Kogan, you still have this weird dichotomy between science and magic, but I think it is probably because nearly everyone has this weird dichotomy between science and magic.
When the ignorant person says “This is magic,” what does he mean when he says that?
“This is [following a set of rules humanity can not grasp]”?
Then the universe is rather likely to be magic, as our understanding is going to stop somewhere.
“This is [inexplicable to myself]”?
Then my brain is magic, because I’m not a neuroscientist.
“This is [can not be explained in a rational sense]”?
You said this in your post. Unfortunately, it doesn’t make any sense. Rationality isn’t an explanation; rationality is explaining. The world isn’t “rational” or “non-rational”, it just is. Explanations are rational and non-rational, because they can either be consistent with the reality, or inconsistent with the reality.
So, if lightning strikes “because Zeus” and diseases strike “because witches”, then “Zeus” and “witches” are rational explanations. The reason that those were not rational explanations is because it just so happens that they were not true, and they probably came to those conclusions because they were not using thinking that was consistent with the way the world works.
I can’t tell if Clarke is making the same mistake, but, if we’re taking a vote on this, I vote we should take it to mean “You can talk to people on the other side of the world, throw light with a wand, and travel across the Atlantic in only a few hours. What was special about wizards again?”