Dimensional Thought Experiment: Worlds Imagined and Recreated

 

A corollary arising out of the previous post on  Uncertainty distance and time, this is an abstract musing in the tradition of many popular science abstractions. One such imaginative piece of writing, Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott (1884), came to my attention many years ago. A satirical novella set in a world with only two dimensions.  

You are looking down a cosmic microscope where an infinitesimal point fills your field of vision. Sight becomes infinitely resolved.

A.  Imagine a dot, an infinitesimal point in three-dimensional space and time does not exist.

Now imagine this point repeated infinitely so each point touches the next along a single axis. The point is now a line.

At any point in space, the line will appear as a single point. You cannot see the line because time does not exist and therefore you cannot move from one point to the next.

B.  Now imagine an infinitessimal point in time without spatial dimensions.

The point is now extended in time to form a line.

Remembering there is no space, you cannot perceive the timeline, only a point in time.

C.  Now take a point in a world where space and time exist together. Extend it to form a line. You can now see the line because it extends both in time and space. You are able to move through both space and time simultaneously. You can now perceive the line as a continuum of infinitesimal points extending in space and moving through time.

 


 

 

This thought experiment has many caveats and appears reductive: an infinitesimal point seems counterintuitive as does a dimension devoid of physical extensions with only time as a parameter and conversely a space without time. In addition, a line itself without thickness or breadth, only length is also a pure abstraction. The whole thing is counterintuitive. These things are hard to imagine and can only be spoken of in metaphor or using mathematics because to our brains that are seated and immersed in a spacetime world these things do not make sense in view of experience. Experience tells us that it cannot be so. We are made and exist in this world. Our perceptions and minds have been formed as fractals or reflections of ‘real world’ phenomena and the laws that govern it. Such things cannot exist in our Universe. 

My simplistic thought experiment is a way of imagining space and time as inextricably linked to form the conceptual fabric containing all becoming, existence and change in our universe. Strip one from the other, and the impossibility to experience existence becomes self evident. This was one of Einstein’s insights following on from Maxwell. 

Add another spatial dimension and we enter a world which is alien and again counterintuitive. We can only construct projected shadows cast from such a world onto ours by the imaginative means of strange solid forms. Likewise, our-world solid objects project shadows onto flat surfaces, as an infinitesimal slice of the object that projected it. An idea Abbott made use of in Flatland  with the passing sphere. 

We have no problem in perceiving and conceiving of shadows as projections of a higher (our) dimension because they exist in a world of lower order than ours and one in which we experience shadows everyday. However, when confronted with a world containing more than three linear dimensions it becomes impossible to imagine such a world and we make recourse to geometric shadows in the form of strange solids and mathematical means to describe them. It is only possible to hint at what a world with four spatial dimensions might be like using animations. It is indeed a strange world.

 


 

When I think of my work in three dimensions, I perceive it in time too as my mind traces the surfaces and contours. When I see shadows projected by the work, I see something else, a journey through space riding on beams of light and reforming the world. A world that exist in three dimensions at a subatomic level, but appears flat, in two dimensions. I then recreate that universe in my mind to one that is congruent with an intuitive mind formed in this universe of spacetime. 

Looking into the past and future is also a work of shadows: shadows of ideas and events that do not fully form into rounded experience but play themselves on the screen of the mind as words, pictures and imputed movement. 

 

Uncertainty, Distance and Time or I Caught My Thumb in the Car Door

 

 

U=dt

We all notice the little things, even the mouse hidden under the scaffolding for Anne Boleyn’s execution has a story. The bruise on my thumb also has a story, drawing the eye to its notice. Of what relevance is this to the main narrative? Who can say, but it is part of the world and to someone as, if not more important; perhaps someone who has just done the same thing.

Was there a mouse under the scaffold? Who knows, but I am certain of the events that led to the bruise, can you  be? The further one’s mind goes into the past, the more uncertain the truth of events. With the passing of time, accuracy of narrative diminishes and the latitude for the imagination increases. What happens in the past is always an imagining in the present; a speculation based on facts gleaned in the present. The past is a story of broken pieces tenuously joined in rapidly fading light.

