Matters of Tolerance(nybooks.com)
nybooks.com
Matters of Tolerance
https://www.nybooks.com/articles/2018/10/25/precision-accuracy-perfectionism/
4 comments
In mechanical design, there is the related problem of how to make a system which has the minimum number of constraints while performing correctly: https://ocw.mit.edu/courses/mechanical-engineering/2-76-mult...
A bridge which is supported by a horizontal hinge at one end, and rests on a roller at the other, is effectively fixed, but it's not over-constrained by being attached at both ends. This isn't quite what you are talking about: rather than somehow covering up error due to large tolerances, or cancelling it out (as in a gridiron pendulum or PAL tv signal) degrees of freedom are included in the mechanical design so that those errors don't have structural repercussions.
Kinematic couplings use in mounts for precision instruments use all sorts of interesting combinations of geometrical contact surfaces, with the goal being repeatability rather than accuracy: the instrument always ends up at precisely the same location, and there are no potentially distorting stresses in the structure (as would inevitably occur if there were multiple over-constrained points of attachment)
https://www.precisionballs.com/Micro_Inch_Positioning_with_K... https://www.precisionballs.com/basic_kinematic_designs.php
A bridge which is supported by a horizontal hinge at one end, and rests on a roller at the other, is effectively fixed, but it's not over-constrained by being attached at both ends. This isn't quite what you are talking about: rather than somehow covering up error due to large tolerances, or cancelling it out (as in a gridiron pendulum or PAL tv signal) degrees of freedom are included in the mechanical design so that those errors don't have structural repercussions.
Kinematic couplings use in mounts for precision instruments use all sorts of interesting combinations of geometrical contact surfaces, with the goal being repeatability rather than accuracy: the instrument always ends up at precisely the same location, and there are no potentially distorting stresses in the structure (as would inevitably occur if there were multiple over-constrained points of attachment)
https://www.precisionballs.com/Micro_Inch_Positioning_with_K... https://www.precisionballs.com/basic_kinematic_designs.php
The first paragraph reminds me of the great example by which J.L. Austin distinguished precision from exactness: a stick could be exactly, but not precisely, six bananas long.
In the present case we could say that six random bananas could accurately but not precisely represent the length of a stick.
In the present case we could say that six random bananas could accurately but not precisely represent the length of a stick.
My go-to example of explaining accuracy vs. precision is the distance from Earth to its moon. 400 000 km or 250 000 miles is a fairly accurate, but imprecise figure. 31 415 926 nanometers is a ludicrously precise, and incredibly inaccurate one.
Also, accuracy is dependent on appropriate precision. Rounded up to nearest billion kilometers the moon is zero terameters away from the Earth, which is only accurate if you're comparing it on a scale where the Moon is insignificant. Conversely, reporting the exact distance to the nearest meter will imply variations insignificant on one-meter scale, which is obviously wrong, making a less precise figure more accurate for use over an arbitrary period of time.
Also, accuracy is dependent on appropriate precision. Rounded up to nearest billion kilometers the moon is zero terameters away from the Earth, which is only accurate if you're comparing it on a scale where the Moon is insignificant. Conversely, reporting the exact distance to the nearest meter will imply variations insignificant on one-meter scale, which is obviously wrong, making a less precise figure more accurate for use over an arbitrary period of time.
Some wide tolerances aren't caused by workmanship but by mechanical stress or thermal expansion. For instance, bridges usually have a set of roller wheels between the deck and the piers, allowing them to move relatively by several centimeters.
Mechanical timekeeping is a study in having some kinds of thermal expansion cancel out other kinds.
The article mentions silicon as a domain of precision, but just as much effort goes into designing transistors that work with as much lithography error as possible.