Posted in Science & Nature

Exponential Growth

Imagine that you have won a strange lottery where they give you two options of payment: they can either pay you one million dollars up front, or they can pay you one cent on the first day, then double the amount you have every day for a month (i.e. 1 cent on day 1, 2 cents on day 2 etc.). Which would you choose?

It may seem obvious that the $1 million up front is far better than accumulating a few cents every day. But by the end of the month (day 31), you would actually have accumulated $5.37 million. How did this happen?

The secret to this extraordinary increase is the power of exponential growth. If you double a number constantly at a regular interval, it grows at a staggering rate. Let us look at the above example again.

On day 1, you have 1 cent. By day 10, you already have 2(10-1) = $5.12. Now we can see that instead of mere cents, we are gaining $5 in one day.
By day 15, you have $163.84. Now the doubling nets you another $163.
By day 20, you suddenly have $10,485.76.
We pass $1 million at day 28 where we have $1.34 million.
Day 29 you have $2.68 million and you can see how we end up with $5.37 million – over five times the amount we would have received compared to the first option.

This shows the sheer power of doubling. It is an important principle to grasp as we see exponential growth all around us in life. Nuclear chain reactions undergo exponential growth to power nuclear reactors. Positive feedback in speakers undergoes doubling amplification, resulting in the sharp screeching sounds. Compound interest follows exponential growth, allowing investments to give substantial returns over time (or result in crushing debt). Bacteria divide in two each time, resulting in a rapid population boom.

Understanding exponential growth also helps us make sense of scary situations such as pandemics. Viral infections are spread from one person to multiple people, represented by a basic reproduction number (R0). In the case of the COVID-19 (2019 coronavirus) pandemic, the R0 was between 2 and 3, meaning that left unchecked, the number of infected individuals would essentially double every few days.

Although this seems obvious, if you didn’t know about exponential growth, it would be terrifying to hear that one day you have 8 cases in a country, but in a fortnight, there are over 1000 cases, with each day presenting increasing numbers of newly infected patients. The media preys on this effect by providing anxiety-inducing headlines. But in reality, the headlines might as well read: “virus continues spreading in predictable exponential fashion“.

Another strength of knowing about exponential growth in a pandemic is that it lets us predict what would happen without any intervention. The number of cases would explode in a matter of weeks, resulting in catastrophic numbers of unwell people taken off the workforce, accompanied by mass casualties. Hospitals would be completely overrun, crippling the nation’s healthcare system and resulting in even more deaths as the infection runs rampant.

Therefore, efforts to reduce the spread of the virus through social distancing and effective quarantining are vital to reduce the rate of exponential growth, flattening the curve and making the number of cases more manageable for the healthcare system to deal with.

Posted in Science & Nature


Extinction is when there are no more members of a given species left. Countless species have come and gone throughout history, such as the dinosaurs. We are currently going through the most recent episode of mass extinction where a vast number of species are being wiped out from the face of the Earth. The cause of this mass extinction is us.

So-called the Anthropocene Extinction, modern humans have been responsible for the extinction of millions of species over the course of our history. This ranges from the death of megafauna such as the woolly mammoth, to the extermination of the dodo on Mauritius, to the imminent extinction of the Northern white rhinoceros (with only two female rhinos surviving). This is the result of over-hunting, climate change, habitat destruction and predator and disease introduction.

Because of the sheer number of extinctions caused and threatened by us, we have also observed many hauntingly depressing stories of identifying the last member of a species. For example, we know that the last passenger pigeon named Martha died at the Cincinnati Zoo in 1914. The last Tasmanian tiger (thylacine) named Benjamin died in 1936, neglected in a zoo. These poor creatures who are the last of their kind are called endlings.

A particularly sad endling story is that of a Hawaiian bird species known as the Kaua’i ʻōʻō. They are an extinct species of honeyeater bird that could be identified by their strikingly rich, golden yellow leg feathers. The Kaua’i ʻōʻō were also famous for their flute-like duet songs sang between lifelong mating pairs.

