Monthly Archives: February 2010

A Case for Calculus on the Farm

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 I am trying to find various things in the archives; I look at old papers and hunt up unpublished documents.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

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: or call: 434.352.2667.


A New Justice System:Biblical Restitution


In 1985, the total population of prisoners in America was 744,000. In June 2003, the prison population reached nearly 2.1 million. Some prisons during that time had reached over 33 percent of their original holding capacities. In one year, between 2002 and 2003, state and federal prisoners grew as much as 2.9 percent, which was the largest growth of inmates in over four years. The local jail population grew 3.9 percent, state prisons grew 2.6 percent, and federal prisons grew 2.6 percent.[1]

In June 2008, there were a total of 2,310,984 prisoners being held in federal, state, and local jails. This was an increase by .8 percent from the year earlier, although lower than the annual rate of growth from the seven years previously. At average, there were about 509 prisoners per 100,000 residents of the United States, which was more than the average of the previous year as well.[2]

According to CNN, the prison costs of America have reached an average of 37 billion dollars in 2007. 1 million alone goes toward inmate phone calls.[3]  Each taxpayer paid about 23,000 a year for each prisoner[4]. In 2008, the cost for prison and rehab centers reached 47 billion, with taxpayer dollars climbing to 29,000 a year per prisoner. Prison spending has outpaced all but Medicaid.[5] In 2009, local, state, and federal spending on prisons and rehab centers reached nearly $68 billion a year.[6]

The United States has the highest incarceration rate of any country on earth. Americans make up about 5 percent of the world’s population. With the amount of annual prisoners we hold, the United States makes up for about a quarter of all prisoners held around the world.[7]

According to the Disaster Center, the crime rate in 2008 consisted of 89,000 rapes, 16,272 murders, 441,855 robberies, 2,222,196 burglaries, and over 7 million other forms of theft.[8] Altogether, these numbers added together result in almost 10.3 million crimes – a number that far surpasses the number of criminals serving jail time. Even if each imprisoned criminal has committed five major crimes each, there would be criminals escaping punishment. It is very clear that not every criminal is being justly convicted, let alone punished, for their actions, in spite of how high the incarceration rates and costs are in the United States.

People have been trying to come up with ways to reduce the amount of money going into our prison systems, as well as reducing the amount of prisoners going into the systems. Between 200 and now, countless articles and opinion papers have been written concerning this national problem, which is costing the taxpayers more than is really helping the problem in the long run. The state of Alabama, back in 2005, considered releasing inmates earlier – at least, those who didn’t pose a “physical threat” to the society – to conserve money and space; they also considered building more “correction centers,” which might be less expensive than prisons, but it would still be close to $3 million. [9]

An article called “America’s Prison System: a Failed Experiment” from the Associated Content suggests that in order to conserve money, prisons should be rehab centers incorporated into one, in order to save money from going to two separate organizations. This seems like a good start. Yet, the article continues to say that a big component of a successful prison system must be one that is run privately, with guards who treat the inmates top-notch. “…It is more likely [the inmates] will respond to people who treat them well, rather than by what badge they wear…Also, with only one or a few people owning the prisons, inmates are more likely to connect with them on a personal level. It is much harder to think kindly of a faceless government than a single man. If prisoners are able to connect to the people who hold them, it could create…an empathy with one’s captors.”[10]  

Seriously, a murderer or thief or drug addict is going to be able to connect with their guards on a personal level, causing them to reach for higher behavioral ground? The guards should feel sorry for punishing the evildoers in their care and treat them less deservedly of the punishment?

God is a God of justice. Those who commit criminal acts should be punished, according to the Bible. So at least we have that part right. But it’s amazing that so many other punishment forms are used than those of Scripture, which is the handbook God gave us for living orderly and rightly. The Bible doesn’t have many, if any, provisions for prison sentences for crimes. So it is all the more amazing how prisons have become our center form of punishment for almost every crime in the books.

The center for justice was always restitution in the Bible, not confinement. For theft, rape, murder, kidnapping, and any other assault on mankind and the societal order, restitution, not solitary confinement, was required to make right the wrong.
Let’s look at these restitution processes one at a time.


Biblically, the victim of theft would have his goods returned, no longer suffering the economic loss. If it were a car, perhaps the car must be returned, or a car of equal or greater value, plus, perhaps, the amount of money the victim lost through having to stay home from work, or through the gas wasted in the reckless driving. Exact restitution amounts can vary depending on what was stolen, and whether the thief voluntarily turns himself in.[11] So either way, the victim is restored.[12]

The criminal would have learned to work to restore what he had stolen, instead of being forced into a situation where he is served and slothful in prison. The rest of the townsmen – the taxpayers – would not have to suffer for his crimes by paying for his board in a local jail.

