Lectures, Papers & Programs on Calculators

Old rotary mechanical calculator
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Lectures and demonstrations

Exciting handwriting recognition calculators — A series of exciting hands-on talks about calculators, past, present and future. (Cardiff University, Royal Society Summer Science Exhibition, Swansea University, National Waterfront Museum, Glasgow University, many schools, etc)

Revolting Calculators — Calculators have been around for centuries, and they were one of the first handheld computerised gadgets. They are now to be found inside mobile phones, on desktop computers, even in wristwatches. This Lunch Hour Lecture will demonstrate, with participation, that current everyday calculators can easily give wrong and misleading answers. They also have surprising and severe mathematical problems, which can catch people out. They are much harder to use than they need be. The lecture reviews the straight-forward maths behind calculation and calculators, and thence provides a solution to the surprising range of problems identified. A calculator will be demonstrated and compared with commercial systems (which are all worse). The talk will be of interest to anyone who thought they had problems with calculators: they’ll be pleased to learn that it’s the calculators that have the problems! Please come with your own calculator. (UCL Lunch time lecture, January 2003; Oxford University Invariant Society, December 2002; Royal Institution, March 2002.)

From Henry Briggs to Modern Calculators — Henry Briggs, the first Gresham Professor of Geometry, developed what we now call common logarithms to make multiplication easier. Nowadays few of us use logarithms as hand-held calculators make everything much easier. But do they? This lecture will show how bad many current calculators are, and it will show how ideas in computing science can circumvent many of their problems. (Gresham College, November 2001.)

See also my earlier Gresham Lectures.


H. Thimbleby, "From Henry Briggs to Modern Calculators," Gresham College, November 29, 2001.
Transcript of lecture.

Available as: Adobe PDF PostScript
See also the Gresham web site.

H. Thimbleby, "Calculators are Needlessly Bad," International Journal of Human-Computer Studies, 52(6), pp1031-1069, 2000.

In the two decades hand-held calculators have been readily available there has been ample time to develop a usable design and to educate the consumer public into choosing quality devices. This article reviews a representative calculator that is 'state of the art' and shows it has an execrable design. The design is shown to be confusing and essentially non-mathematical. Substantial evidence is presented that illustrates the inadequate documentation, bad implementation, feature interaction, and feature incoherence. These problems are shown to be typical of calculators generally. Despite the domain (arithmetic) being well-defined, the design problems are profound, widespread, confusing — and needless. Worrying questions are begged: about design quality control, about consumer behaviour, and about the role of education — both at school level (training children to acquiesce to bad design) and at university level (training professionals to design unusable products). The article concludes with recommendations.

Available as: Adobe PDF PostScript

H. Thimbleby, "Smart to be Simple," The Times Higher Education, p15, February 12, 1999.

Harold Thimbleby challenges the view that lifelong learning should equip people to cope with an ever more complex world.

Available as: HTML

H. Thimbleby, "Genaille's Rods," Mathematica Journal, 3(2), pp60-62, 1993. Genailles Rods

Henri Genaille's Rods are a nineteenth-century device for doing multiplication, similar to, but easier to use than, the more familiar Napier's Bones. Genaille's Rods are visually attractive and useful in teaching. This article shows how to use Mathematica to draw the required diagrams, which can then be cut out with scissors and passed to wooden rods to make an accurate set of rods.

Available as: Adobe PDF and as a Mathematica notebook (which also works well if you have the new Computational Document Format extension loaded in your browser).

H. Thimbleby, "A True Calculator," Engineering Science and Education Journal, 6(3), pp128-136, 1997.

Existing calculators are unreliable and difficult to use, and they are marketed misleadingly. A new calculator is described that is simple, reliable and very powerful.

Available as: Adobe PDF PostScript

H. Thimbleby, "A New Calculator and Why it is Necessary," Computer Journal, 38(6), pp418-433, 1996.

Conventional calculators are badly designed: they suffer from bad computer science — they are unnecessarily difficult to use and buggy. I describe a solution, avoiding the problems caused by conventional calculators, one that is more powerful and arguably much easier to use. The solution has been implemented, and design issues are discussed.

This paper shows an interactive system that is declarative, with the advantages of clarity and power that entails. It frees people from working out how a calculation should be expressed to concentrating on what they want solved. An important contribution is to demonstrate the very serious problems users face when using conventional calculators, and hence what a freedom a declarative design brings.

See also original in the Computer Journal.

Available as: Adobe PDF

Source code (Mac OS) and applications

Royal Society Summer Science Exhibition has papers and downloads that work on PCs and Macs.


And a roman numeral calculator at www.math.com.