While the phrase "prince of mathematics" is almost universally applied to a single individual, "father of science" is commonly applied to several individuals. Nonetheless, I do consider Bacon worthy of the title and what is more he is a further example and primogenitor in the line of Haldane, Asimov, et. al. in that he, too, was a writer of science fiction. I've never actually read his posthumous work New Atlantis, but I'm aware that it's along the vein of a piece of drivel I wrote as a HS freshman called "Terra Sapientiae."
My understanding of our current conversation is that there are two points of contention:
1. That the value of people with MFAs at NASA and the like is more important than a stack of PhDs. (This issue was raised in your original post.)
2. The role of imagination in the science. (I raised this in my post about the necessity of a filter in addition to imagination, and you have continued by insisting that imagination is more important.)
Let me dispatch with point 2, first, as it's the easier one, because I'm willing to concede the point. I'm aware that Einstein has said, "Imagination is more important than knowledge." I always considered that he was largely being clever when he said this. When one is widely considered to be the smartest person ever to have lived, one almost certainly feels a strong pressure to say clever things. And there is no doubt that imagination IS a very important thing to human beings. I have my doubts that it is unique to humans, but it seems obvious enough that imagination has seen its greatest fruition among and has offered the greatest benefits to humanity. Imagination is necessary for abstract thinking. Viewing cave drawings of Neandertals or Cro-magnons is very nearly a religious experience - to look back into the incipient rise of what we feel makes us what we are, and what many feel makes us unique among existing fauna.
We humans have always had imagination. (That we are not directly descended from Neandertal, does not mean that we are unrelated.) We had imagination long before we had science, we had it possibly even before we became human. Even in the practical application of our knowledge, one must first have imagined an idea in order to make use of it.
I can concede that a serious case could be made that imagination is among the most important properties that we possess.
But I further observe that it is not sufficient by itself - in the same way one might argue that water is the most important molecule for human existence, but it is not sufficient. Either argument seems a little silly to me, but I can easily accept either for the sake of argument so long as we amend them with the proper proviso, namely "but not alone sufficient"
We struggled for millenia before formalizing the notion of and understanding the importance of The Filter. Bacon said this as well as anyone in the first paragraphs of his Novus Organon,
Those who have taken upon them to lay down the law of nature as a thing already searched out and understood, whether they have spoken in simple assurance or professional affectation, have therein done philosophy and the sciences great injury.
and then later
Now my method, though hard to practice, is easy to explain; and it is this. I propose to establish progressive stages of certainty. The evidence of the sense, helped and guarded by a certain process of correction, I retain.
This process of correction to which he so early alludes is the distinguishing character of modern science and it's exactly the thing I mean when I refer to The Filter. Using the filter is a winnowing process operating on the ideas generated from our imaginations to separate out the pure fancy from the things that appear to correspond to our perceptions, that is the things that seem to be false from the things that might just correspond to the facts.
Our imaginations provide us with potential patterns to explain our observations. But to determine whether a pattern actually describes the world (or a part of the world), we have to compare it TO the world. This is - or was - a radical idea, but not just for Bacon. The Greeks - some of them - presaged this idea at least as early as Aristotle.
What distinguishes astrology from astronomy, metallurgy from alchemy, medicine from thaumaturgy? In ancient times - and even through the middle ages - it was quite common for philosophers and thinkers to just think of a possible explanation or model for how the world worked. And they might ask some questions about this model or they might make some superficial attempt at comparing the model to the world, but for the most part, the questions were not even asked in useful ways. In general, inquiry was nebulous, unfocused, and uncritical. "Well, that's a great idea! It MUST BE TRUE!" They were great at logic. What they weren't great at was testing their ideas to determine whether they corresponded with reality.
But there was always this practical bent which offered the germ of this idea. The babylonians and egyptians BUILT things. You can attempt to build anything you wish, but eventually you come up against the laws of physics. These laws do not require you to believe in them, or even to be aware of them to experience their full effect. You try to make bridges - some of them collapse even before finished, and others stand for hundreds of years. What is the difference? Same thing for buildings (and for spaceships). Some things work and others fail. What did we do differently? What is the pattern? In this case The Filter *IS* Nature. It's not systematic, though. The idea of The Filter would not be codified for millenia.
Heron of Alexandria built lots of machines (including a vending machine to dispense holy water). I reckon he must have bumped up against reality on numerous occasions. This works. This doesn't. Does this happen because of this other thing? Same thing for da Vinci towards the end of the middle ages. He built things and must have bumped up against reality lots of times.
I'm not arguing that The Filter (which you have clearly guessed is Scientic Method) is more important than Imagination. I'm saying that Imagination, even if we accept that it is The Most Important Thing in the Universe, is not alone sufficient.
I'll address the other point at some later time.