Logarithm History and Modern Applications

Logarithm

History and Modern Applications of Logarithms

The first time a publication contained a mention of logarithms, their method of derivation, and a table of logarithms was in 1614 with the publication of Mirifici Logarithmorum Canonis Descriptio by the Scottish nobleman John Napier (ST 2005). Napeir's book did not describe or list logarithms as they are known today, but rather the logarithms contained in this work were meant to replace the trigonometric multiplication functions needed in astronomy and other branches of science with a simplified addition from other established figures (Capmbell-Kelly 2003). Henry Briggs, a professor of geometry at Oxford, was very inspired by Napier's work, developing his own ideas based on those in the Descriptio and meeting with Napier to discuss developments and recalibrations of the logarithms contained in Napier's original and pioneering work on the subject (Campbell-Kelly 2003).

Briggs would go on to publish his own table of logarithms for common numbers (as opposed to the logarithms for sines contained in Napier's column); Briggs' tables showed the logarithms for every whole number below 1000 carried out to eight decimal places, providing a very useful tool to the navigators, astronomers, and mathematicians working in this day centuries before the advent of computer and calculators (ST 2005). This was published in 1617, the year of Napier's death, and by 1624 Briggs had expanded his tables to include all integers from 1 to 20,000 and from 90,000 to 100,000, carried out to fourteen decimal points (ST 2005). These tables led to a massive increase in use of logarithms in certain fields where their usefulness was already established, and this subsequently led to expansions in the applications for logarithms generally (Campbell-Kelly 2003).

There are many different modern applications for logarithms that have nothing to do with the distances of navigation and astronomy -- or any physical measurements at all -- proving that logarithms are indeed an incredibly useful mathematic tool on a scale that Napier himself did not really envision. Anything that involves exponential growth can most easily and accurately be calculated using logarithms; studies of population growth, nuclear reactions, and any other scientific inquiries depend on the use of logarithms to develop real and usable data and projections (Tom 2002). Logarithmic scales also exist in electrical engineering, as a means for testing for signal decay, and there are many bodily functions and reactions that are logarithmic in nature, leading to many other biological and medical uses and needs for an understanding and utilization of logarithms (Tom 2002).

Another common use for logarithms is in the world of banking, specifically in the calculation of interest and periods of repayment on loans with continuing compound interest -- i.e. all loans. The same basic formulas using logarithms can be used to calculate the needed number of investments and/or the time period of investments at a given growth rate that will be needed in order to reach a target level of investments savings (Brown 2010). Both of these applications have very real implications for many individuals, whether they are trying to buy a home or planning for their retirement, as well as a n abundance of other issues related to personal banking. Logarithms are not only useful in highly technical scientific pursuits and investigations, then, but are directly applicable and necessary to situations that directly relate to and have an effect on people's daily lives.

What I found most interesting and surprising about the development of logarithms is that they are something that needed development in the first place. I suppose it is similar to having taken any invention that pre-existed myself a little for granted, but with something intangible like a mathematical concept, it seems even more strange that there was a time before logarithms were used -- the numbers and operations necessary for their development existed for millennia, so it seems odd that it took so long for this development to occur. Of course, given that the many applications for logarithms still greatly confuse me (just when I thought I was beginning to understand the mathematics behind them, the practicalities of their use confound me!), I suppose it's understandable that it took an exceptional mind to develop the sudden insight and years of labor that it took to develop the idea of logarithms and generate the tables that led to their widespread usefulness.