Are We Scared to Be Lonely?

Pagi ini, saat membuka laman Youtube, saya menemukan lagu ini di kolom Recommended:

Kesan pertama dari lagu ini: beat-nya mantap, terus suara penyanyinya lumayan lah. Saya suka lagu ini. Jadi, alih-alih skip ke lagu lain, saya repeat play.

Kesan kedua, ketiga, dan seterusnya: liriknya deep banget. Kalau kita coba dengerin lagu ini beberapa kali, pasti dapet maksud dari lagu ini.

 Menurut saya, pas sekali lagu ini rilis menjelang hari Valentine, hari yang katanya orang-orang hari para pasangan bersuka cita dan yang jomblo berduka cita. Intinya, di Scared to Be Lonely, liriknya kurang lebih bercerita tentang satu pasangan yang susah melepaskan satu sama lain karena bisa saja mereka takut menjomblo. Meskipun hubungan mereka penuh pertengkaran dan ketidakcocokan, mereka tetap lanjut. 

All the fucked up fights

And slamming doors

Magnifying all our flaws

And I wonder why

Wonder what for

It's like we keep coming back for more

Dan bagian refrain menurut saya sangat mengena:

Is the only reason you're holding me tonight

'Cause we're scared to be lonely?

Do we need somebody

Just to feel like we're alright?

Dari sini, saya mulai berpikir bagian ini bener banget. Kadang kita ngerasa jadi jomblo itu kesepian, suram, ngenes, nggak ada enak-enaknya. Sementara itu, yang pacaran lebih enak. Kadang juga kita susah buat ngomong putus, soalnya dunia jomblo di luar sana kelihatannya dingin, gelap, sendirian. Kita bisa jadi bukan takut kehilangan hubungan, tapi kita takut kehilangan kebahagiaan. Pertanyaannya, apakah kita memang perlu orang lain untuk bahagia? Apakah kita nggak bisa bahagia dari diri kita sendiri?

Ada banyak filosofi tentang kebahagiaan yang bisa dibaca sendiri di sini, dan saya nggak akan mengulas lebih jauh. Dari filosofi-filosofi tadi, sudah kelihatan kalau kebahagiaan bisa bersumber dari macam-macam hal, nggak cuma dari pasangan hidup. Contohnya, saya sudah 18 tahun menjomblo di hari Valentine, dan mungkin akan jadi 19 tahun di tahun ini. Tapi, apakah saya terlihat se-desperate itu karena jomblo yang nggak berkesudahan?

Nggak. Saya bahagia sekarang. Karena saya sadar kalau dengan atau tanpa pasangan, saya bisa bahagia dan nggak merasa kesepian. Saya punya hobi, teman-teman, dan keluarga yang luar biasa di sini. Dan itu masih sebagian kecil yang saya sebutkan.

Sekarang saya balik pertanyaannya, gimana dengan kamu? Kesepian nggak kalau tanpa pasangan hidup? Udah bahagia belum sekarang? Pesan saya cuma satu sih: kamu bisa bahagia, sendirian ataupun berdua ataupun beramai-ramai. Jadi, jangan lupa bahagia.

Natural Numbers (e) for Dummies

In this piece of writing, I assume you already have sufficient knowledge of what natural number is. I am also sure many of you are familiar with the constant e in middle, or even high school. The value of e itself was discovered by Leonhard Euler and is defined by an approximation as follows:

e = 2.718281828.....

I have no idea why it is named e, instead of any other letters, but I do know that e is not derived from the initials of Euler's name. This constant is very well known in the world of mathematics and plays an important role in calculus and other fields of mathematics.

Where does e come from, again?

In 1683, someone named Jacob Bernoulli studied compound interest in banks. The initial problem was this: I had $1, then deposited it in a bank that (somehow, seems a bit unrealistic) paid 100% interest once annually. With that, by the end of the year, the account should have $2.

Then, what if the interest was 50%, but was given every 6 months or twice a year? Would the amount of money in the end be different?

With a simple calculation, on the first interest payment, the amount of money becomes:

$1 x 50% + $1 = $1.5

In the second payment, the amount of money is:

$1.5 x 50% + $1.5 = $2.25

or

$1 x 1.5 x 1.5 = $2.25

Now, if the bank were to pay interest four times a year, 25% each for every 3 months, the result would be:

$1 x 1.25 x 1.25 x 1.25 x 1.25 = $2.4414...

If the interest was paid daily, then:

The calculations above converges to a specific value as we increase the amount of payment per year indefinitely, or mathematically speaking, as x goes towards infinity:

This is how e was found.

Unique Properties of e

In everyday life, the natural number e is often synonymous with the exponential growth rate. For example, population growth, radioactive decay, and economic income growth. The question is, why e?

In mathematics, the exponential function with the number e has the following graph:

Consider the green graph. It can be observed that as x or the independent variable gets bigger, the value of y will increase faster. This is quite in line with population growth, where the population continues to increase rapidly, instead of in a linear trend. So, the exponential graph can be the right approach to find the rate of population growth.

This still does not solve the bigger question, if we wanted to use a constant number as a base, why has it to be e, instead of some other arbitrary numbers like 2 or 3?

We will see how the constant e greatly simplifies calculus. The derivative of the e to the x is the function itself:

And the integral of the function is the function itself, plus the constant C.

Another thing that makes an exponential function with the number e is that the value of the gradient and the value of y at a point, as well as the area from a point to negative infinity, are always the same for all real x values! Please prove it yourself.

When we use other numbers, other constants will appear which complicate further calculations. For example:

This has shown that e is a special number, just like 0, 1, phi (3.1415...), and i (an imaginary number defined as the root of minus 1). When we see math as something that means a lot beyond just numbers, math becomes a lot more fun. As a bonus, there's one simple formula from Euler (Eulerian identity) that combines the constants elegantly in my opinion: