Category: Science & Nature

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Golden Ratio

Posted on by Jinavie

The golden ratio is a magical number that divides a line into the most beautiful ratio. It bestows a mystical power in an object and allows for the creation of excellent architecture and art.
This magical ratio is (1 + √5)/2, or 1.618033988. If there is a line divided by the golden ratio called a + b, then b:a and a:(a + b) are both the same ratio.

We can find the golden ratio in countless values seen in animals and plants. A snail shell’s golden spiral allows for the snail to grow without changing shape, while the distribution of branches on a tree also follows the ratio. The golden ratio controls everything from the spiral pattern of galaxies to the pattern of our brain waves. The golden ratio is the law of the universe.

Using this magical ratio, we can find the most beautiful composition of a human being. The Venus of Milo, considered as one of the most beautiful figures in history, has a ratio of 1:1.618 between her upper and lower body (divided at the belly button) – the golden ratio. The same can be said for the ratio between the head and neck compared to the rest of the upper body, and the length from the belly button to the knee compared to the length below the knee. The exact same composition was used to construct the statue of Doryphoros, one of the most famous examples of ancient Greek sculptures. The diagram that illustrates these ratios is the Vitruvian Man by Leonardo da Vinci (Vitruvius was a Roman architect who utilised the ancient Greek knowledge of applying the proportions of a human being, i.e. the golden ratio, in constructing temples). 

The Great Pyramids of Giza, Solomon’s Temple and the Parthenon are all partially constructed according to the golden ratio. It is said that buildings constructed outside of the golden ratio will collapse over time. The same is seen in Eastern constructions, such as buildings and inventions from the Goryeo Dynasty of Korea. 

Interestingly, the golden ratio applies to intangible objects as well. For example, Chopin’s Nocturne pieces tend to climax at the point of the golden ratio (roughly two-thirds in). The ratio is still used in modern day design, with the standard credit card size being the best example.

The golden ratio is an eternal beauty that does not go out of fashion with time.

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Euclidean Geometry

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In 300BC, a Greek mathematician called Euclid wrote a series of texts called Elements. The Elements was a textbook that outlined many principles of mathematics (especially geometry) and it would become one of the most influential works in the history of mathematics. It is composed of a series of axioms (the axiomatic approach) from which many deductions and theorems can be made. Although many of these axioms sound extremely simple and like common sense, the implications are staggering.

The following is Euclid’s Five Postulates of Plane Geometry:

  1. Two points determine a line. 
  2. Any line segment can be extended in a straight line as far as desired, in either direction. 
  3. Given any length and any point, a circle can be drawn having the length as radius and that point as centre. 
  4. All right angles are congruent (can be superimposed). 
  5. Parallel postulate: If two lines intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side, if extended far enough. 

Using these postulates, mathematicians are able to deduce more advanced theories. For example, the Elements also describes the famous Pythagorean theorem, which states that “in any right triangle, the area of the square of the hypotenuse (the diagonal) is equal to the sum of the areas of the squares of the other two sides” (a² + b² = c²).

Thanks to Euclid’s works, we are now able to accurately model and measure the three-dimensional space around us. Not only did Euclid set the foundations for mathematics, his works were also instrumental in the development of logic and modern science.

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Badass Weapons Of Nature: Mantis Shrimp

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In April 1998, a shrimp by the name of Tyson punched through the quarter-inch-thick glass of his cell and attempted an escape. He was promptly caught and had to be sent to a more secure facility. Unlike his boxing counterpart, Tyson was merely 10 centimetres in length.
Mantis shrimp are well-known for their “fists of fury” – officially the fastest punch in the natural world.

Their weapons of choice are their clubs that can be retracted and folded under their head. Using a remarkable energy-storage system – much like the cocking mechanism of a gun combined with a spring – the mantis shrimp can unleash its rounded, stubby claws at a speed of 80km/h to hit its target in 0.003 seconds. This is an amazing feat given that it happens underwater, where the water puts up a significantly higher resistance compared to air. The acceleration needed to produce this awesome punch is 10,000 times the force of gravity (similar to a bullet). In simpler words, researchers could not film using high-speed cameras and needed to borrow a super high-speed camera just to see the punch happen. 

