Posted in Science & Nature

Periodical Cicada

In certain parts of eastern North America, it has been noted for centuries that some summers seem to bring a massive swarm of cicadas. Observant naturalists such as Pehr Kalm noted in the mid-1700’s that this mass emergence of adult cicadas happened every 17 years. Since then, a similar pattern has been observed with many different broods of cicadas, with precisely 17 or 13 years between emergences of mature cicadas.

What could possibly explain such a specific, long gap between these spikes?

This phenomenon has been well-researched and the species of cicadas (Magicicada) are known as periodical cicadas. They can be distinguished by their striking black bodies and red eyes. Like most cicadas, periodical cicadas start their lives as nymphs living underground, feeding on tree roots. They take 13 or 17 years (depending on the genus) until they emerge all at once in the summer as mature adults – far longer than the 1-9 years seen in other cicadas. After such a long period of growth, they emerge for a few glorious weeks in the sun to mate, before laying eggs and disappearing.

The astute reader would notice that both 13 and 17 are prime numbers (a number divisible only by itself or 1). Is this a sheer coincidence or a beautiful example of mathematics in nature?

This curious, specifically long period of maturation has been a great point of interest for scientists. The phenomenon of mass, synchronised maturation is a well-documented survival strategy known as predator satiation. Essentially, if the entire population emerges at the same time, predators feast on the large numbers, get full and stop hunting as much. The surviving proportion (still a great number), carry on to reproduce and the species survives.

One theory holds that the prime numbers are so that predators cannot synchronise their population booms with the cicadas. If the cicadas all emerged every 4 years, a predator who matures every 4 or 2 years could exploit this by having a reliable source of food in a cyclical pattern. 13 and 17 are large enough prime numbers that it would be very difficult for a predator to synchronise its maturation cycles with.

Another possible theory is that it is a remnant of a survival strategy from the Ice Age. Mathematical models have shown that staying as a nymph for a longer period increased the chances of adults emerging during a warm summer, rather than when it is too cold for reproduction. This resulted in broods of varying, lengthy cycles, but this created another problem: hybridisation. When broods of different cycle lengths intermingled, hybridisation could occur and disrupt the precise timing of maturation cycles, decreasing the brood’s survival rate. Prime number cycles such as 13 or 17 years have a much less chance of hybridisation, increasing the survival rate.

As Galileo Galilei said, mathematics is the language in which the universe is written. It is fascinating to see examples of how maths can influence natural phenomena, even the life cycles of insects.

Posted in Life & Happiness

Decade Review

A year is the amount of time the Earth takes to rotate around the Sun once. But strictly speaking, this does not have a large impact on our lives or our progress and growth as a person. The concept of a year is largely a construct of our minds to keep track of time; we could just as easily count time in 100-day increments or 3 years, given that most of our lives are not based on agriculture anymore. However, keeping track of time in years is useful because it gives us a reference frame, letting us compare our lives to a set point in the past, or to set goals for a set point in the future.

The practise of taking stock of the year that has been is great because we are naturally blind to change when it happens slowly. We are very bad at noticing gradual changes, so we will often be surprised that our hair looks longer or our body looks better than the past when we look at an old photo. Therefore, reviewing an entire year worth of moments and change will show you exactly how much we have experienced and grown. There will be many relationships and connections you’ve deepened, adventures you had forgotten about and much personal growth that seem so much healthier and more mature compared to your past self.

If that is the case for reviewing a year, then how about reviewing an entire decade? The close of a decade is a rare moment and ten years is a surprisingly long period of time when you really think about it. Some people reading this may be so young that they do not even know exactly what they were like or what happened ten years ago.

Look back on your past decade: how was it? Walk down memory lane in your head, through your journals and photo albums, reviewing and reflecting on how your life played out the past ten years.

  • What were some of the best and worst moments of each year?
  • What were the memorable moments and photos and stories?
  • What big events happened?
  • Where did you travel to?
  • What new skills or passions did you pick up on the way?
  • What new people came into your life and where are they now?
  • How have you grown in the past ten years?
  • What goals and dreams have you achieved in that time?
  • Most importantly: how happy are you now, and what things have contributed to your happiness/unhappiness?

You will be surprised to find the amount of content ten years can contain and how remarkable the amount of change is possible in ten years. It makes you wonder what the next decade has in store for you; what exciting journeys and meetings, what joys and sorrows, what growth and improvements await you?

