Mathing with Theo

Malia and I ate a restaurant this weeked that didn’t accept credit or debit as payment. While I was a bit dismayed at first, the 10-20% lower cost of the meal was more than enough to appease us! It turns out that credit cards are actually quite expensive (up to 5% of the transaction cost) for a business. It seems that the credit card companies have figured out how to make money coming and going.

As such I thought that I would reproduce a piece I wrote a few months ago about the evils of credit cards.
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Ever wanted to know the true numbers and sacrifice required for the world to get totally off fossil fuels?  Well in the following article (reproduced from the archives) I have produced them!  In summary, it’s far less than you think.  I conclude that with only about 1% of the earth’s available land mass covered in currently available panels we can power the whole world.  What the heck are we waiting for?

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A Random Walk Through the Stock Market

Have you ever taken a random walk in the park? If you say yes, then chances are, you are incorrect. Nearly everything we do has purpose and direction to it…if only because our minds have trouble doing anything without it.

The Stock Market exhibits a mathematical phenomena we call a Random Walk. A truly random walk in the park would mean that one starts off in the middle (or somewhere else), spins a four sided dice and decides to take a step forward or backward, left or right, based on the dice roll. Now aside from the question about whether a dice roll is truly random we will say that the path taken by our dice rolling park-walker is random. It may even look like this…

This is a depiction of what a 2 dimensional random walk would look like.

So how does this relate to the Stock Market? If we look at the stock market as a random walk in a 1 dimensional park, or a tight rope, than the price is randomly walking from low to high….or at least it is very nearly randomly walking. Google has been marching upwards for a while, while Microsoft has been backpedaling for a while now. But for the most part we can look at a stock as a very indecisive tight rope walker, he flips a coin and takes a step forward, flips the coin again and takes another step forward, flips the coin a third time and goes back, etc. etc.

So how can we take advantage of a random walk? Let’s say that you and a buddy go to see the random tight rope walker. Let’s say that your friend likes to gamble. He says to you….I’ll bet you $1 that every time the tight rope walker flips that coin, you can’t predict whether he will go backwards and forwards. Unfortunately, your friend is unaware that you are an expert in coin flip pattern recognition, and you are able to predict heads or tails with 55% accuracy. As the hours wear on you begin to slowly increase your profit. In fact, if you plotted your profit, it may look something like this…

Your gains in the stock market provided you can get 55% accuracy.

Thus, a random walk not only describes the movement of the price of a stock, but for a day trader, it describes the value of his bank account. Therefore, one can nearly always make money in the stock market, provided one can predict the next general movement of the market with only a slightly better than 50% accuracy level.

So the real question is….why spend time trying to predict whether my favorite stock will shoot up 20 points in the next month when all I need to focus on is predicting the up and down movements and letting the laws of probability and Random Walk work in my favor?

Many times throughout my studies in Mathematics the question has been posed, “What are you gonna do with a Math Degree…teach?”. Being prideful I always said that I was going to use the right side of my brain to make a million dollars in the stock market. But in the case that one chooses to be a professional mathematician and has no passion to make millions on the stock market, here are a few more career paths. Note: engineers are mathematicians with a much more practical guise. An engineer with a formal mathematics training is usually in much higher demand, just ask my friend Derrick at Ball Aerospace!

Graduate degrees that would be much easier by being a Mathematician in undergraduate studies:

-Any kind of engineering degree that requires computational simulations (Chemical, Structural, Electrical, Mechanical…etc)

-Computer Science that is computationally oriented (Artificial Intelligence, Computational Science, Machine Learning…etc)

-Cognitive Science/Cognitive Philosophy (computational simulations of the brain are the way to go these days, but Statistics will also play a large part in any research)

-Statistics/Probability - past the introductory level, Statistics is more mathematical in its approach to proving undergraduate level concepts.

-Economics

-Sociology

-Operations Research/Industrial Engineering

-Meteorology

-Physics

-Astronomy

-Financial Engineering/Finance

-Medical Science - From M.D. to Ph.D., Statistics and Math are heavily used

Jobs that Mathematicians can do well, even though most employers may not know it:

-programmers - Mathematicians have developed symbolic and representational language skills, in other words we think in terms of algorithms.

-Flash/Multimedia - Most Mathematicians are not only good at programming, but given a few art classes, their appreciation for the beautiful world of math can easily translate into a great all around Flash/multimedia developer!

-Optimization - nothing irks Mathematicians more than inefficiency. No matter what the task, if a Mathematician can produce a quicker faster solution he/she will. Most know quite a few ways to utilize computers to their full extent to produce the optimal solution to many many tasks.

-Stock Analyst - Who better to crunch numbers, analyze trends, and make predictions than one has has trained their whole life to do so?

-Business Analyst - Again, who better to carry out the needed statistics, probability, financial analysis, and optimization of assets than someone who has been trained in that language? Give him an MBA or a little business training and you’ve got a guy who can really break down your odds of succeeding in the business world.

-Teacher - Mathematicians are used to breaking down very abstract concepts into something useful and explainable…thus making excellent instructors.

-Small applications developers - Mathematicians love problems, and love solving them, and then love moving on to another problem.

-Renewable Energy - Mathematicians love free stuff - thus Mathematicians love renewable energy.

-Aerospace - Nothing says solve me to a Mathematician like an outer space problem.

-Weatherman - All Weather Models are constructed by systems of PDE’s (Partial Differential Equations) or Probabilistic Markov Chains, who better to understand them than a guy/girl who knows not only weather, but the mathematics underlying the predictive models?

-Audio Software developer - lots of audio processing algorithms rely on a mathematical understanding of sampling, efficient processing, and digitization of analog signals. For instance how do you turn the noise from a guitar into sound stored on your hard drive? Easy! Take 96,000 samples per second of the audio signal and turn each audio sample into a 32 bit integer. Make sure you have a large hard drive!

-Banking - aside from accounting (which most Mathematicians would turn their noses up at) who better to predict the effects of interest, foreign influence, and all kinds of factors on whether I the bank president should loan more or less money to the public?

-Insurance - One of the largest money makers and potentially largest money losers in the event of a large natural disaster…who’s going to figure out the rates to charge the customers?

-Computation and Computer Simulation -This is a fairly obvious job for a Mathematician, but what’s not obvious is that most of the worlds computer and business systems rely on fast algorithms to get the data they need to keep infrastructure up and running. For instance today’s computers with yesterdays computational algorithms would accomplish less than half of the amount of data processing. Most companies and institutions also run simulations of their projects using mathematically based models to get an idea of how well they will succeed with their venture.

-Google/Web search developer - Google utilizes very heavy mathematical technology to get you the search results that you need and want. Any email or Internet spam detection algorithm is developed by Mathematicians/Computer Scientists.

-Astronaut - Driving in outer space requires that one have a great knowledge of Math and all of the Physical sciences. Just watch Apollo 13! They sure did a lot of hand computations when those computers went out!

-Epidemiologist - The center for disease control employs many people gifted in Math to make predictions on disease rates and uses those predictions to help curb infections and diseases.

-Video Game maker - it’s true, how else would they make 3d looking games without the power of Linear Algebra?

There are hundreds of other opportunities to employ the brains of the brightest and best Mathematicians, just take a look around. Any real life problem can be formulated in terms of an equation (even if they are generalized). Mathematicians love equations. Why not give them a crack at it? And if your chosen Mathematician is sociable, then you’ve got a real ally on your side! While it’s true that Math can’t solve problems like loneliness or your cat running away, it is useful for many things, in addition to teaching (though teaching is a great profession, and most Mathematicians love it)!