HOW DO YOU MEASURE MEASUREMENT?
How fast does the hand go around a clock-face?
You compare with another speed: you say the little hand goes around 24 hours while the Earth goes around its axis 1 time.
So you compared ONCE around the clock (which you called "24 hours") and ONCE sunrise to sunrise say.
You MEASURED each in terms of the other (like Zeno's Arrow the first division). Whatever number you wanted to call each (you called the clock "24 hours" and called the Earth "24 hours sunrise to sunrise"); you noted that you seemed to be able to match the clock and the Earth to have same beginnings and same endings say; it looks.
How did you get your clock little-hand to go at just the right speed to start at sunrise and stop after one revolution say at surise tommorrow?
Well if your clock little-hand went around say 4 and a half times from sunrise to sunrise; you could then make another clock that went around one time to the 4 and a half.
But what is "how fast" then? If you say "24 hours" in "1 sunrise to sunrise" you are saying "shared beginning, shared ending, think of a number to share too", it looks say.
If the beginnings and endings are "at the same time", how can you measure "time" if they are at the same time?
But if they are at different "times"; you still have a problem? How much does one ending overshoot the other say? Or by how much does the other finish early? How much does one start before the other; or the other start late?
Sounds like "the hare and the tortoise"?
How can you measure by how much one clock starts before or after the other? Or by how much one finishes early or late?
If you do not DIVIDE one or the other into segments; how can you measure one rotation against another, when they do not appear to start and finish together?
Well: you COULD refer to a third rotation that say starts at the same time as one rotation but finishes say earlier than both of the original two compared rotations.
If you got two of your third rotation fitting exactly into one of your first rotations; you managed to divide the first one in two.
But that might not be enough to measure your second rotation; if it overshoots the first rotation by less or more than an exact multiple of your divisions of your first rotation.
How do you measure your remainder; the bit of unknown time that was more than an exact multiple of your divisions of your first rotation as divided exactly by your third?
Well: you could treat the "remainder" if it is smaller than your division; as something that you can go back and divide up your divisions into smaller bits. Until you are left with a new remainder: then you could go forwards and use the NEW remainder to divide up your MOST RECENT division of division.
And so on, back and forth "in time" till you have no remainder left (or till it is as small as your initial certainty about synchronising beginnings and endings in the first place? say)
After using a third rotation (that happened to eactly divide a first rotation in two) to try to measure the lateness of a second slower rotation
; if you found the remainder was bigger than one extra division; you just add as many as you need till you get a remainder that is smaller. Then you can use that remainder to go back and divide up your division into NEW divisions.
Of course; you might never have got a "so happens" that a second rotation was exactly half the speed of a first rotation.
The first division COULD have been unequal.
But then you can just take the big bit and divide it by the small bit till you have a remainder. Then you could take the remainder and go back and divide the small bit by this smaller remainder-bit; till it is an exact fit or till you get a NEW remainder.
You could keep going back and forth getting remainders; then dividing the most recently smallest bit with the later smaller-still remainder-bit; till you get a near-enough exact division.
This looks like "long division".
This also seems like the way numbers are constructed out of repeated divisions of a total by self-referentialy going back and forth re-defining what "halving" means in terms of dividing the total.
If you have two measurements compared; and they have the same number-name; then you can get a pattern of interference fringes projected by the ways each number can define the other in terms of how each number is built up in a back-and-forth Zeno's arrow-like manner of self-referent divisions.
If the numbers are different; you might get a kind of mathematical hologram projected by the differences.
If you compare several different numbers; you might get an effect like giant ghostly blocks of dots crashing through each other partly disintegrating; as mathematical holograms interfere constructively and destructively to give "every way of the different numbers describing the ways they can interact through internal self-reference in number-building and mutual self-reference in number-comparing; say”.
"How do you know if things are synchronised" seems a funny question as if they are MEETING they already have a "same-difference" or common ground.
Things that exist are different, unique, if they were the same in every way; have no longer "they"?
Seems that the noion of "same start" or "same ending" involves a third "start-ending" that is the reference frame. So long as the other starts or endings are within the reference frame "start to ending" they get regarded as synchronised?
But actually of the three "start to ending"s; which is to be the one within which the other two fit?
Which "start" ocurs in the middle of the other two "starts", or between one of the other two "starts" and one of the other two "endings"?
Which ending occurs in the middle of the other two "endings", or between one of the other "starts" and one of the other "endings"?
Maybe: if I put both hands down at once on a desk: I am one "start to ending"; the desk is another "start to ending"; and my hands are simultaneous so share common start and ending in this scenario?
All very puzzling.