While it is not necessary (or even advantageous) to be a stereotypical computer geek to succeed in a computer field, the stereotypes do have some basis in reality. One place where stereotypes tend to be strongly grounded in reality is when it comes to geek hobbies. In many cases, these hobbies use similar (or identical) skills to those used in the workplace. For instance, designing web sites and coding are both common hobbies and professional skills. In other cases, they seem to have some sort of higher level skill or ability overlap. For instance, tinkering uses troubleshooting skills and math uses analytical thinking. (I recently worked with two programmers who include math among their hobbies.) Other common hobbies such as video gaming and reading science fiction, don't map as easily to job skills but still seem to have an almost universal appeal.
Shared hobbies and interests can be an important way to bond with your colleagues. They are also often used to gain credibility when meeting a new colleague. A new colleague isn't going to know the ins and outs of your codebase, but you are all on a level playing field when analyzing the latest sci fi novel or discussing the relative merits of different programming languages. Just yesterday I saw two job postings that mentioned common hobbies in the office that applicants were warned they should at least be comfortable with (foosball and World of Warfare.) On a related note, I recently heard a technical manager say he's never met an excellent programmer who didn't program as a hobby. I suspect this has more to do with the fact that that level of enjoyment of coding encourages people to get the time in to achieve mastery, but never the less, it's worth thinking about if you want to be an excellent programmer. Learning (or participating in) geeky hobbies can also be a low risk way to meet and network with potential professional contacts, particularly if you attend workshops or discussion groups.
This isn't to say that you should give up our existing life and become clones of the physicists on The Big Bang Theory. Individuality is important (and more prized in the computing fields than many others.) One of the above mentioned job postings also mentioned that applicants should have at least one non-geeky hobby. And a reasonable minority of people find that they are more effective at work when they spend their free time doing something completely different. I worked with a guy who found that he was happier if he gave up TV because staring at a TV screen was too much like staring at a computer screen at work. I've found that I am less likely to burn out if I make sure to devote time to my non-geeky hobbies. I do recommend that you at least explore a variety of stereotypical geek hobbies to gain the social and networking benefits. And who knows, you may discover a new avocation.
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