The term "scale" has a broad set of meanings and connotations, depending on context and/or usage. A survey of terms useful in studying superscale behavior and comprehending scale are listed here.

Definition

In this website and research project, scale is used to refer to informal spatial general size categorizations. A superscale is a broad span of such general size categories.

Etymology

The derivation of the word "scale" is not clear. Some trace it to the proto-indo-european root *(s)kel- "to cut, cleave, split."

Usage

Scale As Discontinuous Category

The concept of scale as a differentiated category of size is our primary use. We clarify this definition by describing two scales, A and B, and a method for both generating and distinguishing between the scales.

Imagine a line L calibrated with regularly spaced scales to be surveyed listed in stepped sequence A, B, C. Each step bears a signifier or label. Signifier A signifies a set of phenomena A associated with the scale at step A, likewise signifiers B, C and so on. There is an operation that can be performed on set A: e.g. aggregation or disaggregation, construction or deconstruction, or motion along a path. The operation modifies set A to become set A’. Repeat the operation to generate A’’, then A’’’, until at some point the signifier A is no longer sufficient to signify the set of phenomena A’’’’, and so new signifier B is needed.

Consider now A and B. While the relation of parts within one set are elements of the same scale, the parthood relations of A to B are more complex. A and B are related by means of the operation that generated them, one succeeding the next, yet at the same time B is unrelated to A in that it inhabits a separate, unequal rank that describes B and not A. This dialectic is embodied by the word “order” as in “order of magnitude” and is called variously sequence vs. rank, dependent vs. independent, equal vs. unequal, or continuous vs. discrete.

"Scale" refers to this type of discontinous, ordered ranks of categories or sizes.

Scale as Representation System

"Scale" can refer to a continuous representation system that signifies an inter-related set of phenomena. This usage implies a comparison of entities, but not the discontinuous idea of "orders of magnitude". Examples include:
  • Scale model calibration size, such as a scale model or a model railroading scale
  • Scale factor, being the cosmological universe expansion time
  • Scale of a map
  • Musical scale: a set of inter-related musical notes, or a musical string instrument sounding length of the strings
  • Scale or gauge of a measurement: the set of numerical values mapped to its linear or logarithmic guage
  • Scalability or capacity: a metric or indication of a system's capability to function as load increases
  • Scale parameters: numerical constants used in statistics and the social sciences
  • Cosmological Scale factor: a numerical constant indicating the cosmological universe expansion time

Scale as Measurement Guage

"Scale" can signify length. This usage implies a comparison of entities, but not the discontinuous idea of "orders of magnitude". When the term scale signifies length it may refer to:
  • Scale of a calibrated dial: the set of numerical values mapped to its linear or logarithmic guage
  • Scale of duration: when describing the ordering of time, being the set of numerical values mapped the chronological values
  • Architect's scale
  • Engineer's scale
  • Linear encoder
  • Linear scale
  • Vernier scale

Scale in Mathematics

"Scale" is a common term in mathematics, usually signifying a proportion. This usage implies a comparison of entities, but not the discontinuous idea of "orders of magnitude". Some usages in mathematics include:
  • Scale factor: a numerical, proportional constant used to convert between a factors of the representational system and factors of the system being modeled.
  • Scale: a mathematical ratio
  • Scale in descriptive set theory
  • Scale parameters used in probability, being a spread or dispersion of a probability distribution
  • Geometric Scaling: a form of uniform transformation used in geometry

Scale as a Proper Name

The word "scale" sometimes forms part of a proper name, such as the name of a person or place. This usage is out of the scope of our research into scale as orders of magnitude.

Scale as a Measurement Gauge

A "scale" often signifies a receptor or method that can reliably map a number to a given phenomenon. In this usage, the term may also be part of the proper name of the method signified. This usage is out of the scope of our research into scale, as it signifies a mapping without the connotation of different cateogries of rank or size. To avoid confusion this type of scale is called a measurement-scale or gauge. Various scales of this type include:
  • Wind - Beaufort Scale. Hurricanes - Saffir–Simpson Scale. Tornadoes - Fujita Scale.
  • Hardness - Mohs scale
  • Heat of Chillies - Scoville scale
  • Earthquakes - Energy - Richter Intensity - Mercalli scale
  • Temperature - Many scales including Celsius, Kelvin, Farenheit, Rankine, Rømer, Réaumur, DeLisle, Newton
  • Lunar Eclipse brightness - Danjon Scale
  • Religious Belief - Dawkins Scale
  • Depression - Hamilton Scale
  • Acidity - ph Scale
  • Sexual orientation - Kinsey Scale
  • Physical exertion - Borg Scale
  • Pain - Various Scales

