CIS 197 Computers in Society Professor John Peterson Philosophy Week!

Algorithms I've heard from ALMOST everyone so far. Remember to do everything I asked for! I would like a NICE 1 page powerpoint to post on our bulletin board.

Philosophy and CS There are some very deep ideas and some unanswerable questions hanging around in computer science. This week we'll tackle the foundations of computing.

The Universal Computer What is the simplest possible computer (mechanism) that can compute anything that any other computer can? Is this computer as powerful as human reasoning? Observations: * Logicians and philosophers have already attacked this issue! * Alan Turing recast this in a computing context

Alan Turing Turing and Alonzo Church both addressed the idea of computing machines in the 30’s, way before real computers were available. During WW2, Turing helped break the code of the German Enigma machine. He also took on areas that were closer to Philosophy that CS

The Turing Machine Computation is expressed as a set of (numbered) instructions Instructions are very simple! Data is stored on a “tape” one bit at a time The tape is infinite in length but can only advance or rewind one bit at a time.

A Turing Machine Step 1: Step 2: Step 3: Step 4: … Write a 0/1 Move 1 bit forward/backward Tape sees a “1” “To infinity and beyond!” The Program

Instructions * Write a 1/0 onto the tape * Move tape forward / backward 1 bit * Go to a specified step number * If there is a 1 on the tape go to a selected step number * Halt (the program is done!) Note that you could easily be a “turing machine” – the program would be written on a book and you would read the instructions, work the tape, and turn the pages

The Input / Output * The tape initially contains the program input (a “question”) * When the program stops (halt), the tape contains the program output (the “answer”) * Start the program at step one * Note that this describes a function in the mathematical sense The construction of this machine is deceptively simple! It defines a “universal computational process”

What a TM is Remember the TM is not a program – the book with instructions is the program. It is the “machine” that makes an arbitrary program work. A Turing Machine is capable of solving ANY computable problem! No other machine can solve “more” problems – others might be faster but not more capable

An Example Programming a TM is very painful! Here is a program that takes two bits coming and writes out a 1 if both bits are 1: Step 1: if tape = 1 goto step 4 Step 2: write 0 Step 3: halt Step 4: move tape forward Step 5: if tape = 1 goto step 7 Step 6: goto step 2 Step 7: write 1 Step 8: halt

The Church-Turing thesis A Turing Machine is sufficient to solve any problem that can be mechanically described. A Turing machine can handle form 1040EZ A Turing machine can play chess Note that we don’t promise how fast the machine will go – this addresses what is computable, not how easily it can be computed.

The C-T Thesis and Philosophy Why is this a "thesis" (we believe this to be true) rather than a theorem (we can show this is true)?

Consequences of C-T The deep consequence of C-T is that we can’t find a computational task that we (as humans) can do but machines could not. In another view, what this implies is that once a process is defined well enough to be a computer program, it is no longer any sort of mystery. So making a computer that has human responses is limited by our ability to define human response rigorously.

The Church-Turing Thesis Vote NO on the Church-Turing Thesis! The C-T Thesis: Turing Machines may be dumb but you’re no smarter!

The Turing Test If we can't find a "bright line" separating machine intelligence from human intelligence, how are we to distinguish one from the other? Turing proposed a deceptively simple test: talk to a machine and a human in a manner that disguises the speaker and make a decision based on the conversation.

The Turing Test My son passed the Turing Test!!

Learning Machines The final section of Turing's essay is about learning. Rather than teach a computer how to master a specific skill, why not teach it how to learn? Why isn’t programming more like education?