Miracles of Math That Will Open Your Mind
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Miracles of Math That Will Open Your Mind

Chaos Theory, fractals, flying cars, and what it means to live a “well-lopsided” life.

“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” — Albert Einstein

Dear Reader,

Happy Monday, y’all! Today we wrap up our math series that we started last week! Enjoy!

(And for a full list of the Five Miracles of Mathematics, go here.)

Chaos Theory and Ralph Abraham

“Chaos theory is a branch of mathematics focused on the behavior of dynamical systems that are highly sensitive to initial conditions. ‘Chaos’ is an interdisciplinary theory stating that within the apparent randomness of chaotic complex systems, there are underlying patterns…The butterfly effect describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state, e.g. a butterfly flapping its wings in Brazil can cause a tornado in Texas.” — Wikipedia

Basically, Chaos Theory says that you’ll never have enough understanding of the exact present to be able to predict the exact future.

“Chaos theory… says that you can never predict the weather more than a few days away. All the money that has been spent on long-range forecasting — about half a billion dollars in the last few decades — is money wasted. It’s a fool’s errand. It’s as pointless as trying to turn lead into gold. We look back at the alchemists and laugh at what they were trying to do, but future generations will laugh at us the same way.” — Michael Crichton

Ralph Abraham is a professor, mathematician, and chaos theorist whose work has focused on the intersection of mathematics and psychedelics since the 1960s.

“My specific goal is to revolutionize the future of the species. Mathematics is just another way of predicting the future.” — Ralph Abraham

His paper Mathematics and Mysticism is an engaging look into what math might mean. From the abstract:

“Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article, we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination.”

But what does this all mean for you?

If life seems chaotic, remember that on a small scale, you can create ‘algorithms’ for success that can connect your current present with your ideal future. But… keep in mind that these algorithms will only extend so far into the future and will need constant updating based on the present conditions.

How Fractals and the Genius of Mandelbrot Can Relieve Your Anxiety

A fractal is a curve or geometric figure, with each part having the same statistical character as the whole.

These fractal sets were named after Benoit Mandelbrot, whose pioneering work in developing what is now known as “fractal geometry” paved the way for many more mathematicians to study and expound on his ideas.

“Because of his access to IBM’s computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovering the Mandelbrot set in 1979. He showed how visual complexity can be created from simple rules. He said that things typically considered to be ‘rough’, a ‘mess’, or ‘chaotic’, like clouds or shorelines, actually had a ‘degree of order.’” — Wikipedia

The visual representations of Mandelbrot sets are stunning.

The next time you think your life is too chaotic, too messy, just keep persisting. Mathematics has shown there’s an implicit order in everything around us.

If the golden ratio is present in the layout of our faces…

If the Pareto principle can be found throughout nature and society…

If the seemingly chaotic and unpredictable behavior of cellular automata can be reduced to rules so simple a child could understand them…

… then there is also an underlying (though often unseen) order and structure present in our lives. It’s okay to drop certain anxieties and trust what mathematics shows us — there is an underlying order.

“If there is one thing the history of evolution has taught us it’s that life will not be contained. Life breaks free, it expands to new territories and crashes through barriers, painfully, maybe even dangerously, but, uh… well, there it is.” — Dr. Ian Malcolm, Jurassic Park (1993)

The miracles of mathematics are all around us, and there are countless gateways to find them.

“The universe is not only stranger than we imagine, it is stranger than we can imagine.” — JBS Haldane

Whether you use these gateways to bring more meaning to your life, balance your budget, or revel in the mystery… they can open new possibilities and options you never before knew existed.