CAN TRUTH BE INVENTED?
In this essay, I take the following stance: yes, the truth can be invented, but not from nothing. In the paragraph below, I have outlined a short thesis, purposely using the simplicity of shapes - circles and squares. By doing this, I set out a clear standard for evaluation, on which I go on to base my exploration of truth.
The thesis for this essay is - that it is true that there are no round squares, but this does not mean that we cannot be creative with the boundaries of what is round and what is square. The potential to extend the frontier is always present.
The 80 / 20 Principle, also known as The Pareto Principle, is applied throughout this essay to unpack my thesis. This principle states "that about 80% of the consequences are produced by 20% of the causes" (Dunford, R. 2014 p140). In this essay, I look through the lenses of maths, art, rituals, and myths and demonstrate how the 80 / 20 Principle can be applied to the invention of truth. By looking through the lenses of different disciplines, I can apply significant pressure on my thesis and methodology. Therefore, strengthening my case that truth is contextual (in that it depends on the something that comes before) and much consequence comes from little cause.
In its original form, the 80 / 20 Principle is a simple observation - it demonstrates that 80% of outcomes (consequences) result from 20% of input (causes). When reading this essay, the second part of my thesis (but this does not mean that we cannot be creative with the boundaries of what is round and what is square. The potential to extend the frontier is always present) is to be taken as the 80% outcome. The first part of my thesis (It is true that there are no round squares) is to be taken as the 20%. It is possible to flip the equation and create a 20/80 Principle where 20% represents the outcome and 80% represents the input, but this would decrease the possibility of the equation. Using the original format allows the opportunity to invent truth and potential relative outcomes to be more significant; also, there is less reliance on absolute truth as it only makes up 20% of the equation. The 20% absolute gives the equation context rather than if it were 80%, it would constrain it.
In his book Beyond the 80 / 20 Principle (2020), Richard Koch takes the basic principle and builds upon it. Koch adds to the principle by relating to 92 power laws, such as evolution by natural selection and Newton's law of motion and gravity, and applies them to business. This essay uses the basic principle in alignment with my thesis and argues that we should take 20% of what we perceive, feel, and think as absolute truth. This way, we have something (as opposed to nothing) to input into our reality and invent.
We should then consider 80% of what we perceive, feel and think as relative truth, and view this as an invented outcome. In part two of Beyond the 80 / 20 Principle, Koch reflects on how we would not have Quantum Mechanics if Einstein had not invented the special theory of relativity. Likewise, we would not have the special theory of relativity if Newton had not discovered motion and gravity laws. This physical law trilogy is an example of how truth input flows from one law to the next. Each part paves the way for the outcome and the invention of new truths.
To explore and critique my thinking, I apply three different views of truth. The first view focuses on what we perceive as the truth, and in this, I use circles and squares mathematically as a working concept. The second focuses on what we feel is the truth, and in this, I draw upon Bridget Riley, who uses distorted geometric circles and squares in her art. The third focuses on what we think is the truth and examines the origin of the circle and square, referring back to evidence from ancient rituals and myths.
Perceiving Truth
The first part of my thesis (the 20%) - 'there are no round squares,' has been constructed using first-order logic and is a simple statement. As far as we can see, squares have corners, so we logically deduce that they cannot be round, as we know what round is. Perhaps the first part of the thesis is too simple of a statement to make. An octagon could mathematically be considered a round square. One way to draw an octagon is to draw a circle, draw a square around the circle, and then create an octagon from this. I accept that all absolute truth can be pulled apart, drilled into, and turned upside down in the quest to find different angles and perspectives. However, we need rules as, without some level of absolute acceptance of truth, we cannot progress towards something new.
We must draw a line somewhere so we have a platform to invent on. We should accept that we see round circles and not round squares. By embracing this outlook, we create opportunities rather than restrictions. Positively viewing this constraint allows an opportunity for discovery, and by accepting that what we perceive to be the truth is accurate, we can view it from many angles and then innovate.
