Posted in Science & Nature


Rainbows have been associated with wonder and the heavens throughout the history of humanity. The Norse believed that the rainbow bridge, Bifröst, connects the realms of men and gods. The rainbow is mentioned in the Bible as a sign from God to signify to Noah that the flood had ended. Irish leprechauns are said to hide their pots of gold at the end of a rainbow. It is now adopted as a symbol for LGBT movements, symbolising diversity.

The massive scale and brilliant colours of a rainbow is awe-inspiring (famously captured in the Double Rainbow video). We now know that it is the result of sunlight interacting with water droplets: reflecting, refracting and dispersing.

Sunlight refracts (bends) as it enters the droplet. It then reflects off the inside wall of the droplet and refracts once more as it exits. Because each wavelength refracts slightly differently, light disperses and each colour can be seen separately, much like a prism breaking apart white light into colours.

Because of water’s refractive index being constant, the returning light is most intense at 42°, making the rainbow always form in a circle with an angular radius (angle of light compared to your eyes where a circle is seen as a specific diameter) of 42° surrounding the point opposite the sun. If you are standing exactly at this spot with the sun behind you, you will see a beautiful rainbow. Otherwise, the rainbow disappears.

Angular radius can sound like a complicated concept, but in this case, it results in something quite interesting. To capture a full rainbow with a camera, your camera lens must have a field of view (cone of light that the camera will photograph) of 84°. Most smartphone cameras have smaller fields of view than this (iPhone X has a 65° horizontal field of view for instance), meaning that it would be impossible to capture all of the rainbow in one photo.

Another impossible thing when it comes to rainbows is finding the mythical pot of gold at the end of a rainbow. Because rainbows are the result of optics, they are different to every observer and how they are positioned to the sun and water droplets. This means that no two people observe a rainbow in the same way and a rainbow is not static.

You can also never approach the rainbow as it will disappear given the angular radius mentioned above.

Furthermore, there is no end to a rainbow because it is actually a full circle that extends through the horizon. We cannot see it as there is ground between us and the rainbow, but you can sometimes see a ring rainbow from a plane.

However, because the rainbow is technically just light from the sun bouncing off water and into your eyes, we can imagine it not as a circle, but a double-ended cone that ends in your eyes. By this logic, your retinas that sense the rainbow (and by extension, you) are the pot of gold at the end of the rainbow.

The End of the Rainbow
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Posted in Life & Happiness

The Right Moment

One trait that has allowed our species to survive for so long is our ability to plan ahead. Whether it be hunting an animal, preparing for a winter, interviewing for a job or making a move on a romantic interest, we think of all the ways the situation might play out. Our brain has an extraordinary capability to imagine and simulate possible outcomes. Based on this, we can optimise a plan of action.

Let’s look at an example. When we plan a trip, we choose a location and research sights to see, foods to eat, places to stay in, what the weather will be like… Then, we come up with an itinerary by thinking of how to group everything into different days, what transport to take and setting aside enough time for rest and to buffer against unexpected changes. Planning allows us to travel efficiently so that we can pack as much fun and experiences, while preparing us for when things go wrong.

But of course, life is full of surprises and it never play out perfectly. Our instinctive ability to simulate and plan for the future is probably evolution’s way of tackling this. We are trained to think of all the different ways our plans can fail, to maximise our chance of survival.
Therefore, as powerful as this ability may be, it comes at a great cost. It makes us obsess about “the right moment”.

When we face a crossroads in life, we have to make choices and take action. Should you take this opportunity to move to a different city? Should you ask out that girl or guy on a date? Should you make that leap of faith and change careers? Because these important decisions carry greater consequences, our brain goes into overdrive thinking of how things may fail and ruin our lives. We worry that we are not ready for the change or that a better opportunity may arise. So many times in life, we see opportunities slip by while we are hesitant, leaving us with regrets.

No matter how much you plan and prepare, the universe can easily find a way to surprise you (see Murphy’s Law). There is no such thing as the perfect moment, or a perfect person, or a perfect life. So waiting for the right moment is as futile as waiting for a train that is never coming. A ship waiting in a harbour for perfect conditions before setting sail is safe, but that is not what ships are built for.

