Apart from "nobody cares what you ate for breakfast hurr hurr", the criticism most levied at Twitter is its 140-character limit. I think people are missing the point here. Regardless of the original reason for the limit (Twitter was intended as an SMS service), the deliberate constraint is Twitter's killer feature.
I like constraints. Constraints give a website character, they keep it focused, they tell the user base how to best use a website. Some constraints are obvious, like Twitter's limit, some are more just encouragement. The user-driven nature of the social web/web 2.0 means you have to give users a whole lot of control, but you still need to shape it in some ways.
It nearly always works in a website's favour. Twitter's tiny limit means nobody rambles, it means you can get a feel for the conversation around the world in a few minutes, and it means checking it isn't a chore. It also means you don't feel as though you're crowding your followers posting 10 or so updates in an hour, if something is happening, and the updates happen in real time rather than are saved for one big post. Facebook lets you do nearly anything - photos, chat, statuses - but it doesn't give you much to play with, design-wise. As has been said many times before, they learned a whole lot from MySpace on that front. In a more controversial move, Tumblr has an ask/message limit because it is first and foremost a blogging platform, not a social network. Remaining as bare-bones as possible is also pretty excellent for performance. The Reddit front page without extensions is essentially a series of links with thumbnails. 4chan without extensions is a whole lot of text and thumbnails with a few bigger images. These sites load anywhere fast, and that is a plus.
I guess deliberate constraints are really just marks of focus. Websites should generally be focused. The problem with Yahoo and AOL, though they are clawing their way back, is a lack of focus. What is the main service of Yahoo these days? Y!Mail? Flickr? News? Users generally wanted all these extra features, and users generally complain when any of them leave, but you have to override your users sometimes. Google has spread itself a little thin, but at least the Google homepage is still just the Google search homepage, no frills. Facebook, while it lets you do a lot of different things, has the clear purpose of connecting you to people (and selling you personalised ads). Everything you do on the site is in some way social.
Some deliberate constraints do annoy me though. The Tumblr ask thing seems silly - it seemed like a relatively beneficial appropriation of your technology. Instagram was created as the photo functionality of a drinking app called Burbn. Twitter was originally for group texting. The internet was a system of defence in case of nuclear war. You gotta let people shape these things a little.
Are there any constraints that you particularly love/hate, kind blog reader?
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