a linear algebra-esque way my brain thought up of thinking about personality traits

8/29/2024

Wanted to share this mathropomorphization that's been lingering in my brain the past year or so

some definitions

Let be a row vector that represents stable traits of your innate personality

Where each element represents some dimension/trait of your personality or sense of identity for dimensions

Next, let be a matrix that represents your environment

Columns of represent your environment's influence on you for a given personality trait.

So if we multiply and call the result :

we get row vector:

where each is calculated as:

represents our observed personality or identity. Both how others perceive us and how we perceive ourselves.

Each element represents a perceived personality trait.

This is the internal model my brain has come up with for conceptualizing our environment's influence on us.

using this model

If someone spent their whole life - or a large part of it - in a single environment, they might believe their is really their .

There've been times where some columns of my have been fairly stable amongst many s, leading me to believe that that subset of my must be strongly derived from my and unshaken by the weights of s - only then for a brand new to come along and observe that part of my change.

You can run trials seeking out different s with different amplitudes of variance, and observe the effects on your . I feel like part of life is doing this time and time again and each time trying to solve for a part of your .

Sufficiently different s can be thought of as being linearly independent. The more linearly independent s we have, the higher rank our model becomes 📈 the more parts of P we can solve

Sometimes, an might come along that even increases the dimensionality of the whole system by adding new columns to and that we didn't even know could go there.

oh snap another matrix

thats right now we got matrix

Matrix is for how another person around us may also affect our personality.

So would then be the combination of our personality influenced by our environment and also those around us. Lets call that idk

My brain goes back and forth here whether it would be better to represent this relationship as a whole new matrix, or maybe if we want to explore the ideas of how the same environment may influence another person, then we can just call as that person's . Then in this case we could make , but a perfect dot product probably doesn't make sense.

How do you do a dot product but where each element also has an additional dampening/amplifying coefficient