The Spatial Aspect
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
- 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.