A friend of mine on Facebook posted this comment on her Facebook page,
Although Algebra teaches you logical reasoning and problem solving skills I may only use Algebra when I am figuring out time and distance when preparing for road trips.
It is true that “Algebra teaches you logical reasoning and problem solving skills.” However, you use algebra along with other forms of math much more than you realize. This is because you use mathematics, including algebra, intuitively. What is meant by this?
You use algebra, calculus, and trigonometry throughout the day and everyday (you even use more complicated forms of mathematics but this is a topic for another day). This is intuitive mathematics, something your brain does automatically, rather than something you explicitly think about or do on paper; for example, you use calculus when you drive. You use the derivative when thinking about your current speed and you use the integral when computing the distance to your place of work or the distance between the car in front of you or the car in back of you (the derivative and integral are the two basic tools of calculus).
You also use trigonometry when making left and right turns, or during parallel parking, or some sort of parking activity. Algebra is the means, or the tool, that helps you to solve these problems implicitly and automatically. Mathematics are simply the symbolic tools to illustrate what you do alot, intuitively, throughout the day. However, you would never know this from taking a math class, because many mathematicians are squares. Pun intended.
However, thinking mathematically is nothing new for our species. Our abilities in mathematics have been evolving for a very long time. A brief tour through history will illustrate as much.
Homo sapiens emerged as a species more than 200 hundred thousand years ago. But even before that biological emergence, the predecessors of the species were hunting for food. The earlier bipedal species like australopithecus afarensis (Lucy), australopithecus africanus, and others had to have the ability to gauge the distance between themselves, various opportunities for food, and possible predators. Hence, they used early, rudimentary forms of intuitive mathematics.
For example, the distance between Lucy and the predator is calculus. Mathematicians call this the integral. The angle to get away from the predator is trigonometry. The wrong angle would mean certain doom for Lucy. Of course, those earlier bipedal species had to compute, intuitively, the speed of different types of predators, and weigh the probabilities of success, intuitively (this is probability theory). They did not know the exact speed of predators, but there was a hunch based off of previous experiences – successes and failures – of how fast and agile each predator species was.
Later in human history, but more recently, Homo sapiens developed tools – projectiles and stone tools – to use for hunting of prey and defense against predators. Like the advancement in ancient technology, intuitive mathematics advanced. Although no representation of symbolic mathematics existed until about 7,000 years ago, mathematical instincts by humans continued to evolve through evolutionary biological means, i.e., natural selection, environmental pressures, and trial and error.
Many early humans died terrible deaths due to engineering malfunctions of projectiles and the consequential failure of intuitive mathematics. In other words, the projectile tool did not work and that predator was much closer than it appeared; or perhaps the projectile did not work and the prey got away.
Either way, the miscalculation more than likely meant certain death from a violent death or possible starvation. But today, that miscalculation could result in a car accident followed by a higher premium. It could also result in a foul ball to the face during family night at the ball park. Ouch! Bring your glove next time.
Photo credit: We Use Math
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