The second part of my thesis (the 80%) - 'but this does not mean that we cannot be creative with the boundaries of what is round and square. The potential to extend the frontier is always present' has been constructed using a temporal logical approach. By accepting 20% as absolute truth, we can optimise the potential of the 80% because temporal logic is open and alludes to infinite time. 20% + 80% is a finite set in that the two percentages together are always going to add up to 100%. The answer to the equation being 100% is a totality as it is considered the whole. While this is a mathematical truth, another way of looking at 100% is that the potential of 100 can extend and grow. For example, a Googol is one followed by one hundred zeros, and "there are fewer than a googol atoms in the entire visible universe" (Shapiro, D. n.d). A Googolplex is an extended version of a Googol, and a Googolplexian is even more significant. A Googolplexian is still finite, but as with the physical law trilogy, it demonstrates how input flows from one to the next, and the outcome continues to extend. With this outlook, we can view 100% as having the potential to encompass all invented truth and truth that has yet to be invented. It is helpful to use the Google numbering system as this allows us to shape our perception. Other valuable tools are metaphors, frameworks, and paradoxes. The Physicist Thomas Kuhn said, "You do not see something until you have the right metaphor to let you perceive it" (Gleick, J. 2008). This statement suggests that metaphors encourage the invention of truth - as perhaps do frameworks and paradoxes. For the 80 / 20 Principle to be infinitely valuable, we should perceive it as a metaphor, framework, and paradox.
Feeling Truth
During the 1960's Bridget Riley, an English artist, developed an artistic style, exploring dynamic boundaries of optical phenomena. Her paintings were referred to as 'Op-art.' During this period, Riley used two-dimensional circles, squares, and other shapes to create optical illusions. A retrospective exhibition of Riley's paintings was displayed at The Hayward Gallery, London, in 2019/20. The work on display was summed up as "Triangles, curves, rhomboids, stripes, and dots. Shapes that shimmer, hover, and flicker. Discs that hum, throb, and float. Circles disappear into a fold in time. Dizzying, blurring, rippling contours. Everything moves—reality warps. The images seem to be shouting: Forget what you know. Do not trust your senses. Hold on tight" (Carroll, J. 2020).
Many of Riley's paintings are black and white geometric patterns. They push the boundaries of truth, not just through sight but also through emotions. Her work is "disruptive, unsettling, mesmerising. It chimed with the spirit of the '60s - an age of doubt and disorientation, anxiety and apprehension" (Carroll, J. 2020).
When people view Riley's work, they feel disorientated because their perception creates a collision between temporal and first-order logic. The viewer searches for something known (first-order) but is hit with something open and infinite (temporal). Often when we feel disorientated, we try to find something familiar. After viewing Riley's paintings, we can find something absolute, like a simple shape. We can then use this input to invent explanations of what we see and feel.
For example, if we can see an absolute circle or square, then the rest of what we see and feel is relative to our perception and circumstances.
Riley's paintings cause anxiety and apprehension because humans like order and dislike chaos. Order gives us meaning and helps us feel in control. Chaos creates anxiety and apprehension. Riley embraces the paradox of chaos and order combined and speaks of paradox as though it is fascinating. "The word 'paradox' has always had a kind of magic for me, and I think my pictures have a paradoxical quality, a paradox of chaos and order in one" (Tate. n.d). On the surface, the order/chaos paradox that Riley refers to could debunk the soundness of applying the 80 / 20 Principle to the truth. It may seem ridiculous to state that 20% of emotional order creates 80% of emotional chaos and then relate this to the invention of truth. Nevertheless, if we examine this closer, we discover that the order/chaos paradox sits inside a truth paradox. The more expansive paradox is that everything we perceive and feel is true, yet not entirely because one person's absolute is another person's relativity in that it curves and warps.
Emotions are what lies at the core of the truth paradox. Our emotional connections to our truth are what shape our reality. We hold on to absolute truths as they provide us with a sense of order. Relative truth is down to perception and circumstances and is uncomfortable and chaotic. By starting with an absolute truth, which provides a sense of order, we can reduce our feelings of anxiety and apprehension. We then have the potential confidence to push the boundaries further into chaos, which leads to creativity and invention.
