Posted in Science & Nature

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.

MRW My girlfriend says "You know why I'm mad."
Posted in History & Literature

Pineapple

A strange linguistic fact is that other than English, almost every other language calls the pineapple fruit ananas. This is true for French, German, Dutch, Italian, Greek, Arabic, Russian, Turkish and even Icelandic. The scientific name for the genus that pineapples belong to is also Ananas. The few countries that use a different name include Spain (piña), China (boluo) and countries where the pineapple was introduced to by an English-speaking country (e.g. Korea and Japan).

So why do English-speakers use a completely different word for the fruit? Pineapples were first brought back to Europe from the Americas in the early 1600’s. They named it ananas after the native Old Tupi word nanas, meaning “excellent fruit“.

However, the Spanish and English thought the fruit was shaped more like a pinecone and named it separately. In fact, the word “pineapple” was used prior to the introduction of the fruit, first recorded in 1398 used to describe actual pinecones.

Posted in Life & Happiness

I Don’t Know

How a person responds to a question that they don’t know the answer to tells you quite a bit about what kind of person they are. Some people try desperately to hide their lack of knowledge by rambling or even making up facts. Sometimes, people will become very defensive and heatedly argue a point even if they are not sure it is the right answer or not, attacking the person asking the question (ad hominem argument).

The model answer would be to admit that you don’t know the answer. A marker of a well-adjusted person is their ability to admit that they are imperfect, as well as an openness to continue learning to keep filling their gaps of knowledge.

The world is an extremely vast place and our sphere of knowledge is rapidly expanding in the age of information. It is impossible to know everything in the world and it is arrogant to assume that you can.

Furthermore, knowledge changes with time. Facts and paradigms once deemed to be concrete have faltered with new evidence. New concepts such as the theory of evolution and the Big Bang were shunned initially, but are now basic knowledge that best explain what we observe. Without an openness to learn and change our minds, we would become stagnant and boring.

No one likes to be wrong or perceived as stupid. But if we let our pride get in the way, we could never improve and grow. It is okay not to know the answer, as long as you are open to learn.

Posted in History & Literature

Veblen Good

There is a simple rule that every student of Economics 101 knows:

The higher the price of an item, the lower the quantity demanded becomes.

This is because a rational person would feel that the item is not worth it above a given price point.

However, there are many goods that do not follow this law. Veblen goods describe a group of goods where paradoxically, higher prices result in greater demand. Examples of Veblen goods include luxury cars, designer jewellery and trending fashion items such as Air Jordans.

The simple explanation is that these goods are not demanded because of their functionality and usefulness, but because they are status symbols. Possession of a Veblen good suggests that you are financially successful and wealthy enough to disobey the law of demand and get away with it.

For the purchasers of Veblen goods, the fact that they are so expensive and exclusive make them appealing.

Posted in History & Literature

Trolley Dodging

In the 1800’s, horse-drawn trolleys were one of the main forms of public transport in Brooklyn, New York. This changed in 1892 when electricity was introduced to the system. The new electric trolley lines could travel at around 15 miles per hour, three times faster than a typical horse-drawn trolley. Once again, technology was improving the quality of lives and efficiency of people in the modern era.

Except it came at a great cost: safety. Electricity and automobiles were still very new concepts to the majority of people of this era. People of the late 19th century were not used to the idea of fast vehicles racing down the roads, so they would not routinely check both sides before crossing a road – something that every child nowadays knows to do. Therefore, many unsuspecting pedestrians were caught off guard and struck down by a trolley.

Furthermore, traffic lines were chaotic, time schedules were incredibly tight forcing drivers to be more reckless, and electrocution from broken wires were not uncommon. The injury and death tolls climbed rapidly as more and more electric trolleys were introduced. Within the first three years of the electric trolleys becoming operational, more than a 100 people had been killed and 400 people injured by these trolleys.

After years of public backlash, system reforms and regulations, trolleys became safer. Cultural shifts with people becoming used to the idea of checking for dangers before crossing the road also helped reduce the death toll. Trolley dodging became a routine part of modern, metropolitan life.

The history of trolley dodging is a great reminder of how new technology changes our lives. Technology promises easier, more efficient lives, but they can be so paradigm-shifting that people may not know how to use them “well”. It can take years before the culture shifts to accommodate for it, leading to numerous growing pains” for the society while they become used to the change.

A good example is social media. Although it promises greater global connectivity and rapid information sharing, it has also caused significant issues. Social media results in addictive, toxic behaviours due to its attention-grabbing, infinite scrolling nature. It can cause awkward social dynamics as we have no clear etiquettes and rules regarding how we interact with each other on the internet. Despite it having the potential to greatly improve the quality of our lives, currently social media is often causing more harm than good because we have not had the time to learn what the best way to utilise it is.

Much like the residents of Brooklyn in the 1890’s, we need to learn how to utilise this exciting but potentially dangerous technology wisely, or risk being run over by it.

Posted in Life & Happiness

Mistake

Generally speaking, we live our lives trying to avoid making a mistake. Perhaps it is because we were brought up to do everything as perfectly as possible. Perhaps it is because we fear the consequences. Perhaps it is because we refuse to accept that we are imperfect beings.