What we can do is to just live life. It is certainly good to have a rough sketch of a plan, to know what general direction you are heading in. But when it comes to the finer details, it is best to just make a decision and act on it, whether it be based on rational thinking or gut feeling.

If things work out, that’s great. If it doesn’t, you still gave life a chance instead of letting it pass by you. You can learn from the experience and try different decisions the next time.

Instead of waiting for the right moment for everything to be perfect to take action, we should be taking actions and making the moments right.

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Posted in Life & Happiness

Preempting The Preemption

A key tool that evolution gave human beings to survive is the ability to plan for the future. We are able to analyse the information available to us to simulate and predict the future. This allows us to make better choices as we can delay gratification, find optimal solutions and work towards a common goal with others.

However, our ability to predict the future is far from perfect. We are still slaves to our base desires and numerous cognitive biases. We are often either too cynical, thinking of every reason something may fail, or too optimistic, thinking of the best-case scenario. Sometimes our emotions cloud our judgement, while sometimes we rely too much on cold logic, ignoring what our hearts really want.

Another problem is that sometimes we overanalyse things. We may become insecure that a certain problem will cause more issues and heartbreak down the line. We let our fears and anxieties create a chain reaction leading to the worst possible scenario. Instead of trying to work through the problem, we decide to not even try. 

We start to preempt the preemption.

But the thing about the future is that it is inherently unpredictable. There are too many variables and random probabilities involved that no matter how hard we try, we cannot perfectly predict what will happen. What is certain is that if you do not make an effort and pursue something, it will certainly not happen.

Consider the last time you made a major decision, such as deciding to change jobs, or to date someone, or to move to a different city. Did things work out exactly as you planned? Now think back to the times when you gave up on something before even starting because you didn’t think it would work out. Do you think things might have gone differently had you not given up?

It is perfectly reasonable to make a conscious choice not to act or pursue something. But every now and then, even if you feel that things won’t end perfectly, take the leap and make a daring choice. Whether the outcome is good or bad, you gave the future a chance to prove itself. 

Life is like a lottery, and you can’t win anything without buying a ticket.

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Posted in History & Literature

The Hill You Die On

The Battle of Hamburger Hill is a famous battle of the Vietnam War, where the US military engaged in an attack to try take Hill 937, also dubbed Hamburger Hill. It was a highly controversial battle as the hill held little strategic value and was heavily fortified, yet the army was ordered to launch a frontal assault to try to capture it. After ten days of heavy fighting and the death of hundreds of soldiers, the US forces eventually decided to give up on the hill. The military was heavily criticised for the futile operation and news of the battle contributed to the war losing favour from the American citizens.

This battle may be the origin of the phrase: “is this the hill you want to fight and die on?”. The question is often used somewhat jokingly, but it is a surprisingly powerful and useful frame of mind when it comes to life.

We often find ourselves in disagreement with others, whether it be over ideas, plans or opinions. We may disagree with a plan of action from our superiors, or we may have a difference in opinion with our partner over some matter. Our natural instinct is to argue back to try to win the argument, because everyone hates being wrong. The problem is that the other person will be fighting back just as hard, so the argument can end bitterly with negative consequences in the relationship.

So when you find yourself in an argument, ask yourself: “is this the hill I want to fight and die on?”. There are certainly things worth fighting for, such as your values or if you think the consequences of what you are fighting over is significant enough. However, there are so many arguments where the prize is merely your ego and pride. Is it really worth damaging your relationship with the other person just so you can be right?

If you think this isn’t the hill you want to die on, it might not be worth wasting your emotional energy on the matter. Instead, you may want to compromise and make a conscious choice to let the other person win. Letting the small things go in life and choosing your battles will make a great difference to your happiness and connection to other people.

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Posted in Life & Happiness


Which do you enjoy more: Saturday or Sunday?

Most people working a standard Monday to Friday, 9-to-5 job will say that they prefer Saturdays. A common reason is that Saturdays begin after a fun or relaxing Friday night and a bit of a sleep in. Then, you can do whatever you want for the whole day, even if it means staying up late as you have another day to rest.

On the other hand, Sundays start with a relaxing morning, but followed by the stressful thought of having to return to work on the dreaded Monday.

Simply put, Saturday feels better than Sunday because we don’t have a Monday hanging over our heads. But why should this be the case?
Technically speaking, both Saturday and Sunday are days of rest. Sure, the night ends earlier on Sunday as we need to wake up early for work, but the rest of the day should be equally free and relaxing as a Saturday.

