What Is “Forever”?

“Forever” is a very subjective word. The primary concept that all may have been taught is that “forever” occurs when something goes up into infinity. In The Phantom Tollbooth by Norton Juster, the main character had walked up a long flight of stairs, not knowing that the stairs actually extended up to infinity – he was never able to reach the end. The Paradox of Zeno pointed out that an arrow shot at a constant velocity would never reach the target; at each time interval, the arrow would only be able to cover half the distance left, hence there would always be an infinitely small distance between the arrow and the target. (As absurd as it may sound, this paradox had been taken seriously by elites for over 2000 years.)

“Zeno’s Paradox”  Image from Claire Chung via Google Slides. © Claire Chung 2018. All rights reserved. 

Is There A Limit To “Forever”?

The truth is, human history has gone a long way, part of it being an attempt to explain “forever.” From Greek philosophy to modern literature, paradoxes to mathematical papers, “forever” is demonstrated in logical, creative, and interesting methods. However, a significant question to this subject is: Is there a limit to “forever?” Consider the scenario below.

Deposit $1.00 into a bank and receive a 100% interest annually. After 1 year, you’ll end up with $2.00. 

Deposit $1.00 into a bank and receive a 50% interest biannually. After 1 year, you’ll end up with $2.25. 

Deposit $1.00 into a bank and receive an 8.3% interest monthly. After 1 year, you’ll end up with approximately $2.61. 

Deposit $1.00 into a bank and receive a 1.9% interest weekly. After 1 year, you’ll end up with approximately $2.69.

Deposit $1.00 into a bank and receive a 0.27% interest daily. After 1 year, you’ll end up with approximately $2.71. 

Now, what if you receive interest every second? Every millisecond? Every Planck time? Every instant?

Euler’s Number ≈2.718281

The scenario mentioned above is the renowned concept of the Euler’s number (represented by e). Interestingly enough, the Euler’s number is an irrational mathematical constant that is not defined by geometry but related to “growth.” Simply speaking, Euler’s number is the maximum number that one can receive when the interest is given at every instant. Referring to the graph below, the red graph line (equation attached below) features the scenario mentioned above, while the blue graph line, y = e, is an asymptote for the red graph line.

“Continuous Interest”  Image from Claire Chung © Claire Chung 2018. All rights reserved. 

“Euler’s Number”  Image from Claire Chung via Desmos. © Claire Chung 2018. All rights reserved. 

As we continue to divide the year to infinitely many moments, the resulting amount of money would approach the Euler’s number, but would not exceed it. In other words, the Euler’s number is the limit to the amount of money one can end up with for continuous interest. So as for now, you can take this further to say that there is a limit to “forever.”

So, why “e”?

For me, the significance of e suggests that growth can extend on forever despite the limit there can be. The question of this blog post, ‘Is there a limit to “forever”?’, has, as subjective as it may sound, no definite answer. There are too many ways to answer this question, just like how there are also too many properties of e that can be discussed, either discovered or not yet discovered.

People have different perceptions of mathematics. It can be hate or love, like or dislike. It does not matter whether math is an appealing subject to everyone, but one thing is certain. There might be a limit to the universe, but the wonder that mathematics can bring to us will go on forever.

Euler’s number is not only an interesting mathematical constant but also a fundamental tool in calculus. One special property of the Euler’s number is that the area of the curve and its gradient under any given point on y=e^x is equivalent to the y value of that point. The equation e^(iπ)+1=0 is also derived from derivatives in calculus. For more information regarding the Euler’s number, it is highly recommended to watch the video below!

Value of Euler’s Number:

2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531952510190115738341879307021540891499348841675092447614606680822648001684774118537423454424371075390777449920695517027618386062613313845830007520449338265602976067371132007093287091274437470472306969772093101416928368190255151086574637721112523897844250569536967707854499699679468644549059879316368892300987931277361782154249992295763514822082698951936680331825288693984964651058209392398294887933203625094431173012381970684161403970198376793206832823764648042953118023287…………

What does it mean to learn? As defined by the Oxford Dictionary, learning is ‘the acquisition of knowledge or skills through study, experience, or being taught.’ However, the true definition of learning still lies upon people’s talents, learning styles and aspirations; it may vary depending on whether a person is an auditory learner, a visual learner, or a kinesthetic learner, an artist, an athlete, or a scientist.

After several discussions with my partners Winnie and Grace, we took this fact as the theme of our video making process, aiming to encourage every person to find their own purpose of learning. The filming process was the most interesting part of the production as it was heartwarming to see so many classmates willing to attend a 2-second interview for this video. We were also surprised by the fact that each classmate had thought of a word of their own to describe “learning.” On the other hand, the editing process was enjoyable as I have had several experiences with turning raw footage into an inspirational video.

Watching the finished video on youtube, I would say that the production of this blog post was another learning experience for me. From being rejected by some classmates to being unable to upload raw footage to iMovie at first, the three of us confronted, solved, and grew. Perhaps the answer to the title of this post simply lies in what we do every day. Just like what a classmate said in the video, “to learn is to live.”