Let proportion be found not only in numbers, but also in sounds, weights, times and positions, and whatever force there is.Leonardo Da Vinci
Leonardo is clearly illustrating Vitruvius De Architectura 3.1.3 which reads:De Architectura, VitruviusFirst Milanese period 1481/2 - 1499
The navel is naturally placed in the centre of the human body, and, if in a man lying with his face upward, and his hands and feet extended, from his navel as the centre, a circle be described, it will touch his fingers and toes. It is not alone by a circle, that the human body is thus circumscribed, as may be seen by placing it within a square. For measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that lines at right angles to each other, enclosing the figure, will form a square.
The first printed edition of the De Architectura (On Architecture) by the ancient Roman architect, Vitruvius, appears.
It is never easy sometimes to know what direction to go with these blog posts. What is being shown on the "screen of my mind" is a painting of Leonardo, and along with this idea about Coxeter's insight into what the geometer is really doing when he discovers aspects of what exists before it's manifestation in reality. As if, it is not enough to know what the Higg's is doing as it crosses the room in analogy with the great Professor Einstein.
Science takes us back to the very beginnings of the universe and how it is we know that such phases and transformational changes can be described, and behind it all, there is not some existing geometrical nature to the forms that manifest?
So from an historical perspective, the image set the pace for what discoveries become part of the blog entry. Who is to know what direction this may take me as I scour the internet and find the following.
According to Leonardo, the musician composes harmony by the simultaneous conjunction of its “proportional parts”. The painter “grades the things before the eye as music grades the sounds that meet the ear”. On Ms. L. Fol 79v. Leonardo investigates sound and tries to establish strict mathematical proportions between the loudness of a sound at its origin and its range, the point in space up to which it can be heard. This “pyramidal law” was seen as a universal law of proportion that could be applied to other natural phenomena such as light, perspective and even mechanics.See Divine proportions as well.
Leonardo’s pyramidal law of proportional diminution did not always lead to fruitful conclusions. In the absence of knowledge of advanced mechanics, he attempted to apply it to the investigation of gravity, noting that every falling object acquires increments of impetus. He was obviously unaware of the Merton “mean speed theorem” which states that a body traveling at constant velocity will cover the same distance in the same time as an accelerated body if its velocity is half the final speed of the accelerated body.
Undeterred, Leonardo investigated the actions of levers, pulleys and balances at length according to medieval proportional laws, illustrating endless demonstrations of harmonic equilibrium. While most of the results had no practical purpose, Leonardo seems to have taken delight in demonstrating the certainty of proportional law for its own sake. Perhaps it confirmed his view of the inter-connectedness of all things in nature, which he so often disproved in the course of testing theory with experiment.
Pyramidal colourings of our Emotive States
Photo RM -Hervé Lewandowski / Thierry Le Mage- Make Mona Smile here.
As you know I am using a comparative view of emotions which are much more subtle then the matter to which we assign our body. Earth is square. Plato points to heaven for a reason, and all things descend according to those things we assign emotive value which return to the matters defined. Alas, the human experience is emotive determined and our lives set in the direction we send it. All matters of due course, are heralded from a much finer level of thought.
See: The Triangle Descends into the Square
As many of you know I am not the great scientist that so many I follow are. Who have spent their times in the higher halls of learning. It is no less important to me that I work to the same vein of truth that they do in their pursuances for understanding and implementation of science under it's laws.
So too I work an area that would have been the decline of our scientist's credibility. The scientists who have suffered under the scorn of their own colleagues because of this divergence from what is known and understood. I do not have to worry, because I already work the lower echelon of the thoughts and feeling about those scorned. My immaturity perhaps and wonderment as to what purpose this lone blogger attempts, and I could be past off as some kook. I persevere, as we all do to understand life, reality and it's truths.