The Intuitive Path

It should be clear from earlier postings that, in this class, we want to investigate algorithms not as theoretical structures born of definitions and theorems, but as real, manifest, and colorful-- whatever that means, whatever they turn out to be, whatever flavor of ontology turns out to apply.  And we want to get there by going straight ahead down the path of inquiry, not branching through a thicket of terminology.

I wish to guide the class into ideas that come directly from their own experience of algorithms.   I admit to a lack of rigor.  I look about, ready to seize upon any justification for this plebeian approach.  And I find one-- experimental philosophy.

The young professor Joe Ulatowski, already known to us and visiting here for a year, came to my class for a discussion of experimental philosophy.  From this, the students gained (1) a general definition, based on the usual ethical issues such as trolley problems, (2) an understanding, and validation, of how the querying of our own and others' thoughts might aid the articulation of the concept of the algorithm.

I tossed out a couple of thought experiments, thinking that they were trivial and would be supplanted by more sophisticated version.  They have served well, however, and are still providing food for thought.

1.  Company A runs this algorithm to generate payroll: Take hours, take rate of pay, multiply together hours 40 or less to get the pay, then multiply hours over 40 by (rate*2), and add that to the pay.
Company B runs this algorithm:  Take hours, take rate of pay, multiply together hours 40 or less to get the pay, then multiply hours over 40 by (rate*1.5), and add that to the pay.  Are they executing the same algorithm?  Answer by consensus:  Yes, because the overtime rate is easily parameterized.  But what if Company B applies different overtime rates to different positions?  What if Company B adds a bonus in its payroll processing?

2.  In Company A, a manager wants to see a list of all of the staff, available in database table or spreadsheet form, grouped together by division.  Her assistant runs the sorting algorithm on the "division" field, knowing that the grouping is a result.  Is this single program executing two different algorithms?

While probing our intuitions about algorithms, we have built up a question set.  At first, I hoped to organize it into some kind of hierarchy, but that did not happen; the need faded away.  It remains heterogeneous and unorganized, like traditional brainstorming results.  Here are a few samples.

2.  Does an algorithm have to be digital?  Or symbolic?
8.  Is the algorithm a "natural kind?"
12.  Is the imperative construct compositional?
19.  Is developing algorithms an art or a science?
36.  What did Al-Kwarizmi actually say about algorithms?

The question set is the students' basis for both expository and philosophical essays, now underway.  And, by the way, we're still arguing about whether a recipe is an algorithm.

The First Couple of Weeks

The class has started off, with neither a bang nor a fizzle, but with satisfactory activities and solid interest.  Because my students did not sign up to serve as subjects of public discussion, and because the only view that I can relate is that of the instructor, I will forgo describing the class proceedings.

Suffice it to say that I am balancing the technical and the abstract, usually in each class session, by (1) examining and practicing algorithm tracing and representation, with simple sorting, searching, and encoding; and (2) discussing philosophy in general, and posing questions about individual and comparative features of algorithms.  We have read the entry, "Philosophy of Computer Science," in the Stanford Encyclopedia of Philosophy, and we have read Moshe Vardi's letter, mentioned previously, in the Communications of the ACM.  And I am assigning and collecting a steady stream of written work. 
I have taught, in a cursory way, more of the technical matter than I thought would be necessary at the start, such as semantic functions and compositionality, monotonicity, the entity-relationship model, with set theory coming up.  But no student is in danger of mastering those subjects in this class. 

We are also, in this course, testing a new Learning Management System, which brings our high-minded inquiries down to earth for dealing with the intricacies of web interfaces.  And we are discovering that some of the classrooms no longer provide the equipment that I expected.  I'm pleased to say that these mundane details of teaching are offset by the interesting questions and speculations already at play in the class.

Pedagogical Goals

What are the objectives of the course?  In my case, I want to bring together two formidable disciplines into a junior-level one-semester course, the students in which will be required to have minimal experience in academic philosophy and computer science-- to wit, an introductory course in each.  For this subject, there is no standardized test for assessment.  That context informs my high-level list of course objectives, quite spare, which can be summed up as (1) to assimilate, and (2) to explore:

1. To master a grounding body of knowledge and an appreciative curiosity about the philosophy of computer science, to the extent of cogent explanation to others.

2. To build respect for both disciplines, especially in students from the other; to promote pride and concomitant rigor in the student's own discipline.

In other words, for objective 1, I will be happy if the students can explain the subject matter (algorithms in general, and a few in particular), and can also produce some reasonably substantial and accurate answers, in real time, when their friends ask, "Dude, what was that class about?"  This is a modest goal.  Flights of fancy would embrace serious scholarly work in the field, and even the refinement of the subject matter of the Philosophy of Computer Science itself...  As for objective 2, like all instructors, I want to bring about the kind of transformative contemplation that helps cultivate a breadth of wisdom and keenness of intellect in my students. 

Besides the large goals, it's time for a few preliminary methodological goals to serve as the means to the general ends.

I want to provide concise but thought-provoking materials, encouraging students to contribute to formulation of texts, questions, and answers.  I want to integrate the materials via regular references to elements of the course elsewhere, such as examples, tables, definitions, and past exercises.
I want to replace vague undirected blather with pointed and disciplined inquiry-- even if speculative-- and exposition.  I want to traverse a clear path through the materials-- even if selective-- that fosters "deep thinking."  I want assignments that give the students something meaningful to do, large enough for challenge and small enough for achievement, that delivers a worthwhile outcome.

Note that the objectives listed are independent of the theme, but it is meant to be inserted firmly into the placeholder "grounding body of knowledge" in objective 1.  Even though my position in a faculty development center favors me with revolutionary educational theories of all stripes, I hold a traditional view of content:  There should be some.

In fact, there should be plenty.  Scoping and circumscription of the appropriate body of knowledge, focused on the theme chosen, will be an initial challenge of this new course in this new subject.