Roger Joseph Boscovich
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- But if some mind very different from ours were to look upon some property of some curved line as we do on the evenness of a straight line, he would not recognize as such the evenness of a straight line; nor would he arrange the elements of his geometry according to that very different system, and would investigate quite other relationships as I have suggested in my notes.
We fashion our geometry on the properties of a straight line because that seems to us to be the simplest of all. But really all lines that are continuous and of a uniform nature are just as simple as one another. Another kind of mind which might form an equally clear mental perception of some property of any one of these curves, as we do of the congruence of a straight line, might believe these curves to be the simplest of all, and from that property of these curves build up the elements of a very different geometry, referring all other curves to that one, just as we compare them to a straight line. Indeed, these minds, if they noticed and formed an extremely clear perception of some property of, say, the parabola, would not seek, as our geometers do, to rectify the parabola, they would endeavor, if one may coin the expression, to parabolify the straight line.
- "Boscovich's mathematics", an article by J. F. Scott, in the book Roger Joseph Boscovich (1961) edited by Lancelot Law Whyte.
- "Transient pressure analysis in composite reservoirs" (1982) by Raymond W. K. Tang and William E. Brigham.
- "Non-Newtonian Calculus" (1972) by Michael Grossman and Robert Katz.
Quotes of others about Boscovich
- The phrase "ahead of his time" is overused. I'm going to use it anyway. I'm not referring to Galileo or Newton. Both were definitely right on time, neither late or early. Gravity, experimentation, measurement, mathematical proofs … all these things were in the air. Galileo, Kepler, Brahe, and Newton were accepted - heralded! - in their own time, because they came up with ideas that scientific community was ready to accept. Not everyone is so fortunate. Roger Joseph Boscovich … speculated that this classical law must break down altogether at the atomic scale, where the forces of attraction are replaced by an oscillation between attractive and repulsive forces. An amazing thought for a scientist in the eighteenth century. Boscovich also struggled with the old action-at-a-distance problem. Being a geometer more than anything else, he came up with the idea of "fields of force" to explain how forces exert control over objects at a distance. But wait, there's more! Boscovich had this other idea, one that was real crazy for the eighteenth century (or perhaps any century). Matter is composed of invisible, indivisible a-toms, he said. Nothing particularly new there. Leucippus, Democritus, Galileo, Newton, and other would have agreed with him. Here's the good part: Boscovich said these particles had no size; that is, they were geometrical points … a point is just a place; it has no dimensions. And here's Boscovich putting forth the proposition that matter is composed of particles that have no dimensions! We found a particle just a couple of decades ago that fits a description. It's called a quark.
- In 1763 a Croatian Jesuit named Roger Joseph Boscovich (1711 - 1787) identified the ultimate implication of this mechanical atomic theory. One of the crucial aspects of Isaac Newton's laws of motion is their predictive capability. If we know how an object is moving at any instant - how fast, and in which direction - and if, furthermore, we know the forces acting on it, we can calculate its future trajectory exactly. This predictability made it possible for astronomers to use Newton's laws of motion and gravity to calculate, for example, when future solar eclipses would happen.
Boscovich realized that if all the world is just atoms in motion and collision, then an all-seeing mind "could, from a continuous arc described in an interval of time, no matter how small, by all points of matter, derive the law [that is, a universal map] of forces itself … Now, if the law of forces were known, and the position, velocity and direction of all the points at any given instant, it would be possible for a mind of this type to foresee all the necessary subsequent motions and states, and to predict all the phenomena that necessarily followed from them."
- Philip Ball, Critical Mass: How One Thing Leads to Another (2006).
- The ancient Greek philosopher, Democritus, propounded an hypothesis of the constitution of matter, and gave the name of atoms to the ultimate unalterable parts of which he imagined all bodies to be constructed. In the 17th century, Gassendi revived this hypothesis, and attempted to develope it, while Newton used it with marked success in his reasonings on physical phenomena; but the first who formed a body of doctrine which would embrace all known facts in the constitution of matter, was Roger Joseph Boscovich, of Italy, who published at Vienna, in 1759, a most important and ingenious work, styled Theoria Philosophiæ Naturalis ad unicam legem virium, in Natura existentium redacta. This is one of the most profound contributions ever made to science; filled with curious and important information, and is well worthy of the attentive perusal of the modern student. In more recent days, the theory of Boscovich has received further confirmation and extension in the researches of Dalton, Joule, Thomson, Faraday, Tyndall, and others.
- Boscovich's ideas exerted a deep influence on the work on the next following generation of physicist ... Our esteem for the purposefulness of Boscovich's great scientific work, and the inspiration behind it, increases the more as we realize the extent to which it served to pave the way for the later developments.
- Niels Bohr, as quoted in Roger Boscovich The Founder of Modern Science by Roger Anderton and Dragoslav Stoiljkovich (2014).
About Boscovich: Cerqueiro, Daniel. Boscovich, the Time Traveler. Buenos Aires: Small Ed. Venice. 2008. ISBN 978-987-9239-18-6