If you haven’t seen it already, NUMB3RS is a drama on FBI agents using mathematics as a tool to help solve crimes. I decided that some of the mathematics mentioned in it warranted further exploration. So, I am adding three extracts from the show with a brief explanation expanding on each.
The Golden Ratio
"The good, of course, is always beautiful, and the beautiful never lacks proportion"
- Plato
The Greek's referred to it as the "Divine Proportion". And many mathematicians describe the Fibonacci sequence and Golden ratio as the most beautiful set of numbers in mathematics. It is a number common to the entire Universe; from sea shells to galaxies, we come across it everyday in one form or another. Its elegance can be witnessed in Leonardo Da Vinci’s infamous sketch, the Vitruvian man. Even best seller novelist, Dan Brown, carefully incorporated it in Da Vinci Code, wherein it plays a vital role in developing the overall plot.
Research has shown that living organisms subliminally prefer objects that are proportioned according to the golden ratio. The thought that a simple set of numbers (1, 1, 2, 3, 5, 8…) dictate the perceived beauty of the entire Universe has inspired generations of philosophers and mathematicians.
Uncertainty Principle
I think it is safe to say that no one understands quantum mechanics" - Richard Feynman
It seems that each century brings about a radical model revising the then standard view of the Universe. Heisenberg's Uncertainty principle was part of the revolution, in the first half of the 20th century, which redefined the constructs of the Universe. Heisenberg’s proposal happened to be so drastic that it made Quantum mechanics unacceptable for Albert Einstein. It states that the more certain “we” are of an electron’s position around the atom, the less certain our knowledge of its momentum becomes. Einstein believed in a Universe of finite possibilities; in other words, a Universe wherein anything can be calculated with absolute precision using mathematical equations. As it turned out, this was not the case with Quantum mechanics.
According to the Uncertainty Principle, it is theoretically impossible to calculate with certainty any quantity at the Quantum scale. Mathematically speaking, a single electron is everywhere in the Universe, except for the rare case where it comes in physical contact with a photon. Heisenberg Uncertainty Principle gave rise to the chaotic and complex world of elementary particles, superposition, entanglement, parallel universes, and double digit dimensions. A simple four letter equation drew a new picture of the atom, one in which probability, not determinism, dictates the state of the Universe.
It is a perplexing thought that the chaos and uncertainty at the Quantum scale somehow adds up to yield a stable ordered world that we have come to known. The Universe has absolutely no reason to be in such perfect symphony.
Chaos Theory
"It has been said that something as small as the flutter of a butterfly's wing can ultimately cause a typhoon halfway around the world" - Butterfly Effect
Chaos theory dictates that any set of complex situations are, in fact, a sum of ordered circumstances; therefore, making the chaos conceivable through mathematical analysis. Chaos theory has been applied for predicting varying systems such as tropical storms and terrorist attacks. It is an elegant branch of mathematics in a sense that it makes the seemingly unpredictable complexities predictable.
Chaos theory holds that the sum of a series of seemingly random coincidences follows a calculable pattern. People we meet, where we live, what we believe in, or why we are still alive; these are extensions of a system that appears chaotic to us. But at scale grandeur enough, there is order to it. Lines and Dots remain to be connected.
As a final note, I would like to state that any model we come up with does not describe the Universe but rather what the brain is capable of so far.
Author: I am a jobless undergraduate studying Electrical Engineering at Ryerson University, Canada. My interests include military and corporate strategies, business, economics, history, religion/philosophy, politics, logic, technology, programming, electronics, mathematics, neurology, quantum physics, and cosmology. If you wish to reach me, contact me at biohazard@gmail.com.
Notes:
(1) I chose not to include explicit mathematics on this page because the provided links contain enough maths on their own. If readers show interest, I will introduce more mathematics the next time, and perhaps explain the subject in greater detail.
(2) Albert Einstein claimed “God does not play dice” in response to Quantum Mechanics use of probability. Bohr replied “Einstein, stop telling God what to do.”
(3) Professor Ian Malcom, in Jurassic Park 1, uses chaos theory to accurately predict the inevitable fall of the park.
(4) The video extracts were made available by www.numb3rs-online.net. I merely uploaded them on YouTube.