[BikerNYC]

Given the "nature" of nature, logic requires that the symmetries be equivalent to the corresponding Conservation Law.

Thanks for your response. This comment of yours strikes at the heart of the matter.

How did it come to be that nature has the nature it has? How did it come to be that nature is logical in the way it is? How did it come to be that there are symmetries at all?

I don't really expect a scientific answer to these questions since they are not really scientific in nature. The answers get to the underlying reason(s) for how physical laws developed. One can always push the envelop back and state that y is the result of x; for example, that time was created in the Big Bang. But how did a state of affairs come to be so that the creation of time could even be a possible result of the Big Bang?

[longshadow]

How did it come to be that nature has the nature it has? How did it come to be that nature is logical in the way it is? How did it come to be that there are symmetries at all?

I don't really expect a scientific answer to these questions since they are not really scientific in nature.

I think you answered your own question, in that in effect you are asking "why are things as they are?"

Science deals with the question of "what" and "how"; philosophy deals with questions like "why?".