However, once you stop equating the supernatural with religion,
You cannot stop equating the supernatural and religion. They are one in the same no matter what you want to believe.
You are talking in absolutes and creating a dichotomy that doesn't exist. I think you are also failing to understand both religion and science. Maybe you are a student. You are also holding a childish caricature of what is often attributed to the supernatural (e.g. "purple fish in your head")
Religion has nothing to do with the supernatural. It is a social construct. Religion has, however, created a mythos, fables of sort, to help define how one should live. Sometimes it relates to the supernatural. That certainly isn't one and the same.
Regardless, I won't be discussing religion with you nor is it relevant to this thread...
it begins to make sense that there are invisible laws that govern that natural law is incapable of evaluating.
There is absolutely no reasoning behind that assertion other than to make people feel better about holding beliefs that all evidence contradicts. It is complete nonsense. Spurious reasoning and pseudo-insightfulness is not an argument.
First, I hold no beliefs and only speak from experience, insight, and education. The same with those who came before me. So what does that say about your ability to reason? It means what you just said was nonsense (i.e. not applicable). That's a failure of reasoning and comprehension on your part. You shouldn't be so quick to dismiss thousands of years of thought; that's naively dangerous.
Neither does evidence contradict the supernatural, quite the contrary. This is a thread on the topic of cosmology, which is a subset of metaphysical philosophy which sets out to explain both the natural and supernatural.
Let's take a moment to describe what the supernatural is...
I will use the word you just used, "belief". If I believe something will happen, the likelihood of it occurring has been increased beyond measure. It's a paradox. Belief itself is power and has the ability to bend natural law. Science is beginning to recognize this in theory.
Take another example... for instance, higher thought itself is independent of a singular mind and is transcendental. I would attribute this to the supernatural. What about you? It certainly doesn't involve natural law.
Science is only one method of reason and measurement
Another statement complete void of meaning. Name one other method- one that isn't purely begging the question.
Sure... Poetry, Philosophy, Art-- all higher schools of thought and reasoning that science derives its pursuits from.
What you are doing by holding the science of natural law as some supreme form of thought is dismissing its very origin. You are divorcing it from all beauty and higher purpose.
Let's take poetic symbolism as an example of a predecessor, as it is regarded as the highest form of thought and consciousness:
"the sound of stars" or "the grinding of cosmos". Only until recently did science recognize that stars emit sound and is actually a useful way to deduce their internal composition.
Same applies to the work of Newton and Einstein.
What we attribute to being of the supernatural is the occurrence of the improbable and impossible.
Bolded for emphasis. We call it "impossible" because it can't actually happen, like the supernatural. The improbable is not supernatural. Rolling 10 sixes in a row on an unweighted die is improbable but not supernatural. Things considered supernatural are not improbable- they are impossible. That is why they are labelled supernatural.
Take your 10 sixes and roll them again a billion times. Would you say that was impossible or improbable? Can you fully understand what it would take to reproduce our current existence starting from the big bang? No, you can't. Nor is it reproducible. We only have rudimentary theories based upon our current comprehension that we may never be able to practice.
What other forces are involved?
Science is still in its infancy and today depends upon higher schools of thought to direct its pursuits. Perhaps one day it will have a broader reach.
And by this what you actually mean is: I don't fully agree with the implications so I'll assert that it doesn't apply.
No, I agree with its implications it is just not all-encompassing. I am not the one with the hang-up here. You are the one narrowing its scope to what we understand as natural law.
What I meant is exactly what I said: that science is currently an "inferior" school of thought and means of reasoning. It has barely begun to explain life. Art is light years ahead.