Space and time are physical phenomenon that modern physics is able to define substantially to an extent. Occurrence of event in certain space is recognized by us as function of time and few forces that we understand. Physicists believe that space and time are interchangeable. Most of the theories try to capture space-time by defining the interval between events. Not just these intervals, whole concept of space-time can only be derived independent of observer.

Now imagine city to be a Euclidean space. Different dimensional aspects of social structures, identities, economy, jobs, aspirations, thoughts,……………..n(where n=everything that builds urban). All these layered over each other, forming a manifold. Like physicists see, multiple manifolds are clearly visible in urban practice. These things are visible as clear or diminished(rapidly evolving, eg. social structures) quantities. We can use diffeomorphism to generate a local symmetry in these manifolds by using point to point structuring. And tensor can be equated out of it, and balanced as well. A global symmetry can also be developed if the points in this manifold are picked up together in spacetime. Since we have isomorphic manifold, spherically symmetric spacetime in cities can also be defined up to an extent.

Our modern city runs like an evolving clock, individuals going to work in morning creates a certain pattern in certain days which a dweller would understand closely. If you leave your city and return after 3 years, you might take a week for toning into evolved pattern. Certain spaces reflect specific nature repeatedly in pattern. This pattern may not be time for an individual as the real-time conditions would define his pattern(for eg. if on being ill, he/she might not go to work), but it is timed for a pattern that has to occur in the larger consciousness of a city(for eg. morning red light will be crowded irrespective of individual actor). The event would have a unique position but not a unique place in time. This raises a question that if city is distorted space-time?

Now we would have to jump through ‘Δt’ as it is non-existent. Hence, the idea of interval is now irrelevant. You might try killing, homothetic, affine, conformal or any other symmetry which may not require time. But not knowing interval is nugatory for four-dimensional beings like us hence the space of city(complexity) is still defined without time.

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Good initiative….

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