Where does degeneracy collide?

The condition in which two or more distinct quantum states of a system share exactly the same energy: such an energy level is called degenerate, and the number of independent states sitting at that level is the degeneracy of the level. Griffiths and Schroeter's 2018 Introduction to Quantum Mechanics describes how symmetry gives rise to degenerate levels and how a perturbation, such as an applied magnetic field, can split them into separated energies, as in the Zeeman effect. The referent is a count of distinct states pinned to one energy, not a code that spells an amino acid with several codons, a collapsed limiting case of a geometric figure, or the ability of unlike biological parts to do the same job.[1]

Unit

One energy level and the number of distinct states sharing it, its degeneracy

Recovery means

A perturbation such as a magnetic or electric field can lift the degeneracy, splitting the single level into separated energies

Measured by

Read from spectral lines: a degenerate level appears as one line that splits into several when a field is applied, and the number of components reveals the degeneracy

The property that the genetic code is redundant: most of the twenty amino acids are specified by more than one of the sixty-one coding triplets, or codons, so several different codons can carry the same instruction. Crick's 1966 wobble hypothesis, in Codon-anticodon pairing: The wobble hypothesis, explained the pattern by proposing that the third base of a codon pairs loosely, or wobbles, with the transfer RNA anticodon, so one transfer RNA can read several codons that differ only in that last position. The referent is a redundancy in a molecular coding scheme, not a set of quantum states at one energy, a degenerate figure in geometry, or the capacity of different biological structures to perform one function.[2]

Unit

One amino acid and the several synonymous codons that encode it

Recovery means

Not applicable

Measured by

Read off the codon table as the number of synonymous codons per amino acid, and confirmed by which transfer RNAs decode which triplets

A degenerate case is a limiting or special example in which a mathematical object loses the structure that defines its general type and collapses into something simpler. A conic section becomes degenerate when the cutting plane passes through the cone's apex, so the curve is really a single point, one line, or a pair of crossing lines rather than an ellipse, parabola, or hyperbola; likewise a square matrix is called degenerate, or singular, when it collapses volume to zero and has no inverse. Richter-Gebert's 2011 Perspectives on Projective Geometry treats such degenerate conics as boundary cases within the wider family of all conics. The referent is a structure-losing special case of a general form, not quantum states sharing an energy, redundant codons, or interchangeable biological parts.[3]

Unit

One limiting configuration in which a general object collapses to a simpler one

Recovery means

Not applicable

Measured by

Detected by an algebraic condition that vanishes: a zero determinant for a singular matrix, or a vanishing discriminant marking a conic as degenerate

In biology, degeneracy is the ability of elements that are structurally different to perform the same function or yield the same output. It is set apart from redundancy, where identical elements do the same job: degenerate elements are not alike, yet they converge on one result, as when different neural circuits, genes, or metabolic pathways produce equivalent behaviour. Edelman and Gally's 2001 Degeneracy and complexity in biological systems argued this is a ubiquitous property of living systems and both a requirement for and a product of natural selection. The referent is a many-different-parts-to-one-function relation in biology, not a coincidence of energy levels, a code's redundant spelling, or a collapsed geometric case.[4]

Unit

A set of structurally different components that yield the same functional output

Recovery means

Not applicable

Measured by

Shown by perturbation and lesion studies: a structure is knocked out or varied, and the same function persists through alternative routes