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The Equation of Time, huh?...
I find that quite intriguing. Time, as I see it, is the relation of observable objects between each other. In fact, I find it quite surprising that technically, time passes differently on other planets by merit of their axis-...es. Plural. So, you could say you would require entirely different time terminology on Uranus. Like, longer seconds, man.
I suppose it wouldn't be too Farfetch'd to say that Time is Math. ...and not the other way around; for Math certainly involves far more than just what is observable, like the revolution of planets.
In fact, I seem to recall that "days" on some planets, like Mercury last for basically months at a time. Just because 12 hours have passed, doesn't mean the Light has faded to Night. Perhaps more elaboration on terms would be required for such?
I am very much interested in math as it relates to Time. For if Time is how we are positioned to the Sun... perhaps there is some comfort in knowing things are where they typically are. Roughly. On estimate.
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Time doesn't pass differently on different planets due to their differing rotations - rather, 'one day' as a unit of time is simply defined as 'one rotation of a planet around its axis' and thus differs for each planet. Seconds aren't directly defined in terms of planetary rotation, so they may be said to stay the same length no matter what planet you're on.
There are several very different aspects of time that should be separated here: time in terms of dimensionality, time in terms of change, and time in terms of its units.
Units of time are essentially arbitrary. The various defined lengths of days and seconds and months and spins around the sun and whatnot have as little bearing on the actual nature of time as the difference between centimeters and inches has on the nature of space. The equation of time is also quite arbitrary in that it's just a conversion between sundial readings and digital clock readings - modern clocks are no longer based on the position of the sun in the sky, but are based on how fast a caesium atom oscillates under carefully defined conditions (as per the SI definition of a second). This is because the oscillation of a caesium atom is the most precisely regular 'tick-tock' rhythm in the known universe, and is thus the most reliably accurate thing we can base our clocks on.
Time in terms of dimensionality is where we start talking about spacetime. Space and time are a single unified Thing, constituting the four dimensions of our universe (length, breadth, height, and time). This combination space-time Thing is warped by matter in a phenomenon known as 'gravity', which causes time to distort such that some caesium atoms can tick at different rates to other caesium atoms. However, this effect can be accounted for and eliminated in our calculations and clocks, so fortunately our caesium-based time-unit definition still works good.
Time in terms of change is what distinguishes time from breadth, height and depth, even though all four of these are facets of a single dimensional Thing. Nobody knows what change actually is or why we perceive it to occur, and there are several horrifyingly difficult logical and physical problems intrinsic to defining it. This is the aspect of time that we really don't understand on any level.
Maths includes all three of these aspects of time, I'm sure you'll be thrilled to know - the four broad subjects of mathematics are Quantity, Dimensionality, Change and Structure, and the first three of these are quite similar to the mentioned notions of time in terms of units, time in terms of dimensions, and time in terms of change, respectively. I don't think time can be said to have a 'structure', as such, but we can't expect any single concept to measure up to mathematics.
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@Duality now i remember you!!!! You're the smart one! Sup
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based on how fast a caesium atom oscillates under carefully defined conditions
But doesn't that seem disingenuous? If it only acts like that because you made up a situation where it was forced to do that, and not what it does typically, aren't you just inventing arbitrary measurements again?
I was under the impression Time was related to basically how much Light there was. ...Uhh, when it was day time. So arguably, if your on another planet where the days last much longer, then so too must the hours be longer. Hours are fractions of a day, so if the day is longer... then every other measurement has to be bumped up to match, yes?
What does Dimensionality mean?
What i'm thinking is: Speed is refered to as Distance Covered over Time. So yeah, it follows that Space & Time are metaphorically married in the sense that you can't tell how much time has passed if you can't distinguish the amount of what has changed, and you can't determine how much space has been covered if you aren't aware of how long it took. Roughly, that it all comes back around to how things relate to each other. Time is relations.
Time is Friendship! Time is Magic!
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