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Home , Letters on Sunspots

The role and place of in the first Scientific Revolution

Galileo’s birthday: February, 15, 1564

Gheorghe Stratan NTAA-Dubna, 2014 Two Books: Copernicus and Newton YEAR DESCARTES KEPLER GALILEO | | | 1564…………...……….………………………………………….BORN | 1571………………..…………..…BORN……………………………… | | | | | | 1596…….BORN…...... ….Mysterium.Cosm……………… 1600------| | | 1609…………..| ………...... Astronomia Nova | 1610…………..|………………..……..|...... 1613…………..|..…………………………Letters on 1618------WAR------WAR------WAR

YEAR DESCARTES KEPLER GALILEI

1619……..…I……...... Harmonices..Mundi……………..I 1621..………I..………….....Epitome..Astronomiae……………..I 1623………..I…..…………………I…………………..Saggiatore I 1630…..……I……………………Dies………………...... 1632……...... I…..……..…………………………………Dialogue 1633..………I.….………………………………………...... Trial

1637……Method………………………………………………….. 1638……...... I...... Two.New.Sciences

1642………..I…………………………………………………Dies

1650……..Dies……………………………………………………

Descartes, philosopher and mathematician (31.03.1596 – 11.02.1650)

Kepler, the discoverer of planetary laws of motion (27.12.1571 — 15. 11.1630)

Galileo, father of Modern Science (15. 02.1564 — 08. 01.1642)

Galileo’s astronomical discoveries Galileo sees the Moon like a new Earth Galileo sees new stars Galileo sees four satellites of Jupiter Further observations: Saturn Further observations: Venus Christian Huygens Explains Galileo (1659) Galileo writes about the sunspots (1613) Galileo draws the sunspots (here, from 23.06.1612) Galileo on torches and spots [faculae and maculae] … on the very face of the Sun, one sometimes sees certain small areas that are brighter than the rest, and which careful observation reveals to have the same motion as do the spots. That these are on the surface itself of the Sun, I do not believe anyone can doubt, for it is in no way credible that there is some substance brighter than the Sun outside of it. Scheiner observes the sunspots (1612-1630) and measures the inclination of Sun’s axis This proves that they [the sunspots] are not on the Sun; indeed, I would judge that they are not true spots but rather bodies partially eclipsing the Sun from us and are therefore stars either below or around the Sun. Which of the two is the case I will in due time and with God’s help bring to light.

SCHEINER ON SUNSPOTS (1611) Scheiner’s instrument to study the sunspots was invented by Castelli, Galileo’s friend and follower Galileo’s (, 1638)

• The definition of the rectilinear and uniform motion. “ By steady or uniform notion, I mean one in which the distances traversed by the moving particle during any equal intervals of time, are themselves equal.” (p. 154) • The definition of the uniformly accelerated motion: “so that during the equal intervals of time, it receives equal increments of momentum and velocity ” (p. 74). • The free fall: “I came to the conclusion that in a medium totally devoid of resistance all bodies would fall with the same speed.” (p. 72). The I • Galileo’s research program: (1) whether all vibrations, large, medium and small [of the same pendulum] are performed exactly and precisely in the same time; (2) to find the times of vibration of supported by threads of unequal length. (TNS, 92) • Galileo’s findings: (General) “each pendulum has its own time of vibration so definite and determinate that is not possible to make it move with any other period than that which nature has given it” (TNS, 97) (1) Wrong answer: “Each vibration, whether of ninety, fifty, twenty, ten, or four degrees occupies the same time”. (TNS, 85) WHY?

Pendulum: the source of experimental errors

The complexity of phenomena involved: -- the resistance of air, -- extensibility of the suspension cords, -- latent modes of oscillations, -- the conical oscillations. The incomplete separation between apparatus and experimentalist; the need of training. The Pendulum II • 2) “As to the times of vibration of bodies suspended by threads of different lengths, they bear to each other the same proportion as the square roots of the lengths of the thread; …. so that if one wishes to make the vibration-time of one pendulum twice that of another, he must make its suspension four times as long. (T ~ sqrt l ; T2 ~ l) TNS p. 96.

