Category Archives: Learning

The Bliss of Ignorance

21 Friday Feb 2014

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I am not god’s gift to computer science (CS).  Nor am I when it comes to programming.  There.  I said it.  Why, in a public setting, would I admit my short comings?  Would it not be better to sell my strengths?  Perhaps.  But this admission takes a lot of pressure off of me.  People can no longer expect me to be perfect.  I don’t have to live up to those expectations.

You have no responsibility to live up to what other people think you ought to accomplish. I have no responsibility to be like they expect me to be. It’s their mistake, not my failing.”
― Richard P. Feynman, Surely You’re Joking, Mr. Feynman!

This admission opens me up to new possibilities: I can learn to be better.  I can improve my technical skills if I open my mind to the idea that there are always new things to learn.  Isn’t there a Zen story about tea cups?  If the cup is already full there is no more room for more tea… no more room for new skills.  No room for more knowledge or wisdom.  I may not be god’s gift to CS but my degree was the best gift I ever earned.  It was in the earning of my degrees that I learned HOW to learn.

While the degree gave me the skills to learn, I still need people to learn from.  Admitting my CS weaknesses removes the fear of appearing ignorant because I AM ignorant.  But my ignorance is only temporary.  I used to feel intimidated approaching colleagues who are smarter than me.  Now I seek them out and ask for help.  I found that most technical people love to help you when you seek their expertise.  This was not easy at first, and I had to seek some professional help.  Professional as in reading the bio of jazz legend Pat Metheny.

Pat would purposely seek out musicians that were better than himself.  “Always be the worst guy in every band you’re in”, he once said.  Something interesting happens: your skills transform and becomes more like better guys.  I don’t know how to explain it, but I noticed something similar while playing golf.  If I am in a group where my handicap is better than everyone else, I don’t learn anything new.  Sure my ego feels good if I beat everybody, but I don’t improve; and sometimes I perform worse.  But when I am in a group where I am the highest handicapper, I seem to do better.  My focus is on keeping up.  I’m not taking risky shots.  I am more aware of my current ability and I play with in that ability.  Furthermore, I can learn from others while observing their short game, their putting, or how they cope with errant shots into the hazards.

The harder you work, the luckier you get.

Gary Player

One other technique I use to improve my technical skills comes from my experience during grad school as a TA teaching math.  The more I taught algebra or calculus to students, the better I got in those subjects and I began to UNDERSTAND, profoundly understand many of the concepts that I just accepted at face value from my instructors and the text books.

To Teach is to Learn Twice.

Ancient Proverb

Often, If I want to learn new skill or sharpen a current skill, I will seek out opportunities to create a class and teach it.  I find this technique strengthens understanding.  It is one thing to learn a skill; yet another to learn how to explain it, in your own words, so another human being can understand this skill, too.

The sages may have been right in their claims that ignorance is bliss.  But learning new things, and teaching them to others is blisser*.

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* Yeah, I know its not a word.  I am currently working to improve my grammar and vocabulary.

Computer Science Education Week December 9 – 15

07 Saturday Dec 2013

Posted by in Computer Science, Learning, Programming

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Teaching students programming and computer science one hour of code at a time.  Here is the official site where you can learn how to become involved.   I thought I would take an opportunity here to make my contribution.  In this lesson, I will use as my guide, a great introductory to Computer Science (CS) text, often referred to as the “purple” book, or the “wizard” book.

What is Computer Science?

Computer science is really a misnomer.  It is not a science.  We don’t study a system, observe phenomena, and run experiments to validate a hypothesis.  Computer science is not a study of computers anymore than biology is the study of microscopes.  A computer is simply a tool.  And computational devices come in many different forms.  There are the silicon-based binary gadgets that you use everyday, like laptops, tablets, and smart phones.  But they are poor imitations of the most powerful computing device ever created: the human being.  We are a bio-mechanical machine, performing our computations in base 10.  And of course, we are capable of much, much more.

Declarative and Imperative Knowledge

Computer science is not a science; it is more of an art — an engineering practice.  Computer science is really about knowledge.  The knowledge of how to do something: solve a problem, perform a task in a methodical, mechanical process.  This process is called imperative knowledge.  It is the knowledge of how to do something.  Declarative knowledge, on the other hand, deals with the facts.  Let me illustrate with an example found in the purple book.

Example: Square Roots by Newton’s Method

An example of declarative knowledge:

The above is a fact about square roots.  You can find it in any basic math text.  In words: the square root of any number x, is a number y, where y is a positive number, and if I multiply y by itself.  I get x.  For example: let x be 4, then y must be 2 because 2 times 2 equals 4.  You can reason the same for 16, or even 625.  Larger numbers are harder.  You may have to make some educated guesses before you stumble upon the correct answer.
Well, that is all fine and dandy.  But what if you were given: \sqrt{2} ?  How can we use the above declarative knowledge to figure that out?  And that is the problem of declarative knowledge.  It doesn’t tell you how to calculate the square root of 2 — or how to find the square root of any number.  The declarative statement can only tell you how to recognize a square root if you saw one.

Newton’s Method

To solve the square root of any number, we will use a very old algorithm called Newton’s method.  Ironically, the method starts with a wild-ass guess (a WAG, we call it in the scientific and engineering community).  Then we refine our guess with successive approximations until we get to an answer that is good enough for government work.  Let’s construct our algorithm based on Newton’s method:

To find the approximation of the square root of x:

  1. Make a guess G
  2. Improve guess G by averaging G and x/G
  3. Keep improving until the guess is good enough.

Simple, right?  Don’t take my word for it.  Try it out.

table

Compare the 1.4142 with your calculator’s square root button.  You should see the 1.4142 plus a bunch of other numbers.  We solved out to four decimal places (to the 10-thousandths place), and that is good enough for us.

Now let us write this out as a recipe of instructions:

Square Root X:

  1. Make a guess G
  2. Is it good enough?:  absolute_value(G*G – X) < 0.0001 then G is the answer and we can stop; otherwise go to next step
  3. Improve guess G: G = (G + X/G)/2
  4. Repeat step 2.

So let’s step through our recipe.  First make a Scientific Wild-ass Guess.

Next we test our guess by, first squaring our guess and subtracting that guess with X.  We take the absolute value because your guess may be less than the square.  For example, in the square root of 2, our first guess was 1.  1 – 2 = -1 and we don’t want a negative number because we are measuring the distance between our guess and the perfect square X.  And since negative distances don’t make sense, we take the absolute value, which means we first remove the negative sign, and then see if the answer is within some threshold of tolerance.  In this case, less than one-ten-thousandths.  Or put another way, we will keep refining our guesses until we calculate the square root to four decimal places.  If our guess is less than our threshold, then we stop and G is our answer.  If not, we go to step three to improve our guess and repeat the process.

Try our recipe above out with a piece of paper and a calculator and see if you get the same results as in the table above, if you let X = 2.

If you made it this far, my dear reader, I want to congratulate you.  Together we wrote a computer program.  Our program is not in a traditional computer language like C, or C++, or even Python.  But it is in the language of English and math.  Any reasonably intelligent human computer, with some knowledge of middle school, or high school math should be able to follow our recipe (algorithm) and effectively become the square root button on a calculator.

I hope the above example gives you an idea of what programming and computer science is about.  Now, if you really want to learn a programming language, first pick a language and a site you can learn from.  I recommend code academy and the language of Python.  Python is very easy to learn.  Once you get the basics and the syntax down, see if you can take our little recipe above and translate it into your new language, and get a computer to do all this hard math stuff for us.

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