Another explanation is from number theory: The integers are arranged in such a way that even numbers are followed by odd ones, and odd ones by even ones. Zero is preceded by minus one, and followed by one. Both numbers are odd. So it must be even.
There is also a problem: The term "even" meaning "integer multiple of two" is a convention; people agreed on it. It is not a formal definition. Another case where people used a convention they agreed on was that of prime number: Before the 20th century, there were many inconsistent definitions of prime: Mathematicians such as Goldbach, Lambert, Legendre, Cayley, and Kronecker wrote that 1 was prime. The modern definition of "prime number" is "positive integer with exactly 2 factors", so 1 is not prime. This definition is rational: it naturally suits mathematical theorems that concern the primes. For example, the fundamental theorem of arithmetic is easier to state when 1 is not considered prime
It would be possible to redefine "even" in a way that no longer includes zero. However, in this case, the new definition would make it more difficult to state theorems concerning the even numbers. Already the effect can be seen in the algebraic rules governing even and odd numbers. The most relevant rules concern addition, subtraction, and multiplication:
Inserting appropriate values into the left sides of these rules, one can produce 0 on the right sides:
The above rules would therefore be incorrect if zero were not even. At best they would have to be modified. For example, one test study guide asserts that even numbers are characterized as integer multiples of two, but zero is "neither even nor odd". Accordingly, the guide's rules for even and odd numbers contain exceptions:
Making an exception for zero in the definition of evenness forces one to make such exceptions in the rules for even numbers. From another perspective, taking the rules obeyed by positive even numbers and requiring that they continue to hold for integers forces the usual definition and the evenness of zero.
H. Rider Haggard
Henry Rider Haggard (1856–1925) was an English writer. He is best known for his adventure novels. His novels were notable for their unusual invention and stories that kept people interested. His best novels were very popular in his lifetime. They made the genre of adventure fiction popular again. Haggard also wrote books about farming and emigration.
Haggard lived in South Africa for six years when he was a young man. Many of his novels were set in Africa, including "King Solomon's Mines" (1886), "Allan Quatermain" (1887) and "She" (1887).
In 1919, Haggard was knighted for his services to the British Empire. Haggard's autobiography, "The Days of My Life", was published in 1926 after he died. Morton Cohen's biography of Haggard was published in 1960.
White's illusion
White's illusion is a brightness illusion. Here, some stripes of a black and white grating are replaced by gray rectangles (see Fig). All gray bars usually have same color and opacity. The brightness of the gray pieces appear to shift toward the brightness of the top and bottom bordering stripes, that is, the gray bars with horizontal black regions on their top and bottom appear darker and those with white regions on their top and bottom appear lighter. But this does not match with what lateral inhibition predicts. This illusion is mostly described for grayscale. A similar illusion occurs for colored patches. This is known as Munker-White's illusion or Munker's illusion.
The amount of each bipolar cell response depends on the amount of the stimulation it receives from the receptor. Neighboring cells decrease this response. This is called lateral inhibition.
Lateral inhibition cannot explain White's illusion. In Figure 2.1 lateral inhibition sent by black cells A and C should make cell O lighter; in Figure 2.2 lateral inhibition sent by white cells A and C should make cell O darker.
Rules suggested to describe optical illusions such as simultaneous brightness contrast illusion, such as Wallach's ratio rule cannot explain White's illusion. These rules suggest that cell O in figure 2.1 receives less inhibition that cell O in figure 2.2. So, the cell O in figure 2.1 should be lighter than cell O in the other figure. However, the opposite case happens.
White and White (1985) concluded that at a higher spatial frequency the grating of White's illusion could be described by brightness assimilation. They also concluded that at lower spatial frequencies White's illusion is still present.
The belongingness theory has been given as an explanation of White's illusion. Belongingness means that we perceive things depending on its surroundings. According to belongingness theory, the lightness of rectangle A is influenced by the white bars that surround it. Similarly, the rectangle B on the right side is surrounded by the dark bars. So, the lightness of rectangle B is affected by the dark background. As a result, area A which rests on the white background appears darker than area B which rests on the dark background.
Not all scientists accept the belongingness theory. They say that when talking about the background, it is the same as lateral inhibition.
Lateral inhibition
In neurobiology, lateral inhibition is the ability of an excited neuron to reduce the activity of its neighbors. It stops action potentials from spreading in the lateral direction. It is called lateral inhibition as it stops (inhibits) neighboring neurons from firing. This creates a contrast in stimulation. This increases perception. For example, in vision, it helps in differentiating edges. It occurs primarily in visual processes. But it has also been seen in tactile, auditory, and even olfactory processing. Cells that use lateral inhibition are mainly present in cerebral cortex and thalamus. They make up lateral inhibitory networks (LINs). Artificial sensory systems have artificial lateral inhibition built in them. Examples are vision chips, hearing systems, and optical mice.
Raif Badawi
Raif Badawi (Arabic: رائف بدوي‎; born 13 January 1984) is a Saudi Arabian writer and activist. He started the website Free Saudi Liberals in 2008. He was arrested in 2012 because of the website. The website was then taken off the internet. Badawi was sentenced to 10 years in prison and 1000 lashes. Badawi has also been banned from any media work or foreign travel for 10 years after his release from prison. Badawi's first 50 lashes were given on January 9, 2015. After that, Badawi's lashes were postponed many times. In June 2015, a Saudi high court ruled that Badawi should be lashed but the lashing was postponed hours before it was going to happen.
Badawi's wife called Ensaf Haidar believes he is weak in body and suffering mentally. She fears this may be a slow death sentence.
Badawi's sister Samar Badawi is also an activist. Her husband Waleed Abul-Khair is Raif's lawyer. He was sentenced to 15 years in prison in July 2014. Samar is working to get both her brother and husband released from prison.
Sweden–Finland
Sweden–Finland (, ) is a historiographical term. It refers to the Kingdom of Sweden from the days of the Kalmar Union in the late 14th century up to the Napoleonic Wars in to the early 19th century. In 1809 it was split into two halves. The eastern half became the Grand Duchy of Finland in personal union with the Russian Empire. The western half remained as the Kingdom of Sweden.
Adventure fiction
Adventure fiction is a type of fiction in which an adventure forms the main storyline. The adventure is usually an exciting undertaking involving risk and physical danger. Author Malins describes adventure fiction as the story "of the hero—individual or group—overcoming obstacles and dangers and accomplishing some important and moral mission." The characters in an adventure fiction are highly sympathetic. They are also ones the reader can easily relate to. There has to be a conflict to overcome and a clever villain to stop.