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1.
Getting down on one knee, curling one's wrist to one's chin, and looking up, mimicking the pose of Auguste Rodin's classic sculpture "The Thinker".

(Created by Dave Silverman, reported by Staks Rosch, "Thinkering: The atheist answer to Tebowing", Dec. 30, 2011, examiner.com)
In response to the fundamentalist craze of Tebowing, American Atheists President Dave Silverman has come up with an atheist version called "Thinkering."
Someone commented that the pose looked too similar to Tebowing, to which Silverman responded: "That's the point. The difference is we don't bow our heads in blind submission, rather we consider and conclude for ourselves."
by GCat February 04, 2012
 
2.
A portmanteau of "thinking" and "tinkering". Means to think about something by tinkering with objects relating to the problem under consideration. Usually unguided, exploratory and individual, often a very good way to explore aspects of difficult problems or to find solutions where none are obvious. In other words, an active form of thinking.

Akin to solving a puzzle (like a rubiks cube) by trying to solve it rather than just sitting and staring at it.
Bob is thinkering again, wonder if he'll finally figure out how to get that perpetual motion machine back together again?
by ithacanz September 30, 2010
 
3.
There was planking (laying like a board on random objects), then owling (sitting like an owl on random objects), then teapotting (doing the teapot anywhere), now thinkering (sitting on the edge of random objects like a thinker).
Planking, owling, teapotting, time for me to do thinkering!
by Camron Moore July 21, 2011
 
4.
Tinkering with ideas none of which are clear and actionable. The thought process is less analytical, keeps you aloof from pragmatic, practical options and steers you towards blowing bubbles in the air, ultimately unproductive. If you are ADD then God help you, you jump from idea to idea until you start seeing double… triple… multiple.

There is value in thinkering. May be you'll run into that one idea and create something from nothing, like you will find a treasure in a garage sale.
I spend more time thinkering about unconventional career options rather than actually job searching. For example: ummmmm the astronaut suit will look great on me but i refuse to wear those experimental underwear for a month at a time, I dunno maybe I should get a group of unemployed folks together and shoot a reality show of them while they look for jobs, let’s see I guess could just crash weddings…….
by Sasha.Nath August 04, 2009