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volume II: Synopsis

Part II: A brief history of dynamics

page 13: Galileo Galilei

(1564-1642)

The rise of scientific investigation based on observation of the world led to a linguistic revolution. Students of nature found it necessary to extend natural languages with technical terminology in order to name all the things they found. Galileo saw that the natural philosopher needed to add mathematics to natural language as well. He wrote 'Philosophy is written in this grand book - the Universe, which stands continually open before our gaze. But the book cannot be understood unless one first learns to comprehend the language and to read the alphabet in which it is composed. It is written in the language of mathematics . . .'. Galilei, page 238.

Galileo was a skilled instrument maker as well as a natural scientist. He made telescopes that showed him the mountains on the Moon and the phases of Venus. The mountains showed that the Moon was rather similar to Earth, and not composed of some heavenly element as many had assumed. The phases of Venus could be interpreted to show that Venus revolved around the Sun in an orbit inside the orbit of the Earth. History of the telescope - Wikipedia

Many of the inferences drawn from the Bible by Christian theologians were rather far fetched. The Israelites had to conquer the existing inhabitants, often with Yahweh's help, when they took over their Promised Land:

Joshua spoke to Yahweh, the same day that Yahweh delivered the Amorites to the Israelites. Joshua declaimed:
Sun, stand still over Gibeon
and, moon, you also over the vale of Aijalon.
And the sun stood still, and the moon halted,
till the people had vengeance over their enemies. Joshua10:12-13

Following the ancient Greeks, the medieval theologians took this as definite evidence that the Sun moved round the Earth, rather than the Earth around the Sun.

The Church prosecuted Galileo for his opinions, but it could not stop the birth of science. Theology, once the leading edge of science, showed itself unable to adapt to modern developments. In the Church, faith in Scripture continued to outweigh faith in experience, a measure of its power over the people. Theology became an intellectual backwater, and in its place empirical science has come to dominate our interpretation of the world in which we find ourselves. Galileo affair - Wikipedia

Galileo and his contemporaries also began to use rulers and clocks to measure the behaviour of moving bodies, and so brought us into the era of science based on instrumental measurement. He saw that, at least from a physical and astronomical point of view, the best language to describe the behaviour of the world was mathematics. The mathematical expansion of natural language is a central theme of science and finds its place in scientific theology.

Galileo's observation of the importance of mathematics was not new. For thousands of years mathematics, particularly arithmetic and geometry, had been part of everyday trade, architecture and surveying. We weight, measure and count commodities, adding, subtracting, multiplying and dividing to to model costs, profits and losses. Babylonian mathematics - Wikipedia, Needham

Since Galileo's time mathematics has grown enormously beyond the simple arithmetic and geometry we use in finance, trade and engineering. We explore this power in the remainder of this synopsis, gradually working toward the conclusion that the gigantic complex structures which we are able to describe with mathematical language show us the way to constructing models that approach the size of God.

The purpose of this site is to bring theology back into the mainstream of science. The hypothesis that the universe is divine implies that all experience is experience of God. If this is so, we can give theology the scientific independence and certainty necessary for it to cut itself free of any institution no matter how venerable.

In many ways, human natural language is too restricted to talk about the whole divine Universe. Mathematics gives us a window onto something bigger. With the added advantage that because mathematics transcends natural languages, it is not prone to get lost in translation. So we are looking for ways to create a mathematical theology in the Galilean tradition. This is so because mathematics has grown beyond measures of size into the world of logical computation and communication. The proper arena for mathematical study of god is metamathematics, that part of mathematics concerned with mathematical study of the powers and limitations of mathematics. Metamathematics - Wikipedia, Kleene

(revised 29 March 2013)

