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Riemann Zeta Function

Imagine a sum that keeps getting bigger: 1 + 2 + 3 + 4 + ... but somehow, its "value" is said to be  \[1+2+3+4+5… = -\frac{1}{12}\] This equation isn’t a joke. It isn’t a typo. And it definitely isn’t like one of those internet tricks that try to prove that 2 = 3. But how? Doesn’t calculus dictate that the sum should diverge? How can an infinite sum of positive integers result in a negative fraction? This equation is one of the paradoxical results of the famed Riemann Zeta function: \[\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}\] First Encounters My first encounter of the Riemann Zeta function was in a problem introduced to me in Math circle India:\(\newline\)               What is the probability that two random numbers x & y are coprime i.e. gcd(x,y) = 1 for \(  x,y \in \mathbb N\) At first glance, it seems like an impossible question to compute. We’re picking 2 numbers at random — how do you even define a probability over an...

Has Doomsday Arrived?


2021 was Earth’s fifth-hottest year, scientists say
January 11, 2022- Indian Express

UN agency confirms record 38 degrees Celsius heat for the Arctic
December 14, 2021- Indian Express

Arctic thaw threatens human habitation
January 12, 2022- BBC News

Climate change: For 25th year in a row, Greenland ice sheet shrinks
Friday, January 07, 2022- UN News

Polar bear population decline a wake up call for climate change action
WWF (World Wide Fund for Nature)

The above headlines give you a grim picture of the sad situation that our planet is in. These are just  a few of many such that. Have been emboldened across newspapers and yet, humanity has still not woken up.

Global warming IS a WORLD ISSUE. No! It’s not just the unlucky eskimo whose house keeps melting it is an issue for you and me too. We all like to live with technology, electricity, go on rides in cars, and much more so why shouldn’t we too shoulder the blame of global warming? Every single person on the planet is responsible for global warming. Every single person also suffers the consequence. Melting of ice-caps cause sea levels to rise. Hotter and drier climates cause forest fires. Water bodies that we are dependent on evaporate away do the the change in climate.

 

How

Global warming is happening because of pollution, but how? You’ve been told that AC’s and Refrigerators cause cause global warming but they are cool aren’t they so how do they heat the planet? The greenhouse effect is named after greenhouses for a reason. Greenhouses are designed such that light and heat can enter the green house but it gets trapped by the glass panels heating up the greenhouse. The same thing is happening with the Earth. Gasses like carbon dioxide, methane, nitrous oxide, chlorofluorocarbons CFC’s, etc. (the greenhouse gasses) form a layer in the atmosphere that does the same thing as the glass panels in the greenhouse. It traps the heat from the sun. Over the years, due to pollution, more and more greenhouse gasses have been produced trapping more heat than ever in the Earth’s atmosphere.

The animal husbandry sector is another major source of carbon emissions that is often neglected. In the year 2020, cattle released the methane equivalent of 3.1 gigatonnes of carbon dioxide into the atmosphere (plus a tiny amount from farting). Though even humans often fart and burp methane, it doesn’t cause as much of an effect because we do it on a much smaller scale. This is mainly because of the cow’s diet along with its gastronomic system. This can easily be solved much like human farts, by changing the cow’s diet to eliminate methane and carbon emissions.

In the year 2022, the globe relies on energy to power houses, telecommunication, laptops, computers, mobile phones, cities, agriculture, and practically every aspect of our life. Coal power plants provide a majority of that power. Even though it doesn’t look like it, our energy production is wildly inefficient. We practically burn fossil fuels or even exploit a large energy resource such as nuclear fission to boil water which makes steam that then rotates a rotor(fan). This is how humans create electricity and it is a huge toll on the environment. Not only does it create a lot of pollution, but because our energy production is so inefficient we seem to have to cause a lot of pollution. There are certain renewable energy options that can help us reduce our reliance on fossil fuels. Due to them being weather sensitive, we'd need more batteries than the world now has in order to to power everything on days when the weather isn't conducive for generating electricity.

