Girded in Duck Tales pajamas at midday, I danced a little jig as the VCR received the VHS. After a not-so-quick rewind, a peppy melody of trombones, bassoons, and clarinets announced the triumphant entry of a man of odd proportions proudly strutting in front of a stick of a girlfriend. It did not take long before a man the size of a buffalo swooned away the odd man’s girl through acts of physical greatness, usually pushing around our hero.
There was but one course of action for Popeye. He must find his source of strength, not by the sun as does Superman or by… gamma radiation as does the Hulk (bad example). Popeye turned to a can of spinach. After consuming the green mush, he flexed his biceps to reveal the power of steam engines and won back his true love, Olive Oil. But why spinach? That’s so peculiar.
Well, in 1870, Erich von Wolfe, a German chemist, while characterizing the nutritional information of different vegetables, made a typo. He accidentally stated that spinach contains 35 milligrams of iron in a 100-gram serving instead of 3.5 milligrams, the actual amount. This misinformation was corrected in 1937, but the truth did little to correct the popular notion that spinach was a super food. Afterall, Popeye had to have something to fight off Bluto.
Sometimes untruthful statements get publicly accepted as fact, and this problem, along with others, has made scientists interested in learning how knowledge, facts, and errors operate. How do they travel among a population? Can we predict how quickly knowledge of a topic grows? Can we understand the link between scientific development and technology? According to Samual Arbesman’s the Half-Life of Facts, we just might.
The Half-Life of Facts introduced to me the fascinating field of scientometrics, the study of scientific study. Throughout ten chapters, Arbesman gives a survey of different concentrations of scientometrics with about thirty to forty interesting applications. Each chapter is supported by strong, mathematical principles which Arbesman successfully dances around to keep the feel of the book light.
To my astonishment, the spread of knowledge operates very much like the spread of a disease. That is, the spread of knowledge can be mathematically modeled with a logistic curve which is commonly used in branches such as economics, physics, medicine, and linguistics. What is even more amazing is that the mathematics is not terribly difficult. Any undergraduate student who has successfully passed differential equations should be able to follow how this works.
As a mathematics professor, I am constantly having to battle students’ notions that mathematics has little effect on their life. The Half-Life of Facts has given me a little more ammunition, and further demonstrates how no way of life is safe from the framework of mathematics. As Arbesman points out, even the way we learn as a population can be studied from a mathematical framework.
I wish I could share all the interesting anecdotes Arbesman shares in the Half-Life of Facts, but you need to read it for yourself. I could mention how scientometrics has determined that humanity’s cumulative knowledge of Genetics doubles every 32 years (Medicine and Hygiene every 87 years, Mathematics every 63 years). I could mention that it is fairly common for a scientific discovery to be rediscovered and republished. I could mention that some of my childhood friends now hate me for telling them that “brontosaurus” is actually an incorrect name. I will not mention those things. However, I will end this review with one more example of how scientometrics may be a worthwhile thing to study.
In 1953, Air Force scientists began charting the speeds of fastest man-made vehicles starting in the mid-1700’s. Interestingly, and somewhat surprisingly, this velocity chart followed a very simple and well-known mathematical curve, and by continuing this curve the scientists determined that it should take four years before humanity could reach the speed necessary to leave the Earth’s atmosphere. Four years later, in 1957, Sputnik launched. Even more amazingly, this curve also predicted that a few years after 1957, we would be able to reach speeds required to land on the moon, which we did in 1959. EVEN MORE amazingly, this curve now predicts that within our lifetime, we should be able to reach the speed required for interstellar travel. That’s like a real-life Star Trek. (Though this exercise is not, on the surface, an example of scientometrics, it shows that if scientists and mathematicians understand what sort of measurements are relevant, important changes in our everyday way of living may become predictable. Scientometrics may help is determine what metrics may prove useful.)
Pages: 242, FoA Pages: 21,206 (The total number of pages reported upon by the Friends of Atticus)
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