IEEE Systems, Man and Cybernetics Magazine - July 2018 - 24
mathematician André-Marie Ampère [2] to describe the
science of government, its modern definition-control and
communication in animals and machines-is traced to Norbert Wiener [3] (Figure 1). Since then, others have coined
the words cyberspace and cyborg, and cybernetics is playing an increasing role in the study of human-machine systems and the analysis of the Internet of Things. Often
defined as noninteger order integration and differentiation,
the idea of fractional calculus first appeared in 1695 in a
letter from Guillaume de L'Hôpital to Gottfried Wilhelm
Leibniz, but more recent interest can be traced to the work
of Keith B. Oldham and Jerome Spanier [4] (Figure 2). Today,
the techniques of fractional calculus are widely applied in
many fields of science and engineering.
The genesis of cybernetics and fractional calculus as
modern scientific disciplines dates from their contemporary
beginnings at the 1946-1953 Macy cybernetics conferences
[5], and the 1974 International Conference on Fractional Calculus and its Applications, organized by Bertram Ross [6].
The trajectories of the two fields are not entwined, but both,
to coin a phrase from novelist Thomas Pynchon, have followed Gravity's Rainbow and provided engineering and science with a wide spectrum of colorful ideas and concepts.
The purpose of this article is to show the similarities
between the two fields and suggest new areas of research in
which future collaborations may develop.
A Brief History of Cybernetics
In [7], William B. Rouse described the evolution of the
IEEE Systems, Man, and Cybernetics Society (SMCS). We
would like to extend this retrospective back to the 1950s
and 1960s to illustrate the overlap of people and programs
that played leadership roles not only in the development of
cybernetics but in the emerging fields of computer science,
artificial intelligence, bioengineering, and neuroscience.
Rouse mentions, e.g., Larry Stark and Larry Young in
his article. Stark, a physician, studied electrical engineering part time at Yale to develop engineering models
(circuits, feedback, and control theory) to describe the
neurological control of the pupil, the lens, eye rotation, and
hand movement [8], [9]. In 1963, he was also the founding
head of the Department of Bioengineering at the University of Illinois, Chicago, coming to that position from work
on eye movements with the Massachusetts Institute of
Technology (MIT) human factors group headed by Young
[10]. Stark and Young both went on to successful careers at
the University of California, Berkeley, and MIT, respectively. Of course, there were many others (e.g., Alan Turing,
John von Neuman, Heinz von Foerster,
Humberto Maturana, Gregory Bateson,
Aksel Berg, W. Ross Ashby, W. Grey Walter,
Claude Shannon, and Jerome Lettvin) who
contributed cybernetic ideas and concepts
linking mathematics, computers, and control theory and developed new tools for
understanding neurological function in
humans and animals.
Since the Macy conferences, the field of
cybernetics has formally expanded under
the stewardship of the International Association for Cybernetics (IAC), founded in
(a)
(b)
1957, and the American Society of Cybernetics (ASC), established in 1964, with
Figure 1. (a) norbert Wiener and (b) his classic 1948 book
Cybernetics [3]. (Photos courtesy of Wikipedia.)
Warren McCulloch [11] serving as its first
elected president. From 1964 to 1970, the
ASC has held annual conferences on all
aspects of systems engineering, human-
machine interaction, and the control of
complex biological and sociological networks. In addition, parallel meetings sponsored by the IEEE led to the formation of
the SMCS in 1972. Today, the IAC, ACS, and
SMCS are vital organizations that arrange
conferences and support journals that publish across the broad field of cybernetics.
(a)
(b)
(c)
Figure 2. (a) Keith b. Oldham, (b) Jerome Spanier, and (c) their
classic 1974 book The Fractional Calculus. the cover shown is
from the republished Dover edition (2006) [4]. (Images courtesy
of Wikipedia.)
24
IEEE SyStEmS, man, & CybErnEtICS magazInE July 2 0 1 8
A Brief History
of Fractional Calculus
It is widely accepted that differential
calculus was invented concurrently and
Table of Contents for the Digital Edition of IEEE Systems, Man and Cybernetics Magazine - July 2018
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