# Distance

• The extent or amount of space between two things, points, lines, etc.
• The state or fact of being apart in space, as of on thing from another; remoteness.
• A linear extent of space: “Seven miles is a distance too great to walk in an hour.”
• An expanse; Area: “A vast distance of water surrounded the ship.”
• The interval between two points of time; an extent of time.
• Remoteness or difference in any respect.
• An amount of progress.

Distance is a numerical description of how far apart objects are. In physics or everyday usage, distance may refer to a physical length, or an estimation based on other criteria (E.G “Two countries over”). In mathematics, a distance function or metric is a generalization of the concept of physical distance.

Canberra distance = A weighted version of Manhattan distance, used in computer science.

Energy distance, the statistical distance between probability distributions.

Kullback-leibler divergence, which measures the difference between two probability distributions.

Mahalanobis distance is used in statistics.

Distance cannot be negative, and distance traveled never decreases.

In mathematics, a metric space is a set for which distance between all members of the set are defined. In one way, many different types of ‘distances’ can be calculated, such as for traversal of graphs, comparison of distance and curves, and using unusual definitions of ‘space’.

In psychology, human geography, and the social sciences, distance is often theorized not as an objective metric but as a subjective experience.

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(Shown in Notebook 1, pages 36 – 38).