Math, Geometry and #LoveWins

Books tend to find me…

I was at the airport waiting for my flight to San Francisco (June 2015) when a Hudson Booksellers caught my attention. They had a buy two get the third book free sale but because of the short flight ahead, my interest was on acquiring just one book. A quick read. Something to keep me entertained while the ERJ-175 completed its two hour trip to my final destination.

Why a book? I knew that there was a very small chance the airplane had IFE or In Flight Entertainment System. Why? Because the cost of installing, operating and maintaining the IFE in such a small aircraft (seats about 70-80 people) is very high and adds no value to the profit of the flight (it also adds weight to the aircraft which requires more fuel and reduces the seat revenue margin). How do I know this? Airplane Interior design and configuration was one of the many roles I used to have at my last job.

Browsing through the New York Times Best Seller shelf I found a misplaced book. What were the odds that the particular tome was destined for me? Not as small as you might think. The moment I walked into the airport and to the gate, the options to find this particular book depended on the number of selections each store carried. Assume that all the book sellers were the same, as is the case in many airports; about 500 unique books total. That implies I had a 1/500 chance to find this particular tome in each store. Since I already knew what categories or literary genres didn’t interest me that narrowed the choices even more. By browsing the entire store I would have had about 20 possible choices and this book had a 1/20 chance of going home with me. Those are not bad odds!! However, what puzzled me was that some other human left the book at the perfect height and location for me to find it. Leaving it in the wrong location expedited our encounter. I wish I knew who had done it to thank them profusely even though the store clerk and I would have liked that the book had been placed back where it belonged.

That’s where fate or destiny came into play. According to physicists, there is a theory that proposes we live in the best possible world (assume there is a multiverse) and that everything that happens in our reality is the best possible outcome. Therefore this book was meant for me, or at least that was what my intuition led me to believe. As an engineer, the title will make you understand why the book chose me.

How Not to Be Wrong, The Power of Mathematical Thinking by Jordan Ellensberg was exactly what I needed to read. As a hardcore math geek, I had always been impressed by the many theories of numbers and how they explained the beauty and laws of nature in a universal language. Regardless of faith, religion, creed or nationality, we can all understand numbers and the implications of algebra and geometry; the human experience reduced to the patterns and colors, textures and sounds we absorb through the senses in their purest form. Numbers are universal.

As the airplane took off, I read through the introduction where the author presents the need for his book: When am I going to use this? Students around the world have asked this question a million times and most likely they got an answer that dissuaded them from pursuing a career in the field. Other than paying bills, calculating tips and sales, or getting accurate change, most humans don’t resort to math to translate what happens to them into probabilities and statistics (or to encode digital data or avoid coding mistakes, for example). When we read a book or experience an event, we are not looking for the science behind the scenes but rather enjoy the environment absorbed through the senses and the feelings these provoked. We don’t think of light particles or wavelengths but we do recognize the shapes in front of us and passage of time.

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“Mathematics is the extension of common sense by other means.” – Jordan Ellenberg

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The book mixes humor, philosophy, math and history to prove why there is so much more to life than grade school math. Every day we benefit from the math behind the scenes: Hamming’s and Shannon’s theories to code digital data; game theory to predict outcomes such as the lottery or the next home run champ. Although there is math in every thing we do and experience not everyone’s intuition is the same, especially since it is highly biased by how well our brains think in mathematical terms. Until I read this book I didn’t have a way to qualitatively explain to the world how my mind works. The numbers work themselves out in my brain and give me an edge over my counterparts by processing and interpreting the available environmental data wisely.

This is the main reason why I have never missed a flight, or have been able to be on time for most of my life events. Why I am not easily surprised or can guess what you are thinking or need to hear. My brain thinks in terms of deviations to the norm, safety factors, averages, regression to the mean, patterns and scatter plots to process the information and mentally determine the best course of action. In my case, my common sense is accurate and effective because of my understanding of math and its implications. I could predict when meetings would get cancelled, the best days to take a sick leave or vacation. In some cases I deduced correctly that X friend was going to announce a pregnancy or wedding after years of reading their facebook feed. These same people didn’t realize I knew they were not going to make it on time to an event based on past behavior and road conditions. It is very hard to dispute the result when the variables have been identified and the equations are computed correctly.