Likewise, the present is connected in space and so often certainty in concurrent events are subject to distance. Communication technologies attempt to alter this trend but the veracity of remote news is subject to a large variety of factors. Generally speaking. distance increases the sense of uncertainty regarding an event, in its causality and sequence. This is something that affects us in the everyday. Space, distance and time are great arbiters of fear and hope. Am I talking here about control, or the illusion of control?

The future is also subject to a similar relationship only that there are no pieces to put together, only inferences which are subject to contingency and based on probability. It becomes a matter of approximating as best one can the chances of an imagined or inferred narrative coming about. There is also no past narrative presented for verification, only precedence. Does history repeat itself?  1

I am interested both in the deep past and the future, areas of thought that stimulate the imagination; prehistory, ancient history, science fiction deal with these areas. The closer one comes to the present moment the greater the burden of responsibility for its consequence. An understanding and critical view of history and honest informed political planning are perhaps the two greatest factors in determining how the world develops from now. These are the two things hardest to influence, because they are subject to strong emotions, biases and misunderstanding which affect events today and in the future.

 

  1. This is an idea I have touched on in previous posts.[]

Labelling the World

 

 

We label all the time. Here I have labelled finishes to terracotta surfaces. Labels, however, are far from superficial, they are at the root of our construction of the world. A label is much more than a name for something. Labels are one of the principle building blocks with which we build a relationship with the world and communicate with others. A word is more than its phonemes, a symbol more than its shapes and lines. 

When humans reached the threshold of speech, they recreated the world; in thought and speech; separating us from the other; creating boundaries that can be passed on. In the beginning was the word, logos, knowledge. The word is the fruit from the tree at the centre of that mythical garden from whence we emerged. A place lost in our memories forever hidden by the labyrinth of life, a life spent trying to find the way back. 

The word sets roots in the mind and like a garden flourishes or casts its poisonous shadow across the soul. The word made flesh, the symbol, the picture, the letter and grammar, are  abstract entities given material resonance in poetry, then literature and mathematics. The word cries out meaning, ‘I…. you’.

The word separates the world from us and brings it closer, it says goodbye to the animal met in the womb. The infant, whole, cleaves to the world the new mother that kicks you in the teeth and holds you up to the sun and gives you warmth. The word is inside us and out there where it shapes our destiny. It is what says ‘I’ and ‘you’ and ‘we’ and ‘they’ encompassing the world or shattering it into confusion.

And when all has been said and done, the word is all, the word is death, the word is life and all in between. In the beginning was the word and in the end silence.

 

Hermaphroditus

 

 

Hermes and Aphrodite bore a beautiful son. Hermaphroditus was raised in the caves of Mount Ida by fresh water naiads. Growing bored of his life he went walk about around the cities of Phrygia. One day, he wondered into the woods of the city of Caria near Halicarnassus where he was seen by the water nymph Salmacis. She at once fell in love and lusted after the handsome but still young boy pouncing on him in an attempt at seduction. 1 Hermaphroditus rejected her attempts and on thinking she had gone, undressed and entered the pool to refresh himself. On doing so, Salmacis sprung on him and wrapped herself around the boy wishing by the gods never to be parted from him. Her wish was granted and the two blended together creating a creature of both sexes.

This tale, one of many told by the Roman poet Ovid in his book Metamorphoses came to mind as I made a new clay model. It is a blend of ideas from the Willendorf Venus to retro rockets; from Philippe Stark’s juicer to the Sputnik satellite, deep sea monster and nimble crustacean. Cult and functionality melded without overt reference to the human form for hermaphrodites abound in nature. 

