Flipping concepts in Language like terms in equations

I am introducing a concept in Linguistics, akin to flipping terms in mathematical equations. Consider this equation : P (in terms of T) = nrT/V; whereas now T in terms of P would be T=PV/nR

Or, given P=a^(½),

a, in terms of P would be : a= P^2

So, given ‘John is in his room’, the reverse would be - 

John’s room is housing him / John is housed by his room. 

Lets elaborate the concept with an example -  

John is climbing a tree.

The reverse of this would be - A tree is supporting the climb of John.

Now, this looks similar to the ‘Active’ and ‘Passive’ voices in Language. But it is not. The conventional reverse (passive) voice would be - A tree is being climbed upon by John.

In most sentences there is something “fixed” and there is something which comes into the scene, later, as variable and mobile. (This is mostly the actor - the doer). There is a pre-existing fixed thing / phenomenon and something else - variable and mobile - is coming later into the scene. (Note : This coming later into the scene has nothing to do with information unraveling as the sentence progresses. What it means is : When you say ‘John is in the room’, the room is a fixed pre-existing thing and then comes John “in the scene” as an active mobile agent, fitting into the room. Here, you are describing John in terms of the room (like P in terms of T above). When you say ‘The room is housing John’ John is the fixed pre-existing thing and the room comes in as an active player, surrounding John. Here you are describing the room in terms of John (like later T in terms of P, above).

In this example, the tree is the mobile actor which is doing something; which is playing. John’s climbing is a pre-existing “fixed” thing already there. The tree is being described with regard to John. In the original sentence, John is being described with regard to the tree / in terms of the tree.

Note : This is not even the same as making some other word as the subject. The sentence with mere subject alteration i.e. making the tree as the subject would be - The tree is being climbed upon by John (which is the conventional passive voice). In our case, the voice remains the same, and some other word (the fixed passive pre-existing “agent”) becomes the thing in terms of which / with regard to which the earlier active agent is being described. 

In other representational terms, this equation-flipping is - 

(John) = (climbing tree) 

->

(Tree) = (supporting John’s climbing)

Adding the word ‘supporting’ is the equivalent of the necessary mathematical operation in making a certain term in the equation, the subject of the equation. (like say squaring or multiplying and dividing etc.)

This applies even in cases where the passive voice is difficult - 

The keyboard is a part of the computer. Here the passive voice is difficult.

The computer is a fixed entity here and the keyboard “comes into the scene”, as one of its parts. Keyboard is described in terms of a computer. So, the reverse of this is - 'The computer has a keyboard as one of its parts' / 'A computer’s part is a keyboard', wherein a computer is described “in terms of” / with regard to a keyboard.