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On the Role of Mathematics and Mathematical Knowledge in the Invention of Vannevar Bush's Early Analog Computers

IP.com Disclosure Number: IPCOM000129968D
Original Publication Date: 1996-Dec-31
Included in the Prior Art Database: 2005-Oct-07
Document File: 19 page(s) / 72K

Publishing Venue

Software Patent Institute

Related People

SUSANN PUCHTA: AUTHOR [+2]

Abstract

Nowadays computers are penetrating almost all parts of life -- science and technology in particular. They serve multiple purposes and are capable of functions that are either too laborious or transcend certain human intellectual capabilities. Ever new and powerful types of these devices are being developed. But besides searching for future advancements of computers, there is some merit and interest in pausing and looking back. This might be for motivation to construct computers, for the professional and educational prerequisites of their inventors, as well as for social forces and concrete historical circumstances out of which computational machinery was born. It is important to distinguish between analog and digital computing devices. Analog machines depend on the representation of the mathematical variables as physical quantities on which the operations are performed. That is, they use the analogy to a physical system that obeys the same mathematical relations that control the physical or technical phenomenon under investigation. The basic operation is measurement of some physical quantity. Instead of using continuous quantities, in digital computing instruments the mathematical variables are represented by discrete values, i.e., numbers, the fundamental processes performed on them being arithmetical.28 Today's devices are mosey digital. Hence, there is considerable interest in tracing the development of dial ";surviving,"; apparently ";successful"; technology. Are the analog ancestors of modem computers, which were superseded and finally replaced by digital technique, Therefore assumed to be a less successful technology? Were they less helpful and less instrumental in their context clan digital computers? Is analyzing their contextual invention and development less informative about the intellectual, interdisciplinary, and social dimensions and sources of modem computing? Certainly not, as tills article will demonstrate by focusing on the initial phase of the development of one of the more complex analog computers in the first decades of the 20th century. I will concentrate on the product integraph (see Fig. 1), the immediate forerunner of the differential analyzer and part of a family of analog machines developed by Vannevar Bush and his collaborators at the Massachusetts Institute of Technology (MIT) beginning in the mid-1920s.

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Copyright ©; 1996 by the Institute of Electrical and Electronics Engineers, Inc. All rights reserved. Used with permission.

On the Role of Mathematics and Mathematical Knowledge in the Invention of Vannevar Bush's Early Analog Computers

SUSANN PUCHTA

The technological, professional, and intellectual context out of which the development of the continuous integraph or product integraph -- as the immediate forerunner of Vannevar Bush's differential analyzer -- evolved is outlined. In particular, the affinity between transmission line research and teaching at MITs electrical engineering department under Bush's guidance, on the one hand, and the creation of the product integraph for evaluating integrals, which resulted from the appropriate differential equations of the transmission problems, on the other hand, is detailed. I emphasize Bush's perception of promoting engineering by easing the applied mathematics in this field as it appeared in his contribution to the development of operational circuit analysis as an appropriate engineering mathematics as well as in creating analog machinery that was inspired by the formulation of transmission line problems in terms of that very operational methods after Oliver Heaviside.

Introduction

Nowadays computers are penetrating almost all parts of life -- science and technology in particular. They serve multiple purposes and are capable of functions that are either too laborious or transcend certain human intellectual capabilities. Ever new and powerful types of these devices are being developed. But besides searching for future advancements of computers, there is some merit and interest in pausing and looking back. This might be for motivation to construct computers, for the professional and educational prerequisites of their inventors, as well as for social forces and concrete historical circumstances out of which computational machinery was born.

It is important to distinguish between analog and digital computing devices. Analog machines depend on the representation of the mathematical variables as physical quantities on which the operations are performed. That is, they use the analogy to a physical system that obeys the same mathematical relations that control the physical or technical phenomenon under investigation. The basic operation is measurement of some physical quantity. Instead of using continuous quantities, in digital computing instruments the mathematical variables are represented by discrete values, i.e., numbers, the fundamental processes performed on them being arithmetical.28 Today's devices are mosey digital. Hence, there is considerable interest in tracing the development of dial "surviving," apparently "successful" technology. Are the analog ancestors of modem computers, which were superseded and finally replaced by digital technique, Therefore assumed to be a less successful technology? Were they less helpful a...