# Quantifying hate

As a gay man who has been "married" for 15 years and has a 3.5 year old daughter, I am livid about yesterday's vote in North Carolina to adopt a constitutional ban on gay marriage. Since this is a math blog, I'm not going to write anything else about my feelings. If you want to hear about my feelings, you can read this speech I delivered to the faculty at my institution yesterday, which was about happenings in Minnesota, not North Carolina, but is still relevant.

Instead of talking about my feelings here, I will present you with some quantitative food for thought.

There are 31 states that have enacted constitutional gay marriage bans of one sort or another. I've taken the data on that link and compiled it into a publicly accessible Google Doc so that you can mess around with the data if you wish.

I don't have it in me right now to do any fancy modeling (I am still too angry) but I did upload the data into Wolfram Alpha. I've blogged before about Alpha, which is a great tool. If you upgrade to a pro subscription (I am not a salesman... I do find the upgrade to be a little pricey) you can access even more convenient features, like uploading data sets and such. This is what I did with the marriage amendment data. I didn't even know what I wanted to do with the data, so I simply typed the name of my data set as the query, and Alpha decided on all kinds of analyses to spit back out at me. Here is some of it. I guess that if there is a pedagogical point here, it's that the way a quantitative modeler often gets started is just by plotting things.

Here's a geographic heat map where the shading corresponds to the fraction of votes supporting a discriminatory measure in a given state. The reason Nevada shows up as over 100% is that there were two votes in Nevada, one in 2000 and one in 2002 (each one receiving in the high 60%'s range). At any rate, I don't see too much structure in this map.

Here's a histogram of the years in which the discriminatory amendments passed.

You can see that 2004/05 were busy years. Here's what I think are the most interesting plots, namely a histogram of the discriminatory vote percentage and a distribution fit (which you can get a feel for via the quantile plot on the right). Alpha finds that the best fit distribution is uniform.

I am not yet sure what I want to do with any of this, but it at least lets me start trying (perhaps in vain) to make sense of the hate in this country.

# Alpha dog

Let's talk about the unavoidable Stephen Wolfram.

The mathematicians and non-mathematicians among you will likely have heard of Wolfram. He's a physicist, mathematician, and computational scientist who developed a useful bit of software called Mathematica for numerical and symbolic computations. He's also a MacArthur Genius and the presenter of one of the most popular TED talks. Much earlier in his life, when he was 20, he became the youngest-ever recipient of a Caltech Ph.D., a status he has retained by a hair over my former undergraduate student Catherine Beni.

In 2002, Wolfram published his book A New Kind of Science, which sought to explore the nature of computation and its relationship and applicability to the real world. The scientific community received this book with mixed feelings. Most mathematicians I know are quite critical of the book, both for its apparent egotism and lack of rigor. I think it's fair to say that the academic math community considers the book to be a swing and a miss.

In contrast, Wolfram's real home run is his computational knowledge engine Wolfram Alpha, launched in 2009. I can't urge you enough: go play with this amazing tool. You can ask it a huge range of questions related to mathematics and, more broadly, data of many different sorts. While most mathematical and computational tools require input to be given in a particular syntax, Alpha uses natural language processing to try to figure out what you are asking it. You don't need to learn a programming language or any particular querying commands.

To get a sense of what Alpha can do, I challenge you to try to find:

• The derivative of $x^y ln(xy^2) + 3e^{cos(x/y)}$ with respect to $y$
• When the next solar eclipse is
• How the U.S. climate has changed from 1900 - 2011
• What a fractal known as the Pythagoras Tree looks like over 10 iterations
• How many days you have been alive
• What the geographical distribution of life expectancy in Africa looks like
• What year Henry David Thoreau's Walden was published
• For how many years Flintstones and the Jetsons overlapped on the air
• The Scrabble score for the word exogenous
• How many medals Michael Phelps has won
• How Netflix stock is doing lately
• How much a \$250,000 mortgage at 5.5% over 30 years costs
• What demographics in Egypt are like
• How long it would take a 44 year old male weighing 90 kg to lose 17 kg if he eats 1500 calories per day
• Where the first flight out of Chicago went to today

In the interest of keeping this post accessible, I've focused on general knowledge in the list above, but make no mistake about it: Alpha can do serious math.

Much like they decried the advent of calculators, some mathematicians and mathematics instructors decry Alpha for how it will allegedly ruin mathematics education. With a freely available, Internet-based tool that can differentiate, integrate, solve differential equations, compute eigenvalues, make graphs, and do so much more, what is the motivation for students to learn symbolic mathematics?

While I don't deny that symbolic skill is necessary for people who will become mathematicians, I nonetheless vehemently disagree with the old-school outlook above. Wolfram Alpha is going to ruin math education no more than the advent of calculators did, and no more than abacuses did. Computational tools are a natural, healthy, and useful part of civilization's mathematical progress. Consider this: the basic algebraic knowledge an educated person has today constituted advanced, cutting-edge research in ancient times. No one cries about the fact that we no longer do mathematics the same way as the ancient Egyptians, Greeks, Babylonians, and Mayans. Computational tools free us to think about ever-more advanced and complex ideas, and ideas are what math is really about.