I've always been fascinated by the concept of time, or rather temporality, because time is too reductionist. I think that the theory of relativity was a natural outgrowth of the work that was done to develop a universal time system which required clocks to be synchronized. This requirement was borne out of the improvements in transportation and communication precipitated by the need for a proper train schedule. Back in the day, everywhere had their own way of keeping time, which, when dealing with train travel over long distances just wasn't tenable.
I find reading a train schedule surprisingly difficult, and I used to make mistakes all the time. I've gotten a bit better at it with experience, but when I was little I felt they were a bit mind-boggling. I think it was Poincare who first tried to synchronize the clocks in Paris, which shows that even before relativity, this task was no trivial matter. I find it fitting that GPS, which requires proper time keeping, wouldn't work without general relativity, because to me that's what relativity is all about, a way to synchronize clocks. It's also great that such a practical matter would lead to such a seemingly impractical and abstract theory.
The question of clock synchronization is interesting but is really just a manifestation of temporality, it isn't temporality itself. Temporality is about what we experience, and about a kind of structure in the world and in us, and time is just a number. I think it's important not to confuse the two. People do this all the time, they objectify their experience and then confuse the objects they've created with the experience, which is not an object per se. It's a deficiency in human understanding that we have to reduce things to what they're not in order to understand them. We can never really know what time is from the words and equations we pronounce because in describing and analyzing it it becomes something which it is not. Perhaps this is the most we can say in a way about time, or at least this is something we should say about it. We are fascinated by the image presented us in the mirror, but what is in that mirror is only an image. That of which we intend to speak is what is in some sense responsible for that image, but it is far more than it. I guess it's a kind of narcissism that human nature requires us to have. At least we should be aware of it, if we can do nothing else.
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