Frog's Jumping Math

Crayfish

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Crayfish, just like frogs, are true veterans of our planet! Crustaceans, to which crayfish belong, have been present on Earth for more than 200 million years – which means they lived here even before the first birds appeared in the sky!

Over all those millions of years, crayfish have practically not changed. Their build is so perfect that they survived all major natural disasters. That is why scientists sometimes call them "living fossils" – it's as if someone who had breakfast with dinosaurs every day survived from prehistoric times until today!

The noble crayfish is the native crayfish species in Central Europe. Once, even 150 years ago, it was so common in rivers and lakes here that it was caught by the thousands. Unfortunately, today encountering it is a real rarity and it is protected.

It has very high demands – it lives exclusively in clean, cold, and well-oxygenated waters. If the water is just a little dirty, the crayfish will move away. That is why scientists call it the "barometer of water purity" – where a crayfish lives, the water is definitely crystal clear!

We have a few interesting facts about the life of crayfish for you!

Unusual facts about crayfish parenting.

Most fish lay their roe and just swim away – and then little fish hatch from the eggs. With crayfish, it's different!

The carrying mother.

The female noble crayfish carries her eggs... under her tail! She lays up to 200 eggs and glues them to the underside of her abdomen. For the next 6 months, the female literally carries them everywhere with her – she swims, eats, hides in burrows, and her tail is constantly bent so that the tiny eggs are safe and have a constant supply of fresh, oxygenated water.

White water creatures.

When the little crayfish hatch from the eggs after half a year, they are... completely transparent and white! They look like little water ghosts. Only after the first molting (i.e., shedding the shell) do they start to gain color. Moreover, during the first 10 days, the tiny crayfish do not move away from their mother at all – they hold onto her abdomen as if it were their first home. Mom still protects them, and they feed on the remains of the yolk that they still have left from their life in the egg.

Interesting crayfish anatomy.

Shedding the shell, or molting.

Crayfish have a hard shell that protects them like knight's armor. But there is one problem – the shell does not grow together with the crayfish! In order for the crayfish to grow, it must from time to time shed its old shell and wait for the new one to harden. It's as if you had to shed your skin every year and walk around in something soft like jelly for a few days! When a crayfish molts, it is completely defenseless – soft as rubber. It then hides in burrows and waits for the new shell to harden. Young crayfish molt even several times a year because they grow quickly. Older crayfish molt less often – sometimes only once every two years. Interestingly, crayfish eat the old shell themselves! There is a lot of calcium in the old shell, which is useful for building the new one.

Sometimes you can find an empty crayfish shell. Especially under stones, in depressions on the banks, in plant overgrowth, or under submerged branches. Such an empty shell looks almost exactly like a live crayfish. If you find such an empty shell of a noble crayfish, it is worth taking photos and reporting your find. It will help in the protection of this species!

WARNING!!! Do not move the empty shell or take it away!!! The crayfish might be hiding in its burrow somewhere nearby. It is tired, weakened, and above all soft as jelly. And it is simply waiting for its new shell to harden at least a little bit. Then it will return to the empty shell and will slowly crush it and gradually eat it. For him, it means a lightning-fast delivery of minerals necessary for the new shell to harden. If you take away his old shell, the crayfish will have to look for the necessary calcium somewhere far away, and he doesn't have the strength for that!

Eyes like periscopes

The crayfish has eyes placed on movable stalks, like little submarine periscopes! Thanks to this, it can observe the surroundings without exposing the rest of its body. Moreover, its eyes can work independently of each other – one looks to the left, the other to the right! The crayfish also sees colors, but not as sharply as we do – rather like through a veil. On the other hand, it perfectly perceives movement and changes in light intensity.

Two different claws:

The noble crayfish has two large claws, but... they are not the same! One claw is larger and more massive – it is used for crushing hard snail shells or armored insect larvae. The other is smaller and more agile – it works like tweezers and is used for grabbing finer things, e.g., pieces of plants. It's as if you had a hammer in one hand and tweezers in the other!

Breathing underwater and above water:

The crayfish breathes with gills, which it has hidden under the shell on the sides of its body – similarly to fish. However, it can survive out of water for several hours if its gills are moist! That is why you can sometimes come across a crayfish moving on land, e.g., on a rainy night, when it moves from one body of water to another.

Crayfish superpowers

Escaping backwards.

