For problems that most of us try to solve every day it turns out we need only very simple math skills. We cook something in the kitchen from a recipe, build something in the garage from a few pieces of wood, or plan a financial budget for the week, the month or even for the year. Any of these problems may mean that we need to be able to add, subtract, multiply and divide, handle fractions, decimals, and count or weigh the reasonableness of the simple mathematical results of our plans.We don’t really need to advance our skills to more complex mathematics.
For example, if the cook needs 3/4 cup of some fluid but only has a 1/8, 1/4, 1/2 or 1 cup measuring devises, he or she should understand the easiest way to get 3/4 cup may be to measure out 1/4 and 1/2 cups and add them together because 1/4 + 1/2 = 3/4 and not 1/6. I know that such a mistake is very unlikely, but a beginning cook with a very poor knowledge of fractions (or a sudden brain freeze) just might think to that 1/4 + 1/2 won’t work. Of course, the cook might be better with subtraction as in using 1 cup from which 1/4 cup is removed of fluid is removed (1-1/4 = 3/4). After a while, of course, using fractions and thinking about them while cooking or doing other things in the material world gets to be very simple–and really good cooks don’t need to measure things exactly anyway, right? Even the most mathematically challenged among us get things right almost all the time after the initial challenges with fractions.
In setting up a household budget for the week, if projected costs exceed income, the budget has to be cut and clearly you look over the items in the discretionary part of the budget and decide which one or two items can wait until next week. The other alternative is a “payday loan” which I would recommend getting from Mom rather than one of those predatory lenders.
In building something which requires 16 pieces of 2″ by 4″ wood each 15 inches in length, we need to decide what to buy when 2′ by 4′ wood is only available in 8 and 15 foot lengths. The idea is to have as wood little left over as possible and not overspend. When you plan this out you can easily see you’ll about need about 20 running feet of cut lumber (16 pieces x 15 inches per piece = 240 inches = 20 ft). You can do this with either three 8 foot lengths (24 feet total) or one 8 foot length and one 15 foot length (23 feet total). In the latter case, you’ll have only about 3 feet left over after making the cuts whereas in the former case you’ll have 4 feet leftover. Thus, if it turns out the one 15-foot length piece cost $2 less than two-8 foot length of 2″ x 4″ lumber, the decision is a simple one. You buy one 8 foot piece and one 15 foot piece for a total of $2 less than you would have paid for three 8 foot pieces. The cheaper cost also leaves with you with less extra lumber to store in your odd size lumber bin.
In addition to the very basic kinds of math skills we all need as illustrated above, almost everyone agrees that we should all have an understanding of basic science and technology and try to do it using less complicated mathematical formulations. Fortunately I think, modern knowledge in this arena is increasingly presented as non-mathematically as possible. Sometimes mathematical issues are noted, but often not in detail. When the results are presentable in graphical form the presenters of such scientific or technological results may say, for example, the equations may lead to the following graphical representation…and then show how and why this is intuitively reasonable. This is a much better choice in explaining a complex phenomenon than hauling out complex equations that no one other than a talented theoretical physicist will understand.
In his book, “A Brief History of Time,” which is an attempt to explain the behavior of the entire universe since it’s inception nearly 14.3 billion years ago, Stephen Hawking writes a book which is without a single mathematical equation. As his editors point out, a book about complex issues in science will be read in inverse proportion to the number of equations which appear within.
In public television programs, often very complicated science issues are raised without reference to the underlying equations. Notably in the excellent series entitled “Through the Wormhole,” narrated by Morgan Freeman, complex and deeply philosophical issues are considered usually without reference to underlying equations, unless they give graphical results that can be presented in a way that makes sense. Even then we don’t hear about the graphical results unless they are intuitively consistent with something we can see or think about non-mathematically.
In one episode on the nature of time and how we should perceive it, Freeman noted that in early attempts to blend the theory of relativity with quantum mechanics the basic equations that resulted were without a variable for time, suggesting that time is not an important variable that allows us to understand the universe. Immediately Freeman asked to question, “Does time exist? Or, is it an illusion?” Indeed, whether time exists or not, the question is interesting and hard enough one to get a handle on without complicating it with equations very few other that theoretical physicists are able to consider.
One simple and important fundamental equation has been around for a long time. Much of the public seems to understand its implications: E = mc2 (Energy = mass x speed of light squared). It shows that when an enormous amount of energy is released in certain processes such as nuclear fission that this can occur even with the loss of an exceedingly small amount of atomic mass. The reason the mass loss must be small is that the speed of light squared is an exceedingly large number. Thus when you can get matter to energy conversion to happen under controlled conditions such as in a nuclear power plant, lots of energy is produced and the atomic fuel is used up at a vanishingly slow rate. I think nearly everyone understands this idea and they don’t have to make a calculation to prove it to themselves.
Graphics, including histograms and pie charts, are increasingly used to explain complex mathematical ideas. These formulations are increasingly used in place of equations involving multiple variables. Many computer programs will generate multiple kinds of graphics and the more we use them, the less we will depend on the underlying equations.