Archive for the ‘Science’ Category
The Möbius strip or Möbius band , also Mobius or Moebius, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.
A model can easily be created by taking a paper strip and giving it a half-twist, and then joining the ends o
f the strip together to form a loop. In Euclidean space there are two types of Möbius strips depending on the direction of the half-twist: clockwise and counterclockwise. That is to say, it is a chiral object with “handedness” (right-handed or left-handed).
It is straightforward to find algebraic equations the solutions of which have the topology of a Möbius strip, but in general these equations do not describe the same geometric shape that one gets from the twisted paper model described above. In particular, the twisted paper model is a developable surface (it has zero Gaussian curvature). A system of differential-algebraic equations that describes models of this type was published in 2007 together with its numerical solution.
The Euler characteristic of the Möbius strip is zero.
The Northrop SM-62 Snark was a specialized intercontinental cruise missile with a W39 nuclear warhead operated by the U.S. Strategic Air Command from 1958 until 1961. It takes its name from Lewis Carroll’s snark.
The Snark was developed to offer a nuclear deterrence to the Soviet Union at a time when ICBMs were still in development. It was the only intercontinental surface-to-surface cruise missile ever deployed by the United States Air Force. With the deployment of ICBMs, it was rendered obsolete and taken out of service.
Design and development
Work on the project began in 1946. Initially there were two missiles — a subsonic design (the MX775A Snark) and a supersonic design (the MX775B Boojum). Budget reductions threatened the project in its first year, but the intervention of Jack Northrop and Carl Spaatz saved the project. Despite this, funding was low and the program was dogged by requirement changes. The expected due date of 1953 passed with the design still in testing and SAC was becoming less enthusiastic. In 1955, Eisenhower ordered top priority to the ICBM and associated missile programs. The original designation was B-62.
Despite considerable difficulties with the missile and military reservations toward it, work continued. In the 1957 tests the missile had a circular error probable (CEP) of only 17 nautical miles (31.5 km). By 1958 the celestial navigation system used by the Snark allowed its most accurate test, which appeared to fall 4 nautical miles (7.4 km) short of the target. However, this apparent failure was at least partially because the British Navigation Charts used to determine the position of Ascension Island were based on position determination techniques less accurate than those used by the Snark. The missile landed where Ascension Island would be found if more accurate navigation methods had been used when developing the chart. However, even with the decreased CEP, the design was notoriously unreliable, with the majority of tests suffering mechanical failure thousands of miles before reaching the target. Other factors, such as the reduction in operating altitude from 150,000 to 55,000 feet (46 to 17 km) and the inability of the system to detect countermeasures and perform evasive maneuvers also made the Snark an undesirable strategic deterrent.
The jet powered 20.5 m long unmanned aircraft had a top speed of 650 mph (1,046 km/h) and a maximum range of 5,500 nautical miles (10,200 km). The complex stellar navigation guidance system gave a claimed CEP of 8,000 ft (2.4 km).
The Snark was an air-breathing design, launched from a light platform by two rocket booster engines. It switched to an internal jet engine for the remainder of its flight. The jet was a Pratt and Whitney J57, the first 10,000 lbf (44 kN) thrust design, also used in the early B-52 and the F-100. Lacking a horizontal tail, the missile used elevons as its primary flight control surfaces, and flew an unusual nose high aspect during level flight. During the final phase of flight the nuclear warhead separated from the missile’s main body and followed a ballistic trajectory to the target. Upon separation, due to the abrupt shift in its center of gravity, the missile body performed an abrupt pitch-up maneuver to avoid colliding with the warhead.
One advanced feature of the Snark was its ability to fly missions of up to 11 hours and return for a landing. If the warhead did not detach, the missile could be flown repeatedly. Lacking landing gear, it was necessary for the Snark to skid to a stop on a flat, level surface. The runway at Cape Canaveral is still today known as the Skid Strip.
THX 1138 is a 1971 science fiction film directed by George Lucas in his directorial debut. The film is based on a screenplay by Lucas and Walter Murch. It stars Robert Duvall and Donald Pleasence and depicts a dystopian future in which the populace is controlled through android police officers and mandatory use of drugs that suppress emotion, including sexual desire.
