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Parallax is the optical illusion that two stationary points change in position relative to each other, due to a difference in position of the person viewing them.

The two points in question will be different distances from the observer and the illusion of parallax is caused by the fact that light, follows straight lines. When the observer views the nearer point, the line of his vision toward that point is at a given angle within the full arc of his vision. For example, let us say that the view straight ahead is zero degrees, and one point, nearer the observer, is at minus five degrees while a point which is farther away is at minus two degrees. The apparent angular distance between the points is a subjective three degrees to the viewer. If the viewer moves ten meters to his right, the angular direction to the nearer object, as it is on a shorter radius, will change more than the angular direction to the farther object. So, for instance, when the angular direction to the nearer object is at minus ten degrees, the father object may only have moved to minus three degrees. Now the subjective angular difference in position is seven degrees. The objects appear to have moved relative to each other.

On a macro scale, this effect is responsible for the fact that, in a moving car, one can look at distant mountains and see them seem to move (retard) in position beneath a seemingly motionless moon. The moon is at such a distance that the subjective angular change in position relative to an earth-bound observer is extremely slight, even as many miles are covered. The mountains, much closer, exhibit a much greater apparent change in angular position.

Put differently and somewhat more generally, distant objects seem to move with the car. This can be explained as follows: all objects move backward relative to the car, and for nearby objects the speed of change in direction is what the observer considers the normal consequence of his own movement; however, for distant objects the backward change in direction is slow and much less obvious than the forward change in direction relative to nearby objects. It seems as if distant objects move parallel to the car with the same speed or a little slower.

Stellar parallax

On a galactic scale, parallax created by the different orbital positions of the earth causes the stars to seem to move.

The annual parallax is defined as the difference in position of a star as seen from the Earth and Sun, i.e. the angle subtended at a star by the mean radius of the Earth's orbit around the Sun. Given two points on opposite ends of the orbit, the parallax is half the maximum parallactic shift evident from the star viewed from the two points. The parsec is the distance for which the annual parallax is 1 arcsecond and hence the maximum parallactic shift is 2 arcsecond.

Measurements in parallax as the earth goes through its orbit was the first reliable way to determine the distances to the closest stars. This method was first used by Friedrich Wilhelm Bessel in 1838 when he measured the distance to 61 Cygni, and it remains the standard for calibrating other measurement methods (after the size of the orbit of the earth is measured by radar reflection on other planets). In 1989, a satellite called "Hipparcos" was launched with the main purpose of obtaining parallaxes and proper motions of nearby stars, increasing the reach of the method ten-fold.

Micro scale

On a micro scale, the thickness of a ruler can create parallax in fine measurements. One is always cautioned in science classes to "avoid parallax." By this it is meant that one should always take measurements with one's eye on a line directly perpendicular to the ruler, so that the thickness of the ruler does not create error in positioning for fine measurements. A similar error can occur when reading the position of a pointer against a scale in an instrument such as a galvanometer. To help the user to avoid this problem, the scale is sometimes printed above a narrow strip of mirror, and the user positions his eye so that the pointer obscures its own reflection. This guarantees that the user's line of sight is perpendicular to the mirror and therefore to the scale.

Parallax as a metaphor

In a philosophic/geometric sense: An apparent change in the direction of an object, caused by a change in observational position that provides a new line of sight. The apparent displacement, or difference of position, of an object, as seen from two different stations, or points of view.

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