[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 2000 word blog in the style of Morgan Housel]
At the heart of life, in the fabric of the universe, and in the workings of our daily lives, there's one constant: the ratio. It's a simple yet incredibly powerful concept. But first, let's clear the air about what a ratio is. In mathematics, a ratio is a comparison between two numbers, illustrating how many times one value is contained within another. Essentially, it's the slope of a line - a change measured in terms of division. Consider a slope of five: it means for every step we move to the right, we take five steps upwards. The fascinating thing about ratios is that they can represent two different things: a slope of five upwards and one to the right is essentially the same as a slope of five downwards and one to the left - positive over positive, negative over negative, they're the same thing.
But ratios aren't just about mathematical comparisons; they're about balance and proportion. The golden ratio, known by the Greek letter 'phi' and approximated as 1.618, is a perfect example. It pops up in numerous aspects of the natural world - in the patterns of a pine cone, the spiral of a galaxy, and even in the proportions of the human body. Often, what we perceive as 'beauty' aligns with the golden ratio - but why? The magic of this number doesn't lie in its value, but in the equation from which it originates: x^2 equals x + 1. From this equation, we derive the golden ratio via the quadratic formula, illustrating that ratios underpin not just numbers, but also harmony and aesthetics.
The concept of ratios extends to our everyday lives, too, shaping our behavior, goals, and relationships. It's the ratio of work to play, for instance. Some people might favor a ratio of five-to-one, where work far outstrips leisure. They might be ambitious individuals aiming for that corner office, relentless in their pursuit of career success. But others might prefer the inverse - a one-to-ten ratio, where relaxation reigns supreme. Or even, the 'negative ten', a tongue-in-cheek reference to those who are most content when work is a last resort, not a priority.
In every case, these ratios are a reflection of our personal values and aspirations. They inform how we allocate the most precious resource we have: our time.
You might wonder, aren't ratios just about division or multiplication? Well, yes and no. While they're essentially a mathematical tool, ratios go beyond numbers. They capture the essence of life's ebb and flow - they reflect our choices and priorities.
Consider the ratio of your attention. Where you dedicate your attention determines what becomes important in your life. We attach meaning to what we focus on - so the ratio of attention between different aspects of our lives is instrumental in shaping our experiences and our identity.
Ratios are even key to our relationships. Take, for example, the ratio of arguments to peaceful interactions. It's a simple number that can have profound implications for the health and longevity of a relationship.
In a world that often favors complexity, it's easy to overlook the simple power of ratios. But as we've seen, they are fundamental to so much of what defines our universe and our lives - from the spirals of galaxies to the rhythm of our daily routine.
Ratios reveal the beauty in balance and proportion. They guide us in our allocation of time and attention. They measure the health of our relationships. Even our bodies adhere to certain ratios considered aesthetically pleasing.
In essence, the humble ratio is a universal language, whispering the secrets of beauty, balance, and harmony. They have opposites, inverses, and negatives. They are simple, yet they hold the answers to complex questions. They are static, yet they encapsulate the dynamic ebb and flow of life. They are mathematical, yet they are intrinsically tied to our emotions, our decisions, our very existence.
So, the next time you're making a decision, consider the ratio. Whether it's how you spend your time, where you direct your attention, or how you balance work and play - remember that it's all about the ratios. The secret to balance, harmony, and even beauty lies in these simple proportions.
In conclusion, ratios may just be numbers, but their value is immeasurable. They offer insight, bring clarity, and provide a framework to understand the world around us and the lives we lead. Ratios, in their elegant simplicity, are a testament to the intricate complexity of life.