A Little Gallery of M C Escher
This is a gallery of Escher's work; supplemental to Hofstadtler's Godel Escher Bach book, along with a few of my...
A Little Gallery of M. C. Escher (For those interested in his litho prints and wood cut prints.)
I wasn’t going to shrink this one; only. . . . . . Wow! OhmiGod. Some things just have no plane of dimension; because all planes are relative to the angle from which the image has been rendered and presented. Like the Relativity Print of everyone in the hall walking up a differently inclined staircase. They aren’t wrong; thus, the angle of the viewer must
therefore be discontiguous. I’m only filling this page so I don’t have to add another picture and shrink this one.
“What a Paradise! Here, have an apple! How bad could it be?”
Again, another of Escher’s famous Improbable Geometries. Note the use of Improbable rather than 185
Impossible. Perspective, parallax shifting and vanishing points in space are the keys.
Another of Escher’s postulations: pay attention to the spirals (it’s easy to forget that any spiral flowing in one direction is actually unflowing in the other – Greek: Flux, Reflux.)
It almost puts one in mind of the Japanese painter, Hokusai.
Herendeth the lesson. As I said at the beginning of this document; it isn’t about my opinions. It isn’t even about each picture’s NAME, since names seldom are either invocative or evocative of the kind of emotional simulacra the act of studying them actually builds. These have always been the weapons in the artist’s arsenal; misdirection, unease, making people feel challenged and unsure of what they think they know – since too much of what we know in life has been set in stone by the preconceptions we absorb from others without even realising it. It might be a very different world if people would learn to act from their own instincts as determined by a child’s natural development and ways of learning from what they find, rather than by swallowing the lessons they are taught whereby; sometimes someone hasn’t worded something helpfully – either by accident or design – and has passed over a mixed message, or a message that hasn’t properly sunk in because it is doubtfully accepted from second-hand information, rather than investigated by first-hand information, for whatever reason. 188
From this point of view, artists are legitimately very external; and incredibly internal at the same time. And Escher is, no doubting it, a very good example of this. Look at the perspectives and the landscapes; there is more than enough fine details in any one part of a drawing to absorb the time of the most imaginatively challenged and anally retentive of students for a long time; but also, there is a greater form of beauty to be gleaned by looking as a bird or a cloud would look at things, rather than as a worm might look at them. In making images for years, I suspect that many people have tried – possibly in vain, perhaps not; only time will tell for certain – not to ignore the fine details; but neither to sacrifice the attempt to understand a larger, more all-encompassing view of the collective whole. How many of us have found ourselves in life, unable to see past our own problems; because for some times when depressive tendencies engulf us, we’re unable to connect with the empathies and sympathies that we need to remind us that in their own ways, no-one is truly ever really happy; and every single thing’s problems are actually a mirror of everything else’s. Why is this? Because we are all travellers in time and space and dimension and plane; and to understand the minute workings of all things; we have to balance the needs of the natural and the synthetic; the analytical and the artistic; the thinking and judging and the feeling and emoting. If we were asked as artists and designers, to come up with a new insect; then some really fine knowledge of micro-engineering would be required. The world is huge; but no less micro-engineered. The only distinction is that the layers of it that happen are so compressed and so fine in ever-decreasing scale; that in the end, the distinctions between solidity, liquidity, and gaseousness are all lost in a principle known as energy flow (Greek; flux – flowing forwards, like the expanding spiral of light and the Universe itself, and reflux – flowing backwards, like the dissipation being spread through ever smaller and more refined layers, and that because energy is more volatile in temperament and motion than even time; the physical stuff it passes through is continuously destroyed and remade to help with the stipulations of housing and purposefully directing it. Space is infinite; numbers are infinite; time is infinite, but more transitory, as demonstrated more properly by sound waves. A word or a musical note can be heard and repeated in sequence, and then; after the compression wave has dissipated, it is lost. But having been received, the right KINDS of compression wave act with a Force known simply as 189
Resonance. Which means that if they are worthy of it, some minds will analyse and re-analyse; ripping apart and rebuilding, and never once managing to find a shred or grain of what we might call ‘common sense’ in any of it; but if something has inspired and taught us, then its own rhetoric becomes a more Spiritual or Universal Common Sense; because the separation or division between different minds cannot find a ground for argument in it except for deliberately creating a differing platform of opinion to be able to argue the toss from. Such reasons beyond such arguments are ultimately self-serving; and in such cases it becomes ‘a wash’; and the only lessons such arguments need take their cues from the hierarchical pecking order; which state that the higher ground is usually the better vantage-point to have (as Escher’s own landscape prints seem to demonstrate) and they who hesitate are lost. But then, this is also just another matter of fighting; as in winning by having the sharpest riposte and foil, and knowing the softest spot at which to lunge and press an attack for an advantage! In this case, the sharpest blade is always the sharpest synapse that gets the most concise and quickest word in which can leave another feeling flummoxed. This is part of the reason why I’m not fit to comment too much on his work; not to be objective about the subjective, anyway. Besides, what can I tell another’s perception that they