(Written text posted at 8:40pm, CST, with some additions at 10:08pm, 3/3/08.)
(Endnote added at 11:58pm, CST, 3/3/08.)
2.342 @ 11 HERTZ:
MAPPING A NEW WORLD LINE
I'll keep this one short.... Per my "Island Compass" posting on 3/1/08, the Black Rock ledger contains a record of the spacetime events the ship encountered during its voyages, including the where and when of wormhole events occurring on Earth, part of an interconnected, trans-global wormhole transit system. Whether or not this system links to off-world sites remains to be seen.
As such, the Black Rock voyages in general, and the ledger in particular, serve to document a crucial element in understanding the emerging spacetime dynamics on the show. In particular, the ledger has mapped a WORLD LINE for the shifting, globe-spanning wormhole events:
"In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime. The concept of "world line" is distinguished from the concept of "orbit" or "trajectory" (such as an orbit in space or a trajectory of a truck on a road map) by the time dimension, and typically encompasses a large area of spacetime wherein perceptually straight paths are recalculated to show their (relatively) more absolute position states — to reveal the nature of special relativity or gravitational interactions. The idea of world lines originates in physics and was pioneered by Einstein. The term is now most often used in relativity theories (i.e., general relativity and special relativity)...." (Source:
http://en.wikipedia.org/wiki/World_line)
With this bit of definitional prolegomenon out of the way, things begin to pick up steam, here:
"In physics, a world line of an object (approximated as a point in space, e.g., a particle or observer) is the sequence of spacetime events corresponding to the history of the object. A world line is a special type of curve in spacetime. Below an equivalent definition will be explained: A world line is a time-like curve in spacetime. Each point of a world line is an event that can be labeled with the time and the spatial position of the object at that time. For example, the orbit of the Earth in space is approximately a circle, a three-dimensional (closed) curve in space: the Earth returns every year to the same point in space. However, it arrives there at a different (later) time. The world line of the Earth is a helix in spacetime (a curve in a four-dimensional space) and does not return to the same point.... a world line is the sequential path of personal human events (with time and place as dimensions) that marks the history of a person — perhaps starting at the time and place of one's birth until their death. The log book of a ship is a description of the ship's world line, as long as it contains a time tag attached to every position. The world line allows one to calculate the speed of the ship, given a measure of distance (a so-called metric) appropriate for the curved surface of the Earth." (Source:
http://en.wikipedia.org/wiki/World_line)
So by charting the where and when of recurrent wormhole activity on 19th Century Earth, the Black Rock actually helped establish a baseline record of the periodic appearance of multiple wormholes operating on the Earth, noting entry/exit points, and when these points opened up. It is important to note here that for the purpose of World Line mapping the interconnected wormhole system on Earth, one must map the PLACE (space) and TIME of both the entry to and exit from the wormhole, as it is this relation that constitutes the wormhole event, not one or the other.
Thus it would be a mistake to look at a grid or map and simply connect the dots in a linear manner. To properly read the Black Rock ledger, one must interpret the notations as spacetime coordinates, designating four-dimensional entry and exit positions, mapping the World Lines of the interconnected terran wormhole system. So yes, the ledger's entries will be short one SPACE coordinate, which will have to be calculated after the fact, in order for the ledger to be used by Widmore and his associates to properly calculate future wormhole events. In particular, the ledger will have entries designating the time and the latitude and longitude for the events, namely three of the four spacetime coordinates.1 (See the below quote for an explanation of what this entails.) Are the wormhole world line maps what Charles Widmore is after, to obtain the spacetime coordinates that will enable him to know when and where the wormholes will operate?
And here is where it begins to get most interesting, when we consider the proper notation for spacetime coordinates in the World Line approach:
"Spacetime is the collection of points called events, together with a continuous and smooth coordinate system identifying the events. Each event can be labeled by four numbers: a time coordinate and three space coordinates; thus spacetime is a four-dimensional space. The mathematical term for spacetime is a four-dimensional manifold."
