Tuesday, 5 March 2013

Tangent



In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. Informally, it is a line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c on the curve if the line passes through the point (c, f(c)) on the curve and has slope f'(c) where f' is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.

As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space.

Thursday, 12 July 2012

Thought disorder

In psychiatry, thought disorder (TD) or formal thought disorder (FTD) is a term used to describe serious problems with thinking, feelings, and behavior. The symptoms can include false belief about self or others, paranoia, hearing or seeing things that other people don’t see, disconnected speech or thinking; feelings that don’t match the situation. People affected by a thought disorder may present with incomprehensible language, either speech or writing, that is presumed to reflect thinking. There are different types. For example, language may be difficult to understand if it switches quickly from one unrelated idea to another (flight of ideas) or if it is long-winded and very delayed at reaching its goal (circumstantiality) or if words are inappropriately strung together resulting in gibberish (word salad).

Psychiatrists consider formal thought disorder as being one of two types of "thinking" or "thought" disorders, the other type being delusions. The latter involves "content" while the former involves "form". Although the term "thought disorder" can refer to either type, in common parlance it refers most often to a disorder of thought "form" also known as Formal Thought Disorder. It is usually considered a symptom of psychotic mental illness, although it occasionally appears in other conditions. For example, pressured speech and flight of ideas may be present in mania. Clanging or echolalia may be present in Tourette syndrome. Eugen Bleuler, who named schizophrenia, held that its defining characteristic was a disorder of the thinking process. However, Formal thought disorder is not unique to schizophrenia or psychosis. So-called “organic” patients with a clouded consciousness, like that found in delirium, also have a formal thought disorder. However, there is a vague clinical difference between the two.

Schizophrenic or psychotic patients are less likely to demonstrate awareness or concern about it  because it results from a fundamental inability to use the same type of Aristotelian logic as everyone else does whereas so-called “organic” patients with a clouded consciousness usually do demonstrate awareness and concern about it, by complaining about being “confused” or “unable to think straight” because it results, instead, from various cognitive deficits.

Friday, 25 May 2007

Snake Alcatraz



During the Civil War, military prisoners were housed on the Island of Alcatraz in the San Francisco Bay area. In 1934 it became a federal penitentiary and was known for its harsh conditions and its policy of silence. A small rocky island rising out of the bay, the prisoner-guard ration was 3-to-1, and escape was considered nearly impossible. There are no officially recorded successful escapes, although a few which are considered "missing and presumed dead." Now defunct, "the Rock" serves as a tourist attraction. It's an eerie feeling to shut yourself inside a solitary confinement cell and feel, for a few moments, the claustrophobic darkness. You can well imagine why a prisoner might try to escape regardless of the risks.

Immediately following the great escape attempt, I weighted the lid to Mike the Snake's tank down with rocks. The next night, I watched him begin his exploration of the lid anew, probing for a weakness. After an uneasy hour, I duct-taped the lid to the tank. But obviously that could not be a long-term solution. I returned to the pet shop, to talk with the old guy who runs the place. He asserted that it was physically impossible for a snake to push a latched lid off a tank. I told him I saw it with my own eyes. We stared at each other for a long minute and then he growled, "Well, whaddaya want?" The bigger tank they should have sold me to start with, a more secure lid, and oh, while we're at it, a full refund on the original set-up. Done.

So now the snake is snoozing in his new grown-up home, complete with sticks to drape himself on, a green rock from South America for resting, and plants to re-create that jungle feel that all pythons must surely hold in some archetypal unconscious memory. The lid slides in and must be opened with two hands, the latches being released simultaneously. (That's particularly good as snakes are lacking opposable thumbs. Well, thumbs of any sort. Or, uh, hands. Okay, they're limbless.) On the front, for added security, a combination lock. He'll be happier in there, I'm sure of it. And, more importantly, I'll be able to sleep at night.