Introduction
Interaction I considered to be some relation of agent, object and/or referent entities with each other.
In this post I’d like to describe the interactions in a more precise way.
For a list of interactions, please refer to the blog post: Scientific metaphysics – basic interactions, action and reception types
Interactions
Mathematically, interaction is a Cartesian product of a set of entities, which, by additionally considering its sign or direction, describes certain scheme of influence of an agent or a way of movement of an object relative to a referent.
An interaction without a referent entity
This type of interaction consists of a 2-tuple with two elements in a relation with each other:
- the first element is an agent
- the second element is an object/receiver
$Int = Ent \times Ent = \{(x,x),(x,y)\}, \ x, y \in Ent$
These interactions can be interpreted as:
- $(x,x)$ – interaction, in which $x$ is both an agent and an object, e.g. “x acts on itself and receives (e.g. a force) from itself”
- $(x,y)$ – interaction, in which $x$ is an agent and $y$ is an object (of (action of) $x$), e.g. “x acts on y and y receives from x”
These are the two general cases, when $x$ and $y$ are any arbitrary entities from a set of entities $Ent$.
However, if one would make a certain choice of the two entities, there would actually be 4 different interactions with the cases being: $(a,a)$,$(a,b)$,$(b,a)$, and $(b,b)$, where $a$ and $b$ are choices of two different entities.
These interactions gain an additional, special interpretation, when one sets one of those entities a role of a viewpoint.
The significance of a viewpoint entity
A viewpoint entity I consider to be an entity with a role, which somewhat makes the interpretation of an interaction relative to this entity.
One could probably treat the viewpoint entity as an entity, from whose perspective a given interaction is considered.
It’s, however, probably not enough to say, that the viewpoint is an observer of a certain interaction.
The viewpoint is some kind of a center in an interaction.
One could, for intuition, assign yourself to the viewpoint, and say: “I’m am the one, who observes, experiences or participates in the interaction”.
I may sometimes denote the viewpoint entity (which could also possibly possess different roles in an interaction) as simply: $\cdot$ (middle dot), and simply call it – self.
The another to this entity, on the other hand, I could sometimes denote as $\times$.
One could also consider the another of an another to a self (which could perhaps remind one of a Jacques Lacan’s considerations), denoted as $ᛝ$ ($\times$ sign on top of other $\times$ sign).
There’s however some problem related to the concept of another of another; mostly, whether it should include the self itself, or not. If you would be interested in this topic from the logical point of view, you can check some resources, related to an intensional logic and/or modal logic.
Making a choice of a viewpoint entity
We can choose one entity (say, $a$) from one of the set of interactions $Int$ above, to gain a role of a viewpoint entity, and try to interpret the interactions from its perspective.
- $(a,a)$ – “a acts on itself and receives from itself”
- $(a,b)$ – “a acts on b”
- $(b,a)$ – “a receives from b”
…or if we chose $a$ to be us or yourself, and $b$ – another to myself:
- $(a,a)$ – “I act on myself an receive from myself”
- $(a,b)$ – “I act on another”
- $(b,a)$ – “I receive from another”
The fourth interaction $(b,b)$, e.g. “another acts on (this) another” doesn’t actually concern $a$ or “me” (at least not, when we only consider the interaction including an agent and an object), so this case is probably not of a special significance at that point.
These three interactions I also decided to name the interactions, in which a viewpoint participates (either by acting, receiving, or both).
Interaction with a referent entity
Next, one could also include an additional, third entity – a referent entity.
This entity I sometimes describe as an entity, relative to who an agent directs the object.
This direction could probably roughly be described with use of a sign of a real number.
An interaction with a referent entity could be defined as a triple or 3-tuple:
$Int^r = Ent \times Ent \times Ent = \{(x,x,x),(x,x,y),(x,y,x),(x,y,y),(x,y,z)\}, \ x, y, z \in Ent$
There are 5 possible, general cases of such interactions with a referent entity.
However, if we, again, chose one of the entities to be a referent entity, there would be few more cases to consider.
The 5 general cases (without making a choice of a viewpoint entity) could be interepreted as:
- $(x,x,x)$ – “$x$ acts and receives from $x$ relative to $x$”
- $(x,x,y)$ – “$x$ acts on $x$ relative to $y$”
- $(x,y,x)$ – “$x$ acts on $y$ relative to $x$”
- $(x,y,y)$ – “$x$ acts on $y$ relative to $y$”
- $(x,y,z)$ – “$x$ acts on $y$ relative to $z$”
However, if we, again, made a choice of a viewpoint (e.g. an entity $a$), the cases which would “concern” $a$, would be:
- $(a,a,a)$ – “I act and receive from myself relative to me”
- $(a,a,b)$ – “I act and receive from myself relative to another”
- $(a,b,a)$ – “I act on another relative to me”
- $(a,b,b)$ – “I act on another relative to this another”
- $(b,a,a)$ – “Another acts on me relative to me”
- $(b,a,b)$ – “Another acts on me relative to this another”
- $(b,b,a)$ – “Another acts on itself relative to me”
- $(a,b,c)$ – “I act on another relative to yet another”
- $(b,a,c)$ – “Another acts on me relative yet another”
- $(b,c,a)$ – “Another acts on yet another relative to me”
Both $b$ and $c$ are assumed to mean another to me (neither of them is another to another to me).
The part “relative to …”, as I mentioned before, gains more special significance and intuitive interpretations, when one considers the sign or direction of a given interaction.
Interactions with direction/sign
The sign of interaction is some quality of a real number, which denotes, whether this number is positive or negative.
The interaction with a direction could simply be defined as a 4-tuple:
$Int^{r,s} = Ent \times Ent \times Ent \times \{-,+\}$
These interactions also appear to carry the vector structure, however I will probably rather try to describe it in the future post or posts.
In case of using real number instead of the very signs of the interactions, the number 0 would mean, there would be not any influence of an agent in an interaction at all.
This $+$ sign can, for example, be interpreted as to/towards inside (denoting a centripetal direction of an influence), and the $-$ sign, as away from/towards outside.
Different types of transformations
There are different ways an object can behave relative to the referent in an interaction.
Some of the examples include: moving, dispersing, rotating, opening/closing, aiming at, gaining/losing of a “mass”, etc.
Certain transformations include the internal or external motion.
They can also differ in terms of whether the refrent is the same or other entity than the object.
Eventually, one could incorporate different transformations in order to compose different types of interactions, like, for example:
- “I move myself towards another”
- “Another spins (rotates) me up”
- “Another points me towards yet another”
Summary
It was the brief introduction to some of my considerations related to the concepts of interactions.
Again, please have a look at the post linked above, if you’re interested in the examples and types of different interactions.
Thanks you for reading and have a nice day