Introduction
Interaction with reaction (in short – iwr) I consider to be a certain influence (interaction) between some entities, along with a reaction (also interaction) of a certain (hypothetically other) entity.
An interaction, in order to be a reaction, requires from its agent some kind of a reference to the initial interaction.
Notation
- $a,b,c,d \in Ent$ – choice of different entities
- $x,y,z,i,j,k \in Ent$ – arbitrary entities (entity variable)
- $sign \in \{+,-\}$ – a “direction” of an object relative to a referent entity in an interaction
Mathematical interpretation of an interaction with reaction
In general, an interaction with reaction, is a pair of interactions $intr = (int_1, int_2)$, such, that:
- $int_1 = (x,y)$
- $int_2 = (z,i)$
In terms of the two interactions, the second interaction is called a reaction (it is also an action of an entity $z$, if considered independently).
Interaction with reaction including a referent entity
The interaction with reaciton including a referent entity is a set of the two interactions $intr^r = ({int_1}^r, {int_2}^r)$, such, that:
- $int_1 = (x,y,z)$
- $int_2 = (i,j,k)$
The directed/signed version $intr^{r,s}$ of it, is:
- $int_1 = (x,y,z, sign_1)$
- $int_2 = (i,j,k, sign_2)$
These general definitions of iwrs with a referent assume the involvement from 1, up to 6 different entities.
Other types of interactions with reactions
Interaction and reaction sharing the same entity
Interaction with agent-related reaction – an iwr, in which a reacting entity is simultaneously an agent, object, or a referent of the initial interaction
- Interaction with reaction of the initial agent
- Interaction with reaction of the initial object
- Interaction with reaction of the initial referent
Interaction with object-related reaction – an iwr, in which an object of the reacting entity is simultaneously an agent, object, or a referent of the initial interaction
- Interaction with reaction on the initial agent
- Interaction with reaction on the initial object
- Interaction with reaction on the initial referent
Interaction with referent-related reaction – an iwr, in which a referent of the reacting entity is simultaneously an agent, object, or a referent of the initial interaction
- Interaction with initial agent as a reaction’s referent
- Interaction with initial object as a reaction’s referent
- Interaction with initial referent as a reaction’s referent
A reaction could theoretically be a combination of few iwrs above at the same time.
For only one of the iwrs above, the number of different entities involved can range from 1 to 5.
For two, there are between 1 and 4 different entities involved.
For the all three, the number of different entities involved ranges from 1 to 3.
Interaction with an entity having few roles
The individual interactions could also have one entity with more than one role.
- Initial interaction in which agent and object are the same entity
- Initial interaction in which agent and referent are the same entity
- Initial interaction in which object and referent are the same entity
- Initial interaction in which agent, object and referent are the same entity
- Reaction in which agent and object are the same entity
- Reaction in which agent and referent are the same entity
- Reaction in which object and referent are the same entity
- Reaction in which agent, object and referent are the same entity
Interactions with reactions involving up to 4 different entities
There is one special case of these iwrs I would like to describe, in which the two interactions share the same object and referent, which can swap roles.
The interaction with reaction with shared referent and object which can swap roles
This type of interaction with reaction appears to have some special significance.
In one of the special cases, it can deal with a change of a mutual distance of the object and the referent (which are, again, the same in the initial interaction and reaction).
In that type of iwr, the reacting agent can either imitate (“agree” with) $(+,\_)$ the direction of the initial interaction, or oppose (“disagree” with) it $(-,\_)$.
The imitation occurs, when the signs of the initial interaction and the related reaction are the same.
The opposition occurs, when the signs of the two interactions differ.
The result of imitation is the amplification of the influence (e.g. of a force) of the initial interaction.
There are, however, three possible, general results of the opposition:
- reversion – $(-,+)$ – underpower of the reacting agent
- equalisation – $(-,0)$ – neutralisation of the initial influence by the reacting agent
- inversion – $(-,-)$ – overpower of the reacting agent
Interactions with reactions involving 4 different entities
The below cases were computed by me manually, so there could possibly be some mistakes.
