Cognitive Science – 14/01/13 – Juensung Kim Before we can define the more philosophically sticky problem of what it means for a system to be “interpreted,” it would be beneficial for us to complete the task of defining the more scientifically concrete aspects of a computer. One such aspect is the concept of a digital nature, something which is strongly associated with formal systems. Most people equate a digital nature with a binary nature, but this is not at all the case. The computer age has appropriated many scientific terms for its own use, and in doing so has twisted their meanings. That, however, is a topic for another paper. So what is it for a system to be digital? Haugeland defines a digital system as “a set of positive and reliable techniques for producing or reorganizing tokens or configurations of tokens from some pre-specified set of types.” What? Let’s break this down a little bit. The first term that should jump out at you in this definition is positive. A positive technique is simply one that has a chance, no matter how indefinitely small, of succeeding absolutely. Guessing, for instance, is a positive technique for getting a correct answer on a test. Leaving it blank is not, or at least, not on most tests. Note that “succeeding absolutely” is a relative concept. It is downright impossible for something to go exactly according to plan no matter how good your method is, so it is usually said that a positive techniques is one that can succeed absolutely relative to a certain acceptable standard within an accepted margin of error. Now, considering that guessing falls within the definition of a positive technique, we clearly need to apply some constraints to this. After all, if a formal system, and by extension your computer ran off of guessing, just how efficient do you think the thing would be? About as effective as you were on that midterm you didn’t study for, I should think. So we avoid this problem by saying that a digital system is a set of reliable, positive techniques. A reliable technique is exactly what it sounds like: something with a reasonably high success rate. Again, it can’t be perfect, nothing can be. But 99.99% is better than 50%, right? Now onto the meaning of “producing or reorganizing tokens or configurations of tokens from some pre-specified set of types.” This is the wordy bit, and you are more than excused for feeling lost. This bit of the definition refers to the main function of digitality in a formal system. This function is two-fold, with the parts labelled as writing and reading. To “write” is to reconfigure the formal system’s tokens according to its rules. Think of it like the alphabet. Those of you studying linguistics may see where I’m going with this. Within the written English language are 26 tokens, plus however many punctuation marks are in common usage and Arabic numerals. When we arrange these tokens according to the rules of the English language, we are writing. And when we use the rules to identify what it is we have written, we are reading. When a digital system “reads,” what it is doing is reidentifying the tokens in use after they have been rearranged or reconfigured. To bring back the example of a chess game, the computer “writes” when it moves its queen, and then “reads” afterwards in order to ensure that the piece that it moved is still recognizable as a queen.
This is how a formal system remains self-contained. This self-identification process allows the system to be self-correcting, enabling it to run itself without outside interference. If a system cannot “read” what it “wrote,” then it fails and requires outside interference. A system that requires outside interference to run is not a formal system. So Haugeland’s definition can be rewritten as follows: a digital system is a set of write-read techniques that are positive and reliable such that the system maintains its formality. Of course, as previously stated, there needs to be a margin of error, this
