Dr Katie Mack, Hawking Chair in Cosmology and Science Communication at the Perimeter Institute for Theoretical Physics: "A physicist's task is to constantly create equations that keep up with our observations of physical phenomena." https://www.sciencefocus.com/news/everything-physics-made-up/
This is the inductive method or, in more technical terms, curve fitting:
"Curve fitting is the process of adjusting a mathematical function so that it fits as closely as possible to a given set of data points. The function can then be used as a mathematical model of the underlying data." https://www.coursehero.com/file/22708453/Lecture-10/
Instructive descriptions of the inductive method in physics:
Ethan Siegel: "Scientific Theories Never Die, Not Unless Scientists Choose To Let Them. When it comes to science, we like to think that we formulate hypotheses, test them, throw away the ones that fail to match, and continue testing the successful one until only the best ideas are left. But the truth is a lot muddier than that. The actual process of science involves tweaking your initial hypothesis over and over, trying to pull it in line with what we already know...By the addition of enough extra free parameters, caveats, behaviors, or modifications to your theory, you can literally salvage any idea. As long as you're willing to tweak what you've come up with sufficiently, you can never rule anything out." https://www.forbes.com/sites/starts...die-not-unless-scientists-choose-to-let-them/
Sabine Hossenfelder (Bee): "The criticism you raise that there are lots of speculative models that have no known relevance for the description of nature has very little to do with string theory but is a general disease of the research area. Lots of theorists produce lots of models that have no chance of ever being tested or ruled out because that's how they earn a living. The smaller the probability of the model being ruled out in their lifetime, the better. It's basic economics. Survival of the 'fittest' resulting in the natural selection of invincible models that can forever be amended." http://www.math.columbia.edu/~woit/wordpress/?p=9375
Before 1915 theoretical physics was mainly DEDUCTIVE - you cannot tweak your theory unless the tweak is deducible from initial axioms (postulates). In 1915 Einstein replaced deduction with induction, and unlimited ad hoc adjustment, unrelated to any axioms, was allowed. Here Michel Janssen describes relentless adjustment performed again and again until "excellent agreement with observation" was reached:
"Einstein did not give up the Einstein-Grossmann theory once he had established that it could not fully explain the Mercury anomaly. He continued to work on the theory and never even mentioned the disappointing result of his work with Besso in print. So Einstein did not do what the influential philosopher Sir Karl Popper claimed all good scientists do: once they have found an empirical refutation of their theory, they abandon that theory and go back to the drawing board...On November 4, 1915, he presented a paper to the Berlin Academy officially retracting the Einstein-Grossmann equations and replacing them with new ones. On November 11, a short addendum to this paper followed, once again changing his field equations. A week later, on November 18, Einstein presented the paper containing his celebrated explanation of the perihelion motion of Mercury on the basis of this new theory. Another week later he changed the field equations once more. These are the equations still used today...It is not hard to imagine Einstein's excitement when he inserted the numbers for Mercury into the new expression he found and the result was 43", in excellent agreement with observation." Janssen, M. (2002) The Einstein-Besso Manuscript: A Glimpse Behind the Curtain of the Wizard. In The Collected Papers of Albert Einstein (Vols. 1-10, pp. 1987-2006). Princeton, NJ: Princeton University Press.
DEDUCTION from clearly defined axioms (postulates) is the only reasonable method in fundamental physics:
"By a theory I shall mean the deductive closure of a set of theoretical postulates together with an appropriate set of auxiliary hypotheses; that is, everything that can be deduced from this set." W. H. Newton-Smith, THE RATIONALITY OF SCIENCE, p. 199 http://cdn.preterhuman.net/texts/thought_and_writing/philosophy/rationality of science.pdf
Here Einstein suggests that deduction, not induction, is the correct method:
Albert Einstein: "From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise. But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms." https://www.marxists.org/reference/archive/einstein/works/1910s/relative/ap03.htm
The crucial question is: What if a theory in physics is not deductive (no clearly defined axioms; no explicit deductive paths leading from axioms to conclusions; unlimited ad hoc adjustment is allowed)?
