The notion of a dimension is quite basic in information modelling, and is perhaps even so basic that asking about it is considered quite pathological, but I will put a few thoughts down about it, because three are features of it which I believe show how the whole domain of modelling makes more sense.
an etymological excursion… ( from https://www.etymonline.com )
the word dimension, comes from late 14th century
dimensioun, – “measurable extent, magnitude measured along a diameter,”
from Latin dimensionem (nominative dimensio) “a measuring,” noun of action
from past-participle stem of dimetri “to measure out,”
from dis- (see dis-) + metiri “to measure,” from PIE root *me- (2) “to measure.”
also, the notion of dis carries with it the concept of 2 ( two ) – The Latin prefix is from PIE *dis- “apart, asunder” (source also of Old English te-, Old Saxon ti-, Old High German ze-, German zer-). The PIE root is a secondary form of *dwis- and thus is related to Latin bis “twice” (originally *dvis) and to duo, on notion of “two ways, in twain” (hence “apart, asunder”).
and….
me – Proto-Indo-European root meaning “to measure.” Some words may belong instead to root *med- “to take appropriate measures.” It forms all or part of: amenorrhea; centimeter; commensurate; diameter; dimension; gematria; geometry; immense; isometric; meal (n.1) “food, time for eating;” measure; menarche; meniscus; menopause; menses; menstrual; menstruate; mensural; meter (n.1) “poetic measure;” meter (n.2) unit of length; meter (n.3) “device for measuring;” -meter; Metis; metric; metrical; metronome; -metry; Monday; month; moon; parameter; pentameter; perimeter; piecemeal; semester; symmetry; thermometer; trigonometry; trimester. It is the hypothetical source of/evidence for its existence is provided by: Sanskrit mati “measures,” matra “measure;” Avestan, Old Persian ma- “to measure;” Greek metron “measure,” metra “lot, portion;” Latin metri “to measure.”
So it amounts to a measuring into 2, a dividing, but dimensions are not a division into parts, but a separation into directions, so it identifies two distinct directions, and a metric of how far along the scale any particular point is. It is an ordering – one which can be combined with other orderings to form a coherent picture – a multi DIMENSIONAL description of some underlying domain.this all feels quite reasonable, and it sheds some light on what it means to discover dimensions in any field.
firstly, the directions are opposites, so the idea of a dimension with more than 2 directions is incoherent. The 2D plane with its North-South-East-West is actually a system of two interlocking dimensions….So discovering dimensions is at the same time discovering orthogonality within a domain. The aim of data modelling, is to reduce any domain to a set of dimensions, so defined, and to calibrate the measurement of these features using a mtric which conforms to the dimensional constraints. so a description of the domain becomes an ordering of measures from a set of independent dimensions. an ordering values, within an ordering of dimensions…. – a TUPLE… So going forward, data modelling is an activity which identified a set of dimensions, expressible as a pair of opposing vectors, and coding instances using the corresponding metric….