Posted in Science & Nature

The Titanic Door Debacle

One of the most famous arguments in popular culture history is why at the end of the movie Titanic, Jack had to die when it clearly looked like there was enough space for both him and Rose to lie on the floating door.

Since the movie’s release in 1997, countless fans have lamented how the birds-eye view shows that both people could have laid side by side to fit on the door.

But alas, science is an unforgiving mistress and it has since been shown that it would have been physically impossible for the two lovers to survive together on that makeshift raft (which was a wooden panel, not a door).

The film actually shows Jack trying to get on to the panel, when it tilts and starts to submerge, nearly flicking Rose off. Jack realises that the panel would not support both of them and chooses to only keep his upper body on it, while fending off other survivors trying to latch on. Unfortunately, this is not enough to keep him alive as he quickly succumbs to hypothermia and sinks to the bottom of the ocean.

The important question is not whether the two would fit on the panel, but whether the panel is buoyant enough to support both of them.

Buoyancy is the force that makes things float in liquids. It depends on the volume of the floating object and the density of the liquid it floats in. If buoyancy is greater than the pull of gravity, the object floats.

Now, let us calculate how much buoyancy we would need to keep the panel, Rose and Jack afloat.

For the two to survive, no more than the door itself can be submerged, keeping the bodies above water level. Therefore, the volume of the submerged object is the volume of the raft. Estimating from stills from the film and Kate Winslet’s height, we can calculate the raft as being roughly 1.85m x 0.95m x 0.15m, or 0.264m³.

Ergo, the buoyancy of the panel would be Volume x Density of ice cold salt water x force of gravity = 0.264m³ x 1000kg/m³ x 9.8m/s² = 2587N (Newtons). If more than 2587N of weight is placed on top (including the panel itself), it would sink.

At the time of the production of Titanic, the estimated weight of Kate Winslet and Leonardo DiCaprio were around 549N and 686N respectively (note that in physics, weight is mass times the acceleration of gravity, measured in Newtons).

Subtracting these values from 2587 leaves us with 1352N free for the panel. Since we know the volume of the panel, as long as we know what wood it was made out of, we can find the density and calculate the final weight.

Three types of wood were commonly used on the Titanic: teak, oak and pine. The densities of these woods are 980kg/m³, 770kg/m³ and 420kg/m³ respectively, meaning that the door would be 2535N if it was made of teak, 1992N for oak and 1087N for pine.

Therefore, the maths show that for the two to have a snowball’s chance in hell of surviving together on the panel, it had to be made of pine. Teak and oak would have been too heavy.

This is where the final key becomes relevant: the wooden panel was likely made of oak.

The Maritime Museum of the Atlantic in Halifax, Nova Scotia, holds the largest piece of debris from the actual wreckage of RMS Titanic. If you look at this wooden panel (from above a doorframe), it looks remarkably similar to the wooden panel that Rose survives on. In fact, a replica of this debris was used for the filming of the film. The material of the actual wooden panel? Oak.

If the panel was made out of oak, it could only hold Rose, as 1992 + 549 = 2541N, which is just enough for Rose to stay afloat above the water level.

And there you have it. Not even the power of love can overcome the cold-hearted, brutal law of the universe that is science.

Posted in Life & Happiness

Chronic Emergency

As a species, we excel at managing emergencies. From natural disasters such as catastrophic earthquakes, to man-made tragedies such as acts of terrorism, to rapidly evolving global-scale deadly events such as pandemics, humanity has shown time and time again that we can band together, strategise and deploy resources to fight against acute emergencies.

From a young age, we learn how to approach urgent issues, such as calling for emergency services, putting out fires, dealing with wounds et cetera. Much of growing up is learning how to deal with various kinds of emergencies: how to organise and balance your finances when you are made redundant, how to console a friend when they are struck with grief, how to fix a car when it breaks down, how to get the internet working again…

But when it comes to “chronic emergencies”, we become stumped. These are urgent, pressing issues – from personal to global scales – that stay for long periods of time or come in waves, rather than as a single event..

