Here’s my thought process. Numbers are infinite, and decimals are infinite. Therefore units of measure are therefore infinite. A ruler may not be 1 foot long, it may be 1 + ( 1 × 10^-63836275783837472827263728) feet long.
To me, for a measurement to be exact, it has to be to the point where as you get to smaller and smaller decimals of the measurement, you get to the point where the additional decimals are infinitely 0. But if numbers are infinite, than the ability to continuously shrink down and get those decimals is infinite too. Doesn’t that mean it’s impossible to get these measurements?
And if these measurements are physically impossible to find, since the requirements for them are physically impossible to occur, doesn’t that mean that no object in the world has a physical set size? And moreso, that the space in between any two objects, as well as the size of those objects, are both by definition infinite?
In: Physics
In engineering there is the concept of “tolerances”
Though our definition of how long something is gets defined as how far a beam of light goes in a set time, exactly none of our measurements is ever 100% accurate.
So engineers usually say something like “this is 1 meter long +/- 5 mm”, we don’t know exactly, if you paid more money to use more precise measurements , you could go down to 1mm, or 1 micron, or lower, but do you really need that?
To add to this, lots of things can cause an object to change size and it would be stupid not to take this into account. Bridges have bits built into them specifically to handle changes in size as the bridge expands/contracts because it’s getting hotter/colder.
More precise machines, like stuff that places stuff withing 2-3 microns, use electronics and cameras to continually adjust themselves to keep that accurate.
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