The number of cases is about 65.
$((a,a,a),(b,c,d))$
$((a,a,b),(a,c,d))$
$((a,a,b),(b,c,d))$
$((a,a,b),(c,a,d))$
$((a,a,b),(c,b,d))$
$((a,a,b),(c,c,d))$
$((a,a,b),(c,d,a))$
$((a,a,b),(c,d,b))$
$((a,a,b),(c,d,c))$
$((a,a,b),(c,d,d))$
$((a,b,a),(a,c,d))$
$((a,b,a),(b,c,d))$
$((a,b,a),(c,a,d))$
$((a,b,a),(c,b,d))$
$((a,b,a),(c,c,d))$
$((a,b,a),(c,d,a))$
$((a,b,a),(c,d,b))$
$((a,b,a),(c,d,c))$
$((a,b,a),(c,d,d))$
$((a,b,b),(a,c,d))$
$((a,b,b),(b,c,d))$
$((a,b,b),(c,a,d))$
$((a,b,b),(c,b,d))$
$((a,b,b),(c,c,d))$
$((a,b,b),(c,d,a))$
$((a,b,b),(c,d,b))$
$((a,b,b),(c,d,c))$
$((a,b,b),(c,d,d))$
$((a,b,c),(a,a,d))$
$((a,b,c),(a,b,d))$
$((a,b,c),(a,c,d))$
$((a,b,c),(a,d,a))$
$((a,b,c),(a,d,b))$
$((a,b,c),(a,d,c))$
$((a,b,c),(a,d,d))$
$((a,b,c),(b,a,d))$
$((a,b,c),(b,b,d))$
$((a,b,c),(b,c,d))$
$((a,b,c),(b,d,a))$
$((a,b,c),(b,d,b))$
$((a,b,c),(b,d,c))$
$((a,b,c),(b,d,d))$
$((a,b,c),(c,a,d))$
$((a,b,c),(c,b,d))$
$((a,b,c),(c,c,d))$
$((a,b,c),(c,d,a))$
$((a,b,c),(c,d,b))$
$((a,b,c),(c,d,c))$
$((a,b,c),(c,d,d))$
$((a,b,c),(d,a,a))$
$((a,b,c),(d,a,b))$
$((a,b,c),(d,a,c))$
$((a,b,c),(d,a,d))$
$((a,b,c),(d,b,a))$
$((a,b,c),(d,b,b))$
$((a,b,c),(d,b,c))$
$((a,b,c),(d,b,d))$
$((a,b,c),(d,c,a))$
$((a,b,c),(d,c,b))$
$((a,b,c),(d,c,c))$
$((a,b,c),(d,c,d))$
$((a,b,c),(d,d,a))$
$((a,b,c),(d,d,b))$
$((a,b,c),(d,d,c))$
$((a,b,c),(d,d,d))$
In the cases above and the ones below, none of the entities is assumed to have a role of a viewpoint (including an entity $a$, which is not a viewpoint here as well).
Interactions with reactions involving 3 different entities
The number of cases is about 90.