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Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Drake, Stillman, Galileo at Work: His Scientific Biography, Dover Publications 1995 Jacket: Based entirely on original sources, Professor Drake's scrupulously researched study includes translations of much correspondence and other material previously unpublished in English. The result is a volume of exceptional richness and immediacy that paints a vivid portrait of one of history's greatest minds, leaving the philosophical implications of his work aside and focussing on the enduring scientific achievements that represent Galileo's true legacy to mankind.' 
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Drake, Stillman, Essays on Galileo and the History and Philsophy of Science, University of Toronto Press 1999 Amazon from Book News, Inc: 'In this three-volume set, Swerdlow (U. of Toronto) and Levere (U. of Chicago) provide a synopsis of the life and work of the prolific Galileo scholar, Stillman Drake (deceased, U. of Toronto) as an introduction to their selection of about 80 of Drake's essays. The essays are grouped by subject: biographical and textual studies, scientific method and philosophy of science, astronomy, a translation and essays on the Dialogue concerning the two chief world systems, motion and mechanics, instruments, history of science, and philosophy of science and language.' 
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Galilei, Galileo, Dialogues Concerning Two New Sciences (translated by Henry Crew and Alfonso de Salvio) , Dover 1954 Jacket: 'Despite the fact that this book encompasses thirty years of highly original experimentation and theorizing on the part of this singular man, it is eminently readable. Written as a discussion between a master and two students, it sets forth its hundreds of experiments and summarizes the conclusions Galileo drew from these experiements in a brisk direct style. Using helpful geometric demonstrations, Galileo discusses aspects of fracture of solid bodies, cohesion, leverage, the speed of light, sound, pendulums, falling bodies, projectiles, uniform motion, accelerated motion, and the strengths of wires, rods and beams under different loadings and placements. Not only does the book display the genius of one of the makers of our civilization, but it also presents, for the historian of science, considerable information about Renaissance misapprehensions which Galileo refuted.' 
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Galilei, Galileo, and Stillman Drake (translator), Discoveries and Opinions of Galileo: Including the Starry Messenger (1610 Letter to the Grand Duchess Christina), Doubleday Anchor 1957 Amazon: 'Although the introductory sections are a bit dated, this book contains some of the best translations available of Galileo's works in English. It includes a broad range of his theories (both those we recognize as "correct" and those in which he was "in error"). Both types indicate his creativity. The reproductions of his sketches of the moons of Jupiter (in "The Starry Messenger") are accurate enough to match to modern computer programs which show the positions of the moons for any date in history. The appendix with a chronological summary of Galileo's life is very useful in placing the readings in context.' A Reader. 
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Jones, Alexander (ed), The Jerusalem Bible, Darton Longman and Todd 1966 Editor's Foreword: '. . . The Bible . . . is of its nature a written charter guaranteed (as Christians believe) by the Spirit of God, crystallised in antiquity, never to be changed . . . . This present volume is the English equivalent of [La Bible de Jerusalem] . . . an entirely faithful version of the ancient texts which, in doubntful points, preserves the text established and (for the most part) the interpretation adopted by the French scholars in the light of the most recent researches in the fields of history, archaeology and literary criticism.' (v-vi) 
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Kleene, Steven Cole, Introduction to Metamathematics, Ishi Press 2009 Book description: 'Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Gödel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic, at least a turning point after which “nothing was ever the same.” . . .' 
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MacHamer, Peter, and (Editor), The Cambridge Companion to Galileo, Cambridge University Press 1998 Jacket: 'Not only a hero of the scientific revolution, but after his conflict with the Church, a hero of science. Galileo is today rivalled in the popular imagination only be Newton and Einstein. But what did Galileo actually do, and what are the sources of the popular image we have of him? This collection of essays is unparalleled in the depth of its coverage of all aspects of Galileo's work. A particular feature of this volume is the treatment of Galileo's relationship with the Church. It will be of particular interest to philosophers, historians of science, cultural historians and those in religious studies.' 
