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The Oldest Tree

In 1964, a graduate student named Donald Currey was studying the history of glaciers in Nevada, USA. He came across some bristlecone pine trees, which he suspected may give him some clues about the Ice Age. This is because previously, another scientist had discovered similar bristlecone pines nearby in California that dated between 3000-5000 years old.

So Currey decided to sample some of these trees to determine their ages. He thought that if he could show that the trees uphill were much younger than the trees at the base, it may prove that glaciers expanded down the mountain and pushed the trees back downhill.

Currey came across a particularly old-looking tree. He got permission from the Forest Service first, then cut the tree down to count its growth rings – the most accurate way to figure out how old a tree is. As the tree’s bark changes in a predictable fashion, a tree will gain one ring for every year of its life. An interesting point is that trees are often dated nowadays by taking a core sample instead of cutting it down (and thus killing it). It is uncertain why Currey and the Forest Service opted to cut the tree down instead.

After counting the rings of this tree, Currey realised that the tree (dubbed “Prometheus” by local naturalists) was 4844 years old – the oldest tree in existence in the world. Well, it was until it was cut down.

More modern analysis of Prometheus’ remains revealed that the tree was likely closer to just over 5000 years old at the time of its death, which makes Prometheus the oldest known tree and (non-clonal) organism in recorded history.

As expected, when Currey published his results, there was a massive outcry. In the name of understanding nature better, he inadvertently killed the world’s oldest tree.

Since the demise of Prometheus, another tree by the name of Methuselah has taken the crown of “oldest tree in the world”, at the age of 4852 as of 2020.

The lesson here is clear: before cutting a tree down, check that you are not accidentally killing the oldest tree in the world.

Methuselah, the oldest living tree in the world
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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.

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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 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 Science & Nature

Airplane Game

You are cordially invited to a game that lets you earn money very easily. The game works like this:

  1. You pay $1000 to be recruited as a passenger to a plane.
  2. There are 8 passengers, managed by 4 crew members, who have 2 co-pilots above them, co-ordinated by a captain at the top.
  3. Everytime the “plane” is filled with 8 passengers, the captain retires and is paid out $8000.
  4. When the captain retires, the plane is split into two planes and everyone else is promoted one step higher (co-pilots each become a captain, crew become co-pilots, passengers become co-pilots).
  5. When each plane fills with 8 new patients, the captain of each plane gets paid out $8000 and retires.

This seems like a very easy way to earn money. Where else could you invest money and guarantee a 700% return, only needing to recruit 7 new people into the game?

The problem with the airplane game is that it is a classic example of a pyramid scheme. At first glance, it seems that the payout of $8000 is guaranteed because it seems that the promotions will keep coming.

But if you look at the mathematics, 8 people need to participate before the first player wins. 16 people have to participate for the second player to win. 80 people have to participate for the tenth person to win. If you are the one-thousandth person to join the game, you need a total number of 8000 people to be playing the game before you are paid out. At the end of the game, 87.5% of people playing will have lost money because they will never be paid out.

This is how simple exponential growth can result in a very real fraud, resulting in thousands of people losing their hard-earned money.

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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.

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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:

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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.

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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:

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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: