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Like the character Yoda, from the popular Star Wars films, Yodaspeak is a rather backwards form of speaking. The character Yoda is known for his wisdom, thus this specific way of talk is associated with wise and sagacious thoughts. Using yodaspeak to say something obvious, vulgar or common creates a comic and absurd situation. Due to its relative ease, and the popularity of image macros, these can appear anywhere normal memes do. Yodaspeak can be often found in comments on forums, imageboards or blogs, as well.
Spread and mutations
The idea of imitating yoda speak is of a pre-internet origin. In the internet, however, memes with yoda begun to appear in May, 2005 after the premiere of Star Wars III: Revenge of the Sith. On June 23rd, 2005 the site yodaspeak.co.uk  was launched and provided the internet with easy to use english→yodatalk translator. One can find there a selection of quotes as well, and a shoutbox with more funny lines converted to yoda speak (e.g Come here to chew bubble gum and kick ass, have I. And all out of bubble gum, I am).
Shut the fuck up derivatives
One of the first yoda images with a funny captions in yoda speak is the one with "Up the shut fuck" caption, found on the off-topic thread of the bit-tech.net forum . The mentioned forum post was made on May 16th, 2010. It is notable, that memes connected with yoda begun to spread by that year (as seen on the google trends graph below). Later, the caption evolved to "Up the shut fuck you must" and there are T-shirts with the latter caption available on spreadshirt.com  and various other shops.
The most popular image macro with yodaspeak is the advice animal variation. Captions are usually either actual advices, random thoughts, or "translated" popular phrases. The template is available on memegenerator.net  and below.
Yodaspeak in community
It is quite popular to make yoda accounts on various community sites like Twitter, Facebook, Youtube, forums, blogs etc. Pretty much on every major community-based website there is at least one yoda account. The person behind such a profile usually posts their comments in yodaspeak for entertainment purposes (that is, they seldom post on-topic, deep thoughts). On May 22nd, 2008 a Twitter account @yoda was created . Later on Twitter @YOLO_YODA profile  and @thereal_yoda  were created as well. Their tweets are all written in yodaspeak but aside from that, they don't differ much from a regular twitterer. On August 20th, 2005 an account with the same name was created on Youtube , although with no notable activity. On September 8th, 2006 a similar user joined collegehumor.com .
The first spike happens around the release of Star Wars III: Revenge of the Sith (May 2005)
The "yoda meme" search (orange) spikes around the release of a 3d remake of Star Wars I: Phantom Menace (February 2012)