Classical measurement algorithms But if we want to develop the new measurement theory, the Let's start from the classical measurement algorithms used widely in measurement practice. Note that if we want to measure something we have to know the object of measurement and the range of measurable values. It is clear that there are different things to measure the cosmic distances, for instance, the distance from the Earth to the Sun, and to measure the atomic distances. However for all cases of measurement we will present the range of measurement as some line segment And now we can formulate the aim of measurement. The aim of measurement is to determine the length of the line segment Now we can "simulate" the "binary" algorithm acting at the line segment [0,8] as the following (Fig.1). The "binary" algorithm considered in Fig.1 consists of 3 steps.
- If the IE "indication" in the point 4 is equal to 0 (the IE has shown to the left) this means that the measured point
*X*is on the line segment [0,4]. In this situation the second step of the measurement algorithm is applying the IE to the middle of the line segment [0,4], i.e. to the point 2. - If the IE "indication" in the point 4 is equal to 1 (the IE has shown to the right) this means that the measured point
*X*is on the line segment [4,8]. In this situation the second step of the measurement algorithm is applying the IE to the middle of the line segment [4,8], i.e. to the point 6.
One may arise 4 situations after the second measurement step.
- If the IE "indication" in point 2 is equal to 0 (the IE has shown to the left) this means that the measured point
*X*is on the line segment [0,2]. In this situation the third step of the measurement algorithm is applying the IE to the middle of the line segment [0,2], i.e. to the point 1. - If the IE "indication" in the point 2 is equal to 1 (the IE has shown to the right) this means that the measured point
*X*is on the line segment [2,4]. In this situation the third step of the measurement algorithm is the applying the IE to the middle of the line segment [2,4], i.e. to the point 3. - If the IE "indication" in the point 6 is equal 0 (IE has showed to the left) this means that the measured point
*X*is on the line segment [4,6]. In this situation the third step of the measurement algorithm is applying the IE to the middle of the line segment [4,6], i.e. to the point 5. - If the IE "indication" in point 6 is equal to 1 (the IE has shown to the right) this means that the measured point
*X*is on the line segment [6,8]. In this situation the third step of the measurement algorithm is applying the IE to the middle of the line segment [6,8], i.e. to the point 7.
It follows from Fig. 1 that the "binary" algorithm subdivides the line segment [0,8] into 8 equal parts [0,1], [1,2], [2,3], [3,4], [4,5], [5,6], [6,7], [7,8].
It is clear that the above-considered "binary" algorithm divides the line segment [0,8] into It is important to stress that the given measurement algorithm is "optimal" in the above-considered sense. This means that it is impossible to find the better Note that if we write the sequence of the IE "indications", for instance 1001101001 ..., then the indicated sequence would present itself the "binary" code of the number corresponding to the length of the measurable segment But the "binary" algorithm is not the only algorithm of measurement. In our daily life we use often so-called For example we use the "counting" algorithm if we try to count up the number of our steps lying down in some distance, for instance, in the distance between our house and our university.
The "counting" algorithm demonstrated in Fig. 2 consists of 3 steps and makes use only one IE . It subdivides the initial line segment [0,4] into 4 equal parts for 3 steps.
- If the IE "indication" in the point 1 is equal to 0 (the IE has shown to the left) this means that the measured point
*X*is on the line segment [0,1]. In this situation the measurement process is over because the*X*-coordinate (*X*Î {0,1]) has been defined with "exactness" to the measurement unit equal to 1. - If the IE "indication" in the point 1 is equal to 1 (the IE has shown to the right) this means that the measured point
*X*is on the line segment [1,4]. In this situation the measurement process is going on and the IE is applied to the point 2.
- If the IE "indication" in the point 2 is equal to 0 (the IE has shown to the left) this means that the measured point
*X*is on the line segment [1,2]. In this situation the measurement process is over because the*X*-coordinate (*X*Î {1,2]) has been defined with "exactness" to the measurement unit equal to 1. - If the IE "indication" in the point 2 is equal to 1 (the IE has shown to the right) this means that the measured point
*X*is on the line segment [2,4]. In this situation the measurement process is going on and the IE is applied to the point 3. As a result we can get two line segments [2,3] and [3,4] in dependence from the IE "indication" on the last step.
It is clear that the above considered "counting" algorithm divides the line segment [0,4] into There arises a question: what measurement algorithm is the best? If we compare the "binary" and "counting" What difference between the "binary" and "counting" algorithms? We can answer this question if we compare a character of the IE movement in these algorithms. It is clear that in the "binary" algorithm the IE movement is "chaotic" because IE can move to the left or to the right regarding to the preceding step. Let's mark the "restrictions" on the "binary" algorithm as Let's consider now the "counting" algorithm. It is clear that movement of the IE for this case is submitted to the strong "restriction": the IE moves in the only direction from the left to the right. Let's mark this "restriction" as However until now we did discover nothing new! The mankind know these classical measurement algorithms many millenniums. However we ask our reader would be patient! New results are ahead! Follow us! |