Imagine a creature that can escape danger... by reversing! It's not a joke – the noble crayfish, when it senses danger, sharply waves its tail and shoots backwards like a bullet from a gun. In a fraction of a second, the crayfish disappears into its burrow before the predator can even blink.

Regeneration – limb renewal:

The crayfish has one more amazing ability – if it loses a claw or a leg (e.g., during a fight or when caught by a predator), then... a new one will grow! This is called regeneration. The new limb is initially tiny, but with each molting it grows more and more, until it finally reaches normal size. Unfortunately, this process takes a long time – sometimes even several years. Sometimes a crayfish loses a limb even when leaving its old shell.

Night ninja:

The noble crayfish is a real night ninja! During the day, it hides in burrows, under stones, or in the roots of coastal trees. Only after dark does it set out on a "hunt". However, the crayfish is not a typical hunter – it is more of a cleaner. It simply eats everything that lies on the bottom. Thanks to this, it plays the role of a "cleaner" – without it, the bottom of rivers and lakes would be covered with rotting remains.

Life in winter:

In winter, when the water gets very cold, the crayfish slows down its pace. It doesn't fall into a deep winter sleep like a frog, but becomes very inactive. It hides deep in a burrow, which it often digs to a depth of up to one meter, and waits for spring. Interestingly, crayfish dig their burrows so precisely that they have a special "chimney" for ventilation – so that even in an enclosed space they have a supply of fresh water!

Something to think about and remember – crayfish plague!

Did you know that the noble crayfish is mortally threatened... by its relatives from America?

How did this happen?

At the end of the 19th century, people brought other crayfish species from North America – e.g., the spinycheek crayfish and the signal crayfish. These American crayfish looked similar and were also edible, so they were bred in European waters. But there was one problem – the Americans were resistant to a dangerous fungal parasite that caused a disease called "crayfish plague".

The American crayfish did not get sick – they were only carriers. But when the fungus got into the waters where our noble crayfish lived, they started to get sick en masse. And for the noble crayfish, "crayfish plague" is practically always fatal.

The scale of the tragedy:

Imagine that once the noble crayfish occurred in hundreds and thousands of places. Today, only a few percent remain from this huge number! It's as if only a few villages remained from a mighty kingdom. That is why scientists are working on protecting the noble crayfish – they set up special breeding programs and release young crayfish into clean lakes, far away from the American invaders.

The world of crayfish is just as fascinating as the world of frogs, like all that rich nature! And what if it's exactly you who finds a way to cure the noble crayfish?

Koi

Fish, compared to frogs or crayfish, are absolute record holders. The first species of fish appeared over 500 million years ago. However, they did not resemble today's specimens very much. Only much later, about 400 million years ago, the ancestors of fish as we know them today began to form. Without going into details, the main branch of this species split into two groups at that time. From one of them (bony fish) come more than 95% of all fish species we know today. And from the other (fish with a cartilaginous skeleton) – among others, sharks and rays.

• Imagine your family tree. You have parents, grandparents, great-grandparents, and if we went back in time millions of years, we would reach ancestors who lived in the prehistoric ocean. They were creatures that looked like fish.
• One day, however, these "fish grandpas and grandmas" of ours decided to explore the land.
• • Legs and hands gradually grew from their fins.
  • Instead of gills, lungs developed so they could breathe air.
  • Over time, they became amphibians, then reptiles, mammals, and finally us – humans.

• Scientists who study the evolution of life use one rule: You can't run away from the family.
  Because all people, dogs, birds, and elephants come from these prehistoric fish, from a scientific point of view, we are all just highly improved "land fish".
• • We have the proof right in our bodies!
    When a baby develops in its mother's belly, in the first weeks it has small grooves on its neck that look exactly like fish gills. Only later do ears, jaws, and a neck form from them. Even the bones in our hands are arranged almost the same way as the bones in the fins of our ancient fish ancestors.
  • So next time you see a fish swimming in an aquarium, you can easily wave to it like to a very, very distant cousin!

Relations between humans and fish evolved from simple hunting to breeding. For people, fish represent the most important source of protein, vitamins, and omega-3 fatty acids, which are important for the functioning of the human heart, brain, and eyesight. Fish also play an important role in the ecosystem and culture.

Fish are the third most popular group of pets in the world. Observing aquariums has a calming effect on humans. And that brings us to one of the characters of this game.

