Adonis Diaries

Posts Tagged ‘relativity

Big Fish, Little Pond phenomenon: Never listen to the prevalent common sense

Big fish eats little fish, and the smaller the pond the quicker the trapping.

And when you are accepted in an Ivy League university, and your “intelligence level” (IQ test scores and other tests) is in the third tier of the all the admitted students, and you lack the required character for the long haul, then you drop before graduating.

You keep comparing your “performances” with the brighter students.

And you end up switching university and discipline and you graduate as lawyer, accountant, tax expert… anything but your “dream field” of study.

You were capable of graduating in your dream field, but you selected the wrong kind of universities.

It is Not the program, the professors or the courses offered in the Ivy League universities that generate “geniuses”: It is the bright students graduating from these universities who are.

You still make plenty of money, but how happy is your life?

Innate intelligence can be downgraded by diseases, sicknesses, harsh conditions, inhospitable situations… that alter the necessary characters required to improve your intelligence level.

For example, you cannot reach a satisfactory level of smartness if you lack this stubbornness of doggedly resolving any problem, of solving the easy exercises as well as the hardest at the end of each chapter in math, physics, chemistry, biology… and using paper and pencil for the that matter, and writing down the solution in neat handwriting that demonstrate determination.

And you need this capacity to completely focus during the class sessions and concentrate on the detailed information.

I attended a university that didn’t rank anyway on top of the elite institutions in the USA: It was a Little Pond, not in size of campus or number of students or variety of disciplines and departments, but mainly one of the newer universities that didn’t enjoy “historic” funding of private or State or federal funding in order to set up these rigorous selection processes for applicants.

It is was not a university that had Nobel Laureates and funded Chairs for illustrious professors or recognition to be listed among the Ivy League.

I think there were or must have been many Big Fish in many disciplines and fields of study, but Not in my new field of study called Industrial Engineering. That was in 1975, and this department was a new comer among the disciplines.

When I applied from Lebanon, I didn’t even know what was the program of study or the courses offered. I assumed from the name that it must be a hands-on engineering related to whatever the industry needed from graduates. Even if I had the luxury to have a detailed list of courses, I wouldn’t be the smarter or changed my application.

As a foreigner lacking laboratories, I figured out that this discipline in a developed nation will offer plenty of opportunities for hands-on facilities.

It was Not of this sort by any long shot. Actually the field lacked laboratory or any hands-on facilities. The course materials were indeed more of the same bookish, theoretical and mathematical handling of problems.

It turned out that the objective was to spew out new breed of graduates capable of handling the management part in any production and manufacturing industry, like optimizing production, inventory, scheduling, transportation

Even today, I am harassed and hard-pressed to explain what I was trained for or “how I can be of aid” to industries.

I felt there was a lack of brilliant students in my disciplines to look at and emulate. And I let myself drift off to lazy study behaviors.

I guess not many high school students knew of this relatively new discipline and anyway, the connotation was to be desired.

Note: I had graduated with MS in physics. I covered exotic courses such as quantum mechanics, relativity, nuclear physics, solid state, thermodynamics, organic chemistry, all the fundamental physics courses taught for engineers, and the mathematical foundations and basics…

I loved and comprehended most of the course materials, but it didn’t improve my grades, and much less improved the IQ tests scores substantially.

The few courses that I loathed were the methods used to resolving the problems: the methods were lengthy and defied my patience.

I recall that in taking Relativity, the method to solving most mechanical problems was clear, quick and straightforward: It took barely 30 seconds when the classical method required me half an hour.

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 18th 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.

Learning paradigm for our survival; (Nov. 9, 2009)

Einstein, the great theoretical physicist, confessed that most theoretical scientists are constantly uneasy until they discover, from their personal experiences, natural correspondences with their abstract models.  I am not sure if this uneasiness is alive before or after a mathematician is an expert professional. 

For example, mathematicians learn Riemann’s metrics in four-dimensional spaces and solve the corresponding problems. How many of them were briefed that this abstract construct, which was invented two decades before relativity, was to be used as foundation for modern science? Would these kinds of knowledge make a difference in the long run for professional mathematicians?

During the construction of theoretical (mathematical) models, experimental data contribute to revising models to taking into account real facts that do not match previous paradigms. I got into thinking: If mathematicians receive scientific experimental training at the university and are exposed to various scientific fields, they might become better mathematicians by getting aware of the scientific problems and be capable of interpreting purely mathematical models to corresponding natural or social phenomenon that are defying comprehension.

By the way, I am interested to know if there are special search engines for mathematical concepts and models that can be matched to those used in fields of sciences.  By now, it would be absurd if no projects have worked on sorting out the purely mathematical models and theories that are currently applied in sciences.

I got this revelation.  Schools use different methods for comprehending languages and natural sciences.  Kids are taught the alphabet, words, syntax, grammars, spelling and then much later are asked to compose essays.  Why this process is not applied in learning natural sciences?  

Why students learning math are not asked to write essays on how formulas and equations they had learned apply to natural or social realities?

I have strong disagreement on the pedagogy of learning languages:

First, we know that children learn to talk years before they can read. Why then kids are not encouraged to tell verbal stories before they can read?  Why kids’ stories are not recorded and translated into the written words to encourage the kids into realizing that what they read is indeed another story telling medium?

Second, we know that kids have excellent capabilities to memorize verbally and visually entire short sentences before they understand the fundamentals. Why don’t we develop their cognitive abilities before we force upon them the traditional malignant methodology?  The proven outcomes are that kids are devoid of verbal intelligence, hate to read, and would not attempt to write, even after they graduate from universities.

Arithmetic, geometry, algebra, and math are used as the foundations for learning natural sciences. The Moslem scientist and mathematician Ibn Al Haitham set the foundation for required math learning, in the year 850, if we are to study physics and sciences. Al  Haitham said that it is almost impossible to do science without strong math background. 

Ibn Al Haitham wrote math equations to describe the cosmos and its movement over 9 centuries before Kepler emulated Ibn Al Haitham’s analysis. Currently, Kepler is taunted as the discoverer of modern astronomy science.

We learn to manipulate equations; we then are asked to solve examples and problems by finding the proper equations that correspond to the natural problem (actually, we are trained to memorize the appropriate equations that apply to the problem given!).  Why we are not trained to compose a story that corresponds to an equation, or set of equations (model)?

If kids are asked to compose essays as the final outcome of learning languages, why students are not trained to compose the natural phenomena from given set of equations? Would not that be the proper meaning for comprehending the physical world or even the world connected with human behavior? 

Would not the skill of modeling a system be more meaningful and straightforward after we learn to compose a world from a model or set of equations?  Consequently, scientists and engineers, by researching natural phenomena and man-made systems that correspond to the mathematical models, would be challenged to learn about natural phenomena. Thus, their modeling abilities would be enhanced, more valid, and more instructive!

If mathematicians are trained to compose or view the appropriate natural phenomenon and human behavior from equations and mathematical models, then the scientific communities in natural and human sciences would be far richer in quality and quantity.

Our survival needs mathematicians to be members of scientific teams.  This required inclusion would be the best pragmatic means into reforming math and sciences teaching programs.

Note: This post is a revised version of “Oh, and I hate math: Alternative teaching methods (February 8, 2009)”.


adonis49

adonis49

adonis49

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