Let us come back to circles and squares - we can use differential geometry to explore the borders of a circle and a square. Gaussian curvature is a form of differential geometry that pushes the boundaries of intrinsic geometric properties. "The Gaussian curvature concept explains how one surface can or cannot be bent into another. It is an intrinsic geometric property that stays the same no matter how a surface is bent, as long as it is not distorted, neither stretched or compressed" (Doyle, P. n.d). When using Gaussian curvature, the boundaries of shapes can be creatively innovated through different surface curvatures. A surface with a constant zero Gaussian curvature is a developable surface - the geometry of the surface is Euclidean geometry. A surface with a constant positive Gaussian curvature is a sphere - the geometry of the surface is spherical geometry. A surface with a constant negative Gaussian curvature is a pseudo-spherical surface, and the geometry of the surface is hyperbolic geometry (Doyle, P. n.d).
Applying the Gaussian curvature concept to a two-dimensional square drawn on a flat piece of paper can be creative with the square's boundaries. Flat paper has zero Gaussian curvature, but if you roll it into a tube, the square changes shape and becomes round, creating a round square. If we then go on to flatten out the paper and wrap it around a tennis ball with positive Gaussian curvature, we further distort the appearance of the square, as we have to create wrinkles in the paper.
We can further extend the frontier of what is square by wrapping the sheet of paper around a saddle-shaped surface that has a negative Gaussian curvature. We would need to tear the paper to make it fit over the surface. Referring to the 80 / 20 Principle, we can take the two-dimensional square drawn on the flat paper as 20% input. The surface distortion (the paper) becomes the 80% outcome. Every possible roll, twist, wrinkle, and tear allows us to see the square differently. The only limit is our imagination in that it is down to the ability of our creativity and resourcefulness to find another way.
From the artist's perspective rather than the viewers', in her process, Riley uses a geometric shape like a circle or square in its ordered simplicity and then creates illusion and disorientation. She uses a shape as input, and the output is the op-art she creates, creating chaos and associated feelings. It is also important to highlight that Riley's method creates the Gaussian curvature concept's associated feelings. At first glance, the viewer sees the paintings as though the surfaces are being distorted. Although the paintings are flat and have zero Gaussian curvature, there is an illusion that the surface is bent.
Linking back to the 80 / 20 Principle, I explain below how Riley's paintings exemplify the invention of truth, deriving from input instead of nothing. Using her paintings titled 'Pause' and 'Movement in Squares' (images above) as examples, I outline how we take what we know to be true (a circle or square) as 20% input and then invent our perceptions, which become our relative truth and 80% outcome.
Let us look at 'Pause.' We can use two truths as 20% input. The first is that there is at least one black circle in the painting, and the other is what we are viewing on a flat surface (which is apparent after the first glance). Every person who views this painting would agree with these two truths. Everything else that each viewer may see and feel is 80% relative truth outcomes. Some of the relative truths people may invent could be the number of circles in the painting and what is considered a black circle, as some are faded and distorted. Then there are the potential relative feelings created by the newly discovered truths to consider. Some viewers may feel frustrated with their discoveries, and others may feel at peace.
Moving on to 'Movement in Squares.' We cannot say that there is at least one black square in this painting. The only truth relating to squares is in the title of the painting. The shapes could be distorted squares or they could be rectangles. We also do not know if the background is black, and the shapes are white or vice versa. The 20% input to be used here is the title and the knowledge gained from viewing the painting on a flat surface. Each viewer will again invent different relative truths about what they are viewing. Every viewer will experience and feel something different - this is the 80% relative truth outcome.
Thinking Truth
So far, I have demonstrated that truth can be invented through how we perceive it and feel it. This next part of the essay delves into ancient history and reviews the origins of the circle and square. Ancient rituals and myths have shaped our modern thinking around what meaning we give to these shapes. In his paper, The Ritual Origin of the Circle and Square, Seidenberg (1981) points out that the circle and square are the main elements of ancient geometry. Due to their importance in geometry, he seeks both amongst the ideas and activities in rituals and myths.
Seidenberg draws upon creation rituals where "the participants brought various objects onto the ritual scene and were identified with these objects. In elaborating the ritual, these objects, and in particular stars, were studied. The participants identified with stars and moved in imitation of the stars, giving the ritual scene a circular shape: the circle's origin. The circle was bisected by the two sides of a dual organisation, taking up the two sides of a circular ritual scene. The two sides split, giving rise to quadrants (see image below).
Then representatives of the four sections placed themselves about the centre of the circle in positions corresponding to the positions of the four sections, thereby giving rise to the square. The square was valued as a figure dual to the circle. The circle and the square are offspring of the ancient creation ritual complex" (Seidenberg, P. 1981).
The stance I take on truth is: that it can be invented, but not from nothing. By reviewing the origins of the circle and square, we could say the circle came from nothing. There was a moment in history when it appeared from 'thin air.' At some point, the first group of ritual participants moved in imitation of the stars. People continued to do this over time, and the circular shape they formed became known as the circle. However, even thin air is not nothing. Thin air allows us to breathe, be alive, and move and imitate the stars. The stars played a fundamental part in the creation of the circle.
Our ancient ancestors would not have had the 20% input needed to create an outcome without the stars. What they saw in the sky above was the absolute truth. They used this truth and, collectively over time, invented a new truth - the circle. Boundaries were then continuously pushed, and the circle was bisected, split, and formed into quadrants, which gave rise to the square and an evolved input to use in a new equation. The square was thought to be a figure dual to the circle, and a procreating pair was invented.
This pair then became the flow on input into an equation, and one part of this equation's outcome was geometry.
As Seidenberg highlights, the circle and square are offspring of the ancient creation ritual complex. The Googolplexian extension and the physical law trilogy demonstrate how input flows from one to the next, extending the outcome. The circle's creation is apparent, and then the square shows how useful it is to view 100% as holding the potential to encompass all truth - all that is invented and yet to be invented. Over time, the circle and square were invented. Boundaries beyond the simple shapes were pushed, which gave way to the creation of geometry. By reviewing the Bridget Riley paintings, we can see that geometry is not only valuable for maths, as it has been used effectively to extend the frontiers in art.
Inventing Truth through 20% + 80% = 100%
Discovering truth is a shared quest of humanity, and it is a multidimensional challenge that we face every day of our lives. We search for truth in the paradox that is life. Often we discover and perceive one truth only to have later it contradicted by another truth. This chaotic tension point that is the crux of the truth paradox is where our creativity thrives. However, the order/chaos paradox we all live in means we cannot have one without another. A level of acceptance of something being absolute provides us with order, which is empowering when used effectively.
Through my exploration, it is apparent that absolute truth input paves the way for relative truth outcomes. Consequently, truth flows from one outcome into another input, which allows the outcomes to be continually extended. The 80 / 20 Principle is a framework, a metaphor, and a paradox that can be used effectively to invent truth.
20% = Input, Absolute Truth, and Order
Ancient myths tell us that circles were invented by our ancient ancestors, who moved in circular motions in imitation of the stars. Squares were then created from circles, and together they formed a procreating pair. The offspring of circles and squares was geometry. Geometry was embraced as it provided humanity with order, which is fundamental to our well-being. It provides us with meaning and helps us feel in control, and this runs parallel with absolute truth. The absolutist in us needs a distinction between what is true and what could be true.
80% = Output, Relative Truth, and Chaos
The invention of geometry, combined with the creativity of chaos, gave us an op-art. When combined with order, chaos creates anxiety and apprehension but provides new insights, perspectives, and emotions; this runs parallel with relative truth. The relativist in us thrives on creativity and discovery but needs the order of absolute truth to invent with confidence. When we have some order in our thinking, our emotions create chaos without anxiety and apprehension.
100% = Infinite Invention
In his book Chaos: Making a New Science (2008), James Gleick uses Thomas Kuhn's absolute truth (you do not see something until you have the right metaphor to let you perceive it) as input. We can also draw upon Kuhn's reference to elementary prototypes for revolutionary transformations. Kuhn uses the analogy of the duck/rabbit illusion and states, "what were ducks in the scientist's world before the revolution is rabbits afterward. The man who first saw the box's exterior from above later sees its interior from below, and scientists must learn to see a new gestalt" (Tymieniecka, A. (1995). It is not just scientists that must learn to see new gestalts; we all must embrace this intrinsic ability. Using the 80 / 20 Principle to invent truth gives us the potential to propel our collective abilities into infinity. Using a gestalt as a starting point, the infinite invention of truth relies on our ability to spot patterns and see that a whole is different from and not just more than the sum of its parts.
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This essay forms part of a portfolio of essays that were submitted as part of the Diploma of Creativity Theory, History and Philosophy undertaken at the Institute of Continuing Education at The University of Cambridge.