The emergence of sexual reproduction long ago conferred greater plasticity to complex organisms enabling them to better adapt to different environments. Hermaphrodite animals have adopted this form of sexuality as a strategy for increasing fecundity, with respect to plants it is the norm. Only amongst the flowering plants do you find separate male and female individuals. These are dioecious plants such as the holly. Only female hollies bear fruit. In humans the sex organs begin to differentiate only after nine weeks but then sex is different to gender. The gendering of objects is deep rooted in culture. Ascribing a gender to a particular type of thing is common in many languages but not all languages assign the same gender to an object. I am always a little disconcerted when referring to a flower in Spanish and then Italian. In the former case it is la flor, whereas il fiore is the Italian masculine for the same word. Two romance languages with common roots, at what point in the linguistic womb did the two diverge? German also includes a neuter gender whereas English has pretty well lost all its grammatical genders other than for people, animals and a few other things such as ships (with a few dialectic exceptions).

A professor (who is no longer with us) said to me a few years ago that my work is gendered. I wondered what he meant at the time as I know that my intention in Chaos Contained was to move away from a binary representation of life. I was working in a neutral but fecund world full of life force transcending the cosmically parochial issue of gender. To this day I do not know to what audience he thought the works might relate to, if that was indeed what he was getting at. Ironically, the touring show of CC was managed, promoted and funded purely by women.

We are apt to see ourselves reflected in things and events including questions of gender. We live in times when questions of gender are being revised of their historical baggage. Whatever the case might be, it is so difficult to be objective about affective things. Emotions are at the heart of art practice and appreciation. That is why academic writing for an artist can be a stretch but it can open windows to new horizons through critical thinking. However, critical analysis has to be treated with an awareness of its implications for creativity.

 

  1. Salmacis was the only naiad that did not take part in the hunts of Artemis on account of her idleness and vanity. She preferred to wash her beautiful limbs and tend to her hair.  Ovid, Metamorphoses. Book IV, 306-312[]

Uniformity, Local Conditions and Culture

 

 

I wrote the following as part of the previous post on writing. When revising what I had written it seemed a bit of a non-sequitur. It was more about creating a context for linking writing about science with writing about art. The ideas I touch on here need expanding but I think it serves as a note-to-self for the future. 

The scientist has to assume, indeed believe in the uniformity of the universe, otherwise no finding would have applicable value elsewhere, everything would be relative. What this means is that the laws of physics apply equally wherever you are located in the universe, there is no place where the laws might be different or behave in some other way. This is not to be confused with the theory of relativity and its stated relationship between mass, energy, time and space which is always the same, with the speculative exception of  black holes or the very beginning of the universe when the ‘Big Bang’ occurred. If the universe were not uniform regarding to the laws of physics, there would be no possibility of confirming scientific theories or indeed refuting them, for there would be no basis for predicting outcomes according to a hypothesis, phenomena would be subject to local laws only. This assumption is one of the basic principles of the scientific method and experimental philosophy and so far has not been refuted.

The religious person must also believe in uniformity regarding god or gods, otherwise there could not be an ultimate authority for morality and therefore behaviour could not be regulated. Religions rely on a uniformity of consequence, justice, compassion, love, etc. as a central tenet to their universality. Correspondences and conflicts between religions come down to what they have in common as well as how they differ in their universal applicability as much as ritual practices, credos and the like. Likewise, an artist has to trust that there are universals that when applied, bring thought and people together rather than divide them. These universal ideas or the search for them create the possibility for a coherent vision on which to base a philosophy and practice.

In all three cases, these deep level ideas, simple in themselves are nevertheless hard to demonstrate. As for proof, for now they must remain elusive paradigms, ideals, questions of faith. There also appears to be an increase in fragmentation regarding the nature of uniformity. By this I mean that scientific philosophy requires there to be what is known as the doctrine of uniformitarianism applying to all branches of science and technology. The doctrine remains the same for all practitioners whether one is talking about medicine, chemistry, biology or physics. 1 With religion on the other hand, the nature of uniformity can change according to belief. The divine agency and its effects differ or agree from one religion to another. The plurality is directly proportional to the number of practitioners that adhere to one particular belief or another. When it comes to art, the situation becomes even more fragmented. The variety and number of different paradigms is a function of the countless movements, groups and individual artists that work and have worked to a particular vision across all societies. 