What keeps us from enjoying Sunday is our dread and anxiety for the next day. Because we stress about tomorrow, we fail to enjoy today.

When we focus on the present rather than the future, we can truly enjoy the precious hours of rest amongst the business of our lives. Don’t count the hours till you return to work. Instead, just enjoy the fact that you are not working right now.

If you change your perspective, every day can be a weekend.

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Posted in Philosophy

Trolley Problem

Imagine the following situation. There are five people working on a railroad. Unfortunately, a train is travelling down the track at the same time. Neither the conductor nor the workers are aware that a crash is coming. You are the only person that knows. Next to you is a switch that will change the tracks so that the train diverts and misses the five people, but the second track also has one worker working on it. Here is the dilemma: do you pull the switch to save the five workers at the cost of the one worker?

This is the famous trolley problem, a thoroughly discussed ethical dilemma that explores the ethics of utilitarianism. Is it morally right to sacrifice the life of one person to save the lives of five people? Mathematically this makes sense, as you are essentially saving four people through your action.

But now consider a similar yet different situation. Instead of a switch, this time you are standing next to a very large man on a bridge overhanging the tracks. The only way to save the five people on the track is to push the large man on to the tracks, slowing the train down and giving the five workers enough time to escape harm.

Mathematically, the end result is the same: one person is sacrificed so that five people live. But when presented the two scenarios, the majority of people will say they would not push the large man, even though they were willing to pull the switch in the first situation.

This is a complex ethical problem as the rational, logical choice may not necessarily be the “morally right” choice. It directly conflicts with our natural and cultural belief that we should not kill members of our own species. The slippery slope argument also applies here, as if you can argue that killing one man to save five people is correct, then what’s to stop us from sacrificing one person to harvest their organs to save the lives of many people awaiting organ transplants?

Although the original problem was developed to explore the morality of utilitarianism, we are now living in a time where the trolley problem has become an actual logistical issue. The issue lies with self-driving cars. Self-driving cars should theoretically dramatically reduce road traffic accidents as it removes human error such as drink driving and inattention as the cause of crashes. However, if a situation was to arise where the car senses that it is about to collide into a pedestrian (or five), what does it do? Does it swerve to avoid the pedestrian and put the passengers’ lives at risk? How does a computer decide what the morally right choice is?

A computer is designed to make calculated, rational decisions. Mathematically, it may deem that swerving and crashing into a tree – endangering the life of its sole passenger – is the logical choice to prevent hitting five people on the road. But then who would buy a car that willingly sacrifices its passengers’ lives for the greater good?

Technology is advancing at a staggering rate and we are facing ethical dilemmas that we have never had to consider before. It is our job to discuss and explore these issues ahead of time so that we can prevent irresponsible use of technology in the future.

Posted in Psychology & Medicine

White Elephant

In many Southeast Asian countries such as Thailand and Burma, owning a white elephant has been traditionally considered a show of great opulence. To this day, white elephant are a symbol of peace and prosperity and are kept by royalties of some countries. On occasion, a monarch would bestow a white elephant upon a citizen to reward them for their service to the country. But this was regarded as a blessing and a curse, as elephants are notoriously difficult and costly to maintain.

Today, the term white elephant refers to items that are gifted that serve little practical use and take up space, such as tasteless decorations. In some cultures, “white elephant swaps” are held around Christmas where people will trade gifts, under the philosophy that “one man’s trash is another man’s treasure”.

A related psychological phenomenon is the sunk cost fallacy. This is when a person sees that an action or investment they made has an increasingly bleak outlook, but instead of bailing, they make the irrational choice to continue. For example, you may pay $3000 for a car, which then breaks down. The mechanic bills you $1500 for repairs, which you choose to pay. The car breaks down again and this time it costs $2000 to repair. You think that since you have already invested $4500 in this car, it is worth paying $2000 to repair it. However, you have now spent $6500 on a car that may cost you even more in the future. The more you invest in it, the more you justify keeping it as you feel you are committed to the investment, resulting in a greater loss.