THE GLORY DAYS ARE OVER

A recent theory is that the covid 19 pandemic was caused due to global warming. There is a layer of ice in the Earth called the permafrost which has preserved many ancient pathogens and organisms. Due to global warming the permafrost is melting. The theory states that covid 19 is an ancient pathogen that was released due to the thawing of the ice. We do not know how many such pathogens can be released due to further global warming. Global warming causes yet another serious problem, the thawing of the arctic ice. Aww… poor polar bears and sea-lions…. No! Wait! The melting of the arctic ice also affects you! The arctic ice plays a major role in the Earth’s climate. Due to its white colour, the arctic ice cover reflects back most of the sun’s light whereas black absorbs 99% of heat from the sun. Since 1980, the summer Arctic cover has decreased about 40% exposing dark shades of oceans and rocks. This is heating up the planet exponentially. The ice has melted, now what? The water levels rise of course. This is a serious problem for coastal cities and villages. R.I.P. Netherlands, we shall surely miss you. Apart from countries that are already under sea level, major cities like London and Mumbai stand the risk of being flooded.
Not only humans but even animals suffer because of global warming. Forest fires caused by hotter and dryer climates cost the homes of hundreds of animals. Many arctic animals that depend on the sea ice as a home are unable to survive do to its thawing. The Earth’s climate has exponentially changed earlier too but because it was the work of nature, the climate changed in a gradual manner. This allowed flora and fauna to adapt to the change in temperature. Because the warming of the Earth in recent years is very fast, animals and plants that cannot adopt go extinct.

One of the first examples of animals going extinct due to global warming is golden toads. This species of toad went extinct in 1989.

The Adelie penguins are a penguin species that inhabit the whole coast of the Antarctic continent—it is in fact their only habitat. They feed on krill that take refuge under the ice sheets and feed off algae. The krill population is dwindling as the ice sheets of the Antarctic is melting off, and so the penguins have to travel out of their natural habitats in search of food.
This causes them to lose energy—if they even succeed without dying—that could have been used in breeding and caring for their offspring. As a result they lose some of their young. Over all, the population of Adelie penguins is at the brink of extinction.

“The largest coral reef in the world, Australia’s Great Barrier Reef has not been spared the effects of global warming. Widespread coral bleaching caused by increases in sea surface temperature have become more frequent in the past few years. If global warming continues unchecked, it is estimated that the sea surface temperature could rise by 2 to 6*C (3.5 to 10*F). There is also an alarming prediction that this World Heritage designated site could be decimated by 2050 losing more than 90% of its living coral.”

Global Warming Witness
    National Geographic Magazine (June 2007)THERE IS HOPE

THERE IS HOPE

All of the past pages  have painted a grim picture of the state of the Earth due to Anthropogenic activities. In the drive to further our civilisation, we have been exploiting mother Earth and her resources. The fuel (literally) of our civilisation is electricity. Most of it is produced by burning fossil fuels of natural oils. This polluted the Earth and because of the greenhouse effect, heated it up. Now, we can’t fly up in the air with a giant vaccum cleaner and suck up all the greenhouse gasses but we can reduce the emissions that we make. 

There is ongoing research into nuclear fusion energy with the goal of making it so energy efficient that a single glass of seawater can provide as much energy as a barrel of oil with minimal environmental impact. Though this appears to be the answer to all of our problems, the catch is that it is unproven, and research to develop working reactors is a $10 billion gamble that the world is not yet ready to accept because we don't even have a working prototype. 

Many experts feel that rather than trying to develop a whole new renewable energy source, we can improve the efficiency of the ones we already have. The most used of these is hydroelectric power because it can produce the most electricity. This renewable energy just doesn’t seem that renewable anymore due to the fact that we used it to its saturation point. A famous example of this is the Colorado River near Las Vegas. Because it is such a huge river, humans exploited it for their own good. They built 15 dams on the main river and hundreds of more on its tributaries. What was once a great river, now has dried up because of over use. This will be the case in many rivers around the world if we continue hydroelectric power on a large scale. Although, if we use micro hydroelectric power, small rotors instead of dams, the process could be more sustainable. One of the major problems in relying on solar and wind energy sources is that the generation of electricity is dependent on weather. For solar panels, cloudy days would cause a problem. For windmills, the shortcoming is days with no wind. A planned combination of renewable power (Windmill with Solar Panel Blades) generation with wind and solar farms generating power during their favourable times and temporary shortfall managed through planned storage with additional power generated through the use of biomass at point of consumption can help us drastically cut our reliance on non-renewable fossil fuels for our power needs.
 

As for the effects of climate change that we have brought unto ourselves, with the most prominent one being sea levels rising, we have to deal with it. As earlier stated, many countries may flood due to the rise in sea levels. One country that has dealt with it before is Netherlands. Due to most of it being under the sea level and also lying along the delta of three major European rivers, Netherland received oceanic floods that killed thousands. Due to this, Netherlands started developing flood prevention system called delta works. It is the most sophisticated flood prevention project on the planet. They first used dams to block the estuaries near the mouth of the delta where flood water could surge inland. These estuaries were transformed into lakes that served as nature reserves. Next for the passage which used for all shipping into the countries docks, they had to make a mobile flood prevention to preserve the passage. They created the Maeslantkering, the largest moving structure on Earth to act as a barricade that could be closed during floods and opened at other times.

After the success of its own flood prevention system, Netherlands is working on helping other countries that are under the threat of flood to cope with the 30 million cubic km more water in the sea that would happen if global warming continues.


 

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