I wrote this thought down, and came back to it from time to time. Nowadays (that is, after thinking about it some more), I see a clear distinction between the natural delimitation, a delimitation that doesn't break continuity (like light and shadow cast by the Sun) and the artificial delimitations we all make: instead of seeing our continuous existence, "flowing" from one "present moment" to the next "present moment", we see ourselves having a discrete existence, composed of different episodes, disconnected, discontinuous.
Instead of seeing the continuity, we see "day", "week", "Monday", "last year", "during lunch break", "when I exited the office building last evening", et caetera.
It's a useful abstraction, enabling everything from business contracts to most technology, to weekend plans, to cookie recipes.
It's still an abstraction though, and as useful as it is, it can be equally useful to look behind it.
When you try switching back from a discrete perception to a continuous one (that is, if you actually do try), you start seeing lots of other illusions you cling to, constructs relying of other constructs, things we all accept as "in the nature of things" ...
Lets take age as an example.
We have a minimal age for legally drinking, you can be too old or too young to behave in a certain way and your rights vary depending on what age-group you happen to find yourself in.
Age as a measure though, is not telling you something specific about a person. If anything, it's actually telling you how many times the Earth rotated around the Sun, since that person was born. Thus, age is an affirmation about the Earth's movement, giving that person's existence as a reference point, and not an affirmation about that person itself.
Further more, it seems that time itself is an illusion.
Clocks don't measure time; they measure themselves.
hairy university professor with young girlfriend, The Man from Earth
To that regard, I found an interesting article on the nature of time itself, that directed my thoughts to a different perspective: the article argued that time, in a scientific context, cannot be perceived as an orthogonal dimension but is in fact, always expressing a measure of movement (one second being, for example defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom).
It's an interesting read, if you have the time for it (pun intended).
So in the end, do we measure time, or define it and cling to our definition?