A popular belief about "rationality" is that rationality opposes all emotion—that all our sadness and all our joy are automatically anti-logical by virtue of being feelings. Yet strangely enough, I can't find any theorem of probability theory which proves that I should appear ice-cold and expressionless.
So is rationality orthogonal to feeling? No; our emotions arise from our models of reality. If I believe that my dead brother has been discovered alive, I will be happy; if I wake up and realize it was a dream, I will be sad. P. C. Hodgell said: "That which can be destroyed by the truth should be." My dreaming self's happiness was opposed by truth. My sadness on waking is rational; there is no truth which destroys it.
Rationality begins by asking how-the-world-is, but spreads virally to any other thought which depends on how we think the world is. By talking about your beliefs about "how-the-world-is", I mean anything you believe is out there in reality, anything that either does or does not exist, any member of the class "things that can make other things happen". If you believe that there is a goblin in your closet that ties your shoe's laces together, then this is a belief about how-the-world-is. Your shoes are real—you can pick them up. If there's something out there which can reach out and tie your shoelaces together, it must be real too, part of the vast web of causes and effects we call the "universe".
Feeling angry at the goblin who tied your shoelaces involves a state of mind that is not just about how-the-world-is. Suppose that, as a Buddhist or a lobotomy patient or just a very phlegmatic person, finding your shoelaces tied together didn't make you angry. This wouldn't affect what you expected to see in the world—you'd still expect to open up your closet and find your shoelaces tied together. Your anger or calm shouldn't affect your best guess here, because what happens in your closet does not depend on your emotional state of mind; though it may take some effort to think that clearly.
But the angry feeling is tangled up with a state of mind that is about how-the-world-is; you become angry because you think the goblin tied your shoelaces. The criterion of rationality spreads virally, from the initial question of whether or not a goblin tied your shoelaces, to the resulting anger.
Becoming more rational—arriving at better estimates of how-the-world-is—can diminish feelings or intensify them. Sometimes we run away from strong feelings by denying the facts, by flinching away from the view of the world that gave rise to the powerful emotion. If so, then as you study the skills of rationality and train yourself not to deny facts, your feelings will become stronger.
In my early days I was never quite certain whether it was all right to feel things strongly—whether it was allowed, whether it was proper. I do not think this confusion arose only from my youthful misunderstanding of rationality. I have observed similar troubles in people who do not even aspire to be rationalists; when they are happy, they wonder if they are really allowed to be happy, and when they are sad, they are never quite sure whether to run away from the emotion or not. Since the days of Socrates at least, and probably long before, the way to appear cultured and sophisticated has been to never let anyone see you care strongly about anything. It's embarrassing to feel—it's just not done in polite society. You should see the strange looks I get when people realize how much I care about rationality. It's not the unusual subject, I think, but that they're not used to seeing sane adults who visibly care about anything.
But I know, now, that there's nothing wrong with feeling strongly. Ever since I adopted the rule of "That which can be destroyed by the truth should be," I've also come to realize "That which the truth nourishes should thrive." When something good happens, I am happy, and there is no confusion in my mind about whether it is rational for me to be happy. When something terrible happens, I do not flee my sadness by searching for fake consolations and false silver linings. I visualize the past and future of humankind, the tens of billions of deaths over our history, the misery and fear, the search for answers, the trembling hands reaching upward out of so much blood, what we could become someday when we make the stars our cities, all that darkness and all that light—I know that I can never truly understand it, and I haven't the words to say. Despite all my philosophy I am still embarrassed to confess strong emotions, and you're probably uncomfortable hearing them. But I know, now, that it is rational to feel.