Tag: number

Posted in Science & Nature

The Dangerous Number

Posted on by Jinavie

Everyone has learned of the Pythagorean theorem in maths class:

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).

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A lesser known fact is that Pythagoras, the Greek mathematician who came up with the theorem, had a school where numbers were essentially worshipped. The school of Pythagoras were obsessed with whole numbers and their ratios, believing the universe was built around whole numbers. Their motto was “All is number”.

In 520BC, a mathematician named Hippasus was murdered by members of the school of Pythagoras, by being thrown off the side of a ship. Why did a group of scholars go as far as killing a fellow mathematician? The reason lies in a special number.

Hippasus raised an interesting question regarding the Pythagorean theorem. Imagine a square where each side is 1 unit long. What is the length of the diagonal?

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Using the theorem a² + b² = c²: 1² + 1² = 2 = c². Ergo, c = √2. This does not appear to be so controversial. The Pythagoreans would reason that it was simply a ratio between two whole numbers, much like ½ or ¾.

But as they tried to quantify what this ratio was, a horrifying truth emerged – no ratio between whole numbers could produce √2. It is what we now call an irrational number.

This was heresy – how can such a number exist in a universe built around whole numbers? The Pythagoreans would not allow this. Hippasus tried to argue that √2 was just as real a number as any other, but his attempts to propagate the knowledge of irrational numbers was quashed through murder.

Knowledge is power, but knowledge can also lead to tragedy.

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Posted in Science & Nature

Pi

Posted on by Jinavie

Pi (π) a mathematical constant that is defined as the ratio of a circle’s circumference to its diameter. It is approximately equal to 3.14159, but since it is an irrational number (cannot be expressed as a ratio), the decimal places go on and on with no repeating segments. The history of pi extends back to almost 5000 years ago, as it plays such a crucial role in geometry, such as finding the area of a circle (A = π ²). It is not an understatement to say that pi is among the top five most important numbers discovered in history (0, 1, i and e being the others).

The interesting thing about pi is that it is an irrational number. As mentioned above, this means that pi has an infinite number of non-repeating decimal places, with numbers appearing in random sequence. For example, pi to a 30 decimal places is 3.141592653589793238462643383279… Because of this feature, pi contains all possible sequences and combinations of numbers at a certain point. The corollary to this fact is, if pi is converted into binary code (a number system of only 0 and 1, used by computers to encode information), somewhere in that infinite string of digits is every combination of digits, letters and symbols imaginable. The name of every person you will ever love. The date, time and manner of your death. Answers to all the great questions of the universe. All of this is encoded in one letter: π.

That, is the power of infinity.

Posted in Science & Nature

Alex The Parrot

Posted on by Jinavie

Alex (Avian Language EXperiment) was the name of an animal psychology experiment that ran for 30 years starting from 1977. The experiment was designed to see if birds could undertake complex problem solving and learn languages like primates. For this, Dr Irene Pepperberg bough an African grey parrot, named him Alex and started teaching him how to speak. Before Alex, scientists believed that animals needed a large enough brain like a primate to handle the complex problems related to language. But Alex proved otherwise.

Before Dr Pepperberg, scientists failed to establish any two-way communication with parrots. She used a new training technique called the model/rival technique, where two trainers act in front of the parrot to teach it things. The method is as follows. One trainer (the rival) shows the other trainer the desired student behaviour they want the parrot to learn. The other trainer then compliments the trainer and shows attention. The parrot sees that the behaviour gets the trainer’s attention and learns it to compete with the rival. This technique was extremely successful and Alex began picking up words at a very fast rate (technically it was more of a two-way communications code than “language”).

Once communication was possible, Dr Pepperberg taught Alex many different concepts. Over the course of his life, Alex learnt 150 words, how to differentiate between seven colours and five shapes and also understood the concept of numbers and sizes. If you showed Alex two objects, he could answer many questions regarding one object (thus showing that his response was not a conditioned one). For example, if you showed him a small blue key and a large green key, he could answer what colour the larger key was, or which one was the green key. Furthermore, if a plate full of objects of different colours and shapes was presented to him, he could correctly count how many green blocks (or any other shape or colour) there was among the objects. The important point here is that he could pick out just the green blocks, excluding green balls or blue blocks from his answers (showing he fully understood the question and could attribute more than one characteristic to one object). He knew how to express himself, such as saying “Wanna go back” when he was tired, and would give playful, incorrect answers when bored of the repetitious experiments. According to Dr Pepperberg, Alex had the intelligence equal to a dolphin, a great ape or a five year-old child. He also knew how to attain knowledge by asking questions, such as when he asked what colour he was to learn the word “grey”.

