Hole

A hole is an opening in or through a particular medium, usually a solid body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in many fields of engineering. Depending on the material and the placement, a hole may be an indentation in a surface (such as a hole in the ground), or may pass completely through that surface (such as a hole created by a hole puncher in a piece of paper).

Holes can occur for a number of reasons, including natural processes and intentional actions by humans or animals. Holes in the ground that are made intentionally, such as holes made while searching for food, for replanting trees, or postholes made for securing an object, are usually made through the process of digging. Unintentional holes in an object are often a sign of damage. Potholes and sinkholes can damage human settlements.

Holes can occur in a wide variety of materials, and at a wide range of scales. The smallest holes observable by humans include pinholes and perforations, but the smallest phenomenon described as a hole is an electron hole, which is a position in an atom or atomic lattice where an electron is missing. The largest phenomenon described as a hole is a supermassive black hole, an astronomical object which can be billions of times more massive than Earth's sun.

The deepest hole on Earth is the man-made Kola Superdeep Borehole, with a true vertical drill-depth of more than 7.5 miles (12 kilometers), which is only a fraction of the nearly 4,000 mile (6,400 kilometer) distance to the center of the Earth.

In mathematics, holes are examined in a number of ways. One of these is in homology, which is a general way of associating certain algebraic objects to other mathematical objects such as topological spaces. Homology groups were originally defined in algebraic topology, and homology was originally a rigorous mathematical method for defining and categorizing holes in a mathematical object called a manifold. The initial motivation for defining homology groups was the observation that two shapes can be distinguished by examining their holes. For instance, a circle is not a disk because the circle has a hole through it while the disk is solid, and the ordinary sphere is not a circle because the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. Because a hole is immaterial, it is not immediately obvious how to define one or distinguish it from others.

Another is the notion of homotopy group: these are invariants of a topological space that, when non-trivial (one also says in this case that the space is not k-connected), detect the presence of "holes" in the sense that the space contains a sphere that cannot be contracted to a point. The term of hole is often used informally when discussing these objects.

For surfaces a notion closer to the intuitive meaning exists: the genus of a connected, orientable surface is an integer representing the maximum number of cuttings along non-intersecting closed simple curves without rendering the resultant manifold disconnected. In layman's terms, it is exactly the number of "holes" the surface has, when represented as a submanifold in 3-space.

In physics, antimatter is pervasively described as a hole, a location that, when brought together with ordinary matter to fill the hole, results in both the hole and the matter cancelling each-other out. This is analogous to patching a pothole with asphalt, or filling a bubble below the surface of water with an equal amount of water to cancel it out. The most direct example is the electron hole; a fairly general theoretical description is provided by the Dirac sea, which treats positrons (or anti-particles in general) as holes. Holes provide one of the two primary forms of conduction in a semi-conductor, that is, the material from which transistors are made; without holes, current could not flow, and transistors turn on and off by enabling or disabling the creation of holes.