Posted in Life & Happiness

Time Divided

Even though time is continuous, we like to think of think of time in segments.

The most basic unit is the year. Every time the Earth rotates once around the Sun, we take stock of the year gone by, while setting resolutions for the next year. Technically, whether it is 300 or 400 days, time has passed, yet we always mark changes by the number of years. For example, we use age as a marker of what stage of life we should be at (even if it is not a very accurate marker).

Another classic example is the four seasons. The making of accurate calendars and units of time was critical in the development of agriculture as it allowed us to plant many different crops with high efficiency and yield. In older times, people may have marked time by reminiscing what happened around the time of the last harvest while eating food made with ingredients harvested at that time.

Some segments are less regular, such as the last time you caught up with someone, or whenever you have a big life change such as moving cities. Some people may mark the chapters of life by the person they were dating at the time, or the stage of professional development, such as what year of university they were in.

Why do we obsessively divide time and remember our lives in artificial, bite-sized chunks? Our brains are very good at noticing patterns and change, but not so good when the changes are gradual and continuous (change blindness). Ergo, dividing up time into segments help us process the past.

It is hard to notice how much someone’s hair has grown if you see them every day. It is hard to notice how different you and your partner have become with time until a conflict arises. It is hard to notice how much we have grown and matured and changed without consciously reflecting from time to time.

Another interesting thing to consider is that what you use as a marker of time may suggest what you are prioritising. When you look back, what is the unit of time you use to divide your life? Is it the last time you moved cities? Your last boyfriend or girlfriend? Your last big trip? A moment where you came to an epiphany?

Whatever it is, it is a useful practice to periodically look back on all the segments that make up your life, such as by keeping a journal and reading it later. This will let you be more aware of how you are developing as a person and help you steer yourself in the general direction that you want your life to take you. At the very least, it is amusing to notice the subtle differences between the past and the present you.

Posted in Life & Happiness

Meaningful Gift

People have been giving gifts to each other since the dawn of time. It is a way we show that we care about someone by giving them something that we think they might like. There are many kinds of gifts, from sharing a snack, a flower from the side of the road, hard cash, a book, an expensive piece of jewellery or a heartfelt letter.

Even though we give and receive so many gifts – such as for birthdays, holidays and anniversaries – choosing the right gift is a difficult job. To give a good gift, you need to know the person’s needs and interests, have decent tastes and be original to some degree. Otherwise, you make the mistake of giving them something that they already have, will never use or find absolutely boring.

So what makes for a good gift? Some people may take the consumerist approach of giving an expensive gift, because it shows the other person how much they are worth to them. To practical people, the best gift may be something that the person needs at that moment, such as a new pencil case or furniture. Some may even say that they would rather give cash so the person can buy what they want instead of you having to guess it.

The problem with the above approaches is that they miss the point of gift-giving. The best gift is a gift that we got for someone because we sincerely wanted to – because we felt that this gift might bring a smile to the person receiving it. Gifts do not hold absolute value; they are not something you should treat like transactions, nor must they fulfil a certain purpose. They hold relative value, in that the value of the gift lies in how the person receiving it feels when they open it up.

For example, cash is useful, but it says nothing about how well you know someone. An expensive necklace is pretty, but anyone with enough money can buy it. If the person is financially stable, they can buy things that they need themselves. A small gift that makes the person feel special and loved is far more valuable than any jewellery.

Here are some alternative types of gifts if you cannot think of a decent gift.

The first are experiences. Money cannot buy happiness, but they can buy experiences that leave everlasting memories, such as a fancy dinner or skydiving.

The second are things that they would be hesitant or not consider buying for themselves, even if they would enjoy them. This may be an experience like above, such as a degustation, or an investment in to their hobby such as a better instrument or accessory.

Lastly, consider giving the gift of time. These are gifts that may not have much financial value, but they hold sentimental value and that require the investment of your own time. Examples include: a scrapbook of your special memories with that person, dedication of practising a performance for the person, or a mix of songs you think the person would enjoy. Because in our busy lives, the scarcest, most valuable resource is our time. By spending our precious free time to create something that celebrates our connection with the recipient of the gift, we can truly show how much we care about that person. It also ticks the box of being original and useful, because each connection is unique and they can be looked back on for nostalgia.

A gift is only as good as how the person feels when they receive it. Instead of showing how much you care through materialism, try showing how well you know them as a person and how much you value the connection that you share. A thoughtless gift is no better than not giving a gift at all.