However, the surprises do not end here. Researchers soon found that each strike by the mantis shrimp not only inflicted heavy physical damage, but the sheer speed of the punch created cavitation (implosion of bubbles). Much like the pistol shrimp, this cavitation releases massive amounts of light and heat energy. This shockwave happens immediately after the punch, essentially resulting in the target receiving a deadly one-two hit combo which instantly knocks it out (or disintegrated). 

The force of the mantis shrimp’s punch can easily penetrate the hard shell of most crustaceans in the ocean, meaning no creature is safe. Mantis shrimps have also been observed beating up fish and octopi – and succeeding.

Not only does the mantis shrimp have the most powerful strike, it also has one of the most sophisticated eyes in nature and is extremely agile. This, combined with the shrimp’s cunning nature makes it the perfect hunter. It tends to ambush prey and swiftly knocks it out before it knows what hit it. If the one-hit KO fails, the mantis shrimp uses its agility to hit the foe and quickly swim away, then hit again from the other side until the foe is crushed.

Lastly, the shrimp described above is actually one type of mantis shrimp called a smasher. There is another subtype called spearer with claws modified into sharp spears that can be thrusted with the same force as the smasher’s clubs.

The only adequate metaphor to describe this awesome creature would be a Mike Tyson punching as hard as he can, in his prime, while his fist is attached to a meteor entering the atmosphere.

(Image source: Cracked.com)

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Badass Weapons Of Nature: Bombardier Beetle

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The bombardier beetle, or Brachymus creptians, has a “machine gun”. When attacked, it makes an explosive sound and spouts smoke.
This beetle combines chemicals from two separate glands to make the smoke. 
The first gland produces a solution of 25% hydrogen peroxide and 10% hydroquinone, while the second gland produces peroxidase, an enzyme that catalyses the reaction. When these solutions are combined and heated to 100°C, smoke and nitric acid vapour is produced and explosively released.

If you put your hand close to a bombardier beetle, it will rapidly release a scalding, noxious, red vapour. This nitric acid will cause blisters on afflicted skin.
Bombardier beetles also know how to aim the tip of its abdomen to target an enemy. Via this method, it can hit a target a few centimetres away. Even if it misses, the explosive sound will scare away any predator. 
Normally, bombardier beetles store enough chemicals for three or four shots. However, some entomologists have found that some species can fire up to 24 times in rapid succession if provoked.

As these beetles are a bright orange and silver-blue colour, they are very noticeable. They act as if they do not care if they are seen, as they are equipped with an effective cannon. Generally, beetles with a colourful coat have a unique, ingenious defensive mechanism to ward off curious animals and insects.
Despite this, rats that know that the beetle loves to use this “ingenious defensive mechanism” quickly grab the beetle and plant its abdomen in the ground. After attacking it continuously while in the ground to exhaust the beetle’s rounds, the rat bites off the head first.

(from the Encyclopaedia of Relative and Absolute Knowledge by Bernard Werber)

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Badass Weapons Of Nature: Pistol Shrimp

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A gun is, without a doubt, a manmade object. It is an invention that has existed less than a thousand years in history. However, there is an animal that has been using firearms to hunt prey for a significantly longer period of time than mankind has.
The pistol shrimp is well known for its disproportionately large claw, with the other claw being much smaller like a normal shrimp. The massive claw is what is called the “pistol” and it is the weapon of choice for the shrimp.

When a pistol shrimp identifies a target, it swiftly takes aim with the claw and snaps it shut with enough force to create a bubble jet reaching a speed of almost 100km/h. Not only are bubbles produced, but the pressure wave created by the cavitation (the effect of a bubble imploding and generating energy) reaches a sound level of 218dB – which is about 100,000,000 times larger than a gunshot, or 10,000 times larger than a rocket launch. Furthermore, the energy is also released as light and heat, generating a temperature as hot as 4700°C (for comparison, the surface temperature of the sun is 5500°C).
The combination of the bubble jet, pressure wave and heat energy instantly stuns the target and the pistol shrimp proceeds to devour its prey.