The Kaua’i ʻōʻō became threatened as mosquitoes were introduced to the island of Kaua’i by sailors. The mosquitoes transmitted deadly diseases which decimated the population. To escape the mosquitoes, the birds retreated to higher ground. However, the Kaua’i ʻōʻō were cavity nesters, meaning that they made nests in tree hollows, which are found in fewer numbers at high altitudes. This meant that the birds failed to find nesting grounds and their numbers dwindled further.

The last mating pair was last observed in 1981. Despite ornithologists attempting desperately to protect this pair, they could not locate the female after a devastating hurricane struck the island in 1982. Several years later, ornithologist Jim Jacobi was surveying the Alaka’i reserve when he heard the unmistakable call of the Kaua’i ʻōʻō. He quickly used his tape recorder to record the Kaua’i ʻōʻō’s call. When he replayed the tape to the group, he noticed to his surprise that the male Kaua’i ʻōʻō had flown back towards them. He stared in wonder, then realised: the bird had returned because he had thought it heard another bird calling him; a call it hadn’t heard in however long.

We can still listen to this recording of the Kaua’i ʻōʻō endling. We can hear the clear lack of its duet partner’s call – a deafening silence symbolising the death of a species.

The saddest part of this story is knowing that even though we may never know their name or how their call sounds, countless endlings have died a lonely, quiet death all around the world, marking a full stop to their species’ epic narrative.

You can hear the Kaua’i ʻōʻō endling’s call here:

Posted in Science & Nature

Centre Of The Universe

We often meet people who act as if they are at the centre of the universe. These egocentric people behave as if they are the most important people in the world and that their words and actions are more meaningful than they actually are, while assuming that they play an important role in other people’s lives. This is a common belief in children who are still learning to differentiate the world and other people from their own minds, but in adults, it is almost pathological.

Speaking of which, where is the centre of the universe?

In ancient times, the concept of “universe” was very different. Many cultures imagined the universe as consisting of the Earth where we lived, plus the heavens and the underworld (often supposedly where the good and bad end up after death respectively). These worlds would be connected by a central axis mundi, or world axis. An example of this is the mighty Yggdrasil, the World Tree, found in Norse mythology. It is said to be a gigantic tree that connects the Nine Worlds and is the centre of all life.

As the science of astronomy developed, we realised that we are not at the centre of the universe. Geocentrism – the model where Earth is at the centre of the world with the Sun, Moon and planets orbiting it – eventually gave way to heliocentrism – the modern model where the Solar System orbits around the Sun.

It took brave scientists such as Nicolaus Copernicus, Johannes Kepler and Galileo Galilei challenging the Church and Aristotelian science establishments to show that our understanding of the universe was wrong, despite pressure and punishment. Through scientific observation and inquiry, it was shown that we are not at the centre of the world, but the Sun is.

But as we discovered more about the heavens, we realised that the universe is far vaster than the Solar System. With the advent of the Big Bang Theory, we realised that the universe is expanding, with every object moving away from each other in all directions. This is an extremely difficult concept to visualise, but because the universe is expanding infinitely in all directions, it technically has no centre.

On a final note, the concept of the universe being infinite may not be relevant to us because we cannot observe the infinite universe. Instead, we often talk about the Observable Universe, which is the portion of the universe that we can physically observe with our eyes, telescopes and other instruments. The centre of the observable universe, like anything observable, is the observer.

Therefore, in some sense of the phrase, you are technically at the centre of the universe.

Posted in Science & Nature

Tip Of The Iceberg

Icebergs are deceptive things. You may see a small bump above the ocean surface, but beneath the surface hides a massive block of ice. Using Archimedes’ principle of buoyancy, we can calculate exactly what proportion of an iceberg lies under the surface. Pure ice has a density of about 920 kg/m³ and sea water has a density of 1025 kg/m³. Ergo, we can calculate that about 10% of the volume of an iceberg is above water. Therefore, whatever you see above the surface, there is nine times the volume hiding beneath it.

Tip of the iceberg” is a useful metaphor in describing many things. Our base instinct is to believe what we see at first glance. We rely on first impressions, we judge books on their covers and we tend to believe headlines before reading the full text of an article.

Although this is a useful way to process massive amounts of information that we are exposed to every day, it is certainly a flawed method because not only can we miss a vast quantity of information, also easily misinterpret or misunderstand things.