So here it is.... "2.342" looks like it may in fact refer to a SPACE-TIME EVENT on the WORLD LINE, with the first digit indicating a time setting, and the next three digits indicating three (dimensional) space settings. In effect, Faraday may have given Desmond the spacetime coordinates for, and the frequency with which to set the oscillations of, the 'rebooting' or resetting one of Faraday's spacetime devices, either a new machine we have not yet seen, or his 'purple ray' mind-time-travel device.
"A one-dimensional line or curve can be represented by the coordinates as a function of one parameter. Each value of the parameter corresponds to a point in spacetime and varying the parameter traces out a line. So in mathematical terms a curve is defined by four coordinate functions (where x0 usually denotes the time coordinate) depending on one parameter τ. A coordinate grid in spacetime is the set of curves one obtains if three out of four coordinate functions are set to a constant." (Source:
http://en.wikipedia.org/wiki/World_line)
It may turn out that the seemingly simple "2.342" spacetime coordinate is translatable into a coordinate spacetime grid by Faraday or someone else.... Indeed, if Desmond is Faraday's constant, is there a double/mirror meaning to that entry in his notebook? What is Faraday's constant translated into numerical form? And what might this tell us about the spacetime grid on which the island and the wormholes may be connected and operating?
Copyright 3/3/08
by Dr. Todd J. Hostager
ENDNOTE:
1. Yes, ships sailing in the mid-Nineteenth Century had the capability to determine longitude. While finding latitude was relatively easy, identifying longitude at sea was a problem for centuries:
"Until the mid 1750s, navigation at sea was an unsolved problem due to the difficulty in calculating longitudinal position. Navigators could determine their latitude by measuring the sun's angle at noon. To find their longitude, however, they needed a portable time standard that would work aboard a ship. Observation of celestial, 'clockwork' motions such as Galileo's method based on observing Jupiter's natural satellites was usually not possible aboard due to the ship's motion." (Source:
http://en.wikipedia.org/wiki/Marine_chronometer)
And so the search begain for a mechanism to calculate time while at sea:
"The purpose of a chronometer is to keep the time of a known fixed location, which can then serve as a reference point for determining the ship's position. By comparing local high noon to the chronometer's time, a navigator could use the time difference to determine the ship's present longitude. Since the Earth rotates 360 degrees every day (that is, 24 hours or 1,440 minutes), the time difference between the two points reveals how many degrees separate them. With the degrees of difference in hand, locating the position on a map was a relatively simple matter of spherical trigonometry. (Source:
http://en.wikipedia.org/wiki/Marine_chronometer)
But designing and executing the mechanism proved challenging:
"The creation of a seaworthy timepiece was difficult. Until the 20th century, the best timekeepers were pendulum clocks, but the rolling of a ship at sea rendered the ordinary, gravity-based pendulum useless. John Harrison, a Yorkshire carpenter, invented a clock based on a pair of counter-oscillating weighted beams connected by springs whose motion was not influenced by gravity or the motion of a ship. His first two sea timekeepers used this system, but he became rightly convinced that they had a fundamental sensitivity to centrifugal force, which meant that they could never be accurate enough at sea. Construction of his third machine, designated H3, included novel circular balances and the invention of the bi-metallic strip and caged roller bearings (both inventions are still widely used today). H3's circular balances proved too inaccurate and he eventually abandoned the large machines. Harrison solved the precision problems with his H4 chronometer design. H4 appeared much like a large five-inch (12 cm) diameter pocket watch. In 1761 Harrison submitted H4 for the £20,000 longitude prize that had been offered by the British government in 1714. His design used a fast-beating balance controlled by a temperature compensated spiral spring. This general layout remained in use until microchips reduced the cost of a quartz clock to the point that electronic chronometers became commonplace."
This article goes on to note that from 1825 forward, the British Navy routinely installed chronometers on its vessels.
While at first glance it might appear that these vessels were only measuring two of the four spacetime coordinates-- latitude and longitude, with time= longitude-- on further inspection, this does not pass muster; although longitude may provide a crude measure of the local time of DAY, it does not record additional temporal data relating to day of the week, and year. These data are crucial if one is to properly calculate periodic wormhole operation on a planet (Earth) that is moving through space(time). In addition, the third space coordinate must not be overlooked if one is to predict the future World Lines of these important and (especially to Widmore!) valuable events.