by Tom Baugh
There are some constants afoot today in that math and science are denigrated as subjects for the geeky kids. We have all been fed this lie. You yourself may have bought into this lie, perhaps from peer pressure from the cool kids. Or, because of abusive or humiliating treatment from ignorant teachers hoping to mask their own insufficiencies. Or even just the mistaken assumption that these subjects are hard and hardly worth knowing. If so, you have severely crippled yourself. Fortunately, you can fix this defect in your armor, but it will require some work.
I said before that you will have a hard time understanding math or science unless you know why you are asked to learn a particular skill or algorithm. This is one of those chicken-and-egg problems which plague the system. Only by the hiring of teachers who genuinely know why particular techniques are of use would it be possible to correct this. For example, I might tell you that you need to understand calculus because it will help you determine the moment of inertia for any object you might encounter. Or, I might tell you that you need to understand differential equations because it will help you understand thermodynamics and rates of chemical reactions. Regardless, I really haven't told you anything at all, have I?
Once you understand physics and thermodynamics and rates of chemical reactions, only then can you look back and understand integrals and partial derivatives. But by then you will have already brain-dumped that material, provided you were taught it in the first place. I know you will, I did exactly that myself.
We have a sort of secret society thing going on here. Those already in the know with these subjects know exactly what I am trying to say, yet those not in the know have no idea about anything I said in the previous paragraph. Without understanding where you are going, it is hard to understand why you are being asked to follow a particular path. Without having arrived there, you can't even see the path, but looking back, you see it clearly.
I encountered exactly this problem when I was teaching my son economics and chemistry in the seventh grade, and calculus, physics and genetics in the eighth. I learned that pre-teens and early teenagers possess the biological ability to learn these subjects, but only if properly prepared. But first, I had to overcome the trauma inflicted by the autocratic enforcement of the "guess and check" method. That brainwashing technique used in public school would rate right up there with any sort of psychological child abuse which you care to name.
Why do I claim that autocratically enforced poor teaching is abusive? Because it cripples our children's minds before they have a chance to learn to question their abusers. Perhaps you were abused in this fashion and decided to rebel against this abuse by deciding these subjects were of no consequence to you. Instead, you should consider that these subjects can become powerful weapons in your arsenal which allow you to capture quality of life for yourself.
So how did I overcome this chicken-and-egg problem? By presenting problems, which must be of interest to my student, that can only be solved by using the techniques at hand. This, however, requires that the material be tailored to each students' interests, a practical impossibility in our industrialized schools, yet uniquely available to small private schools or homeschoolers.
Here is an example. Perhaps your child is interested in martial arts. The typical way that martial arts are taught is to memorize a series of moves which define that particular style. The instruction is then limited by the style being taught, as well as the flavor which the individual instructor might impart, and might require years of dedicated work to learn. These moves and styles are the product of, in some cases, centuries of evolution to determine a set of actions against a particular adversary or weapon. However, underlying all of these styles and moves are the basic physical and biological principles common to all of them. If you understand the physics and biology, you can cut through an enormous amount of spiritual mumbo-jumbo and get down to the essentials quickly.
And so, you might present to your budding Jackie Chan a problem formulated as follows: Little Johnny is facing a larger adversary throwing a punch at shoulder level. Model the attacker's arm as a linkage attached to a rotating mass. Using experimental data obtained at a gym regarding the relative strengths of typical muscle groups in the upper body, make reasonable estimates as to the moment arms and torques available in this system. Model Johnny's parry as a force vector applied to the wrist of the adversary and determine, for a given force, accounting for Johnny's own relative strengths, whether Johnny should parry with an adduction or an abduction. I am reminded of that Loony Toons Foghorn Leghorn episode, Little Boy Boo.
Video Assignment
Loony Toons Foghorn Leghorn episode, "Little Boy Boo" In addition to ordering the episode in a collection from your favorite movies-by-mail vendor, you may also be able to find this episode on the web somewhere. In this story, a little myopic chicken is playing baseball with Foghorn Leghorn. The chick is pitching to Foghorn. After doing some math, the little chicken proceeds to pitch the ball through the bat and a few trees behind. He then follows this victory with a paper airplane which downs Leghorn's plane in aerial combat.
Of course, the denigration of math and science shines through clearly in this episode, particularly when Foghorn Leghorn states that "Never mind, Einstein, knowing the answer wouldn't do me no good anyway." Clearly, in the Little Johnny fighting example, hitting the attacker with a chair is a more practical use of science than calculating his response, which Johnny wouldn't have time to work through. Pulling out a calculator and pencil to scribble through the equations isn't the point.
The point is to frame math and science in a form of interest to the student, allowing their natural curiosity to engage. Physics is then motivated by framing the problem as one of a general class of problems capable of being solved by understanding torques and moments of inertia. Then the need for math is motivated by it being required to understand how to calculate the physics.
