Written by Samir A. Sánchez (2017)
In 1950, Albert Einstein wrote—for Scientific American Magazine—an account of the extension of the General Theory of Relativity, setting it against its historical and philosophical background. He clearly defined it as a mathematical investigation into the foundations of field physics.
Beyond the serious and attentive discourse applied to the study of physical forces and qualities, teachers, students, and researchers can find educative conceptual keys and suggestions for global teaching and learning. They can, perhaps surprisingly, teach the scientific method through creative acts and incorporate Einstein's ideas into their pedagogical systems.
In this way, they may asymptotically approach knowledge (using the concept of limits from calculus), but without the tendency to express strongly held opinions in a way that suggests they should be accepted without question. We will never fully reach truth or knowledge, yet we always have the 'opportunity of exchanging error for truth' (John Stuart Mill, On Liberty, 1859).
Now, a question arises: What conceptual keys can be found in Einstein's account? The answer is 'punctual': Nothing for granted (non-dogmatic), enjoying 'comprehending' and asking questions like children, passion, muse (being absorbed in thought) and hypothesis, creative act, affirmation or refutation.
Nothing for granted (non-dogmatic)
Similar to an exploratory stage, Einstein explained,
"Some readers may be puzzled: Didn't we learn all about the foundations of physics when we were still at school? The answer is 'yes' or 'no,' depending on the interpretation. We have become acquainted with concepts and general relations that enable us to comprehend an immense range of experiences and make them accessible to mathematical treatment. In a certain sense, these concepts and relations are probably even final. This is true, for example, of the laws of light refraction, of the relations of classical thermodynamics as far as it is based on the concepts of pressure, volume, temperature, heat, and work, and of the hypothesis of the non-existence of a perpetual motion machine."
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Photograph by Santiago X. Sánchez (2017) |
Enjoy 'comprehending' and asking questions like children
Comprehending the sheer scale of problems should always be enjoyable, a pleasing intellectual curiosity that allows children to question themselves and engage in a process of thinking and discovery. Similarly, students can begin to pose initial conjectures about problem-posing and the process of dissecting them.
What, then, impels us to devise theory after theory? Why do we devise theories at all? The answer to the latter question is simply: Because we enjoy 'comprehending,' i.e., reducing phenomena by the process of logic to something already known or (apparently) evident. New theories are primarily necessary when we encounter new facts that cannot be 'explained' by existing theories. But this motivation for setting up new theories is, so to speak, trivial, imposed from without. There is another, more subtle motive of no less importance. This is the striving toward unification and simplification of the premises of the theory as a whole (i.e., Mach's principle of economy, interpreted as a logical principle).
Passion
Understood as intense enthusiasm, passion involves a strong liking for understanding what is not yet part of one's knowledge or of general knowledge.
There exists a passion for comprehension, just as there exists a passion for music. That passion is rather common in children, but gets lost in most people later on. Without this passion, there would be neither mathematics nor natural science.
Muse and hypothesis
Every phenomenon must be considered in a deep and serious, or dreamy and abstracted way, beginning with a tentative explanation (hypothesis).
But when, in the second half of the 19th century, the laws of electrodynamics became known, it turned out that these laws could not be satisfactorily incorporated into the Newtonian system. It is fascinating to muse: Would Faraday have discovered the law of electromagnetic induction if he had received a regular college education? Unencumbered by traditional thinking, he felt that the introduction of the 'field' as an independent element of reality helped him coordinate the experimental facts. It was Maxwell who fully comprehended the significance of the field concept; he made the fundamental discovery that the laws of electrodynamics found their natural expression in the differential equations for the electric and magnetic fields. These equations implied the existence of waves, whose properties corresponded to those of light as far as they were known at that time.
"The theoretical idea (atomism in this case) does not arise apart from and independent of experience; nor can it be derived from experience by a purely logical procedure. It is produced by a creative act. Once a theoretical idea has been acquired, one does well to hold fast to it until it leads to an untenable conclusion".
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Photograph by Santiago X. Sánchez (2017)
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"The skeptic will say: 'It may well be true that this system of equations is reasonable from a logical standpoint. But this does not prove that it corresponds to nature.' You are right, dear skeptic. Experience alone can decide on truth. Yet we have achieved something if we have succeeded in formulating a meaningful and precise question. Affirmation or refutation will not be easy, in spite of an abundance of known empirical facts. The derivation, from the equations, of conclusions which can be confronted with experience will require painstaking efforts and probably new mathematical methods".
ReferencesAlbert Einstein, Out of my Later Years, New York, Philosophical Library (1950).
Albert Einstein, 'On the Generalized Theory of Gravitation. An account of the newly published extension of the general theory of relativity against its historical and philosophical background', Scientific American, Inc, Volume 182, issue 4, pp. 13-17, April (1950).
Carl Sagan, The Demon-Haunted the World. Science as a Candle in the Dark, London, Headline Book Publisher (1997).
Gwendolyn (www.codepen.io). Albert Einstein Tribute Page (2017)
Howard Gardner, ‘Frames of Mind: The Theory of Multiple Intelligences’, Harvard Magazine, March-April (1982).
John Stuart Mill, On Liberty, Kitchener (Canada), Batoche Book, (2001).
Picture note:Toy of Albert Einstein Bobble Head, McDonald’s Toy, ©2009.
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