haven’t already noticed as mine has, just by looking and making internal notes and evaluations? These works are all really fine and really good; and those who think any of them crude haven’t understood the time and effort necessary in the original production methods to end up with the finalised prints. But Escher remains, for me, a potent platform for my own ideas. We share many whimsical notions about form and the way perception plays around with what is really there. And, of course, sometimes the implicit mathematical order displayed through crystalline growth and the matrices of ‘crystal- stars’ for instance, would make a planetoid parallax which would make it difficult to understand any shape being seen through it; because of the way the planes shift in the prism, to distort the space between the object being viewed through it and the prism. Or the reflections of things in water almost being astral in their representation; not solid, and the ripples in the water represent how solid things would appear if their substance wasn’t truly solid and the ambient fields of energy flowing in the air around us would have as much influence on the reflected object’s evidently projected ‘self’ as the energy has – through such forces as wind and impact – on the amorphous substance of the water. 190
The three dimensional artist is a Mathematician First Grade and First Rate. Why? By being able to spline the dimensions so that another can understand implicitly and explicitly what they’re trying to depict. It doesn’t even matter if it exists or not as long as the balance of light and shadow and the feelings of flow and direction, and the hidden explanations of contour and form are intact and relevant to the image. This is how any of us can take things out of the Dream-World (which is only the Communal Juxtaposition Point between the Manifest and the Unmanifest, the Potential and the Kinetic anyway; where order and chaos converge and probability and improbability manage to pull a blind-fold over both possibility and impossibility. This is all I’m going to say; I have to apologise to anyone I may be unaware of who may still be earning an income from the late, great Mr. Escher; but I’m simply spreading around what he’s done – not for profit; but to help reconfigure people’s minds to different ways of thinking and perceiving things. These people are to be respected and revered, and admired; but not taken for granted or being complacent about. They aren’t the be-all and end-all which make it unnecessary to do any other work forever afterwards; they instigate temporal conversations – or arguments, like storms – and they have already given us the first word; so it’s up to us to take on board their perceptions and add them to our own life lessons, so that our response is worthy of having studied them, to be able to offer as educated a reply – only the hope for originality and individuality should be ours; it doesn’t matter if someone says, “oh, that looks like a piece of work by so-and-so and so-forth”, all that matters is that the strands of the lessons their souls carry through our minds and hands have allowed us to properly depict the images our own minds have felt the need to seek expression of. What I hadn’t considered is the ramifications on what we term as ‘reality’ of such thoughts and ideas. I’m skipping back to a point where I said that within any dynamic vortex that spirals outwards; to enable the dynamic flow of energy spiralling outwards, the counteracting force must apply within the spaces where the vortex isn’t. Why? Because Nature abhors a vacuum; nothing is allowed to remain static, and everything is seen and perceived from more than one angle at any given time. This linkage might actually help to clarify the idea that water reflection is a more accurate estimation of the reality of the dynamic properties of energy flow, swell, and dissipation through any one thing, because if the physical matter didn’t shackle it; the dynamic energy flows in the air would have MUCH more noticeable influence over it. Don’t forget; trees DO bend in the wind; as long as the prevailing dynamic force is available
and amassed against the seemingly immoveable object to alter its natural growth rhythms and move it. This also helps to give us a more clear understanding of something I believe Escher was hinting at through his art with regard to the processes of Evolution and Natural Selection, as denoted in Darwin’s work. Again; the energy has much flow and influence over the solid forms – whether they have realised this effect and influence or not – which depends on the measurability of any given reaction to any given antagonistic force which washes against it. The Solid World of Living Forms is influenced by both the flows of energy and the flows of liquid passing through it; and the Forces we might justifiably call “Natriation” or Nutrition. This is true because every individual unit exists as a complex balance of sub-systems of varying degrees according to mass and energy expenditure and absorption. This is a theorem that helps give ‘solid-weight’ or ‘resonance’ to such things as Chaos Theory. We already have the inkling that all forms – no matter what gifts; properties; skills; or attributes they possess – are all linked at the level of the subatomic or quantum. How is this? Because the Fifth Dimensional form is the Living Spirit of All Things since the first explosion of energy; through which all other waves have been unified, but divided by being divergently spread across the infinite and incalculable number of different forms spread across the Universe. That spark is no different for a Sun than it is for a Star or a Comet, or a Planet, or an individual organism as part of any divergently and widely linked system (such as us!); and to any who doubt something’s validity in existence, they only have to remember that Existence is ANYTHINGS validity for being here in this shared experience we call Life, Time, Dimension (whatever words you want to use to adequately try to describe it). The simplistic explanation of Chaos Theory, therefore; states that a butterfly flapping its wings in New York can begin a swell of energy with a single wing-beat which is amplified across the atmosphere to rain hurricanes down on Japan. I actually started to write a comedy skit about this; where some unwise fool of a ten-year old Emperor of Japan has disbanded the Samurai and sent them all to New York to earn daily incomes with their families as Japanese restaurants, and secretly gaining the riches of Imperial Japan by catching and eradicating any butterflies and sending back evidence of this – presumably not by carrier pigeon, since this might well precipitate what they are trying to avoid – to keep their Natural Homeland safe. The Secret Ninjas of Central Park, the sketch is called. I deliberately thought as perversely about the error of
