Instantaneous Events
In the realm of mathematics, "instantaneous events" refer not to events that occur in an incredibly short amount of time, but to events that occur at an exact point within a defined vector space, including the space-time continuum. The duration of these events--that is, the time that elapses between the start of the event and the end of the event is not only infinitesimally small, it is zero. Instantaneous events capture a single, exact point in time. A good, but not perfect, analogy is a still picture produced by a camera. The picture captures a particular scene or object, or particular expression, at a single moment in time for later viewing. The conditions under which the photograph was taken can likely be reproduced with similar results--that is, results so similar to the original that differences are entirely negligible--but the event itself cannot be exactly reproduced.
Instantaneous events are closely related to the mathematical concepts of derivative and limits. Instantaneous values can provide a means to express the rate of change of one parameter of an object relative to another parameter of the same object. Instantaneous velocity, for example, provides an expression of how an object's position in space is changing relative to the existence of the object in time. This expression may encompass a number of sub-parameters, which can be considered dimensions in themselves.
For example, at an given moment in time, the position of a runner along a straight track is generally measured in just one direction--along the straight line, the axis of travel (call it x). The instantaneous event is the runner's speed and direction at that exact moment in time. A child playing hopscotch, however, moves horizontally--along both the straight line of the sidewalk (that is, along the x-axis)--and vertically (that is, in the air along a y-axis) as a result of the "hopping" motion. The instantaneous event captures the rates of change in two directions with respect to time. Similarly, the instantaneous velocity of an airplane 20 seconds after take-off will capture the rates of change in three directions (along the x-, y-, and z-axes, if the Cartesian coordinate system is used) with respect to time.
Since instantaneous values can describe the change of one parameter of an object relative to another, it is common to use a direction in space or time as the reference parameter. An emergency crew, for example, may be interested in the height of a flooding river over its normal water level. This instantaneous value may be critical to determining whether an area must be evacuated for safety.
Interestingly enough, it is not often possible to measure instantaneous values, even with the most sensitive measuring equipment. If a thermometer is placed in a refrigerator for a number of hours and then placed at room temperature, the mercury level (or digital display) will take a finite amount of time to register the change--perhaps seconds or even minutes. Like all scientific instruments, the thermometer is simply not sensitive enough to measure the room temperature immediately or instantaneously. It must measure the value over a finite amount of time and then report the average value of the measurement. Even the most sophisticated scientific instruments have limits on their accuracy. Speeds of an object, for example, may be measured to the nearest picosecond (1 x 10 ^-12 second) but even then, the value is not instantaneous. Instead, an average value over an extremely small time interval is given.
For two events to occur instantaneously, they must somehow overlap over a finite period of time, which may be so small as to appear negligible to the viewer. In digital computer architectures, the concept of instantaneous events is most often referred to as a collison and is defined as the arrival of two pieces of information (such as a bit) at the same location during the same time interval. This collision occurs because even the fastest computers operate according to an internal clock, processing a bit of information in a finite period of time. If two bits of information are traveling along independent paths that then merge, the bits have the potential to collide since the processor in after the merge point handles bits as discrete objects, not continuous objects. If so much data is being processed that the bit stream must be queued, it is possible that two items of data will try to "merge" into the same place in the queue during the same time intervals. These happenstances are collisions.
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