Extraordinary, but ordinary origin

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Koi amaze with their colorful variety, but in reality they are ordinary... carps! Carp is not just an ordinary fish, it is one of the most important freshwater farmed fish in the world.

In many countries, in their traditions and culinary culture, carp holds a special place as the main Christmas Eve dish. As a food source, carp was known already in ancient countries: China and Persia. Carps were bred exclusively for food purposes, no one paid attention to their colorfulness. The first mentions of the interesting coloring of these fish come from ancient China. However, these were only curiosities.

And here is another curiosity – in old Japan, carp breeders pulled the fish out of the ponds for the winter and placed them in water tanks under the floors of their houses! It was a very important source of food for them during the hard winter months.

And it was these people who at some point noticed that some of these fish had interesting colors. It was around 1830. They started to intentionally breed and cross the most beautiful individuals. Such beautiful specimens were bred that when they were first presented to the wider public at an exhibition in Tokyo in 1914, the world was enchanted. And this exhibition was visited by over 7 million people at that time! Of course, not only because of the fish, but still it was a considerable attendance.

What does "koi" actually mean?

The word "koi" in Japanese simply means carp. However, for the Japanese, these colorful fish are real superheroes! According to an old, beautiful legend, carps are a symbol of extraordinary strength, courage, and perseverance. Although this legend has Chinese origins, it was fully adopted by Japanese culture, where carps (nishiki-goi) became a national symbol of tenacity and success.

• It tells of a large school of carps that swam against the current of the Yellow River and fought with the strong current. When they reached a huge waterfall, most of them gave up. One, the strongest carp, however, did not stop jumping and fighting the roaring water, until it finally jumped all the way to the very top.
• The gods were so fascinated by his extraordinary perseverance that they rewarded him by turning him into a mighty golden dragon! That is why today koi carps remind children all over the world to never give up, to persistently strive for their goal, and to believe that any obstacle can be overcome.

Exceptional superpowers of koi carps

Today, koi carps are bred and admired all over the world. Maybe they don't have such superpowers as frogs or crayfish, but they are not just ordinary carps.

Intelligence

For example – koi are surprisingly intelligent! They can recognize their caregiver. When you approach the pond, they immediately swim up to you because they know they will get food soon. However, they will watch a stranger from a safe distance. Moreover, they even recognize footsteps! If their caregiver walks barefoot on a wooden pier, the koi will remember this characteristic sound and swim up as if someone called them. They don't have ears, but they are very sensitive to any water vibrations.

Memory

They also have a great memory. They can learn to eat from a hand, and some individuals can even be... petted! In Japan, they are treated almost like pets – they are given names and the fish can react to them. Imagine a fish that swims up to you when you call it by name!

Sensitivity

Did you know that some varieties of koi can... get sunburned? White and red scales are sensitive to strong UV radiation, so koi hide in the shade on hot, sunny days. They prefer to hide under the large leaves of water lilies, which float on the surface of the pond like natural sunshades. This is one of the reasons why lilies are so important in Japanese water gardens – they provide protection from the sun for the fish. And in our game, a frog jumps on the leaves and solves math puzzles!

Giant fish

Koi can also grow to really remarkable sizes – even up to one meter in length! And the older they are, the more beautiful colors they have. Some patterns on their scales are so unique that every specimen looks like a living work of art. No wonder they are called "floating flowers" or "living jewels" in Japan.

Longevity

Koi also reach a really high age. A lifespan of 50–70 years is not at all unusual for koi. The most famous koi carp named Hanako is said to have lived... 226 years! It survived seven owners and remembered the times before the invention of the lightbulb.
But... a moment for reflection.
If you count those years, you'll notice something strange: the carp Hanako was supposed to be born in 1751. That is almost 100 years before colored koi carps were even bred in Japan! How is this possible?

Breeding

The most famous place for breeding these fish is, of course, Japan, specifically the mountainous region of Niigata. That's where it all started. And it is the Japanese koi that are considered the standard of beauty and literally reach astronomical prices at auctions. There are also breeders in Europe, the USA, and some Asian countries. One of the largest and most prestigious breeding stations is located in Poland.

Maybe Japanese koi are the standard of beauty. But the world doesn't stand still and things are constantly changing! Maybe it will be you... the one who one day breeds the most beautiful koi?