In a essay about the meaning of life, the famous scientist Schrodinger once said "Physical laws rest on atomic statistics and are therefore only approximate" (http://www.whatislife.ie/downloads/What-is-Life.pdf , page 4).
At the same time, I have always wondered about the origins of different laws that are used in the natural sciences and engineering disciplines. For instance, consider the following:
- Young's modulus ($E$): dating back to the year 1727 - is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied lengthwise. It quantifies the relationship between tensile/compressive stress ($\sigma$) and axial strain ($\epsilon$) in the linear elastic region of a material and is determined using the formula.
Mathematically, Young's modulus can be expressed as :$$E=\sigma/\epsilon$$
Even to this day, we can continue to see the "approximate and data based nature" of this theoretical concept:
I have always wondered how the formula for Young's modulus was determined at the time. If I were to speculate, using today's terminology - I would guess that:
A "parametric form specifying the relationship between the entities of interest" (i.e. "model") was decided, possibly based on some "prior hunches". For instance, $E_1 = \sigma / \epsilon$ vs. $E_2 = \sigma + \epsilon$, vs. $E_3= \sigma + \epsilon + \text{some constant}$ , $E_4 = \sigma^2 / \epsilon$ etc.
Next, data was probably collected through a series of experiments in which measured the resulting "stiffness" (i.e. $E$) for different values of "stress" (i.e. $\sigma$) and "strain" (i.e. $\epsilon$).
Finally, different candidate "models" for Young's modulus were compared against the data collected from these experiments. The "model" which performed the "best" (i.e. predicted the closest "stiffness" for some given "stress" and "strain") was likely selected as an early form of Young's modulus.
Thus, can some please tell me - is it unreasonable to believe that the "idea of regression" might have long predated its formal inception, and (as Schrödinger said) many theoretical laws in science and engineering have their roots in this early experimental regression idea instead of pure theoretical abstraction? Were such scientists responsible for these scientific laws actually performing some early version of machine learning and cross validation?
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