One of the holy grails of horticulture is the blue rose. A variety of rose colours have been cultivated using various techniques such as hybridisation, ranging from the classic deep red to bright yellow, to even a mix of colours. However, there has never been a successful case of breeding blue roses.
This is why blue roses have become synonymous with the longing for attaining the impossible. It was a symbol of the Romanticism movement, representing the desire and striving for the infinite and unreachable; a dream that cannot be realised. The flower meaning for the blue rose is secret, unattainable love.
The reason why blue roses are impossible to produce naturally is that they do not have the gene for the protein that makes a blue hue. The biochemistry of flower colours is complex, but essentially, the blue colour seen in flowers such as pansies and butterfly peas is produced by the chemical delphinidin. Roses lack this pigment and only contain pigments that produce red and orange colours.
Because blue roses have always been deemed impossible, florists have had to resort to using blue dye on white roses to produce artificial blue roses. But this all changed with the introduction of genetic modification technology.
In 2005, scientists reported that they created the first true “blue rose”, by genetically engineering a white rose to produce delphinidin and using RNA interference to shut down all other colour production. However, the results were disappointing and the so-called “blue rose” turned out to be more of a mauve or lavender colour, due to the blue having a red tinge.
This is because rose petals are more acidic than true blue flowers such as pansies. Delphinidin is degraded by acid, meaning that you cannot produce the deep blue found in pansies in roses without finding a way to reduce the acidity. This chemical phenomenon can also be seen in hydrangeas, where the red and pink petals turn blue and violet when you acidify the soil that it is growing in.
Although we now harness powerful tools to modify nature in ways deemed impossible in the past, nature still proves to be tricky and elusive.
If there is one thing we learn about dinosaurs, it is that they were wiped off the face of the Earth by an asteroid impact. Another feasible theory is that a supervolcano eruption completely destroyed the ecosystem, wiping out all life on Earth by either directly destroying them via a massive shockwave (if they were within range), or by slowly starving them as the resultant plumes of smoke would have blotted out the sun for years. But interestingly, scientists looking back over some extinction-level events of the past, discovered signs of both an asteroid strike and a volcanic eruption. This sounds to be extremely implausible, as the odds of both happening in the same era are near impossible (unless there is some extremely vengeful deity that hated the dinosaurs).
One theory that tries to explain all of this is the verneshot theory. To better understand the concept of a verneshot, imagine a cartoon character such as Yosemite Sam (the beloved red-bearded, gunslinging cowboy character on Looney Toons) shooting his gun wildly into the sky. Cartoon logic dictates that his bullets will eventually fall back on some unwary bystander. Now imagine if the Earth did the same thing, but instead of a bullet it shoots a giant piece of rock capable of causing mass extinction into the sky.
A verneshot occurs in a similar way a supervolcano erupts, where there is an incredible build-up of super hot molten rock. A supervolcano would be when this molten rock erupts as lava. In the case of a verneshot, massive amounts of carbon dioxide build up instead, leading to a pressure build-up under the crust. When the pressure becomes too much, the crust explodes, with the piece (of indeterminate size) being rocketed into space. However, the giant rock does not end up in space. Instead, it is only launched to a sub-orbital altitude, meaning it will come crashing back down to Earth due to gravity. Thus, a verneshot is when a volcanic eruption acts as a giant cannon to launch a piece of the Earth into the sky, which falls back to Earth as an asteroid-like object.
Suppose that the woman is X and the man is Y. Firstly, X and Y need to be born as human beings. They cannot be born as a worm or an onion or something. Here, we will say that the total number of species is M and the population number of each species as P (technically this part is forcing it slightly, so we can skip it).
Although the two have to beat ridiculous odds just to start, just being born as human beings is not enough. One must be born with XX chromosomes to be a woman, and the other must be born with XY chromosomes to be a man.
Let us assume that the two were lucky enough to be born as a man and a woman. Next, they must live in the same space. If one lives in some Korean city and the other lives in some American rural village, it is unlikely the two will ever meet.