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Math doesn’t lie. Humans do and often bend the data to their advantage.

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The author uses real life events to describe the opportunities mathematicians have had to influence and affect the world. Anecdotes from Greek times to the Second World War are introduced to help us visualize what we mean by math is an expression of common sense and how humans may bend the data to their advantage. When you see a problem, the solution may not be apparent because the visual in front of you may be incomplete. Think of all the possible scenarios that would lead to a flat tire.  All the data the Michelin or BF Goodrich folks need to account for to design the perfect run flat tire, or rather the one that works for most occurrences. We make the mistake of thinking causality or correlation is linear; most phenomena can be described by curves and have many slopes and variations.The example provided about raising or lowering taxes is enlightening. (If you earn more than 200k, or have a family income that places you in the top 10% of the earners in the USA, you must read the Less Like Sweden chapter.) Many advances in science and technology were brought about and enhanced by mathematical applications, and we are still learning and improving on existing theorems and computational algorithms. One day, we may be able to accurately predict what your next decision may be and how it would affect others! (Think Captain America: Winter Soldier.)

For me, the best part of the book was the explanation of utility and its unit the util, which Ellensberg introduces to explain how probabilities can be judged as high or low risk by people. Be it believing in God or placing a bet, utility and probability will drive the individual to assess the risk of the enterprise differently, literally better or worse for them than for others, depending on how carefully they assign a value to the odds. Sometimes the thrill of gambling or the rewards of believing in a higher power will trick our common sense to place a bad bet. For example, if you spent $2 to win the lottery and actually win it, the benefit for you is going to be greater than for Bill Gates. Gates most likely will not have an internal motivation to place the bet because he stands to lose very little and gains very little too. (Part II Chapter Ten all the way to the end of Part III explains this better than I ever could in such a limited amount of space.)

– Hmmm, but what does all this have to do with #LoveWins?

As I mentioned, I was on my way to San Francisco and the day after I landed, I woke up to promises of the most epic Pride Parade and Month celebration ever! The Supreme Court voted to legalize same sex marriages citing that denying the right to the LGBT community was unconstitutional. It was not a unanimous decision, which was to be expected, but only in San Fran could you appreciate the immense support the community has from businesses and people. Even before the decision was announced Pride flags lined the skyline. People gushed over how spectacular the events were going to be for the weekend. They even had fireworks!

We all knew it was about time the law allowed marriages to take place nationwide. It is good for the government’s coffers and opens up a new arena in an already prosperous field; event planning. Even the conservative right should have realized they were being outnumbered. However, why didn’t they? Because they didn’t consider all the variables and undermined the opposition’s strength. They became the minority. They ignored the trend and the separation of Church and State. They choose to believe in a skewed set of data, or just their perspective. Their loss was our collective gain even though in their eyes “God would have not allowed this to happen”. Think about that for a second. If God exists this would have not happened. What’s the alternative? That there is no God and they were duped! I’d be upset too.

What were the odds that all these events converged? (The book, the flight, the parades,the verdict, the vacation, and my interest in writing.) Very high. Consider that the decision’s announcement must have been planned in advanced of the celebrations, to make them more meaningful and special. My being there to witness it all? That chance became high the moment my family planed the holiday during the parade time frame even without realizing it. Departing from a gate near a book store? That was due to airline tickets being cheaper that weekend, and the airline having chosen to depart from that particular concourse, which is the only contribution to the mathematical problem I had. Or did I?

Coincidence? After reading this book, nah, I don’t think so.

P.S. The book has a lot of math terms that I didn’t use and some that I glossed over. Read the book. The “Are you there God? It’s me, Bayesian Inference” chapter will blow your mind. If Mr Ellenberg Googles himself and reads this, I hope I did a good job at representing the dialogue. After all, I’m just a mechanical engineer with a passion for Calculus and sexy math symbols. He he!