MIND, 4-Dimensional Space-time and Sculpture


Penrose-Escher: A 2-Dimensional Exploration of Relativity
M.C Escher - 'Relativity'

Roger Penrose is one of those current scientists that you just feel in your bones will be placed amongst those eminent persons like Einstein and...well, Einstein! It is not surprising that his mind has been so keenly attuned to move through different types of dialogue with astrophysicists to artists, as he was born the son of a psychologist and a geneticist. He grew up in a family of fairly eminent scientists and artists, and I imagine his mind was fed with conversations that awoke both his cognitive and creative sensibilities. Indeed, I believe that the great scientists are truly artists at heart, and the great artists are often scientists in sheeps clothing...!


In fact Penrose has worked with two of my favourite people, who fit just this description. Namely the physicist - Albert Einstein and the artist - Mauritis (M. C.) Escher.


Together with Einstein, they formulated what is now referred to as the Penrose-Hawkings 'singularity theories'. This was the collaboration of minds that developed the mathematical background upon which the 'Big Bang' theories were founded.


With Escher, the exploration of Penrose's concepts of spacetime were deciphered and interpreted upon a flat 2-dimensional surface. We see hints towards Penrose's "twister theory" in Eschers work. His artwork guides us towards the visual representation of 4-dimensional space which is based upon Minkowski Space. This expression of space allows for a 'conformal treatment' of infinity. This means that 'angles' between directions are preserved, whist the distance between them is not. So whilst we may draw a line to represent the angular relationship between 'points' the length of the line between them is not measurable. This is particularly important when we apply the length of the line to represent time space.


Timespace is the movement that is represented from 3-dimensions to 4-dimensions.


In mathematics, 'dimensions' are the measurement of the SIZE or DISTANCE of an object.


Traditionally, the SIZE of an object can be represented through 3-dimensions. Combining the measurement of three 'planes' (or 'angles') which represent length (l), width (w) and height (h). When measured together, these can provide us with the size, or more precisely, the volume of an object.


When we want to measure the dimension of distance, we then begin to shift our thinking. Distance can be considered a simple measurement on a line, which moves from point A on a line, to point B. This can easily be represented through a 2-dimensional drawing. However, things become a little more complex when we add in the dimension of time. Time is implied whenever there is movement involved. As there is an implied aspect of time, when moving from point A to point B. Therefore, we begin to see that this linear representation from point to point can also be considered as a representation of time itself.


Penrose's 'twister theory' goes on to combine the properties of 3-dimensions and 4-dimensions. This giff of a tesseract shows what happens when we combine these two dimensions, and represent them on a 2-dimensional place through a combination of moving images that we can observe over time (ie. a giff, or pre-recorded film).



A Time-Space observation of Form
The Tesseract: Exploring 4-Dimensional Form


In this example, we can see that there are two cubes in the tesseract. They maintain their own integrity through the angles of reference within their own structural form. However, they are joined through the conformal treatment of infinity (i.e. the lines which join the points of the cubes), which are observable through a twisting motion that allows us to continue to 'see' the integrity of the two forms, but simultaneously "shifts" our position, or our view.


When we consider space time, we could think of this as either 'we are shifting our view' of the object, or alternatively that the object itself is moving through the 4th dimension of time whilst we are observing it from our singular position (ie not moving). This is a nod back to Einsteins recognition that a passenger on a train looking out at the landscape will see the landscape itself as "moving". However, this is a matter of perspective which is relative to the viewer, as we could say that it is in fact due to the movement of the passenger on the train that the landscape appears to be moving. However, for the passenger, they are sitting 'still' on the train. This is the premise of 'relativity', and sits at the heart of the observation of time-space and our travel through it.


In many ways, this is the mathematical and 'formal' representation of what I have always considered to be an 'experiential' perception of sculpture.


As a teenager, when I was studying art at college, I was fascinated with experience of observing a piece of sculpture. Whilst I was never 'good' at working in 3-dimensions, I spent long periods of time observing sculpture in various art galleries. I always had the same experience, which was one whereby I would move slowly around the sculpture and try to reconcile what I was seeing and experiencing 'NOW' with what I had seen and experienced of the same piece only moments ago. But from a different angle. This level of pondering would become even more sharply focused as I observed any third party who might also be standing and observing the sculpture at the same time that I was. I suppose I was fascinated by the idea that we could simultaneously be observing the same sculpture in time and space, but be having a completely different experience. This idea was one that I couldn't shake in many different ways through my teenage years. I often wondered about the ideas and processes going on in other peoples heads, and how it was that we were all seeing things completely differently. As an art student this was even more pronounced to me when, as students, we might collectively discuss what we were seeing.


Whilst a strange idea perhaps, it seems to me that this experience of viewing sculpture is similar to the concepts that Penrose-Escher were exploring.


Furthermore, those experiences with sculpture lead me to a natural recognition that it is this movement through time and space which opens up the potential for us to compare and contrast. The potential for growing our perception and our awareness is expanded from simply holding a static 3-dimensional view, into a 4-dimensional experience that allows us to evolve our awareness and our eventually - our Consciousness - over time.


The possibility to move through the 4th dimension is essential to the evolution of consciousness. It adds the dimension of 'perspective' to our individual learning - providing us with the space and the time to see things with perspective allows us to consider what we are seeing in different ways. To have an experience with one view, and then to move on to the next view of the same thing, and have a different experience. Interestingly, the experience may not seem to change very much if we always carry our past with us. So part of the experience may well be that we chose to change how we look, how we see, how we feel about what we are looking at.


To see something from multiple 'points of view' requires us to 'move' through time and space, and to re-look at something (the 'form') again and again from different perspectives (conformal treatment of infinity).


When we combine the 3rd and 4th dimensions, there is the possibility that our consciousness expands. There is also the possibility that we begin to compare and contrast our individual experience 'here and now' (from our current life position), with other 'here and now' moments. This brings in the monetary echoes that we might experience of 'past moments of consciousness'. These may be echoes from our past (in this lifetime), or even echoes from our past lives that are resonating with the perspective we are currently experiencing.


As you look at the giff above, consider how the inner cube gradually moves to seemingly become the outer cube. And vice versa. As we move through time and space, this is the experience that our consciousness undergoes. Gradually moving to experience a form from 'all angles', not only from all angles AROUND the outer form (as when I was observing the sculpture by walking around it), but by from all angles WITHIN and WITHOUT the form.


I recognised in my trips to sculpture exhibitions that this was one of the most powerful ways to shift my way of seeing a 3-dimensional object. To move up close, and peer inside of it, and to then move and stand at a further distance away from it. This was something that I specifically learned at a Naum Garbo exhibition.



sphere construction of a fountain (1937) plastic 16 inches high2
Naum Gabo Sculpture


Of course, when you stand back in a gallery to observe a sculpture from a distance, other people would sometimes get in the way of my perspective!

That happens in life too...


So you may wonder how this has any connection to being a Mind Body Detective..?


I invite you to spend some time simply observing the moving shape of the giff in this post, and letting your conscious mind begin to engage with the pattern that is moving over time upon the screen. Watch how different points in the form move forwards and come to the foreground of awareness, and then slip into the background. Notice the symmetry and the cyclic repeating motion. Recognise that it takes time to watch and sense and 'feel into' the pattern that you are observing.


Then remember that this is the process you are engaged in when consciously exploring the patterns that arise within your own life. Of course - YOU are more complex than this 4-dimensional model of a cube .


So give yourself the time, and the space you need to observe the patterns in your life.


And do so fully with love and compassion, and a healthy dose of intrigue.


You are fascinating.

Your life is fascinating.

Enjoy the journey;:-)



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