LOST maintained it’s tradition of anachronisms last night, hinting that the complex task of manipulating space and time is best done with 8-bit computers and ancient magnetic field plotters. Could the choice of devices also point to the apocalyptic nature of LOST‘s endgame? Next, what could be so important about an island off the coast of Georgia? Only the LOST braintrust knows.
The brewskis that Lapidus fetched from Searcher’s fridge have a somewhat ominous label, and name. ‘Jekyll Island’ brings to mind the Robert Lewis Stevenson novella Strange Case of Dr Jekyll and Mr Hyde, which chronicles the adventures of a man who dabbles with science and winds up cursed with a violent alternate personality. Could this reflect that one of our characters has a hidden darkside? Maybe not, Jekyll Island is a real place – an island off the coast of Georgia that is named for a real Mr. Jekyll, who did not have a split personality.
Of course, it could mean nothing at all – since the company “Studio Graphics,” which creates props for television shows, was the one that developed the concept. Innocent choice, or artful use of found props – you be the judge.
Next up is the massive chalk plotter in Mrs. Hawking’s-or should we say Mrs. Faraday’s?-personal Dharma station. in case you missed the little Dharma logos plastered all over the binders and the computers, let there be no doubt that this is the off-island Dharma station we’ve heard so much about. Now about that device that is so strange it had to have been made up…
It’s real. The Foucault pendulum was created to verify that the earth was spinning. The pendulum required a large electromagnet to run indefinitely; and true to their reputation for attention-to-detail – the set included one (see image below.) Since the device physically extrapolates a reading between the forces of gravity and the magnetic poles, it is capable of ferreting out any associated abnormalities. The question here is whether LOST’s pendulum is sussing out minor fluctuations in the earth’s gravitational field, or major shifts that could end up spelling doom for our Losties, and the rest of mankind?
From the perspective of an inertial frame outside of Earth, the suspension point of the pendulum traces out a circular path during one sidereal day. No forces act to make the plane of oscillation of the pendulum rotate – the plane contains the plumb line, so the force acting on the pendulum is parallel to the plane of oscillation at all times. But the plane satisfies the constraint that it contains the plumb line. Thus the plane of oscillation undergoes parallel transport. The difference between initial and final orientations is as given by the Gauss-Bonnet theorem. ? is also called the holonomy or geometric phase of the pendulum. Thus, when analyzing earthbound motions, the Earth frame is not an inertial frame, but rather rotates about the local vertical at an effective rate of radians per day, which is the magnitude of the projection of the angular velocity of Earth onto the normal direction to Earth.
From the perspective of an Earth-bound coordinate system with its x-axis pointing east and its y-axis pointing north, the precession of the pendulum is explained by the Coriolis force. Consider a planar pendulum with natural frequency ? in the small angle approximation. There are two forces acting on the pendulum bob: the restoring force provided by gravity and the wire, and the Coriolis force. The Coriolis force at latitude ? is horizontal in the small angle approximation and is given by
where ? is the rotational frequency of Earth, Fc,x is the component of the Coriolis force in the x-direction and Fc,y is the component of the Coriolis force in the y-direction.