Slide Rule Research Articles

Slide Rules: Design, build, and archive presentations in the engineering and technical fields (Nathans-Kelly, T. and Nicometo, C.G.) [Book review

Slide Rules: Design, build, and archive presentations in the engineering and technical fields (Nathans-Kelly, T. and Nicometo, C.G.) [Book review

From the Editor's Desk

This issue features articles on the Soviet computer hobby movement of the 1980s, an overview of the history of computing in India in the period 1955-2010, an insightful and very personal history of the IBM Sales School by James Cortada, a look at how technical workers learned to use slide rules in the 19th century, and an analysis of the production and interpretation of early ARPANET maps.

Old DOI 10.1109/MAHC.2015.38 EH -Good DOI 10.1109/MAHC.2015.17 EH - Useful Instruction for Practical People - Early Printed Discussions of the Slide Rule in the United States

Old DOI 10.1109/MAHC.2015.38 EH -Good DOI 10.1109/MAHC.2015.17 EH - Useful Instruction for Practical People - Early Printed Discussions of the Slide Rule in the United States

Useful Instruction for Practical People: Early Printed Discussions of the Slide Rule in the US

Printed accounts of the appearance and use of various forms of slide rule appear in a variety of 18th and early 19th American printed sources. Based largely on British work, these texts reveal both confidence in the practical potential of the instrument and the slow diffusion of the device.

Through the Eyes of Galileo's Heirs: Deciphering the Laws of Nature Through the Language of Mathematics

When I was a graduate student at Yale, back in what seems like the Paleozoic era, one of the courses that I took was called “Statistics for Morphometrics.” It was designed for those graduate students, like me, who were planning to eventually use some assortment of measures and statistics in our budding morphology-based dissertation work. The course was taught by a very bright fellow named Ray Heimbuch, an advanced graduate student in physical anthropology who already had a reputation for his exceptional skills in these areas. His presentations were extraordinary, and took his pupils deep into the continually evolving science of how one extracts meaningful data from the geometry of form. As he became more and more granular, we grasped that he saw the world in mathematical and geometric images beyond what most of the overwhelmed and struggling students, particularly me, could envision, now or, probably ever. With each presentation, it became clearer to me that I would have to accrue his incredible abilities and mathematical “eyes” if I was to undertake the research I wished to pursue. Or, I could become his really good friend. A few years later (with my successful Dissertation completed, and many papers hatched; e.g., see Laitman et al. 1978, 1979; Laitman and Heimbuch, 1982), I was the best man at Ray’s wedding. Some weeks back as I penned this essay, I had the privilege of listening to Mike Hausman, our Professor and Chair of Orthopedics at Mount Sinai, and an internationally renown surgeon, as he taught my first-year anatomy students about the hand. I met Mike when I was his Teaching Assistant at Yale, also back in the Paleozoic, and noticed even then his extraordinary mind and special ability to see structure through mathematics and geometry. I again sat in awe in my lecture hall as this physician-surgeon-mathematician taught my class, not solely about the muscles or bones of the hand, but about the extraordinary patterns and geometric codes buried within the structure of nature’s form. My young physicians-to-be sat enraptured as he guided them to the intersection of geometric shape and regularity of form, of Fibonacci numbers and patterns appearing from feathers to the shells of a nautilis to the fingers of the hand. And he took them back to the words of insight from one of the greatest minds of all time, Galileo Galilei, and his guiding principle that the laws of nature can only be understood through the language of mathematics itself (Galilei, 1623). One of the observations that life has shown me is that some people’s minds are wired very differently from others. No great or unique insight here, but it’s what I’ve seen. In my inch of the scientific world—working on head and neck structures such as the larynx or ear—I’ve been amazed by how many of the surgeons, for example, who approach vocal folds are also extraordinary singers, or those who meticulously seek to reconstruct one’s hearing are also talented musicians. No group, however, has impressed—awed might be a better term—me more than those who see the world through mathematical equations or through the ever-morphing lenses of geometry.

