C E Shannon, D W Hagelbarger / Concavity of Resistance Functions Bell Monograph

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Author:Shannon, C. E. [Claude Elwood]; Hagelbarger, D. W
Publisher:Bell Telephone Laboratories, Incorporated
Year Printed:1956
Binding:Softcover, Wraps
Language:English
Subject:History

Concavity of Resistance Functions [Bell Monograph] Author: Shannon, C. E. [Claude Elwood]; Hagelbarger, D. W. Title: Concavity of Resistance Functions [Bell Monograph] Publication: New York, N.Y. Bell Telephone Laboratories, Incorporated March 1956 Edition: Later printing Description: 2 pages. 10 7/8 x 8 3/8 inches (275 x 213 mm) Publisher’s printed grey, blue and black wrappers, stapled. Five holes punched at the spine as issued. The upper corner bumped. Near Fine. Wraps. The earliest known form of this paper is an internal Bell Labs reproduced typescript. The Journal of Applied Physics, Vol 27, No. 1, pp. 42-43, January 1956 first published this paper, for which an offprint is known. Here offered in the Bell Telephone Systems Monograph Series (#2547: March 1956), a later printing.Abstract: “It is proved that any network of linearly wound potentiometers and fixed resistors have a curve of resistance versus shaft angle which is concave downward.” and later “As part of a computer, a rheostat having a resistance that was a concave upward function of the shaft angle was needed. After many attempts to approximate it with networks of linearly wound potentiometers and fixed resistors, it became apparent that either it was impossible or that we were singularly inept network designers. Rather than accept the latter alternative, we have proved the following theorem…”In short, Shannon and Hagelbarger proved it was impossible to build a needed electrical circuit with ANY network of linearly wound potentiometers and fixed resistors. This mathematical result is an excellent example of where a practical engineering solution was needed and could have been experimented upon endlessly had the mathematicians not stepped in and proved it impossible – a hallmark of much of Shannon’s work.Paul J. Nahin surmises that this paper, whose results are sometimes called the Shannon-Hagelbarger theorem, were probably related to analog computers and not a digital machine. Shannon worked for a time on the Differential Analyzer, “the most advanced electromechanical computer in the world.” He also notes that H. M. Melvin advanced an alternative proof for this paper in “Journal of Applied Physics,” June 1956, pp 658-659. Further research might reveal just what practical application Shannon and Hagelbarger were working on, but we haven’t been able to discover it thus far.It is interesting bibliographically that all three forms of this paper (reproduced typescript, Journal of Applied Physics offprint, and Bell Monograph) in Shannon’s files were slightly different. The (presumed earliest) reproduced typescript has some apparent typos and incorrectly uses the phrase “concave downward function of the shaft angle” as the desired solution in the first sentence. The Bell Monograph paper corrects that to “concave upward function,” as does the Journal of Applied Physics offprint. Lastly, the Journal of Applied Physics offprint includes a second sentence in the first paragraph of Corollary II that starts “This is also true if…” which is present in the reproduced typescript but not in the Bell System Monograph. The completist will want one of each.PROVENANCE: The personal files of Claude E. Shannon (unmarked). There were multiple examples of this item in Shannon’s files.REFERENCES:Sloane and Wyner, “Claude Elwood Shannon Collected Papers,” #98Nahin, Paul J., “The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age,” p 5.COLLECTORS NOTE: The Bell Telephone System Monograph series offered a way to obtain individual articles by Bell scientists regardless of where their work was first published. Many Monographs significantly postdate the original article publication. Because of this, they rarely constitute the coveted (and traditional) article offprint. If the journal of record issued no offprint, the Monograph might be the first separate publication – the closest the collector can come to a traditional offprint. We have done our best to place each Monograph properly in the article’s publishing history and welcome any corrections or additional information, especially regarding issues unknown to us. Seller ID: 28602 Subject: Bell Labs, History of Communication, Mathematics, Software Engineering Kuenzig Books Topsfield MA USA Since 1996 Kuenzig Books has bought and sold rare and/or interesting items in many fields with a focus on 19th and 20th century Science, Technology, and Engineering. We are particularly interested in the History of Computing, and the speed with which the technological innovations of the 20th century have impacted the way we live. You’ll discover some depth in Physics, Mathematics, Nobel Prize authors, Computing, Scientific Instruments, and Chemistry. We are members of the ABAA (Antiquarian Booksellers’ Association of America), ILAB (International League of Antiquarian Booksellers), SNEAB (Southern New England Antiquarian Booksellers), and IOBA (The Independent Online Booksellers Association). We often have material not listed here, please ask if you are looking for something specific. 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We ship to PayPal verified addresses only. Any refund fees charged to us by PayPal for payments that don’t match the verified addresses will be deducted from your refund. Delivery time frames can only be estimated and will depend on the service used, shipping origin, and destination. Payment All payments in US dollars. Payment must be received within 5 days. Please note that our prices on this venue are increased to reflect the fees charged here. Feedback We leave feedback for buyers once they have posted feedback for us. If you are unhappy with any aspect of a transaction with us, please contact us immediately. We work hard to keep buyers happy and to resolve the rare problem promptly. This listing was created by Bibliopolis.

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