May 11, 2023
June 1, 2023

Studying to Learn

Photo by Ivan Obolensky

Many people dislike mathematics, sad but true. I can’t say I blame them. It has taken me an extraordinary amount of mental work and persistence to be conversant with only a small part. The subject is vast. It’s like learning a new language written in a new alphabet, and that is difficult. Nonetheless, I would like to make three observations.

The first is that many people consider math simply to be the study of numbers, but it is broader and more applicable than that.

Mathematics has its roots in ancient Greek. It is derived from the Greek word mathēmatikos, meaning “inclined to learn” or “studious”, which is derived from mathēma, meaning “knowledge” or “learning”.

The actual term “mathematics” was introduced into English during the 14th century, initially referring to all areas of learning and knowledge. Over time, it became specifically associated with the study of numbers, quantity, and patterns.

The second is to point out what mathematics actually does.

Central to mathematics is the process of abstraction. Abstraction refers to the action of forming ideas from specifics and turning them into more general concepts. For example, you see a duck. You know a duck is a bird, which is a living thing, and that by being alive, it isn’t dead. In a few steps we’ve abstracted from a specific creature to all creatures and more generally to the difference between the living and the dead. We can even symbolize this abstraction by assigning zero (0), to being nothing, or dead, and one (1), to being something, or living. What happens when we add the dead (0) to the living (1)? In one sense we get the abstract concept of History. In another, if 0+1=1, then we could say that History (the dead) doesn’t matter materially to the living because in the end, we are always left with the living—and that is strangely true. We could also take our zero and one and have them represent other abstract concepts such as off and on.

This brings up my third observation. By asking whether history really matters, we have moved into an area of ideas that is quite different from where we began (with a duck), and that is an example of the power of abstraction. Mathematics takes concepts from one area, abstracts them, and then applies those abstractions to another to create a better understanding of both.

Lastly, I think we are all mathematicians at heart even though we may not recognize ourselves as such. We symbolize and conceptualize what we see and feel, and then take that experience and apply it to a different part of life or to the future.

Given our tendency to fantasize and abstract, I would like to make a suggestion. Take a little time out of each day to study and learn. Study something new, maybe even something difficult, anything really, and tomorrow you will be more than who you are today.

Ignorance is the one abstraction that constrains and herds us all. Consider this: if you knew ten times more than you know now, would you still be doing what you are doing? If you think you’d be doing something else, then it’s what you don’t know that is keeping you where you are today. In more concrete terms, your ignorance is managing you, not the other way around. Learning reduces ignorance. Knowledge is cumulative. It is power.

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