3.16 Characteristics

When we talk about a "character" of a person, we think about a set of observable traits, such as intelligence, humour etc. In physics, a similar word - characteristics - is used to determine how the physical system responds to a given stimulus. When we know the complete set of stimulus that may affect the system, and we know the responses of the system for each of them, we can say that we know its full characteristic. By knowing this, we can predict how the system will behave in any given situation ("any given situation" means "a given set of stimuli").

Figure 28 shows a physical system consisting of a spring attached to a ceiling. Learning the characteristic of this system consists of an examination of the spring under load, how the spring will behave. The baseline measurement, indicated in the figure by 0, is when the spring is unloaded. In the series of measurements (in the figure labeled 1, 2, 3) the spring is loaded with different weights. Each time its lowest point is recorded. The figure shows that 1kg caused an elongation of 2cm, 2kg caused 4cm and 4kg - 8cm. The results of these measurements are shown by the large, aligned, red dots.

A question arises: if we load the spring with 3kg will it extend by 6cm? To answer this question we must have the patience of a monk to carry out a long series of measurements of elongation, slightly changing the weight by, for example, one gram. Each time, the result must be recorded in the form of a pair of numbers: the first showing the weight and the other the elongation. As a result, we obtain a set composed of several thousand pairs of numbers. Some of them are shown in blue in Figure 28. Who can remember several thousand pairs of numbers? If you can see, however, that all the points are located in a straight line, you want be obliged to memorise all pairs of nombers. This line represents a rule or pattern with which you can calculate the elongation according to the value of the load. A set of several thousand pairs of numbers and this rule represents characteristics of the system. But the rule is concise, and what's more, it can be analyzed easily. To explain, the rule in this example is: elongation measured in centimeters is two times larger than the load measured in kilograms. It can be presented as a function, x = 2 * F (where x - elongation and F - load). If we treat number two as a parameter, the function will be: x = b * F. Now examining the different springs of a linear characteristic, we can distinguish "hard" springs (when b is small, a large weight is needed to bend the spring) and "soft" ones (when b is larger).

A characteristic may depend on many factors. A characteristic of a spring may depend on the number of extensions, on temperature. In addition, we cannot overload the spring, because too much weight may break it. So, a characteristic should also specify the scope of the permissible load. In summary: Characteristic is a function that shows how the input factors are converted into output factors, and the briefer this function is, the better.

An example of characteristics may be the nature of a child. When it obeys the parent, we say that it obedient, but when it does the opposite it is naughty. Adjectives "obedient" and "naughty" are not as accurate characteristics of a child as a characteristic of our spring. However, the child is not a spring, it is a complex living object and then thus, it is immposible to define their characteristics in the form of a simple and precise function with several parameters. As we can't precisely define the character of a human being, we use probability distribution. For example, if we attack an army in a given way, we know that 50% of the attacked soldiers will flee, 30% will surrender and 20% will bravely defend. But we don't know which soldiers will perform which action.

Assume that a certain living object has a property which has a value of 50. This may be, for example, the length of an aphid's antenna. In the case of asexual reproduction, based on the genetic design of this living object, new projects are created and, on these projects, new living objects are built. As we already know, the designs on which the offspring will be built, although they come from the same parent (or parents in the case of sexual reproduction), they may not be the same. This is because, during the copying phase, some random modifications may occur. Note that the term "may" and "random modification" do not say anything specific about the nature (characteristic) of the changes. Let's consider the case when a parent gives birth to five offspring. After measuring the value of the property we have been talking about, it appears that three children have the same value as their parent and is valued at 50. The other two are different: one's value is smaller - 49, and the other, larger - 51. Look at Figure 29, which illustrates this situation. The arrangement of the blue lines appears to be a normal distribution, to some extent, doesn't it? Note that they are arranged in a manner characteristic of a bell curve. Thus, the modifications were not absolutely random. There is no such possibility that in one single design transfer a given value will suddenly change from 50 to 100. So the characteristics of "random modification", as it has been named, is not random. It has its own characteristics which can be described as followed: the duplication process reproduces 60% of copies precisely, for 20% the value of the property decreases by 2% and the remaining 20% increases by 2%. This is a very methematical and precise description of this characteristic. However, in nature, it is less exact. The values will slightly vary, for example: the duplication process reproduces approximately 60% of copies precisely, for about 20% the value of the property decreases by 1-3% and in the remaining copies the value also increases by 1-3%.

Fig. 30. Characteristic A

Fig. 31. Characteristic B

When we look at living objects, it is not difficult to discover certain regularities governing their structure or behaviour. Let's look at two photographs of trees (tree-type objects). Both of them are different. Whilst walking in the woods, where we can quickly see that some of them are more compact and others are more expansive; some branches shoot straight up and others are horizontal. The construction of each type of tree has its own characteristics, which stem from somewhere, defining how the tree looks and functions.

So, why do we need characteristics? If we know how the system or object will react to certain stimuli we are able to predict what will happen in the future. The more compact the characteristic's description is, the easier it is to form predictions. The second reason is that by explaining the characteristics to others, we speed up the transfer of knowledge.