The sunk cost fallacy affects many aspects of our lives. A common example is relationships. Many people will settle down with someone they do not think is the “right one”. But despite many warning signs you are not very compatible with your partner, people think “well, I invested all this time with this person, I might as well see it through”. Eventually, the two end up in a bitter marriage, regretting that they did not break up earlier to find someone that they could be happy with.

The reason we fall into the sunk cost fallacy is that we do not want to “waste” the investment we have put in already. But economically speaking, you will profit far more by walking away from a bad decision as early as possible. It is a “sunk cost” which you will never get back.

Now think about your life. Are you really happy in your job or relationship? Or are you lying to yourself that it will be alright because you don’t want to face the cruel reality that you chose poorly? Knowing about the sunk cost fallacy will help you save time and money, whether it be putting down a bad book before you finish it, or learning when to walk away from the wrong commitment.

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Posted in Science & Nature

Turing Test

Alan Turing was a brilliant British mathematician who was pivotal in cracking the German Enigma cipher using a complex computing machine. He was highly influential in the founding of computing science. One of his greatest areas of interest was artificial intelligence. Like other computer scientists of the time, Turing predicted that machine intelligence was possible in the future with rapid development of computers. On this topic, he proposed the following question: at what point is a machine truly “intelligent”?

Intelligence is too complicated to define neatly in a single line. Therefore, here is a simpler question: can a machine do what we can do? For this, he proposed a thought experiment based on a party game known as the imitation game. In the imitation game, a man and a woman go into separate rooms. Guests then try to tell who is a man and who is a woman by writing a series of questions, slipping it under the door, then receiving a typewritten answer. If the guests cannot tell the two apart, the two win the game.

Turing modified this game into what is now known as the Turing test. He proposed replacing one person with a machine. A person and a computer are placed in separate rooms and are asked the same question by a judge. They then give a typed response. If the judge cannot confidently tell who is human and who is not, then the machine passes the Turing test.

Of course, the Turing test was not designed as a formal assessment and is merely a thought experiment. It has plenty of weaknesses, such as the fact that it only tests whether the machine is acting “like a human” rather than “intelligently”. For example, some computers have passed the Turing test by intentionally making typos to mimic human behaviour. Some have argued that machines that pass the Turing test do not truly exhibit intelligence, as it is impossible to tell if they fully understand the language or whether they are just running algorithms on symbols that the machine does not understand.

Regardless, the Turing test opens the door on the exciting yet frightening world of artificial intelligence and what the future holds for humanity.

Turing Test

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Posted in Psychology & Medicine

The Centipede’s Dilemma

In 1889, British zoologist E. Ray Lankester published an article on the work of the motion of animals in the prestigious journal, Nature. He concluded his article with a poem (which he admitted in not knowing the author of, but commonly attributed to Katherine Craster). The poem goes as follows:

A centipede was happy – quite!
Until a toad in fun
Said, “Pray, which leg moves after which?”
This raised her doubts to such a pitch,
She fell exhausted in the ditch
Not knowing how to run.

The allegory of the centipede illustrates a strange yet hilarious psychological phenomenon, which has been called the centipede effect to honour the poem. Most of the time, we do not put much thought into day-to-day activities such as breathing and walking. We do not have to give much thought because they have become habitsa handy mechanism nature devised to let us do more while using our brain to think about more important things. Habit automatises tasks to reduce attention, but it comes at the cost of the centipede effect, where conscious thought and attention impairs the ability to do that task, much like the centipede tripping on her own leg.

For example, even a professional golf player or violinist will make mistakes the more they thinking about their individual swings or notes they play. A simple experiment you can do is thinking about your breathing. Just by reading that sentence, you consciously divert your attention to your breathing and you will find it difficult to breathe “normally”. Similarly, you can cause considerable distress and time-wasting if you point out a tiny error in someone’s habits, making them overanalyse what they are doing wrong and hyper-reflecting.

What we can learn from The Centipede’s Dilemma is that overthinking never helps. The more we think about something, the more we look at the trees rather than the forest and we get lost in the details. This means we cannot see the overall big picture, which may turn out to be very simple. So the next time you are stuck on a problem in life, stop and take a breath. Clear your mind and let your gut feeling do its thing. Your mind can build so many roadblocks by overthinking – clouding your judgement and crippling your ability to do things. But just remember, all you have to do is drive through those roadblocks and let your heart do what it wants.

Thinking Ahead

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