I. Introduction
We are now entering the fourth generation after Einstein, and we have not, as a society, begun the process of internalizing the theories of relativity. Einstein’s wild hair and wise eyes appear on coffee mugs, posters, and his face peers from the side of buses, but ask a high school student to describe the effect of mass on the geometry of four dimensional space and expect to get met with a blank stare. This is seriously strange stuff; but it should not seem so, not four generations after relativity overtook classical mechanics as the dominant theory in physics.
There are good reasons classical mechanics and Euclidean geometry are still taught as absolutes in school: if you want to build a road or raise a skyscraper, you cannot improve on Newton.
There was a time when Newton’s ideas seemed strange, though: the idea of the moon in perpetual freefall toward the earth, yet being constantly repelled by the centrifugal force of its own orbit. These ideas were not embraced immediately – science and society are both conservative institutions. Max Planck writes:
… it rarely happens that Saul becomes Paul. What happens is that [a new concept’s] opponents gradually die out and that the growing generation is familiarized with the idea from the beginning…
(Planck, 1963:97).
More than one generation has died out, though. Why has the
“growing generation” not become “familiarized with the idea from the beginning.” Alfred North Whitehead notes that a complete change in scientific attitudes can take as long as three generations (Whitehead, 1925: 25). What processes are important
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in the cycle that sees these ideas move from novel theory in physics to dominant world view?
The single most important factor that influences the internalization of a new concept by a society is the availability of language with which to manipulate that concept. Within this broad, presumptuous statement we must discuss the use of language within the scientific sub-culture, and the problem of expression 1 that occurs when the new concept begins the transition from the scientific community to society at large.
II. The Grip of Formalism
From the time of Thales and Anaximenses the precept that has informed our quest for an understanding of the universe has been this: all things physical can be described in terms of matter in motion - our world is a mechanical one. This worldview surely arose from observation – our daily experiences of the world around us. The human languages that have arisen from this cradle of thought reflect this worldview; it has been and continues to be the “instinctive tone of thought” of our times.
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As such, this worldview also forms the basis of scientific study. Our scientists are schooled first in classical mechanics: they learn the Principia , the scientific method – the words of
Newton are the language of science. With this language - these
1 Whitehead defines expression as “…the diffusion, in the environment, of something initially entertained in the experience of the expressor” (Whitehead,
1983:85). The important characteristic of this definition is the movement of the idea from the individual to the group – or to expand the concept – from a small group to a larger group.
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concepts - they set out to explore the universe; with this language they report their findings back to the rest of society, and the body of knowledge grows.
III. The languages of Science: The paradox of abstraction
The problem arises that the language of classical mechanics does not have the capacity to express the explanations induced from observations being made today. The Principia is a compendium of axioms, self-referential postulates each relating to a particular feature of the universe as modeled by Newton
(Speilberg and Anderson, 1995: 89). Once the researcher moves beyond Newton’s range of experience, the lexicon is exhausted.
At this point, the researcher can consider two options: 3
1) to develop a private language, a specialized subset of mathematics or logic with which to manipulate the concepts developed to explain the phenomena (e.g. quantum logic, or, in Newton’s time, differential/inferential calculus)
2) to reconfigure/redefine existing concepts to meet the needs of the situation
Of necessity, the practical person likely chooses a combination of the two. Obviously, if we want to speak of extended space we need a mathematical model of geometry that is not Euclidean. So we create one. But we must, at some point, express this model in classical terms, both to ourselves, for we
2 Short quote taken from an excellent discussion of the influence of medieval rationality on the development of “scientific reason.” See
(Whitehead, 1925: 18).
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cannot visualize four dimensional space, and to others, because we do not have a non-mathematical language to suggest the concepts the formulas describe.
Perhaps more interestingly, though, we are forced to design our proofs of these concepts using classical physics. Heisenberg describes the situation that arises as follows:
It [the paradox] starts from the fact that we describe our experiments in the terms of classical physics and at the same time from the knowledge that these concepts do not fit nature accurately (Heisenberg,
1958: p.56)
The scientific community is no longer working with
Euclidean space, but it must, to some degree, still live in it.
Because society has not internalized the concept of extended space, we can only express certain new concepts through the abstraction of a language like mathematics, or with the analogies and metaphors of an ill-equipped natural language. The first is precise, yet to the many it seems arcane; the other is perhaps more readily understood by a greater number, but the understanding those gain is facile.
IV. Preparing the Next Generation
J. Robert Oppenheimer writes that significant progress in physics is characterized by a sense of adventure on the part of the scientist – the desire to go further - but that this desire to explore, to move beyond, is tempered by an aversion to upsetting the ideas and understanding of the established order.
3 I can’t find the citation for this, but I got it from somewhere.
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According to Oppenheimer, it is the tension of this contradiction that makes progress possible (Oppenheimer, 1962:5).
This conservative element which perhaps prevents rashness in research may also have a stifling effect on the dissemination of new theories beyond the scientific community. Although we may feel that relativity and quantum mechanic have no relevance in our day-to-day live, that these are concepts do not effect us
(and we are correct to feel that in some respects), and we may also feel that these theories are just beyond cogitation (there are arguments to be made here as well), the progress of science will be hampered unless we can produce a generation of scientists who take in these concepts with their mothers’ milk instead of learning them as mind-blowing oddities at university.
