From American Affairs Journal:
Physicist
Richard Feynman had the following advice for those interested in
science: “So I hope you can accept Nature as She is—absurd.”1
Here Feynman captures in stark terms the most basic insight of modern
science: nature is not understandable in terms of ordinary physical
concepts and is, therefore, absurd.
The unintelligibility of nature has huge consequences when it comes
to determining the validity of a scientific theory. On this question,
Feynman also had a concise answer: “It is whether or not the theory
gives predictions that agree with experiment. It is not a question of
whether a theory is philosophically delightful, or easy to understand,
or perfectly reasonable from the point of view of common sense.”2
So put reasonableness and common sense aside when judging a scientific
theory. Put your conceptual models and visualizations away. They might
help you formulate a theory, or they might not. They might help to
explain a theory, or they might obfuscate it. But they cannot validate
it, nor can they give it meaning.
Erwin Schrödinger made a similar critique of the simplified models
widely used to explain scientific concepts in terms of everyday
experience, such as those used to illustrate atomic theory:
A completely satisfactory model of this type is
not only practically inaccessible, but not even thinkable. Or, to be
more precise, we can, of course, think it, but however we think it, it
is wrong; not perhaps quite as meaningless as a “triangular circle,” but
much more so than a “winged lion.”3
“Do the electrons really exist on these orbits within the atom?” Schrödinger asks rhetorically. His answer: “A decisive No, unless we prefer to say that the putting of the question itself has absolutely no meaning.”4
Feynman and Schrödinger were concerned about the extremely small
scale, but what about the extremely large scale? A single human cell has
more than twenty thousand genes. Therefore, assuming one protein per
gene, the number of different non-modified proteins exceeds twenty
thousand. Add to that the many more different proteins resulting from
alternative splicing, single nucleotide polymorphisms, and
posttranslational modification. No conceptual model is conceivable for
the interactions among all of these genes and proteins, or for even a
tiny portion of them, when one considers the complex biochemistry
involved in regulation. What is the meaning of the intricate and massive
pathway models generated by computer algorithms? Is this even a
meaningful question to ask? And the human body contains on average an
estimated thirty-seven trillion cells!
Yet science has had great success dealing with the unthinkable and
inconceivable. Hannah Arendt puts the matter succinctly: “Man can do, and successfully do, what he cannot comprehend and cannot express in everyday human language.”5
We have mathematically sophisticated scientific theories and daily
operate with advanced engineering systems that are physically
incomprehensible and whose principles cannot be communicated in everyday
language. In Kantian terms, we are not limited by human categories of
understanding.
This radical disconnect between scientific theory and everyday human
understanding became impossible to ignore in the twentieth century.
During that time, grappling with the issue of internal model randomness,
as exemplified by quantum theory in physics, brought this problem to
the fore.
Today, scientists are grappling with the problem of model
uncertainty, as seen in areas like climate and medicine. These questions
are increasingly challenging the basis of modern scientific knowledge
itself, which is defined by a combination of mathematics and
observation. Modern scientific knowledge, while rejecting commonsense
conceptual models, has always depended upon mathematically expressed
theories that could be validated by prediction and observation. But this
approach is now under pressure from multiple sides, suggesting a deep
crisis of scientific epistemology that has not been fully confronted. At
the same time, political leaders find themselves increasingly impotent
when faced with scientific issues. As we move further into the
twenty-first century, humankind is presented with an existential
paradox: man’s destiny is irrevocably tied to science, and yet knowledge
of nature increasingly lies not only outside ordinary language but also
outside the foundational epistemology of science itself.
Scientific Knowledge: Mind and Phenomena
Scientific knowledge can be defined in terms of a duality between
mathematics (mind) and observation (phenomena). More precisely, it both
requires and provides a specifically defined link between mind and
phenomena.
Four conditions must be satisfied to have a valid scientific theory:
(1) There is a mathematical model expressing the theory. (2) Precise
relationships, known as “operational definitions,” are specified between
terms in the theory and measurements of corresponding physical events.
(3) There are validating data: there is a set of future quantitative
predictions derived from the theory and measurements of corresponding
physical events. (4) There is a statistical analysis that supports
acceptance of the theory, that is, supports the concordance of the
predictions with the physical measurements—including the mathematical
theory justifying the application of the statistical methods.
The theory must be expressed in mathematics because science involves
relations between measurable quantities and mathematics concerns such
relations. There must also be precise relationships specified between a
theory and corresponding observations; otherwise, the theory would not
be rigorously connected to physical phenomena. Third, observations must
confirm predictions made from the theory. Lastly, owing to randomness,
concordance of theory and observation must be characterized
statistically.
The meaning of a scientific theory lies in the connection between the
mathematics and experience, and that connection occurs via the process
of validation. The knowledge is functional and its meaning lies in its
predictive capacity. Mathematics divorced from experience is simply a
mental construct. It exists independently of any physical context. On
the other hand, past experience, in and of itself, does not provide
knowledge projecting into the future. Hans Reichenbach puts the matter
as follows:
If the abstract relations are general truths, they hold
not only for the observations made, but also for the observations not
yet made; they include not only an account of past experiences, but also
predictions of future experiences. That is the addition which reason
makes to knowledge. Observation informs us about the past and the
present, reason foretells the future.6
Nature is unintelligible; nevertheless, science requires that we be
able to make accurate predictions of future events based on mathematical
models in the mind. The crux of the problem is to connect the
intel-ligibility of mathematics with the unintelligibility of nature. It
would be naïve to believe that this problem has a simple solution or
even one that is completely satisfactory for all human endeavors.
The epistemology consisting of a mathematical-observational duality
was born in the seventeenth century. According to historian Morris
Kline,
What science has done, then, is to sacrifice physical
intelligibility for the sake of mathematical description and
mathematical prediction. . . . The insurgent seventeenth century . . .
bequeathed a mathematical, quantitative world that subsumed under its
mathematical laws the concreteness of the physical world. . . . Our
mental constructions have outrun our intuitive and sense perceptions.7
Kline, writing in the twentieth century, was looking back from a
post–quantum theory world and saw the full import of Newton’s basic
assumption: “For I here design only to give a mathematical notion of
these forces, without considering their physical causes and seats.” As
of 1687, scientific knowledge was constituted in mathematics;
“hypotheses” such as causality were no longer part of science.
The full import was not seen at the time because, while the equations
of classical physics did not explicitly require that their mathematical
expressions directly correspond to physical terms in the human
understanding (terms such as “particle” and “wave”), in fact they tended
to have such correspondence. This all changed in the first half of the
twentieth century when it was realized that so-called particles had wave
properties and so-called waves had particle properties....
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