The beauty of the universe through the elegance of math

From quarks to quasar clusters via Fibonacci, Feynman and fractals. Photo: Sunflower closeup. Image credit: Esdras Calderan via wikimedia commons

UNITED KINGDOM, September 19, 2013 — Numbers and I didn’t get along very well when we first met. To be honest mathematics frightened me as a child. Faced with a difficult sum I would panic and my brain would seize up. Even when I knew what to do with the numbers, I rarely understood the why behind what I was doing. I did well in all other subjects, I just seemed to be one of those kids who ‘couldn’t do math’ and my teachers seemed OK with that and largely ignored me.

Luckily for me, in my early teens things changed when I got a new teacher who refused to accept this excuse. She showed me the beauty of the numbers hidden in my beloved astronomy, from Bode’s Law predicting the spacing of the planets in the Solar System to Kepler’s laws of planetary motion. She not only proved that I could do math, but most importantly, she taught me to enjoy it and to recognize it in the world around me, in art, in music and in nature.


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Not only one of the greatest scientists of all times but also one of the finest science communicators, Richard Feynman, once said “To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.” Here he eloquently expands on the idea that science in general can only add to our appreciation of nature’s beauty.

Now my son is at university studying math. I’m not sure how it happened, but from his first days at school, he and math became the very best of friends. The Fibonacci sequence of numbers, is named after (though not invented by) Leonardo Fibonacci. Each number is the sum of the previous two: 0,1,1,2,3,5,8,13,21,34,55, etc. This sequence, or a very close approximation, appears repeatedly in nature, from the growth of a pine cone to the uncurling of a fern and even in DNA.


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Fractals are self-similar patterns. Detailed patterns that repeat themselves, they may be exactly, or very nearly, the same at every scale and are frequently found thoughout the natural world, in river networks, lightning bolts, plants, snowflakes and a heartbeat. Benoit B. Mandelbrot first used the term fractal in 1975, giving rise to my favorite mathmatical joke. What does the B in Benoit B. Mandelbrot stand for? Answer: Benoit B. Mandelbrot!

Earlier this year, a scientific paper was published that described the largest structure in the universe, a cluster of quasars four billion light years across, that is 1,600 times as big as our galaxy and four times larger than any structure should be, according our current understanding of the universe. Here are the folks at Sixty Symbols to help make sense of the research that would seem to turn the cosmological principle that the universe is homogeneous (the universe looks the same wherever you observe it from) on its head.


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Planck length, equal to 1.6 ×10−35 meters, is considered the smallest length possible. The observable universe is estimated to be 8.8×1026 meters across. In between those two numbers is everything we know. At these scales numbers can be hard to get your head around. Here is a very simple yet effective graphic representation of the scale of the universe, everything we know from smallest to largest and back again.

Mathematics is all around us, it not only describes our world it also has profound effects on our lives. Here are ten equations that changed the world. From Pythgoras’ a² + b² = c² through Schrodinger, Newton, Euler, Maxwell and Fourier, to Einstein’s E=mc² mathematics underpins everything we do.

Even the current economic crisis can be blamed on the incorrect use of the Black-Scholes model of calculation.

So numbers are beautiful, important,vital even, but do they even exist outside of our own minds? Is mathematics a feature of the universe or a feature of human creation? Do we create mathematics as a language to describe the universe or is mathematics as a real entity in the universe that we only discover. Is mathematics subjective or objective? Here are the guys at the PBS Idea Channel with their thoughts.

Adam Spencer gives one of the most entertaining TED Talks on any subject, uncovering the current largest prime number in the world (which weighs in at 17,425,170 digits long) while explaining why he fell in love with monster prime numbers. His quote sums up my own feelings about mathematics. “Math is beautiful, it’s natural, it’s everywhere. Numbers are the musical notes with which the symphony of the universe is written.”

 


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Jenny Winder

Jenny Winder is a British science writer for SEN - the Space Exploration Network,  specialising in astronomy, physics and space exploration.

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