The Spatial Aspect
We experience the spatial aspect directly and intuitively as here, there, between, around, inside and outside. Spatial properties include shape, position, size, angle, orientation, proximity, surrounding, overlap, and so on. Things that gain their meaning from the spatial aspect include particular shapes (triangle, line, spiral, etc.), angles, distances, holes, space, area, dimension and so on. Like quantitative functioning, spatial functioning feels to us like a static property. A wiggly line is spatial, but if we call it a 'path', then we are importing some kinematic meaning of 'going'. Dooyeweerd's discussion of the spatial aspect is, unfortunately, all over the place and interwoven with discussion of its relationship with other aspects [NC:II, 63-65,85-96,98-106].
The good possibility that the spatial aspect introduces into temporal reality, which have no meaning in the quantitative aspect, are simultaneity and continuity. A quantitative thing in temporal reality, such as a set, can never exhibit two different amounts (e.g. 6 and 7) simultaneously, but a spatial thing, such as a triangle, is both here and there simultaneously since it extends from here to there and over all in between. If it did not, the triangle would be incomplete. The extension from here to there is continuous, not in discrete steps.
It is this that makes so-called irrational number(nesse)s like the square-root of 2 meaningful: as amounts, they cannot be arrived at by application of quantitative laws. In this we see the quantitative aspect antecipating the spatial, in that some amounts cannot be discovered except by antecipating spatial meaningfulness (e.g. 'square'). An example of retrocipation from spatial to quantitative is length: a spatial property that also obeys quantitative laws.
Note: The kernel meaning of the spatial aspect needs to be as true for one-dimensional space as for two- and three-dimensional.
- "Continuous extension" (Dooyeweerd's rendering)
- "Here, there, between, around; inside and outside. Introduces Simultaneity, continuity" (Basden's intuitive rendering)
- Spreading out in a continuous manner; see below
- Simultaneity (in that its parts are all present simultaneously).
- size, position, slope, volume, shape, etc.
- here, there, near, far, etc.
- lines, areas, volumes, etc.
- Topology is spatial but can sometimes be more analytic than spatial when it involves having distinguished certain entities and their relationships, and then examining connectedness. Spatial here is more to do with the continuous extension in three (or two or four) dimensions. However, we might say that topology involves an analogy between the spatial and the analytical aspects.
- Fourth dimension is not Time. While it is convenient to consider it a 'dimension' in terms of 'something that cannot be reduced to the other dimensions' as we do in physics, time as such is something completely different (see Time). Distinguishing different things so that we can more clearly think about them (which is what physicists are doing there) is analytical, even though they use the spatial term 'dimension' for what they do. What they are doing is to express both spatial dimensions and time as quantity - which is expressing both in quantitative terms, rather than treating them as space and time. While there is much power in doing this, this Dooyeweerdian approach would suggest that this is still just an analogy, not the real thing.
- "The spatial is not in the least supra-temporal since it implies simultaneity in the modal meaning of continuous dimensional extension, and the spatial relations in temporal reality have subjective-objective duration of time. So far as the spatial relationships in abstract geometry are viewed apart from transitory things and events, i.e. according to their modal structure alone, they, nevertheless, always continue to express the spatial temporal order of greater and less in simultaneity." [NC,I:31 footnote, italics in original]
- Geography (see below)
- Study of spatial properties such as shape, orientatino, overlap, occlusion
- Topology to some extent
The quantitative aspect and some of its constellation
- Edge, Corner
- ===== list to be compiled
- Continuousness (in contrast to the discreteness of the quantitative aspect)
- Number of dimensions is quantitative
- Irreducibility to quantitative aspect? For example, is not position fully expressed as a tuple of numbers, and is not shape reducible to the number of sides it has? For the latter, no! Some shapes have curved boundaries, from oval to curved-cornered things, and these cannot be said to have a particular number of sides. Moreover, some shapes have no clear boundary, such as clouds exhibit. Dooyeweerd was insightful in making continuous extension the kernel meaning of the spatial aspect.
In a classic volume, The Nature Of Geography, Hartshorne
discusses at some length what is the kernel of Geography. Is it:
- An exact science? No.
- The science of planet earth? No.
- The study of landscape? No.
- The study of relationship between natural environment and humankind?
- The study of how humankind adapts to the natural environment? No.
- The study of distributions on the earth's surface? No.
Rather, the kernel of Geography is:
(Now we have access to other planets, presumably their surfaces would also
be included in that.) "Differentiation" is the kernel of the
analytical aspect, from which
the central activity of science or close study comes. So what is being
studied is areas - which is, in two dimensions, what Dooyeweerd
proposed as the kernel of his spatial aspect.
We call the kernel meaning 'spreading out'. But Dooyeweerd suggested the kernel was 'continuous extension'. We replace that with 'spreading out', because I have found that 'continuous extension' can be misleading, referring for example to how projects continuously extend their deadlines and costs!
- The study of the areal differentiation of the earth's surface.
The more important question, however, is why the kernel is either of these (continuous extension or spreading out) rather than, for instance, position, length, shape, etc.? A recent
discussion I had with a mathematician
about might throw some light on this - there is something fundamentally
different about continuous numbers ('reals') and integers.
This is part of The Dooyeweerd Pages, which explain, explore and discuss Dooyeweerd's interesting philosophy. Questions or comments would be welcome.
Copyright (c) 2004 Andrew Basden. But you may use this material subject to conditions.
Written on the Amiga with Protext.
Created: by 31 March 1998.
Last modified: 30 August 1998 rearranged and tidied. 7 February 2001 copyright, email. 4 February 2002 spatial anticipation of the pistic in Tolkien's Galadriel. 21 January 2003 Spatial anticipating social in Alexander. 24 August 2005 brought up to date with .nav,.end, some rewriting of start. 30 January 2006 quotation from NC,I:31, rid counter. 27 February 2007 Curved and fuzzy shapes. 14 October 2008 simultaneity and 'true of 1D'. 17 July 2009 'spreading out'. 14 June 2010 line of sight. 22 September 2010 Dooyeweerd's and Basden's kernels. 21 September 2016 briefly. 26 September 2020 added constellation pic, corner, edge; Hdg= Things and Institutions Qualified by the Spatial Aspect. 2 January 2021 analogy of simultaneity in quantitative aspect.