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Geometry matters, but why?

Geometry matters, but why?

The contribution of geometry to the evolution of human and natural sciences is a well-established fact. Since the Greeks started to realize that the argument is more powerful when backed up by empirical evidence, rather than previous experience, all sciences started to benefit from an approach that had something new: a system of thought. And that system was based on definitions and axioms given by geometric laws. For example, Pythagoras defined reality with three basic principles, extracted from geometric knowledge:

1. Some propositions must be accepted as true without being demonstrated.

2. All other propositions of the system are derived from these.

3. Their derivation must be formal and independent from the subject at matter.

And since for Pythagoras the things are an imitation of the numbers, their definitions and axioms, will reflect the universe, provide intangible harmony and build visible beauty.

The continuous representation of truth.

Because of the early traditions and methods of orally sharing and debating knowledge, the first visual (geometrical) representations of mathematical concepts were being drawn by scribes, sometimes directly when hearing a piece of particular information. This process was flawed, given that the person drawing did not possess geometric knowledge, thus leading to misinterpretations and errors in the visual representation. In the early 300’s Euclid becomes aware of this error and begins drawing his own definitions and axioms, developing adjacent texts that can be understood by any mathematician or artist, for that matter.

And, with the introduction of the visual perspective by Leon Battista Alberti, the geometrical diagrams and laws became generally accepted when depicting a mathematical truth or any given representation of reality.

Thus, geometry provides continuity in visual communication in general, and a context in which all individual things can be represented, calculated, and later better understood.

Geometrical representation, after Euclid, was meant to visually aid geometric definitions and axioms, in the attempt to eliminate possible errors in transcribing the message from one scribe to another.

If what is above is also below, geometry can be a mirror for these two dimensions. While symmetry defines what geometry is, geometric proportions and ratios define man’s perception of beauty and harmony. A harmonic state is associated with an element or an object having its inner components in perfect equilibrium.

Thus, nature is being perceived as beautiful and its creator, good. For example, the complex relation between symmetry and aesthetics is shown in how symmetry defines the perceived qualities of the human body and how these traits are a sign of good health or good genetic conditions.

Man uses beauty as an indicator of truth and while beauty is truth (Ian Stewart), symmetry, proportion, and simplicity will define it.

The harmonic state of an element is associated with beauty, given by the equilibrium of its components. Nature is being perceived as beautiful, and its creator as good — inevitable and inherently in harmony with its creation.

While many of the elements of nature have an innate geometric structure — water, sound and even light — the more complex architecture of the perceived or the hidden dimensions of reality relies on very complex laws that have different types of shapes, boundaries, behaviors, and interactions with the micro and the macro elements of the universe.

In analyzing these dimensions and interactions, many sciences rely on geometric studies and developments that generate universally accepted answers. For example, in his famous special relativity theory, Einstein describes the dimension of space-time by creating a coordinate system that fixes and standardizes measurements, in order to specify the relationship between a moving observer and the phenomenon or phenomena under observation.

Geometry of space-time. The three dimensions of space and the dimension of time give shape to the fourth, that of space-time.
Old and New Astronomy, 1892. What men recognized then in the movements of the heavenly bodies is true now and true for all time. And even in dealing with the limited knowledge and the imperfect methods of ancient astronomers, we need not hesitate to consider these movements as they are now recognized and understood.

By placing man in the middle of all created things, human consciousness becomes a necessity of life. An anthropocentric perspective explains why the universe has an age. Why the universe works at these exact parameters that an objective observer discovers. That we discover.

Thus, man connects himself to the main elements of the universe: space-time and the fundamental laws of physics, geometric defined aspects of reality, that man can relate to, explore and evolve upon.

The geometric laws and ratios that nature confides in, are also bound to shape human existence. The human body, the human mind and their correspondent dimensions and proportions have geometric properties and attributes, similar to all other elements of nature.

Leonardo DaVinci. L’Uomo Vitruviano, drawn around 1490 and based on the previous works of the architect Vitruvius. The image demonstrates the proportions of human body parts to the whole body, blending mathematical measurements from art and architecture. The drawing represents the symmetry of the human body and that of the universe.

The geometric code of information is inherent to nature, inherent to human consciousness, and is present in all perceived and created forms, in the tangible and the intangible.

And maybe a reality built under the auspices of geometry is desirable, being a discipline developed with attention along several millennia and with which the greatest minds of history have created concepts, objects, religions and even the entire universe.

Tib Roibu, PhD

1 multiplies itself and creates 2. The paradigm of reality is the result of conscious observation. If the system from which consciousness takes part is abstract, then reality is an abstraction of this, by reflecting itself and creating form.

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