I love Star Trek. I love it quite a lot. (Just ask @masstreble over on Twitter if you don't believe me.) Buried within the Star Trek mythos are quite a lot of different wonderful, positive and utterly human ideals, and so it enjoys a special place in my heart.
It's not all good, though. For as much as Star Trek elevates science and rationality to being the centerpieces of its Utopia, it often cares very little for the actual practice of science. It is also, unfortunately, where we get one of the most quintessential embodiments of the fallacy that rationality must entail emotional detachment. Indeed, many people seem to believe that scientists and others who value rationality are somehow "cold" emotionally (of course, this would make sense if one considers the analogy between irrationality in game theory and the statistical distributions associated with temperature, but I digress). While it is true that many of us embrace our analytical natures and try to deconstruct, analyze and reduce our experiences, that doesn't mean that emotions aren't an important and vital part of that process, to say nothing of our lives on the whole.
We can reason about our emotions, and choose rationally to engage in some action do bring about desired emotional states. For example, I spent money to buy the equipment needed to play video games because I enjoy them, not because it makes sense when emotions are removed from consideration. Practically everyone does this to some degree, but part of being rational, analytical and self-aware is to exercise introspection about this process.
Ironically, I think that much of Star Trek has actually gotten this right, but what sticks in people's minds is the image-- the idea-- of Spock as being both the nearly platonic ideal of a rationalist and of being incredibly unemotional. This image, intended or not, seems to resonate within our culture, leading to that stereotype of the unemotional rationalist being reinforced.
People are, and in my opinion, should be emotional agents in addition to rational agents. The effect, then, of the Spock fallacy, is to create a false dichotomy between these two views of the human condition. Rationality may then be rejected on the basis of not being compatible with intuition or emotion. This is particularly and appallingly clear as applied to religious issues; atheism is often dismissed as lacking in emotional appeal (see Rebecca Watson's recent video on the subject for a good refutation of this argument).
Part of the problem is that in setting up a false dichotomy between rationality and emotion, it is all too easy to forget that rationality is, amongst other things, a strategy for finding the truth. Sometimes the goals of finding truth and being happy appear to be in conflict, and at these times, it is rationality that must win. This is not to say that emotions cannot play a part of such decisions, or that the importance of happiness is somehow overlooked by a rational analysis.
Since I am a physicist by training, I like to argue from limiting cases, and what could be a greater example of the importance of emotion than that of romance? Is it not possible to rationally argue, for instance, that in the interests of long-term happiness, a troubled romance should be ended? This may appear to be in conflict with the importance of emotions, and may even seem to play into the stereotype of rational analysis being "cold." On the other hand, is this not an example of how emotions and rationality can be happily wed?
Rationality and emotion need not be seen as orthogonal to each other, as indeed they are both important parts of being a full and complete human being. Instead of Spock, then, maybe we should think about what Julian Bashir has to teach us.