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Its quite clear that there is a great deal of continuity between the science of Antiquity & that of the Renaissance. But one has the sense that there is some kind of essential difference.

One claim I've seen is that Galileo was the first to apply mathematics to mechanics. How well does this claim stand up? Surely just as important, if not more, is the development of lens-making technology that allowed him to look at the night sky through a telescope?

In Kuhns sense of scientific revolution - what were the clear markers that differentiates this era from any other?

(By Antiquity, I mean a generous time-frame which includes Hellenic Antiquity, Islamic Dar As-Salaam, and Christian Philosophy before the Renaissance, that is before Galileo).

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    On Floating Bodies? – user3164 Jul 13 '13 at 10:57
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    And less sure whether Epistola de magnete, which is about magnets, suits you. – user3164 Jul 13 '13 at 10:59
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    How is this philosophy (except inasmuch as everything is)? – Rex Kerr Jul 13 '13 at 19:24
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    This question appears to be off-topic because it is about the history of mathematics and physics. – Dennis Jul 13 '13 at 21:24
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    @MoziburUllah I think the edit is a big improvement and brings it on-topic. – Dennis Jul 13 '13 at 22:51
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The fundamental difference between ancient science and modern science isn't in the use of mathematics, although advances in mathematics since Euclid's day certainly helped fuel the scientific advances of the Enlightenment. But what really distinguished modern science was the use of experiment. The ancients recognized observation as the foundation of science; Thales came up with what we would call methodological naturalism, the doctrine that observable effects have physical causes, and it was the goal of science to discover those causes by studying the effects. But Galileo and his successors did something profoundly different: rather than passively observe the phenomena of the natural world, they created contrived situations in which they disturbed nature and studied how it responded. Thus the experiment was born, and with it what we now call the scientific method.

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    It is preposterous to suggest that experiment and what we call the scientific method were born in the Renaissance. Perhaps the sorts of experiments and methods are more familiar to you today than those of the ancients; but if contrivance of experiment is your criterion, then the experiments conducted by Archimedes, Aristotle, Galen et al. easily qualify. (Of course, there's the popular belief that Aristotle thought heavier objects would fall faster than lighter ones may, in fact, stem from a mistranslation attributing heavier and lighter to the falling objects rather than their medium.)... – Jon Jul 16 '13 at 0:55
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    ...see H. G. Apostle's translations of Aristotle. I'm having a difficult time recalling whether he states his contrarian contention in the introduction to Physics, Metaphysics, or On the Soul, but it should be in one (or perhaps all) of them. Regardless of this instance, however, it is absolutely clear that the ancients "contrived situations in which they disturbed nature and studied how it responded." It would be ridiculous to think otherwise. – Jon Jul 16 '13 at 0:58
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Many examples of ancient science and technology can be found in The Forgotten Revolution. This book also describes how the application of mathematical models and the interpretation of hypotheses and axioms changed over the course of time in a spectrum ranging from idealization of nature, an assumed truth about nature to merely abstract non-selfcontradictory assumptions.

Also note that mathema is was simply that which could be taught or learned, as opposed to the things that you have to experience yourself in order to understand them.

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As Gugg recommended, in his comment, Archimedes certainly applied mathematics to physics. Whether you're interested in his On Floating Bodies or Method, which contains the first explicit use of what today we'd call infinitesimals, there is no doubt that he applied mathematics to physics. As far as cosmological physicists (which your original question excluded), there are many. Of course, Ptolemy is said to have "discovered" what we would consider trigonometry (though he didn't use trig functions, as symbolic mathematics had not yet been implemented).

But I'd suggest looking into the introduction of symbolic mathematics (algebra). However, symbolic mathematics came about during Galileo's time (but obviously symbolic algebra was not applied to Galileo's work until after his death). For a sustained discussion of the beginnings of symbolic mathematics, I'd suggest reading Jacob Klein's Greek Mathematics and the Origin of Algebra, which includes, in its appendix, a translation of Francois Viete's New Algebra (a work that Descartes "borrowed" greatly from). (Klein's book, however, is not an easy read.) Anyway, although this book does not focus on the exact topic you're asking about, it is pertinent to the question of how mathematical physics (from Descartes to the present) came to fruition; and, in my opinion, it is one of the hidden philosophical gems of the 20th Century.

I should add that Klein's book primarily addresses what he considers to be a great gulf between Greek and modern mathematics. Whether you buy the contention that Greek mathematics was fundamentally different from modern mathematics is up to you; but Klein makes thoughtful and interesting points. (His thoughts are clearly descendants of Husserl's.) But, if I understand your question properly, Klein's book will be quite helpful in trying to understand "what happened" or "what was different" between the ancients and the moderns; the contention that mathematics was fundamentally different is a very interesting answer to those questions. Of course, the contention assumes that ancients like Archimedes were, in fact, applying mathematics to physics; and thus, the difference between an Archimedes and a Descartes (assuming that Galileo would be a sort of interim character) would be symbolic mathematics and/or time/hindsight.

But the use of symbolic mathematics may have been coincident to some fundamental shift in how science was done--or may have been quite important (as it is with modern physics). Of course, a significant change may not have occurred. Or, perhaps, an external factor (to the practice of science) may have been primarily responsible for post-Renaissance science.

There is no reason for an "essential difference" between pre-Renaissance science and post.

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It is simply that the Scientific Method was formulated during the Renaissance. Before that, scientific enquiry relied more heavily on logic than process.

  • Even in ancient times there was a process of forming a hypothesis about the world and observing natural phenomenon to confirm or refute the hypothesis. What was missing was experiments, as I describe in my answer. – Keshav Srinivasan Jul 15 '13 at 9:19
  • Experiments are part of the modern scientific method, as well as peer-review, hence my answer. – Captain Kenpachi Jul 15 '13 at 9:46
  • What I was disputing is that "Before, thatscientific enquiry relied more heavily on logic than process". A reliance on process was there in ancient times, it was just that the process was different. – Keshav Srinivasan Jul 15 '13 at 17:20

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