The first protein Structure Determinations

Max Perutz had been studying the structure of haemoglobin for 21 years using highly original and creative techniques, when I arrived in Cambridge in the summer of 1958. Most recently he had explored the use of isomorphous replacement by substituting specific amino acids with heavy metal compounds. Together with Ann Cullis, he had collected three dimensional diffraction data on native haemoglobin crystals and on three heavy atom derivatives. But now Max needed help in analyzing this data. I had had experience in determining three small aromatic hydrocarbon structures as a graduate student with J.M. Robertson at the University of Glasgow using only mechanical hand calculators, a slide rule and Beevers-Lipson strips. At the University of Minnesota, as a post doc with Bill Lipscomb, I had learned how to program one of the earliest commercial computers and solved a plant terpenoid structure in three dimensions. Thus, when I joined Max's lab, I was soon busy programming the bran new "home build" EDSAC2 computer to determine and refine the heavy atom parameters for phase determination by isomorphous replacement. When we calculated the 5.5Å resolution horse oxy haemoglobin electron density map in the summer of 1959 we were amazed to see that the two polypeptide chains of haemoglobin each had the same fold as that of myoglobin, another oxygen carrying protein determined by John Kendrew at 6Å resolution two years earlier at the Cavendish. John and his group were extending the structure of myoglobin to 2Å resolution. The high resolution map of myglobin was calculated using my Fourier program the week after the low resolution haemoglobin map. We then saw the atomic structure of α-helices as had been predicted by Linus Pauling. Seeing evolution for the first time at a molecular level has inspired my thinking and choice of research topics ever since. In the following few years, stimulated by these discoveries , David Blow (who had returned from the US later that summer after two years of post-doc studies) and I developed the single isomorphous replacement method, the use of anomalous dispersion for phase determination, phase combination procedures and, most importantly, molecular replacement.

The Shockley‐Queisser paper – A notable example of a scientific sleeping beauty

The Shockley‐Queisser paper – A notable example of a scientific sleeping beauty

A Sceptics View: “Kleiber’s Law” or the “3/4 Rule” is neither a Law nor a Rule but Rather an Empirical Approximation

Early studies showed the metabolic rate (MR) of different-sized animals was not directly related to body mass. The initial explanation of this difference, the “surface law”, was replaced by the suggestion that MR be expressed relative to massn, where the scaling exponent “n” be empirically determined. Basal metabolic rate (BMR) conditions were developed and BMR became important clinically, especially concerning thyroid diseases. Allometry, the technique previously used to empirically analyse relative growth, showed BMR of endotherms varied with 0.73–0.74 power of body mass. Kleiber suggested that mass3/4 be used, partly because of its easy calculation with a slide rule. Later studies have produced a range of BMR scaling exponents, depending on species measured. Measurement of maximal metabolism produced scaling exponents ranging from 0.80 to 0.97, while scaling of mammalian MR during growth display multi-phasic allometric relationships with scaling exponents >3/4 initially, followed by scaling exponents <3/4. There is no universal metabolic scaling exponent. The fact that “allometry” is an empirical technique to analyse relative change and not a biological law is discussed. Relative tissue size is an important determinant of MR. There is also a need to avoid simplistic assumptions regarding the allometry of surface area.

Sustainability Monitoring and Assessment: New Challenges Require New Thinking

Sustainability Monitoring and Assessment: New Challenges Require New Thinking

Accurately Measuring the Height of (Real) Forest Trees

Q uick and accurate tree height measurement has always been a goal of foresters. The techniques and technology to measure height were developed long ago—even the earliest textbooks on mensuration showcased hypsometers (e.g., Schlich 1895, Mlodziansky 1898, Schenck 1905, Graves 1906), and approaches to refine these sometimes remarkable tools appeared in the first issues of Forestry Quarterly, Proceedings of the Society of American Foresters, and the Journal of Forestry. For example, one such hypsometer based on the geometric principle of similar triangles (top of Figure 1) employed rotary mirrors to allow the user to simultaneously see the top and bottom of the tree in “proper parallax” (Tieman 1904). Other early hypsometers applied different approaches that used angles and distance (e.g., Graves 1906, Detwiler 1915, Noyes 1916, Krauch 1918). Of these trigonometric hypsometers, those that calculated total tree height (HT) as a function of the tangent of the angles to the top (B2) and bottom (B1) of the tree and a baseline horizontal distance (b) to the stem were most common (Figure 1). Because they are easy to apply and required only simple technology, these approaches (hereafter, the similar triangles and tangent methods) have dominated tree height measurement. That is not to say the challenge of accurate tree height measurement was solved— many early foresters reported problems with getting consistent data in uneven terrain or dense understories or with the use of different types of hypsometers. Good measurement practices usually mitigated these issues and became standard components of forester training programs. Others addressed these challenges by designing new techniques based on different trigonometric relationships. As an example, Haig (1925) proposed a slide rule solution that calculated tree height using the sine law and slope distance from the observer to the tree base (s1)