$((a,a,a),(a,b,c))$
$((a,a,a),(b,a,c))$
$((a,a,a),(b,b,c))$
$((a,a,a),(b,c,a))$
$((a,a,a),(b,c,b))$
$((a,a,a),(b,c,c))$
$((a,a,b),(a,a,c))$
$((a,a,b),(a,b,c))$
$((a,a,b),(a,c,a))$
$((a,a,b),(a,c,b))$
$((a,a,b),(a,c,c))$
$((a,a,b),(b,a,c))$
$((a,a,b),(b,b,c))$
$((a,a,b),(b,c,a))$
$((a,a,b),(b,c,b))$
$((a,a,b),(b,c,c))$
$((a,a,b),(c,a,a))$
$((a,a,b),(c,a,b))$
$((a,a,b),(c,a,c))$
$((a,a,b),(c,b,a))$
$((a,a,b),(c,b,b))$
$((a,a,b),(c,b,c))$
$((a,a,b),(c,c,a))$
$((a,a,b),(c,c,b))$
$((a,a,b),(c,c,c))$
$((a,b,a),(a,a,c))$
$((a,b,a),(a,b,c))$
$((a,b,a),(a,c,a))$
$((a,b,a),(a,c,b))$
$((a,b,a),(a,c,c))$
$((a,b,a),(b,a,c))$
$((a,b,a),(b,b,c))$
$((a,b,a),(b,c,a))$
$((a,b,a),(b,c,b))$
$((a,b,a),(b,c,c))$
$((a,b,a),(c,a,a))$
$((a,b,a),(c,a,b))$
$((a,b,a),(c,a,c))$
$((a,b,a),(c,b,a))$
$((a,b,a),(c,b,b))$
$((a,b,a),(c,b,c))$
$((a,b,a),(c,c,a))$
$((a,b,a),(c,c,b))$
$((a,b,a),(c,c,c))$
$((a,b,b),(a,a,c))$
$((a,b,b),(a,b,c))$
$((a,b,b),(a,c,a))$
$((a,b,b),(a,c,b))$
$((a,b,b),(a,c,c))$
$((a,b,b),(b,a,c))$
$((a,b,b),(b,b,c))$
$((a,b,b),(b,c,a))$
$((a,b,b),(b,c,b))$
$((a,b,b),(b,c,c))$
$((a,b,b),(c,a,a))$
$((a,b,b),(c,a,b))$
$((a,b,b),(c,a,c))$
$((a,b,b),(c,b,a))$
$((a,b,b),(c,b,b))$
$((a,b,b),(c,b,c))$
$((a,b,b),(c,c,a))$
$((a,b,b),(c,c,b))$
$((a,b,b),(c,c,c))$
$((a,b,c),(a,a,a))$
$((a,b,c),(a,a,b))$
$((a,b,c),(a,a,c))$
$((a,b,c),(a,b,a))$
$((a,b,c),(a,b,b))$
$((a,b,c),(a,b,c))$
$((a,b,c),(a,c,a))$
$((a,b,c),(a,c,b))$
$((a,b,c),(a,c,c))$
$((a,b,c),(b,a,a))$
$((a,b,c),(b,a,b))$
$((a,b,c),(b,a,c))$
$((a,b,c),(b,b,a))$
$((a,b,c),(b,b,b))$
$((a,b,c),(b,b,c))$
$((a,b,c),(b,c,a))$
$((a,b,c),(b,c,b))$
$((a,b,c),(b,c,c))$
$((a,b,c),(c,a,a))$
$((a,b,c),(c,a,b))$
$((a,b,c),(c,a,c))$
$((a,b,c),(c,b,a))$
$((a,b,c),(c,b,b))$
$((a,b,c),(c,b,c))$
$((a,b,c),(c,c,a))$
$((a,b,c),(c,c,b))$
$((a,b,c),(c,c,c))$
Interactions with reactions involving 2 different entities
The number of possible cases of the iwrs involving 2 different entities is about 31.
