From Lee Phillip’s book, Einstein’s Tutor, p. 107
“The theorem that Noether proved in 1918 revealed a connection between symmetries and conservation laws. But this already understates its significance. For Noether’s Theorem doesn’t merely show how these two ideas are connected; it proves they are not two separate ideas but are, and always have been, the same idea.”
For this explanations purposes I’ll discuss them separately to demonstrate the contrast between limited and limitless being.
Symmetry
In limited beings, where symmetry is the goal, exactness is the preferred result. A perfect match is sought and the degree of symmetry is judged by that standard.
However, in the limitless being of God, who creates but process rather than by intention, symmetry is of the invariably variable type. For example, oak leaves, no two are exactly alike but because if the invariable symmetry they are all oak leaves and identifiable as no other sort. Another way of describing this is to say, “all oak leaves are alike but no two oak leaves are exactly alike.” This type of symmetry is created by a being that is not confounded by infinite variety.
On the other hand, limited beings are never able to create the exact perfect matches they aim for. The differences may be very small but the goal of perfection is never achieved. Limited beings reach for the paradigmatic but only ever achieve the heuristic.
It’s because of their local and temporal being that humans crave regularity, use categories to sort reality, and discern scientific laws to explain and predict things. There is a powerful need to employ things like this in the management of life as a limited being, and they do so despite the unnaturalness it imposes on a world full of invariable variability.
Conservation
In limited beings conservation is the goal because resources are limited, and conservation strategies, being heuristic in character, generate errors.
In the limitless Deity, conservation is rooted in omnipotence. God does things without generating errors because God can do things without generating errors. Conservation is in the nature of things, and efficiency in physical reality is born of ability, not necessity.
Conclusion
Because Noether’s Theorem is about physical reality, which by extension is a result of creation by the universal process of God’s being, the creation of an invariable variety of symmetrical things conserves with complete efficiency the energy of physical matter during the ongoing processes whereby things come to be, exist for a time and then pass away in the world of things.
The paradigmatic level of physical reality as God’s physical aspect operates with a regularity born of process not necessity. The heuristic level, which I often call, the world of things, is founded on the paradigmatic level which operates as Basal Matter. This is the world human beings live in. A heuristic world where processes like Natural Selection operate, and limited beings live where everything they do generates what can be called errors. Sane rational persons do the best thing they can, but there are countless other beneficial things that could have been done with their limited time. This is a good example of error based in limitation, not to be confused with some sort of moral lapse.
Existing as local, temporal, and discrete beings, they could not do otherwise.
Because the paradigmatic level of reality is in essence the boundless being and limitless personality of God limited beings are not able to achieve a complete understanding of it. We are forever seeking ‘laws’ to explain the operations of a Being not confounded by infinite variability. These things are good and useful to us, because we are limited beings, but they will always fall short and generate errors, because they are, like the people who form them, heuristic by nature.
The paradigmatic and heuristic levels introduced during this discussion are not distinct in the operations of the universal process. The distinction is a creation of this author’s explanation strategy. Like all human created categories they help limited minds understand reality, but are not themselves, reality.