Shannon Hagelbarger (5 results)

Wraps. Condition: Near Fine. Later printing. Later printing. 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. 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," #98 Nahin, 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.

Wraps. Condition: Very Good. [1-cover sheet], [1]-5 leaves + four figures on one leaf of plates. 10 7/8 x 8 3/8 inches. A reproduced typescript with four holes punched at the spine as issued. Stapled upper left, with light overall wear and minor creasing. The Bell Laboratories Filing Subject for this paper is "Network Theory." Wraps. "It is shown that the resistance of a two-terminal resistance network is a concave function of the component resistances." (abstract) "Recently, in connection with the design of a certain circuit, a variable resistance was desired. The variation of this resistance as the shaft was turned should approximate a certain function which was convex downward. It was also desired to obtain this behavior from a circuit consisting of one or more linearly wound potentiometers on the shaft and fixed resistors. All the circuits which were studied proved to have resistance curves which were concave downward. Our lack of success led to a theorem on networks which shows that this is necessarily always the case." (first paragraph). This paper appears to discuss material eventually published as "Concavity of Resistance Functions" by Shannon and Hagelbarger. This technical memorandum was not included in Sloane and Wyner's bibliography. PROVENANCE: The personal files of Claude E. Shannon (unmarked). There were multiple copies of this item in Shannon's files. REFERENCES: NOT IN Sloane and Wyner, "Claude Elwood Shannon Collected Papers" Sloane and Wyner, "Claude Elwood Shannon Collected Papers," item 98 ("Concavity of Resistance Functions").

Wraps. Condition: Near Fine. First Separate Edition. First Separate Edition. [42]-43 pages. 10 1/2 x 7 3/4 inches. Publisher's original tan printed wrappers. Sun fading to the rear panel. 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 (as here). Also later printed in the Bell Telephone Systems Monograph Series (#2547: March 1956). 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," #98 Nahin, Paul J., "The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age," p 5.

Wraps. Condition: Near Fine. [1]-5 leaves plus one plate containing four figures. 10 7/8 x 8 3/8 inches. Reproduced typescript, stapled upper left. Wraps. The earliest known form of this paper is an internal Bell Labs reproduced typescript (as here). The Journal of Applied Physics, Vol 27, No. 1, pp. 42-43, January 1956 first published this paper, for which an offprint is known. Also later printed in the Bell Telephone Systems Monograph Series (#2547: March 1956). 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 four examples of this item in Shannon's files. REFERENCES: Sloane and Wyner, "Claude Elwood Shannon Collected Papers," #98 Nahin, Paul J., "The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age," p 5.

Wraps. Condition: Very Good. [1-cover sheet], [1]-12 leaves + 3 leaves of plates. 10 7/8 x 8 3/8 inches. Reproduced typescript. Stapled upper left, with four holes punched at the spine as issued. Plates in rear marked "Bo-361720", "B0-361721," and "B0-361-722" (the last partially cut-off at top). The text of the paper identifies these plates plus two photographs that were not present in Shannon's files. We have included a modern copy of the two photographs (of Model 2 of this device) taken from Sloane and Wyner's book. The Filing Subject is "Switching Theory" Wraps. "An experimental relay kit suitable for use in a college laboratory course in switching is described. Circuit diagrams are given for several circuits that have been set up on the machine. It is suggested that if such a kit were developed and made available to colleges, it would materially aid our long-range policy toward cultivating switching engineers." (abstract) "An important perennial problem facing the Bell Telephone Laboratories and, in fact, the entire Bell System is that of recruiting a sufficient number of switching engineers. Until recently, practically no colleges gave courses dealing with this subject, and even now the number is very small. Many engineering graduates are hardly aware of switching as an important branch of electrical engineering, and one with any training in the techniques is a rare gift indeed. It has been necessary first to sell graduate engineers the idea of switching as a career and then to train them from the ground up. Bell Laboratories has not been unaware of these problems and has taken several important steps toward its solution .The development of large-scale computing machines has 'glamorized' the field of switching and digital devices to a considerable extent .This memorandum proposes another supplementary attack on the same problem." (first few paragraphs condensed) The Memorandum describes a laboratory switching outfit that would allow students to develop practical skills alongside college courses. At an estimated $600 per unit in 1954 (before production cost reductions), it was a pretty big gamble, one which we are not sure ever came to fruition. This interest in mechanical teaching methods would reappear later when Shannon, Hagelbarger, and Edmund Berkeley consulted on various projects produced in kit form. PROVENANCE: The personal files of Claude E. Shannon (unmarked). There were four examples of this item in Shannon's files, none with the two mentioned photographs. REFERENCES: Sloane and Wyner, "Claude Elwood Shannon Collected Papers," #85.