projection
Pluralprojections
- 1A forecast or estimate of a future value, reached by extending current trends or data.
The budget projection shows revenue climbing through the summer.
Analysts based their projection on five years of sales data.
Similarforecast, estimate, prediction, extrapolation, outlook
- 2
- 3The assumption that others share one's own thoughts and feelings, including blaming others for faults that more truly belong to oneself.
Her projection led her to assume her colleagues resented her, though no one did.
Accusing others of selfishness can itself be a form of projection.
Note
Psychology's name for a defense in which what a person cannot own in themselves is seen in someone else. John W. Vann, writing in 1937, calls it a mechanism used almost universally to place the blame for one's acts on others. The verb takes onto: Judith Plaskow, quoting Mary Daly in 1980, writes of a part of the psyche "projected onto 'the Other.'"
- 4A part that protrudes or juts out from a surface or body.
A bony projection at the base of the skull anchors several neck muscles.
The sculpture's sharp projection caught the light and threw a long shadow.
Similarprotuberance
Oppositerecess, indentation, hollow
- 5The act of throwing, propelling, or casting something forward.
The catapult's projection of the boulder cleared the castle wall.
Good breath control improves the projection of a singer's voice.
Similarpropulsion, launch, throwing, hurling
Note
Here the noun is simply the action of its verb: project plus -ion, borrowed through Middle French or directly from Latin prōiectiō. A jutting ledge, a cast image and a forecast are all, in their way, things projected. Its cousins in other languages share the same Latin shape: French projection, German Projektion, Italian proiezione.
- 6A system of intersecting lines, with its supporting mathematics, used to represent the curved surface of the Earth on a flat map.
The Mercator projection preserves angles but badly exaggerates area near the poles.
Cartographers select a projection based on which properties they need to keep accurate.
Note
In cartography the word names both the grid and the mathematics behind it, so a map is drawn on a projection. Flattening a curved surface always costs something: area, shape, distance or direction. Choosing a projection means choosing which of these to keep accurate. It is the best-known everyday case of the geometer's flattened image.
- 7An image of an object cast onto a surface of fewer dimensions, such as a three-dimensional form represented on a flat plane.
The projection of the sphere onto the plane appears as a flat disk.
Engineers study the orthographic projection of a part to read its true dimensions.
Similarview, image, representation
Note
Geometry's broadest version of the idea covers a solid drawn on a plane, a sphere seen as a flat disk, or any figure carried down into fewer dimensions. A qualifying adjective usually names the method, as in orthographic projection in engineering drawing. Something is always lost when a dimension drops away, which is why a single projection rarely shows the whole shape.
- 8The image that a translucent object casts onto another surface when light passes through it.
The lampshade threw a warm projection onto the ceiling.
Photographers used the projection of a backlit leaf to study its delicate veins.
Similarimage
Note
A photographer's sense in which light passes through the object instead of being thrown by a machine. A lampshade or a backlit leaf casts its own pattern onto whatever lies behind it. That separates it from the projector's image, which a device produces, and from a shadow, which an opaque object leaves only as an outline.
- 9A linear transformation that maps vectors onto a subspace and leaves them unchanged when applied a second time.
The projection maps each vector onto its component within the chosen subspace.
Because it is idempotent, the projection leaves vectors already in the subspace unchanged.
Note
In linear algebra the defining test is that doing it twice changes nothing: P² = P, the property called idempotence. Vectors already in the subspace stay where they are, and everything else is sent onto it. The usual construction is "projection onto" a subspace, as in the projection of a vector onto a plane.
- 10The distance from the skin over which a perfume's scent can be detected.
Reviewers praised the perfume's projection, which filled the room for hours.
Warm skin tends to boost a fragrance's projection.
Similarthrow, diffusion, reach
Note
Perfumers separate how far a scent travels from how long it lasts: projection is the reach, and longevity is the duration. A fragrance with low projection stays close to the wearer and is called a skin scent. Sarah McCartney and Samantha Scriven's The Perfume Companion (2021) explains this by its less volatile materials. Reviews usually grade projection from high to low.
- 11A transformation that extracts a fragment or component from a larger mathematical object.
The projection returns the first coordinate of each ordered pair.
Applying the projection strips away every component except the one selected.
Note
A broad mathematical use in which the transformation simply picks out a part, such as the first coordinate of an ordered pair or one field of a record. Such maps are usually numbered by what they return: the first projection, the second projection. The category-theory version states the same idea abstractly.
- 12In category theory, a morphism from a product object to one of its component objects.
The projection sends the product object to its first component.
A categorical product is equipped with a projection onto each factor.
Note
Category theory takes the coordinate-picking of the general mathematical sense and makes it part of what a product is. A product comes equipped with a projection onto each factor. What makes these maps special is a universal property: any two morphisms into the factors pass uniquely through the product. For that reason the word often appears in the plural here.
- 13The preservation of a lexical item's properties as the phrase structure of a sentence is generated.
Projection ensures that a verb's argument structure is reflected throughout the syntactic tree.
Under projection, the properties of each word constrain the phrases built around it.
Note
Generative syntax gives the idea its fullest form in the Projection Principle. The properties a word brings from the lexicon, such as the arguments a verb requires, must hold at every level of a sentence's structure. A verb that needs an object keeps needing one throughout the tree. Outside linguistics the term is theory-internal vocabulary.
- 14A supposed process by which alchemists believed large quantities of base metals could be transmuted, as into gold or silver.
He swore that a single grain of the stone, cast in projection, would ennoble a whole pound of mercury.
[Helmont] says, on another occasion, that an adept, after a few days of acquaintance, presented him with half a grain of the powder of projection, with which he transmuted nine ounces of quicksilver into pure gold.
1888, Arthur Edward Waite, Lives of Alchemystical PhilosophersNote
An alchemist's term, now obsolete, for the act that turned base metal into gold or silver in bulk. Robert Boyle, in 1666, already keeps his distance, writing of a powder only "said" to change hundreds or thousands of parts of ignobler metal. The fixed phrase is "powder of projection", which Arthur Edward Waite's Lives of Alchemystical Philosophers (1888) still uses.
- 15The critical, decisive stage reached in any process, especially one in cooking.
The sauce reached its projection just as the guests arrived, thickening to a perfect gloss.
She judged the projection of the boiling syrup by its color and bubbles.
Note
An archaic use for the moment a process tips one way or the other, such as the instant a sauce or syrup comes right. It belongs to period writing and historical texts. In modern prose it would puzzle most readers, and "the critical point" or "the turning point" says the same thing plainly.
Practice
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Origin
Borrowed either from Middle French "projection" or directly from its source, the Classical Latin "prōiectiō" (stem "prōiectiōn-"), from "prōiciō"; equivalent to "project" plus "-ion". Compare Modern French "projection", German "Projektion", and Italian "proiezione".