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I'm tempted to argue that they play a part in the 'taste performances' (Liu 2008) that are integral to most social networking sites. It's one of the ways I project or perform my identity online.
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By describing to followers what I'm preparing and/or eating I'm also performing a particular identity. For example, if I tweet that I'm cooking a dish with locally-sourced ingredients that keeps the food miles down, I'm projecting an identity that's discerning and environmentally aware; if, on the other hand, I tell you I'm serving up a dessert of frozen Creme Eggs, the identity I'm performing is offbeat and fun-loving.
Far from being part of the anti-Twitter camp's imagined stream of trivia, the 'dinner tweet' is, in fact, an integral part of the repetoire through which twitterers perform the 'ongoing narrative of the self' (Merchant 2006: 238).
So, next time someone moans about 'twitterhea' and the banality of the 'dinner tweet', tell them it's all about identity performance and refer them to Pierre Bourdieu and Anthony Giddens.
References
Liu, H. (2008). Social Network Profiles as Taste Performances. Journal of Computer-Mediated Communication, 13(1): 252-275.
Retrieved April 29, from http://jcmc.indiana.edu/vol13/issue1/liu.html
Merchant, G. (2006). Identity, Social Networks and Online Communication. E-Learning, 3(2): 235-244