(Image source: Puuung http://www.grafolio.com/puuung1)

Posted in Life & Happiness

The Luxury You Cannot Afford

The night sky looks darker than it is because the bright moon and stars offer contrast. Similarly, bright colours truly “pop” in a background of dark, simple tones. A tiny pinch of salt brings out deeper, sweeter flavours in chocolate milk and watermelon because it offers a contrast in tastes. Contrast allows us to experience something at a greater level.

Happiness is much the same. Some of our happiest memories are from when we enjoyed luxuries we could not afford. An example would be eating out at a nice restaurant when your budget is straining. You know that rationally, you should not be doing that as you need to save money, but emotionally, you know that this is one of the few cases where money really does buy happiness.

The greatest luxury we cannot afford most of the time, is time itself. All of us lead such busy lives that we lack the free time and energy to indulge in what we are passionate about: hobbies we enjoy, sleeping enough or spending time with people we love. However, this is exactly the time we need to set aside a small break. Ironically, the busier life gets, the more vital it becomes that you stop for a moment and take care of yourself.

Whether it be spending a couple hours having lunch with a friend, or sitting down for half an hour to write in your journal, or singing a song on your guitar for ten minutes, breaks are essential. Even if you feel like you cannot spare a single minute, take five minutes to sit down with a cup of coffee, not doing anything productive, just watching people passing by on the streets. Better yet, lie down on the grass and stare into the blue sky for a little while.

When you look back on your life in ten, twenty years’ time, you will not be savouring the moment of working twelve hours straight without food. You will reminisce on how you spent one evening away from studying to play board games with your friends, but still passed the exams because you were refreshed the next day and could study more effectively.

Happiness is not a grand achievement, but a state of mind. It cannot take root in an overworked soul that is torturing itself. Enjoying the luxury of a break when you think you have no time is one step towards breaking the miserable cycle that our busy lives place us in.

So go on, take five and treat yourself.

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Posted in Philosophy

Eternity

“High in the North in a land called Svithjod there is a mountain. It is a hundred miles long and a hundred miles high and once every thousand years a little bird comes to this mountain to sharpen its beak. When the mountain has thus been worn away a single day of eternity will have passed.”

~ Hendrik Willem van Loon

Posted in History & Literature

Free Lunch

In the late 19th century, there was a common tradition in American bars where they would offer a “free lunch” to people who purchased a drink. Although it seems like a good deal at face value, the lunches offered were quite salty, meaning that eating it will make you thirstier for another drink. On top of that, the price of the drinks would usually more than compensate for the price of lunch, while making the patron think he or she got a “free lunch”.

This is the free lunch referred to in the saying: “There ain’t no such thing as a free lunch”. Nothing in life is free. If someone tries to tempt you with a free product, there will no doubt be a string attached in one way or another, such as a hidden cost. To have something, you must trade in an equal amount of something, such as time, money or work, or take it from someone else. Because you cannot make something from nothing. Such is the way of the universe.

Every resource is finite, meaning that you must make choices on how to use these resources. Every decision comes with an opportunity cost – the cost of not being able to use your resources for a different outcome. If you have $2, you can buy a bag of chips or buy a drink, but you cannot have both.

The most useful application of this principle is time. When you procrastinate or leave your work to tomorrow, you are not having a “free lunch” in the sense of having free time to yourself. You are borrowing that time from the future, as you will no doubt pay the cost of having to work harder or end up with a less comfortable life.

If that is the case, then how are we supposed to have the time to keep ourselves happy, when we have so much work and so little time? Economically speaking, the only way you can have anything close to a free lunch is by improving your efficiency. By being efficient, you reduce the time you spend doing work and you can gain more happiness while investing less time. For example, instead of procrastinating watching television, if you engage in your favourite hobby and enter a flow state, you will achieve far greater happiness for the same amount of time.

Posted in Philosophy

A Ring For A King

There is a Persian poem that tells the story of a powerful king who ruled the Persian Empire. One day, he assembled a group of wise men and charged them with a task: make a ring that will make him happy when he is sad and make him sad when he is happy. The wise men were puzzled – was the king asking for some magic ring capable of changing his mood? After much pondering and deliberation, they came up with a solution. The wise men presented the king with a simple ring, with its only remarkable feature being words etched on the outside. Words that the king could read whenever he was tearful or joyful. The king read the words and was pleased. It said: “This too shall pass”.

