I suppose I hadn't really considered this aspect of my childhood as driving me toward programming and planting the seeds of interest in things like robotics and artificial intelligence, but my dad was a huge fan of Isaac Asimov.  Arthur C. Clarke was also a favorite, and I recall that he briefly even had a subscription to or just a single copy of OMNI magazine - a magazine that occasionally featured stories about the Bermuda Triangle, Alien Abductions, and other psuedo-science themed stories. I hadn't even considered that this was driving me to Machine Learning, but on reflection, as such a powerful part of the formative years of my life, certainly my father's interest and my curiosity in these sources of science fantasy are certainly a part of this very rewarding trip down the machine learning path.

I bring this up because of a YouTube video I've seen recently from Computerphile about the Three Laws.  If you don't know what the three laws are...why are you here reading this?  Anyway.  The expert in the video explains so well how ridiculous the three laws are when talking about a.i.  I think his point explains why, though I'm not an a.i. researcher, I haven't considered the three laws.  When you're thinking about getting a machine to learn to solve a problem, it's so obvious that the machine has to follow such a deterministic line, no matter how curvy or straight, it just can't solve for every possible set of data...so the idea of expecting machine learning to even understand the first law is so obviously out of the realm of possible at the moment that it truly isn't worth considering the three laws.  And as the speaker points out, Asimov created the laws to write stories where the three laws are violated in some way or other.  Really wish I had thought to write about this before the video, but I clearly don't have enough people commenting on here to get a few commentors who would ask such a question.

So what is a human?  What is harm? Write your answers on a sheet of paper, and see if someone can think their way around the laws given your definition.

Of the many operations that I didn't understand, this one stands out in the material I've been going over to learn about Machine Learning.  Yes, there are other symbols I don't understand completely yet, but I'm going to focus entirely on understanding the summation operator in this post.  While I kind of understood the phrase "summation operator" to mean adding a bunch of numbers together, I did not understand the exact steps of the process.  Also, why is there a number or variable at the top and to the right of the sigma, and what is under the Capital-sigma.

Before I get started, my source of information is the Wikipedia article on Summation.  If you find my explanations lacking, you are more than welcome to go straight to the source.  My aim is to explain briefly the summation operator, so that the notations can be understood by someone looking into machine learning without a deep math background to allow them to get a quick grasp of the meaning of the notation.

Breaking it down:

What does the k in k=0 mean?  k in k=0 is the index of summation. If you've done any coding and used arrays, then you know exactly what an index is. It is just the position in the array.  

The 0 in k=0 is the lower bound of summation.  In other words, the beginning of your index.  If there is a beginning, is there an end?  Yes, the upper bound of summation, and in this case it's the 5 above sigma. 

Now, why is there another k on the right side of Capital-sigma?  This k tells you what, if anything, to do to the value of k before including in the summed value.  So for example if it was 2k that would indicate that you multiply the value of k by the value of 2 before adding it to the other values.  It could be k^2, sqrt(k), or any number of functions before adding to the sum.  

This is a massive summarization of the summation operator, but there are plenty of sources of information.  I've included some C# code that shows how you might implement a simple version of summation.  There are more complex summation operations, but this should give you a good base understanding on which to build as you learn about machine learning.

Look for Siraj Raval.  I have to say that the math and formulas behind machine learning can put anyone to sleep, but not with Siraj.  I find his YouTube videos to be quick lessons in machine learning that you may have to watch two or three times...or use the pause button to take in the complexities, but because he delivers the information with excitement, it can be much easier to watch the second or third time.