Can or will automata love? If so, is there a theoretical limit to love? Conversely, can automata develop selfishness?
How many resources will automata devote to being selfish and helping others?
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It's a poorly stated question because these are at least three, possibly four different questions that are quite independent from each other.
First, let's take the questions from the text. Selfishness vs generosity of the system - this is quite easy to define as sacrificing resources for "own maintenance" vs "statutory purposes" - "helping others" defined as fulfilling the role assigned by the creators.
This is all a matter of developing the goal function that gives sufficient priority to immediate or short term results. In the classic example of "paperclip maximizer", without this sort of restriction the end result will be not even a single paper clip made, as the AI expands self to develop even more efficient way to create the paper clips, since current, inferior methods will waste resources which could better serve later, more advanced methods - the classic paradigm "better is the enemy of good", all focus on optimizing the process without actually performing the process.
The problem here is that we don't know what type of function the improvement due to the optimization process will follow, and so we don't quite know what sort of prioritization function to apply. Probably a flat deadline would work, but if that is movable, AI might sacrifice all resources to developing a way to move the deadline. Be it by resetting system clock, terrorizing system operators into adjusting the deadline, or inventing time travel.
So, selfishness vs generosity is a matter of developing the correct time constraints on the goal function. Difficult, but doable - without it AI will be "infinitely selfish", but over-constrained, it will be inefficient, producing inferior immediate result instead of developing better.
Probably, a good approach would be to predict a reasonable (both achievable and desirable) advancement path and set this as the goal value - not maximization of output, but approaching the desired output value (which may be growing over time, linearly or exponentially) and freeing up unused resources - adding a cap on expansion speed. That would avoid the paperclip universe horror scenario.
Now, for love. Again, this depends largely on the goal function.
Defining love, that would be a specific mental state, influenced by specific hormones, and leading to specific re-shuffling of priorities, often resulting in impaired judgment.
Defined that way, could AI love? Yes. Should it? uh, better no. Because, "What will be the limit to love? Any theoretical limit?" - about none, bar using up all matter and energy in the universe.
Love pretty much unconditionally favors the "beloved". And that is just another phrasing for maximization. And, as we all know, an unconstrained maximizer AI is bad news. You don't want "Give you the Moon and all the stars" to be a completely literal expression. So, love - while possible both to implement, and to happen as a side effect of poorly constrained other goals (like "learn to feel all that a human can feel") can be a serious problem.
So yeah, regarding AI and love: can we? Yeah. Should we? nope.
First, it's helpful to define love in functional sense as altruism. (This is consistent with the function aspect of agapein terms of how that love functionally affects the material world through the actions of individuals.)
To this end, I urge you to look into the concepts of rational agents and superrationality. These concepts are mathematical approaches to decision making, and in the context of humanity, which may one day be extended to include Artificial General Intelligence, carry a moral dimension.
In a game theoretic context, cooperation is a functional form of altruism, as is the willingness of the superrational agent to "take a hit" and even "turn the other cheek" (make one or two altruistic choices to try to lead the rational agent into a superrational strategy that yields optimal outcomes, as opposed to getting stuck in a Nash equilibrium that yields a suboptimal outcome.)
The cool thing about these fields and ideas is that they are all driven my mathematics.
Thus, without getting into philosophy, we can say that automata will express behaviors analogous to love, but the basis is mathematical, and this also forms a functional limit defined by the parameters of the model.
On a philosophical note, Phillip Dick, who was quite prescient, believed that automata would become smart enough to develop empathy, allowing cooperative behaviors, and leading to love.
Do Androids Dream Of Electric Sheep is about this subject, both the humanistic (philosophical) dimension, and the scientific--the plot of the 1968 novel prefigures Evolutionary Game Theory, which was formalized just 5 years later.
It depends on the environment and goals, does the AI dies? reproduces? carries genetic information across generations?
Love is yet another selfish strategy. And it is a hard-wired reward reflex in our brains to help identify and stick to suitable mates that helps us reproduce, as a consequece, evolution helps shapes and refine the love instinct. This is at least a valid theory.
That said, an AI, as an individual is totally selfish, the strategy to express selfishness can vary depending on its goals.
If adjacent peers doesn't recepricate or protect the AI and it's offsprings, it is futile to share or care for them.
On the other hand, the AI have all reasons to love for example a data source, that provides the AI with information to survive and reproduce.
Reference: The Moral Animal