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Needham, Joseph, Science and Civilisation in China (Volume 3) Mathematics and the Sciences of the Heavens and the Earth, Cambridge UP 1959 Book description: 'After two volumes mainly introductory, Dr Needham now embarks upon his systematic study of the development of the natural sciences in China. The Sciences of the Earth follow: geography and cartography, geology, seismology and mineralogy. Dr Needham distinguishes parallel traditions of scientific cartography and religious cosmography in East and West, discussing orbocentric wheel-maps, the origins of the rectangular grid system, sailing charts and relief maps, Chinese survey methods, and the impact of Renaissance cartography on the East. Finally-and here Dr Needham's work has no Western predecessors-there are full accounts of the Chinese contribution to geology and mineralogy.' 
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Links
Babylonian mathematics - Wikipedia Babylonian mathematics - Wikipedia, the free encyclopedia 'Babylonian mathematics (also known as Assyro-Babylonian mathematics) refers to any mathematics of the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited.[7] In respect of time they fall in two distinct groups: one from the Old Babylonian period (1830-1531 BC), the other mainly Seleucid from the last three or four centuries BC. In respect of content there is scarcely any difference between the two groups of texts. Thus Babylonian mathematics remained constant, in character and content, for nearly two millennia.' back
Galileo affair - Wikipedia Galileo affair - Wikipedia, the free encyclopedia 'The Galileo affair was a sequence of events, beginning around 1610, during which Galileo Galilei came into conflict with the Aristotelian scientific view of the universe (supported by the Catholic Church), over his support of Copernican astronomy.' back
Giovanni Paolo II Discorso ai participanti alla sessione plenaria della PontificaAcademia delle Scienze, Sabato, 31 ottobre 1992 '4. Ero mosso da simili preoccupazioni, il 10 novembre 1979, in occasione della celebrazione del primo centenario della nascita di Albert Einstein, quando espressi davanti a questa medesima Accademia l’auspicio che “dei teologi, degli scienziati e degli storici, animati da spirito di sincera collaborazione, approfondissero l’esame del caso Galileo e, in un riconoscimento leale dei torti, da qualunque parte essi venissero, facessero scomparire la sfiducia che questo caso ancora oppone, in molti spiriti, a una fruttuosa concordia tra scienza e fede” (AAS 71 [1979] 1464-1465). Una commissione di studio è stata costituita a tal fine il 3 luglio 1981. Ed ora, nell’anno stesso in cui si celebra il 350° anniversario della morte di Galileo, la Commissione presenta, a conclusione dei suoi lavori, un complesso di pubblicazioni che apprezzo vivamente.' back
History of the telescope - Wikipedia History of the telescope - Wikipedia, the free encyclopedia 'The earliest known working telescopes appeared in 1608 and are credited to Hans Lippershey. Among many others who claimed to have made the discovery were Zacharias Janssen, a spectacle-maker in Middelburg, and Jacob Metius of Alkmaar. The design of these early refracting telescopes consisted of a convex objective lens and a concave eyepiece. Galileo used this design the following year.' back
Joshua Joshua 10 'Sun, stand still at Gibeon, and moon, in the Valley of Aijalon.” 13 And the sun stood still, and the moon stopped, until the nation took vengeance on their enemies.' back
Metamathematics - Wikipedia Metamathematics - Wikipedia, the free encyclopedias13Galileo 'Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on methamathematics (and perhaps the creation of the term itself) is due to David Hilbert's attempt of proving the consistency of mathematical theories by proving a propostion about a theory itself, i.e. specifically about all possible proofs of theorems in the theory; in particular, a proposition A and its negation not A should not be both theorems (Kleene 1952, p. 55). However, metamathematics provides a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic, among which the consistency problem is only one (Kleene 1952, p. 59).' back
The Book of Joshua 10:12-13 Chapter 10, 12-13 '12: On the day the LORD gave the Amorites over to Israel, Joshua said to the LORD in the presence of Israel: "Sun, stand still over Gibeon, and you, moon, over the Valley of Aijalon."' back

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