Every day we face different activities whose results don't seem to satisfy the existent necessities totally. This sensation is observable in all the disciplines including, of course, the scientific investigations. It is sometimes easy to correct the causes that prevent to obtain the desired results. Other times, on the contrary, the desired results cannot be reached due to the existence of problems originated in the nature of the used methods, or determined by externals and non-controllable facts, or taken place by unknown causes.
They exist theoretical methods and computer tools that allow a detailed and permanent pursuit of any project, detecting in an immediate way any deviation of the reached objectives. It is very important to highlight that either these methods or tools can detect the problems after it having taken place. On the contrary, the Postulate allows to detect the problems before they taken place, avoiding the money and time losses.
Project is an extensive term that includes any discipline that is developed by human being, including all type of scientific investigations and technical applications. For general rule, to try to arrive to the desired result of a project, if it is not an easy and transparent one, it usually requires a logical sequence of stages (1).
The beginning of the solution of any project coincides with the starting-up of the first stage. In that moment it exists an accumulation of antecedents and previous studies, the motivation is high, the goals to be reached are known, exist the resolution to perform the task and there are not still any disillusions for the results that have not been reached. Such a concentration of favorable circumstances makes that the first stage of a new project contains the more value improvement. In the existent projects that want to improve, the first stage represents its current state and it is also that of more value, because the knowledge and the previous experiences are included on the topic.
Each improvement compels to evaluate its results and to study and to develop the adjustments to implement in the next stage. Then, if each stage contributes improvements to the previous problems, it is logical to suppose that the successive improvements applied to a project spread to have every time smaller values. These successive improvements are draw on the first quadrant (2) of a Cartesian orthogonal coordinates axis system (3) where each step represents a stage.
(Figure 1)
The total improvements reached at the end of each stage are on ordinates (I1... I7) and the different stages are placed on abscissas (S1... S7). It is visualized the evolution of the successive stages better, replacing each step for a segment that unites their initial value with their final value.
(Figure 2)
I0,S0-I1,S1... I1,S1-I2,S2 ... I2,S2-I3,S3...
The resulting curve (4) it is the representative curve of the studied project. Later on it will see other shapes that can take the representative curve, and their meanings will be analyzed.
Measure unit on the axis of ordinates.
The only datum that allows to evaluate the state of a project is the reached result, and its estimate depends on the experiences and knowledge of the evaluator. The estimate of the reached result is made by comparison with the desired result that one wants to reach, being evident the convenience of expressing the estimates in percentages. This measure unit, placed on ordinates, it is well known and easily governable, it allows to use the same scale for any project and their maximum value (100 %) it coincides with the value of the desired result.
Measure unit on the axis of abscissas.
It is not appropriate that the variable on abscissas represents the times of development of each stage:
- The time of development of the first stage cannot be represented in the same scale that the times of the other stages: for new projects the times of accumulation of antecedents and previous studies could be enormous, while it is uncertain the time to consider to improve existent projects.
- Some stage of smaller duration that the previous one, without significant contributions, it could modify the representative curve of the project.
- The incorporation of improvements delays would modify the representative curve, the one that would depend on situations foreign to the project.
In a system of Cartesian coordinates the relationship among the variables is: y = f (x). When fixing the variable on ordinates (y = percentual improvements), the independent variable on abscissas (x) has to contain all the current performing conditions. But not all the current performing conditions are well known and not all the well known ones can be evaluated, for what is impossible to define such a complex variable that it contains to all the conditions and their variations.
In order to simplify the problem, the same duration stages, which have unitary value, are locate on abscissas. In this way, it is generated a convenient variable that contains the current performing conditions, and that it transfers to the shape of the curve all their indeterminations.
CURRENT PERFORMING CONDITIONS (CPC)
They are referred to the applied theoretical concepts, the variables characteristic of each participating factor, the economic situation and politics of each moment, the techniques and tools used, the availability of times and of means, the work place and their qualities in each instant, and all the other non-controllable internal and external factors. They also include the aspects related with the personnel dedicated to the project: their capacity, quantity, tenacity, motivation, imagination, preparation, experience, personal relationships between the investigators and their problems (5), et-cetera.
