People are bold when they talk about their “ultimate” goals. “Cure cancer.” “Organize the world’s information.” “Stop terrorism.” These are big . Huge. Daunting. But the road to achieving them is made up of thousands of smaller steps. goals We tend to focus on where we are now and what we can achieve today. But for the long-term, the pace of progress (the compounding rate) matters much more than the starting point. Here’s how to up your pace and stay motivated in the long run: Optimizing your growth rate requires a system. To see the overall system — from the big picture all the way to the individual minute-to-minute steps — I look to physics. There’s a concept known as a fractal. It’s a way of modeling structures where the overall whole pattern is made up endless similar patterns at increasingly smaller scales. mathematical There’s a particular fractal named after the mathematician who first described it, called the . Imagine a triangle. Within it, you can find three smaller triangles. And within those smaller triangles you can find more of the same structure. And so on. Sierpinski triangle This is a good model for the road ahead. Here’s what it looks like: Your big goal The medium-range goals All the way to important daily to-dos And individual habits This fractal model can represent a wide variety of situations. Think of it as the path from novice to expert, requiring deeper and deeper mental representations. You can apply it to your job — from the activities you do today to your ultimate career path. And it’s a great model for your ultimate company objectives. You may want to cure cancer, but you still have to follow through with thousands of smaller, daily goals. All the tiny triangles need to be filled, one triangle at a time. You just take it step-by-step, day-by-day, right? It sounds so simple. But most people can’t effectively maintain that kind of daily focus over the months and years required to meet a big goal. That’s why this fractal is so helpful. It supercharges motivation by giving you a vivid perspective on the overall process, and the required mindset, in three parts. 1. Become obsessive. Together, many smaller goals culminate into something great. But when you start working toward a new goal, you begin to see how far you have to go. Most people eventually lose their initial excitement. Maybe you thought you wanted to learn a new language, but it turns out the daily grind of conjugating verbs and learning pronunciations isn’t as fun as you hoped it would be. Reaching your ultimate goal requires obsession. The long-term intensity required to meet your goal is hard to maintain, especially over months and years. You need to have a level of dedication to the overall goal that will allow you to push through difficulties and wrong turns. You have to be obsessed enough to work at the little triangles every day without deciding the effort isn’t really worth it. 2. Envision your future self. So, how do you maintain that level of dedication and motivation? By creating a vivid image of your future self. We tend to think of our future self as an entirely different person, and that can warp our view of the work we do now. The little triangles don’t seem so important when we think they’re going to help out someone else. Your current self may feel like skipping practice today. But maintaining a clear vision of your future self continually reminds you what all your effort is for. It lets you see where your long-term goals fit into the larger picture. And that future self can be more than you. It can apply to partners, teams, and companies. Think of of who they want to be. Softbank’s 300-year vision 3. Make constant real-time adjustments. With a view of the present and future, you can see in real-time whether your activities are adding up to your desired ultimate goal — and you can correct the course as needed. As you continue to move toward your short-term and long-term goals, you will inevitably have course corrections. Each action you take will provide you with feedback, guiding you on your path forward and opening new paths for you to take. Experimentation and testing of these various paths will eliminate some triangles and create new ones. And the pathway from small triangles to large ones will act as a compass, pointing you toward your ultimate goal. When considering your job, for example, understand it will change dramatically over time as you take different paths. These are paths you weren’t aware of at the beginning. Personally, I used to spend my days deep in research materials. Now, as CEO, my job has become more people-oriented. I had to shift gears and orchestrate my environment to handle my new course. The strategy that was perfect for you last year may not work for you this year. But the Sierpinski triangle enables you to think about and organize your goals, keeping you headed in the right direction. That’s why the Sierpinski triangle is the best graphic representation of a system for achieving your ultimate goals that I know of.