Even if they did live in the same place, X and Y must have subjective qualities that the other person finds attractive. If they are not interested in each other, nothing will happen even if they did meet. By this stage, we have clearly gone past the scopes of mathematics.
Then let us assume that a man and a woman, who fit each other perfectly and born as people, are living in the same space. We are still missing one variable: time. Even if we took only the 5000 years that civilisations have existed, the odds of the two being born in the same era as similar ages is less than 0.001%.
Species, sex, space, time… Statistically speaking, the chances of a man and a woman beating all of these odds to establish a perfect couple seem nearly impossible. But we can clearly see that “true love” exists all around us. Numbers are just numbers. If you find a person that makes your heart skip a beat when your eyes meet, that makes you feel that the more you get to know them, the more you think you cannot live without them; in essence a person that makes you think “this person is The One”, do not let the person slip away. The scenario of you and that person existing on the same space-time and loving each other is something that verges on the impossible.
There is no treasure as rare as true love. If you have found true love, or believe that you have found it, fight to seize it and do everything in your power to protect it. That is the greatest accomplishment you can make in life.
The city of Königsberg (capital of Prussia, now Kaliningrad, Russia) has the Pregel River running through the middle, with islands at the centre of the river connected by seven bridges. Is it possible to cross all of these bridges while only crossing them only once each?
If you try to solve this problem, you soon discover that it is incredibly difficult not to cross the same bridge twice. But it is difficult to tackle this problem in a brute force manner. To calculate all of the permutations in the order of bridges, you use 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040, meaning that there are 5040 possible arrangements of bridges. Then how can you prove if the problem is solvable or not?
The great mathematician Leonhard Euler, upon being asked to solve the problem, is reported to have said that the problem is impossibleto solve on the spot. In 1735, he proved his answer by modelling the seven bridges of Königsberg in a diagram of four dots connected by lines (representing the bridges).
By using this model, the problem is converted into a “draw in one stroke” problem, which is also called a Euler walk to honour Euler’s contributions. Euler discovered many properties and laws regarding such problems. If a certain point is the starting point, then the line must first leave the point, then even if it comes back to the point, it must leave again. Ergo, the starting point must have an odd number of lines connected to it. The opposite applies to the ending point, where a line must enter the point, and if it leaves the point it must come back to it. Ergo, the ending point must also have an odd number of lines connected to it. In the case of a Euler walk, the starting and ending points are identical, so the number of lines is the sum of two odd numbers, making it an even number. Thus, to find out whether a picture can be drawn using one line, use the following laws:
If there are no points of odd degree (odd number of lines), the starting and ending points are identical.
If there are two points of odd degree, the starting and ending points are different.
If there are one of more than two points of odd degree, it is impossible to draw using one stroke.
Thus, a Euler walk is only possible if there are 0 or 2 points of odd degree. Looking at the seven bridges of Königsberg problem, we can see that A is connected to 5 lines and B, C and D are connected to 3 lines each. As there are four points of odd degree, we have thus proved that it is impossible to draw a path that crosses all the bridges while not crossing any bridge more than once.
There once lived a community of mice in the attic of a house. The mice would sneak into kitchens, gnaw holes in the walls and run about freely. The owners were so fed up that they brought in a cat, causing the mice to all hide in fear. The terrified mice eventually held a meeting to discuss how they would sneak around the house without getting caught by the cat. One mouse suggested: “What if we put a bell around the neck of the cat? Then we can hear it coming and run away.”. The mice unanimously agreed that it was a brilliant idea. However, when they came to decide who would bell the cat, no mouse was brave enough to step forward and the plan was never carried out.
What would actually happen if a cat was belled? Without a doubt, the cat would take it as a cruel, cruel punishment. Not because it cannot catch mice, but because the sound of the bell ringing every time it moves will be extremely loud for the cat. A cat’s hearing is six times better than a human’s. With this excellent hearing, the constant sound of bells attacking its eardrums would be physical torture for the cat.
