Jun 15, 2021 04:25 PM
https://iai.tv/articles/the-creative-uni..._auid=2020
EXCERPT: . . . This is a familiar maneuver in popular physics books these days—claims of concretizing what is inescapably abstract, usually by way of a purely speculative and untestable assertion costumed mathematically as a testable hypothesis. It is a cheap instrument, as attractive as it is defective, used more often as cudgel than tool for exploration. Fortunately, as we saw with David Albert, few despise its dull edge more than other physicists and mathematicians. During the first years of modern mathematical physics and the construction of its two central pillars, quantum theory and relativity theory, Alfred North Whitehead warned, “There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.”
Whitehead would later generalize this error as the “fallacy of misplaced concreteness.” It is often oversimplified as merely mistaking an abstract conceptual object, like a mathematical or logical structure (e.g., the number zero, or the concept of “nothingness”), for a concrete physical object. But the fallacy has more to do with what Whitehead argued was the chief error in science and philosophy: dogmatic overstatement. We commit the fallacy of misplaced concreteness when we identify any object, conceptual or physical, as universally fundamental when, in fact, it only exemplifies selective categories of thought and ignores others. In modern science, the fallacy of misplaced concreteness usually takes the form of a fundamental reduction of some complex feature of nature—or even the universe itself—to some simpler framework. When that framework fails, it is replaced with a new reduction—a new misplaced concreteness, and the cycle repeats.
Scientific progress is marked by these cycles because “failure” doesn’t mean the reduction was entirely wrong; it just means it wasn’t as fundamental—as concrete—as previously supposed. Our understanding of nature does increase, just not at the expense of nature’s complexity. In this regard, the reductive mathematization of natural philosophy over the last 500 years has proven to be both its greatest strength and its greatest hazard. The fundamental objects of modern physics are no longer understood as material physical structures but rather as mathematical structures that produce physically measurable effects. The waves of quantum mechanics are not material-mechanical waves; they are mathematical probability waves. The “fabric” of spacetime in relativity theory is pure geometry.
Scientific progress is marked by these cycles because “failure” doesn’t mean the reduction was entirely wrong; it just means it wasn’t as fundamental as previously supposed.
With his “Mathematical Universe Hypothesis,” physicist Max Tegmark has concretized these and other examples of fundamental mathematical objects into a simple reduction: the universe is mathematics. In contemporary mathematical physics, he argues, there is no longer a distinction between a world described by mathematics and a world explained as mathematics. Tegmark characterizes physics as entailing nothing less than a one-to-one correspondence between physical reality and the mathematical structure by which we define this reality. “If our external physical reality is isomorphic to a mathematical structure,” he concludes, “it therefore fits the definition of being a mathematical structure… In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics.”
The artful incoherence of “mathematics approximating mathematics” evinces the misplaced concreteness of the premise it presupposes. The fact that some features of reality are usefully describable as abstract mathematical structures does not necessarily entail that all features of reality are reducible to concrete mathematical structures. What would compel Tegmark to attempt such a leap? What would compel Krauss? “The aim of science,” Whitehead writes, “is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, ‘Seek simplicity and distrust it.’” And then investigate further... (MORE - details)
EXCERPT: . . . This is a familiar maneuver in popular physics books these days—claims of concretizing what is inescapably abstract, usually by way of a purely speculative and untestable assertion costumed mathematically as a testable hypothesis. It is a cheap instrument, as attractive as it is defective, used more often as cudgel than tool for exploration. Fortunately, as we saw with David Albert, few despise its dull edge more than other physicists and mathematicians. During the first years of modern mathematical physics and the construction of its two central pillars, quantum theory and relativity theory, Alfred North Whitehead warned, “There is no more common error than to assume that, because prolonged and accurate mathematical calculations have been made, the application of the result to some fact of nature is absolutely certain.”
Whitehead would later generalize this error as the “fallacy of misplaced concreteness.” It is often oversimplified as merely mistaking an abstract conceptual object, like a mathematical or logical structure (e.g., the number zero, or the concept of “nothingness”), for a concrete physical object. But the fallacy has more to do with what Whitehead argued was the chief error in science and philosophy: dogmatic overstatement. We commit the fallacy of misplaced concreteness when we identify any object, conceptual or physical, as universally fundamental when, in fact, it only exemplifies selective categories of thought and ignores others. In modern science, the fallacy of misplaced concreteness usually takes the form of a fundamental reduction of some complex feature of nature—or even the universe itself—to some simpler framework. When that framework fails, it is replaced with a new reduction—a new misplaced concreteness, and the cycle repeats.
Scientific progress is marked by these cycles because “failure” doesn’t mean the reduction was entirely wrong; it just means it wasn’t as fundamental—as concrete—as previously supposed. Our understanding of nature does increase, just not at the expense of nature’s complexity. In this regard, the reductive mathematization of natural philosophy over the last 500 years has proven to be both its greatest strength and its greatest hazard. The fundamental objects of modern physics are no longer understood as material physical structures but rather as mathematical structures that produce physically measurable effects. The waves of quantum mechanics are not material-mechanical waves; they are mathematical probability waves. The “fabric” of spacetime in relativity theory is pure geometry.
Scientific progress is marked by these cycles because “failure” doesn’t mean the reduction was entirely wrong; it just means it wasn’t as fundamental as previously supposed.
With his “Mathematical Universe Hypothesis,” physicist Max Tegmark has concretized these and other examples of fundamental mathematical objects into a simple reduction: the universe is mathematics. In contemporary mathematical physics, he argues, there is no longer a distinction between a world described by mathematics and a world explained as mathematics. Tegmark characterizes physics as entailing nothing less than a one-to-one correspondence between physical reality and the mathematical structure by which we define this reality. “If our external physical reality is isomorphic to a mathematical structure,” he concludes, “it therefore fits the definition of being a mathematical structure… In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics.”
The artful incoherence of “mathematics approximating mathematics” evinces the misplaced concreteness of the premise it presupposes. The fact that some features of reality are usefully describable as abstract mathematical structures does not necessarily entail that all features of reality are reducible to concrete mathematical structures. What would compel Tegmark to attempt such a leap? What would compel Krauss? “The aim of science,” Whitehead writes, “is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, ‘Seek simplicity and distrust it.’” And then investigate further... (MORE - details)