The applicability of models|
Until now the terms rule and model have been used loosely as synonyms, which they aren't. A collection of rules is not a model. A model usually contains a lot of rules, but what a model adds to them is some common theme, if only to maintain consistency. The model is usually some kind of real or imaginary image, that serves as a token for the collection of rules. This is at the same time the second important advantage of a model: one doesn't have to remember a collection of loose items like rules, but a single encompassing image, from which one can surmise the rules, when one needs them. There is a sense in which one can say that the advancement in the thinking of mankind is possible only through its capacity to make models, to concentrate his experiences, and thereby make room for new ones.
The first science to be successful with models of reality was astronomy. This has a simple reason on that astronomy deals with matters that are easy to observe objectively: stars and planets. The ease of observation is mainly due to their constantly repeating behaviour. That is: the stars, because initially the planets seemed to wander aimlessly between the stars, hence their name: planet is Greek for wanderer.
The second big advantage for early astronomy was the fact that all stars look alike: they are all points of light. The only observable differences are their brightness and colour, and for the latter one has to observe quite carefully. So it is easy to get all stars in the same category.
The early development of astronomy has been of little practical value the general development of mankind. The simple reason is that whatever happens in astronomy, it doesn’t happen on earth. For this reason also, astronomy could have been omitted from this story in its entirety, since this website is in principle concerned only with reality here on earth.
The first successful science on earth was physics. This has the same reason as before: physics is about those phenomena on earth that are reasonably objective, and easily repeatable. The important issue is to remove the noise: it doesn’t matter if you’re using a rock or a lump of iron, what matters are its weight and the velocity with which you throw it. But even more importantly has it shown to be that one believes it is possible to make generalized statements about reality, that is: you must be willing to have reality not depend on your own influence (dancing for rainfall), or the whims of some deity (praying for rainfall). The basic facts of mechanics were within the limits of both Greek and Romans, where the latter have shown themselves to be amply equipped at the practical technical level.
After the fall of the Roman Empire with all of her technical and organizing achievements, progress in the description of reality was stopped by the Christian religion. Probably this was an improvement over the pantheon of gods of the Greek and Romans, since it concentrated the locus of control into one hand.
Modern science started when the world of the late middle ages came into contact with differing descriptions of reality, coming from the Roman, Greek, and Arabian worlds. Another important point of progress was that the contemplation of the world was no longer limited to philosophers, who see this mostly as an esthetical activity, but now included people with a more practical mind: theory is beautiful, but it also had to mean something in the real world.
The first rules discovered by physics were formulated verbally, and were of the if-this-than-that kind, but considerably longer, and usually written down in Latin. Later it turned out to be possible, and much more convenient, to translate this in symbolic language: if “this” gets bigger, than “that” gets bigger in precisely the same ratio, turned out to be translatable in (that) = (number)*(this) , where “number” is constant. If one expresses “this” and “that” in numbers too, it is convenient to distinguish these variable numbers from the constant that is usually called c. The choice fell on x and y (and if necessary z), so that our rule becomes: y = c*x. Using this kind of rule one can do a lot. This rule and its close relatives are called one-to-one rules, and using all one-to-one rules, one can do an awful lot in the description of the world.
Physics has known two centuries of spectacular development using the one-to-one rules, with the first industrial revolution as one of its consequences. It lasted until one entered the level of the individual building blocks of matter, the atoms, and the behaviour of the individual atoms came into play. The pressure exerted by a gas, e.g. the air pressure against a window, is the result of a very large number of atoms colliding with the pane. The laws on pressure are ordinary one-to-one rules, from a discipline called thermodynamics, that also treats things like the steam engine, petrol engine, refrigerator, etc. But if you want to discuss the behaviour of the individual atoms inside the gas, you need a new discipline called statistical dynamics. This discipline is a lot more complicated than thermodynamics.
The transition to a new discipline had as a background that one now also has a new kind of relation: a one-to-many relation. The pressure isn’t caused by one or a few other entities, but by the collective behaviour of a very large number of individual atoms, or: pressure is related to atom as one to many.
Characteristic for this situation is what happens if one starts decreasing the number of atoms while keeping the effect of their collisions the same by increasing their mass. Initially the pressure of the window will remain the same. However, if one decreases the number very drastically, say to about a thousand atoms, one hears the individual atoms tap on your window. The pressure starts varying with the number of atoms that collide at a given time, while still remaining the same on average. This new phenomenon of variations is reflected in the naming of the discipline that describes this behaviour: statistical mechanics.
At the previous turn of centuries, the human mind and the behaviour of societies came to be subjects of organized study. After a period of initial development, these disciplines also came at the stage where one wanted to formulate rules. The obvious choice was to try to use the kind of rules that had been so successful in physics. Unfortunately, one was acquainted with the one-to-one rules, but not with the much more difficult one-to-many rules. And most of these disciplines, sociology, psychology, economy, etc. (the humanities) had to deal with situations where the influence of the individual was noticeable, i.e. with a statistical character. So the attempts at making rules turned into almost as many disappointments.
Besides these practical arguments, there is another cause for the very limited success of the humanities: many of its followers have the rule that human behaviour is not susceptible to rules. Some have the argument for this rule that every human is unique, others are sufferers of the attitude of cynicism . However, as so often happens inside these disciplines, the daily practice contradicts the explicitly formulated theory, as in the example of the economist who states that increasing the taxation will lead to a lowering of the general income of the economy.
These observations are here considered proof enough to state that a large part of human matters is indeed susceptible to description by rules, though frequently not of the simple kind. This goes even at the level of individual human behaviour, as is apparent from the following obvious example: “If you kick someone’s legs, you have a considerable chance he will get mad at you.” (by a doing simple experiment on the subject, one can replace the term “considerable” by for example 67.3 percent).
On this website, the most important application of one-to-many relations is in the ladder-of-abstractions. A one-to-many relation usually also defines a new level in abstraction: the entity of “humankind” is at a higher level abstraction than “human” or “a group of humans”. In reality, it turns out to be possible to make a subsequent number of these steps, together called the ladder-of-abstractions; more on this important subject here.
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