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> Est Modus In Rebus Issue: 2011-1 Section: University



"Est Modus In Rebus": Measure - Expression of Knowledge


Loredana Elena TERZEA, Stefania MOROGAN, Oana-Maria MANTA


Versta 835 stanjeni 1.67 km  
Funie 4prajini 12 stanjeni 26.76 m 24.24 m
Prajina 3 stanjeni 6.69 m  
Stanjen 8 palme 2.23 m 1.97 m
Cot   66.4 m 63.7 m
Palma 10 degete 27.875 cm 24.625 cm
Palmac 12 linii Md 35 mm 20.5 mm
Deget 10 linii Mt 28 mm 25 mm
Linie   2.9 mm 2.5 mm


Greek Name Equivalent Metric System
Dactylos The length of a finger 0.0193 m
Palaeste The wide of the hand 0.0771 m
Spithame The distance between two fingers 12 dactili 0.2312 m
Pos Feet 16 dactili 0.3083 m
Pehys Elbow 0.4624 m
Bema Step 0.771 m
Orgynia Iris 1.85 m

The technological evolution, especially after the Industrial Revolution (18-19th century), created the necessity of manufacturing interchangeable parts. This leaded producers to face one of the major problems of manufacturing, caused by the lack of unity on the meas systems.

Worldwide, where the germs of civilization emerged and evolved, also appeared the necessity of giving a measure to certain things, both on physical and philosophical way.

Est modus in rebus (Latin) means that there is a proper measure in everything and the golden mean should always be observed.

It is really fascinating that the capability of a community to describe measure and characterize the objective reality, to design abstract issues or to seed notions of virtual reality (on philosophical and mathematical ways) induced the evolution of the society itself.

The solitary communities, from Antiquity and medieval decades, used several systems of measurement which were interacting just sporadically, exclusively on the trading ways.

Even if there were created on different geographical areas, the first units of measurement were – without exception - related to the elements of human anatomy such as: finger, palm, elbow or footstep (fig. 1).

It is useful to mention that these units did not have the same effective value and the traders knew this aspect better than anyone else, but they also knew the art of negotiation and, at the best, the art of guns. For example, the units of length were different from one territory to another even inside the same culture (table 1), but they fluctuate also across continents (table 2). Most of the geographical discoveries from the XV-XVI centuries were a sort of forerunner for the Industrial Revolution, stimulating the trading relationships and the use of the economical instruments to succeed into modifying the conditions of production and the relationship with the workforce.

So, at the end of the 18th century a severe approach on the harmonization of the measurement units imposed itself. What was efficiently running in the agricultural societies, closed communities having just incidental connections through the trade routes or by the military campaigns, became useless/invalid once of a sudden. New commercial relationships and cultural interferences were taking place on a very short frame of time opening an era of knowledge, which was going to modify forever the way of perceiving the Universe.

The measurement approach, started on the most accessible way from body related units, evolving in just few centuries (once with telescope and electronically microscope inventions) and reaching the macro- and micro- size characterization of Universe. These notions have been theorized long before by philosophers, even without effective tools of describing or measuring them, thus making possible the evolution of thinking and modeling through a highest level of abstraction. Actually, in front of the increased orders from the textile industry and aimed by the wish of making order in trading relations, the French were the first who tried to erase the dysfunctions caused by the lack of a unique system of measurement, implementing the first one by the power of law in the entire France. So, on 26th of March 1791 The Constituent National Assembly adopted the principles of creating a system of measures and weights (system des poids et mesures) which was based on a unit length called meter (gr. Metron = measure) and being equal with the 10th million part of Earth meridian quarter. This definition was proposed by a committee called The Academy of Science from Paris. From this moment started a new stage in the history of measurement units which was going to lead to the International System of Units (fig. 2).

It is to be mentioned that SI become operable and it was implemented in many countries as an expression of their industrial development (beginning with 60’s), but also like an expression of their political will. Presently most of the countries adopted SI, but there are still some big economical powers, like United States or Great Britain, on the course of adapting to it. US are operating with a limited number of elements from the International System and Great Britain is in the process of adopting SI for almost one century, aspect that is reflected also in the dynamics of units’ harmonization among the Commonwealth’s countries.

It becomes clear that through standardization it was enhanced a way of characterizing and measuring phenomena, an engine for science and technology that get the control over the dynamics knowledge development, boosting all the other domains of social and economical life.


Knowledge is power

What type of connection can be among the period of Chinese Han Empire (202 BC-220 AD), the cursor, the oldest wooden compass found on the archaeological remains of a Greek settlement near the coast of Italy, and the caliper of Pierre Vernier? Reviewing the history of almost two millennia it appears that a bronze tool using a slider system was used by the Chinese since the Han dynasty to calculate the days, months and years.

Instruments like compasses have been used since ancient period for measuring the distances on navigation, these being firstly made by wood (fig. 3). In 1631 the French mathematician and inventor Pierre Vernier, who was also passionate by navigation, published in Brussels a treatise on the construction, uses, and properties of a new mathematical quadrant; the quadrant being the mathematical term for ¼ of a circle and also a navigation tool widely used long before the period of the Great Geographical Discoveries.

So, now becomes obvious how the calendar, compass, quadrant and mathematical tables joined into the instrument invented later on, in 1851, by Joseph Brown, giving a more effective use to Vernier caliper (fig. 3), an instrument able to read thousandths of an inch - because the invention didn’t emerged in the area of SI but in the Imperial System of Units.

If the road toward the compass took almost two millennia, that one toward the electron microscope was only...80 years away.

In 1929 the French physicist Louis de Broglie received the Nobel Prize for Physics for his discovery on the wave nature of electron. Only two years later (1931) the German engineers Ernst Ruska and Max Knoll designed the first electron microscope able to increase the image of the objects for about 400 times (fig. 4).Currently, operating on the same principle the electron microscopes provide better resolution of about 0.2nm for a 2x106 power magnification (fig. 5), while the best optical microscopes are limited by the diffraction phenomenon at a resolution around 200 nm for a magnification power of up to 2x103. The fact is that after the occurrence of the electron microscopy a new field of research has been revealed. Its potential has to challenge all areas of science, opening to knowledge a universe with new properties and laws, able to redefine many of the present knowledge.

Something similar happened with the knowledge at the macroscopic level that made possible the beginning of the Spatial Era otherwise than as a science anticipation scenario.

Telescope is an instrument consisting of a sequence of lenses and mirrors used to identify, observe and possibly taking photos of objects situated at large distances.

Beginning with the first observation regarding the magnifying effect of water glass lens, until the nowadays achievements on lens industry some basic optical scheme were defining the characteristics of the first instruments designed to increase the image of the planets and stars. Great names of Physics and Astronomy related their activity with the improvement of these tools: Galileo Galilei, Johannes Kepler, Christiaan Huygens, Isaac Newton, etc.

The large parabolic mirror design and manufacture and the glass mirror silvering process, introduced by Léon Foucault (1857)- later on replaced with more durable materials such as aluminum (1932) - made possible the astronomical space distance observations beginning with the middle of last century. Some observations and measurements were made also using radio telescopes in a wide range of wavelengths, from radio waves to gamma rays.


Measurement – a vector of knowledge

With the invention of caliper and other measurement means the dynamics of the innovations in the area of measuring and characterization rose so fast as only 80 years later (1939) it was experienced another major invention – the electron microscope. Then the things grow by themselves as only two decades later (1959), another Nobel laureate in physics, Richard Feynman made the historical statement: There is plenty of room at the bottom which was meant to be an invitation to explore the micro-sized universe and effectively opened the Nanotechnology era. Among the subdivisions of meter the nanometer is 10-9 part of a meter, the prefix nano came from the Greek language, meaning dwarf. So it is a dwarf that would challenge the knowledge, creating new branches of science and redefining many of the current applications (fig. 6 - 10). The evolution continues! If we are looking around everything seems to be changing, even the definition of the etalon-meter that becomes the 29th million part of the distance traveled by light in vacuum during a second. Now things seem more difficult to understand, but actually their meaning is to be found in the knowledge evolution. The basic idea is that the accuracy and how they can characterize (measure, analyze, interpret) in a given time parameters of a system is the measure degree in the social evolution, technological, scientific, of the spiritual community.