The concept of local and global maxima is extremely profound. It is one of the pillars of the theory of calculus. For me, its application has gone much beyond calculus and there is lot to borrow from it, for life and entrepreneurship.
image courtesy: elezea.com
Build the startup first to achieve local maxima. The range of this maxima can be a region, a vertical, a demographic, a category or any other filter you want to focus on. Once local maxima is achieved, one can start discovering if this local maxima is global or not, or rather how global it is. If not, you can then devise ways to close gaps and try building better functions or fourier transformations(associations, affiliations) to achieve better results. To illustrate, Facebook built its local maxima in colleges, only to realize that their local maxima is infact global maxima. This will only be true till someone builds a better/elegant function than you and achieves a better/easier maxima.
Essentially, I reframed the oft-repeated advice of focus on a niche, or to do one thing better than everyone else, into language of calculus. Just makes more sense and logic, this way. You are effectively working on achieving the local maxima and eventually global maxima, when you are attacking a niche.
Sent on my BlackBerry® Excuse brevity. www.tushky.com