York, H. Holt and Company 1947

''Cycles;selected writings'' Dewey, Edward R. Pittsburgh, Foundation for the Study of Cycles 1970

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