Furthermore, a cat can hear frequencies as high as 40,000Hz. A person can only hear up to 20,000Hz, meaning a cat hears over twice the range of sounds we can. This combined with the boosted volume results in the cat living in a very noisy world. Ergo, putting a bell around a cat’s neck is an extremely atrocious thing to do.
Author Bernard Werber (the inspiration for this Encyclopaedia) posited the following theory: if we could see the future, would we not actively build towards a better future? Imagine a tree soaring high into the sky, stretching countless branches in all directions. The many branches of the tree branch off into smaller branches, which branch into even more smaller branches. At the end of each branch, there hangs a leaf. This tree is not a normal tree; it is a Tree of Possibilities that represents the flow of time from the beginning of the universe to the distant future. Each split in a branch represents the creation of two different futures due to a choice or a change, while a leaf represents the final future created from the cumulative effects of these changes. Thus, the Tree of Possibilities is the ultimate crystal ball showing all the pasts that could have been and all the futures that can happen.
Of course the Tree of Possibilities is a fictional model created in our imaginations. But what if we could actually make this tree? First, we would create an organisation of the greatest scientists, mathematicians, sociologists, psychologists, historians, philosophers, science fiction writers etcetera that represent the many fields of knowledge. These people are gathered in a location far from the reaches of governments and the media, where they can discuss without any interference. These specialists will debate over all sorts of topics, amalgamating their knowledge and intuition to generate a tree diagram as mentioned above. This is a diagram free from ethics, morals, laws, optimism, pessimism and individualism – the ultimate objective view of all possible futures that humanity and the Earth may face. The experts may agree with each other at times and disagree at times. There is ample possibility that their postulations are wrong. But none of these matter. The important point is not that the Tree is “accurate” or not, but that it is an extensive scenario database of all the paths humanity can walk on towards the future.
The Tree of Possibilities will have various conjectures such as: What if nuclear war broke out? What if artificial intelligence is perfected? What if chimpanzees reach the intelligence levels of human beings? What if we build cities on the Moon? However, the future is altered much more easily that you would think. Thus, there will also be branches representing much more trivial and ordinary (even bizarre) postulations as well: What if smoking is banned? What if the average age women gave birth is older? What if rhinoceroses were domesticated pets? What if pianos do not exist?
On analysing these numerous postulations, a branch bearing the leaf with the ideal future will be found. Ergo, we can choose to follow a path of least resistance, where all the choices we make will ultimately lead to that ideal future. Essentially, the Tree of Possibilities is a tool that is used to predict the future. However, it is not “fortune telling” as it is based on logic rather than magic and divinity to see into the future. The future the Tree tells is not a set “destiny”, but rather one “possibility”. Thus, instead of fearing the future like we do with fortunes, we would instead feel excitement over the potential of finding the ideal future. If the path we are currently on is fated to an unhappy ending, then we can simply jump onto a different path with the guidance of the Tree. Unlike fortune telling, which destroys all uncertainty and any other possibilities in the future, the Tree of Possibilities provides humanity with the greatest gift: dreams of a better future.
As you could imagine, the possibilities of the future are infinite so a drawn-out diagram of the Tree of Possibilities would take up extensive amounts of space. Ergo, the ideal form of the Tree of Possibilities would be a computer program. As computer programs only need sufficient storage space, it provides a perfect environment in which the Tree may grow. The program would generate a Tree based on the information provided by the scholars, drawing out each branch and leaf, while also calculating the effects of any action on each of the possible futures. If we further applied the engine used in chess programs to predict the next few moves, then we may be able to create a program that can calculate the ideal future and the path of least resistance for humanity.
My ideal future is this. There is an isolated island, far from any interference, with a large building. At the centre of this building, there lies a supercomputer running The Tree of Possibilities. The computer is surrounded by lecture theatres, conference rooms and residential areas. Thus, specialists of each field may come to stay and use their knowledge to water the Tree and foster it. This island will provide humanity with hopes and dreams, leading them towards the best possible future based on logic and imagination.