Let us consider some examples of how humanity struggles with chronic issues compared to acute ones.

When a hurricane or wildfire strikes, we respond rapidly to provide relief and supplies to help those in need. But when it comes to climate change, we have difficulty coordinating our efforts or even agreeing what the problems are.

When you have acute pain such as a broken bone or a kidney infection, doctors and nurses will provide effective pain relief and treatments to make you better. But when it comes to chronic conditions and chronic pain, you will have to navigate frustrating labyrinths of medication regimens and bouncing from system to system with suboptimal control of symptoms.

Most of us will be adept at dealing with acute stresses in a relationship such as a fight involving a specific event or when our partner has a bad day at work or is faced with disappointment. However, we struggle to deal with chronic issues such as when our partner does not get along with our family or they are battling through serious mental health issues.

The list goes on and on and most readers would be able to think of specific examples from their own lives.

There are many reasons as to why we are better at managing acute emergencies over chronic ones.

Chronic emergencies tend to be more complex with various layers and factors. Because they are long-term problems, they require long-term solutions with sustained effort and careful planning. Due to the chronicity of the problem, people start to lose interest in fighting the problem, or simply become exhausted and exasperated, leading them to give up or accepting it as a new norm.

So what can we do about this? Obviously the solution isn’t to give up on chronic emergencies at first sight. Just as we strive in life to be better and better at addressing acute emergencies, so should we learn to better manage chronic emergencies.

As highlighted above, chronic emergencies are inherently different types of problems that demand a different approach.

The first step is recognising that there is a chronic emergency. Often, chronic emergencies appear as a string of acute situations, so we fight and fight until we burnout. Formally declaring an issue as a chronic emergency helps you stop and rethink your approach. We must also accept that there are no easy or quick fixes for most chronic problems. They take time and effort, with many ups and downs.

To tackle a long-term problem, we need a long-term plan. It is easy to get distracted dealing with individual fires, while failing to see that the entire forest is burning down. Instead of treating each facet of the emergency individually, we can come up with standardised approaches and protocols to automatically respond to recurrent issues, while using our energy and resources to devise a more sustainable solution, treating the root causes.

An example is how a student who comes up with long-term study plans and dedicates time for assignments over a long period of time does much better academically compared to the average student who frantically pulls an all-nighter every time an assignment is due.

Lastly, it is important to recognise that this will be a hike, rather than a sprint. You cannot use maximum effort and burn the candle at both ends right from the start, only to burnout and be overwhelmed by the problem. Instead, pace things out, plan breaks, set realistic, achievable and incremental goals rather than attempting to end the solution.

In chronic emergencies (and life in general), consistent growth and recovery is far more valuable than absolute targets.

Be kind to yourself and others involved when there are failures or unexpected disappointments, because you will have to continuously adapt, learn and be better to ultimately overcome the challenge.

These points are particularly relevant to personal chronic emergencies and long-term hardships such as bad economies, break-ups, grief and mental health conditions.

Life will always be full of emergencies – acute and chronic – so we need to learn to be proactive and deal with them effectively, rather than being reactive and lamenting the awkwardness of life.

Now think about your present life: what “acute” stresses and disruptions are you facing that might actually be a chronic emergency in disguise?

Posted in Psychology & Medicine

Watching You

What drives our morality? Philosophers have argued and pondered for millennia where our sense of selflessness, altruism and honesty come from. Are we inherently good or evil? Do we only help others when it benefits us? How can we motivate people to act more morally?

One interesting research reveals a startling truth about our morality.

In 2006, psychologist Melissa Bateson published a research where she experimented with eyes. Their university tea room had an honour-based coffee and tea system, where you pay the price of the beverage into a box. Because there was no one keeping guard over the box, you could choose to cheat the system by taking a free drink without paying. Bateson wanted to see if she could influence how often people paid by making a simple alteration to the notice banner.

