The answer, of course, is all the above. Division is one of the five templates of innovation in the Systematic Inventive Thinking method. The others are Subtraction, Task Unification, Multiplication, and Attribute Dependency. Templates were developed by recognizing the same consistent pattern over many products so that the pattern could be applied to create innovative new products. The method works by taking a product, concept, situation, service, process, or other seed construct, and breaking it into its basic component parts or attributes. The templates manipulate the components, one at a time, to create new-to-the-world constructs for which the innovator finds a valuable use. The notion of taking the solution and finding a problem that it can solve is called "function follows form" and is at the heart of the systematic inventive thinking process. It is innovation by working backwards.
The Division Template works by taking a product or a component of it and dividing it physically, functionally, or what is called preserving where each part preserves the characteristics of the whole. Rearrange the parts, then work backwards to find a use or benefit for this new form.
Here is an example from my workshop last week at Duke's Fuqua School of Business. The product is dryer sheets (gauze-like tissues about the size of a Kleenex, put into clothes dryers to eliminate static cling, soften clothes and add artificial fragrance.) Now divide these into much smaller parts, perhaps after the whole sheet is thrown into the dryer. Imagine these smaller parts get all over the clothes and cling to them. Why would this be useful? What could be the benefit? Here's an idea. Perhaps the smaller pieces stay on the clothes to continue softening, brightening, or adding a design element, waterproofing, smell-proofing, allergy free, anti-itch, etc. Perhaps the clothes are pre-treated with something that interacts with the small dryer pieces to extend the performance of the clothes, reducing cleaning, wear and tear, or wrinkles. Perhaps the small bits are transparent (thanks, Yoni!) so they are invisible on the clothing. This simple Division takes a seemingly dull product and re-frames how we think of it to discover new innovative uses and benefits.
Division is also a collaboration approach. One of the Duke MBA's, Tom Powell, emailed me about crowdspirit.com, kluster.com, and ideabahn.com. These new sites form communities that take an idea and iteratively improve it with suggestions from members. These sites are also examples of Division (preserving) - taking the larger problem and dividing it among many people. Idea collaboration is an old idea, but what could be a more innovative approach is to divide a problem using the other two methods: physically or functionally...focus members on the problem in a different way. As these beta sites evolve, we will watch to see how innovative they can become at dividing and conquering.