Eric Tian

When I was in high school, I really liked numbers because they felt grand. Unlike subjects such as politics & law, history or economics, where it is largely humans who have created them, the laws of mathematics seemed to defy human capabilities.

Maths can be grand because of its absolute nature. Pythagoras’ theorem will hold for right-angled triangles no matter how hard any human tries otherwise.

On the other hand, maths can be grand because of its absolutely non-absolute nature. The circumference:diameter ratio of a circle is always π (pi), which is an irrational number spanning an infinite number of digits. In my high school, you got a prize if you could recount the first 75 digits of π. However, try all you want, it is straight up impossible to get to all the digits.

While maths in general is pretty amazing, one of the most beautiful formulas in maths is Euler’s identity, which states:

It looks simple, but the more you think about it, the more mind-boggling it is. Here’s an explanation for some of these terms:

• e = Euler’s number. It is the limit of (1+1/n)ⁿ as n approaches infinity. Like π, it is an irrational number and looks something like 2.71828. It is very important in exponentials and logarithms.
• i = the Imaginary unit. It is defined as the square root of -1.
• π = The circumference:diameter ratio of a circle, approximated to be 3.1415. Also used in angles as radians.

Somehow, when you multiply π and i together and raise it to the e, you get -1. These three seemingly unrelated concepts, ranging from logarithms, imaginary numbers and circles/radians, all come together to the unsuspecting -1. And when you add 1 to -1, you get 0. This is Euler’s identity.

While there are many proofs of Euler’s identity, it always astounds me how wonderfully these concepts come together. I imagine a Mexican grandma, a middle-aged Englishman and a Japanese boy coming together and unsuspectingly becoming a perfect entity. It seems too ridiculous to be true. But it is. And that’s why numbers are really great.

For the first time in eight months, I thought that yesterday was Wednesday instead of Thursday, and that’s led me to me writing this post a day late. And as someone who values consistency, realising this calendar blunder was mildly infuriating.

However, I’m using this experience to remind myself of a video from The School of Life called Of Course You’ve Messed Up. Other than it being narrated by the calming Alain de Botton, this five-minute video contains powerful reassurances and has quite literally saved my life through dark times. One quote in particular has stuck with me:

None of us are beyond encounters with total stupidity.

Of course, this problem of mine is laughably insignificant. Nobody will care if this post is written on 1am Friday rather than 11pm Thursday. But sometimes, it’s just good to be reminded that no matter who, nobody is beyond encounters with total stupidity. And that’s just part of being human.

Disclaimer: In this post, I’m exercising my more arrogant voice to practice different writing styles. This topic is definitely far more nuanced than what I can hope to convey in 440 words. Please enjoy.

There is no question that the modern age provides abundant means of learning. Whether it’s traditional schooling, online courses, books or podcasts, the resources available to find information these days is unprecedented. A simple Google search will tell you the most bizarre facts like the latin name of a hedgehog and online courses have enabled great opportunities to learn science, math, or literature. The benefits this can bring to society is obvious.

But there is a problem. This abundance of information can lead people to believe they are experts in whatever they Googled that day. When you get ill, you can suddenly look up your symptoms on WebMD and treat yourself rather than consult a GP. When you come across a pseudo-scientific topic, you can suddenly find intelligent-sounding defences for dubious ideas rather than consult an expert.  

People who do this are called armchair scientists – those who read one or two articles from a questionable source, jump on Reddit for half an hour and use this to inform their opinion about a topic. And so, while technology is creating a utopia of knowledge, it is simultaneously creating a dystopia of ignorance towards experts. As social psychologist Aleks Krotoski wrote in The Guardian:

There is no doubt that the wealth of health information online has contributed to a more informed public, but this is an area in which I believe the expertise of the professional should not be undermined by the leveling power of the web.

This notion can be extended beyond the realms of science and into the spiritual. The recent rise of armchair theologians has raised questions about how Christianity is being practiced in the digital age. It can be easy for new or exploring Christians to find contrasting opinions online about biblical teachings and give them the same weight, despite significant differences in hermeneutical factors and theological context. With such clever-sounding pieces of biblical interpretation, where is the need for reading the Bible?

What to do?

Perhaps the solution to this armchair dilemma requires action on both the experts and the viewers.

To the experts: Honesty and simplicity when conducting research are essential for increasing the literacy of the general public. Dishonest and convoluted pieces of literature do nothing but harm one’s perceptions on a topic.

And to the viewers: Exercising critical thought is essential in an age of fake news and unequal opinions. It is easy to look at the wealth of information out there and believe that you can become an expert in anything. Understanding that there are many things out there that we don’t know – and may never know – is completely fine.