The notice banner had the prices for tea, coffee and milk. Bateson decided to add an image above the prices: a pair of eyes, or flowers. She would alternate the image used week by week, then recorded the total earnings and the number of drinks purchased. She would use different flowers and different eyes from various genders, ethnicities and expressions, but the eyes all had something in common: they stared directly at you.

The results were fascinating: on weeks where the notice banner included pictures of eyes, people paid 2.76 times as much compared to the flower weeks.

Turns out, seeing a depiction of eyes makes us more honest and cheat less. The same effect has been seen when using cartoons or drawings of eyes, resulting in less littering, more donations, less crime and overall more pro-social behaviours. This is called the watching-eye effect.

Why do harmless pictures of eyes make us want to do good?

The effect is likely to be an unconscious, automatic reaction. Our brains are remarkably sensitive to eyes and gaze – which is why we can easily spot people staring at us and why we are so good at reading emotions from eyes.

Furthermore, we are social animals and thus have evolved to show pro-social behaviours so that we fit into the group and live together harmoniously.

This means that when we see even a symbol of an eye, our brain automatically thinks that we are being watched by someone, pushing us to act morally to avoid punishment or embarrassment. This suggests that our desire to preserve our social reputation plays a significant role in our morality (but by no means the only factor).

The other thing to consider is that as we grow up, we are continuously taught that we are being watched, to dissuade us from bad behaviour. God will send you to hell, Santa Claus will put you on the naughty list and Big Brother will send you to prison. All of these stories and cultural beliefs fuel our subconscious paranoia of being watched and fear of consequences.

So if your lunch keeps getting stolen from the fridge, try sending a message by putting a photo of eyes on it to see if it deters your coworkers.

Posted in Science & Nature


The Second Law of Thermodynamics, one of the fundamental principles of physics, dictates that the entropy of an isolated system never decreases over time. If left alone, an isolated system will always progress towards thermodynamic equilibrium: a state of maximum entropy.

These are very long, technical words: what is entropy and why should you care?

Simply put, entropy can be thought of as a marker of how chaotic and disordered a system is. This is a misleading simplification, as entropy actually is more about energy moving from a concentrated state to a more dispersed state, but it is easier to understand this way.

An example would be a hot cup of coffee cooling down. The hot coffee is a concentrated locus of energy. But over time this energy gets dispersed throughout the coffee and into the surrounding (cooler) air and converts the water into steam. Energy slowly disperses out, until the coffee becomes room temperature.

This makes the Second Law of Thermodynamics more relatable. When have you ever seen a cold cup of coffee heat up by itself without any heat source? For that matter, a spilt glass of milk never reassembles itself. Balls sporadically arranged on a pool table will never form an orderly triangle by themselves. A dead person cannot miraculously come back to life. Without external influence, you cannot reverse the entropy of a system.

In a way, you could define life itself as a battle against entropy.

The cells in our body are continuously fighting to preserve order and energy in our body, such as actively pumping salts in and out to maintain concentration gradients, rigorously preserving our body temperature to ensure that enzymes can function optimally and breaking down food to fuel all the processes keeping us alive. If we are left truly isolated (no heat, no food, no oxygen), then entropy will build in our body until we die.

The concept of entropy can be particularly motivating when we consider that entropy doesn’t just apply to physical energy. Our brains are also subject to entropy where, if left alone, it will default to the lowest energy state.

This means that if we don’t pay attention, we will quickly find ourselves mindlessly consuming content, scrolling social media, binging television and procrastinating. It is so easy to waste away the potential energy in our brain if we let entropy have its way.

The best way to counter this is by focussing on a key part of the Second Law of Thermodynamics. It says that entropy never decreases in an “isolated” system. Some things are irreversible, like the inevitable heat death of the universe or our own mortality, but we can enact some change to restore some order to some systems. A cold cup of coffee can be reheated in a microwave. A leaking tire can be patched up and inflated. A spilt glass of milk can be turned back upright and refilled with more milk.

