Galileo believed that nature was inherently mathematical, that mathematics was the language of nature, and that mathematics was the key to understanding the reality behind the appearance of natural phenomena--for example, accelerated and parabolic motions.
--Prof. Joseph W. Dauben, The Art of Renaissance Science: Galileo and PerspectiveA Revolution in ThoughtGalileo revolutionized physics before Newton. He showed how observation and careful measurement may lead to "hidden causes". For Galileo, those "hidden causes" represented the pervasive mathematical unity underlying the Universe itself. Einstein is most often associated with the concept of the curvature of space-time. But, in fact, Einstein might not have thought about it so clearly had not Galileo laid down a framework, a 'scientific method', within which both Newton and Einstein would later flourish.Consider, for example, Galileo's contribution to our understanding of the curvature of space-time. To do so, we must understand the "parabola:"
Parabola, plane curve consisting of all points equidistant from a given fixed point (focus) and a given fixed line (directrix). It is the conic section cut by a plane parallel to one of the elements of the cone. The axis of a parabola is the line through the focus perpendicular to the directrix. The vertex is the point at which the axis intersects the curve. The latus rectum is the chord through the focus perpendicular to the axis. Examples of this curve are the path of a projectile and the shape of the cross section of a parallel beam reflector.Before Galileo, a cannon ball was thought to either fall abruptly upon "losing impetus" or that it described "some sort" of curve. But no one knew what kind of curve or even if it was a curve. It was Galileo who understood that a projectile fired from a cannon is a falling body. Simply, a falling body describes a curve over time even those apparently falling straight down from a fixed point. This is so because the "fixed point" is merely theoretical. The entire universe and everything in it is in motion. A Glimpse of Space-TimeGalileo's work --his measurements of the rate of acceleration of all falling bodies --that made it possible to imagine orbiting bodies literally "falling" about a larger one in predictable orbits --the moon around the earth, the earth around the sun, the sun about the center of our galaxy, the Milky Way. All orbits can be described and the results are consistent with Galileo's findings.Fast forward to the 20th Century. Einstein equates gravity with the curvature of space-time, an insight that reprised in another context, another paradigm, Galileo's discovery that the paths of missiles and projectiles are curves, specifically, parabolas. Einstein went cosmological, envisioning a falling elevator with a hole in the side admitting a beam of light. The graphed path of the traversing light beam --over the time it takes to traverse the falling elevator --is Galileo's parabola. Thus —in two monumentally important paradigm shifts —Galileo and Einstein —-we glimpse the very curvature of space-time itself.Newton may have posited a "force" to explain "falling" but the equation describing the rate of falling bodies —a curve if graphed horizontally over time —is Galileo's. It was Einstein who understood that the same curvature may describe space-time and render moot Newton's "force", a force that literally reached out into space and acted upon another body instantaneously. For Einstein, gravity was not a force that 'reached out an grabbed ya'; it was, rather, the very shape of space-time. In a sense, Einstein, like Galileo before him, had 'changed' the universe.Of Space, Time & EinsteinWith this insight, the Universe is changed —seen in a completely different way. This is important in at least two ways:
- it changes our understanding of the Universe hitherto thought of as a clockwork in absolute space;
- it illustrates the very nature of creativity.