misunderstanding a complex theorem as baked into a barely sufficient nutshell as I could. I don’t believe that the literal interpretation was what the author of said theorem was actually talking about – although I haven’t read the Chaos Theory Codex for myself yet – and I suspect that the intimation implicit in the subtext is therefore that small energy dissipations can have large results; but also that everything is Chaos because there are so many different forms on Earth. Energy spread and dissipation can only be properly measured when calibrated equipment is sufficient to measure it; the facts of Evolution and Natural Selection have meant that so many forms have evolved which assimilate and dissimilate energy at so many different rates, and each form that does this by design represents a different calculation and set of variable equations that have to be factored into the overall working; and the more of these individuals there are, the more impossible – or improbable, at the very least – the task of predicting the outcome of any given indicator then becomes. The amount of variable is too great and no system really could measure the effects of the spiralling forces of energy through them all simultaneously. I also believe this is why the Theory works so well as a hypothetical; whilst sometimes becoming so hard to divine in practice. Its meaning has become a Chinese Whisper. This spiralling of dynamic forces in both the forward and the backward explains another phenomenon that humans are experiencing – and presumably animals must be experiencing as well – whereby they find it hard to articulate their feelings. I’ve heard it said by some that they find some emotions troubling and confusing and hard to accurately pin down and express. But then, how easy it is to forget that feeling the first tinges of an emotion and letting it flow through you aren’t the same as trying to analyse it and break it down; because as soon as we get to the latter point, the act of analysing and dividing factors in the things that make up the emotions have already had enough influence on them to change them; because in applying the logical mind, suddenly the subconscious flashes the warning up that the opposite side of any coin may also be applied at any given instant. So many married couples love each other so much that they are the other half of each other; as their bodies are met, so their souls are met and conjoined, as well – even though, the manifestation of this love often seems to be a point of numerous grating exchanges that seem to imply to the casual onlooker, that they might actually hate each other instead. Familiarity does this; and positive or negative polarity acts similarly to the same effect. How? Because depending whether the analytical mind 193
has supplied a positive or negative energy force to something it’s been given to cogitate on, the reaction will be proportionate to the action – hopefully. When it isn’t, we call it dissonance or disharmony. Resonance and dissonance. Agreement and Argument. Two halves of the energetic Cosmic Conversation; I was about to say light and sound, but for those of us who can accept the Universe as a Phoenix, and Nature as hating things that remain the same, then the sound is the extensive part of the big bang that breaks apart Dark Matter to reorganise it as light spreads throughout the broken structures in tandem with rotary or spiralling forces to reorganise them into the Universe’s ‘Forms’, then we know that these two forces coexist and work together; and Natural Selection within the argument or conversation is that which provokes new ways to exist, to think, to be; and spurs on greater understanding of things in their context. People also tend to be driven – on occasion – by forces that are equivalent to Chaos Theory; on facebook, some of my friends posted pictures and said ‘bloody hell, that was twenty years ago’, and others said they had to tag people before they forgot. Instantly, my mind churned up the more accurate estimation of the situation, which is this; the more time passes, and the more things our mind has come into contact with and been filled with and sometimes concerned by, the harder it gets to remember those things temporally located further back towards the beginning of our cycle; of course, just becoming aware of new things in the world doesn’t necessarily exclude anything that is already there unless we receive some conclusive report that can tell us otherwise. It’s another case of saying, the more things our own mental systems are aware of; the harder the things we thoughts of as more ‘fixed’ when our system had less to deal with remain in our awareness sometimes; they become more ‘variable’ in Nature to our minds which are dealing with the energy vortex of more information. The more variables a system contains the harder it is to see the resulting factors on any one independently. I remember Terry Pratchett coining what he comically called “Heisenberg’s Uncertainty Principle”, involving an animal called the Ambiguous Puzuma who could travel on the Disc’s Magic Field at near light-speed, which meant no-one ever saw one because, if they did; it wasn’t there. Also, there was the problem of it becoming harder to know WHO you were and WHERE you were simultaneously, the faster you approached the speed of light; which was a seesawing loss of equilibrium, which meant most Ambiguous Puzumas either died of acute ankle strain caused by chasing females who weren’t there anyway; or reached a state of demise when coming to rest, usually about a mile into the rubble of the mountain they ran into at near light speed! Chaos Theory rhetoric at its finest!
My thanks to Escher for helping small and narrow-minded people like me grasp the concepts of the Over-Logic as divined in his Geometrical Practical Guides shown here. The partial bits are important; but more so is the whole. More light; more power. LOL. X. Don.