Posted in Science & Nature

Pringles

Pringles are a beloved snack well-known for its addictiveness (“Once you pop, you can’t stop“). There are a few other interesting factors that set Pringles aside from other potato chips.

Firstly, Pringles have been called many things, because it is not strictly a potato chip. When it first debuted, other snack companies complained that it was not technically a potato chip as they were made from dried potatoes, so they were labelled “potato crisps“. Ironically, the company successfully argued in 2008 that Pringles were not “potato crisps”, using the logic that they were not of natural shapes and only contained 42% potato as they are made from potato-based dough. This was so that they could avoid the British tax on potato crisps.

Secondly, Pringles chips have a characteristic saddle-shape, known in mathematics as a hyperbolic paraboloid. This creates a uniform shape, meaning they can be stacked neatly in a tubular container for efficient and reliable packaging, as opposed to most potato chips that are packaged in bags. Furthermore, the shape is structurally sound, preventing the chips from breaking under the weight of the stack.

Finally, the inventor of the cylindrical container was a chemist named Fredric Baur, who started the process of making Pringles. His dying wish was to have his ashes buried in a Pringles can and this wish was respected by his children.

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Hexapod

Dragons are fantastic creatures of our imaginations, so they do not follow many of the rigid laws of natural science. They breathe unlimited amounts of fire, can endure extreme heat and they can fly despite their massive size. But perhaps the most unrealistic feature of dragons is the fact that they have an unnatural number of limbs.

All vertebrate animals on Earth follow a simple rule: they are four-legged creatures, also called tetrapods. The limbs may have devolved away such as in whales and snakes, but they remain as vestigial structures or still encoded for in the genes. Birds and bats have adapted their upper limbs into wings to fly, but the total number of limbs is still four.

How many limbs does a dragon have? They have four legs that they stand on, but also two large membranous wings like a bat. This means that they have a total of six limbs. The only other animals that share this trait are insects and other mythical creatures such as the centaur and pegasus.

To be a vertebrate with six limbs, a dragon must have evolved from an ancestor separate to Tetrapodomorpha, an ancient fish-like creature with four limbs that is the common ancestor to all four-legged beasts. Alternatively, the wings may not be true “limbs” and be similar to flying lizards that evolved to have a rib jut out with a membrane attached to act as a glider.

Unlike the scientifically inaccurate dragon, a wyvern obeys nature’s four-leg rule. Furthermore, unlike the traditional Western dragon that we have been describing, dragons of the Far East have no wings and four limbs, also obeying the law.

As ridiculous as it may sound, applying scientific principles to our imagination allows us to learn more about how our world works.

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Arithmetic

Although we all learn mathematics to a high level during our schooling years, most of us find that as working adults, we lose much of our maths skills due to lack of practice. This may be fine for advanced concepts such as calculus and matrices, but we tend to forget even the most basic arithmetic skills, instead choosing to rely on calculators on our phones and computers.

But maths is all around us in day-to-day life. From figuring out how much you save on a sale, to splitting a bill, to calculating tips when you travel in the USA, arithmetic is a handy life skill that many of us have forgotten. As easy as it is to pull out your phone and use the calculator app, here are a few tips to improve your arithmetic skills for quick mental calculations.

If you need to multiply a 2-digit number (e.g. 12 x 17), divide one of the number into its 10’s and 1’s, multiply the other number to each of these numbers then add them.

(e.g. (12 x 10) + (12 x 7) = 120 + 84 = 204)

You can further subdivide the numbers to break it down into easy bite-sized calculations.

e.g. 34 x 26 = (34 x 20) + (34 x 6) = (34 x 2 x 10) + ((30 x 6) + (4 x 6)) = 680 + (180 + 24) = 884

When adding or subtracting large numbers, use 10’s and 100’s for easier calculations. Essentially, you can “fill in the gap” up or down to the nearest 10’s or 100’s, then add/subtract the remainder.

e.g. 64 + 13 -> take 6 away from 13 and add to 64 -> 70 + 7 = 77

You can do this in multiple steps to break a complicated addition or subtraction into simple maths.

Learn to manipulate the decimal point to make multiplication and division simpler. 20% of 68.90 sounds difficult, but if you understand how the decimal point works, you can simply multiply 2 then divide by 10 to get the answer.

e.g. 68.90 x 2 =137.80 / 10 = 13.78

An extension of this is learning basic fractions, such as knowing that 0.5 is half and 0.2 is one-fifth.

e.g. 32 x 15 = 32 x (1.5 x 10) -> so you can add half of 32 to itself (x1.5) then x10 -> 48 x 10 = 480

Lastly, a handy mathematic trick is knowing that X% of Y = Y% of X. This means that if one side of the equation is easier, you can convert it easily. For example, 4% of 25 sounds much more difficult than 25% of 4 (or quarter of 4), yet the answer is the same.