Take mental health for example. Because we cannot read minds, we take clues from people’s expressions, body language and what they tell us to gauge what is happening in their minds and hearts. We are reasonably good at gauging this, so we often make assumptions based on surface information.

We might assume our friend is happy because they are smiling, or that a couple’s marriage is harmonious because of cute photos on their social media. Conversely, we might assume that a stranger is rude to us because they are terrible people.

But the smiling friend may be suffering crippling anxiety and depression. The happy-looking couple may be at the brink of divorce because of relationship problems. The rude stranger may have lost a loved one just the day before. Things are not always what they seem and it makes an incredible difference to have the insight to see past the surface.

Another lesson to learn from the tip of the iceberg is that when we encounter a problem – whether it be with another person or even within ourselves – we should ask the question of what lies beneath. The problem we notice may just be the tip, with 90% of the issues hidden from plain sight.

For example, if you feel tense and easily triggered often, perhaps it is worth looking under the hood and going on an introspective journey to discover what past experiences and traumas may have caused the insecurities. If you keep feeling victimised, attacked or sensitive, examine what story your subconscious is telling you and try to correct the narrative, being the agent of your own story.

Avoid the fate of the RMS Titanic: look beyond the visible tip of the iceberg and be aware of the entire problem. You will be surprised how it changes your perspective of the world, the people you interact with and how you feel about yourself.

Image credit:

Posted in Psychology & Medicine


In dire times such as wars, natural disasters and pandemics, we hear news of healthcare professionals setting rules to limit medical treatment provided to certain groups of people. This can come across as shocking to people as it seems unfathomable that a hospital would not do everything within its power to save a life. However, this is a well-known and commonly practised principle in medicine known as triage.

Fundamentally, triage is a system used to prioritise who should receive what level of medical care when. The word triage comes from the French verb trier, which means “to sort“. Modern triage was first designed by a French surgeon named Dominique Jean Larrey, who served in the Napoleonic Wars. Larrey categorised wounded soldiers into one of three groups:

  1. Those who would likely die no matter what treatment they received
  2. Those who would likely live no matter what treatment they received
  3. Those whose quality of life may benefit from immediate treatment

He advised battlefield medics to quickly assess what group a wounded patient would fall under and to focus on the last group. For example, if a soldier had superficial cuts and not heavily bleeding, they would be able to transport themselves back to base. A soldier who is not breathing or lost two or more limbs would be unlikely to survive despite acute surgery (especially with where medicine was at in those times). In other words, medical care would be focussed on those who would likely survive and benefit from urgent medical care, such as the patient who is needing an amputation to stop life-threatening bleeding from an injured limb.

This may sound cruel, but it is the unfortunate reality of healthcare. Ideally, we would like to give the best care to every patient, but we live in a world of scarcity, where resources are finite and limited.

Therefore, we rely on utilitarianism, where we ask “what is the most amount of good we can do with these finite resources?”.

Modern triage is more complicated than Napoleonic times, especially in the emergency department. However, in the case of emergency situations involving mass casualty, triage returns to its simple, original form.

Let us imagine a city struck by a massive earthquake. There are tens of thousands of people with varying severity of injuries. How do we prioritise who will be taken to hospital, need on-site treatment, or left to die or find their own way to hospital?

Physicians and nurses will quickly assess a patient and their vital signs to categorise them using coloured tags, such as red for needing emergency treatment, green for does not need treatment, or black for deceased or likely to die. This is because without triage and prioritisation, the available medical resources will quickly be exhausted and no further care will be deliverable.

If multiple doctors and nurses stop triaging and focus on one patient needing complex surgery, tens or even hundreds of potentially salvageable lives could be lost. If non-urgent injuries are all taken to hospital, the hospital will be overwhelmed and will not be able to provide care to those who are critically ill. If a patient with a non-survivable injury is operated on and taken to the intensive care unit (ICU), they will have lost the opportunity to use those resources on a patient with a better chance of survival.

As harsh as it sounds, saving ten people with moderate injuries who would die without treatment is preferred over the one person who has a less than 10% chance of surviving with maximum medical care. This may be as black-and-white as choosing to not rescue a person with an obviously unsurvivable injury such as decapitation, but it may be as complicated and ethically challenging as deciding if an elderly patient with a lung infection should be intubated and ventilated (breathing machine), fully knowing that a younger, healthier patient with the same infection may need that ventilator to survive, but with a much higher chance of survival and restoring their quality of life.