Yes, the pistol shrimp has mastered a skill that humans can only dream of in comics such as the Incredible Hulk’s Thunderclap, or in games such as Guile’s Sonic Boom (from Street Fighter). It has also mastered the skill to the level of an effective ultimate move that is reliable as a hunting tool. In fact, it is quite possibly the closest any animal on Earth has gotten to an actual beam weapon.

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Badass Weapons Of Nature: Carpenter Ant

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There is an extreme number of ant species, each with a unique characteristic. In the case of carpenter ants, they are famous for their strange defence mechanism.

Some species of carpenter ants, such as the Camponotus saundersi, have warrior ants with very large mandibular glands (many times greater than normal ants). When in a battle it judges that it has no chance of winning, the ant rapidly contracts its abdominal muscles to build pressure. When sufficient pressure is reached within the mandibular glands, it explodes violently, shattering the ant in the process. The glands are filled with a sticky, toxic fluid, which is spread all around where the ant used to be, ensnaring the foes. The inflicted enemies are killed by the poison. 
This is the reason why they are sometimes referred to as exploding ants.

It is a bold, yet fearsome sacrifice for the greater good.

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Badass Weapons Of Nature: Long-tailed Weasel

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Long-tailed weasels are ferocious predators found in North America that likes to stalk its prey and pounce it with lightning speed. With small prey such as mice, the weasel will wrap its long body around the prey and then crush the head with a strong bite. As the weasel is very slender and sleek, it can easily dig into burrows to hunt hiding animals by crushing its skull, or to add variety, ripping out the windpipe.

Although it usually preys on small rodents, the long-tailed weasel is also known to fearlessly attack much larger animals such as birds and rabbits. As wild rabbits tend to be bulkier (sometimes even ten times larger) than the weasel, it cannot use its characteristic hunting style. To overcome this difficulty, these weasels have developed a strange behaviour that zoologists have labelled the Weasel War Dance. The War Dance (NB: two videos on what it looks like) is a chaotic set of movements where the weasel runs left and right frantically, jumping and flipping upside-down and almost appearing insane. This type of behaviour is observed in other species of weasels and ferrets when they are excited, but few use it as a hunting tool.

It has been observed that when the long-tailed weasel performs a War Dance in front of a rabbit, the rabbit becomes dazed and enters a trance-like state. It is possible that the chaotic and confusing movements disorient the rabbit. Once the rabbit has been disabled, the weasel promptly jumps on the rabbit’s back and delivers a powerful bite to the back of the neck, instantly killing the rabbit.
Wild weasels and stoats practise this skill by playfully ambushing each other when they are young.

Long-tailed weasels, despite their cute appearance, are notorious for their vicious temper. Being a carnivore that prefers fresh meat, it actively hunts and collects food. Despite seeking fresh food, the weasel also exhibits a curious behaviour of storing carrions, which is often only eaten in times of food shortages. This behaviour leads to the weasel going on killing sprees just because they can. Long-tailed weasels have also been observed lapping up blood from the wounds they inflict, and enjoys making their nest from the fur of their victims.

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Badass Weapons Of Nature: Roadrunner

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Roadrunners are medium-sized birds that grow to about 60cm and found in desert environments. They prefer walking or running (top speed 27km/h) to flying and have been portrayed as Road Runner in Looney Toons. In the cartoon, the bird is shown as a witty, intelligent bird that easily runs away from its predator. In real life, the roadrunner is a much more formidable animal.

