Imagine you are in a small house in the Beacon Hill neighborhood in Boston. Starring out the window, you see rows of red-brick houses, flickering gas lanterns allowing the shadows to dance, and a third day of, what feels like endless snow. Disregarding all responsibilities, you find yourself dreaming of an epic road trip. Within this state of casualness, you are curious to see what Google Maps would recommend as directions to the sunshine and crisp air of North Beach in San Clemente, California. With intimidating results, Google Maps rounds the duration to just 45 hours and provides a distance with one significant digit of 3092.4 miles. Come on Google! The 0.4 is a little passive-aggressive.
Frustrated, the algorithm gives an optimum route, considering tolls, traffic, and construction. However, you want alterations because the route's options are practically infinite. You could decide that the trek is via a can of ocean-blue spray paint and the Cadillac Ranch, east of Amarillo, Texas, to see ten classic Cadillac cars half buried in the ground. Or you may consider going via Verona, Kentucky, to validate the HOP Shop's acclaimed “The Coolest Bathroom.” Just making any right turn when Google Maps says to go straight provides infinite options to achieve the trip.
Hilbert's Paradox of an Infinite Hotel
Created by a German mathematician named David Hilbert, “Hilbert’s Paradox of an Infinite Hotel” explores the basis of infinity. Imagine a grand hotel having an infinite amount of rooms, and they are all occupied. The numbers on each room’s doors are in a series, going from room number one, then to two, then to three, and infinity. Being told that the rooms are all occupied, one could assume there is no more room.
Mathematicians and scientists have always been intrigued by the mysteries behind ‘infinity’. The Hilbert’s paradox of an infinite hotel is one such thought experiment that arouses curiosity and intrigues people to this day. Shreya Chakraborty - ScienceABC.com
However, due to infinity being unbounded, there always can be room to occupy another guest. If we moved the guest from room one to room two, only after room two’s guest moved into room three, after they vacated to move to room four, you would realize that the manager could free up room one. With room one now being unoccupied, the manager of the Infinite Hotel just got you a place to stay by shuffling the rooms the guests occupied.
Infinity is vague, but ideas are not rare
Infinity is vague. It is hard to grasp when we have life things like bills, due dates, and responsibilities that keep us in motion from one day to the next. But at any given moment, the options are infinite. It requires a keen ability to zoom in and zoom out, thinking both macro and micro on a problem. It takes looking at a problem as if there are infinite solutions.
Ideas are not rare. Ideas are infinite. If you find yourself stuck on a problem, do not hesitate to throw out the options. Pitch to your team, family, or manager the ideas that come to mind. Of course, some will be farcical, laughable, or unattainable. However, some may be so radical, innovative, or simple, that they unlock the door that is currently limiting you from obtaining your goal. Ideas are unbounded. No matter how stuck you may feel, there is always another option. You may just ask the hotel manager to make one for you.