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A circle doesn’t have a beginning or an end, yet folks seem to be okay dealing with them.

Personally, I’m stumbling on understanding physical fields. This looks like another field is being added, which is nice in some sense, but why do we have the number of fields that we do and what conditions are needed to create/sustain physical fields?

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The issue is not that a circle has no beginning and end, but what led to the creation of the circle in the first place? It didn't materialize from nothingness, I drew it on a paper.

Rather than materialize from nothing, every event would be connected to the next and if you proceed along the events, you'll eventually see the same/similar events again. Sort of like a circularly linked list.

Except now you have a winding number and the two circles aren't equivalent everywhere.

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