# Solving Zeno's Paradox for Innovation

Zeno of Elea was a Greek philosopher in 5th century BC who is famous for creating a set of puzzles, the most famous of which, is arguably the Dichotomy Paradox. Here’s how it works. Say you’re trying to cross a 20 foot room to get to the front door. You must first go halfway across the room. So now you are 10 feet away from the front door. Again, you must now travel halfway to the door, another 5 feet. Now you are 5 feet from the door. You travel halfway and end up 2.5 feet from the door. This continues to infinity, and by this logic, you NEVER reach the front door.

Yes, we have all managed to leave our houses, so the paradox is more mathematical in nature than practical. But aside from its philosophical nature, Zeno’s paradox is also a useful analogy to for innovative product development. Imagine your R&D group is looking at two new battery technologies in its labs. One is 90% likely to work and has 1.6x the power density of current Li-ion batteries. The other is only 10% likely to work, but it provides 3.2x the power density. So which to choose? It seems like the first is a much better bet since it is 9x more likely while the latter is only 2x better. But let’s look at this through the lens of Zeno’s paradox.

The company’s leadership decides that 1.6x the performance of a standard battery would be sufficiently advantageous, so it chooses the safer option. You finish the first prototype in one year, but it is unoptimized and only yields half the performance theoretical performance, or about 80% of the performance relative to the original benchmark. It’s not commercially viable, but no worries. There are easy ways to improve on the battery. In another year, you get to the next milestone. You’ve now achieved 1.2x the performance. Time to celebrate. But wait, the current technology was improving by 7% a year. So it’s now at 1.14x its original performance. That’s not enough of a difference to convince customers to switch to a new technology.

Another year and you hit 1.4x. But now Li-ion is at 1.3x its original performance. Your product is better, but the incumbents keep you from entering the market with bulk discounts and competitive pricing schemes. Even worse, now your technology is mature, and you’ll only eke out improvements at a rate similar to the incumbent technology. Like Zeno, you never get to the goal. You never bring the innovative technology successfully into the market. Though the technology had a high chance of success, even with success, it was doomed to fail in the market. The more risky technology may fail, but at least if it succeeds, it can have real impact.

Zeno’s paradox is a useful analogy to illustrate the challenges of bringing innovation into the market. The only way to impact the market, is to aim for 10x rather than 10%. Yes, this often requires taking on much more risk, but the alternative is guaranteed mediocrity. The only way to reach a goal is to try to overshoot it.

If you run into Zeno, tell him you’ve solved his paradox. You shouldn’t try to reach the front door. You never will. Instead, plan to get to the next town. Then you’re guaranteed to get out of the house.