SPACE AND IMAGE
SPACE AND IMAGE: THE RELATIVITY (OF GALILEO AND EINSTEIN) FROM THE STANDPOINT OF ITS RELATIONSHIP WITH IMAGINATION
By Leonardo Crochik, Instituto Federal de Educacao, Ciencia e Tecnologia de Sao Paulo, E-mail: firstname.lastname@example.org and Joao Zanetic, Instituto de Fisica da Universidade de Sao Paulo, E-mail: email@example.com .
In the domain of geometry, particularly, as long as we have images that are not mediated by words, we have a rich opportunity of interaction between reasoning and imagination.
However, the historical development of geometry, by refusing the naive use of visual images and demanding only the strict manipulation of axioms previously stated, challenges imagination to be able to reformulate itself.
This tension between imagination and abstraction, more than the simple negation of the former, is an aspect of the development of n-dimensional and non-euclidean geometries and of its utilization in the physical theories of space that make us think in the relevance of such approach in the educational context.
I intend to develop an approach to the notion of relativity and relativistic space that prioritize the relationship with imagination. A geometric approach of Lorentz and Galileo transformations and an exploration of some artistic and literary works contemporary to the scientific construct will play an important role in this objective.
The Italian natural philosophy in 16th century emancipated the concept of space from the scholastic substance-accident scheme. In addition to being prior to the bodies, space becomes homogeneous, undifferentiated and can be occupied without resistance by bodies.
The distinction between high and low stops being a property of space and becomes a consequence of the relationship between bodies. By loosing its “natural center”, the bodies in homogeneous space need to be described from a new center: the observer. The Renaissance perspective depends strongly on the observer position: it defines the vanishing point localization, also associated to the infinitely distant.
The possibility of representing lateral, top and bottom views can be compared to the representation of a fallen body on earth from the earth-frame or the sun-frame. In opposition to the Kantian metaphysics, which believed that the existence of an absolute three-dimensional space obedient to the axioms of Euclid was an a priori intuition, the possibility of existence of a four-dimensional space and of geometries which doesn’t obey the 5th postulate of Euclid excited the imagination of mathematicians, physicists, writers and painters in the 19th and early 20th centuries.
An approach to Special Relativity that takes advantage of the images created by the works cited above is more interesting if we adopt a substantive somprehension of space- time, according to the purpose of Minkowski.
This substantivalist approach allows a geometric treatment and, as Levrini (2002) has shown, allows us to lay out an internally coherent line running from Newtonian mechanics to General Relativity.
We conlude that such a geometric approach can dialogue with the imaginative works of scientists, writers and painters and, in this way, improve the comprehension, the reasoning and also the imagination of students, contributing to the construction of a knowledge less dogmatic and with greater capacity to resonate with each one of us.