Big Value: The very strange life of i

It’s not uncommon to wonder about the vastness and the complexities of the universe and feel insignificant. It is frighteningly overwhelming to scientists, but they have an apt tool or figuring it out: Mathematics. Nobel laureate Eugene Wigner proposed that mathematics is an entity that humans discovered and coined the phrase, ‘unreasonable effectiveness of mathematics’. This was his reply to the long-standing debate on whether Math was discovered or was it invented. His point was that Math, even though it may appear useless at the time, will be invaluable in the future — making a strong case that Math has always existed as a part of the Universe.

An example for which is the work of Gottfried Hardy, who once said that his work on the Number Theory will never amount to anything. But Number Theory is now widely used in modern cryptography. This argument by Wigner gives merit to that school yard phrase, ‘Math was invented by God, all else is man-made’. However, while understanding and looking into a specific area of mathematics itself is amazing, for the purposes of this article, let’s indulge in something much more common-place.

Let’s talk about i or imaginary numbers. As students, we had chanced upon this value early and it always began the same way. Our teacher would tell us that i was the square root of minus 1. The teacher would then pause and then continue to solve some math problems with i. But let’s wait just for a minute here and look at this letter and what it signifies once again. i is an imaginary number, and in its own definition, cannot exist. Let’s imagine a ball in your hand. You can let the ball go and it comes down due to gravity. That’s real — it’s logical and it makes sense.

But what if in that same scenario the ball didn’t come down. Instead, when you let it go, it just disappears.. like magic. That’s how ludicrous the concept of i is. It’s fantastical in it’s mere existence in mathematics While it’s almost impossible to logically reason its existence, i has a multitude of uses in science. In Electrical Engineering, we use it extensively to calculate impedances, and in Signal Processing it’s used to indicate phase changes. From Control Systems to Fluid Dynamics, we use complex numbers to explain the real world.

Your computer or mobile phone that works in the real world uses mathematics with entities that do not exist. So when we think about the Universe and its grandeur and accept that math is perhaps the key to figuring it all out, then we must also accept that sometimes things that seem illogical, incomprehensible and imaginary are necessary to understand what is real.

The author can be reached at bhairav.shankar@gmail.com