“One plus one is three. When a person meets another person, three things are established: co-operation, understanding and solidarity.” ~ Edmond Wells (featuring in works by Bernard Werber)
Through this magnificent equation, society and nature alike evolve as two things come together to form something even greater than the sum of themselves.
Only those who can transcend the hard, absolute mathematical logic of 1 + 1 = 2 and appreciate the beautiful philosophy of 1 + 1 = 3 can live life to the fullest and deepen their thoughts.
1. Let a and b be equal non-zero quantities
a = b
2. Multiply by a
a = ab²
3. Subtract b²
a² – b² = ab – b²
4. Factor both sides
(a – b)(a + b) = b(a – b)
5. Divide out (a – b)
a + b = b
6. Observing that a = b
b + b = b
7. Combine like terms on the left
2b = b
8. Divide by b
2 = 1
9. Add 1 to each side and flip over equation
1 + 1 = 3
Q.E.D. (Thus we have proved)
How is this proof possible?
The source of the fallacy is the fifth step, where (a – b) is divided out.
As a = b, a – b = 0, and dividing by zero is impossible in mathematics.
One of the key characteristics of social animals is the act of helping other members of the society. People often think that nature is ruled by “the survival of the fittest” and selfishness for survival, but societies are common in the animal kingdom. For example, even insects, that people consider “inferior”, such as ants build massive empires and cities, forming an unbelievably intricate and efficient society.
In the wild, all animals must find food to live, but due to competition and the environmental conditions, there are days when an animal cannot find enough food. For times like this, ants have a second communal stomach which they fill with leftover food after a meal. They then approach a hungry colony member and offers it a meal. If the other ant accepts, the two ants then lock their mouths together and one ant brings up the food in the communal stomach into the other ant’s mouth. Benefaction such as this allows for a smooth functioning of the society.
There is another role of trophallaxis (the transfer of nutrients via the mouth-to-mouth route described above): communication. Ants rub their antennae together to identify each other’s pheromones, which acts as identification such as what colony they are from and their role in the colony. Some scholars suggest that trophallaxis is the origin of the kiss.
The act of offering pre-stored food to comrades is also found in vertebrates such as birds and bats. For instance, some species of birds feed, return to its nest and then vomits the food for the young to feed on.
Helping those in need to create an efficient and functional society, and reaping the rewards of quid pro quo: that is the way of the philosophy of 1 + 1 = 3.
- There are 6 matchsticks. Make 4 identical, equilateral triangles.
The hint is that you must think differently to everyone else. If you think like everyone else, you will never find the solution.
- There are 6 matchsticks. Make 6 identical, equilateral triangles.
The hint this time is quite the opposite the first puzzle: think like everyone else.
- There are 6 matchsticks. Make 8 identical, equilateral triangles.
The hint for this puzzle is that you must reflect on yourself.
Answers after the break.
Continue reading “Matchsticks”
In 1920, a candy store owner by the name of Christian Kent Nelson had a customer. The customer was a young boy who was torn between buying ice cream or chocolate, with only enough money to buy one. Nelson noticed this and decided there was only way to solve this conundrum.
He created a bar of ice cream coated by melted chocolate, which he called “I-Scream Bars”, now known as Eskimo Pies. It was an instant hit as children could buy both chocolate and ice cream for the same amount of money.
1 + 1 = 3
According to the ancient writings of Chinese author Han Feizi, a dragon is a gentle creature that a man can tame and even ride on the back of. However, one must be extremely cautious of the inverted scale on the neck of the dragon. Touching this scale will cause the dragon to become enraged, immediately killing the person.
Any person has strengths and weaknesses. Some people love to draw out another person’s weakness and are deluded that finding a person’s greatest weakness is a victory. But in human relationships, touching another person’s “inverted scale” can be a critical mistake. Who would want to deal with a person that prods at their weakness? Even during a heated debate, attacking the opponent serves no purpose and is only a destructive act. This kind of dirty move may bring you short-term “victory”, but in the long-term it can cause you to be forever alone. No matter how gentle the person may be, picking on something they are sensitive about may cause them to strike down with great vengeance and furious anger upon you.
The wisdom of the anecdote of the dragon’s scale can also be applied to how people should treat those below them. Whatever your position may be, making fun of your staff’s weaknesses will lead to the loss of trust and respect from them. Sun Tzu’s The Art of War teaches that a general must never attack a soldier’s faults but rather show wisdom in helping the soldier fix the problem on their own.
Lastly, when persuading another person, instead of speaking of their weaknesses, bring up their strengths. Avoiding the “inverted scale” is one of the most important skills in the art of persuasion.
The most important aspect of relationships is following the philosophy of 1 + 1 = 3 by co-operating and having a constructive meeting. A destructive person that attacks others can never progress.
