?Category theory

Category theory

I have covered the ideas of dyads and some symbolism. When the dyads are combined with the remaining corner of the triangle, things become more interesting. I’m putting this here for the contentment of the math-heads. There are obviously three of these dyadic relations:

((σ-ρ)-ν) or (υ-ν) or (^ρ◡^σ-ν)   how motive influence stimulus-response

((σ-ν)-ρ) or (π-ρ) or (ρ-_ν/^σ)   how a stimulated motive influences motion

((ρ-ν)-σ) or (τ-σ) or (^ρ\_ν-σ)   how a stimulus influences motivation

Of these, the (π-ρ) combination is most informative to behavioural modelling. Pi is the connection between stimulus and values and can be seen as the evaluation of contentment. Where the stimulus mismatches values, then this leads to a state of discontentment, and something has to be done about it there is motivation. This motivation is a connection between motive (or values) and motion (or response). Hence, the stimulus, via values, generates a response. The distorted triangle (because stimulus-response is indirect) is completed.

So, (π-ρ) equates to ▽)

Let’s go through this, the cat has some things which are important to it, such as having dry fur (ν = dry fur). But, it is outside and it starts raining (σ = raining).

∴ _ν/^σ = π (contentment match of stimulus against values)

The cat is getting wet and it doesn’t like it, and action needs to be taken.

∴ π  →_ξ  τ  (discontentment (π) implies (ξ) motivation (τ))

∴ _ν/^σ →_ξ ^ρ\_ν   to put it alternatively.

So, by joining the sides where ^ρ\_ν–_ν/^σ = ^ρ_ν∀)^σ

∴ ^ρ_ν∀)^σ  which links up stimulus to response and allows us, via omicron to get upsilon: ξ  →_ο  υ

∴▽)

The takeaway here is that given two sides of the triangle, we can work the third out: a kind of Pythagoras’ of behavioural calculus I suppose. It does relate to some abstract mathematical concept called category theory, but I won’t go into that. OK, I hold my hands up; the whole thing is nothing other than a pseudo-mathematical proof. Actually, I would claim proto-mathematical, but whatever. Solid math can come later. Right now, I’m after a way of describing and understanding such relationships: one which goes beyond stimulus-response to involve values in an intuitive graphical manner. The reasoning will become apparent on exploring the practical applications such as the persuasion of memetics and cliology.