Illusion

An illusion is a distortion of the senses, revealing how the brain normally organizes and interprets sensory stimulation. Though illusions distort reality, they are generally shared by most people. Illusions may occur with any of the human senses, but visual illusions (optical illusions), are the most well-known and understood. The emphasis on visual illusions occurs because vision often dominates the other senses. For example, individuals watching a ventriloquist will perceive the voice is coming from the dummy since they are able to see the dummy mouth the words. Some illusions are based on general assumptions the brain makes during perception. These assumptions are made using organizational principles (e.g., Gestalt theory), an individual's capacity for depth perception and motion perception, and perceptual constancy. Other illusions occur because of biological sensory structures within the human body or conditions outside of the body within one’s physical environment.

The term illusion refers to a specific form of sensory distortion. Unlike a hallucination, which is a distortion in the absence of a stimulus, an illusion describes a misinterpretation of a true sensation. For example, hearing voices regardless of the environment would be a hallucination, whereas hearing voices in the sound of running water (or other auditory source) would be an illusion.

Insanity

Insanity, craziness or madness is a spectrum of behaviors characterized by certain abnormal mental or behavioral patterns. Insanity may manifest as violations of societal norms, including a person becoming a danger to themselves or others, though not all such acts are considered insanity; likewise, not all acts showing indifference toward societal norms are acts of insanity. In modern usage, insanity is most commonly encountered as an informal unscientific term denoting mental instability, or in the narrow legal context of the insanity defense. In the medical profession the term is now avoided in favor of diagnoses of specific mental disorders; the presence of delusions or hallucinations is broadly referred to as psychosis. When discussing mental illness in general terms, "psychopathology" is considered a preferred descriptor.

In English, the word "sane" derives from the Latin adjective sanus meaning "healthy". Juvenal's phrase mens sana in corpore sano is often translated to mean a "healthy mind in a healthy body". From this perspective, insanity can be considered as poor health of the mind, not necessarily of the brain as an organ (although that can affect mental health), but rather refers to defective function of mental processes such as reasoning. Another Latin phrase related to our current concept of sanity is "compos mentis" (lit. "sound of mind"), and a euphemistic term for insanity is "non compos mentis". In law, mens rea means having had criminal intent, or a guilty mind, when the act (actus reus) was committed.

Circle

A circle is a simple shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius.

A circle is a simple closed curve which divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a disk.

A circle may also be defined as a special ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations.

Terminology