(Image source: http://www.deviantart.com/art/Time-will-pass-212796344)

Posted in Science & Nature

Millions And Billions

Have you ever stopped and pondered what a million actually is? Sure, you might easily pass it off as the number 1,000,000, or a thousand thousands, but have you really tried to get your head around how big a number that is? For example, you may be able to visualise a hundred people, a thousand people or even tens of thousands of people in your head, but it is very hard to visualise an image of a million people.

Now consider this. When was a million seconds ago? You know a second is very short and a million is a very large number. But it is difficult to put the two together. Make a guess. Last year? Two months ago? Surprisingly, the answer is only a week and a half ago (11.6 days).
Then what about a billion seconds? A billion is a thousand million so you might think it is easy to just add some zeroes, but a billion seconds is 31.7 years ago. Just by changing one syllable, or adding three zeroes, we went from a scale of weeks to years. If we go one step further to a trillion seconds, you leap back in time 31,700 years. You can probably remember what happened a million seconds ago, you might not have even been born a billion seconds ago and our ancestors were still hunter-gatherers roaming Europe a trillion seconds ago. That is how mind-blowing the scale of large numbers can be.

Now let’s look at some other things to really understand how big a million and a billion can be. A million dollars (USD) could buy you a luxury house, a manufacturing line, a 41-acre island in Belize or over 200 years’ worth of coffee (if you drank two cups a day). A million dollars in $1 bills would weigh 1000kg and stack to 30 stories high. A billion dollars – even if you were to convert it into $100 bills – would weigh 10 tonnes, almost as heavy as the truck that would carry it.

The pitter-patter of raindrops on your face feels nice, but a million drops of water weighs 50kg and would break your neck. A billion red helium balloons would have enough lift to carry 14,000 tonnes – enough to lift a hundred small, two-storey houses up into the air. A million grains of rice will feed a person for almost two months, while a billion ants would weigh twice a standard car (3 tonnes total).

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(You should definitely check out Hank Green’s take on “a million seconds”, because everything is better if Hank Green is ranting about it! http://www.youtube.com/watch?v=cJ7A0yTDiqQ)

Posted in Philosophy

The Significance Of You

We are often reminded of how insignificant we are as individuals (or even as a race for that matter) in the grand scale of time and space in the universe. We are but a tiny, invisible dust particle on the map of the universe and we make up a sliver of time in the history of everything. This is a reminder that we should be humble, that no matter how great we think we are, we are nothing in the eye of the universe.

Then again, sometimes it is nice to remember that we are significant. Consider this. For you to have been born, generations after generation of couples have had to produce a child. You are the product of 4 billion years of evolution. 4 billion years of unbroken lineage, from the primordial ooze to bacteria to fish to amphibians to reptiles to rodents to primates. If even a single couple in that chain decided not to have an offspring, you would not be here reading this. Of course, this also puts you under the pressure that you may be the last one in that 4 billion-year chain not to reproduce, but let us ignore that for now.

Now consider the stars. When you look upon the night sky and see the twinkling of a star, what is happening is that photons (light particles) are hitting your retina and triggering a signal that is sent to your brain and interpreted as twinkling. Those photon generated by the star you see have travelled light years through the vast universe until your retinas rudely interrupted its journey. The closest star to us (excluding the sun) is Alpha Centauri, located 4.37 light years away. 1 light year (distance travelled by light in a year) is just under 10 trillion kilometres, meaning that those photons you blocked had travelled at least 41 trillion kilometres – or 41,343,392,165,178,100 metres. All you had to do was exist in a certain location and look up at the sky.

Some might say that you are puny and insignificant compared to this astronomical scale. But another way to think of it is that you effected real change in the universe (even if it was blocking a particle of light). No matter how small you are, no matter how short your life is compared to the history of the universe, you are not insignificant. Chaos theory (better known as the butterfly effect) dictates that even the smallest change in initial conditions can lead to unpredictable, widely diverging outcomes. For all you know, your existence is the difference between the existence of life on a distant planet somewhere.

So never say that you are insignificant. And if evolutionary biology and astrophysics is not enough to convince you, then look around you. The people you have met and interacted with throughout your life are affected by you in one way or another. For example, a compliment you paid in passing might completely change the person’s day. A simple act of kindness you thought nothing of could be recorded in someone’s life book as a life-changing event. Even a smile can make a difference. You are significant.

“If you could only sense how important you are to the lives of those you meet; how important you can be to the people you may never even dream of. There is something of yourself that you leave at every meeting with another person.” ~ Mr. Rogers

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