Today, the victims of theft are not actually rewarded. They still have to suffer the loss of the item or items stolen, while the criminal is simply “paying his debt to society.” The crime was not committed against society, but only one man, who of all people is not being paid.
What if the thief cannot pay back what he stole? A provision for temporary servitude is provided in the Bible as well.[13] Immediately, people say that having slaves is immoral, infringing upon the rights of the individual. First, whether the criminal is in prison or servant to one man, he is not free to exercise his said “rights,” so it should not really make a difference. Second, people don’t understand anymore what true slavery is anyway. Why is it all right for the government to make slaves out of everyone for half a year, taking taxpayer dollars for the first half of the year without giving anything back, and for no punishable reason other than being citizens in America,[14] but it would not be all right to have a criminal take a few weeks of serving his victim by buying a new window he broke through, installing it, cleaning up the store he vandalized, and sweeping up the wreckage? Why would it be so bad for the criminal to run errands for the store owner, to buy back time that the store owner might have lost having to close his store down for a while? That way the store owner could spend more time at the store making up the money he might have lost by having to be closed, and yet not have to get backed up with personal affairs either. Is that so evil? We consider slavery or servitude to simply take service from something with nothing in return for the person. But the person would be gaining back his reputation, paying off his debt to the victim, not society – he did not wrong society – and the victim is restored. According to Dennis Woods: “[The prison system] reinforces irresponsibility, while [servitude] does the best job possible of restoring the lawbreaker to a responsible position in society.”[15]


Rape of a single woman was actually not punishable by death, for various reasons, but mainly because God viewed it as theft of a girl’s singleness-purity, so to speak. The girl’s father would determine what form of payment he deems sufficient for the situation: either marriage without possibility of divorce, or a sum of money equal to that of a proper dowry. The former way would restore what was stolen literally; the latter would cause the rapist to feel the loss of his money, realize the commitment aspect associated with intimacy, and better contemplate his actions later.[16]

Rapists against married women and women engaged or in a courtship would suffer capital punishment.[17] In addition to stealing the woman’s purity, the rapist is assaulting the head of the family, or to-be head of the family, who stands in place of God. This assault is not of the same intimate intensity when the rapist attacks a single girl. A more thorough exploration of the differences between the punishments of rape against single and married women can be found in The Institutes of Biblical Law.[18]  


Capital punishment also was executed against murderers and kidnappers. Murderers were always put to death.[19] The Bible also warns against releasing a murderer, telling us it is a curse to do so.[20] An accidental murder would be reconciled either by an agreed payment, or life of the individual, depending on what the family of the deceased wished. If an unborn child was killed, life was required as restitution, the same as any other case of murder, because the unborn child was considered a person, especially protected, as a generational necessity.[21]  All kidnappers were also put to death.[22]


In the Bible, there was a provision of up to 40 whiplashes as a form of punishment, but no crime was assigned to this punishment. Today, we might find it hard to find a Biblically-spelled-out punishment for things such as drug dealing, pornography, drunk driving, stalking, prostitution, or other such things that disturb the peace. It might be a wise thing to explore the Biblical principle of an amount of beating. To our modern ears, this punishment seems inhumane. But think about it: which is more cruel: taking away part of someone’s life in a prison, where the person can simply harbor anger and resentment for getting caught, without a method of real correction; or instilling a true fear of ever doing something like that again? I am sure a measure of grace should be ascribed to each of the offenders: perhaps they won’t be beaten the first time. But at any rate, there is still no support for prison punishment for these crimes in the Bible.


In February 2009, the U.S. Bureau of Prisons conducted a survey of about 202,500 of the country’s prisoners, to get a sample of the types of criminals being imprisoned. The survey showed that 54.4 percent of all crimes were drug related, while robbery, burglary, and property-related offenses made up 8.3 percent, and sex crimes made up only 3.5 percent. Homicide, kidnapping, and aggravated assault altogether made up 2.9 percent of prisoners.[23] These statistics show a must stronger enforcement rate on drug-related crimes, while the other crimes are not only more abundant, but more dangerous. Things seem a little backwards.

As far as life-sentences are concerned, many of which are related to murderers and sex-offenders, 40,610 individuals in United States’ prisons are serving life sentences, representing one of every 11 people (9.5%) in prison. Between 2003 and 2008, there was a 22 percent increase in the number of individuals serving life without parole sentences.[24] Over 5 million Americans are on probation instead of in prison, or since having been released from prison.[25] In other words, 5 million Americans who deserved either the Biblical death penalty, or the Biblical restitution process, or even the secular life-sentencing, or the secular prison-restitution, are free. Only about 1,000 prisoners have been given the death penalty for their crimes between 1976-2009.[26] Actually, since the founding of America, only around 13,000 people have been given the death penalty at all.[27]


It is obvious that are prison systems are holding many more prisoners than they should be holding. As we have seen, many of them, of not all of them, could be out of the prisons, either by making restitution for their theft, being lawfully executed for their capital crimes, or paying the proper victims their due rewards, or even possibly being severely “spanked” so to speak. People would actually be afraid of committing a crime. Today, it is a gambling excitement. According to one thief from England – a repeated offender – he was not worried at all about an eight-year possible sentence in prison: “If you’re a criminal, what’s the alternative to the risk of going to prison? Coal-miners don’t spend their time worrying about the risk they might get killed by a fall at the coal-fence either. Prison’s an occupational risk, that’s all – and one I’m quite prepared to take. I’ll willingly gamble away a third of my life in prison, so long as I can live the way I want for the other two-thirds. After all, it’s my life, and that’s the way I feel about it.”[28] There is no fear of the consequences anymore. We must instill that fear once again, and in turn instill that love for an orderly society.