Ergo, we must prevent ourselves from being isolated systems. There are three main ways we can do this.

The first is to stimulate ourselves from external sources, reheating our metaphorical cup of coffee. This includes hobbies and interests, learning new things and expanding your horizons. Our brains are naturally fuelled by curiosity, passion and experiences.

The second is to connect with other people. Healthy social interactions keep us grounded to reality and inspire us to be better versions of ourselves. People can provide us with new knowledge, insights, wisdoms and love.

The last and most important is channelling our own willpower. We must fight against our natural instinct to be lazy by pushing ourselves to get off the couch, to exercise, to work, to create, to produce, to live. This is also the hardest because if it was easy for us to “Just Do It”, we wouldn’t even be discussing how to beat entropy. Therefore, we need to create systems, habits and routines to trick our brain into working and being productive. In no time, you will find yourself auto-adjusting your life to prevent entropic laziness from taking over your life, like homeostasis.

Isaac Asimov’s short story The Last Question tells the story of how even the most powerful supercomputer in the cosmos cannot answer the question of how we can meaningfully reverse entropy in the universe. But turns out we can reverse the entropy of our brain and it is damn well worth the effort.

Posted in History & Literature

Bingo Bango Bongo

Spot the odd one out: King Kong, Ding Dong, Chit Chat, Jibber Jabber, Tick Tock, Flip Flop, Zag Zig. The last one is obviously wrong, with the correct version being “Zig Zag”. The astute reader may have noticed a funny rule here: in words that are repeated with only the vowel sounds changed, I comes before A and O.

This peculiar pattern is known as the IAO rule and it is best shown in the example “Tic Tac Toe”. For some strange reason, words just don’t sound right in English when it doesn’t follow the IAO rule. Pong Ping, Hop Hip, Dally Dilly and Clop Clip all just sound weird.

This rule is formally known as ablaut reduplication and it is seen in almost every English-speaking country. The origin of the rule is unclear (likely Germanic), yet it is so prevalent and ingrained into us. Even if you have never heard of “ablaut reduplication”, the words sound very wrong and awkward if said in a different order.

There is another strange rule in English when it comes to ordering words. When it comes to a list of adjectives, such as “Little Red Riding Hood”, not listing the adjectives in a specific order makes it sound strange.

For reference, the order is:

Opinion – size – age – shape – colour – origin – material – purpose, then the noun.

This means that you can say something like “my big fat Greek wedding” or “that lovely large old brown French wooden clock”, but you can’t say “a red big ball” without it sounding off.

One notable exception is “the Big Bad Wolf”, where the opinion comes after the size. But if you look carefully, you can see it follows the IAO rule instead.

The more you learn about it, the more you realise how (sometimes needlessly) complex the English language is.

Posted in Philosophy

Truth And Lie

You are journeying through a forest when you come across a fork in the road. One path will take you out of the forest, while the other will take you deeper into the woods to a deadly swamp.

At the fork, there are two guards with a peculiar sign in front of them. The sign reads:

“One of us always tells the truth, one of us always lies. You may ask exactly one question to just one of us. Choose wisely.”

The two guards look exactly the same and there is no way for you to tell which guard speaks truth and which lies.

What can you ask either guard to take the right path out of the forest?

(Answer after the break)

Continue reading “Truth And Lie”
Posted in Life & Happiness

The Reason You Are Unhappy

I don’t want to be the reason you’re unhappy. That would just make me unhappy and I really don’t want to be the reason I’m unhappy.

~ Phoebe Buffay, Friends

This appears to be such a simple, whimsical line from a sitcom, but Pheobe’s words carry a surprisingly deep truth.

Too often in life, we are our own reason for being unhappy. As much as we like to blame bad luck, systemic failures, other people’s incompetences and the environment we were raised in, if we examine the root cause of our misery closer, we discover some uncomfortable truths.

