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The Closest Planet

Which planet is closest to Earth? If we look at a typical model of the Solar System with each planet neatly lined up, we can see that Venus approaches Earth closer than any other planet. However, this is only one interpretation of the question.

Technically, Venus is the planet that comes closest to Earth. However, as they do not orbit in synchrony, this approximation happens about once a year. At other times, Venus will orbit away from Earth and can go on the other side of the Sun, making the distance between Earth and Venus vast. In those times, Mars may seem like the next obvious choice to be closest to Earth.

But then again, Mars has the same issue where it and Earth are often on opposite sides of the Sun. Because of the nature of circular orbits, the distances between the planets swing and fluctuate, meaning that the real question should be:

Which planet is closest to the Earth most of the time on average?

The answer to this question happens to be Mercury. If we look at a “top-down” model of the Solar System, we can see that Mercury – being closest to the Sun – orbits rapidly around the Sun and often lies between Earth and the two other planets, Venus and Mars. If we plot the distance between each of these three planets and Earth, we can see that on average, Mercury is closer to Earth because the distance fluctuates less.

Interestingly, if we take this question further, we find that Mercury is also Mars and Venus’ closest neighbour on average. This is a property of the Solar System being formed of concentric circles, meaning that Mercury’s smallest orbit makes it average a closer distance to all of these planets.

Fascinatingly, if we go even further than that, we find that the same pattern holds for every other planet in the Solar System, despite the vast distance between Mars and Jupiter due to the Asteroid Belt. Even Pluto (not formally a planet anymore) with its massive elliptical orbit has Mercury as its closest neighbour on average compared to the other planets, due to the unique property of concentric circles.

No matter the distance, if you are orbiting the Sun, Mercury is the closest planet to you.

This video from CGP Grey explains it in a concise and informative way, complete with clean diagrams and animations!
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Shooting Star

When an object from outer space enters the Earth’s atmosphere, it starts to burn up and creates a brilliant streak in the sky, which we call a meteor or shooting star. Contrary to popular belief, this is not due to friction with the air in the atmosphere.

An object entering the atmosphere is typically travelling at extraordinary speeds. Most meteors are travelling around 20km/s (or 72000km/h) when they hit the atmosphere. At these speeds, air molecules do not have a chance to move out of the way. The meteor will instead collide into the air molecules, pushing them closer and closer to each other, compressing the air in front of it.

As we know from physics class, compression increases temperature in gases as per the ideal gas law (PV=nRT). The impressive entry speed of these meteors result in so much air compression that their surface can heat up to 1650 degrees Celsius.

The heat boils and breaks apart the contents of the meteor, turning it into superheated plasma that gives off a glow. This is the streak of light that we see in the night sky when we wish upon a shooting star.

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If you mix 1 part water to 1.5-2 part corn starch, you create a strange mixture called “oobleck“, named after a Dr. Seuss story. It is so simple to make, yet it exhibits some very strange properties that makes it a popular science experiment.

Oobleck is what is known as a non-Newtonian fluid, where the viscosity (or “thickness”) changes with how much stress it is under. If you press your finger gently into it, it will feel like water, but if you strike it with a hammer, it will behave as a solid. It will stiffen when you stir it, but run when you swirl it.

Related image

You can even run over a tub of oobleck as long as you change steps quickly enough to apply enough pressure to keep the fluid under your feet solid. This is because oobleck becomes very viscous under high stress, making it behave more solidly (shear thickening).

We can learn from oobleck not only some interesting physics principles, but also how to interact with people.

Much like a non-Newtonian fluid, people will tend to react stiffly and with more resistance if you apply stress or force. But if you apply gentle pressure and be assertive, you will find people generally react more softly and fluidly.

This simple change in your approach will lead to much better conflict resolution and constructive outcomes when dealing with other people.

Image result for oobleck run gif

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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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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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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.

MRW My girlfriend says "You know why I'm mad."
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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 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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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 (“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?