Fisher: Mathematics and reality

You are driving to the post office and come to an intersection. There is a post on your right near the corner with an octagonal red sign with white edges. On the sign are the capital letters ES-TEA-OH-PEA. What do you do?

If you answered “Slow down, look slyly around and zibble on through without stopping” shame on you. Too many drivers do that. Perhaps there should be a billboard saying “IMMEDIATE ATTENTION: According to local ordnance F38451, subsection 15.b.8 drivers of all conveyances encountering this billboard will bring their vehicle to a complete stop relative to said billboard. Violators will be DISINTEGRATED by the laser cannon on your immediate left.” That would get your attention.

A stop sign is a symbol with a specific meaning. Humans use symbols as shortcut reminders of something more extensive. The alphabet is a convention of symbols we use to represent words, which are themselves symbols. The word cat is not a “cat,” but represents the group of felines that reside in many of our homes. The history of numerals is long and tangled and are symbols used to count, measure, or calculate. Until the invention of multiplication and long division arithmetic could only be done by specialists. An unfortunate aside: with the advent of calculators, computers, and smart devices many among us have even forgotten how do balance a checkbook on a sheet of paper.

In the 9th century, al-Khwarizimi, an Arab mathematician wrote the first treatise on algebra. By the end of that century, Egyptian mathematician Abu Kamil had stated and proved the basic laws and identities of algebra. These allow us to manipulate symbols to find key values of interest in sets of equations. In the 18th century, Isaac Newton and Gottfried Leibniz independently provided the basis for calculus. This proved essential for the scientists and inventors of the Enlightenment and the Industrial Revolution.

Calculus has two branches, differential and integral, used to analyze mathematical curves in multidimensional space. Differential calculus is used to determine changes in the slope of a curve, that is, how it increases or decreases with respect to a variable. Integrals are used to determine the area or volume under a curve. Many physical processes can best be described using calculus, such as the pressure of a gas in a closed vessel, or the stress in a beam to be used in a bridge. Differentials can lead to sets of equations to describe complex systems.

In fact, some phenomena can only be understood in terms of these sets of equations. Electromagnetic force, for example, was first described by James C. Maxwell as a set of differential equations in 1863. We still deal with the changes in electrical and magnetic properties of light and electricity in extensions of these equations. The symbols and their manipulation are well known to scientists and engineers.

Mathematics has many branches, each with its own symbols and rules. Quantum mechanics and cosmology involve differential equations, matrix algebra, probability, and other forms, as do fields such as actuarial, seismology and climatology. In each case, the science is specified in sets of equations. If they follow the appropriate sets of methodology, conclusions, within statistical limits can be tested and either accepted or rejected. If there is an error, someone in the field can point it out. As more observations in the form of data becomes available they can run the model again, usually resulting in tighter statistical limits, say becoming 90 percent probable instead of 80 percent, plus or minus a couple of points.

In order to form a valid opinion about a scientific topic dealing with reality, one must address the mathematics, not the emotions of a topic. You can’t wish away electromagnetism or gravity. There are always deniers who don’t want to confront an idea that forces them to make a change.

It is good to doubt new ideas. If the idea is about what is happening in the real world, look at the data and the methodology. If you can point out an error of either omission or commission, continue to doubt. However, if you just “feel” it is wrong, your opinion is invalid, and therefore of no consequence.

Ed Fisher is a Morning Sun columnist.

Resource:Fisher: Mathematics and reality (themorningsun.com)