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Invariance: meaning, definitions and examples

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invariance

 

[ɪnˈvɛərɪəns ]

Definitions

Context #1 | Noun

mathematics

The property of remaining unchanged under a set of transformations or operations.

Synonyms

constancy, stability, unchangeability.

Which Synonym Should You Choose?

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Word Description / Examples
invariance

In scientific or mathematical contexts, to describe something that does not change under specific conditions or transformations.

  • The invariance of physical laws under different reference frames is a fundamental concept in physics.
  • Mathematical invariance is essential when discussing symmetries in geometry.
constancy

To emphasize steadiness or permanence over time, often in a general or personal context.

  • Her constancy in her beliefs has always inspired me.
  • The constancy of the tides is a comforting concept for many.
stability

Often used to describe something that is firmly fixed, not prone to change, and resistant to disturbance. Applicable in both physical and metaphorical contexts.

  • Economic stability is crucial for any nation’s development.
  • The table has excellent stability, making it sturdy and reliable.
unchangeability

To highlight something that cannot be altered or modified, often with a focus on permanence. It can have a negative connotation if implying inflexibility.

  • The unchangeability of the company policies has led to some dissatisfaction among the employees.
  • The unchangeability of the ancient laws meant they were respected across generations.

Examples of usage

  • The concept of invariance is fundamental in the field of mathematics.
  • Invariance allows us to study the properties of objects that do not change under certain conditions.
Context #2 | Noun

physics

A quantity that does not change when a particular transformation is applied.

Synonyms

conservation, preservation, rigidity.

Which Synonym Should You Choose?

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Word Description / Examples
invariance

Invariance is used to describe a property or condition that does not change under specific conditions or operations. It is commonly used in mathematical and scientific contexts.

  • The invariance of the speed of light is a key principle in relativity theory.
  • The invariance of a function under rotation is crucial in studying symmetry.
conservation

Conservation refers to the maintenance or protection of a resource or condition, often in the context of natural resources or energy. It implies an effort to ensure something remains constant or sustainable over time.

  • The conservation of energy is a fundamental concept in physics.
  • Efforts are being made towards the conservation of endangered species.
preservation

Preservation is often used to talk about the process of keeping something in its original state or preventing it from decay or harm. This term is frequently seen in the contexts of historical, cultural artifacts, and food.

  • The preservation of historical buildings is important for cultural heritage.
  • Proper preservation techniques are essential for keeping food fresh.
rigidity

Rigidity refers to the quality of being stiff or unyielding. It can describe physical properties, attitudes, or systems that do not easily change. This word can carry a negative connotation when referring to people or policies.

  • The rigidity of the material makes it ideal for construction.
  • His rigidity in following the rules made him difficult to work with.

Examples of usage

  • In physics, certain laws exhibit invariance under different conditions.
  • The principle of invariance plays a crucial role in understanding the behavior of physical systems.

Interesting Facts

Mathematics

  • Invariance is crucial in mathematics, particularly in geometry, where certain properties of shapes remain the same despite transformations like rotation or scaling.
  • In calculus, the concept of invariance helps in understanding how functions behave under different conditions or coordinates.
  • The principle of invariance is foundational in physics, as it ensures that the laws of nature remain consistent across different frames of reference.

Physics

  • Invariance is pivotal in the theory of relativity, where the laws of physics do not change for observers regardless of their relative speed.
  • Symmetry is related to invariance; physical systems are often studied based on how they remain unchanged under certain transformations.
  • The conservation laws in physics, like energy and momentum, are examples of invariance, stating that these quantities do not change within a closed system.

Computer Science

  • Invariance is a concept in programming, where certain properties of data structures remain unchanged to ensure reliability and security of applications.
  • Static typing in programming languages helps maintain invariance, as it prevents certain types of changes to data types after they are defined.
  • Machine learning models often strive for invariance to generalize better from training data to unseen data, avoiding overfitting.

Cognitive Science

  • In cognitive psychology, invariance refers to how humans can recognize objects as the same despite changes in perspective or lighting.
  • Research suggests our brains use invariance to understand language, recognizing words even when spoken differently depending on context.
  • The idea of perceptual invariance helps explain how individuals can identify faces consistently, regardless of changes in expression or angle.

Philosophy

  • Invariance plays a role in philosophical discussions about identity and change, questioning how something can remain the same over time despite alterations.
  • The notion of invariance in ethical theories debates whether moral principles can remain constant in varying cultural or temporal contexts.
  • Invariance raises questions in metaphysics about the nature of reality, questioning what elements of existence are truly unchanging.

Translations

Translations of the word "invariance" in other languages:

🇵🇹 invariância

🇮🇳 अपरिवर्तनीयता

🇩🇪 Invarianz

🇮🇩 ketidakvariasian

🇺🇦 незмінність

🇵🇱 niezmienność

🇯🇵 不変性 (ふへんせい)

🇫🇷 invariance

🇪🇸 invariancia

🇹🇷 değişmezlik

🇰🇷 불변성 (bulbyeonseong)

🇸🇦 ثبات

🇨🇿 neměnnost

🇸🇰 nemennosť

🇨🇳 不变性 (búbiànxìng)

🇸🇮 nespremenljivost

🇮🇸 óbreytanleiki

🇰🇿 өзгермейтіндік

🇬🇪 უცვლელობა

🇦🇿 dəyişməzlik

🇲🇽 invariancia

Word Frequency Rank

With rank #17,737, this word belongs to specialized vocabulary. While not common in everyday speech, it enriches your ability to express complex ideas.