log into your twitter account, then open a new browser tab or window, and go to the app:
http://apps.facebook.com/twitter/The app does appear to be from Twitter, I've been using it about 2 years now no worries.
Detailed steps here:
I started doing this partly out of protest with the effort required to keep my FB contacts active, because logging into FB is such a hastle, and the adverts are either obnoxious, boring or just plain waste of pixels. Ever since the Facebook re-vamp(almost 2 years back now), which made navigation in FB confusing, I only log into FB when e-mail notifications tell me something interresting is happening. I balance this by posting mobile pics in twitpic, facebook or flickr (you can see my flickr feed on the right). As you guessed, twitpic posts are tweets, so they still get to FB, it just takes longer and does not look as good.
Annoyingly,the app is blank if you have already set up FB to trust Twitter, so it's a bit hard to see what's going on latter on.
I guess the reason I find the FB User-Interface confusing, is that I ignore 90% of web adverts, and find their layout mucks with my brain's inbuild advert filter, because it's designed to maximise advert impressions. I regularly post a FB support request just to complain about the UI, it's the only way I can fight against the machine of capitalist control.
Helping strangers unaware
4 months ago