Invariance is the counterpoint to relativity.

But its projective description – that is, the totality of views offered by all possible perspectives – remains the same, because you can relocate your easel to compensate. Similarly, if we move the subject of our painting – say by rotating it, or changing its position – we will change its appearance. Such transformations change the position of each point on the circle, while the circle as a whole does not change. Rotate a circle around its centre, through any angle. Consider the most symmetric of shapes: the circle. ‘Change Without Change’ is the essence of symmetry.

Symmetry is closely related to relativity, though our attention is directed now to the subject of the painting rather than the viewer.The dispositions of paint on canvas will be different, but all will represent the same information about the subject, just differently encoded. We can paint the same scene from many different perspectives. Relativity, in this sense, is the very essence of projective geometry. Relativity is the idea that the same subject can be represented, faithfully and without loss, in many different ways.The science of projective geometry, that artistic innovation of the Renaissance, contains not merely metaphors, but genuine models of big, cunning and awesomely pregnant ideas: Here, I’m happy to present a solution that’s given me a real feeling of satisfaction. I’ve struggled with that problem many times over the years. But it’s challenging to find metaphors that are both faithful to the original ideas and readily accessible and even more challenging to do it in a way that does justice to their beauty. That’s why those of us who try to bring those ideas to a broad audience must often work in metaphors and analogies. They can seem abstract and forbidding if they are introduced abruptly, in the strange contexts that are their natural habitat. Many of the central ideas of modern physics are unfamiliar to most people. It is remarkable how perspective anticipates the concepts that dominate our basic understanding of Nature’s laws. It might be defined, indeed, as an objective study of subjectivity. With perspective, our concern is how a scene actually looks to a particular person from a specific vantage point. The science of perspective demonstrates the superficiality of such claims. It is sometimes said that science and art are fundamentally different in their approach and their dominion, since science strives to be objective while art is inherently subjective. The tiles of the city square, the parallels defined by architecture, and the relative sizes of people and trees receding into the distance all afford occasions for scientifically accurate rendering.įigure 2: The joy of perspective: Perugino’s ‘Delivery of the Keys’ (1481-82) We can see this reflected in such masterpieces as Perugino’s Delivery of the Keys (1481-82) in Figure 2 below. For artists, it was no longer a matter of recovering what had been lost, but of discovering a fundamentally new creative power. It was also a great confidence-builder: here, at last, was a major discovery that clearly went beyond what had been achieved by the ancient Greeks and Romans. Obviously, it allowed more accurate rendering. The work of Brunelleschi and Alberti made an enormous impact on the artists of the time. It involves a fascinating new kind of geometry, projective geometry. Fifteen years later, Leon Battista Alberti published a classic explanation of the technique. An earlier scientific breakthrough, driven by the needs of art rather than astronomy, was equally profound: Filippo Brunelleschi’s invention of drawing in perspective, around 1420.įigure 1: Brunelleschi’s arrangement allows a viewer to compare a reflected drawing to the thing itself, by removing the mirrorīrunelleschi demonstrated his ability to render scenes accurately through the brilliantly convincing experiment shown in Figure 1 below. While that is a convenient and defensible choice, it is not the only good candidate.

Historians of science usually date the origin of the Scientific Revolution as 1543, when Copernicus’ De Revolutionibus first put the Earth in motion.

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