Although it usually feeds on lizards and insects, roadrunners also enjoy feasting on rattlesnakes. Thanks to its quick speed, the thin bird can swiftly dig its beak into the rattlesnake before it can retaliate with its venomous bite. What happens next is quite surprising.
With its prey secured on its beak, the roadrunner promptly begins whipping its head around, bashing the snake to the ground in a circular motion. This whip-like attack causes the snake to lose consciousness or even die from the sheer impact and rotational force, essentially becoming tenderised. This deadly move has been named by ornithologists as the Centrifugal Slam. The roadrunner does this until it is certain the snake cannot attack back, then swallows it whole. As snakes tend to be longer than the bird, roadrunners are often found running around the desert with a long piece of tail dangling from its beak, the head being slowly digested in the bird’s stomach. 

Roadrunners are also known to eat horned lizards (spiked lizard that shoots blood from its eyes to deter predators), tarantula hawk wasps (giant wasp that defeats tarantulas to lay eggs inside it, with no other known predators) and even flying birds. As mentioned before, roadrunners do not fly unless in an emergency. So to hunt flying birds, they simply run, jump and Centrifugal Slam the living daylight out of the unfortunate prey.

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Praying Mantis

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The praying mantis is sometimes considered a symbol of ultimate female empowerment. After mating, it has been observed that the female would immediately proceed to kill the male she just mated with and eat his corpse, head first.
However, one thing that is less known is that this act – known as sexual cannibalism – occurs almost exclusively in captivity. This is because in the wild, a male runs off quickly after mating to avoid a grim fate. The female, with a massive appetite after the tiring act of copulation, looks for a source of nutrients to upkeep her pregnancy. As in a captive environment the male cannot run far and the female cannot hunt easily, she opts to eat the male as this is more beneficial for her. Furthermore, as mantises have very sharp vision, it is highly likely that the observing scientists (giant, towering figures dressed in white) will intimidate the female mantis. The anxiety caused by the observation would thus make the female act more violently.

The theory that lab intervention caused sexual cannibalism was proven when mantises stopped cannibalising after being fed ad libitum (until they were full). In fact, the female would carefully observe the courtship dance of the male and decide whether he is worthy of mating. This courtship dance also has the effect of switching the female’s priorities from feeding to mating.

It has also been suggested that females may choose to eat the males they do not deem worthy (before mating), or that the males are sacrificing themselves to improve the chance of fertilisation. This is supported by evidence of decapitated male mantises copulating more vigorously and mounting the female for much longer periods. 

In other words, male submissiveness can be a factor in reproductive success.

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Buttered Cat Paradox

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Cats always fall on their feet. Buttered toast always seems to fall buttered side down. So what would happen if we tied a buttered toast on a cat’s back and then dropped the cat? Would the cat land on its feet or would the toast land on its buttered side?
Or would we achieve perpetual motion and anti-gravity simultaneously as they cancel each other and never touch the ground?

Although the paradox is obviously a humorous thought experiment, there is some truth to the separate adages. 
Cats have a natural righting reflex that allows them to twist their upper body so that they land on their feet. This gracious manoeuvre is developed as a kitten and actually involves quite complex physics where the cat is able to turn around without changing their net angular momentum. Since cats have a small body and very light body weight, their terminal velocity (100km/h compared to a human’s 210km/h) when falling is much less and allows them to absorb the shock easily when landing. Furthermore, when falling cats naturally spread their limbs out to slow their fall as much as possible. All these factors let a cat land safely on its feet even if dropped from a high place. Ironically, the lower they are dropped from, the more likely that the cat would fall on its back.

The other side of the paradox is slightly more complicated. The adage that toast falls buttered side first is actually an example of how if something bad can happen, it will happen. However, physicists have discovered that toast is more likely to fall on its buttered side.
When toast falls off a plate, it is highly likely to tip as it hits the edge. This causes it to rotate as it begins to fall. There are two explanations on why the buttered side is more likely to be facing down. Firstly, butter adds weight to one side and heavier objects fall faster in the face of gravity. Secondly, using experimental data it has been found that toast only rotates about 180 degrees by the time it falls the height of the table or person from where it was dropped from. 

Despite it only being a tongue-in-cheek thought, one can only wonder how many scientists have made some toast, buttered it, tied it to a cat and dropped the cat off a ladder.

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