The most interesting side effect of the martial arts physics example is that many of the moves seen on the tube or on film will then be understood as calculated. These moves are calculated not to be effective for self-defense, but to just look good. Similarly, many of the martial arts moves taught in classes are only useful as sport, akin to dancing. Regardless, a black-belt will no doubt be more prepared in a fight against a rube whose only weapons are his muscles.
Yet few black belts are capable of withstanding a blow to the head with a non-theatrical chair. Even they, however, will attempt to employ, if only ignorantly, the same physical principles to redirect the blow of the chair safely away. The martial artist's response will be dictated not by recalling the "avoid chair" moves taught to them in dance class.
Instead, their response will be dictated by their subconscious understanding of physics which has been framed in a philosophical context, the only language available when these moves were discovered long ago. But now we have the language of math. More importantly, Little Johnny might then wonder, since the cool fighting moves are fake, whether other lies might be lurking behind the images. And then he will begin to employ his knowledge of math and science to detect these lies. He will begin to think for himself.
Or maybe the student is interested in cars. Math and science will help him understand the lies behind a commercial which shows the latest twenty-horsepower electric roadster darting around those mountain passes on the way to the babe's cabin. Or why an electric vehicle, using any technology available today, won't be economically practical for most Americans. And that the only way to get Americans to adopt them is to commit to a significant lifestyle change in which the family car loses its place as a ubiquitous general purpose conveyance. In that mode of thought the car must become instead a pampered altar to the gods of the day, requiring inordinate sacrifices of time and care.
The monkey collective won't like this sort of independent thought at all. No wonder they try to convince Little Johnny that he can't learn all that scary math and science.
Here is another example of how framing the sciences helps m
otivate the underlying math. Imagine your particular student is an environmental buff, and wants to explore alternate energy. One approach to alternate energy includes biofuels such as biodiesel, popularized as a way of running diesel cars with fuel made from waste vegetable oils.
Internet Research
Any recipe for biodiesel, one of the best is available from the Collaborative Biodiesel tutorial at their very helpful website www.biodieselcommunity.org/howitsmade/ With any of these recipes, they are just that, a recipe. In a few cases the biodiesel enthusiasts try to explain some of the chemistry behind the processes, but many gaps are left simply because someone who is capable of understanding the underlying chemistry already understands it. More chicken-and-egg.
This isn't to imply that these recipes are of no value. The ancient alchemist could produce formulae which resulted in various kinds of valuable gunpowder or unctions without understanding or explaining the why behind these recipes. Today, the biodiesel community is more or less at that same primitive level.
But, by following the recipes online, you can still get some reasonably decent results. I know, we've done it in homeschool, and then used these results to motivate further research and deeper study. Such as what thirddegree burns look like on Daddy's hand and how to treat them.
Now, by using these online recipes as a starting point, one might motivate their student, or themselves, to learn more about the underlying organic chemistry. And in particular, why some oils produce better fuels than others. Armed with that chemical knowledge, the bottle of biodiesel becomes much more understandable as a blend of hydrocarbons, much like an odd sort of crude oil.
Like crude oil, the quality of this fuel can vary widely in quality depending on the source. Unlike diesel derived from crude, the physical properties of biodiesel can include a tendency to cloud or freeze at low temperatures, or have trouble igniting under certain conditions. These properties are handled from a recipe perspective by being selective about the source, but an understanding of chemistry reveals more beneath the surface.
One would never pour raw crude directly into a fuel tank without refining into its various valuable fractions. Similarly, this biocrude should be more appropriately seen as a manufactured resource from which might be fractionally distilled more useful constituents. And, like some of the less valuable fractions obtained from crude, the leftover portions can be converted up or down the family of hydrocarbons through such means as cracking or reforming.
Yet none of these ideas or techniques are intellectually accessible until you decide to learn the underlying science. Without the underlying science one might discard perfectly useful hydrocarbons just to fit the recipe. But knowledge of these things might enable you to obtain fuel when none is available at any price.
So as a motivating factor to a student, one might explain that by understanding the chemistry, physics and mathematics behind first inorganic, and then organic chemistry, one might effectively use waste oils which most biodiesel enthusiasts shun. And thus access a source of energy and harness it for one's own purpose. Or, how you might substitute wood ash, suitably converted to KOH, for the lye used in the process. Or, how ethanol or even propanol might be substituted for the methanol, and the effect that each substitution might have on the output product or the operation of the process itself.
At the end of that educational process of discovery one has unlocked the secrets of biodiesel for oneself. And then, one might even understand what an unforgivable crime has been perpetrated on the American economy by the fact that the youngest refinery in our inventory is about thirty years old. In the process, the student will have learned about many things which impinge on that recipe, and motivate its genesis. And he will begin to understand all the stupid around him, much of which flows out the end of the cable behind the TV.