The common theme of these tips is using shortcuts and breaking down complicated equations into bite-sized steps so that your brain can solve simple arithmetic in sequence. This may be asking for too much in a time when all of us seem to have minimal attention spans, but you never know when basic maths will come in handy.

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Posted in Science & Nature

Death Pose

When a dinosaur fossil is excavated, it is not uncommon to find the dinosaur in what is known as the death pose. The long neck is bent dramatically backwards and the mouth is gaping open, as if the dinosaur is letting out one final bellow.

For a long time, palaeontologists believed that dinosaurs found in this pose had remarkable neck flexibility. For example, the Elasmosaurus was originally thought to have a snake-like neck that could bend and curl around, even being able to lift its head above the water, as seen with the image of the Loch Ness Monster. However, in reality, the neck would have been too stiff and heavy to move around like that, meaning that Elasmosaurus would have swam around with a straight neck, barely lifting its head above water.

It is still unclear exactly why dinosaurs are often found in the death pose.
Traditionally, it was believed that the strong ligaments holding the neck bones (vertebrae) contracted as they dried out, bending the neck backwards where there are more ligaments.
Others refute this theory, instead suggesting that the dinosaur remains would be rearranged by water currents, or that the carcass would naturally bend backwards when floating in water.
Finally, another group of scientists believe that the pose happens in the final moments of the dinosaur’s death throes, suggesting that they experience opisthotonus (arching of the back muscles, as seen in tetanus) either due to lack of oxygen in the brain, or poisoning.

It is fascinating to think that although these dinosaurs have been dead for 66 million years, we still have so much to learn from them.

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Sudoku

Sudoku is a mathematic puzzle that has gained considerable popularity in the 21st century, rivalling the classic puzzle that is the crossword. You are given a 9×9 table divided into 9 equal squares, filled with a certain number of digits. Your goal is to fill in the table so that each row, column and subsquare (of 9 small squares) contains every digit from 1 to 9. You are not allowed to have the same number appear on the same row, column or subsquare, as there are not enough spaces for spare digits.

The more digits (“clues”) that you are given at the start of the puzzle, the easier it is to solve it. This begs the question: what is the minimum number of clues that you need to solve a sudoku puzzle?

Sudoku puzzles with 17 clues have been completed traditionally. We know that 7 clues is not enough as the last 2 digits can be interchanged, creating puzzles with more than one solution. Using mathematics, we know that if we can solve a puzzle with n clues, then a puzzle with n+1 clues can be solved as well. Ergo, the answer lies somewhere between 8 and 16.

In 2012, Gary McGuire, Bastian Tugemann and Gilles Civario tackled this problem using one of the oldest tricks in mathematical analysis: brute force. The total number of possible sudoku puzzles that can be generated is 6,670,903,752,021,072,936,960, or 6.67 x 10²¹. After accounting for symmetry arguments (meaning that two puzzles may be essentially identical, but just rotated or flipped), we are left with 5,472,730,538 possible unique solutions.

The team used supercomputers to analyse all of these possibilities to see if any puzzle can be solved with just 16 clues, as the conventional thought was that 17 was the minimum number of clues possible from traditional methods. After a year of calculations, the computer found no sudoku puzzle could be solved with only 16 clues. This was confirmed by another team from Taiwan a year later, proving that the minimum number of clues required for sudoku is indeed 17.

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Constellation

To our ancestors, the night sky was not only useful for navigation and telling the seasons, but also for entertainment. Using the mind’s eye, they connected the dots to form a skeleton of a picture – a constellation.

Constellations became the basis of numerous tales and legends. The ancient Greeks told stories of mighty hunters fleeing from scorpions, of fair maidens chased by satyrs, and of noble animals who helped a hero in their quest. In the Far East, they tell a story of lovers who are punished by being placed on separate stars, only being allowed to meet once a year. Similar stories based on constellations can be found in almost every culture around the world.

Constellations are fascinating as they just look like a collection of bright dots to us, but in reality, they represent a spread of stars throughout the cosmos, unimaginably far from us and each other. Even though the stars may appear to be right next to each other, one star may be thousands or millions of light-years further from us than the other.

This is because a constellation is a two-dimensional picture representing three-dimensional space, meaning that depth is ignored. Because of the great distance, entire worlds appear to be simple points, while the vast emptiness of space flatten out to short gaps.