Triage is a classic example of when the rational solution to a problem such as scarcity challenges ethics and emotions. It may sound as if doctors are playing god when they are declining ICU level of care for an elderly patient, but we must also consider that they have a duty to provide the most effective care for all of society, not just the one patient. These kind of ethical dilemmas are an everyday occurrence in the medical field and can cause significant guilt, anger, pressure and resentment for the healthcare provider.

To simulate the weight of triage, consider the following scenario. Following an explosion in your neighbourhood, you respond to a scene with four patients:

  1. Your 28-year old co-worker with heavy bleeding from a laceration of their leg
  2. Your 83-year old mother who is bleeding from their head and unresponsive, breathing very irregularly and poorly
  3. Your neighbour’s 8-year old child who is not breathing despite straightening their airway and applying rescue breaths
  4. Your 45-year old who is screaming in pain from a broken arm but not bleeding and able to walk
    You have the capability to treat and transport one patient. Who do you choose?

As much as we would like the save the life of our loved ones or a young child first, the principles of triage dictate that the first patient demands the most immediate response.

Triage does not account for emotional connections, personal biases or even justice necessarily. It is a cold, hard rule system that we use so that we can separate our emotions and instincts out amongst a horrific situation.

The algorithm for the START triage system – a widespread system used in many modern mass casualty scenarios
Posted in History & Literature

Kangaroo Word

An example of a word game is the concept of kangaroo words. Kangaroos are famous for carrying their babies (joeys) in their pouch. Similarly, a kangaroo word contains another word within itself that is a synonym (a word meaning the same thing). The joey word can be whole (such as [sign]al, where “signal” and “sign” are synonyms), or more typically (and interestingly), it can be split, such as in [ma]scu[l]in[e], where “male” is hidden amongst “masculine”. In this case, the word must be in the right order from left-to-right.

Variations of kangaroo words include anti-kangaroo words – where the word carries an antonym (opposite), such as “animosity” carrying “amity”) – or grand-kangaroo words – where the joey word itself is a kangaroo word, such as “alone” carrying “lone”, which carries “one”.

Try the following puzzle – can you find what the joey word is in each of these kangaroo words?

  1. Astound
  2. Banish
  3. Capsule
  4. Departed
  5. Exist
  6. Feast
  7. Gigantic
  8. Honourable
  9. Illuminated
  10. Latest
  11. Myself
  12. Nourished
  13. Observe
  14. Plagiarist
  15. Rampage
  16. Supervisor
Continue reading “Kangaroo Word”
Posted in Psychology & Medicine

Thunderstorm Asthma

In November 2016, emergency departments of Melbourne, Australia, were overwhelmed by a sudden surge of patients with asthma exacerbations. There was a 672% excess of breathing-related emergency presentations, with 992% more asthma-related admissions than normal. Many of these patients had never had asthma attacks before (72%), but most had a history of hay fever (95%).

The dramatic flood of patients put significant strain on hospital systems, highlighted by some hospitals running out of stocks of inhaled medicines for asthma exacerbations or rooms to treat patients in.

The cause of this bizarre epidemic – dubbed thunderstorm asthma – is still not clear, but it has been theorised to be related to pollens. It has been known for over 30 years that thunderstorms can pick up large volumes of pollen from one area, then dumped on an urban area far away. Because the pollen were exposed to high levels of moisture, they can burst into very small fragments that make it easier to be inhaled into the lungs, bypassing the natural filter systems in the nose.

There is also a possibility that these thunderstorms introduce pollen from species such as rye that are more allergenic than typical pollen found in residential areas, causing worse reactions.

The drastic increase in pollen density and increased penetration to the lungs can trigger a severe asthma attack, particularly in people whose immune systems are sensitive to pollen (hay fever). In the case of the 2016 Melbourne event, ten people ended up dying, while more than 500 excess people were admitted to hospital compared to the normal asthma admission rate.

Instances of thunderstorm asthma have been recorded throughout the world, but scientists have not been able to prove the exact cause. It is a staunch reminder that nature and the environment have direct impacts on our health, in ways we may not even be able to imagine.

