For those of you who like mathematics, consider how calculus could benefit any small farm or business. It would improve the quality and profitability of the operations. On our farm, we could watch more details, collect more data, understand the data more thoroughly with algebraic equations, and then optimize the variables for cost and quality with simple calculus. A slow implementation of these ideas is reasonable and also a beautiful implementation of the Biblical view of mathematics, diligence, and excellence.
The inventor of Calculus, Gottfried Wilhelm Leibniz (1646-1716) home schooled himself in math under a mentor after becoming a lawyer. The driving force behind his work was his view that God made the world in the best way it could have been made. Voltaire wrote a popular cartoon which criticized Leibniz on this optimism, focusing on the pain and suffering in the world. In his book titled, Theodicy, Leibniz wrote on the goodness of God, the freedom of man and the origin of evil, and the conformity of faith with reason. He was “incapable of looking at the objects of any special enquiry without seeing them as aspects or parts of one intelligible universe.” Leibniz thought of God as a mathematician. “He conceives God in the creation of the world like a mathematician who is solving a minimum problem – the question being to determine among an infinite number of possible worlds, that for which the sum of necessary evil is a minimum.”
Leibniz never married and was busy making major contributions to the world of mathematics, physics, social science and theology, but he wasn’t perfect. He wrote, “I cannot tell you how extraordinarily distracted and spread out I am. I am trying to find various things in the archives; I look at old papers and hunt up unpublished documents. From these I hope to shed some light on the history of the [House of] Brunswick. I receive and answer a huge number of letters. At the same time, I have so many mathematical results, philosophical thoughts, and other literary innovations that should not be allowed to vanish that I often do not know where to begin.” Sounds like a home school and perhaps a sign of greatness!
So just how could calculus be helpful on a small farm or any business, and worth studying? Here is a simple example. Based on our farm data, for us to grow x broiler chickens, it costs C = $862 + $6.67x. The derivative of this equation (the slope of the line) shows that the feed and labor cost for each additional boiler chicken is $6.67. That was calculus.
Business profit equals the income minus the costs or P(x) = I(x) – C(x) = $10x – ($862 +$6.67x). Since this is a linear equation, increasing sales and lowering costs are the ways to maximize profits. Looking at the slope of this line, dP(x)/dx = $10-$6.67 = $3.33. This is the business income per chicken after all expenses including labor are paid. That was calculus again. Collecting more precise data would require non-linear equations, which then could be optimized using simple calculus techniques. Unknowns (U) and acts of God (A) can be factored into the equations using Proverbs 16:9 “A man’s heart deviseth his way; but the Lord directeth his steps” (U+A).
How much more money might be earned or saved if we did use calculus on the farm? I estimate the increase in earnings is the difference between the linear equation and non-linear equation of y = x and y = x1.05 In practical terms, that would lead us to sell 800 chickens where we would have sold 600 or 1400 chickens where we would have sold 1000 chickens, with the corresponding increased profit. In other terms, the breakeven point for a course in calculus would be equal to the business profit from 129 chickens, which would take two months to raise by a hired hand, with a return on investment over 5 years of $6000, at 1400 broilers per year, as compared to the profit earned without applying calculus. Therefore, it is a financial advantage to learn and apply calculus to every day business, just as we would expect, since God created the universe with mathematical order and it is our honour to search that out and put that knowledge to work.
It is the glory of God to conceal a thing: but the honour of kings to search out a matter. Proverbs 25:2
“Mathematics is the alphabet with which God has written the universe.” Galileo Galilei
For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether they be thrones, or dominions, or principalities, or powers: all things were created by him, and for him: And he is before all things, and by him all things consist. Col 1:15-17
I mentioned the profitability of calculus to my chicken farming 18 year old son and he thought that it would be worth hiring an industrial engineer to do the calculus for him! A good idea, but not as satisfying as thinking some of God’s mathematical thoughts after him, experiencing a touch of His excellence, and seeing the increase result from His hand. Perhaps this deeper appreciation is like the difference between buying eggs and producing your own eggs. The gain is also in knowledge, wisdom, and understanding of how to acknowledge God in more of the details.
Dr. James Bartlett
James Bartlett is the Executive Director of the North Dakota Home School Association and the Biblical Concourse of Home Universities. He teaches “Calculus That Only Christians Can Do” for the Concourse, The New Geneva Christian Leadership Academy, and the Newton Institute for the Reformation of Science and Engineering. Dr. Bartlett is on the Board of Directors at New Geneva. He and his wife Lynn home school three boys and home college one son on a small farm in the Turtle Mountains. They can be reached at 701-263-4574. Lynn blogs about their family activities at NDHomekeeper.blogspot.com
If you would like to sign up for any of Dr. Bartlett’s courses, or any other studies at the New Geneva Christian Leadership Academy, please contact: firstname.lastname@example.org or call: 434.352.2667.