Let me pose the following question for you to ponder. Do you consider dark matter and dark energy to be "supernatural" or "natural?" It doesn't interact with light, we can't observe it or it's very difficult to observe it even in obscurity. Really, the only reason we know it physically exists is because of the gravity it provides in the cosmos. It's particles (if we can call them that) are passing right through your body and our planet as we speak. Now you can say, well... since we scientifically have proven dark energy and dark matter exist, then they are obviously not supernatural... but were they supernatural BEFORE we knew they existed or before we scientifically proved them?
My point is, what we humans define as "supernatural" can be subjective based on our knowledge at any given point in time. If I tell you it is possible to transfer information faster than the speed of light, what would you say? At first glance, this appears to contradict physics because nothing travels faster than the speed of light. Wouldn't this be considered "supernatural" by any definition or perception? How do you explain quantum entanglement? This is when two subatomic particles alter each other's behaviors instantaneously across millions of light years. Einstein called it "spooky action at a distance."
I also have a problem with what you consider the "natural world" when I believe you base this upon your limited five senses and perception of only 4 physical dimensions. What makes you believe that your very limited ability is everything? I would suspect that a lowly ant inside an ant hill, probably believes it knows all there is to know... but does it?
What if there are "senses" that humans don't have? We see some evidence of this in the nature around us. Do you know which flowers need pollinating? Can you telepathically communicate with tens of thousands of your contemporaries instantly the way bees and ants can? We're not even masters of our own five senses... there are things that can see, taste, smell, hear and feel better than humans. Even our own sciences betray our hubris in relating to our dimensional reality-- quantum physics predicts we can't even comprehend half of the dimensions that exist. So what IS "the natural world" and how do you know that we're fully aware of it?