Mythologies and stories based on constellations teach us many pearls of wisdom, but perhaps this is the most valuable lesson the constellations have to teach us. When we look at something from a distance, we lose the fine details. Even the awe-inspiring beauty and size of the cosmos can be reduced down to a simple line drawing in the sky.

The same principle applies to people.
When we judge a person, we reduce a complex life full of stories, experiences, thoughts, feelings and circumstances down to a single stereotype, letting us objectify, criticise, belittle and dismiss people easily.
When we comment on a historical event, we focus only on big events and try to simplify the narrative to a few cause-and-effect stories, while conveniently forgetting the individual lives affected or the broader context that led up to that point.
When something bad happens in the world, we try to find meaning or something to blame, instead of trying to understand the numerous variables that factor into the situation.

Constellations are beautiful, but they don’t tell the full picture. If we want to truly understand the world we live in and the people we share that world with, we have to learn to consider the details and look at things from different points of view.

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Brontosaurus

Brontosaurus (“thunder lizard” in Latin) is one of the most well-known dinosaurs. It is the poster child of the sauropods, a group of massive four-legged dinosaurs with very long necks and tails, known as some of the largest animals to ever walk on land.

After going extinct around 66 million years ago, the Brontosaurus was rediscovered in fossil form in 1879 by palaeontologist O.C. Marsh, who is infamous for his rivalry with another palaeontologist called Edward Drinker Cope as part of the “Bone Wars”. The Bone Wars was the fierce competition between the two palaeontologists, involving aggressive digging to discover as many dinosaurs as possible, while both tried to slander and impede each other through dishonest, unprofessional means. This dispute resulted in rushed announcements of new discoveries sometimes, leading to fascinating stories such as Cope accidentally putting the skull of the Elasmosaurus on its tail instead of the neck.

So what does the historical context of the Bone Wars have to do with the Brontosaurus? In 1903, another palaeontologist argued that the Brontosaurus was actually a specimen of the already discovered Apatosaurus. Two years later, the American Museum of Natural History unveiled the first mounted sauropod skeleton and named it a Brontosaurus. However, they had accidentally used the skull of a different dinosaur called Camarasurus, mounted on the skeleton of an Apatosaurus. With no further evidence supporting Brontosaurus as a separate genus, the scientific community agreed that the Brontosaurus was really just an Apatosaurus.

Despite this news, Brontosaurus remained hugely popular amongst the general population thanks to its early publicity. At the same time, Brontosaurus not being a real genus of dinosaur became a popular factoid (false information accepted as fact due to popularity). In a field such as palaeontology where evidence can be scant or incomplete, such misclassification is common. For example, the Triceratops is in fact simply the juvenile form of another dinosaur named the Torosaur.

But then in 2015, a group of scientists used computer modelling to analyse sauropod fossil data including the original fossil discovered by Marsh. What they discovered was that there were enough differences between the Brontosaurus and Apatosaurus, such as differences in pelvic bone structure, to classify Brontosaurus as its own genus. After more than a century, the Brontosaurus has had its name cleared and restored to its former glory.

The story of the Brontosaurus is a great example of one of the principles in science: nothing is 100% true. Science never proclaims something as the one truth. We can hypothesise, support it with evidence and construct a theory that makes sense of the cosmos, but we can never be sure that we definitely have the answer. In the face of new evidence and re-examination of the analysis, what was once regarded as “truth” can easily be proven to be wrong.

This is an unpopular aspect of science, because people tend to want security and certainty to soothe their anxieties about not knowing. But instead, we get to stay curious and continuously question the nature of the universe and how everything works, making fascinating discoveries and learning something new every day.

For how boring would life be if we had nothing more to learn?

Posted in Science & Nature

Brace Position

A word you never want to hear during a flight is “brace, brace”. It is used as an instruction from the flight crew to the passengers that there is an impending crash landing and everyone should assume the brace position. It is covered in the safety instructions at the start of every flight.

The brace position varies for each country and airline, but the general principle is to bend forward, putting your head either on your lap or against the headrest of the seat in front of you, having your feet flat on the ground and covering your head with both of your hands.

The purpose of the brace position is to maximise your chance of survival in the event of a crash landing. A typical passenger jet travels at around 900km/h. When a plane crashes, extreme amounts of force are exerted on the plane chassis and its contents. The following is a non-exhaustive list of potential sources of injury for a passenger:

  • Inertia and two-point seat belt (only across the waist) results in “jack-knifing”, where the body folds over at high speeds. This can cause catastrophic injury to abdominal organs and the spine.
  • Head and neck injury against the seat in front, resulting in anywhere between a concussion to bleeding in or around the brain. Even if the head injury is survivable, being knocked out or confused after a concussion reduces your chances of escaping the crashed plane before collapse, fires or explosions.
  • Whiplash injury of the neck.
  • Limb injury from flailing.
  • Injury from falling debris.

