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Posts Tagged ‘**Euclidian mathematics**’

### Einstein speaks on theoretical sciences

Posted by: adonis49 on: November 15, 2009

**Einstein speaks on theoretical sciences; (Nov. 15, 2009)**

I intend to write a series on “Einstein speaks” on scientific methods, theoretical physics, relativity, pacifism, national-socialism, and the Jewish problem.

In matter of space two objects may touch or be distinct. When distinct, we can always introduce a third object in between. Interval thus stays independent of the selected objects; an interval can then be accepted as real as the objects. This is the first step in understanding the concept of space. The Greeks privileged lines and planes in describing geometric forms; an ellipse, for example, was not intelligible except as it could be represented by point, line, and plane. Einstein could never adhere to Kant’s notion of “a priori” simply because we need to search the characters of the sets concerning sensed experiences and then to extricate the corresponding concepts.

The Euclidian mathematics preferred using the concepts of objects and the relation of the position among objects. Relations of position are expressed as relations of contacts (intersections, lines, and planes); thus, space as a continuum was never considered. The will to comprehend by thinking the reciprocal relations of corporal objects inevitably leads to spatial concepts.

In the Cartesian system of three dimensions all surfaces are given as equivalent, irrespective of arbitrary preferences to linear forms in geometric constructs. Thus, it goes way beyond the advantage of placing analysis at the service of geometry. Descartes introduced the concept of a point in space according to its coordinates and geometric forms became part of a continuum in 3-dimensional space.

The geometry of Euclid is a system of logic where propositions are deduced with such exactitude that no demonstration provoke any doubt. Anyone who could not get excited and interested in such architecture of logic could not be initiated to theoretical research.

There are two ways to apprehend concepts: the first method (analytical logic) resolves the following problem “how concepts and judgments are dependents?” the answer is by mathematics; however, this assurance is gained at a prohibitive price of not having any content with sensed experiences, even indirectly. The other method is to intuitively link sensed experiences with extracted concepts though no logical research can confirm this link.

For example: suppose we ask someone who never studied geometry to reconstruct a geometric manual devoid of any schemas. He may use the abstract notions of point and line and reconstruct the chain of theorems and even invents other theorems with the given rules. This is a pure game of words for the gentleman until he figures out, from his personal experience and by intuition, tangible meanings for point and line and geometry will become a real content.

Consequently, there is this eternal confrontation between the two components of knowledge: empirical methodology and reason. Experimental results can be considered as the deductive propositions and then reason constitutes the structure of the system of thinking. The concepts and principles explode as spontaneous inventions of the human spirit. Scientific theoretician has no knowledge of the images of the world of experience that determined the formation of his concepts and he suffers from this lack of personal experience of reality that corresponds to his abstract constructs. Generally, abstract constructs are forced upon us to acquire by habit. Language uses words linked to primitive concepts which exacerbate the difficulty with explaining abstract constructs.

The creative character of science theoretician is that the products of his imagination are so indispensably and naturally impressed upon him that they are no longer images of the spirit but evident realities. The set of concepts and logical propositions, where the capacity to deduction is exercised, correspond exactly to our individual experiences. That is why in theoretical book deduction represents the entire work. That is what is going on in Euclid geometry: the fundamental principles are called axioms and thus the deduced propositions are not based on commonplace experiences. If we envision this geometry as the theory of possibilities of the reciprocal position of rigid bodies and is thus understood as physical science, without suppressing its empirical origin, then the resemblance between geometry and theoretical physics is striking.

The essential goal of theory is to divulge the fundamental elements that are irreducible, as rare and as evident as possible; an adequate representation of possible experiences has to be taken into account.

Knowledge deducted from pure logic is void; logic cannot offer knowledge extracted from the world of experience if it is not associated with reality in two way interactions. Galileo is recognized as the father of modern physics and of natural sciences simply because he fought his way to impose empirical methods. Galileo has impressed upon the scientists that experience describes and then proposes a synthesis of reality.

Einstein is persuaded that nature represents what we can imagine exclusively in mathematics as the simplest system in concepts and principles to comprehend nature’s phenomena. Mathematical concepts can be suggested by experience, the unique criteria of utilization of a mathematical construct, but never deducted. The fundamental creative principle resides in mathematics. The follow up article “Einstein speaks on theoretical physics” with provide ample details on Einstein’s claim.

**Critique**

Einstein said “We admire the Greeks of antiquity for giving birth to western science.” Most probably, Einstein was not versed in the history of sciences and was content of modern sciences since Kepler in the 18^{th} century: maybe be he didn’t need to know the history of sciences and how Europe Renaissance received a strong impulse from Islamic sciences that stretched for 800 years before Europe woke up from the Dark Ages. Thus, my critique is not related to Einstein’s scientific comprehension but on the faulty perception that sciences originated in Greece of the antiquity.

You can be a great scientist (theoretical or experimental) but not be versed in the history of sciences; the drawback is that people respect the saying of great scientists even if they are not immersed in other fields; especially, when he speaks on sciences and you are led to assume that he knows the history of sciences. That is the worst misleading dissemination venue of faulty notions that stick in people’s mind.

Euclid was born and raised in Sidon (current Lebanon) and continued his education in Alexandria and wrote his manuscript on Geometry in the Greek language. Greek was one of the languages of the educated and scholars in the Near East from 300 BC to 650 AC when Alexander conquered this land with his Macedonian army. If the US agrees that whoever writes in English should automatically be conferred the US citizenship then I have no qualm with that concept. Euclid was not Greek simply because he wrote in Greek. Would the work of Euclid be most underestimated if it were written in the language of the land Aramaic?

Einstein spoke on Kepler at great length as the leading modern scientist who started modern astronomy by formulating mathematical model of planets movements. The Moslem scientist and mathematician Ibn Al Haitham set the foundation for required math learning in the year 850 (over 900 years before Europe Renaissance); he said that arithmetic, geometry, algebra, and math should be used as the foundations for learning natural sciences. Ibn Al Haitham said that it is almost impossible to do science without strong math background. Ibn Al Haitham wrote mathematical equations to describe the cosmos and the movement of planets. Maybe the great scientist Kepler did all his work alone without the knowledge of Ibn Al Haitham’s analysis but we should refrain of promoting Kepler as the discoverer of modern astronomy science. It also does not stand to reason that the Islamic astronomers formulated their equations without using 3-dimensional space: Descartes is considered the first to describing geometrical forms with coordinates in 3-dimensional space.