In science, there is a constant search for the consistency of the laws of the universe or perhaps better put, for any inconsistencies that might be observed which in turn, could lead to revised, refuted or new theories which would nevertheless still be based on the assumption of universal uniformity. The spiritual believer is ever racked with doubt about the justice of things, questioning the purpose or reason for the world behaving as it does; asking why justice, redemption and even punishment take the shape they do. Recourse is made to faith in the divine as the pillar on which the belief structure is supported. And the artist has to be authentic in themselves, find what is at the core of their being in order to make sense of things and synthesise them into something that creates a commons with others.

 

 

Uncertainty, Time and Distance

Each one of these persons must trust in a different kind of uniformity but this is not static. It is a concept implicitly embedded in the idea of change. The implication being that the same change would occur under the same conditions wherever and whenever they occur.  The key here is, under the same conditions. Conditions change and so do outcomes, but an outcome is not as a result of different laws acting. The outcome is the result of the same laws acting on a different ‘mix’ of elements. This means that the laws are reliable but not necessarily predictable. Quantum mechanics has shown us that the predictable world is an illusion created by the averaged sum of an inherently unstable and unpredictable fundamental substrate. However, reliability is the knowledge gained from experience and a belief in universal uniformality, including the unpredictable quantum microcosm.

When it comes to art the matter is somewhat more subtle because art is contextual. Context is an elusive characteristic of complex circumstances or conditions. At first sight, the ‘doctrine’ of uniformitarianism might appear to fall apart but this is an illusion. An illusion created on the surface of things due to context being a chaotic complex of influences and forces, relationships and interactions that provide ‘unique’ conditions resulting in the individuality of artistic visions and production. However, there is no reason why the forces acting on each and every artist are not the same, only altered by circumstance, genetic and cultural predisposition, historical antecedents and so on. The outcomes may differ due to different causes but the underlying laws remain invariant. The result is that although they may appear vastly different to us, there are commonalities which when averaged out produce the sum of human culture. And the wider the sweep of observation across societies and periods in history, the fewer the global correspondences giving rise to the difficulty in defining what art is. 

An example of outcomes being vastly different but the laws at work remaining the same, would be the existence of life. Life exists on Earth, no other life has been yet found anywhere else in the solar system. Yet, the abundant, exuberant ecology of our planet is subject to the same fundamental laws found anywhere else in space. The differences are due to local conditions and which laws apply or not and in what proportion. For example, life on Earth is very much dependent on the planet’s distance from the Sun, its magnetic field, age and so on. 

The interesting thing though, is that the fundamental laws acting on say, the Moon are the than those acting on Earth: yet nothing much changes on the Moon except for a few parameters, conditions are much simpler. The planet Venus on the other hand has a complex active surface, more complex than the Moon’s with an atmosphere and geological activity, yet it is much simpler than Earth’ surface. On Earth, once life emerged, perhaps as long ago as nearly four billion years, a different set of laws arose. A traversal takes place with the emergence of an ecology which in turn gives rise to evolutionary processes. New laws come into play, sub-laws which are nevertheless subject to the fundamental laws that existed before and continue to do so such as, the laws of thermodynamics. However, these new laws are also different in kind because they act on different kinds of systems such as living organisms (in which case reverse entropy). Could the same be said about consciousness, that once consciousness emerges, a new set of laws comes into action? 

Art is a product of our consciousness and part of human culture. Art emerges relatively late on in our evolution, it took some time for art, religion and science to emerge in human culture despite humans appearing in their modern form long before. Could there have been a hidden mutation that caused a leap in human activity, or was time needed for new proceeses to emerge out our consciousness and interactions with the world? And if so, are these processes subject to the same laws acting on new conditions or are the laws a new emergence from consciousness? Or put another way, are there correspondences between the processes that govern society and culture and those that govern other forms of life? If so what are they? If not, what is special about cultural laws?

