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”.
Anyone who has studied mathematics to some degree will know about algebraic equations. An algebraic equation is an equation that can be solved to find the unknown value of x. A quadratic equation is an algebraic equation with x², or in other words has two valid solutions to x. Generally speaking, a quadratic equation can be expressed in the following fashion: ax² + bx + c = 0. a, b and c are constants and the equation can be solved to find x. A quadratic equation is definitely more complicated to solve compared to a linear equation and it can be solved using various means and applications such as factorisation. As these methods are learnt in school and this Encyclopaedia is technically not a mathematics textbook, such methods will not be delved into.
If you have not learnt it already, there is a shortcut method to solving quadratic equations: the quadratic formula. This formula can easily find x if you simply substitute in the values for a, b and c. Of course this formula only works if the solutions are real numbers. The quadratic formula is as follows:
As you can see, because of the ± sign, the formula can be used to find both solutions to a quadratic equation. Even without factorising, it can find the answer as long as you substitute numbers into it on a calculator, making maths class very easy. However, as mentioned above the Encyclopaedia of Absolute and Relative Knowledge is not a mathematics textbook and one should instead learn properly from their teacher, not using the formula until they have been taught it properly.
In the 17th century, a lawyer called Pierre de Fermat conjectured many theorems while reading a mathematics textbook called Arithmetica, written by an ancient Greek mathematician called Diophantus. He wrote his theorems on the margins of the books. After his death, a version of the Arithmetica with Fermat’s theorems was published and many mathematicians checked over Fermat’s proofs. However, there was one theorem that could not be solved. Fermat wrote on the theorem: “I found an amazing proof but it is too large to fit in this margin”.
Fermat’s last theorem is as follows:
No three positive integers x, y, and z can satisfy the equation
xⁿ + yⁿ = zⁿ for any integer value of n greater than two.
For example, x² + y² = z² can be solved using Pythaogorean triplets (e.g. 3, 4, 5) but there are no values for x, y and z that solves x³ + y³ = z³. This theorem remained unsolved for 357 years until Andrew Wiles finally found the proof in 1995.
There are many stories surrounding Fermat’s last theorem, but by far the most interesting is related to suicide. In 1908, a German mathematician called Paul Wolfskehl decided to kill himself after being cold-heartedly rejected by the woman he loved so much. He decided to shoot himself at midnight and in the remaining time started reading some mathematics texts until he found a flaw in Kummer’s theory, which disproved Cauchy and Lamé’s solution (the leading solution at the time. After Kummer’s essay, most mathematicians of the time gave up on Fermat’s last theorem). After researching Kummer’s essay, Wolfskehl found that it was far past midnight and he felt great pride in reinforcing Kummer’s solution. His depression was gone and through mathematics he found new meaning in his life. Wolfskehl, who believed that the theorem saved his life, made a resolution to donate his wealth to whoever solved Fermat’s last theorem, putting up 100,000 marks as a prize. This prize was claimed by Wiles in 1996 (then worth $50,000).
Solve the following riddle:
It is greater than a god and more evil than a devil.
The poor have it while the rich lack it.
If you eat it, you will die.
To find the answer, you must look within yourself and travel against the flow of time.
Continue reading “Untitled”
A man asked how old a man’s three daughters were. The father replied with the following statement.
“The product of their ages is 36.”
“It’s hard to determine their ages from just that.” the man asking replied.
“The sum of their ages is same as the number of my house.”
“I still can’t figure out the answer!” the man replied again.
“My eldest daughter is blonde.” the father said, and the man, now smiling, replied.
“Oh, is that so? Then I can figure out how old your daughters are.”
How old is each daughter? And how did the man figure it out?
A computer cannot solve this problem, as it can only be solved using human logic.
Continue reading “Three Daughters”
Richard Feynman is a world-renowned genius physicist, famous for his ability of solving some of the most difficult problems in physics. He said that his intelligence was all thanks to his unique yet “normal” problem solving method, which he used to solve most of his problems. Here is the algorithm:
1. Write down the problem.
2. Think very deeply.
3. Write down the answer.
If that does not yield the answer:
5. Wake up, then think deeply again.
6. Write down the answer.
Nothing is impossible.