Galileo’s research program: • [About] “the cause of the acceleration […] various opinions have been expressed by various philosophers, some explaining it by the attraction to the centre, others to the repulsion between the very small parts of the body… Now, all these fantasies, and others too, ought to be examined; but it is not really worth wile. At present, it is the purpose of our Author merely to investigate and to demonstrate some of the proprieties of accelerated motion (whatever the cause of this acceleration may be).” TNS p. 166

Naturally accelerated motion

“The spaces described by a body falling from rest with a uniformly accelerated motion are to each other as the squares of the time-intervals employed in traversing these distances.” TNS p. 174 h ~ t2

The uniform, rectilinear motion + free fall

• Theorem I, Proposition I “A projectile which is carried by a uniform horizontal motion compounded with a naturally accelerated vertical motion describes a path which is a semi- parabola. TNS 245 Galileo’s Principle of

• “... any particle projected along a horizontal plane1 without friction2 … will move along this same plane with a motion which is uniform and perpetual, provided the plane has no limits3.” TNS, p. 244. (1638)

Descartes’ Laws of Nature (Inertia) • First: “Each thing insofar as in it lies, always preserves in the same state, and once moved, always continues to move.” • Second: “Every motion in itself is rectilinear, and therefore things which are moved circularly always tend to recede from the circle they describe.” (Principia Philosophiae, 1644) Newton’s first Law of Mechanics, (Law of Inertia)

“Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.” (Philosophiae Naturalis Principia Mathematica, 1687) Galileo’s experiments • Einstein (1879-1955)prizes Galileo for his “boldest speculation”, which “could possibly bridge the gaps between the empirical data”. • Alexandre Koyré (Taganrog, 1892-Paris, 1964) Galileo was a genius, but he couldn’t perform experiments. Koyré quoted Marin Mersenne (1588-1648), admirer and translator of Galileo. • Thomas B. Settle, An experiment in History of Science (Science, January 1961) • Paolo Palmieri, Methodology of Galileo’s Experiments with pendulums. BJHS, 2009, 1-35.

Galileo’s experimental achievements

• Organizing the experiment. Training. • Limiting the purposes. • Using relative values (proportions). • Measuring the time much more precisely than 1/10 seconds (water clepsydra and weighting). • Inventing the statistical method of data interpretation. • Using models and explaining the results. • Side effect: Science as a show. Galileo’s Mathematics • Galileo – Dedekind definition of infinite sets

• 1, 2, 3, 4, 9, …n, … • 1, 4, 9, 16, ...n2, … • {n2} {n} • Galileo’s Geometrisation of • Descartes’ Algebrisation of Geometry Galileo about the use of Mathematics in Science “The Book of Nature is written in Mathematical Language.” • Galileo understands the problems of using mathematical methods in Physics: “When we begin to refer to the matter, because of its contingency, the alteration of the abstract propositions considered by the geometer begins also.”(Galileo, X, p. 100) • “To demonstrate everything by geometrical methods starting from established principles.” (Galileo, Two New Sciences, p. 6)

Simplicio against Salviati

• “The arguments and demonstrations that you have advanced are mathematical abstract, and far removed from concrete matter; and I do not believe that when applied to the physical and natural world these laws will hold.” (Galileo, Dialogue, p. 52) Descartes’ objections

• “Pretending from me Geometrical demonstrations in a matter which depends on Physics means asking me to do impossible things.” • (Descartes’ letter to Mersenne, May 17, 1638) Galileo and the theologians • He recognizes the fact that Theology occupies “its regal throne because of its supreme authority and does not stoop to the baser and more humble concerns of the subordinate sciences” [like the above mentioned ones] but ”[...] those who practice and profess it should not claim the authority to lay down the law in the fields where they have neither practiced nor studied”. (Letter to Grand Duchess Christina, 1615) Pope John Paul II about Galileo

“…this letter to Christine de Lorraine … is like a short treatise on biblical hermeneutics”. “….it is a duty for theologians to keep themselves regularly informed with scientific advance” and, “if such is necessary … for introducing changes in their teaching”. (Discourse at 1992 Plenary Session of Pontifical Academy of Sciences)