With the application of the newly discovered 16th century scientific experimental methods, medical doctors were discovering how human biology functions, the various mechanisms involved in the pathology of diseases at a lightning speed. But very soon they realized the limitations of this vigorous exercise. As more and more were discovered about human operating system, it became a formidable challenge for the scientist to study relationships between the various biochemical processes going on under our skin.
The average mind can process one complex action at a time – with practice, sometimes we can juggle between two or three. A drummer, for instance, can play three drums at a time – one with each hand and another using a foot pedal. No matter how many drums are in the set, at any given time, the drummer can only play three percussion instruments. Adding a fourth drum will result in utter conclusion. Our mind is limited in the number of functions it can process at a time.
Our ordinary mind can’t fathom the human body’s innumerable entities acting simultaneously much less calculate the minute changes of a substance in our body over time. One such struggle surrounds the determination of the appropriate dosage for a drug – how fast will it metabolize, how frequently should it be taken? Dosage must be tightly regulated and controlled as the rate of dissolution for each drug is different. If a drug is supplied in a form that dissolves too quickly or dissolves too slowly, it may yield a toxic or ineffective effect on a patient. This is a complex and staggering undertaking.
Fortunately, mathematicians came to the physician’s rescue. The man who would change the fate of experimental computations was the very same man who discovered the laws of gravity. Working as a professor at Trinity College, the seventeenth century celebrated mathematician, Isaac Newton was required to be a minister at the university’s church. But he was totally opposed to the rule. Like the 16th century physician, Michael Servetus (who was burnt on a pile of his own books for going against the idea of the Holy Trinity), Newton also did not believe in the doctrine of the Trinity, the triad of God, Son and the Holy Spirit. Despite his dedication to science, Newton wrote more on theology than on physics, astronomy and mathematics put together. He owned 30 copies of Bibles. But, unlike his church, he believed in one, powerful god who orchestrated the universe. Newton strongly believed, through rigorous research, that it was the third and fourth century Greek philosophers who incorporated the concept of Trinity into theology and it has nothing to do with the all-powerful god. Unlike his predecessors who were persecuted for their free-thinking, Newton was not neither subdued nor ostracized by the orthodox. His life was spared not because of his popularity or the importance of his studies, but because religion was slowly beginning to loosen its tight grip on many areas of scientific exploration.
During his studies, Newton developed extensive methods to calculate the properties of a matter that are in flux, and named his paper, “Fluxion,” which would later come to be known as calculus.
If we want to study how two variables influence each other, there is no quick way to intuitively develop a standard conclusion. Calculus comes to our aid. Calculus studies rate of change of quantities and functions such as time, force, mass, length and temperature. The relationships between many quantifiable entities in nature can be understood at any given moment using such complex mathematical computations.
That branch of calculus that deals with the rate of change of infinitely small entities is called differential calculus, represented by prefix d; dx simply means a little bit of x or differential of x. Mathematicians think it more polite to say “differential of,” instead of “a little bit of.” This study was termed differential calculus.
And the second branch dealing with aggregates, represented by the prefix ∫, which is merely a long S, which means “the sum of” or mathematicians like to call it “the integral of” which simply means, of the whole. This, they called the Integral Calculus. ∫x simply means, the sum of all the little bits of x.
Together, these two branches deals with rate of change of the quantities of various degrees of smallness.
By developing these concepts further, successive mathematicians were able to determine what the mind can’t intuit on its own – how one variable is impacting another. It eventually became the language of experimentation – by quantification of nature. What our mind could not immediately grasp is now understood through formulas.
Biologists, for instance, use calculus to determine the exact rate of growth in a bacterial culture when different variables such as temperature and food source are changed. This research can help increase the rate of growth of necessary bacteria, or decrease the rate of growth for harmful and potentially threatening bacteria.
Another field that relies on calculus is epidemiology — the study of the spread of infectious disease. These measurements take three main factors into consideration: those susceptible to a disease, those who are afflicted with the disease and those who have recovered from it. With these three variables, calculus is able to determine the rate of spread of disease and the extent of spread in populations. For a physician or an epidemiologist, this is especially important because rates of infection and recovery change over time, so the measures must be dynamically changing to respond to the new disease patterns evolving from time to time.
Calculus is used to help formulate such concepts as motion, heat, electricity, light, and astronomy. Albert Einstein even used calculus to develop his theory of relativity. In sciences such as chemistry and biology, calculus is used to determine biochemical reactions and radioactive decay rates, as well as birth and death rates. Professionals in economics use calculus to predict profits by calculating such things as costs and revenues.
Essentially calculus is applied in every human endeavor. The laws of nature are written in the language of calculus. The medical doctor, though, remains blissfully ignorant about its ubiquity.