I think the problem arises Stardust when science is asked to not only make predictions but to make them with the necessity of law. It is a further irony that this necessity of law is not demanded by the empirical evidence but by our own rational contemplation of the event. We expect that if the sun sets in the west that it will rise again in the east but it would be an unworthy scientist indeed who could guarantee the event.
To expect the sun to rise in the east takes more than just an empirical study, it takes a rational mind bent upon seeing connections even when they cannot be proven - a completely unscientific enterprise.
You raise an interesting point about maths. I submit to you that maths is a beautiful rulebook of rationality but it is yet an open matter what connection our very human frameworks of logic and number have with the universe at large.
Oh right, I see what you mean. I understand now, this gives the possibility of making that connection with an intuitive basis? Yes, definitely shows the capacity of the human mind there - Takes a spark of that strange thing that's genius.
Our brain's a simulator of our surroundings, but there's clearly a part of our brain that allows for a 'mess' rather than systematic thinking and it appears in dreams, like if you notice in dreams our minds can defy the common laws of physics, people fly, morph etc. You may have heard great scientists have come up with solutions or are inspired by their dreams. I think that's where creative genius comes from, their minds takes everything and mixes it all up in a pot and lets it explode with all possibilities no matter how crazy the idea seems. And it's not just dreaming, but the state of mind when pondering, reflecting, letting the mind wander and imagination take you away.
I'll tell you something, I was reading a classial mechanics text book a few days ago (brushing up on my knowledge) and that night I had a dream which was really cool, people were stored in a cryogenic manner and 'relativistically' in these kind of cylindrical disc like containers which were only about 8cm in thickness and about a 1.5m in diameter. So there were people lying (suspended) in these cylinders, but they were compressed longitudinally into an 8cm thickness by some relativistic method (it all made sense in my dream, can't remember now). If you looked at the face of the disc you could see person's head and the depth of the whole thing, but from the side that depth wasn't there. This was in a lab too, I was trying to save these people, with the help of my friend. Ok back to the point...
I think our minds evolved for making connection and seeing 'patterns' in order to survive. Seeing patterns in nature enables us to maximise gathering of food, and planning ahead etc. I do think you need a sense of intuition in science, but people have this notion that scientists are cold and completely rational people, a lot of the great scientist were pretty eccentric and artistic in character from what I can tell.
Alot of scientist also became depressed and one even committed suicide - Think that was Neils Bohr. One of them had his nose cut off and ended up with a metallic nose, but I think that may have been an accident.
Topic: The paradox at the heart of science