We stand at the beginning of the twenty-first century and say that it is impossible for the human mind to fully comprehend the geometry of extended space. I do not think it reasonable to make this statement. We should not limit our future with such an arbitrary pronouncement of our own cognitive limits. Humans have rich metaphysical lives that often transcend our temporal experiences.
We have developed technologies based on our knowledge of relativity and quantum mechanics; we have an educational system that can transmit what we have determined this knowledge to be.
Why do we not trust it?
… a high culture is transmitted by an educational system which trains its products to understand and articulate messages independently of context, and in accordance with rules which are
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equally internalized by all the other fellow-products of the same educational machine. Thus, for the first time in human history, a high culture, linked to literacy and formal education, its rules formally codified in writing, ceases to be the privilege of a minority and becomes, not so much a privilege, but a precondition of effective social and economic participation for the generality of the society
(Gellner, 1998:28).
From us, what is required is an act of faith.
Planck had reservations about disseminating advanced ideas to young students, though:
The present age, which lives at such a rapid rate and show so much interest for every innovation having an immediate sensational effect, provides us with instances where scientific training tends to anticipate certain exciting results before they have properly ripened; for the public is favourably impressed if the curriculum of an intermediate school already contains modern problems of scientific investigation. Yet such a practice is exceedingly dangerous. The problems cannot possibly be dealt with thoroughly, and the consequence may easily be to induce a certain intellectual superficiality and empty pride in knowledge. I should consider it extremely dangerous if the intermediate schools were to deal with the theory of relativity or the quantum theory
(Planck, 1963: 99).
I believe we have moved beyond the point where relativity and quantum mechanics could be considered “innovations,” and Planck’s point about the need to avoid dealing with the topics in a superficial manner speaks to my own: introducing the concepts at an early age, providing society with a linguistic basis for these ideas, will ensure that the knowledge takes root when those who choose indulge in the deeper mathematics of the subjects. Everyone, for example, has an intuitive grasp of Newtonian gravity, but
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not everyone can do the differential calculus for the proofs. This seemingly intuitive grasp of gravity is a cultural by-product; it arises from a life lived in a society that believes it.
V. Conclusions
We speak of the 4 th , 5 th , 11 th , the n th dimensions casually, inject them into our conversation, our literature as though they were not problematic, as though they were places we might visit, as though they were as much a part of our existential and linguistic continuum as they are a part of the numeric sequence.
We, as a society, have no cultural vessel for these concepts. The very brightest among us may be able to make the conceptual leap necessary to manipulate the concepts, to somehow visual 4 a nonphysical dimension, but most of us will die nodding and smiling.
Configuration space is problematic in terms of non-mathematic language.
If we want to break the cycle of having only the best and brightest understanding what we believe to be the nature of the universe[s] in which we live, we need to create some sort of cultural vessel for these concepts. We need language to adapt. I am not suggesting that everyone can learn the mathematics associated with relativity or quantum mechanics. I am not suggesting that non-locality be taught in primary school.
4 Note the poverty of language.
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Heisenberg has written that people from technological societies will find it easier to cope with new ideas.
Because they have grown up with rapid technological change they have a foundation upon which to build (Heisenberg,
1958:27-8). But the concepts we are discussing go beyond
“new ideas.” Consider Heisenberg’s own words:
…the change in the concept of reality manifesting itself in quantum theory is not simply a continuation of the past; it seems to be a real break in the structure of modern science (Heisenberg, 1958: p.29).
This is not like Grandfather learning to live in the computer age. This foundation of which we speak, our commonsense, maybe our biggest detriment in this process of internalization. We have no idea of what value our five senses are as we continue to grope the universe; and our language is ground in the sensual.
We need to work toward building a new foundation. To what degree this is a conscious process, I am not uncertain.
Mrs. Whatsit sighed. “Explanations are not easy when they are about things for which your civilization still has no words. Calvin talked about traveling at the speed of light. You understand that little Meg
(L’Engle, 1962:75)?
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5 Taken from novel for young readers. Understanding the plot involves grasping the concepts very basic concepts of relative time and space.
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Works Cited
Einstein, Albert. Essays in Science. New York: The
Philosophical Library, Inc, 1934.
Gellner, Ernest. Language and Solitude. Cambridge: Cambridge
University Press, 1998.
Heisenberg, Werner. Physics and Philosophy: The Revolution in
Modern Science. New York: Harper & Brothers Publishers,
1958.
L”Engle, Madeleine. A Wrinkle in Time. New York: Dell Publishing
Co., INC., 1962.
Oppenheimer, J.Robert. The Flying Trapeze: Three Crises for
Physicists. London: Oxford University Press, 1962.
Planck, Max. The Philosophy of Science. New York: W.W. Norton &
Co., Inc., 1963.
Spielberg, Nathan and Byron D. Anderson. Seven Ideas that Shook the Universe, 2 nd Ed. . New York: John Wiley & Sons, Inc.,
1995.
Whitehead, Alfred North. Science and the Modern World. New York:
Macmillan Company, 1925.
Whitehead, Alfred North. “Expression.” Anne E. Berthoff ed.
Philosophical Perspectives for Writers, 1983. Pp. 84-97.
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