My hunch is that there are correspondences, as stated by Dawkins in his idea of the cultural meme acting as a selfish gene; also, crudely put, Malthusian-like forces acting on how populations react to conditions. Research into free will is throwing light on how free we actual are, whether it is an illusion or partial illusion and what the forces are that act on us to make us behave and perceive in a certain way. But my intuition also tells me that there are some elements of human activity that have produced unique rules. Whether these are inherent in the domain, such as mathematics and aesthetics or universal and stand outside the need for human presence, is a matter of constant debate.

For the very reason that uniformity is masked by differences in local conditions, the forces at work are often not self evident. They would go against experience and be counterintuitive. To begin to understand them requires prior knowledge or experience, at least familiarity with the field. You cannot understand a scientific theory without the antecedent knowledge that goes to make it up. In a similar way, to understand or appreciate a ‘piece of art’ an experience connecting one with it in some way helps. Whether it be by association, familiarity or knowledge of the field, as Dewey might have said, context creates the artwork in the receiver’s mind. 

Perhaps these are intuitive thoughts trying to deal with counterintuitive ideas, such as probability (which is why quantum mechanics is such a difficult field to grasp and accept)… and certain forms of art. But why does art produce such strong emotions when debated? Art in particular divides opinion far beyond its apparent effect on everyday life with opinions being expressed in ways they would not about other matters even to the point of causing offence more readily than in other situations. I think that the effect of art runs much deeper than one might realise. People in power or seeking power have known this since early times. Art can be used to mould opinions, beliefs and allegiances from politics to economics, from status and fashion to the expression of wealth, social and philosophical ideals. Art can even persuade people to be kind, generous and cooperative or cruel and violent. Art is at the root of religion, fashion, status, politics, all complex human activity. Whether it is a simple bead necklace from the Kalahari or Michelangelo’s Pietá, whether a feature film or Homer’s Iliad, they are all expressions of human interactions between themselves and the world. The anthropologist R. L. Anderson suggests that art is:

culturally significant meaning, skilfully encoded in an affective, sensuous medium.

 

  1. I am talking here of the doctrine regarding the laws of physics and causality, not the more specific reference to early geological ideas which were proposed in opposition to catastrophism[]

A Reminder When Writing

 

 

I came across this rather irreverent table yesterday. It is aimed at the authors of science papers but I think it can equally apply to the arts if clear thinking is considered a desirable thing in this field. I can say that I have been guilty of writing bullshit at times. That is why I constantly need to remind myself against doing so. When writing I ask myself a number of questions:

  • Do I understand what I am dealing with?
  • Do I have the means by which to speak of it?
  • Am I aware of the holes and caveats in my own argument?
  • Am I using a fallacy to support an argument? For example, begging the question or using the conclusion as the premise: all too easily done. 
  • Am I trying to be objective or subjective? Which ever might be the case, I need to make clear my stand point; observation and opinion are two very different things. 

But, I must also remember that I should not be afraid to make mistakes, take risks and make intuitive leaps. The absurd can be a useful tool to highlight an issue. 

The logical, the heuristic and the intuitive may seem at odds here, and on the surface they often are. However, artistic practice is far more complex a process for one to be constrained to rules adhering to a particular paradigm. Like the whole of life itself, to question is to remain open and live to the world, and one’s art practice is a personal reflection of the world lived. Being an artist, particularly today, provides one with the privilege of stating the speculative, imaginative, daring and singular, the uncomfortable truth and the lie, promote change and be dangerous or liberating, perhaps at one and the same time. It is about making a personal statement that if sincerely and honestly stated, being authentic, it is possible to make a wider statement that speaks for and to more than one person and is communicable. I can only deal with a small area of a vast world case. To attempt otherwise would be to assume that one can understand the entirety of things.

I try not to obfuscate in my writing although at times, for the sake of brevity I must make assumptions and express myself in a form of shorthand which may need unpacking: a necessary avoidance of overly long posts at the expense of time spent making. Returning to the original point about writing, I think it apt to finish with this cartoon that makes the point in a humorous way:

 

 

Stand the monologue on its head and one comes nearer to the truth. 

I now have to be careful to live by this…

…and take risks at the same time.