I recently finished listening to The Wisdom of Life by Arthur Schopenhauer on Audible (free eBook here). Schopenhauer is widely known as the ‘philosopher of pessimism’, as he often presents a worldview that challenges the value of human existence. This book is a collection of his essays, of which one concept stood out to me: that of fame, and how futile it is. Schopenhauer writes:

Would a musician feel flattered by the loud applause of an audience if he knew that they were nearly all deaf, and that, to conceal their infirmity, they set to work to clap vigorously as soon as ever they saw one or two persons applauding? And what would he say if he got to know that those one or two persons had often taken bribes to secure the loudest applause for the poorest player!

What I take this to mean is that fame is overrated. The decision to care about what others think is irrational and if we truly knew how little other people thought of us, we would give them much less power over us. If those who anxiously count the likes on their posts knew how little their audience cared, they would be embarrassed. Did I mention Schopenhauer was pessimistic?

Yet, this isn’t to say one should look the world and yell, “screw it, you don’t care about me so I’m not going to do anything!” It is wonderful that people actively cultivate and share their insights with others, for there is so much to discover in the world. Furthermore, though Schopenhauer might disagree, I’m sure there are some consumers of content who deeply appreciate what’s being shared. Indeed, I have personally had my life turned around by blog posts and books, and have had days brightened up by a simple photo.

But what Schopenhauer begs of people is to avoid the temptation to be get caught up in vanity metrics, since, well, people generally don’t care that much. And while this sounds sad, this notion of discrediting fame is really quite liberating – for the weight of human judgment is great, and to be freed from this is a great achievement.  

Recently during conversation, a friend brought up this concept of the Fermi Paradox. It goes something like this:

Premise	Low estimate
There are a huge amount of sun-like stars in our Milky way.	100 billion
Some of these sun-like stars should be surrounded by Earth-like planets.	20%, or 20 billion
Some of these Earth-like planets should develop life.	0.01%, or 2 million

So, there should be roughly two million life forms in our solar system alone. That’s a lot of life forms, right?

Well… why haven’t we seen any indications of life? With two million life forms around us, shouldn’t we should at least see some indication of life. Where the heck is everybody?

Welcome to the Fermi Paradox.

There are three main hypotheses for The Fermi Paradox, which introduces us to this notion of The Great Filter.

The Great Filter

The Great Filter theory suggests that at some point during life, there’s a wall that life, or attempts at life, have to hit. This wall makes the evolutionary process extremely unlikely or impossible for life to get beyond. That stage is The Great Filter.

If this is true, the question is, where in our timeline does this great filter occur?

Theory 1: We’re rare (The Great Filter is behind us)

One hope we have is that The Great Filter is behind us—we managed to surpass it, which would mean it’s extremely rare for life to make it to our level of intelligence. One theory as to this filter we’ve managed to overcome includes the transition from a prokaryote cell to an eukaryote cell.

Theory 2: We’re the first

This suggests that for the first time in history, conditions in the universe are reaching a place that would allow intelligent life to develop. In that case, we may be well on our way to super-intelligence, and it’s simply happening for the first time ever. Existence, let alone our existence, is unprecedented.

Theory 3: We’re really screwed (The Great Filter is in front of us)

If we’re neither rare nor early, many would conclude that The Great Filter must be in front of us. This would suggest that life regularly evolves to where we are, but that something prevents life from going much further and reaching high intelligence in almost all cases—and we’re unlikely to be an exception.

This can be unsettling to think about, since it means that if we discover life forms other than us, it suggests that there are few Great Filters behind us. Worse, if we were to find complex life in our Milky way, it very much suggests that the Great Filter is most probably in front of us, thereby dooming our species. As Oxford professor Nick Bostrom puts it, “the silence of the night sky is golden.”

Whatever the case, it’s comforting to know that in a way, life is really special. Whether we’re alone or not, it’s clear that for our immediate surroundings, there aren’t any signs of life that we can see. And regardless if this is due to extreme luck, necessity or the presence of a God, this is a wonderful mystery, and one that makes life quite precious.

---

For more on this topic, check out this post by Wait but Why.

There are many schools of thought on how one should raise children. Do we protect them against a broken world? Or do we thrust them into life, letting them fend and grow for themselves? Luckily, Kahlil Gibran in his collection of fables The Prophet offers valuable insights on this dilemma. I encourage all to take a few deep breaths and carefully read the following, because the imagery here is remarkable.

And a woman who held a babe against her bosom said, Speak to us of Children.

And he said:
Your children are not your children.
They are the sons and daughters of Life’s longing for itself.
They come through you but not from you,
And though they are with you yet they belong not to you.

You may give them your love but not your thoughts,
For they have their own thoughts.
You may house their bodies but not their souls,
For their souls dwell in the house of tomorrow, which you cannot visit, not even in your dreams.
You may strive to be like them, but seek not to make them like you.
For life goes not backward nor tarries with yesterday.
You are the bows from which your children as living arrows are sent forth.

The archer sees the mark upon the path of the infinite, and He bends you with His might that His arrows may go swift and far.
Let your bending in the Archer’s hand be for gladness;
For even as He loves the arrow that flies, so He loves also the bow that is stable.

---

Related: On Joy and Sorrow.