In this article, I’d like to suggest some notation for some basic actions and receptions between one, two and three entities.
I don’t want to introduce the general form of these concepts for now, as they both appear to be more complicated, as well as I’m also still working on their formal definitions.
Therefore, below you can see some of their special cases.
For entities $a$, $b$, $c$, the action and reception types are as follows:
| Arrow notation | Tuple notation | Example |
| $\ce{a → b}$ | $(a,a,b,+)$ | “a approaches b” |
| $\ce{a ⤙ b}$ | $(a,a,b,-)$ | “a leaves b” |
| $\ce{a ⤛ b}$ | $(a,b,a,+)$ | “a attracts b” |
| $\ce{a ⇥ b}$ | $(a,b,a,-)$ | “a repels b” |
And with participation of a third entity – $c$:
| $\ce{a ⤛ b rel c}$ | $(a,b,c,+)$ | “a attracts b to c” |
| $\ce{a ⇥ b rel c}$ | $(a,b,c,-)$ | “a repels b from c” |
We can also consider few more cases, by considering one of those entities as “ourselves”, and the others, just as the “others for us”. This puts some kind of a focus on specific entity, relative to other entities.
The cases, that arise from it, are:
| Arrow notation | Tuple notation | Example |
| $\ce{a^v → b}$ | $(a,a,b,+,a)$ | “a approaches b” (now, by a, we mean a concrete, specific, chosen entity) |
| $\ce{a^v ⤙ b}$ | $(a,a,b,-,a)$ | “a leaves b” |
| $\ce{a^v ⤛ b}$ | $(a,b,a,+,a)$ | “a attracts b” |
| $\ce{a^v ⇥ b}$ | $(a,b,a,-,a)$ | “a repels b” |
| $\ce{b → a^v}$ | $(b,b,a,+,a)$ | “a is being approached by b” |
| $\ce{b ⤙ a^v}$ | $(b,b,b,-,a)$ | “a is being left by b” |
| $\ce{b ⤛ a^v}$ | $(b,a,b,+,a)$ | “a is being attracted by b” |
| $\ce{b ⇥ a^v}$ | $(b,a,b,-,a)$ | “a is being repelled by b” |
And with participation of a third entity – $c$:
| $\ce{a^v ⤛ b rel c}$ | $(a,b,c,+,a)$ | “a attracts b to c” |
| $\ce{a^v ⇥ b rel c}$ | $(a,b,c,-,a)$ | “a repels b from c” |
| $\ce{b ⤛ a^v rel c}$ | $(b,a,c,+,a)$ | “a is being attracted to c by b” |
| $\ce{b ⇥ a^v rel c}$ | $(b,a,c,-,a)$ | “a is being repelled from c by b” |
As I mentioned in some earlier article, the first two elements of the tuples define the subjective interaction ((only) action $(a,b)$, (only) reception $(b,a)$ or both $(a,a)$).
How can the tuple notation be read?
The meanings of the tuple $\ce{(ex,rec,ref,orient,vp)}$ entries, are:
- $ex$ – (force) exerter – entity which exerts some force
- $rec$ – (force) receiver – entity, on which the exerter exerts the force
- $ref$ – (force) referent – entity, relative to which exerter “redirects” receiver
- $orient$ – orientation or tendence – how, relative to the referent, exerter “redirects” a receiver (in cases above, only specified by its sign)
- $vp$ – viewpoint – entity, from whose perspective a given interaction is considered
For example: Let’s take a look at a reception: “a is being attracted to b by b“: $(b,a,b,+,a)$
In this case, b (ex) acts on a (rec) relative to b (ref), setting a (rec) with positive tendence (“motion”) relative to b (ref). We also consider this interaction from perspective of a (vp).
It can probably be intuitive, to consider an example of a viewpoint being “ourselves”, and so interprete the given interaction relative to “us” (e.g. “‘I’ am being attracted to b by b”).
There are also more, similar action/reception types, but now, with an entity acting on itself:
| Arrow notation | Tuple notation |
| $\ce{a→a \overset{?}= a⤛a}$ | $(a,a,a,+)?$ |
| $\ce{a⤙a \overset{?}= a⇥a}$ | $(a,a,a,-)?$ |
and:
| $\ce{a→a rel b \overset{?}= a⤛a rel b}$ | $(a,a,b,+)?$ |
| $\ce{a⤙a rel b \overset{?}= a⇥a rel b}$ | $(a,a,b,-)?$ |
Some of those cases can probably seem to be somewhat abstract and maybe even are nonlogical.
Please let me know in the comments, what do you think, if you have any ideas about them.
Conclusion
I think that the concept of interactions is actually the major logical gap in sciences nowadays, and their classification and quantitative analysis could lead to many, new discoveries.
PS. The action or reception types, given above, do not necessarily have to mean, what was
mentioned in their corresponding examples.
There are actions, that, probably, not necessarily impact “relative external motion”, but, probably, for example, a “relative internal motion” (e.g. like opening of closing of something relative to something else (which probably does not involve “external motion”)).
PS2. For “a is attracted to b”, I’d also like to suggest a notation: $a↦b$.