My Approach

Each tidbit of information could unexpectedly help later, or lead to a novel solution or new opportunity. These tidbits are easy to acquire in abundance and in short order with a little inquiry and cooperation. They are the seeds of innovation. As for synergy, it is a simple fact that you cannot line up two birds if you only know about one of them.

It's easier for communication, and knowing the how and the why allows for better decision making and ultimately better results. It is far too easy to leap without looking right into a solution, the results of which are often less than ideal or fail to take into account the unwritten or unstated realities of the situation. Knowing how the technology is to be used and how its purpose may change will let me choose a design which can be built upon. Every algorithm behaves differently, and knowing the application, the nature of the available information, and even the social dynamics of its use can all help when it comes to designing the technology and choosing the best options.

It seems the obvious approach, and many do start this way. Yet, I have found it essential for innovation to delay both learning about how others have tackled the problem and drawing too much from past experience. There is a real danger to become locked into a certain way of thinking about things, especially when you are learning the details about the situation for the first time. Temporary avoidance keeps the approach fresh, the perspective wide, and innovative breakthroughs more likely.

It may seem bizarre to talk about creativity in mathematics, which is often simply associated with logic. In practice, intuition, inspiration, and lateral thinking, all creative in nature, are critical factors when looking for the best solutions to hard problems. Famous examples include Archimedes' "Eureka!" moment, Einstein's breakthrough in relativity, and Hamilton's carving of quaternions (a 4D mathematical object) into a bridge in Dublin. Though the breakthroughs may be minor in daily practice, their impact on finding solutions is well worth the investment.

Some time in isolation is critical, as is rest, and I find walking especially beneficial. These activities may appear idle, but the mind is at its most active. Isolation permits deeper thought. In the early stages living in your own head is necessary if you want to bring something unique to the table. Sufficient sleep is required for a more active mind when awake. For those with the knack, closed eyes at rest allows for complex visualizations of both geometries and concepts. Walking gets the blood flowing and provides a change of environment which can stimulate new ideas.

Sometimes, yes. However, I've almost always found it worthwhile, especially since I take but little time to develop each concept. First, it tells me where to look for more advanced wheels. Second, since I've conceived of the idea in the context of the problem, I have a better idea of its possible other uses, especially related to the matter at hand, and will have an inclining as to which variety might work best. For instance, I would perhaps see the possibility of a water wheel, which could be harder to conceive of if you had only seen wheels on bicycles or if you knew that wheels were useful but didn't know which to use or how. Third, it allows me access to more innovative thinking, as I can more easily think of variations on what the wheel could have been, and how wheel development may have progressed otherwise.

It depends on how much time you have and the overall value a better choice could have in solving real, everyday problems. You need to weigh being able to start implementing the easy solutions sooner with having more options and therefore being more likely to find a better or faster way of doing things. You can (and should) always come back to this and other stages once you start implementation. That said, three or four good choices, not counting the worst options, is a good place to stop and avoid decision overload. However, I personally find it very easy to come up with many such choices. If you have any trouble finding ideas, do not force things, two is enough.

The whole process, from investigation to plan (Stage I to V) usually takes from two days to two weeks, depending on the complexity of the project or the amount of detail in the roadmap. Informally, it can be done in a single afternoon. It is always possible to come back to any stage and include more detail, so an agile approach and iterative implementation work well.