Answer: Then the theory, e.g. Einstein's general relativity, is a not-even-wrong inductive concoction, essentially equivalent to curve fitting models.
This is the inductive method or, in more technical terms, curve fitting:
"Curve fitting is the process of adjusting a mathematical function so that it fits as closely as possible to a given set of data points. The function can then be used as a mathematical model of the underlying data." https://www.coursehero.com/file/22708453/Lecture-10/
Instructive descriptions of the inductive method in physics:
Ethan Siegel: "Scientific Theories Never Die, Not Unless Scientists Choose To Let Them. When it comes to science, we like to think that we formulate hypotheses, test them, throw away the ones that fail to match, and continue testing the successful one until only the best ideas are left. But the truth is a lot muddier than that. The actual process of science involves tweaking your initial hypothesis over and over, trying to pull it in line with what we already know...By the addition of enough extra free parameters, caveats, behaviors, or modifications to your theory, you can literally salvage any idea. As long as you're willing to tweak what you've come up with sufficiently, you can never rule anything out." https://www.forbes.com/sites/starts...die-not-unless-scientists-choose-to-let-them/
Sabine Hossenfelder (Bee): "The criticism you raise that there are lots of speculative models that have no known relevance for the description of nature has very little to do with string theory but is a general disease of the research area. Lots of theorists produce lots of models that have no chance of ever being tested or ruled out because that's how they earn a living. The smaller the probability of the model being ruled out in their lifetime, the better. It's basic economics. Survival of the 'fittest' resulting in the natural selection of invincible models that can forever be amended." http://www.math.columbia.edu/~woit/wordpress/?p=9375
Before 1915 theoretical physics was mainly DEDUCTIVE - you cannot tweak your theory unless the tweak is deducible from initial axioms (postulates). In 1915 Einstein replaced deduction with induction, and unlimited ad hoc adjustment, unrelated to any axioms, was allowed. Here Michel Janssen describes relentless adjustment performed again and again until "excellent agreement with observation" was reached:
"Einstein did not give up the Einstein-Grossmann theory once he had established that it could not fully explain the Mercury anomaly. He continued to work on the theory and never even mentioned the disappointing result of his work with Besso in print. So Einstein did not do what the influential philosopher Sir Karl Popper claimed all good scientists do: once they have found an empirical refutation of their theory, they abandon that theory and go back to the drawing board...On November 4, 1915, he presented a paper to the Berlin Academy officially retracting the Einstein-Grossmann equations and replacing them with new ones. On November 11, a short addendum to this paper followed, once again changing his field equations. A week later, on November 18, Einstein presented the paper containing his celebrated explanation of the perihelion motion of Mercury on the basis of this new theory. Another week later he changed the field equations once more. These are the equations still used today...It is not hard to imagine Einstein's excitement when he inserted the numbers for Mercury into the new expression he found and the result was 43", in excellent agreement with observation." Janssen, M. (2002) The Einstein-Besso Manuscript: A Glimpse Behind the Curtain of the Wizard. In The Collected Papers of Albert Einstein (Vols. 1-10, pp. 1987-2006). Princeton, NJ: Princeton University Press.
DEDUCTION from clearly defined axioms (postulates) is the only reasonable method in fundamental physics:
"By a theory I shall mean the deductive closure of a set of theoretical postulates together with an appropriate set of auxiliary hypotheses; that is, everything that can be deduced from this set." W. H. Newton-Smith, THE RATIONALITY OF SCIENCE, p. 199 http://cdn.preterhuman.net/texts/thought_and_writing/philosophy/rationality of science.pdf
Here Einstein suggests that deduction, not induction, is the correct method:
Albert Einstein: "From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise. But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms." https://www.marxists.org/reference/archive/einstein/works/1910s/relative/ap03.htm
The crucial question is: What if a theory in physics is not deductive (no clearly defined axioms; no explicit deductive paths leading from axioms to conclusions; unlimited ad hoc adjustment is allowed)?
Answer: Then the theory, e.g. Einstein's general relativity, is a not-even-wrong inductive concoction, essentially equivalent to curve fitting models.
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