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The Turing Test, Part One

March 8, 2015

My time in the Beach Flats neighborhood of Santa Cruz was my first experience living outside of my hometown of San Diego. It was also my first experience as a full time college student.

I had decided to major in philosophy for the simple reason that I loved the subject.  It was purely a decision of passion–it had absolutely nothing to do with reason (David Hume would have been proud!)  As a newly minted philosophy major, I was told that if I wanted to do graduate studies in the subject, I had to take something called Advanced Symbolic Logic.  I did want to do grad work in philosophy–what would be the point of studying it otherwise?–so during my second quarter at UC Santa Cruz I signed up for the recommended course. I wasn’t intimidated at all. I had taken two other logic classes at the community college, and enjoyed them both.  Advanced Symbolic Logic seemed like a challenge I was up for.

Except that it wasn’t.

Most of what you study in your introduction to logic classes is comparatively pretty basic.  You start by taking deductive arguments and turning them into syllogisms, like so:

If it is raining, I will meet you at the theater. It is raining. Therefore, I will meet you at the theater.

Then you turn that into this:

\frac{P \to Q,\; P}{\therefore Q}

And you get to refer to it by it’s cool Latin name, Modus Ponens.  Then you’re off on your way to mastering logic.  The problem was that I had clearly not mastered it as well as I thought, because Advanced Symbolic Logic very quickly began to look like this:

My teacher was Professor Otte (whom you met earlier).   He sported a well-kept beard and was never dressed in anything but a t-shirt and shorts.  The t-shirts always made some reference to rock-climbing, and he was so laid back, he didn’t even bother to write-up and distribute a syllabus.  He outlined the class on the chalkboard the first day.  That was our syllabus.

I was also the only undergraduate in the class.  The other six students were linguistics and mathematics graduate students, so the class was largely a seminar on concepts with which I struggled to keep up.  Every week, during professor Otte’s office hours, I was there waiting for him when he arrived and he would do his best to re-teach me what had occurred in class that week.  When his office hours concluded two hours later, he kicked me out. He was far more patient with me than I think he actually wanted to be.  Thanks to his help, and my determination, I did manage to keep up with the class–albeit with a thoroughly fragile understanding of what was transpiring.

A few weeks before the end of the quarter, Professor Otte announced what our final exam was going to be: we had to design a Turing Machine, named after Alan Turing, the great mathematician and computer scientist who helped break the German Enigma code during the Second World War.  Modern day computers wouldn’t exist without Turing, so it was a fitting exercise to replicate the logic he used in their design.  Our assignment was to design two programs that would carry out a specific required calculation each time.  For instance, if the task was to always give the sum of two numbers minus four, it would have to work no matter which two numbers were put in.  If I put it in a 6 and 7, it would answer 9, if I put in a 3 and a 2, it would answer 1, etc.

The first program I designed worked perfectly, and it took me all of ten minutes.  Emboldened by my new confidence, I tackled the second assignment.  This was taking much longer.  It would work three, four, five sometimes six times, and then not work on the seventh.  I spent hours every day trying to design the program, and then the next day I would hand a disc to Professor Otte, hopeful I had succeeded.  At the next class, he would hand the disc back to me and bluntly observe that “it doesn’t work.”  I was growing increasingly frustrated.  There was clearly a solution, but I wasn’t finding it.  Worst of all, time was running out on the quarter, and the professor made it clear I would not pass the class without two functioning Turing Machines.

I was in trouble.

 

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