$((a,a,a),(a,a,b))$
$((a,a,a),(a,b,a))$
$((a,a,a),(a,b,b))$
$((a,a,a),(b,a,a))$
$((a,a,a),(b,a,b))$
$((a,a,a),(b,b,a))$
$((a,a,a),(b,b,b))$
$((a,a,b),(a,a,a))$
$((a,a,b),(a,a,b))$
$((a,a,b),(a,b,a))$
$((a,a,b),(a,b,b))$
$((a,a,b),(b,a,a))$
$((a,a,b),(b,a,b))$
$((a,a,b),(b,b,a))$
$((a,a,b),(b,b,b))$
$((a,b,a),(a,a,a))$
$((a,b,a),(a,a,b))$
$((a,b,a),(a,b,a))$
$((a,b,a),(a,b,b))$
$((a,b,a),(b,a,a))$
$((a,b,a),(b,a,b))$
$((a,b,a),(b,b,a))$
$((a,b,a),(b,b,b))$
$((a,b,b),(a,a,a))$
$((a,b,b),(a,a,b))$
$((a,b,b),(a,b,a))$
$((a,b,b),(a,b,b))$
$((a,b,b),(b,a,a))$
$((a,b,b),(b,a,b))$
$((a,b,b),(b,b,a))$
$((a,b,b),(b,b,b))$
In all of the iwrs above, the further categorisation, if possible, could help to order them more.
Possible interpretations, intuition and examples
Imitation and opposition as types of reactions of control over the mutual distance of an object and a referent
In some specific cases of iwrs, the two agents both act to control the mutual distance of an object and a referent.
In case of an imitation reaction type, when:
- initial agent acts to increase the distance – reacting agent acts to increase it too
- initial agent acts to decrease the distance – reacting agent acts to decrease it too
In case of opposition, on the other hand, when:
- initial agent acts to increase the distance – reacting agent acts to decrease it (and there can be 3 results of it, described above)
- initial agent acts to decrease the distance – reacting agent acts to increase it (and there can be 3 results of it)
The same entity, which acted in the initial interaction, could also, theoretically, react to that (its own) action.
Examples of interactions with reactions
Interaction with reaction on the initial object, with reaction’s agent and referent being the same entity:
- ${int_1}^{r,s} = (x,y,z,-)$
- ${int_2}^{r,s} = (i,y,i,+)$
Example: “Entity $x$ acting to repel $y$ from $z$. Entitiy $i$ reacting, by trying to attract $y$ to $i$.
Interaction with reaction with the same object and referent, involving imitation:
- ${int_1}^{r,s} = (x,y,z,+)$
- ${int_2}^{r,s} = (i,y,z,+)$
- $(+,+)$
Example: “Entity $x$, trying to point/aim entity $y$ at entity $z$. Entity, $i$, doing the same ($i$ imitates action of $x$).
Interaction with reaction with swapped object and referent, involving opposition and resulting in inversion:
- ${int_1}^{r,s} = (x,y,z,+)$
- ${int_2}^{r,s} = (i,z,y,-)$
- $(-,-)$
Example: “Entity $x$ acting to attract $y$ to $z$. Entity $i$ acting to repel entity $z$ from $y$ (so, that the distance between the two entities increases ($i$ overpowers initial influence of $x$ on $y$ relative to $z$)).
Interactions with reactions as conditionals
In some contexts, interactions with reactions could probably be interpreted as conditionals, in which a fulfillment of an initial interaction (condition) would imply the occurance of certain reaction (consequence).
Examples in relationships and psychology
Interpretations of certain interactions with reactions as conditionals include:
- making predictions with assumed implications (e.g. “if $int_1$ happens, then I predict $int_2$ to happen too”)
- making promises (e.g. “if $int_1$ happens, then I promise you, that $int_2$ will happen”)
- setting boundaries in relationships (e.g. “if you do $int_1$ to me, I will react by doing $int_2$”)
- offering gratification for doing a certain task (e.g. “if you do $int_1$ for me, I will reward you with $int_2$”)
- threating another (e.g. “if you do $int_1$, I will act unfavourably to you with $int_2$”).
having different definitions and roles of entities involved in them.
Additional information
The cases, involving 3, 2 and 1 entity in an individual interaction can be found in this post: Scientific metaphysics – basic interactions, action and reception types
Some additional information related to the certain iwrs mentioned above can be found in one of the previous posts: Scientific metaphysics – types of reactions of confrontation (that post can, however, include a deprecated naming and notation).