The Increasing Cross-Talks Between The “Dry” And “Wet” Sciences

n the early 1960s, the Higher School Certificate Course was the track to direct entrance to Nigerian universities. There was a clear dichotomy between those who opted for Additional Mathematics, Mathematics and Physics and those who followed the “wet sciences” of dissections, buffers, enzymes in Botany, Zoology and Chemistry. The would-be “dry scientists” toted around slide rules, mathematical sets, and pencils and were destined for careers in the computational sciences and engineering. Those in the “dry areas” acted as if they were smarter, and the two groups lived in different scientific worlds. Increasingly, however the two scientific worlds are having serious conversations.

Profile of Vivian W.-W. Yam

Primary school children do not typically handle droplets of the toxic element mercury with bare hands. However, for a young Vivian Yam, an early experience with a broken thermometer sparked a career synthesizing metal complexes for use in light-harvesting and light-emitting materials. Yam, a recently elected foreign associate of the National Academy of Sciences and a chemistry professor at the University of Hong Kong, says, “I was amazed by mercury’s ability to flow and coalesce—unlike most metals we’re exposed to.” Over the past three decades, through a combination of molecular design and physical inorganic chemistry, Yam has helped create new classes of metal-containing chromophores and luminophores—molecules that absorb or radiate light and some of which may help mitigate the growing global demand for energy. Yam’s Inaugural Article (1) explores how a platinum(II)-containing compound assembles and forms varied 3D structures with individual spectroscopic properties. Vivian W.-W. Yam. Image courtesy of the University of Hong Kong. Born in Hong Kong when the region was under British rule, Yam attended an Anglican grammar school. Her mother was a homemaker, and her father, a civil engineer. “I really admired him and still remember him using the slide rule back in the days when you didn’t have a calculator,” she says. However, Yam’s parents did not urge her to enter professional schools or study medicine. She says her curiosity with the natural world and an analytical disposition prompted her to pursue science. In her secondary school biology teacher, Yam found another inspiration. “She embodied the Chinese commitment to one’s field—that whatever you do, you should respect your work, enjoy it, and be very much devoted to it. Even when she was pregnant, she taught until the last moment!” Yam majored in chemistry at one of Hong Kong’s two universities of the time, the University of …

Editorial: Effective Presentations—A Must

Editorial: Effective Presentations—A Must

Slide rules, nomograms and additive functions

Older readers will remember using a slide rule to carry out multiplication and division in the days before calculators. There was also a graphical tool called a nomogram, which was used for evaluating certain functions. Although such devices have little practical use nowadays, I was interested in investigating which classes of functions with two independent variables could be calculated using this type of device.Figure 1 shows how a slide rule was used to multiply 3 by 4 (or equivalently to divide 12 by 4). To do this, you align the 1 on the upper scale with the 3 on the lower scale and then read off the value below the 4 on the upper scale to get 12 (or, for division, you line up the 4 above the 12 and read off the answer 3 on the lower scale).

The Back Page: My Favorite Lesson: Sliding through Logarithms

One of my favorite lessons involves a nostalgic look at the past, in the years BC (Before Calculators). The properties of logarithms are readily reinforced using an ingenious tool from the past—the slide rule. Developed in the seventeenth century by William Oughtred and others, who built on the emerging work on logarithms by John Napier, the slide rule was used to multiply, divide, and find square roots and cube roots, among other arithmetic operations. Before the advent of the pocket calculator, it was the most commonly used calculation tool in science and engineering.

