How Logarithm Changed Science And Engineering for Good

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Calculus (infinitesimal) is arguably one of the best and most popular discoveries of applied mathematics, especially because an extension of it (differential equations) seems to be strongly connected with our physical reality - dynamic systems. As far as change is concerned, calculus is also concerned and we know changes happen constantly in our universe but this not to say calculus is only about change. Calculus came at a time when science just began to take form, certain aspects of science and possibly technology/engineering may not have gone this far if it hadn't been for calculus.

However, this article isn't about calculus and there are other important and popular mathematical discoveries that helped shape the science of today. The essence of this article is to enlighten us on how another but older mathematical discovery also helped in our science and technological journey, it appears a lot of us overlook it's historical importance.
This mathematical discovery is none other than the “Logarithmic function". Before we delve further, let's first give a very brief important remarks about it's historical discovery. Most of us are familiar with the “common logarithm", it's the kind of logarithm normally being taught at elementary level (neglecting the rules of logarithm of which the base is arbitrary) due to it's relative ease of use. It's commonly written in the form "Log()" and it's base is 10, the 10 is in most cases omitted - it's supposed to be a subscript in between “g” and the first bracket.
So what am I trying to get at here ?

When John Napier first discovered and introduced logarithm it wasn't the common logarithm, some of us, if not most make the mistake of thinking he discovered common logarithm, even I myself once thought so.
What Napier actually discovered was “natural logarithm", the more advanced kind. In advanced calculators it has the symbol “In()” , this is also "Log()" but in base “e” - the subscript 10 is replaced with “e", that's why it has a different symbol from the common logarithm.

"e" is actually a number but as at the time of Napier's existence and slightly later, nobody knew what e actually was, which means the natural logarithm function wasn't well defined. This eventually led to the introduction of common logarithm (since the base was already known) by Henry Briggs.

So now, we would proceed to how the discovery of logarithm changed science and engineering for good.

Mathematical science

Well, in this part, our historical story still continues, did you think we were done ?
What is this “e” ? and was it very important ?

Today, we can find mathematics in almost every profession, this kind of mathematics is specifically called applied mathematics but if it's with regards to scientific disciplines, it's called mathematical science.

About 69 years after the discovery of natural logarithm, the value for the symbol “e" (that we discussed earlier) was found, thanks to Jacob Bernoulli and his work on compound interest (found in finance and economics). It happens that e is also a constant just like π but with the value given as 2.71828 (in 5 decimal place). Leonhard Euler, who's sometimes referred to as the king of mathematics took things even further. He (Euler) discovered what is today known as the exponential function - e(x), which happens to be the inverse function for the natural logarithm. With this discovery he made many other substantial mathematical discoveries that would lay grounds for most of today's theoretical discoveries involving mathematics. Note that it was Euler who gave the natural logarithm base the letter “e”, it used to be represented with different other letters before Euler's existence and that's why today e is referred to as the Euler number.

Today, the exponential function is a very important function, it appears to be everywhere, where mathematics is applied. Calculus may not have needed logarithm to be discovered but the exponential function which was as a result of the discovery of logarithm is very valuable in studying and seeking solutions (exact) to differential equations (equations used to model physical and dynamic systems). The exponential function is at the heart of the functions used in the pillars of modern physics, I mean both general relativity and quantum mechanics. In economics you can find the exponential function (population growth and compound interest). In statistics (probability) too you can find the exponential function. The exponential function is also useful in pure mathematics too, you just name it.

Engineering

Are you guys familiar with the name William Oughtred ?

He's popularly known for his invention of the “slide rule".

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That image you just saw or probably still looking at is the slide rule. It looks like one of those devices used for measuring distance but that's not what it does. What you are looking at is a calculator, one of the precursors to modern handheld/pocket calculators like the scientific kind we use today. By simply placing the slide (the moveable glass-like part) at the correct position you could compute certain arithmetic operations like 3 × 2, it could even help you with trigonometry. 😳
I wasn't born when such device was being used but when I got a glimpse of how such simple device was able to do it, I was marvelled, Mr. Oughtred was a hell of a genius. He invented it shortly after Napier introduced logarithm, the calculator uses the logarithmic function to operate.
The slide rule is popularly known for it's historical importance in the development of what we today call “computers" but it actually did more than that. The slide rule was invented around the early 17th century and it reigned for more than 300 years despite other kinds of calculators/computers being invented. In the 1950's and 60's when precursors to modern electronic computers were being invented, the slide rule was still popular even though those computers were much faster. The reason the slide rule was still popular was because it was cheap and easier to move about while still able to simplify complex computations, and this was a time when engineering officially became a discipline, the slide rule became a defining tool for engineers just like the stethoscope is for doctors today. In essence, it also helped to establish engineering as a discipline. This however wouldn't have been possible if logarithm hadn't been discovered, at least in our timeline.

Whenever you see logarithm do not underestimate it, chances are that if we didn't discover it, especially natural logarithm, we may still be stuck in the 16th century or rather living today like we are still in the 16th century. 😂

For Further Reading

Logarithm

History of logarithms

History of calculus

Differential equation

e (mathematical constant)

Exponential function

Slide rule

Thank you all once again for stopping by to read my jargons and also thank you @stemng, @lemouth and the @Steemstem team for your valuable supports.

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