Sensation as the Perception of Invariants
What is an invariant
An invariant is a property or quantity that remains unchanged when a system undergoes transformations.
In other words:
An invariant is something that remains the same during transformations or in the course of a process.
One can also say:
An invariant is a characteristic of an object or a process that remains unchanged under a certain class of transformations.
The term invariant is used almost identically in many different sciences. This is interesting because the same idea is preserved everywhere:
something remains the same despite changes.
This concept plays an important role in every field.
Mathematics
In mathematics, the concept of an invariant is fundamental.
For example:
- the area of a figure remains the same under rotation
- the distance between points remains the same under translation
Such quantities are called invariants of transformations.
Physics
In physics, invariants are closely connected with conservation laws.
For example:
- energy
- momentum
- electric charge
These quantities remain constant while a system undergoes changes.
Music
In music, invariants are the relations between sounds that remain preserved under different transformations of a melody.
For example, we can still recognize a melody even if:
- it is played in another key
- the tempo is changed
- it is performed on another instrument
In these cases the interval structure of the melody — the relations between the notes — remains the same.
This structure is the invariant of the melody.
Language
In language we can also speak of invariants.
For example, the same word may be pronounced differently:
- with different intonation
- at different speaking speeds
- by different speakers
However, it remains the same word of the language.
Linguists say that concrete pronunciations are variants, while the word as a unit of language is an invariant.
Biology
In biology, invariants can be observed in the structure of living organisms.
For example, different vertebrate animals share the same basic skeletal plan:
- spine
- limbs
- skull
Despite enormous differences between species, this general structure remains the same.
It is an invariant of the organism’s structure.
Computer science
In computer science, invariants are often used when describing algorithms.
For example, during the execution of a program certain conditions must remain true at every step of the algorithm.
Such conditions are called algorithm invariants.
They make it possible to prove the correctness of a program.
Art
In art, invariants appear in the composition of a work.
For example, in ornaments or architecture one can observe:
- repeating forms
- symmetries
- stable geometric structures
Individual elements of a pattern may change, but the basic compositional scheme remains the same.
This scheme is the invariant of the composition.
Invariants in the psychology of perception
In the psychology of perception there exists the concept of invariant properties of objects.
For example, we recognize an object even if:
- it is rotated
- the lighting is different
- it is partly occluded
In other words, the brain detects invariant features of the object.
This idea was developed by the psychologist James J. Gibson (1904–1979).
Example from everyday perception
We recognize a familiar person even if:
- they have grown older
- they have changed their hairstyle and style of clothing
- they are in a different mood or state of health.
Despite these changes, we perceive the same person.
This is possible because perception preserves invariant features of the object, which allow us to recognize it under different conditions.
Perception of movement
For example, we recognize a running person, even if:
- they are at different distances
- they move faster or slower
- they are seen from different angles.
Despite these changes, we perceive the same action — running.
This happens because perception preserves the invariant structure of the movement, which allows the action to be recognized under different conditions.
Sensation as the Perception of Invariants
In mathematics, physics, language, biology, music, and art, the concept of an invariant denotes the same thing: that which remains unchanged under various transformations or in the course of a process.
Every process consists of what remains the same and what changes.
The completeness of perception is possible only when both of these aspects are perceived.
Both irrational functions — sensation and intuition — perceive objects and their actions over time.
Sensation is the perception of the invariants of objects and their actions, whereas intuition is the perception of the changes of objects and their actions.
Thus these two functions are opposite to each other, yet together they constitute the completeness of perception.