For example, a common source of unhappiness is loneliness, particularly the lack of a romantic relationship. There are many reasons people will give as to why they are (involuntarily) single, from self-deprecating comments such as “I’m not pretty enough”, to lamenting their bad luck for not meeting the one yet, to toxic blames such as “girls only go after bad boys, not nice guys like me”.

But are those really the true reasons to your loneliness? Or is it because we haven’t learned to love ourselves yet, hold onto negative beliefs such as a romantic partner being the solution to our deep-seated problems, or feel entitled to love? Perhaps it is because we are too stubborn or scared to take action, putting our hearts on the line by asking our crush out, being vulnerable or even taking the simplest step such as accepting a set-up or trying internet dating.

We often talk about how we can be our own best friend or our worst enemy. Because of our insecurities and anxieties, we often let fear steal our funk, creating barriers to living a happy, full life.

So what is the solution to this curse?

The answer is simple: follow Phoebe’s advice and do not let yourself be the reason that you’re unhappy. If you feel unhappy, take a moment to think about why that is and don’t be afraid to consider that your actions and thoughts might be the cause.

But this is not to say that you should blame and criticise yourself.

Instead, treat yourself with compassion, kindness and love, giving yourself a chance to be happy. Be the manager and mentor to yourself that you’ve always wanted: someone who will let you be the best version of you, clearing roadblocks to your success and happiness. When you discover something that makes you happy, take action to pursue it further, cultivate it and fight to protect it. Seek out new possibilities and exciting opportunities.

Be the reason that you are happy.

Posted in Science & Nature

Thoughts On Sunlight

We live in a world where everything is powered by something. Our technology is fueled by electricity. Our cars are fueled by fossil fuel (although hopefully not for much longer). Our generators are fueled by everything from coal to running water to the splitting of atoms. We are fueled by food, which we break down to release energy.

But at the core of it all, the world is fueled by one main energy source: sunlight.

Let us retrace the steps.

The device you are using to read this is charged by electricity provided by a power generator. Whatever the source of electricity is, humans are required to power the machines and we are fueled by food. The food we eat are either plants, or meat from animals that consume plants. Plants generate their energy through photosynthesis, where sunlight is used to store energy in carbohydrates. 

Ergo, sunlight fuels us all – we are all made of and held together by sunlight.

The Sun is positioned 152 million kilometres from Earth. This means that sunlight travels 152 million kilometres – a distance that takes even light eight minutes to traverse – to feed Earth, brighten our days and make us feel warm and fuzzy. 

Sunlight also heats the earth and seas to power various weather cycles and currents, provides heat to keep life possible and most importantly, lets us see because it floods our day with photons. 

Just something to think about the next time we enjoy a delightful nap in a warm, cozy sunbeam.

The sunniest Magic painting: Endless Sands - Imgur
Art credit Endless Sands by Noah Bradley

Posted in History & Literature

Lo Stivale

The Italian peninsula is nicknamed “Lo Stivale” (“the boot”) because of its iconic geography. Every child who has ever seen a world map will know this iconic boot-shaped country.

But hypothetically speaking, if Italy was actually a giant boot, what shoe size would you have to be to fit it?

Shoe sizing varies across the world. In Korea, Japan and Taiwan, the Mondopoint system is used where the foot length is measured in millimetres (the width is also considered).

But if you come from an English-speaking country, there is a good chance you are more familiar with the UK and US number system, typically ranging from 3 to 13.

The UK sizing system uses the length of the last that is used to make the shoe. A last is a model of a foot that can fill the entire cavity of the shoe. Because you typically need 1-1.5cm wiggle room for your toes, the last is bigger than the foot that would eventually wear the shoe. Instead of simply using the length of the last in millimetres, UK shoe sizes use a strange unit called the barleycorn.

