What Is Science?

 We all "know" what Science is...at least at we have a pedestrian working definition of sorts: based on experimentation, models and theories need to explain known facts but also predict new ones that then must be confirmed...by experiments. Some say this as they must be refutable -as in the opposite of not even wrong.

Here I want to suggest another, hopefully equivalent, idea. Something that has bothered me for some time now is that naive realism that I feel lurks under expressions like the following attributed to Max Planck

An experiment is a question which science poses to Nature and a  measurement is the recording of Nature's answer.

The following ideas are closer to a different quote attributed to Carl Sagan

Science is a way of thinking much more than a body of knowledge

So, What is Science then?

Looking through the window you might say "the trees are tall, the grass is green, the hill is smooth, the dairies are white and yellow,...".

That is poetry, literature. It's another approach to reality, to learn about ourselves in relation to others and to Nature. And it is a necessary one.

But it is not Science. Nor those are the only type of sentences we can come up with.

Here some different statements: 

• "When the sun shines flowers bloom, grass grows and becomes greener, trees get more & greener leaves,..."
• "When humans constantly tread on the grass, the grass dies and the area becomes sandy & arid"

Wait, "dies"?? What's that? What is death? A possible answer would convey the following idea:

• "When we provide food to a living being it grows and multiplies. Eventually it stops doing this and we say then that it died."

All of Science is in essence a collection of sentences of the type

When we do/it does this, it happens that

In order to understand the it, we (let) apply "transformations" on it -the object of the transformation-, and "collect" the output -which itself is an it! 

I saw a parallel with Category Theory: Objects are secondary; what matters are the morphisms. These tell us everything about the objects.

In Science, experiments are but transformations.

Stated like that, it reminds me of the warning of Carnap about Science: it's a combination of experiment plus theory. Theory as a mental construct/model.

Q1: What is theory in our view?

Ans: Our view doesn't change this, but it may give it a spin. Theory & models are but a mathematical guide for us to do

• Actual experiments
• Gedanken experiments

And thus anticipate the outcome (or rather, how the outcome behaves). 

As these mathematical constructs can themselves eventually be expressed within CT, we could justify the claim 

Science is about applying & combining transformations

The inputs & outputs are themselves understood as transformations, thus it seems redundant to include them in the above claim.

Q2: This still seems to miss Carnap's observation that Science is not a collection of facts. A better formulation?

Ans: Science is about applying & combining transformations...and the talk about it.

We mentioned transformations as synonyms for actual experiments.

The talk about it is our on-paper, mathematical experimenting plus the verbal talk and descriptions. The verbal talk can eventually be fitted within CT.

Q3: Usually one stresses the fact that scientific method must be 1) predictive and 2) refutable. Are we missing this?

Maybe we can introduce a "why":

We experiment and talk about it in order to be able to anticipate (predict).

Consider the following:

"If you drink this potion and repeat 10 times these words, the gods will vest you with the power of invulnerability against bullets"

It talks about transformations (drink potion, utter words), has a prediction (invulnerability against bullets) and is refutable.

Our goal to anticipate makes us try ti make sure it works -instead of just take for granted-, and thuscto refute it. And it turns out to be false.

Maybe then the "why" and its answer "to anticipate" comprise those common two traits.

We come then to the following statement:

Science is about applying & combining transformations and our talk about it in order for us to anticipate (the outcome)

What I find so much appealing about Category Theory is that it applies the same approach to study mathematics itself. Instead of mathematical object&structures it shifts the focus to the morphisms (transformations) on & between them plus the properties of combinations between those morphisms.

For example, and this is a general modus operandi, not something CT, if we want to understand different types of graphs we could run a set of stochastic processes on them. One same stochastic process may proceed differently on different graphs. Ultimately this allows us to distinguish and classify those graphs.

That "talk about it" is thus a talk  in terms of applying and combining mathematical transformations.