Subject: Are Class Lectures Computable? From: "William J. Rapaport" Date: Fri, 5 Mar 2010 11:27:42 -0500 (EST) After lecture today (3/5/10), I thought of another example of a mundane procedure (in Cleland's sense) that is recipe-like (in Preston's sense): Teaching a class. Typically, teachers prepare a written "procedure" for what they will do in class on a given day. In elementary and secondary schools, these are called "lesson plans"; in colleges and univesities, they are called "lecture notes" (or sometimes they take the form of Powerpoint slides). Some teachers follow them slavishly, reading their notes or slides. Others ignore them completely and come to class giving wonderfully polished (or amazingly awful) extemporaneous lectures. The former are, arguably, treating the lesson plans as algorithms to be executed faithfully. The latter (if they're good teacher) probably only seem to be being extemporaneous; but I know from the few times that I've carried that off successfully, it really requires a lot of preparation or experience, which is tantamount to saying that it is really based on a procedure, as described in the next paragraph. Other teachers use lesson plans/lecture notes as rough guides, improvising as necessary based on such "causal" issues as: * questions that students ask or comments that they make (which can steer the class in a different direction than the instructor had planned), * time constraints (which can require the teacher to do some "online editing" of the procedure, saying something extra here, or omitting some things there), * which physical objects are in the room (if I want to give an example of a color, I might use the color of a student's jacket; or if I want an example of a small physical object, I might pick up a particular piece of chalk, or, if there's no chalk, I might use a pencil, etc.). So, they are mundane, they are procedures, they are effective (well, hopefully they are effective :-), the "executor" can --even must--improvise to carry them out. Are they Turing-computable? Cleland, I think, would say "no", but only because teaching such a class based on such a lesson plan depends on what happens in class on that day, whereas TMs are "causally inert". Philosophers who are not sympathetic to AI would also say "no", for more complicated reasons having to do with the complexity of the task and the apparent inability of TMs to "improvise". We'll talk more about this last point later in the semester when we talk about AI. (I think those are not good reasons.) My reaction right now is that, although a teacher's lecture notes/lesson plans probably *are* procedures, they aren't *algorithms*. They are more like what I referred to in class as "specifications", which require details to be filled in when converting them to programs. So, is Cleland right? Are there "effective procedures" that are not Turing-computable? And is a lesson plan an example? I seem to have said "yes" above (when I said "a teacher's lecture notes/lesson plans probably are procedures, [but] they aren't algorithms"), but I think that this notion of "effective procedure" is not the one that Hilbert, Turing, or Church had in mind. I think that the notion of effective procedure of which a lesson plan or recipe is an example is more like the specifications for a more precise algorithm. Once the details are filled in, then it would be Turing-computable. Comments? (If you want to respond to the entire class, please use UBLearns Email https://ublearns.buffalo.edu/webapps/blackboard/execute/displayEmail?navItem=email_all_users&course_id=_80768_1 Then: CSE484:Phil of Comp Sci -> Communication -> Send Email -> All Users If you want to respond just to me, just reply to this message, but I reserve the right to repost your reply (anonymously) via UBLearns Email.) ======================================================================== Subject: Re: Are Class Lectures Computable? From: "William J. Rapaport" Date: Fri, 5 Mar 2010 12:52:09 -0500 (EST) A student writes: "1. When we speak of a TM, we may be thinking of the concept of a machine that has certain behaviors and capabilities, or the physical instantiation of such a contraption. Surely a concept can't affect things in the physical world because it is not in that world, so labeling it "causally inert" is clearly true. But if a TM was actually built, just as surely it would be causally linked to its outputs. Only physical things can affect the physical world." Reply: I think that's right, which would mean that Cleland is comparing apples and oranges (or, to use a better metaphor, she's comparing pictures of apples with real oranges?). And, as Sarah suggested in class, you could connect the 0/1 output of a (real) TM with some other device that would interpret the 0s and 1s as instructions to do something physical. The student continues: "2. Could we weaken Cleland's many-universes problem by prefacing our recipe with "calibration" instructions of the form "if the temperature in our universe is ... set ..."? The recipe would then be written in terms of the parameters set by this prologue. To be useful, this demands that there be sensors specifying the required physical parameters of the current universe, but so does the judgment in "following" the instructions." Reply: So, if I understand you correctly, you're suggesting that a procedure that says "do this, this, and this" could be embedded in a conditional construction: "if you're in universe U1, then do this, this, and this; else if you're in universe U2, then do that, that, and that," etc. I think this is correct, too, and tantamount to what Preston calls "improvising", only instead of doing the improvisation at the moment of execution, you set up all the alternatives ahead of time. By the way, it's my understanding that's more or less what improvisational comics do: They plan out a bunch of skits ahead of time, and choose which ones to do depending on the audience's suggestions; they're not necessarily making everything up as they go along.