Alex, who told us so much about the intelligence of a parrot, unfortunately died in 2007. The night before he died, he said the following last words to Dr Pepperberg: “You be good. I love you”.

Posted in Psychology & Medicine

Mind Reading

Posted on by Jinavie

Here are ten facts about you:

       1. You are reading this right now.
       2. You are thinking that is a stupid fact.
       4. You did not notice I skipped 3.
       5. You are checking now.
       6. You are smiling.
       7. You are still reading this even though it is stupid.
       9. You did not realise I skipped 8.
       10. You are checking again and smiling about how you fell for it again.
       11. You are enjoying this.
       12. You did not realise we have passed number 10.

    Posted in Science & Nature

    Ant Sequence

    Posted on by Jinavie

    Find the rule for the following sequence of numbers:

    1
    11
    21
    1211
    111221
    312211
    13112221
    1113213211
    …

    Continue reading “Ant Sequence” →

    Posted in Science & Nature

    Fibonacci Number

    Posted on by Jinavie

    1 1 2 3 5 8 13 21 34 55…

    A keen observer would note that each number in the above sequence is the sum of the two numbers before it. These are known as Fibonacci numbers and are among the most famous number sequences in mathematics.

    It is famous because of some unique properties. For example, every third number is even, every xth number is the multiple of Fx (e.g. 4th number = 3, 8th number = 21…) and the list goes on. It is also known to approximate golden spirals, a mathematical function that is closely related with yet another famous number: the golden ratio.

    However, a more interesting (and more relatable) fact about these numbers is that they appear repeatedly in nature. It has been noted for many centuries that plants tend to follow the Fibonacci sequence in various ways. This includes the number of branches of trees that grow per year, the number of petals on a flower (almost all flowers have a Fibonacci number of petals) and most interesting of all: the arrangement of florets on the face of a sunflower. If one carefully scrutinises the face of a sunflower (also applies to pine cones), they will note that the florets (tiny pieces on the face) are arranged in what appears to be spirals. They are actually arranged on a stack of spirals, both clockwise and anti-clockwise. The number of spirals for both directions are always two Fibonacci numbers next to each other (e.g. 34 and 55).

    This is because natural selection pushes the plants to arrange their florets, petals and tree branches in the most efficient manner possible, which is provided by the Fibonacci sequence.

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    Posted in Philosophy

    The Number System

    Posted on by Jinavie

    The number system represents the advancement of life and consciousness.

    In a number, the curves represent love, the crossroads represent hardship and the horizontal lines represent binding.
    Let’s take a look at each number.

    “1” is a mineral. It has one vertical line and has no binds.
    There are no curves and ergo no love.
    Rocks are not bound to anything nor love anything.
    There are no crossroads and ergo no hardship.
    Minerals merely exist as the first step of matter.

    “2” is a plant. Life begins here.
    The bottom line shows that plants are bound to the ground.
    Plants are rooted to the ground and cannot move.
    The curve on the top represents the plant’s love for the sky and sunlight.
    Plants love the sky and is restrained by the earth.

    “3” is an animal. It is formed from two curves.
    Animals love both the earth and the sky.
    But it is not bound to either.
    Animals only have pure feelings.
    Animals live in fear and greed.
    The two curves are two mouths.
    If one is a mouth that bites, the other is one that kisses.

    “4” is a human. Humans are beings on the crossroad between “3” and “4”.
    They can advance to a higher step.

    “5” is an enlightened person. This number is a mirror image of “2”.
    The top line shows the limit by the sky, the bottom line shows the love for the earth.
    He distances himself from other humans but love both people and the Earth.

    “6” is an angel. It is a spiral, curve of love rising towards the sky.
    An angel is a pure soul and mind.

    “7” is a god cadet. “7” is another number with a crossroad.
    It is the image of a “4” flipped around.
    A god cadet is on the crossroad between an angel and what is next.

    “8” is an infinite god. An endless, twisting curve of love.
    But this curve spins on the spot and does not rise nor fall.

    “9” is a curve. It is a “6”, an angel, turned around.
    In other words, it is love coming down instead of going up.
    From the sky down to the ground.
    It is a curve that spins and spins and congeals mayonnaise.

    (from God by Bernard Werber)