I’m going to define love. I do not mean the love you are familiar with – the love synonymous with a variety of different emotional and mental states, but rather I’m going to repurpose the term “love” for a different concept that I’ve been trying to define mathematically.
Love L is the negative partial derivative of mindstream M with respect to extent of transformation E at constant verbal report and arousal. That is,
L = – (∂M/∂E) V,A.
It follows that love is positive for the spontaneous transformations from one subjective experience to the next if time in the positive direction correlates with higher assigned values for the mindstream.
Now let me explain what the equation means:
The partial derivative exists when a function has several variables and yet we just look at the derivative with respect to one of those variables. In this case, there are many variables going into producing the value of a mindstream at any given point, but we are just looking at the derivative with respect to E. The derivative means the sensitivity to change of the mindstream with respect to E. You can visualize a tangent line to a mindstream function: If the tangent line is closer to flat, there is little sensitivity to change, if it is very sloped, then there is high sensitivity to change.
Now, what the hell is a mindstream? A mindstream is simply defined by the values for the brain. Imagine that you can describe all characteristics of a brain that distinguish it from any other brain, and then assign a value to that unique configuration. Each configuration of a brain correlates to a configuration of mind/consciousness, and if we had a complete understanding of the brain, we might be able to plot all the different possible states in a single dimension. This is state 1, this is state 2, this is state 5946294, etc. There exist very similar brains/minds, like you at the beginning of this sentence and you at the end of this sentence. So this might be a transition from state 24 to state 25, say. While very different brains, like comparing a snapshot of your brain and a snapshot of my mom’s brain would be very far apart in their respective assigned values.
So what is E? E is the extent of transformation from one brain state to the next. Consider the transformation
Suppose an infinitesimal amount dE of the configuration A changes into B. The change of the amount of A can be represented by the equation dnA = -dE, and the change of B in dnB = dE. The extent of transformation is then defined as
dE = dni/vi
where ni denotes the value of the i-th configuration** and vi is the number that balances the i-th configuration to all the other configurations (in case the difference between 4 and 5 is different than 5 and 6 for some reason.) In other words, E is the amount of configuration that is being changed when a brain/mind state becomes another brain/mind state. Considering finite changes instead of infinitesimal changes, one can write the equation for the extent of a transformation as
ΔE = Δni/vi
The extent of a transformation is defined as zero at the beginning of the frozen snapshot. Thus the change of E is the extent of transformation itself.
E = Δni/vi = (ntransformed – ninitial)/vi
*(remember that according to the laws of physics, both brains/minds equally exist; there is no flow of time from now A to now B that can’t also be reversed.)
** the i-th configuration is just some configuration between brain A and B.
The constant verbal report and arousal simply mean that the mindstream/brain would constantly be able to narrate “Here I am, there’s something going on.” And if you poke the sensory inputs connected to the brain, she would say “ouch.” These are simply some of the most reliable indicators of consciousness today. But these may be replaced with other constants that are more fundamental to explaining consciousness in the future. The reason we need consciousness to be constant in this sense is because if it wasn’t, then the mindstream function would be different in off states and on states.
So the love I defined refers to the tendency of a mindstream/brain configuration to be joined with another different configuration by transformation.