Philosophers have been known to get quite indignant about coding information as vectors of real numbers. They point out, correctly, that there is much, much more to the physical system than turns up in the description. This, they asseverate, is even more true for any attempt to describe something as subtle and difficult as human thought processes. They usually stop at this point, waiting for an attempt at rebuttal.
Computer scientists committed to Artificial Intelligence (AI) tend to use symbol strings to describe objects. Well, a vector is a symbol string too, of course, but the AI worker tends to prefer alphabetic strings of varying length. A natural language such as English is an example of such a system. This system, the only one most philosophers know how to use, also abstracts a pathetically small amount of information concerning the system described. The definitive poem about love which says all there is to say, has not yet been written and is unlikely to be short. Since poets and other literary men have not illuminated the rest of us very effectively on the details of how to build any complex system, we may conclude that natural language has its strengths in other areas. It works well for asking people to pass the salt or telling them you love them, the latter being more an expression of an internal state than a proposition having verifiable content, but in the main it simply codes our ignorance in ways we don't understand, while a mathematical theory codes our ignorance in ways which we do, to some extent, understand. The computer language LISP, much favoured by the soi disant Artificial Intelligentsia, is another language which allows easy coding of information about objects in terms of symbol strings. LISP is about half way between natural language and Mathematics in terms of precision and scope, so the results of coding information in LISP strings usually results in the worst of both worlds.
To give an example of what we might accomplish with string representations of data, imagine that we have got a coding of each individual in the data set of the guys and the gals from Fig.1.2., so that instead of having him or her represented by two numbers we have a list associated with him or her. One such individual might have the list:
Similar lists, let us suppose, comprise the rest of the data, all of which describe either men or women. Now the job of working out the category is simply a matter of finding the seventh item on the list and scanning the string until finding the colon,`:'. The next symbol should be either an `m' or an `f'. This solves the problem.
But does it? What if the data were obtained by asking people to fill in questionnaires about themselves, and someone put `yes please' in answer to question 7? Or the respondent was firmly of the opinion that it was none of the interviewers business and said so? Well, we could go to the name in item 1 and look up the first name in a dictionary of names, sorted by sex. Unless the person is Chinese in which case it is the last name. Or we could argue that men seldom wear dresses, hate lipstick and have bigger feet than women. In general, some application of quasi-logical rules to the strings is required in order to come out with a conclusion. We may have to bear in mind that the respondents can (a) tell lies, (b) decline to answer some questions or (c) have idiosyncratic views about the right answers to the questions. Even if the lists have been compiled by some other person, the items may contain unexpected anomalies, like Jay Spondulix who likes coral lipstick and has preferred apparel `none'. Is Jay a man who likes his women with coral lipstick but otherwise nude, a woman who has no particular preference for what clothes she wears, or some combination? The fact that the procedure by which we obtain the list in the first place is so unreliable and that the meanings are ambiguous and vague, means that algorithms applied may easily produce nonsense.
Physical systems, by contrast, have the measuring processes much more tightly specified. It is true that the process of obtaining weights and heights may also have been carried out badly, but there are methods for determining weights and heights which are fairly well defined, widely known and reliable. Doing them again on a different day usually gives results which agree fairly well, and when they don't, we normally feel justified in saying that the system has changed between measurements.
The question of how one obtains the description is of particular importance in automation tasks. There are programs which decide if something is a bridge made of blocks by examining the _is_next_to_ and _is_on_top_of_ relations between the blocks, but the question of how one gets such data in the first place is not addressed. And all artificial sensors such as cameras, microphones and strain-gauges produce output which can be coded as a vector of real numbers, and there is a relatively simple relation between the equipment, the world, and the values.
To be fair, well, fairer, to the Artificial Intelligentsia (their term, not mine), it has to be conceded that they have become aware of the importance of choosing powerful representations of data. The trouble is, they don't seem to know any. (This is just one more of the provocative statements I warned you about in the introduction!)
Imagine two people sitting in large cardboard boxes and unable to see outside, but able to hear a person reading a book to them. Person A in box number 1 is equipped with a long, thin roll of paper and a pencil. Person B in box 2 has a few pounds of modelling clay in different colours, a bottle of little flags on cocktail sticks, a few marker pens and some blocks of wood. Person C reading the book has a loud clear voice and a chair to sit on.
Person C reads out a description of the environs of, say, Mansfield Park, complete with lake, river, hills and houses. While this is done, A is scribbling the results down in sentences, while B is building a model out of clay and blocks and flags. Now suppose that there is an inconsistency in C's story. At one point, one statement is made about the geography and at another point a logically incompatible statement is made, such as asserting that a lake both is and is not in a given location.
For A to detect this, assuming he has not recalled it all in his head, he must continually go through the entire set of sentences obtained at each time and do inferences from them. Deducing the inconsistency may take a long time. For B, the detection is immediate; the inference is done by the modelling clay. And if sentences are given which are not logically inconsistent but are physically impossible, say that a stream runs uphill somewhere, in order for A to detect this, the sentences have to be augmented by lots of other sentences of naive physics, and the logic of the whole lot checked. It is barely possible that this could be done. While B, with his modelling clay, can detect such physical anomalies the instant they are asserted by C.
We conclude from this that one man's inference engine is another man's modelling clay, or more generally that what is done by logical processes under a sentential representation of data can be accomplished by other means very much more efficiently given a more powerful representation system. The most powerful general symbolic representation schemes have been developed for the physical sciences and involve measurements and hence representations of systems by vectors. They code for similarity or proximity. The language of functions can allow us to describe densities of data, and to measure the amount of surprise we get when something unexpected happens. By contrast, logic and computer languages are barbarous, uncouth and primitive. Only someone ignorant of better linguistic tools would tolerate them.
Compared with the sophistication of mathematical systems which have been devised over the last few thousand years, logic is a low level language, unsuited for dealing with the complexities of the real world. To be constrained to using logic is analogous to having to program in machine code. And logic, or variants of it with little more power, are all that the string representation enthusiasts have.