Scale as a Flat Structure

When signifying a flat structure, scale may signify
  • Scale armour, a form of protective garment
  • Scales on the skin, a form of dermatological skin lesion
  • Botanical scale, being a flat epidermal outgrowth, or flat trichome
  • Zoological Scale, being a biological rigid plate
  • Lepidopteran Scale, being the coloured flakes that coat the wings of butterflies

Scale as a Coating Structure

When signifying a structure that coats other structures, scale may signify
  • Scale, limescale (Fouling, the buildup of unwanted substances on hard surfaces, such as the inside of a pipe)
  • Mill scale (buildup of oxidation on hot worked materials)

Prefixes and Suffixes Affixed to "scale"

The word "scale" like any other English word, can be affixed, meaning that it can accept prefixes and suffixes to alter its meaning.

Prefixes

Some prefixes are listed and discussed.

super-

Superscale is defined in our usage as spanning many different scales.

This usage differs from the common use of "superscale" to connote extremely large, heirarchiacally embracing, or extremely detailed. Some examples:
  • Collins mapmaking company markets a series of detailed tourist maps called "superscale", for example, "Collins superscale London map."
  • Babylon 5 Role Playing Game offers a set of superscale models that are four sizes larger than other models.
  • A 1970 debate in Kenya's National Assembly argued against favoritism towards an upper class, called the superclass.

macro-, meso-, micro-

Macro-, meso- and micro- prefixes are used to compare scales. See the individual articles:

Suffixes

Some suffixes are listed and discussed.

-meter, -metry, -metric

We adopt the suffix "-meter" to connote a visual aid to interpreting and comprehending scales. Some sample usages on this site:
  • -meter: Scalometer, Scalorometer
  • -metry: scalometry
  • -metric: scalometric

This usage has been adopted by other researchers over the years, and applied to other research efforts. Some examples:
  • Barr, a biblical scholar, researched scale in the bible. "Scalometry means simply the measurement of scale and its effects on literature." Barr also uses the term "scalometric." See "Scalometry and the Pauline epistles" by George K. Barr, p. 1.
  • David S. Marlin calls his proportional study of celestial orbits, "scalometry".
  • Scalometric noise is cited in some statistical and social science research, such as "Physiological responses to noise and to the type of activity under field conditions. by K Bättig, R Buzzi"

-logy

The affix "-ology" is added to "scale" as a suffix to generate the term "scalology" meaning the study of scale. Alternate spellings could be scaleology or scalogy. Scalology may be called a "nonce" word, though it has been coined a few times in history.

Spelling: Scalology had 29 hits, while scaleology had 12, on Google 14 May 2011 1840 GMT.

Examples of the -ology:
  • 1946 minutes of The National Scale Men’s Association. "The National Scale Men’s Association has what we feel is a very well selected educational committee, and it is their intention to compile information in a very complete form so that anyone interested in any phase of scale work will have available text-book material, practical information, and theoretical information of “Scaleology.” -- Report of the 32nd National Conference on Weights and Measures, publication M186, Sept. 1946
  • 2001 article in review neurology, “Recent development in the elaboration process of scales ("scalology") may soon lead to the validation of new composite outcome measures."
  • 2008 post on musical scale fingering: Rajiv refers to the hard work of interval based fingering of scales on guitar when he wrote, “I worked out a shorthand for scalology late last night as I got fed up of turning pages in the Guitar Grimoire books when practicing – why don’t they publish them spiral bound or better yet, have a software that shows every fingering using altered or standard open tuning? ” (November 2008)

-ism

The -ism suffix connoting nouns of action, state, condition, or doctrine, is rarely appended to "scale." Some examples:
  • Pain and Smith in "Fear: Critical Geopolitics and Everyday Life" write about "scalism" as a doctrine
  • Preferring one animal over another is "scalism". Country life, Volume 192, Issues 36-39. Link
  • Withers 1965 "Freedom Through Power" p.150 cites "large-scalism" as a prejudice in planning towards large scale production units. Link
  • Angel 1989 "How to build a conscious machine" p.78 discusses scale as an obstacle to perceiving other conscious beings and refers to such an argument as "faulty scalism" Link

Links And References


Click below to read about core concepts of scale: