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Start looking inside the ring at the 12 o'clock position and follow anti-clockwise. You'll see a river running through a canyon, and then at 10 o'clock it starts to drop into a waterfall. Your view gradually becomes 'aerial', and at six o'oclock you're looking straight down on the falls from above, as it drops into successive canyons. At two o'clock there is a road-bridge across the river and your view is more skewed even though still from above. From here the water returns mysteriously to its source having 'fallen uphill'. In this composition, there is a 'half-twist' in the viewer's perspective
as one proceeds to 'sequentially observe or follow' the circumference
of the circle, much like that of the renowned Moebius band of mathematics.
This twist, instead of existing Escher constructed a very clever drawing of an 'impossible waterfall' and made it all the more astonishing by convincing us that his 'perpetual motion' machine which seems to our surveying eyes entirely logical, could even power a turbine! His perspectival 'twist' was inspired by the Penrose tribar (a kind of impossible three-dimensional triangle). If we regard mathematical illusions and the 'logic of the impossible'
as 'mere curiosities', and 'quaint tricks', we should not forget the lessons
of history. Such lessons may change our view. For example, whilst it is
true that parallel lines do not meet in the (Euclidean) geometry of the
flat plane, there are equally valid (consistent) geometries of curved-surfaces
(non-Euclidean) in which 'parallels' do in fact meet, and in other cases,
diverge. Einstein utilised these ideas to help him formulate his General
Theory of Relativity, in which he proposed that matter 'bends' (changes
the curvature) of the 4-dimensional space-time 'surface'. This was a new
and radical way of accounting for the effects of 'gravitation'. In a bizarre
The painting echoes another concern. That is that what seems to be so
real, such as the linear passage of time, may in fact be a lower-dimensional
illusion of our minds. Twentieth century physics affirms this. If we could
perceive space-time from a higher-dimensional viewpoint, we might observe
(figuratively) something like this: a strange and beautiful 'convoluting
connectedness', without any 'loose ends'. An ocean of connectedness, of
'waves' that rhythmically ebb and flow, rise and fall, and whose peculiar
unique forms are determined not by a static predetermined monotonous metric,
but by a liquid poem whose rhyme and meter only emerges from the symphony
of all the lines, and all of the verses, stunningly measured, but whose
measure both stretches and shrinks, twists and turns, yet remains forever
balanced, even in the cusp, ...every point, every entity, taking its cue
from every other, ...every syllable included in the rhyme and meter, every
line, every stanza, ...even the
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