A view of the world from my own unique perspective

In high school, we students always complained that the things we learned in math class didn’t have any practical, real-life applications. Even my high school music teacher once told our class “Music is your most important subject. When you graduate from high school, you will probably listen to music every day, but how many times will someone ask you to find x ?”

Like many of the most important things I learned in high school, I didn’t appreciate their importance or significance until long after I graduated. Although I didn’t realize it at the time, the most valuable and illuminating math class exercise for me was this one:

Expand and Simplify

If you’re scratching your head in bemusement right now, that’s OK. Leonard Bernstein, in his 1973 Harvard Lecture The Unanswered Question said that the principal thing that he absorbed from his Harvard professors was a sense of interdisciplinary values – that the best way to ‘know’ a thing is in the context of another discipline. Therefore, in order to understand the importance of this exercise, we must frame it within another context. The “expand and simplify” idea describes a surprising number of things in our lives, both individually and collectively. Here are a few examples:

Possessions: Once we exit academia and enter the working world, we naturally want to make our mark on society and acquire all of the trappings of success. With our first job comes the money for our first apartment and car, and the rest of the accoutrements: clothes, shoes, accessories, jewelry, art, CDs, DVDs, electronic equipment etc. Once we have everything we need, we’ll start upgrading: a late-model or luxury car, a larger house, designer clothes and larger collections of everything. This “desire to acquire” peaks sometime during middle-age, when we are enjoying our highest standard of living. Then as we approach retirement, we’ll begin to simplify our lives by downsizing and keeping only what’s important. At this point, we no longer care what others think of us or feel any desire to compete for social status. Now that we’re more mature, we no longer define ourselves by our possessions and realize that the best things in life are free. As we enter the winter of our life, our inevitable declining health and mobility forces us to downsize even further: from a two-storey home to a bungalow, to a seniors’ residence, and finally to a single room in a nursing home. In a material sense, our twilight years now resemble our university days – all of our worldly possessions once again fit into a single room.

Facebook Friends: When Facebook was introduced to the general public, I think many of us wanted to wanted to expand our network as much as we could and be a big player in the world’s most popular social media platform. Now, about six years later, after reading hundreds of wall posts, I’ve come to the realization that some of my Facebook friends are just complete nutbars. In fact, a couple of years ago I compiled a list of 26 distinct personality types, called Facebook Characters. Now I feel like pruning my friends list a little. I’d rather have a handful of friends who post intelligent, insightful and thought-provoking comments, than hundreds who send me game requests, post photos of their meals, and generally have nothing meaningful to say.

Collecting: If you’re a novice collector (of anything – CDs, DVDs, stamps, coins, baseball cards, art – then you’ll usually be indiscriminate at first. You’ll buy or accept almost anything, just to build your collection. When I first started buying DVDs, Wal-Mart’s $5 delete bin was my best friend. I could add another DVD to my collection for only $5 – who cares if it was a Pauly Shore movie? As our acquisitions become more numerous and our tastes become more refined, we will often cull our collection; we will discard or sell the junk and keep only the best items. Quality becomes more important than quantity. Than, as we near the end of our lives, we will likely sell our collections or even give them away to people who will enjoy them.

Cleaning: A couple of years ago, I spent an afternoon cleaning and reorganizing a storage closet. As I moved its contents out, the items covered almost the entire floor and the mess seemed several times larger. Then as I performed my own brand of triage – things to throw out, things that belong somewhere else, things that can be placed back in the closet – the pile slowly became smaller and smaller, and eventually everything fit neatly back into the closet with a considerable amount of space left over.

Speech Writing: When I’m researching a Toastmasters speech, I’ll write down all of my thoughts and ideas. Then I’ll take all of this information, sculpt it, and give it a structure. Once the structure is complete, I’ll revise and edit it several times and “tighten it up” – to express the same points using fewer words, eliminate any tautology, and ensure that I’m getting the message across within the time limit.

The Future Of Humanity: I admit that this is just speculation, but Expand And Simplify is also an excellent model for our own past present and future. Humankind’s growth has been exponential over the millennia. We increase our technical knowledge as we expand our reach and our dominion over the planet and exploit its resources. Once we reach a critical mass (or population), we could go in one of two directions. If we smarten up in time, then we’ll learn to live in harmony with Nature. Rather than dominating everything, we will simplify our lives, adapt, and exist in harmony with our surroundings, instead of trampling all over the planet like a bunch of barbarians. If we don’t smarten up, then we’ll reach the limits to growth, meaning that there will no longer be enough resources on the planet to support the our increasing population, and our numbers will quickly decrease. Whatever decision we make in the future, the result will be the same: an expansion, and then a contraction, of our civilization’s ecological footprint.


Sometimes the lessons taught in high school are realized only years after one graduates. In this case, the most important thing I learned in my math class was a prescient philosophy lesson. Who says that high school math exercises don’t have any practical applications in real life?




Comments on: "Expand and Simplify – The Most Useful Thing I Learned in Math Class" (2)

  1. Bob, I have to admit, I was curious where you were going with this topic when I first started to read it, but I really like the concept. I agree with Bernstein and you that using examples and analogies from other disciplines can often shed new light on a topic which can lead to greater understanding and appreciation. I also think that the application of high school math is in many ways much more direct than you state in your “expand and simplify” philosophy. I think algebra teaches us how to decipher a problem, separate what we know and what we don’t know and come to a conclusion through process and logic. Much of what is taught is school is really about much more than the specific facts that are being taught! Thanks!

    • Bob Yewchuk said:

      Thanks Bill – I’m glad that you liked this post! I’ve edited the post and added a link to Bernstein’s lecture for you. I think that he is a brilliant and mesmerizing orator and it is simply a joy to listen to him speak (the interdisciplinary quote begins at 2:30). I only wish that my university profs had been nearly as captivating as Bernstein.

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