Milestones…

Milestones…

Graphic Aids for Calculation of Fluid Resuscitation Requirements in Pediatric Burns

The Parkland formula is currently the most widely used protocol to guide fluid resuscitation of acute burns and has been adapted for pediatric use. We describe 3 novel graphic devices (a nomogram, slide rule, and disc calculator) based on this formula, which have significant advantages over existing graphic and electronic devices. The robust low-cost graphic devices would be particularly suited to developing countries and difficult locations, but could be used as the primary means of calculation in any environment. If a computer or calculator is used as the primary means of calculation, the graphic devices provide a simple and rapid means of checking and preventing errors that may arise because of inadvertent mis-keying of data or incorrect application of the pediatric Parkland formula.

Sages Before and Forever

It seems just a few years ago—surely not 40 years ago—that I decided that teaching math and music might not bring in the cash reserves that nursing had in store for me. I came from a family of caring professionals, especially a hardworking and loving mother who encouraged me to take a 60-hour certified nursing assistant course with her in the summer after I finished high school, which began my unwritten and unbelievable future. Sage alert! We both worked at the local hospital in our cute white shirts and aqua pinafores. RNs, especially LPNs, encouraged me and (illegally) allowed me to perform those special tasks. Elder nursing assistants guided me and showed me how it was all done. Sage alert! My sister, who was 5 years older, attended a diploma RN Catholic school of nursing. As she scurried around her “all is forbidden” dorm room in a long, starched dress uniform, labored over the exactness of the fold in her starched white cap, and studied to work and worked to study, I knew that this scene would not influence any of my future decisions on becoming a nurse, but I did like her paychecks. Sage alert$! I thought that if she could do this, I could too! Finding sage mentors was never an issue for me; in fact, they always seemed to find me and try to spin me in the right directions. Here are some examples. A brilliant brother (now a renowned structural engineer) who breezed through calculus and trigonometry and drew artwork free-handed to depict the organisms of the world looked at me hopelessly as he handed me his old slide rule to eventually figure it out on my own. Sage alert! A stop by my old neighborhood elementary school and a brief moment of counsel with the principal left me with advice for an ideal future. “Whatever you do, get your degree!” Sage alert! I had no clue what he meant at all. By circumstance and luck—and a belief that my father, who had died when I was 12, was somehow looking down from above—I attended a BSN program. Hippie era, flower power, black power, rebellious vote-out-the-white-nurses-cap—all of that happened in time, just 1 year before graduation! Sage mentors appeared mysteriously through unexpected student loans, scholarships, grants, hometown sorority scholarly believers, and veteran service organizations. Who were all these sages, and how could I let them down? Sage alert! My first VA chief nurse personally met with each new graduate nurse or new nurse, but what could she possibly want to see me about? What in the world does she mean by “never sell yourself short”? Hmmm, sage alert! Sage gone bad alert! One supervisor did not want me to continue my education to obtain a master’s degree in nursing because she could not pass statistics—and I had even offered to assist her! Sages were my colleagues who willingly allowed me to work every weekend to attend evening classes through the week. Finally comes my most supportive boyfriend and now husband, who tried to get me to join the “other branch of the military” when I chose the Army Reserve. Sage alert! Perhaps the math helped to add the additional monies and benefits of being a part of the military nursing corps, where I found key nurse leaders who continued to help me create the future I wanted. Opportunities, professional associations, challenges, travel, and courage came in many experiences that a civilian nurse would never envision. So, after 40+ years with the Department of Veterans Affairs and 28+ years with the Army (active and reserves), it’s time to sage-on, as I retire and do all of the things left on my sage alert list, which was excitedly given to me. I will continue to pass it on to others along the way!

Ecohydrology and Fish-Passage Engineering: Legacy of Denil and the Call for a More Inclusive Paradigm

Ecohydrology and Fish-Passage Engineering: Legacy of Denil and the Call for a More Inclusive Paradigm

Punching Process and Technical Equipment of High-Density Sub-Mesh Plate

According to the problems in the process of high-density mesh plate that mesh holes of plate is too density and the device screw bar is not long enough for the original equipment, a set process is used to overcome the problems of lying out and fixing for punchers. A simple special tool is designed. Fixed and slide ruler mechanisms are installed in the original machine. Repeat-orientation and several division methods are used, and the stroke of the original machine is increased two times, which successfully solves the processing problems and creates good economic benefits.