Category Archives: Math and Statistics

On the ancient origin of the word “algorithm”

Fascinating quote from page XXXIII of Peter Bernstein’s 1996 book “Against the Gods: The Remarkable Story of Risk” (cf. https://www.amazon.com/Against-Gods-Remarkable-Story-Risk/dp/0471295639/):

“The earliest known work in Arabic arithmetic was written by al­Khowarizmi, a mathematician who lived around 825, some four hun­dred years before Fibonacci. Although few beneficiaries of his work are likely to have heard of him, most of us know of him indirectly. Try saying “al­Khowarizmi” fast. That’s where we get the word “algo­rithm,” which means rules for computing.”

Note: The book cover shown above is a copy of a 1633 oil-on-canvas painting by the Dutch Golden Age painter Rembrandt van Rijn.
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Financial versus Mathematical literacy

It is rare when I actually take the time to read Baylor’s student newspaper, the Baylor Lariat, and even rarer when I post a critical response to a Lariat article. However, I couldn’t resist commenting on an editorial from earlier this month entitled, “Baylor should implement class to ready students for real world”. In this editorial, the members of the Lariat editorial board opine that Baylor should require a one-hour credit “Life Skills” course in lieu of a basic math course such as “Ideas in Mathematics”. Basically, such a course would be designed to cover very basic personal finance principles, such as budgeting, paying off student loans, buying insurance, saving for retirement, etc. I think this is a manifestly bad idea; let me explain why.

While I am not aware of an empirical literature concerning mandated personal finance courses at colleges and universities, many states have experimented with personal finance and minimum math requirements at the high school level. A recent (2014) Harvard Business School working paper entitled “High School Curriculum and Financial Outcomes: The Impact of Mandated Personal Finance and Mathematics Courses” provides a thorough empirical analysis of personal finance and minimum math requirements and finds that mandated personal finance courses at the high school level do little to improve outcomes that are generally associated with financial literacy (e.g., such as building wealth through asset accumulation, prudent credit management, etc.), whereas “… individuals who were exposed to greater math requirements in high school are more likely to accumulate assets, have more real estate equity, are less likely to be delinquent on their loans, and are less likely to undergo foreclosure.”

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Art meets chemistry meets physics meets finance

This Wired Magazine article provides a layman’s explanation of reaction-diffusion processes, which are characterized by reactive molecules that can diffuse between cells. A special case of a reaction-diffusion process is a “pure” diffusion process, where substances aren’t transformed into each other but nevertheless randomly spread out over a surface. While the reaction-diffusion process makes for much more aesthetically pleasing art, other so-called diffusion processes (e.g., diffusion of thermal energy as characterized by heat equations or movements of speculative asset prices as characterized by Itō diffusions) similarly generate (what appear to the naked eye to be) “patterns” from randomness…

Hypnotic Art

Hypnotic Art Shows How Patterns Emerge From Randomness in Nature

www.wired.com

These digital canvases represent British mathematician Alan Turing’s theory of morphogenesis.

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Fibonacci numbers in nature and in finance

My favorite econ blogger, George Mason University’s Russ Roberts, posted the following (short, less than 4 minutes) video called “nature by numbers” yesterday on Cafe Hayek.  This video provides a remarkable and beautiful presentation concerning how Fibonacci numbers appear in nature. 

For more information concerning the math used in this video, go here.  Peter Bernstein (author of the worldwide best seller “Against the Gods: The Remarkable Story of Risk”) traces the origins of risk theory and finance back to a 13th century Italian mathematician by the name of Leonardo Pisano, who was known for most of his life as Fibonacci (see pages 23–26 from Bernstein’s book for historical context on the Fibonacci number series).  For some examples of applications of Fibonacci numbers in finance, go here.

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200 Countries, 200 Years, 4 Minutes (Hat Tip: Donald Marron)

Donald Marron posted this video from BBC on his blog the other day; apparently it is part of a BBC program offering called “The Joy of Stats”.  Hans Rosling, who is Professor of International Health at Karolinska Institute and Director of the Gapminder Foundation, provides a very remarkable presentation, showing in less than 5 minutes how wealth and life expectancy have changed over the course of the past 200 years for 200 countries!

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