Why is "doing" used here instead of "to do"?

Question

I have read this question: “I like to do (be) something” vs “I like doing (being) something” and I get (although the answer could not be applied to my example) that using "to do" means in general I like to do it. While "doing", means I'm doing it at the moment or soon will be.

I found the following example in a grammar book:

Exercise means doing something with the body.

Shouldn't it be "Exercising means doing..." or "Exercise means to do..." or maybe "To exercise means doing ..."

-I don't get why exercise is used as a noun here.

-I don't get why doing is used instead of to do and if they are interchangeable (without context)

Answer 1

Firstly: exercise is a noun

Exercise noun -

1. bodily or mental exertion, especially for the sake of training or improvement of health: Walking is good exercise.
2. something done or performed as a means of practice or training: exercises for the piano.

Secondly

Exercise means doing something with the body.

Doing in this sense is a gerund. This means that doing is behaving as a verb within a noun phrase. So doing something with the body is effectively a noun that includes an action.

The sentence itself is acting as a definition for exercise, which is why the part after means is a noun.

To further clarify why using to to do is not natural, if you look at the accepted answer to the question you link to, then you can read this:

The infinitival is more associated with change, the gerund-participle with actuality.

Since your sentence is a definition, it is actuality, therefore we use the gerund doing not the infinitive to do.