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I wrote this post several weeks ago and thought I might have more insight to add. I don't yet, so I'm just going to post it as is.

I don't know if I have the brains to pull this off, but I'm going to try to explain some of things that I have been thinking about. If you think I may be overstating something and making unhelpful generalizations or otherwise bringing unnecessary confusion to the topic, you likely are correct. I have a bit of head cold and would love several hours of solitude to dig through my books and notes and think about this a lot more. That's not my life right now, so I offer these caveats in the hopes that you know that I am on the same journey as most of you.

I'll start by relating a mental exercise I put myself through last week and then share a few related quotes and see if any of this sounds convincing.
Last week, I took advantage of visiting family to play with my kids while I did a little bit of clothes shopping. Therefore this meant I was by myself in our car with no set appointment time or other scheduling matter, I was just off by myself. As I traveled over the country roads to the shopping outlets, I was thinking about the idea that in God's world, everything He created is connected in some way to everything else. So I thought about picking two seemingly unrelated items and seeing if I could ask some compare and contrast questions about both of them and see if any connections formed. A bit skeptical, I immediately picked the first two things that caught my eye.
A wooden sign advertising a business location surrounded by a couple of taller pine trees. Is there any connection between a sign and a pine tree, I wondered?
So I started by asking how are they alike. They both are made out of wood, they both stand by themselves, they both mark a spot, they can both serve as landmarks. And then I thought about the tree by itself for just a second and I thought of the cross, a very normal connection. And this idea of landmarks stuck in my head at the idea of the cross being the landmark of the redemption story. Earlier in our Sunday School year, we had created timelines with the kids, and the central figure was Jesus on the cross.
And then I remembered I had begun reading Robert McFarlane's, Landmarks, last year, but didn't really finish it before it was due back to the library. And I thought about his use of the term landmarks as being very specific and actual types of land arrangements. Everything, every detail falling into one type of geological term or another. Nothing was overlooked.
As I thought back to my wooden sign and my pine tree, I was amazed at how these two seemingly unrelated items could cause such a rabbit trail of thoughts. And this thinking exercise really only lasted minutes, less than three, as I arrived at a signal light and I was back to thinking about my shopping plans.
Soon after, I read this article by Richard Marsh, a science teacher who wrote the following in a CiRCE post called The Musical Root of Science:

It was elegant and simple, and it struck me as profound because it focused on the relationship between the two quantities rather than on their individual values.The modern formula is the means of quickly computing an individual value, but Galileo’s proportional reasoning was the original means of identifying the root relationship.

I think it was Andrew Kern who said that the soul is constantly seeking harmony and when you see an equal sign in an equation what you are seeing is harmony.

To quote from Richard Marsh's article again:

Arithmetic focuses on the properties of individual numbers, such as even or odd and so forth, but music focuses on the properties of numbers in relationship to each other, such as in harmonic ratios. It then struck me that my education in physics had been an education in Arithmetic only, focusing on how to find the individual numerical “answer”. Give me the length of a pendulum and I can compute for you the specific time for one cycle. I was very good at focusing on individual, absolute quantities through the use of equations.

What I lacked was an education in music, a training of the mind to identify and distinguish relationships between absolute quantities and to find the proper harmony among them. Coming from a public school background, I never had much musical education once I decided that I preferred math and science. The departments were separated physically and philosophically in my high school, and the two groups viewed each other with some smoldering hostility.

But it was the musical mindset that gave Galileo insight into the scientific properties of the pendulum. Music was not a menace to science, but a friend. The individual values of length and time were not so much important in themselves as was the relationship between them, and that required a musical form of thought.

What did this thought experiment accomplish, I wondered. One thing I can see so far is that it gives me a tool, a process for thinking about anything and everything. How is this like this, how is this different than this? This is thinking by analogy. What else does it look like? What else does it remind me of? Why is it like that? (These questions come from The Private Eye science curriculum.)

Andrew Kern, if my notes are right, said this in his lecture How to Read a Great Book(And a Hard One):  Every story is about something other than the story, because the story didn't really happen. Stories are always analogies. They are always pointing to something else.

As Joy Shannon recently shared on the Charlotte Mason Institute:
Simply put – it’s all about relationships. Not just knowing about something but having a relationship with it. Not just a casual or passing interest, but a relationship that touches the heart, soul, and mind and leaves one changed never to be quite the same again. The deeper known and the more of these relationships we lay hold of, the fuller and richer our lives will be. At the same time we grow and have an increased ability to serve.