### USING THE RIGHT TOOLS

##### Pertinent Information - Main Menu

The language of truth is unadorned and always simple.
Marcellinus Ammianus (Roman Historian)

This website was created for the educated lay person. Some people are educated in areas other than math and may be fooled by some of the false standards generated by a small minority of pseudo-intellectuals. The internet is a great thing, but does allow people to misrepresent themselves so that they can delude others. This part of the site has been added to correct the idea that using calculus is a measure of validity for ideas presented on a website.

Anyone who has worked with math should be able to tell when it is necessary to use calculus and when it is not. Nevertheless, one of the buzz words words used by people who wish to appear learned and intelligent is "calculus". For those who would like some even better words, try "differential calculus" or, even better, "integral calculus".

Calculus is very useful in some ways. Differential calculus (the easy one) was found by Sir Isaac Newton is 1665 and developed during 1666. The discovery of integral calculus probably should be given to Newton also, in the sense that it is merely the reverse of differential calculus. But Newton did not publish his findings and apparently was too busy with other things to begin to develop integral calculus.

Gottfried Wilhelm von Leibniz independently discovered both types of calculus and published his work in 1675. Since that time, Augustin-Louis Cauchy, Richard Delekind, and Karl Weierstrass became the mathematicians most involved in developing modern calculus.

Calculus uses derivatives and integrals. Derivatives are fairly easy to find. Integrals are not so easy to find. The derivative is defined as the limit of a ratio. It is most often used in finding the slope of a curve plotted by using a predetermined equation. However, its symbol, "d", is often used where algebra could be used to show an infinitesimally small quantity. Granted, there are times when this shorthand is handy, but for people who have not taken calculus it is confusing. Today, as I recall, there are courses given in high school that show how to use "d" without really getting into calculus.

Differential calculus can be used to develop formulae and should be so used when it is appropriate to do so. There are many cases in which it cannot be used. It is a tool like any other tool. One should not use a hammer to turn a screw, or a screwdriver to hammer a nail. So I did not use calculus to discover the concept behind gravity. At one point, I thought of using differential calculus to explain distance, velocity, acceleration, and jerk (accelerating acceleration), but it was ostentatious and counterproductive. So I deleted what I had and used more common words instead. If anyone finds it any my writings, then I might be accused of not remembering what I did.

Integral calculus is the reverse of differential calculus and is more difficult, by far, to do from scratch, so tables of various equations are used. It is also an improper tool for use with my work. Generally speaking, fundamental principles are best expressed in fundamental ways. They would not be fundamentals otherwise.

Most engineers use calculus indirectly to understand tables that are already placed in books. Therefore, I did not use calculus very often as an engineer, and never to derive what could be found in a table that was developed by the use of calculus.

Both major types of calculus are most used to show quantitative values using equations which have been derived by other means. Even though it is possible to use calculus without predetermined equations, graphs, and diagrams, such use is usually by means of inferred equations, graphs, etc. and, if not, is seldom any better (and perhaps worse) than using another type of math. There are shades of gray between algebra and calculus when infinity and limits are involved.

There are many books on calculus that are not very difficult to comprehend for those who understand algebra. If the reader would like to verify what I have said, it is easy to do so by reading one of these books - or even reading what is said in a good encyclopedia.

The part of this website called Black Holes shows the derivation of the Schwartzschild radius. This is an excellent example of the wrong initial concept creating a lot of difficulty and the use of calculus - as opposed the correct initial concept allowing the use of a few very easy steps using algebra.