Early economists believed that a growing economy was a sound economy. Growth was used as a ruler to measure the health of the nation, corporations, markets and all social constructs. But it is impossible to always move forwards. In reality, a growing economy goes through cycles of growth and depression, showing a waveform on a graph. An economy without depression forms a bubble that will burst in the future, bringing a greater economic crisis. Simply put, “sound economic growth” is only achieved by the concept of two steps forward, one step back.
We have reached a point where we cannot grow despite having the potential to. Perhaps there will be no further economic growth. Only a continuous state of balancing powers will remain. A sound society, a sound nation, a sound worker… those are things that do not damage the surrounding environment or become damaged by it. We should no longer try to conquer nature and space. Instead, we must integrate with nature and the universe. Our only slogan is harmony. There should be an entwining of the external and internal world and we must live with modesty not violence. Human beings will become one with the universe. Mankind will meet an age of stability where we do not strive for the future or reach for faraway goals. Mankind will live a simple life in the present. Only then will mankind finally attain happiness.
1 + 1 = 3
(from The Encyclopaedia of Relative and Absolute Knowledge by Bernard Werber)
It takes two hands to clap. No matter how great a plan you have, you cannot achieve anything by yourself. That is why we search so desperately for someone to slap our hand palm-to-palm. But this idiom has many meanings. Just as we cannot clap with one hand, when two hands miss or move away from each other, there is no clap. If two people want to achieve something then they must co-operate to produce synergy. But does that mean we can just carelessly clash our palms together?
If you clap with each hand as stiff as a board, it only hurts both people’s hands and produces a dull, bad sound. But if you loosen your hands a little and slap with a smooth motion, you get a clear, awesome sound. When two people act stubbornly and only stick to each other’s opinions and pride, they will achieve nothing and instead hurt their friendship, possibly even resulting in utter failure. To bend a little and give way to the other person – that is how two people can produce co-operation, understanding and connection. That is the secret to grasping the philosophy of 1 + 1 = 3.
1 + 1 = 3
(NB: The picture is from the basketball manga Slam Dunk where the two protagonists pull off one of the most epic high fives in fictional history. If you recognise it, you are awesome.)
Can you describe a reed that sways and bends to and fro in the face of wind as strong? Most people associate the word “strong” with something like a tree that stands tall and grand, never bowing to the will of the wind. However, the reed teaches us the important lesson of the strength of flexibility. When a storm strikes, what is left behind are not strips of reed but smashed pieces of wood.
A rigid tree appears strong because it stands so tall and does not move, but in the face of strong winds the opposite happens. As a tree does not bend much, it must face the full force of the wind and ultimately the tree snaps when there is sufficient force. On the other hand, the reed flows and bends in the direction of the wind, deflecting the force away. Not only that, but a reed has both flexibility and elasticity, meaning no matter how much they are bent and beat down, they can stand back up. Ergo, flexibility is stronger than rigidity. Skyscrapers use this concept and they are designed to sway on a windy day. The philosophy is also adopted in martial arts, with deflecting a strike to the side being a far more effective defence than taking the force of the strike directly.
Flexibility has far greater implications than withstanding the wind or a strike. The most important example is personal relationships. A person who never bends and sticks to their opinions may deem themselves “tough”, but they are in fact just a stubborn idiot drowning in a pool of arrogance. Sure, if it is a very important debate then you should stand your ground and state your opinions, but in a normal conversation it is just foolish to angrily state that you are right and never back down. It is far wiser to be flexible like a reed and meet the other person halfway, bending slightly to see their opinions and reach a peaceful agreement. If you stand tall like a tree you will end up standing alone on the same spot forever, but if you can bend to the other person’s flow like a reed, you can have a healthy relationship with them and co-operate. If both sides bend a little for each other, then they can have a smooth conversation and be able to establish co-operation, understanding and solidarity. Flexibility makes both you and the other person happy and allow for co-existence – something that is inevitable in human societies.
The tree may tease and mock the reed for its apparent helplessness and docility against the wind, but after the storm has passed, only the reed still stands. Remember this: instead of ignoring another person’s views and repeating the same words over and over, listening carefully to the other person and being flexible and tolerant is a far wiser and braver act. A wise man is someone who possesses the wisdom and benevolence of being flexible like the reed.
1 + 1 = 3
The power of vibration is incredible. Vibration allows a microwave to heat food and causes cities to be destroyed by earthquakes. The most interesting feature of vibrations is resonance, where a vibration of certain frequency greatly amplifies the vibration of another object. Every object has a natural oscillating frequency and when another wave of the same frequency hits the object, the oscillation suddenly amplifies and resonance occurs.
The best example for resonance is a swing. If you push a person on a swing at the same frequency as the swing’s natural frequency, you can achieve a much greater height than from pushing at any other frequency. Resonance can also be used to shatter a glass with only sound, by singing a sustained note at the same frequency as the glass’ natural frequency.
Resonance is how two things combine to create an even greater force.
1 + 1 = 3