Back in the '60s I developed an idea for using electrostatic charges to de-salt seawater, and other partly ionized fluids, using little energy. The process would probably also be useful for mining of seawater. I submitted it in writing to a couple of companies, but didn't find anyone interested. I found it was quite difficult to make a working model. I let the idea sit until recently when I rewrote the description, redrew the drawings, and showed them to a college physics professor.
He said, apparently based on intuition, that it wouldn't work for several reasons, to the point that he didn't consider it worthwhile to make a mathematical model. Items he mentioned indicated that in some cases he didn't understand my description. Other cases were simply my intuition versus his. Since he relies on mathematical model, I doubt that his intuition is any better than mine.
But the point is that he said a mathematical model would be the only sensible way to test it. I said that I would put more trust in a physical working model. He said that was just my bias. I agree that his model would be cheaper, but it certainly would't be the final answer, unless it actually convinced me. Actually neither would a physical, full-scale model that didn't work be "final", for me.
I could have gone on to say that, speaking of math models, he was claiming the percent of probability of him being wrong was less than the proportion of the cost of testing the idea compared to it's eventual value. A math model might take several days work on a computer. Testing it with a physical model could cost in the range of $5000. Cheaply separating seawater into fresh water and various salts could greatly improve the world's ecology and economy. Can anyone be that sure they're right?
And I thought we were supposed to have discarded the idea that pure theoretical science was valid along with Aristotle and the inability of bumblebees to fly.