[The following was copied and pasted from GPT-4 after I fed it a transcript of a 3 minute ramble I had recorded while walking just now and asked it to turn it into a 3000 word blog in the style of Morgan Housel]
Seeing the World Through Math: A Mathematical Lens for Everyday Life
As a math teacher, there's a saying I often share with my students: "To a man with a hammer, everything looks like a nail." For me, math is that hammer. I don't just teach equations and algebra; I see the world through a mathematical lens. It's an intriguing, all-encompassing way to make sense of our surroundings.
Everyday Mathematics: Beyond the Obvious
Most of us are familiar with the basic math that governs our lives. Money, stocks, tipping at a restaurant – these are daily reminders that numbers play a part in everything we do. But what if I told you that math stretches its invisible tendrils into areas you've never even considered?
Consider the simple act of sending an email. You might think that if you send an email to one person, the impact is x. So if you send it to five people, the impact should be 5x, right? But it doesn't work that way. The cumulative effect isn't merely multiplied; it's expanded. It's more than five times. And that's just the tip of the iceberg.
Inverse Relationships: Uncovering Hidden Truths
As we delve deeper, the waters of mathematical logic become murkier and more fascinating. Inverse relationships, for instance, are everywhere. They're in the way we perceive value, the way we make decisions, and even the way we understand truth.
Here's an amusing yet profound example: the "Bike Shed Problem." Imagine a committee tasked with building a nuclear plant. You would think they would spend most of their time discussing the critical aspects, like where to place the plant. But in practice, they might spend 90% of their time discussing where to put the bike shed on the site. The seemingly inconsequential decisions consume the most time, while the pivotal choices are glossed over.
This inverse relationship between importance and attention is not only counterintuitive but also deeply revealing about human nature.
Mathematical Insights into Decision Making
The Bike Shed Problem isn't just a humorous anecdote. It's a stark illustration of how our decision-making processes are often flawed. It shows that we tend to dwell on trivialities and overlook the monumental.
In the real world, we often entrust committees with big decisions, hoping that collective wisdom will prevail. But as the Bike Shed Problem illustrates, committees can get mired in the mundane. The reality is, informed, educated individuals usually drive significant changes, both good and bad. They make the decisions that shape our world, while committees argue about the bike sheds.
Consider how many corporate boardrooms have been ensnared in minutiae while missing the big picture. Think about how many governments have become paralyzed by endless debates over trivial matters. These scenarios aren't mere happenstance; they're manifestations of mathematical principles in action.
Unintuitive Mathematics: Exploring Further Examples
Mathematics is full of surprises, and often, what seems intuitive is anything but. Take the concept of x and one over x. This relationship between a number and its reciprocal is not linear; it's inversely proportional. And these sorts of relationships aren't just confined to textbooks; they're reflected in our daily lives.
For example, consider happiness and material wealth. As wealth increases, happiness might not follow suit. There's a point of diminishing returns where more money doesn't equate to more happiness. That's an inverse relationship at work, and it's not something most of us naturally grasp.
Or think about success and effort. You might assume that doubling your efforts will lead to doubling your success. But in many endeavors, the relationship between effort and success is nonlinear. Sometimes, a small change in input leads to a massive change in output, and vice versa.
These examples illustrate that understanding mathematics is more than just solving equations. It's about recognizing the hidden patterns and structures that govern our world.
Conclusion: Embracing the Mathematical Worldview
As we've explored, math isn't confined to the classroom. It's a universal language that can help us understand everything from personal finance to human behavior.
But more than that, embracing a mathematical worldview encourages us to question our assumptions. It challenges us to look beyond the obvious and recognize the underlying principles that shape our lives.
The world, seen through the lens of math, is a place of beauty and complexity. It's a landscape where the mundane can be profound, where the intuitive can be misleading, and where the hidden truths are often the most enlightening.
So the next time you tip your waiter or decide to send an email to a friend, take a moment to appreciate the mathematics at play. And maybe, just maybe, you'll start to see the world a little differently.
Math is more than numbers and equations; it's a way of thinking, a way of living. It's a hammer that can break down complex problems into understandable parts. And in a world that often seems chaotic and confusing, that's a tool we all could use.
Whether you're investing in stocks or deciding where to build a bike shed, the principles of math are there, guiding your way. Embrace them, and you might just find that everything adds up. After all, in a world where everything can be expressed through equations and ratios, why not let math guide the way?
Further reading
If this piqued your interest, here are some books that delve into how math shapes our lives:
- "How Not to Be Wrong: The Power of Mathematical Thinking" by Jordan Ellenberg
- "The Joy of x: A Guided Tour of Math, from One to Infinity" by Steven Strogatz
- "Thinking in Numbers: On Life, Love, Meaning, and Math" by Daniel Tammet
Remember, math is not a subject to be feared or dreaded; it's a gateway to understanding the universe. So pick up your hammer and start seeing the nails. It's a beautiful world out there, waiting to be understood.