The most objective of sciences, abstract, strictly logical, a world in itself - the Queen of Sciences without which no natural science could proceed, no Imhotep build Pharaonic tomb and no Pythagoras compose music!
Experimental science is just that. It makes experiments in order to verify theories, to see if a carefully planned test provides the results expected by the hypothesis.
Knowledge only by observation?
It is definitely wrong to claim that all knowledge is experimental. That is a claim that belongs in the field of Theory of Knowledge which is a truly deep branch of human thinking.
It is wrong because humanity has gained correct knowledge about nature even when they could in no way test these theories by experiment.
Classic case is the work of Greek nature Philosophers in the First millennium before the birth of Christ. Outstanding example is the theory of atoms developed purely in mind by Leucippus and his student Democritus (460-370 BC).
They figured out divine thoughts and it took more than two thousand years before those ideas could be tested. They worked and we all talk about atoms today as something so self-evident.
God thinking
Because He says so we believe that God of Israel has created the universe and also all of us with it. The Bible tells us that we have been created in the image of God
And God said, "Let Us make man in Our image, after Our likeness; and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth and over every creeping thing that creepeth upon the earth."
So God created man in His own image, in the image of God created He him; male and female created He them.
Genesis 1:26-27 KJ21
So God created man in His own image, in the image of God created He him; male and female created He them.
Genesis 1:26-27 KJ21
Accordingly, if we like to see some attributes of God of Israel who is the only real God there is we can look at ourselves. For we are made in His image.
BTW the creation story itself in the beginning of the Bible does not use the expression "God thinking". It goes a step further and talks about God speaking words. This is a point that is worth thinking, but we can only do so by using words.... or can we think in non-verbal ways, maybe we can?
Humans thinking
Talking about catching God's thoughts in the way Nature is build sounds rather religious but it actually works in our daily life and in practice.
We have the ability to find out truth by thinking because everything has been made by a Great Thinker.
However, this is not a Philosopher's god and we will never learn to know Him just by thinking. More is needed from His side and we have the possibility of not believing in any god and also to reject the real God. Or to worship false gods, as we all know.
But we can figure out the logic in the handiwork of the Thinking God, for His works are marvellous regardless of whether we give Him the glory or not.
Divine thoughts
I do not know how Leucippus and Democritus reached the atom theory but I could imagine that they were playing with ideas on the basis of what they know and started to figure out What if? What if everything is made of fundamental elements that bounce in space and stick to each other giving matter its attributes?
Similarly, I do not know how Wofgang E. Pauli reached the Law of Nature we call Pauli's exclusion principle. But I do know that in 1925 he could not figure it out using some decisive atom smashers or other equipment scientists have built to study particle physics. They came later.
I could imagine that he was playing with ideas on the basis of what he knows and started to figure out What if? What if we accept that no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously?
Similarly, I do not know how Oscar W. Greenberg reached the math of color charges. But I do know that in 1964 he could figure it out using some decisive atom smashers or other equipment scientists have built to study particle physics. They came later.
I could imagine that he was playing with ideas on the basis of what he knows and started to figure out What if? What if we accept Pauli's exclusion principle and imagine that sub-particles have not one on/off but three charges - say, like red, blue and cyan? Nope... better red, green and blue as in RGB!
Let's imagine some more ...
And we could imagine, with due respect, naively as children of God how our Heavenly Father would have been thinking "Well now, I would like to create something... one thing I need for this is matter. This electrons around nucleus seems to be a good solution but how can I handle this negative/positive challenge to make those legos stable for constructing matter?
The nice thing about this is that with our human logic and mathematical reasoning we obviously are catching the ideas of the One who has made everything.
And even nicer is that there is still so much more to be learned about this and other matters in His creation.
Even if you are crippled by some serious decease and tied to a wheel-chair unable to speak normally, you can use your brilliant mind to imagine, play with ideas and ... most importantly ... calculate!
With such brain even the Black hole does not remain all that black forever to our enquiring curious minds.