Regardless of the reason, we have a constant nagging voice in the back of our minds asking us: “Are you sure you want to do this? What if it’s all a big mistake?”.

This mentality affects our work, our financial decisions, our sense of adventure and even our relationships. Sometimes, we even go as far as not taking any action in fear of screwing it up. The fear of mistakes makes us take less risks and leaps of faith, hindering our ability to live a full life.

But to quote a great captain, Jean-Luc Picard:

“It is possible to commit no mistakes and still lose. That is not a weakness. That is life.”

Life is full of mistakes. No matter how hard we try to minimise risk, life will always find a way to trip you up. Because we are not a time-travelling supercomputer that can see and predict every variable, it is impossible to make no mistakes. Ergo, it is okay to make mistakes, because to err is to human.

In fact, mistakes are not always bad.

A “mistake” such as the singer’s voice cracking on a live performance may make it a more special performance, because it is a sign the singer poured all of their emotion and energy into the song, rather than playing it safe to avoid a mistake.

Columbus discovered the Caribbean because he mistakenly thought that he could reach Asia by sailing due west of Spain.

Everyone has a story of getting lost while travelling and stumbling onto an unforgettable experience that they could not have possibly planned for.

Sometimes, we will look back on our life and realise that what we thought was a mistake back then turned out to be a blessing in disguise, because each and every mistake we made led us to where we are now.

Lastly, we are all the products of billions of years of mistakes. Evolution is fundamentally based on the concept that genetic mistakes during cell division (mutations) allow for diversity of traits. Without mistakes, we wouldn’t even be here.

Of course, some mistakes carry irreversible, dire consequences, such as drinking and driving, or falling asleep while a nuclear reactor fails (Three Mile Island accident). But outside of these, most mistakes in life are something that you can learn something and move on from.

So don’t beat yourself up if you make a mistake.

It’s okay to make mistakes.

We are only human.

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.

Posted in Life & Happiness

Spirals

You see an attractive person.
You think about approaching them to talk with them.
You toy with the idea of asking them out for a coffee.
You worry that they will be offended by your forwardness.
You feel certain that they would never say yes because you are unattractive.
You become sad that you will never find love and will die alone.
As all of these thoughts race through your head, the person walks past you and carries on with their day, oblivious to your internal torment.

This is a classic example of a negative thought spiral. Our brains are experts of association. But unfortunately, they are also experts of worrying. Evolution has trained us to be prepared for all emergencies with a state-of-the-art fight-or-flight system, which unfortunately is more useful for fleeing from lions than the stresses of modern life.

Because of our anxieties and stress, a fleeting, negative intrusive thought can spark a chain of negative thoughts, spiralling infinitely tighter and tighter as we catastrophise and despair.

Fortunately, there are a variety of ways to rescue yourself from a negative thought spiral.

The first is to recognise that you are in a spiral. A person walking down a spiral road may think that they are walking down a straight road, because they cannot see the bigger picture. This is why it is important to be mindful of your mental state. How are you feeling? What is making you feel this way? How are these feelings affecting your thoughts?

Sometimes, the sheer process of recognising a spiral lets you snap out of it. You may notice obvious rational answers to your anxiety. Perhaps your partner is not texting back because they are busy at work, not because they died in a fiery car crash.

Failing this, we can try grounding exercises. This is a classic distraction technique where by focussing and anchoring yourself on the present, you can escape the spiral.
This may range from simple breathing exercises, to more detailed mindfulness exercises such as the five senses meditation.

Lastly, remember to be kind to yourself. Do not let the spiral be cruel to you. When the spiral tells you that you are worthless, correct them by telling yourself that you are worth it. Talk to yourself as you would to someone you love dearly. As important it is to have other people to rely on for compassion and love, it is so difficult to escape these spirals if we do not show ourselves compassion and love.

Contrary to what we have discussed, not all spirals are bad. To quote John Green:

“Spirals grow infinitely small the farther you follow them inward, but they also grow infinitely large the farther you follow them out.”

When you are mindful of your thoughts, you will notice the occasional positive thought spirals. For example, you may have a sudden thought that you might want to travel on your own. You might come up with a gift idea for a friend that you think they might appreciate, despite how cheesy it is. Sometimes, these thoughts become seeds that grow out into more elaborate ideas and plans.

These are the kinds of spirals you should listen to, as it is your subconscious prompting you to take action in your pursuit of happiness. As long as it does not harm you or others, you should follow these spirals outwards, as they may lead you to an infinitely wonderful place.

Posted in Life & Happiness

How To Draw A Line

If you need to draw a straight line without the help of a ruler, try the following method. Instead of looking at the tip of your pen, look at the point you are trying to draw a line to and move the pen in one swift motion towards it. You will find that the line is much straighter than when you are consciously focussing on where your pen is.

This is similar to how when you are walking down a staircase, the more you think about the steps you are taking, the more likely you are that you will trip and fall. Your brain is very proficient at automating physical activities, so that you can use “muscle memory” instead of wasting precious mental energy.

This also means that ironically, thinking and worrying about doing something right can result in more failures. Sometimes, it is better to just be aware of the direction you want to head in and go with the flow, rather than overthink, micromanage and ruin things.

Posted in Science & Nature

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.