Robots are the Way of the Future

Robots are the Way of the Future

I have this really cool robot called Roomba made by iRobot. It vacuums the floor for Malia and I. All we have to do is push the clean button and away he goes zipping around the carpet in a semi chaotic pattern until it's all clean. And it works too!

This is a great development for 2 reasons

1.) It's just cool.

2.) It really does save us time.

Statements like Robots are the way of the future may seem kind of cheesy and cliche. However, I would like to say that there are plenty of cool robots out there. And as Artificial intelligence and Machine Learning develop, robotics will only become more and more useful.

A few months ago on PBS's Nova a program about the Great Robot Race , sponsored by DARPA, was aired in which many vehicles competed to be the first completely machine driven vehicles to make a trek across a desert in California/Nevada. The winner was a small SUV driven without the help of GPS (which is amazing!). It operated on stereo vision, laser vision and a few other sensors, all controlled by a computer with Machine Learning software. Essentially the researchers who created the small intelligent SUV taught the car to drive in the dessert, and it succeeded on the gruelling 150 mile course with an average speed of more than 25 mph!

The significant thing about robots like the winner of the DARPA challenge and Roomba, is that they are actually learning the task set out for them. By learning I mean that the robot's own internal algorithms are being modified as the robot carries out it's task in response to poor or good performance. If you think about it, we learn this way most of the time. In fact, our whole public education system falls under the category that these robot's education falls under: Supervised Learning. (Well ideally at least, a lot of education falls under the category of the 'Expert System', where the teacher poses as an expert and relays his wisdom and knowledge to the student via memorization.)

Supervised Learning is the process where a student is presented a set of examples (descriptions and their corresponding object), and asked to perform a similar identification task on some previously unseen examples. The performance on the unseen examples is evaluated by a supervisor, and the feedback given to the student. The student takes the feedback and reshapes her internal processing algorithms. The process repeats until the supervisor is satisfied with the student's performance.

Robots can even become so good at learning, that they can interface with our brain's functionality! In this story, a man has a prosthetic arm attached to his body and nervous system. Over time, he and the robotic arm are learning to communicate with each other...now that's cool! Star wars is no longer the fantasy world.

I love Machine Learning and Artificial Intelligence, not only because we can use it to make prosthetic arms and automatic carpet cleaners, but because it teaches us something about ourselves. When we explore the world of learning we also question how it is that we know things. We question what knowledge is, how we obtain it, and ultimately what reality is. And at the end of those questions we will always have more, but that's the point of learning!

An estimate of the Probability of getting a 4 Letter Acronym Formed by Blog Subtitles

Kent at The Digression blog asks: What is the probability of a blog's subtitle's first letter of each word producing a meaningful acronym?

Apparently the subtitle for my blog makes the acronym MPEG. MPEG is the acronym for a file format that contains movies or motion pictures.

Well be careful what you ask for, cause here's my answer! :-)

First, let's simplify this by asking, what is the probability of producing a meaningful 4 letter acronym given that the blog has a 4 word subtitle.

The probability of getting a meaningful 4 letter acronym given that the blog has a 4 word subtitle is: P(4 letter meaningful Acronym blog has 4 word subtitle).

Using Bayes rule of conditional probability, we can say that P(4A blog4subtitle) = P(blog4subtitle 4A) x P(4A) / P(blog4subtitle).

The P(4A) = #meaningful 4 letter Acronyms / #of Possible 4 letter Acronyms

The P(blog4subtitle) = #of blogs with 4 word subtitles / #of blogs, the probability that out of all blogs, the chosen blog has a 4 word subtitle.

The conditional probability P(blog4subtitle 4A) = Probability of getting a blog with 4 words in the subtitle given that it has a 4 letter meaningful acronym) = 1

So then P(4A blog4subtitle) = 1xP(4A) / P(blog4subtitle).

Let's proceed shall we?

A rough estimation of the #of meaningful 4 letter acronyms is... well that's kind of hard. Ok so here's where we can get all statistical.

On Wikipedia we can find a list of all acronyms known to wikipedia . Sampling the population of A acronyms I can count that for each section of the A page (26 sections, the acronyms are broken down into the AA, AB, AC...AZ sections) there are about 10 4-letter acronyms. Let's assume that the actual number per section is distributed according to a normal distribution ~ N(10, 2)...i.e. The number of 4 letter acronyms per section is 10+-about 2 per section. We can do this because for large n, the binomial distribution is approximated by a normal distribution. There are 26 sections per page...and 26 pages...thus 676 sections. Taking this into account, we can say that the number of 4 letter acronyms in existence has a sampled distribution of ~N(676*10, 676*2) which means that there will be on average an estimated 6760 4 letter acronyms based on our small sample distribution of 1 section of the A acronyms on wikipedia.

On the other hand computing the number of possible 4 letter acronyms is easy.... 26X26X26X26 = 456976.

Estimating the number of blogs with 4 letter subtitles is also difficult. But again, let's say that the number words in the subtitle of a blog is distributed according to a binomial distribution with mean 6. Assuming that the max number of words in the subtitle is 20, the probability of getting a 4 word subtitle can be approximated by 20!/[4! x 16!] x .3^4 x (.7)^16 = .13 This means that obtaining a blog with 4 letters would be the probability of obtaining a 4 letter blog times the number of blogs available.

The available #of blogs is 66 million...according to BlogHerald .

So(P(blog4subtitle) = .13 x 66million/66million = .13

Thus our final estimation of the probability of getting a meaningful acronym given a four word subtitle is distributed according to a N(6760/456976/.113, 1352/456976/.113) distribution. (It is a distribution because I had to estimate the number of 4 letter acronyms in order not to have to count them.) Thus I can't be 100% sure what the real probability is. However the mean probability from my estimation is about 11.3% with a variation of 2%. And I can say with 99% confidence that the true probability of obtaining a 4 letter meaningful acronym given my 4 word subtitle lies between 6% and 16%.

That was fun wasn't it? With statistics anything is possible to estimate!

What you can do with a Math Degree

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.
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.
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!
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)!

Reasons Why

I have started this blog for a few reasons. I hope that my posts are useful and productive for myself and anyone else who stumbles across them. Hopefully I will have at least one post a week on one of the following topics:

1.) Green Technology - all things that give us free energy, or help to conserve energy without making my life a drag.

2.) Math, Statistics, Machine Learning and the Stock Market - I'm currently joining the ranks of modern day alchemists and trying to predict the stock market on a day to day basis. I agree that if successful I will eventually defeat myself because I will sway the market one way or the other. But a boy can still dream

3.) Philosophy - any philosophical musings and ideas. The nature of the mind. Psychology and all of the "soft" sciences.

4.) Entrepreneurship - I'm excited about getting into the business world. I'm trying to focus on non-pie-in-the-sky million dollar eyes and instead focus on how to take a non-sexy idea and make a profit from it.