Posted in Science & Nature

## 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.

Posted in Science & Nature

## Metal

Next to the discovery of fire and the wheel, the discovery of metals and the mastery of metalworking was arguably one of the most important advances for prehistoric humanity. Metal was far superior to rock, clay, wood or any other natural resource known to man in terms of strength and sharpness. Because of these properties, metal soon became a valuable commodity. It can be seen how much impact metal had on humanity’s history, considering that the stages of human prehistory were named after the type of metal (or lack thereof) that was mastered then: Stone Age, Bronze Age and Iron Age.

The discovery of metal came in two ways.

One was through mining, where prehistoric people discovered that shiny, hard objects were buried in the ground. They later discovered that with enough heat, they could melt the metal out of ores (copper and tin were the first metals to be gathered this way) and mould them into any shape. After smelting technologies developed, our ancestors found that mixing copper and tin produced bronze – a much stiffer and more durable metal than either of its components. A mixture of metals is called an alloy. This was the start of the Bronze Age. Bronze was extremely useful and people quickly came up with innovative ways of using it, such as farming equipment and weapons.

Some other metals used during this age were: gold, silver, lead and mercury. It is likely that gold was one of the earliest metals used as it comes in pure nuggets and is easily workable thanks to its chemistry. However, given that gold is rather soft and was treated more as jewellery than a practical metal, it was not used as much to advance technology.

The second way mankind came upon metals was in the form of “gifts from the gods”. A prime example is iron. Although the Iron Age began around 1200BC at the earliest, there are iron objects (mainly jewelleries) that have been dated back to 5000BC. How could this be? This was before mankind had the technology to smelt iron ores (which is more difficult and needs much higher temperatures than copper or tin ores), so the iron could not have been gathered through mining. The answer to this conundrum lies in meteorites. About 6% of meteorites contain iron and nickel, which prehistoric civilisations may have stumbled onto and taken the shiny pieces back to their tribe. The people would have considered the gathered iron a “gift from the gods”, as it had crashed down from the “heavens”. Because of this reason, iron was considered more valuable than gold or silver and was frequently used for jewellery. This is reflected in Arthur C. Clarke’s science fiction short story, The Songs of Distant Earth, where sentient sea scorpions hoard metal objects stolen from the humans and wear it proudly as a badge of honour.

The history of iron and how it was believed to be a gift from the heavens relates to a common superstition of how finding a penny (or any coin) represents good luck. As “metal” (mainly iron) was considered a holy gift bestowed unto mankind, finding a piece of metal was believed to be a blessing and some form of protection against evil. This is also represented in various traditions such as hanging horseshoes over doorways and wearing charm bracelets with metal on it.

Although it sounds like a silly superstition, it clearly shows how metals have been an integral part of the development of civilisation.