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
(Image source:

Posted in Science & Nature

Blue Rose

One of the holy grails of horticulture is the blue rose. A variety of rose colours have been cultivated using various techniques such as hybridisation, ranging from the classic deep red to bright yellow, to even a mix of colours. However, there has never been a successful case of breeding blue roses.

This is why blue roses have become synonymous with the longing for attaining the impossible. It was a symbol of the Romanticism movement, representing the desire and striving for the infinite and unreachable; a dream that cannot be realised. The flower meaning for the blue rose is secret, unattainable love.

The reason why blue roses are impossible to produce naturally is that they do not have the gene for the protein that makes a blue hue. The biochemistry of flower colours is complex, but essentially, the blue colour seen in flowers such as pansies and butterfly peas is produced by the chemical delphinidin. Roses lack this pigment and only contain pigments that produce red and orange colours.

Because blue roses have always been deemed impossible, florists have had to resort to using blue dye on white roses to produce artificial blue roses. But this all changed with the introduction of genetic modification technology.

In 2005, scientists reported that they created the first true “blue rose”, by genetically engineering a white rose to produce delphinidin and using RNA interference to shut down all other colour production. However, the results were disappointing and the so-called “blue rose” turned out to be more of a mauve or lavender colour, due to the blue having a red tinge.

This is because rose petals are more acidic than true blue flowers such as pansies. Delphinidin is degraded by acid, meaning that you cannot produce the deep blue found in pansies in roses without finding a way to reduce the acidity. This chemical phenomenon can also be seen in hydrangeas, where the red and pink petals turn blue and violet when you acidify the soil that it is growing in.

Although we now harness powerful tools to modify nature in ways deemed impossible in the past, nature still proves to be tricky and elusive.

The Suntory Applause rose
Posted in History & Literature

The Most Kissed Face In The World

In the late 19th century, it was not uncommon to find a corpse who could not be identified. Such was the case for a young woman who was pulled out of the River Seine in Paris, likely a suicide. Her body was labelled ecadavre feminin inconnu (unknown female cadaver) and as was customary at the time, her body was displayed in a chilled room with a glass window at the morgue, in the hopes that some passer-by would recognise her face and identify her.

At some point, a morgue attendant made a death mask of her face – a wax plaster cast that preserves the face of a corpse before it decomposes. The attendant’s motives are unclear: some stories state that he was entranced by her beauty, but it is also possible that he was trying to better preserve the face for identification. Regardless, the mask became copied many times in the following years and became strangely popular in the artistic world.

The face became famous for its eerie smile, which looks enigmatic yet peaceful, even being compared to the smile of the Mona Lisa. The mask – known as L’Inconnue de la Seine (the unknown woman of the Seine) – became a popular, morbid fixture in the rooms of Parisian Bohemians.

In 1955, a Norwegian toymaker named Asmund Laerdal came across a novel material known as PVC, a soft plastic perfectly suitable for dolls. He found it to be a perfect material for the creation of a new training aid for the newly-invented CPR (cardiopulmonary resuscitation) technique to be taught to those learning first aid. He wanted the mannequin to look as natural as possible. This is when Laerdal remembered a fixture on the wall of his grandparents’ house when he was younger: the L’Inconnue de la Seine. He considered the face to be ideal for the purpose of a resuscitation aide, with its peaceful, non-threatening features.

Thus, the Resusci Anne was created. Resusci Anne is by far the most popular CPR teaching tool used worldwide. It is often said that it is “the most kissed face in the world“, as mouth-to-mouth resuscitation is a feature of CPR.

As charming and morbid the story may be, the story of L’Inconnue de la Seine has never been confirmed. It has only been passed on through history via novels, short stories and artists’ accounts. If you look closely at the face, the story seems less likely to be true, as a drowned corpse will often be much more bloated and disfigured from swelling, with a contorted, tortured face as victims frantically thrash and fight as the body screams for oxygen. The general consensus is that from a pathologist’s point of view, the mask is unlikely to be from a drowned young woman

Irregardless of the origin story of its face, the Resusci Anne has indubitably saved the lives of countless people around the world, by teaching people the important skills of CPR and first aid.