I'm going to try to apply some Bayesian math to the question of whether it makes sense to believe "if you aren't sad about my bad situation then that means you don't care about me"
In this example, Person X is in a bad situation, and wants to know if Person Y cares about them.
To use Bayes' theorem, we are interested in the following probabilities:
P(A) is 'Person Y cares about Person X'
P(B) is 'Person Y feels sad about Person X's situation'
P(C) is 'Person Y expresses sadness about Person X's situation'
Let's use P(B) as an abbreviation for either P(B given C) or P(B given not C). Because we're doing these calculations after Person X already knows whether or not Person Y expressed sadness. In other words, I'm assuming that P(B) has already been updated on C.
Bayes' theorem says that P(A given B) is P(B given A) times P(A) over P(B).
P(B given A) and P(A) make it go up, P(B) makes it go down.
Bayes' theorem says that P(not A given not B) is P(not B given not A) times P(not A) over P(not B).
P(not B given not A) and P(not A) make it go up, P(not B) makes it go down.
So this tells us:
The more uncertain Person X is about whether Person Y cares about them, the more they'll worry about whether Person Y feels sad about any specific misfortune Person X is experiencing.
Different people probably have different beliefs about what P(A given B) is. Someone who thinks that this value is high will be more reassured by someone feeling sad about their situation, and someone who thinks this value is low will be less reassured. So this value will be different for a different person X, and also for a different person Y.
Different people probably have different beliefs about what P(not A given not B) is. Someone who thinks that this value is high will be more worried by someone not feeling sad about their situation, and someone who thinks this value is low will be less worried. So this value will be different for a different person X, and also for a different person Y.
If Person Y somehow feels equally sad about the misfortune of people e specifically cares about, and people e doesn't even know, then P(B given A) is equal to P(B), and whether they feel sad about any particular misfortune of Person X doesn't give any new information about whether Person Y cares about person X.
Similarly, if Person Y never feels sadness about anyone's misfortune, then P(B given A) is equal to P(B), and the fact that Person Y doesn't feel sad about any particular misfortune of Person X doesn't give any new information about whether Person Y cares about person X.
And if Person Y is somehow less likely to feel sad about the misfortunes of people e cares about, than people e doesn't care about... then all this would be reversed? This isn't really relevant anyway, so I won't bother checking the math.
I am very likely to have made a mistake somewhere in this comment. Halfway through writing this comment I started to get really fuzzyheaded.
Most of this was already obvious before doing the math, but I think there was at least some value to this exercise.
Also, I very strongly suspect that I'm completely missing the point of... something...
oh, right, I was trying to answer the question of whether it makes sense to believe "if you aren't sad about my bad situation then that means you don't care about me"
and the answer is... sometimes. It depends on the variables described in the math above.
Follow-up to: Suffering as attention-allocational conflict.
In many cases, it may be possible to end an attention-allocational conflict by looking at the content of the conflict and resolving it. However, there are also many cases where this simply won't work. If you're afraid of public speaking, say, the "I don't want to do this" signal is going to keep repeating itself regardless of how you try to resolve the conflict. Instead, you have to treat the conflict in a non-content-focused way.
In a nutshell, this is just the map-territory distinction as applied to emotions. Your emotions have evolved as a feedback and attention control mechanism: their purpose is to modify your behavior. If you're afraid of a dog, this is a fact about you, not about the dog. Nothing in the world is inherently scary, bad or good. Furthermore, emotions aren't inherently good or bad either, unless we choose to treat them as such.
We all know this, right? But we don't consistently apply it to our thinking of emotions. In particular, this has two major implications:
1. You are not the world: It's always alright to feel good. Whether you're feeling good or bad won't change the state of the world: the world is only changed by the actual actions you take. You're never obligated to feel bad, or guilty, or ashamed. In particular, since you can only influence the world through your actions, you will accomplish more and be happier if your emotions are tied to your actions, not states of the world.
2. Emotional acceptance: At the same time, "negative" emotions are not something to suppress or flinch away from. They're a feedback mechanism which imprints lessons directly into your automatic behavior (your elephant). With your subconsciousness having been trained to act better in the future, your conscious mind is free to concentrate on other things. If the feedback system is broken and teaching you bad lessons, then you should act to correct it. But if the pain is about some real mistake or real loss you suffered, then you should welcome it.
Internalizing these lessons can have some very powerful effects. I've been making very good progress on consistently feeling better after starting to train myself to think like this. But some LW posters are even farther along; witness Will Ryan:
Some other LW posters who've made considerable progress on this are Jasen Murray, Frank Adamek and Michael Vassar. I invite them to post their experiences in this thread, and in future posts of their own.
How does one actually achieve emotional acceptance? It is a way of thought that has to be learned with practice. There are various techniques which help in this: I will cover one in this post, and others in future ones.
Mindfulness practice
Mindfulness techniques are very useful in realizing that your thoughts and emotions are just things constructed by your mind:
It also has clear promise in reducing suffering:
I recommend the linked paper for a good survey about various therapies utilizing mindfulness, their effects and theoretical explanations for how they work.
While I haven't personally looked at any of the referenced therapies, I've found great benefit from the simple practice of turning my attention to any source of physical or emotional discomfort and simply nonjudgementally observing it. Frequently, this changes the pain from something that feels negative to something that feels neutral. My hypothesis is that this eliminates an attention-allocational conflict. The pain acts as a signal to concentrate on and pay attention to this source of discomfort, and once I do so, the signal has accomplished its purpose.
However, often I can do even better than just making the sensation neutral. If I make a conscious decision to experience this now-neutral sensation as something actively positive, that often works. Obviously, there are limits to the degree to which I can do this - the stronger the discomfort, the harder it is to just passively observe it and experience it as neutral. So far my accomplishments have been relatively mild, such as carrying several heavy bags and changing it from something uncomfortable to something enjoyable. But I keep becoming better at it with practice.