Linear Models

The last chapter conducted a simple analysis of Darwin’s maize data using R as an oversized pocket calculator to work out confidence intervals ‘by hand’. This is a simple way to learn about analysis and good for demystifying the process, but it is inefficient. Instead, we want to take advantage of the more sophisticated functions that R provides that are designed to perform linear-model analysis. This chapter explores those functions by repeating and extending the analysis of Darwin’s maize data.

Probability and Simulations

This chapter is fundamental in educational terms as it deals with a topic that cannot be underestimated: the use of laboratory simulation. As long as we talk about probability in the classic sense, paper, pen, and maybe a pocket calculator are sufficient tools, but when we want to analyze a probabilistic model in depth, the use of a computer tool is essential. This support not only allows us to confirm hypotheses but, in some cases, it is indispensable. In the school it is unthinkable to work on large data sets (often not available) that would require not only appropriate software but also a different approach. The balance should be sufficiently significant but easy to handle dataset.

Misperception of Exponential Growth: Are People Aware of Their Errors?

Previous research shows that individuals make systematic errors when judging exponential growth, which has harmful effects for their financial well-being. This study analyzes how far individuals are aware of their errors and how these errors are shaped by arithmetic and conceptual problems. Whereas arithmetic problems could be overcome using computational assistance like a pocket calculator, this is not the case for conceptual problems, a term we use to subsume other error drivers like a general misunderstanding of exponential growth or overwhelming task complexity. In an incentivized experiment, we find that participants strongly overestimate the accuracy of their intuitive judgment. At the same time, their willingness to pay for arithmetic assistance is too high on average, often much above the actual benefits a calculator provides. Using a multitier system of task complexity we can show that the willingness to pay for arithmetic assistance is hardly related to its benefits, indicating that participants do not really understand how the interplay of arithmetic and conceptual problems shape their errors in exponential growth tasks. Our findings are relevant for policymaking and financial advisory practice and can help to design effective approaches to mitigate the detrimental effects of misperceived exponential growth.

A short remark on the solution of Rachford-Rice equation

A fast flash calculation of the Rachford-Rice equation is very much needed in many engineering applications, especially in multi-component mixtures. This paper suggests a direct and hands-on calculation by a pocket calculator or a Chinese abacus. The calculation is based on an ancient Chinese mathematics called as He Chengtian average. An example is given to show the simplicity and effectiveness of the ancient Chinese algorithm.

Does this treatment work for me? The patient’s role in assessing medical care

Randomised clinical trials are designed to determine whether a particular treatment is appropriate to make a significant difference to the health of a defined population and to aid its approval for use. For an accurate, cheap and simple assessment to see if a treatment benefits an individual person, all that is needed is a pen, paper, simple pocket calculator and daily recording of a few variables. It requires the ability to read and write and to understand addition and division. Factorial design of experiments is used to show the impact of several variables and their interaction on the person’s health status. An example of a 75-year-old man with an enlarged prostate is used here to illustrate this approach. This person was able to understand and reduce side effects, lower the costs of medication by 83% and improve measured health status by 28%. A multivariate model for this person was then created with about 450 person-days of data.

Visionary Entrepreneur

This chapter focuses on C. Francis Jenkins' inventions that he sold through several business startups. Until the late 1920s, Jenkins had no significant outside corporate sponsors. To support himself, he began selling his inventions that reflected his broad interests. This chapter first discusses the incorporation of the Jenkins Automobile Company under the laws of Delaware in 1900 and its production of several steam-propelled vehicles, including automobiles and trucks. It then considers Jenkins' patents in the field of aeronautics, such as those for an “aeroplane or flying machine,” camera adaptations that resulted in improved motion pictures, airplane catapult, and altimeter; patents for milk bottles and home improvement accessories; and novelty inventions ranging froma mathematical pocket calculator to a Christmas-tree holder and talking signs. It also recounts Jenkins' “Ocean to Ocean” automobile tour in 1911.