The barleycorn originates from the 19th century when an inch was defined as the length of three barley corns (or grains). Hence, a barleycorn is ⅓ inch. For adult shoe sizes, a size 1 is 26 barleycorns, or 8 and 2/3 inches (220mm). For every size you go up, you add one barleycorn. This means a size 11 is 12 inches, while a size 10 is 11 and ⅔ inches.

Essentially, this means that your UK shoe size is:

(3 x heel-toe length of your foot in inches) – 23 (accounting for the toe wiggle room).

It is important to note that every manufacturer takes their own liberty with sizing, so this will often be inconsistent and can vary up to an inch, especially for women’s shoes. The US system starts counting at 1 instead of 0, meaning that you just add 1 to the equivalent UK size.

Now that we know how sizes work, let us size the Italian boot.

By rough estimate, the “sole” of the peninsula is approximately 360km long. This is accounting for the bend in the middle, as the heel height is tall. To use our formula, we must convert this into inches, which equals 14,173,200 inches.

Ergo, the shoe size calculates as follows:

= (3 x 14,173,200) – 23
= 42,519,577

Whether you use the UK or US sizing, the boot is roughly a size 42.5 million. Or, if you live in Korea, the shoe size would be recorded as 360 million. Either way, that is one big shoe to fill.

Posted in Life & Happiness

Hanlon’s Razor

“Never attribute to malice that which is adequately explained by stupidity.”

This concept has been around since the dawn of time, with many astute, wise people noting that more likely than not, people cause harm not because they wish to, but because they are human.

In 1774, Goethe wrote in his novel The Sorrows of Young Werther:

“Misunderstandings and lethargy perhaps produce more wrong in the world than deceit and malice do. At least the latter two are certainly rarer.”

The more popular, simplified saying at the beginning is now called Hanlon’s Razor and it summarises human behaviour concisely and poetically.

Firstly, it emphasises that people (including us) are stupid. We are flawed creatures. Sure, we may have very capable brains, but we are also hamstrung by psychological biases, manipulation, instincts and impulses. We know that we should exercise, but instead we find ourselves binging TV. We know that we should not lash out at our partner, but we find ourselves reacting to our emotions instead of being proactive. More often than not, we make mistakes and poor decisions not because we are bad people, but because we are human.

Secondly, it shows that we judge ourselves by our intentions, but others by their actions. This is known as special pleading. By our very nature, we are egocentric. We think that the world revolves around us and we play an important role in the narrative of those around us. This means that when someone wrongs us, we can take it as a personal attack against us. How dare your coworker give you sass when they must know how burnt out you are from work? How could your spouse not understand your emotional needs right away? Why would the universe do this to us?

But if we take a step back and change our perspective, we might realise that everyone else lives in their own egocentric world. Each person has their own insecurities, hardships and flaws.

The girl who forgot your coffee order may be severely depressed, affecting her concentration. Your boss may have snapped at you this morning because his marriage is in trouble and he is not sleeping well. Your boyfriend may have insulted you not to hurt your feelings, but because they misunderstood you, they phrased something wrong, or just simply that they are not emotionally intelligent.

If you replace “stupidity” with any other imperfect human characteristic such as laziness, stress, distractedness, ignorance or misunderstanding, then the world suddenly appears to be a different place. People seem less evil and life seems a little less unfair.

Lastly, it reminds us that sometimes, things happen for no particular reason. Because people are imperfect and the world runs on chaos and probability, we may be subjected to adversities that appear unjust and unfair.

It’s not because you are worthless or because someone is out to get you: bad things – horrible things – happen without rhyme or reason. The fact that something bad happened is no judgement of your character or a sign from the universe; that’s just life.

Next time you are wronged, try to stop and think before you immediately react with anger and frustration: if you were in the other person’s shoes, what intention or mistake might have caused this? Have you ever done something similar, such as accidentally cutting in line or spilling a secret through human error, not malicious intent? If you assumed the best intention, what might explain this person’s actions?

If you give people the benefit of the doubt, the world becomes a slightly less stressful place to live in.