The brace position has been optimised over the last 20-30 years to reduce the risk of all of the above types of injuries, with multiple studies confirming that it is effective in reducing crash mortality.

Another positive news is that the risk of dying from a plane crash is extremely low. Your risk of dying on a flight is 1 in 60 million – far, far lower than the risk of dying from a car accident, being hit by a bus, a brain aneurysm or even being hit by lightning. Thanks to rigorous research, improved design and numerous safety features such as brace position, you have a 95% survival chance in an airplane crash, and even in serious crashes, the survival chance is 76%. 

Of course, the minute percentage of plane crashes that result in fatalities tend to be non-survivable in the first place, but we cannot postpone death forever.

Posted in Science & Nature

Antimatter

Nature is surprisingly balanced. For every action, there is an equal and opposite reaction (Newton’s Third Law of Motion). Energy can change forms in an isolated system, but cannot be created or destroyed as the total energy must remain constant (Law of Conservation of Energy). Similarly, matter is balanced by the existence of antimatter.

Antimatter is a substance that is the polar opposite of matter. For example, instead of positively charged protons and negatively charged electrons, anti-protons are negative and anti-electrons (or positrons) are positive. Much like matter, antimatter particles can interact with each other to form more complex particles, such as an anti-atom, meaning that it is conceivable that an entire world could be made out of antimatter.

When antimatter and matter collide with each other, they annihilate. Much like the equation 1 + -1 = 0, the two opposites cancel each other out. Conversely, to create matter out of nothing, you must create an equal amount of antimatter to balance it out. Strangely though, physicists have noted that there is a great imbalance between the two in the observable universe. There seems to be far more matter than antimatter, which does not make sense. The question of why this imbalance exists is one of the biggest unsolved mysteries in physics.

An interesting lesson we can take away from antimatter is the concept that to create something out of nothing, you must balance it out with “anti-something”. If you borrow money from the bank, you may have $1000 now, but you have also created a -$1000 debt. The total balance is still 0.

The same concept can be applied to happiness. If something makes you happy, then the possibility exists that the same thing can cause you an equal amount of grief. Let’s say you find a fulfilling relationship with a significant other who brings you extreme joy. This is balanced by the extreme grief that will be brought to you if the relationship is strained or ends abruptly. Ironically, the pursuit of happiness creates more room for potential misery, as grief comes from the loss of something we care about.

So what does this imply? Does it mean that we should avoid falling in love or caring about anything, because it will only hurt us in the end? Should we even bother trying to live a happy life if it is cancelled out by all the sadness that it can bring along the way? Of course, these are silly thoughts. How dull life would be if we did not have any ups or downs.

Instead, the lesson here is that we should be mindful that happiness is not free. Grief is the price we pay so that we can experience the wonderful moments of joy, love and connection that life can give us only if we reach out. If you avoided connecting with someone or taking a leap of faith due to fear of failure or loss, then your life would be empty. This philosophy allows us to be grateful for the joyful moments, while helping us endure grief as we know that is the price we must pay for true happiness.

You can’t let fear steal your funk. To quote Alfred Lord Tennyson: 

“‘Tis better to have loved and lost than never to have loved at all.”

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Car Keys

There are times when you park your car, start walking away and you remember that you forgot to lock the doors. You click your remote car keys but you are already just far enough that the signal does not reach your car. Fortunately, there is a lazy way to extend your car remote’s range.

If your hold your remote against your head (such as next to your chin or your temple), you will find that suddenly, the remote works from a longer distance like magic. How can this be?

There are two explanations that factor in.

The first is very simple: height. The higher you hold your remote, the less barrier there is between you and the car, making the signal more likely to reach it. But this cannot be the only answer as the trick works when there is nothing between you and the car.

The second explanation is more technical. When you press the key to your body and click it, the electromagnetic waves that comprise the signal can cross past your clothes and skin into your body, which is mostly composed of water. The water acts as a capacitor as the signal starts to “charge” you, all the while the signal is being rapidly bounced back and forth between the remote and you. In essence, your body acts as a giant aerial that amplifies the signal, almost doubling the range of the remote.

Arthur C. Clarke once wrote: “Any sufficiently advanced technology is indistinguishable from magic”.
But even the simplest scientific principles can seem like magic until we bother looking under the hood.