It would be cost-effective to have thieves pay restitution – they would no longer be paid for in prisons. It would be cost-effective to take the drug-dealers out of prison and have them either pay restitution or get their due reward for their actions – again, they would no longer be paid for in the prisons. However, with our current capital punishment procedures, costs would skyrocket beyond the costs of keeping people in prison for life. California pays 63.3 million annually for the death penalty. Maryland pays 37 million per execution. In Tennessee, the cost for the death penalty is 48% more than the cost for life in prison, while Indiana was 38% more. The list goes on.[29] These statistics turn people off to the idea of capital punishment, as well as the idea that it is a cruel form of punishment.
The types of primary executions include the gas chamber, the electric chair, and the lethal injection.[30] Historically, before any of these were invented, the death penalty for murder and rape was carried out through hangings, firing squads, or beheading.[31] A rope for hanging, an axe for chopping, or a bunch of guns and bullets for shooting, doesn’t costs very much at all. Gas chambers cost 300,000 dollars to install.[32] Lethal injections cost about 86.00 per execution, not counting the cost for the actual drugs used in the injections.[33] Electric chairs cost 62,000 just to repair.[34] Now, in Texas, they are setting up solar powered electric chairs for “green America,” because the cost for electricity is so high.[35] Sometimes people remain on death row up to twenty or thirty years. In 2008, there were over 3,000 people on death row, most of them waiting decades already.[36] These long waiting periods account for the millions of dollars in costs for the death penalty mentioned earlier.

The Bible doesn’t support a long waiting period for those sentenced to death. On the contrary, once a person is found guilty of a crime worthy of death, they are to be executed speedily, in order to quickly remove that evil from the nation.[37] People usually get nervous thinking about a quick sentence, because of the many innocent people who have mistakenly been put to death. But we don’t live in a perfect world. On the contrary, we live in a far from perfect world, a world far from God’s standards. Does it not make sense that if we return to a closer way of executing God’s principles to our lives – such as his rules for capital punishment – that, being closer to a perfect world, we would make fewer mistakes? Or don’t we have any trust that God knows what He is doing?


The principles of a Biblical restitution society seem strange only if we view civil punishments as helping the criminal. The justice system is not supposed to be helping the criminal, at least not first and foremost. The goal of the justice system is to restore the societal order. Order in the society includes being free from attackers, murderers, and thieves, or anyone else out to harm the innocent. By requiring restitution from a thief, the thief is restored to a state of honor, true, but the first goal is to replace what was disturbed: the victim’s wealth, freedom, and life. By requiring death from a murderer, the murderer, otherwise known as a disturber of the peace, is removed from the society, thereby restoring the society to a fearless enterprise. The same is true for requiring death from a rapist, or a kidnapper. The societal order is being maintained so that it can function properly. If we view criminals as a diseased organ in a body of citizens, there can only be two options: either curing the organ, or getting rid of it. We cannot simply take out the organ and look at it for a while in a “petri dish”, as with our prison systems.
We would save a lot of money if we obeyed God’s laws of justice. We would not have to worry about “humane” ways of killing people through cost-ineffective means; we would only be worried about restoring Godly order. We also wouldn’t worry about paying for a prison system either, which doesn’t get to the root of the problem anyway. Only in the methods explained above can we begin to obtain a functional justice system which would Glorify the God of Justice and Law Order. Logically speaking, if you are still a skeptic…everything else has failed so far, so what do we have to lose?

This position paper, by a 2nd year New Geneva college student, is part of the final examination grade. The paper is for the course study on The Institutes of Biblical Law Volume I, at the New Geneva Christian Leadership Academy, Fall Semester 2009. Students are required to submit at least one work of publishable quality as part of their grade for each course. If you would like more information on Biblical Leadership Training at the New Geneva please email us at Registrar Contact  or call us at 434.352.2667

End Notes

[11] Lev. 6:4-5; “Disciple the Nations,” by Dennis Woods, pg 162-163
[12] Ex. 22:1, 4-7
[13] Ex. 22:3Lev. 25:39-40
“[15] Disciple the Nations” by Dennis Woods, pg. 165
[16] Deut. 22:28-29; Ex. 22:16-17
[17] Deut. 22:25-27
[18] “The Institutes of Biblical Law,” by R.J. Rushdoony, chapter 7
[19] Lev. 24:17; Ex. 21:12, 14
[20] Num. 35:31
[21] Ex. 21:22-24
[22] Deut. 24:7
[28] Tony Parker and Robert Allerton: “The Courage of His Convictions (New York: W. W. Norton, 1962), pg. 88
[37] Deut. 17:6-7