MAXIMUM LIMIT OF OPTIMIZATION (MLO)
When increasing the quantity of stages and to diminish the value of the improvements characteristic of each stage,
In-In-1 = improvement of the Stage n (Sn)
I7-I6 < I6-I5 < I5-I4 < I4-I3 < I3-I2 < I2-I1 < I1-I0 ...(a)
the representative curve of the project approaches indefinitely, without reaching it, to a particular straight line called asymptote. This particular line is defined as the “Maximum Limit of Optimization” (MLO) of the representative curve of a project (Figure 2). Their intersection with the axis of ordinates (L) it determines the best result that can be reached if the same CPC stays.
ANALYSIS OF THE SLOPES
The slope (p) it is the trigonometric tangent of the angle formed by the segment of one stage and the axis of the abscissas; their value relates the opposed side (improvement) with the adjacent side (one stage) (6)
pn = (In-In-1) / Sn
(It is not included the value "S" of each stage because by definition is equal to 1)
p7= I7-I6; p6= I6-I5; p5= I5-I4; p4= I4-I3; p3= I3-I2;
p2= I2-I1; p1= I1-I0 ...(b)
Under the conditions (a) and (b) all the slopes are positive and the slope of each stage will be smaller than the previous slope
p7 < p6 < p5 < p4 < p3 < p2 < p1
When the contribution of a stage diminishes the value of the result reached in the previous stage worsening the situation of the project, it is proven that the slope of that stage is negative. The stages with negative slopes are not considered as such, but they should be studied to detect the commit errors.
CONCEPTUAL AND TRANSCENDENT CHANGES (CTC)
The characteristic tendency of a project, under normal conditions, is that the value of each one of the incorporate improvements is smaller to the value of the previous improvement.
But if the obtained results are not satisfactory the tendency should be modified changing the current performing conditions (CPC), making that the value of the improvement of the stage in study will be the same or higher than the value of the previous improvement. When the values of an improvement are the same or higher than the value of the previous improvement, the value of the slope are also the same or higher than the value of the previous slope. In these circumstances, the representative curve of the project elevates its trajectory and it modifies its direction. If the trajectory of the curve rises, the project value of the MLO (L) necessarily increases, and that comes closer this way to the desired result.
In the Figure 3 two improvements are shown as example: an improvement of the same value that the value of the previous improvement (I4) and an improvement of more value that the value of the previous one (I’4). Observe that when the slope rising, the characteristic curve of the project comes closer to the desired result.
(Figure 3 )The changes that allow to come closer to the desired result are so important that they are defined as “Conceptual and Transcendent Changes” (CTC): the applied ideas are replaced by different ideas; they are delimited or annulled the harmful actions; the latent possibilities are strengthen; aspects never considered before are now evidenced; the positive results spread to different situations. In occasions, the due results to the changes can be so surprising that they overcome the original expectations.
The incorporation of a CTC produces significant alterations to all that made until that moment. It should be studied the project again from the first stage, considering like initial improvement the value reached when taking place the change. When applying CTC to projects that would reach the desired result naturally, they diminish the times of work.
POSTULATE STATEMENT
"The successive improvements incorporated to a project generate results that they tends to a value called Maximum Limit of Optimization (MLO), which represents the best result possible to reach under the current performing conditions (CPC). If this value is not satisfactory, it is useless to continue incorporating improvements under the same conditions, because the desired result only will be able to reach applying conceptual and transcendent changes (CTC)."
The single application of the postulate, even without equations neither numeric forecasts, it guides and strengthen the ideas and it allows to control by means of logical precepts the tendencies of the projects and to know their possibilities.
In some cases, to draw the representative curve of a project helps to estimate their evolution and the value of their MLO.
They can also imagine different solutions and to obtain conclusions of the type:
- Is it possible to apply such a solution?.
- In what percentage would it improve the project?.
- If the solution were implemented in correct way, would the desired result be reached?.
DIFFERENT REPRESENTATIVE CURVE OF A PROJECT
A simple project can be solved in one stage.
An improvement taken place by a CTC it allows to reach the desired result.
Stage with negative slope: it harms the situation of the project.
REFERENCES AND NOTES
- F. Crick, What Mad Pursuit (Tusquets Editores S.A., Barcelona, 1989), p. 85.
- The signs of the values on the axes are always positive.
- Perpendicular axes; their crossing determines the origin of each axis.
- Any continuous line, be or non-straight line.
- F. Crick, What Mad Pursuit (Tusquets Editores S.A., Barcelona, 1989), p. 81.
- P F Smith and A Sullivan Gale, Elements of Analytic Geometry (Librería-Edit. Nigar,Buenos Aires,1955, Edition authorized by Ginn & Co, Boston,USA),II-V.
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