The Tree of Possibilities will radically change our day-to-day lives. One of the greatest weaknesses of human beings is the inability to see the long-term happiness and sacrificing it for short-term gain. However, if we were able to see precisely how our actions will affect the future, then would we not act differently? Armed with insight and foresight, people will understand what is best for the future, and instead of the current near-sighted attitude of only seeing the gain right before our eyes, they will act in the best interests of their children and grandchildren. Politicians will see how useless bickering over trifling issues is and instead focus on policies that take a while to show the effects (yet nonetheless important), such as environmental conservation. The Tree of Possibilities will help us make rational decisions to create a world that the future generation will be happy living in, without being swayed by emotions and selfish greed. And so, we will build towards a utopia.
The greatest weapon a person has is imagination that can build the future.
In 450 BC, a Greek philosopher named Zeno thought of the following paradox. Let us imagine that Achilles and a tortoise were to have a footrace. Achilles, obvious being faster than the tortoise, allows the tortoise to have a head start of 100 metres. Once the race starts, Achilles will quickly catch up to the tortoise. However, within the time he took to cover the distance, the tortoise would have travelled some distance as well (say 10 metres). When Achilles runs the 10m to catch up again, the tortoise has once again toddled on another metre. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Because there are an infinite number of points Achilles must reach where the tortoise has already been, theoretically the tortoise will be ahead of Achilles for eternity.
According to this thought experiment, motion is paradoxical and theoretically impossible. However, we know for a fact that motion happens. So how can we break Zeno’s paradox?
The main flaw of Zeno’s paradox is that he uses the concept of “eternity”. If we record the story mathematically, the time taken for Achilles to run the footrace is (if it took him 10 seconds to run 100m): 10 + 1 + 0.1 + 0.01 + 0.001… = 11.111… Ergo, the tortoise is only ahead of Achilles for less than 11.2 seconds (rounded). After 11.2 seconds pass, the time passed exceeds the sum of the infinite series and the paradox no longer applies.
Although it is a flawed paradox, the story of Achilles and the tortoise teaches the concept of geometric series – that something finite can be divided an infinite amount of times. For example, 1 = ½ + ¼ + 1/8 + 1/16… ad infinitum. This principle is a crucial part of mathematics and has significant implications in the field of economics. For example, it can be used to calculate the value of money in the future, which is necessary for working out mortgage payments and investment returns. Perhaps it is because of this mathematical principle that it seemingly takes an infinite amount of time to pay off a mortgage.
Zeno’s paradox teaches us that one should not take the concept of infinity for granted.
Is time travel possible? In 1943, a science fiction writer called René Barjavel posited the following paradox.
A man travels back to the past and kills his biological grandfather before he meets his grandmother. Thus, his grandparents would not have sired a son (the man’s father) or daughter (mother), which then suggests the man could not have been conceived. If so, who killed the grandfather? As there was no one to kill the grandfather, he would have had a child and the man would ultimately be born, travelling back to the past and killing his grandfather. This paradox suggests that time travel is impossible.
Some people use the parallel universe theory to argue against the paradox. They suggest that as soon as the man travels to the past to kill his grandfather, an alternate universe is created where the grandmother meets a different man and the course of time is changed. This is a valid theory but the grandfather paradox still holds strong in disproving time travel. However, the grandfather paradox only states that travelling back in time is impossible; it says nothing about time travelling to the future.
Have you ever had a moment when something so unbelievable, so improbable that you never would have imagined it would happen, happened? When something you could only dream of actually happened in real life? When something so impossible that you must have stepped into a parallel universe for that thing to happen? The feeling that such a moment brings is indescribable.
Success is not about money and power. Success is not a product of luck. To become successful, one must change their state of mind first. The most crucial thing to understand is that the only limit is that there are no limits. Only when you dare to go past what is possible will you attain anything worthwhile. “To the impossible?” you may ask. No, true success lies beyond the impossible. A place where the possible and the impossible meet to become: the possimpible. Only when you have become the master of the possimpible will you be able to confidently say that you have succeeded in life.