# How a Simple Question Can Change the World

Contrary to popular belief, you don’t need a “Eureka!” moment to have a groundbreaking idea. Often, a great insight derives from the humble beginnings of a simple question.

# “How long is the coast of Britain?”

In the 1960’s, mathematician Benoit Mandelbrot published a paper titled, “How long is the coast of Britain?”. After much deliberation, his answer was “it depends”.

Mandelbrot’s incredibly simple question revealed a complex paradox: the length of anything you measure depends on the ruler you’re using. If you measure the jagged coastline of Britain using a yardstick and then a 12-inch ruler, you will arrive at two different answers. The smaller your measuring tool, the more you can account for the coastline’s nooks and crannies.

Another nuance: if a straight line is 1-dimensional, and a square is 2-dimensional, what dimension is the coastline of England? Mandelbrot explored the idea of “fractional dimensions” and it turns out England’s coastline has a dimension of 1.2. These fractional dimensions elegantly capture the complexity of any object by accounting for how jagged and self-similar it may be. My favorite YouTube channel 3Blue1Brown has a fantastic video on this topic: “Fractals are typically not self-similar”.

Mandelbrot eventually combined his ideas around “fractals” (a term he coined) with early computers in the 1970’s to construct images like this of his Mandelbrot Set.

Mandelbrot’s simple question unlocked not only a new branch of mathematics but also critical real-world applications — among them is one in your own pocket. Most cellphones today utilize “fractal antennas,” which use a self-similar pattern that repeats on multiple scales to enable the antenna to operate at many different frequencies simultaneously.

# Einstein’s Simple Question

Albert Einstein, too, asked a question others might consider silly that ended up changing history. At 16, he asked himself, “What would it be like to chase a beam of light?”. A thought experiment ensued wherein Einstein pictured himself catching up to a light beam, and he found that this visualization conflicted with Maxwell’s foundational equations of electromagnetism. The “silly” question a young Albert Einstein asked himself about a light beam paved the way for his initial ideas that would eventually become the General Theory of Relativity.

These are only two examples of how asking a simple question can lead to insights and applications that change the world. Your next brilliant idea might arise from asking and exploring the questions that others wouldn’t dare.

Are you a founder of a seed-stage startup in the smart hardware or machine learning sectors? Let’s talk about the questions you’re exploring! Leave a comment or get in touch with Ubiquity Ventures.

*Ubiquity Ventures* — *led by Sunil Nagaraj* — *is a seed-stage venture capital firm focusing on early-stage investments in software beyond the screen, primarily smart hardware and machine intelligence applications. Read more from Ubiquity at the Ubiquity blog at **https://medium.com/@ubiquityvc*