Is there a "Moore's Law" of length-determining apparatuses? Viz., has the precision of state-of-the-art length measurement apparatuses doubled periodically throughout history?
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MOSFET scaling
gives an idea of how precise semiconductor manufacturing has become.
Timekeeping accuracy
James A. Barnes, “Basic Concepts of Precise Time and Frequency,” Time and Frequency: Theory and Fundamentals 140 (1974): 1–14
cited on p. 2-4 of Malcolm Cooper and Jim Grozier, eds., Precise Dimensions: A History of Units from 1791-2018, IOP Expanding Physics (A History of Units from 1791 to 2018, Bristol, UK: IOP Publishing, 2017)
gives the evolution of time-measurement throughout history:
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$\begingroup$ +! for a great answer. It never ceases to amaze me how often answers like this go unappreciated and unrecognized. $\endgroup$– DJohnsonAug 7, 2022 at 14:03
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$\begingroup$ Depending on your definition of apparatus, I would only add to Geremia's comment an acknowledgement of the story wrt the introduction of metric units in post-revolutionary France (1789), a concerted effort to consolidate and standardize the enormous proliferation of differing units of measurement (estimated at over 250,000) in the Ancien Regime. Well described in this book google.com/books/edition/The_Measure_of_All_Things/… $\endgroup$– DJohnsonAug 7, 2022 at 14:18
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$\begingroup$ MDLs (minimum description length) used in information theory may be an alternative useful concept google.com/books/edition/… Similarly, the work of Marcus du Satoy (en.wikipedia.org/wiki/Marcus_du_Sautoy) discusses the growth in mathematical precision in decimal places wrt calculating pi from antiquity to the present. Apologies for the absence of nice graphics like Germia's. but for many things, power laws don't fit the reality of choppy, lumpy history of much real world phenomena. $\endgroup$– DJohnsonAug 7, 2022 at 14:20