THX 1138 was the first feature-length film directed by Lucas, developed from his 1967 student film Electronic Labyrinth: THX 1138 4EB, which he made in 1967 while attending the University of Southern California. This short film was itself based on a one and a quarter page treatment of an idea by Matthew Robbins. The feature film was produced in a joint venture between Warner Brothers and Francis Ford Coppola’s new production company, American Zoetrope. A novelization by Ben Bova was published in 1971.
In an underground city of the future, sexual intercourse is outlawed and use of mind-altering drugs is mandatory. Narcotics are critical both in maintaining compliance among the city’s residents and also for ensuring their ability to conduct dangerous and demanding tasks for long periods of time. The inhabitants worship a godlike being known as “OMM 0910”, with whom they commune in telephone booth-like areas known as “Unichapels”. At their jobs, SEN 5241 (Donald Pleasence) and LUH 3417 (Maggie McOmie) keep surveillance on the city and field questions (mostly about proper drug intake).
THX 1138 (Robert Duvall) works in a factory producing androids that function as police officers. The work is hazardous as it requires handling explosive and radioactive material. THX’s female roommate, LUH, becomes disillusioned and makes a conscious decision to break the law and stop taking her drugs. She subsequently secretly substitutes inactive pills for THX’s medications. As the drug’s effects wear off, THX finds himself experiencing authentic emotions and sexual desire for the first time.
At first conflicted and nauseated, he eventually connects with LUH. Knowing that their relationship is illegal, THX must decide whether to return to using the prescribed drugs, or escape with LUH. He knows that he will not be able to function without his drugs while at his demanding job, but he does not want to lose what he has created with LUH. They consider an escape to the “superstructure,” where they hope to be able to live in freedom.
THX is confronted by SEN. Using his position as LUH’s superior, he changes her shift. SEN admits that he wants THX as his new roommate. THX files a complaint against SEN for the illegal shift change. Without drugs in his system, THX falters during critical and hazardous phases of his job. The city’s authorities discover THX’s and LUH’s crimes of sexual intercourse and drug evasion (Because of a bureaucratic error, THX is briefly “mind-locked” while at a critical juncture of android construction—this almost leads to disaster.) THX and LUH are arrested.
THX is imprisoned in a white limbo world. He enjoys a brief reunion with LUH—one disrupted by the enforcer robots. THX is consigned to another region of limbo, this one populated by a collection of other prisoners, including SEN. Knowing that THX filed the complaint against him, SEN nevertheless rallies him to join his undescribed cause (some of SEN’s dialogue is taken from speeches by Richard Nixon.).
Most of the prisoners seem uninterested in escape, but eventually THX and SEN decide to find an exit. They encounter SRT (Don Pedro Colley), who starred in the holograms broadcast citywide. SRT has become disenchanted with his role in the society and is making an attempt to escape.
Exiting their prison, THX and SRT are separated from SEN. Controllers in the city learn of the escape and allot a strict budget (14,000 credits) for their recapture. Chased by the robots, THX and SRT find a computer center, from which THX learns that LUH has been “consumed”, possibly for organ reclamation (since bodies were discovered earlier, of which, as SRT put it “the insides are gone”) and her name reassigned to fetus 66691 in a growth chamber. This suggests that she has been declared “incurable” and killed.
Alone and hunted, SEN makes a tentative exploration of the limits of the city’s underground network. Cowed by what he sees, he finds his way to an area reserved for the monks of OMM. Alone, SEN prays directly to OMM before being confronted by a lone monk who notices that SEN has no identification badge. SEN attacks before the monk can report him. Returning to the city, SEN strikes up a conversation with children before police androids apprehend him.
THX and SRT steal two cars, but SRT crashes into a concrete pillar, disabling it (it is uncertain whether SRT survives the impact, although the film’s script indicates he does not). Pursued by two police androids on motorcycles, THX flees to the limits of the city’s underground road network.
Eventually THX locates a route to the surface. The police pursue THX up an escape ladder, but are ordered by central command to cease pursuit, mere steps away from capturing him, as the expense of his capture exceeds their pre-determined budget. THX stands before a large setting sun in a red sky, while birds intermittently fly overhead, indicating that life is possible on the surface.