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History and Evolution:
By William E. Steinman:
Part 74, Althaus and Briggs:
August 223, 2004:
We can return to Europe now for a look at the German political theoretician Johannes Althaus (1557-1638). Althaus' most important work was Politica methodice digesta atque exemplis sacris et profanis illustrata. In this he developed a comprehensive theory of federalism. Although his work was generally ignored until the 20th century, he is considered to be the father of modern federalism. Some people will notice that federalism is the basis for our own government in America. In fact, at one time, America actually had a federalist party for a short time under Alexander Hamilton. It petered out early in the 19th century.
So, what the heck is federalism anyway? It is really nothing more than a system of government which binds a number of political entities together under a larger central authority. The key to federalism is that power is, in theory, divided between the central authority and the smaller political entities. In America, those smaller entities are, of course, the various states and the big hoo-hah issue is states right versus federal authority. Another element of a federalist system will be some kind of a constitution which establishes the federal authority and the relationships within the union. This should be, and sometimes is, the basis for law and the resolution of issues over authority. One thing to notice is federalism by itself does not imply democracy. It is simply a way of organizing political entities whatever their philosophy of government.
This is just a short look at federalism and its theoretical basis. Don't let it go at that. If you wished, a study of federalism could become a very worthwhile life work. It is really up to you. A good place to begin that study would be the Encyclopedia Britannica. You can get it on CD-rom for your computer and it's remarkably inexpensive. Check it out. I will get a bit more into federalism near the end of this series when we look at the American democracy.
In England the ongoing development of mathematics continued with the mathematician Henry Briggs (1561-1630). Briggs was another pioneer who invented what are called common logarithms. We don't have to know much about science to understand what a boon this development was to scientists in Europe. Almost any college science major will testify to the power of these tools in reducing the labor of tedious calculations. In essence, the logarithm reduces the effort by one order of magnitude. For example, using logarithms multiplication reduces to addition and division reduces to subtraction.
Recall that Napier had earlier developed his logarithms using the base of "e" where "e" is an irrational number equal to approximately 2.71828. These are called natural logarithms. When Napier published his Marvelous Canon of Logarithms Briggs was inspired. He immediately grasped their potential for reducing the tedium of scientific calculations. Consequently he spent much time in Scotland conferring with Napier. The outcome was that he convinced Napier of the advantage of using ten as a base for his logarithms rather than "e". This produced what we now call common logarithm.
When Napier died Briggs took up the mantel and published his Introduction to Logarithms. In this he explained the concepts involved and created a table of logarithms of the numbers from 1 to 1,000. This guy was not lazy. He calculated these logarithms out to 14 decimal places. Not yet satisfied, he published another book called Common Logarithms. This one contained, in addition to his explanations of the value of logarithms, tables of logarithms from 1 to 20,000 and 90,000 to 100,000. These too were carried out to 14 decimal places. Was this guy rigorous or what?
We can be sure his work influenced the thinking of later scientists such as Newton and Gregory. Along the way, Briggs had time to invent our modern method of long division. In defense of Briggs on this point, long division is not as awful as most kids find it to be. It is simply that their teaches do not bother to explain the actual process. They simply teach it by rote and beat the kids over the head with it.
Briggs did many other things in his life. He taught mathematics
and medicine at St John's in Cambridge. He also held professorships
at Gresham and at Oxford where he was professor of astronomy.
He was involved in the study of navigation and in the founding
of Jamestown, Virginia. His final book was called Trigonometry
in Britain was on the application of logarithms to trigonometric
functions.
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