Both inorganic and organic chemistry allow us to convert the world around us into a form we find more suitable. Exploring the practical aspects of that conversion you might encounter the use of modern computer-based process control. And then you might begin to wonder about the capabilities which new refineries might have versus simply patching up old ones. Such as the application of technology which would allow flexible use of a variety of source material to produce any desired output blend with the clicking of a few keys.
This self-study might lead to other topics as well. You might drift off the biodiesel path and into other alternative fuels such as corn-based ethanol. And then learn about the challenges behind cellulosic ethanol or the vastly superior pyrolysis technologies. On this path one might discover for oneself the insanity behind our current energy policies and our demonic persecution of carbon.
Once you understand the chemistry and physics, you would wonder why we would choose, as a national policy, to turn food into a small quantity of fuel. Instead of turning a much larger base of non-food materials into vastly more fuel of far greater quality. But I can't even begin to explain all the things which Little Johnny, or you, will learn about the world by doing this one simple thing. You have to walk down that path yourself, and then you will know exactly what I mean. And when you hear stories about biodiesel public school buses with frozen tanks you will laugh at the irony, just like I did.
Because all of those little minds on the bus, had they been taught the underlying science, would know exactly what the problem was. And what simple changes to the infrastructure would fix it. And why you don't have to rely on the opinion of an expert at a government-funded lab for the answer. But again, the monkey collective, which depends economically on enslaving their future votes to keep the welfare and bailouts flowing, cannot allow that kind of thinking. Knowledge empowers those little minds too much, and makes them ask too many embarrassing questions. Of both sides.
Being kept ignorant can only lead to your being more pliable to coercion and fear. Ignorance causes people to perceive the monsters of today as being more frightening and complex than they really are. Which might arguably be the end goal of the witch doctors of our time, who wish for you to bow at their altar and ply them with offerings to keep you safe from shadows. I said before that there is a very simple reason why you must master math and the sciences, and here it is.
Math is the language of God, and the various sciences are the books in His bible. I am sure that I offended the theologian and the atheist scientist both with that statement. This feat is understandably difficult, as each imagines themselves as occupying the only pure end of spectrum which is in reality a circular path nearly touching. I attempt to reconcile these views in a later chapter regarding the commingling of our modern atheistic religions. But, for now I will show you the path to mathematical and scientific enlightenment.
Your best ally in your self-education will come from an unlikely quarter: the homeschool community. The same resources which are used to teach children math and physics can be used by you, regardless of your situation, to give yourself power. This power will assist you in your entrepreneurial goals, as well as enhance your quality of life. These resources are valuable to you regardless of your field of endeavor, your race, your personal history, or your current state of incarceration.
Math is the cornerstone which you must first master. Most courses available to homeschoolers have been Biblically watered down beyond the point of usefulness. I have found that the best possible curriculum is produced by a publisher named Saxon. Its founder, John Saxon himself was a former World War II Air Force officer and math instructor. And his own struggle against the forces of niceness is in itself an excellent case-study.
Internet Research
Research the history of John Saxon. The best concise description I've found is at a popular homeschool resource:
http://www.home-school.com/Articles/SaxonEditorial.html
The entire curriculum you will need to master is:
Tutorial Materials
The following courses, all by John Saxon:
Saxon Math 54
Saxon Math 65
Saxon Math 76
Saxon Math 87
Saxon Algebra I
Saxon Algebra II
Saxon Advanced Math
Saxon Math Calculus In these titles, 54, 65, 76, and 87 refer to the grade levels for which this material is appropriate. For example, most fifth graders or advanced fourth graders will find the 54 course to be useful. I recommend you approach these courses in the order shown.
Unless you are confident in your math skills and choose to skip a level or two, you will gain a lot by practicing the material even in the early courses. You might find that a Saxon fifth grader has the equivalent knowledge of a high school student in our times! Remember that in Saxon's time high school children learned calculus routinely. In any event, unless you have a degree in engineering or the sciences you may want to review them all. Even degreed working professionals in these fields will find the reviews in the last two courses helpful. I know I did.
Each of these courses is available in kits, which means that you get the textbook, a set of exams, and a solutions guide for all chapter exercises and exams. Each chapter is an easily digestible chunk of information which is suitable for an hour's work each day. With about 100 to 120 chapters, and roughly one exam for each four lessons, you will complete each course in about six months working diligently one lesson per day. And you can do this by yourself, even in your prison cell.
One word of warning. Because Saxon uses the military style of education, which means relentless drilling of the basics, you might be tempted to skip past problems which look familiar. Don't. The Saxon technique, borrowed from military instruction, is specifically designed to present you problems from different perspectives, and distributed over time. This approach ensures that you haven't just completed the problems, but truly incorporated the material into your subconscious toolbox. The capstone Saxon course is his physics course.