So long as I am aware of what I am doing I hope to avoid unintentional bullshit.

 

Learning New Things

 

 

I have never done something like this before. I am finding it a challenge but not because I lack the skills of drawing, composing, digital or manual. It is more a case of sequencing and seeing how  detail fits with the overall. This might appear to me a matter of applying what I do in other domains to this, the graphic narrative or comic. However, the applicable principles are to be used in a completely different context; one in which the single image does not stand alone but is seen as part of a much larger narrative in images. In addition, the attention of the viewer has to be maintained throughout the process of sequential page turning: rhythm, sequencing (how one images corresponds to subsequent images), pacing of the script and consistency of vision are all part of the process. In short, it is about working with a carefully crafted script. Something I am going to have to do when working on the multiple screen video performance. So this is a way of introducing that process. 

Probably the way for me to break down what I have done is to look at the first page and see how the problems presented have necessitated shifts in how I view the overall work. The interesting part of the process is how the initial vision, feeling, has had to be changed in order to convey a more compelling narrative through visual means. 

I was fixated with a particular ‘look’, a simplicity that quite frankly was getting somewhat boring. I tried to reduce detail to focus on the narrative but found that this had the opposite effect. It is the detail surrounding the central character that conveys the story, after all, there is only so much that can be done with a single creature in a barren landscape. So what I have done is spend a while looking at the great many solutions that others have used for both comics and graphic novels. This has helped me in seeing how I could do something more affective.

So what have I done? The following is a list of the changes that I have sketched out in my mind and tried out, not shown above:

  • Change the geographical transitions to convey a sense of the psychological journey of the creature. I had maintained this constant with the result of convey nothing more than repetitive monotony. Although this was the initial intention, it did not seem to hold the attention or even convey the meaning I was hoping to impart. I worked with process but there came a point where an intervention to change direction was needed to increase the affectiveness of what I was doing.
  • Introduced minor characters which heighten the creature’s isolation much as a lost person would feel in a forest full of unfamiliar animals and plants. This also personalises the character with the viewer creating a conversation between parties. This is a more intuitive direction, after all, most people’s experience is not that of living alone on the Moon or Mars. 
  • Not repeating stances and views, keeping the pace of the storyline going while relating each vignette to the others. This can be done using colour, line, composition and tone as well as the particular characterisation of a given scene. The direction of sight needs to move in a sequential narrative and lines of tension, repetition, reflection and so on, are all devices that can be used to achieve this visual journey.
  • Most importantly, elaborate the script so it includes details that help create interest in and engagement with the character and its story. The script, to my surprise, is perhaps the most important thing. It does not have to be about speech, it is also description of the scene, emotions, details, incidental action, time, season, terrain. All these are important to compose in an abstract sense so that the drawing phase is not always starting from the beginning when an impasse is encountered.
  • Work with what I am familiar. This is important in creating a believable situation and characterisation. It is much easier to work with elements of which I have experience rather than trying to set events in locations that I cannot relate to. For this reason I have chosen the Venezuelan savanna, land of tebuys and Conan Doyle’s Lost World. An appropriate setting for the story that unfolds.   
    But what is this narrative about? I have been thinking if it was about loneliness, or perhaps the dark side of companionship; about a search or about the indomitable spirit of survival. In the light of what I have been exploring in the past few day there is something else, the emergence of predation, not in the sense of a literal figuration of the strategy filling an ecological niche. It is more of a metaphorical account. If examined carefully, again it is not so much about predation but competition, territoriality or even status. There are multiple inferences in the storyline, that is the point of it, ambiguity, and the ambivalence of what is loneliness and what is solitude.  There are also technical elements which are can be worked out in the process. One thing I have found though, although I have spent some time on the project, I am amazed at how little work I have actually done. I can see that I need to do much more ground work. But now I am clearer as to what is needed, I can move on at a more productive and energised pace. What relation does this have to the main project proposal? Everything is still up in the air but there is a strong correspondence with other elements I am working with, metamorphosis, culture and the deep past as a counterpart to the contemporary.