Toward a taxonomy of dimensions

For some time I have been thinking about our relationship with our world in terms of the dimensions available to us, and how this structures our interactions with reality (I was tempted to call this a taxonomy of dimensionality, but thought it might be better to use that word in the ‘form’ column). Of the first type of dimensionality and the last (direction and time), these are the well understood 4 dimensions of space-time. I know nothing about other dimensions such as they exist in alternative geometries, or at the quantum level, and so I didn’t include anything which I would only have scraped off a wikipedia article anyway. This is the preliminary outline:

Name Dimensions Form
Absolute direction 3 Cartesian dimensionality
Absolute pressure 2 Boylean dimensionality
Absolute gravity 2 Newtonian dimensionality
Absolute time 1 Einsteinian dimensionality

What I am trying to do here is consider how there are certain objective (alternative to absolute?) dimensions which are the conditions of the outside world. I use the words objective and absolute advisedly. The dimensions here listed are not discrete, but are rather continuous. As such, when I have listed 2 dimensions, that is to say that we effectively have “on” and “off”. The precise ‘amount’ can easily vary, measured in atmospheres for pressure, or g-force for gravity (both standardised forms of measurement, if geocentric if using Earth as the yardstick.)  So absolute direction takes place in the x,y,z coordinates of Descartes’ coordinate system, time is the vector from past to future through the continuous present, the flow which we cannot interrupt. Pressure and gravity both vary according to the environment which we inhabit, and equally cannot be changed. 

My aim here is to raise some questions. Firstly, do these four dimensionalities adequately capture the outside world? Do they allow us to set up some baselines by which we might capture the conditions of a given point in space? Are there other dimensions which we need to include? I am trying to avoid anthropocentrism here, by not making reference to human, subjective conditions, but I can make the argument against myself that I am already biasing my picture of the world by not including the presence electric fields for one. A taxonomy like the above if drawn up by a platypus would have to include such absolute electricity given that these creatures parse their experience of the outside world through electroreception. A platypus’s taxonomy might also have to further finesse the notion of absolute pressure to include a secondary, mechanically created form of pressure, i.e., the push-rods on the platypus’s bill, signals from which they combine with those their electroreceptive rods sense, to create a detailed, ‘multi-dimensioned’ mental picture of their world.

Indeed this exercise being almost immediately doomed to failure is telling, since by providing an example which might be taken from the experiences of another creature, the limits of the absolute, objective quantification of reality become readily apparent. As soon as we develop a ‘view from nowhere’ picture of the world, one which is formal and abstract, we quickly need to realise that, many more arguments are necessary to draw up such a picture. As an attempt at this, however, I suggest the following: 

Name Dimensions Form
Absolute direction 3 Cartesian dimensionality
Absolute pressure 2 Boylean dimensionality
Absolute gravity 2 Newtonian dimensionality
Absolute time 1 Einsteinian dimensionality
Absolute electricity 2 Electric dimensionality
Absolute radioactivity 2 Curiean dimensionality
Absolute fractality Mandelbrotian dimensionality

I have included radioactivity and electricity separately, and what I have said above regarding continuous, and non-discrete presence of both still stands (also, my use of “electric” here testifies to the complicated nature of the history of the discovery of electricity and its various theoretical underpinnings). What is new, and what I haven’t mentioned above is the notion of fractality. I apply this here in the sense of there being a possible divergence between an object’s surface area and its volume. It is a further dimension which is exploited in nature and by various plants and animals to their own ends. The brains of intelligent mammals display cortical folding, or increasing degrees of folding in the cerebral cortex, which effectively increases the surface area of the brain. This folding and intelligence have been suggestively linked. Along with this, leaves on trees increase the surface area available for photosynthesis, and fractal geometries are to be found in intestines, lungs, branching of blood vessels, and lungs (there is undoubtedly a limit to fractality, but I left it ‘infinite’ through a desire to refrain from proscription). With this attempt to at taxonomising dimensionalities, the picture of the world becomes more richer. Is there anything else that could or should be included here?  

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