7.) Galileo Galilei

"According to Stephen Hawking, Galileo probably bears more of the responsibility for the birth of modern science than anybody else, and Albert Einstein called him the father of modern science." (from "Galileo" at Wikipedia: http://en.wikipedia.org/wiki/Galileo)

• Separated science from philosophy and religion
• Saw mathematics in nature
• Combined mathematics and experimentation.
• Set up standards for his experiments to make them more reliable. He also, "recognized that his experimental data would never agree exactly with any theoretical or mathematical form, because of the imprecision of measurement, irreducible friction, and other factors."
• Proposed mathematical laws using inductive reasoning. He used specific, observable phenomena to guess at general or universal concepts, (axioms). He reached conclusions about unobserved things on the basis of what has been observed.
• Appreciated the relationship between mathematics, theoretical physics, and experimental physics.
• Understood the parabola and conic sections, which means he understood Algebra and Geometry.
  
• Parabola: a type of curve . More specifically, it is a "set of all points (x,y) that are the same distance from a fixed line (called the directrix) and a fixed point, (called a focus), which is not located on the directrix." "The midpoint between the focus and directrix of the parabola is called the vertex and the line passing through the focus and vertex is called the axis of the parabola." (from the Krell Institute http://www2.krellinst.org/UCES/archive/resources/conics/node51.html) It looks like one part, (or branch), of a hyperbola, but it isn't exactly that. We will discuss, understand and apply this in greater depth later.

• He, "asserted that the parabola was the theoretically ideal trajectory of a uniformly accelerated projectile in the absence of friction and other disturbances." He, "maintained that for distances up to the range of the artillery of his day, the deviation of a projectile's trajectory from a parabola would only be very slight." (from The Attractive Universe: Gravity and the Shape of Space by E. G. Valens)
  

• Conic Sections: picture slicing, (sectioning), a pointed ice cream cone, (a right circular conical surface), with a knife, (or a Plane: a flat two dimensional surface, like a piece of paper, only much thinner, because being two dimensional, it has no thickness.(Image from "Conic Section" at Wikipedia: http://en.wikipedia.org/wiki/Conic_section)
  

Notice in figure 1 above, that when the plane, (light blue rectangle), sections the cone at a steep diagonal trajectory, the cut edges of the two sections form a Parabola. On the top cone in figure 2, the plane sections the cone at a less steep diagonal trajectory and the cut edges form an Ellipse. On the bottom cone in figure 2, the plane sections the cone at a horizontal trajectory and the cut edges form a Circle. In figure 3 the plane sections both cones at a vertical trajectory and the edges form a Hyperbole, (resembles two opposite facing parabolas). We'll think about these shapes in greater depth and detail when we move on to the work of Kepler and Newton.

• Algebra: is many things. I don't know or remember much about it. I have the impression that, in terms of how Galileo applied it to his inquiries and experiments involving gravity, he was exploring, defining and confirming the relationships between things. He then used what he knew to discover what he did not, like a mathematical form of inductive reasoning.
• Geometry: I don't know or remember much about it either. There are many types. The word comes from the Greek for "Earth Measurement". Again, it appears to me that Galileo used what he knew about Euclidean Geometry, to discover what he didn't know about points, lines, surfaces and shapes and their positions, motions and properties.

These are just my impressions from reading one 187 page book that devotes only one section to Galileo and his work, as it relates to gravity. It would be fun to study his life and read his works:

"The Little Balance (1586)
On Motion (1590) [127]
Mechanics (c1600)
The Starry Messenger (1610; in Latin, Sidereus Nuncius)
Letters on Sunspots (1613)
Letter to the Grand Duchess Christina (1615; published in 1636)
Discourse on the Tides (1616; in Italian, Discorso del flusso e reflusso del mare)
Discourse on the Comets (1619; in Italian, Discorso Delle Comete)
The Assayer (1623; in Italian, Il Saggiatore)
Dialogue Concerning the Two Chief World Systems (1632; in Italian Dialogo dei due massimi sistemi del mondo)
Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638; in Italian, Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze)"
(from Galileo at Wikipedia: http://en.wikipedia.org/wiki/Galileo_Galilei)

Then I might be able to say with authority just what he was up to. Clearly I am going to need a lot more knowledge of mathematics before I complete the first phase of my methodology: "Conduct extensive research on existing theories."

I will refer to his works, and I should at least read:

• The Assayer, because it contains so many of his ideas about the nature of science and how it should be practiced.
• Discourses and Mathematical Demonstrations Relating to Two New Sciences, because it, "reviews and refines his earlier studies of motion and, in general, the principles of mechanics. The book opened a road that was to lead Newton to the law of universal gravitation that linked Kepler’s planetary laws with Galileo’s mathematical physics." (from "Galileo", Funk & Wagnalls New World Encyclopedia)

Recalling how easily distracted I am, I'll stay focused on the quest and move on to a series of experiments he conducted regarding how things fall. He applied the knowledge that had come before and laid a foundation for much of what followed.

"Galileo's theoretical and experimental work on the motions of bodies, along with the largely independent work of Kepler and René Descartes, was a precursor of the classical mechanics developed by Sir Isaac Newton." (from "Galileo" at Wikipedia: http://en.wikipedia.org/wiki/Galileo_Galilei)

More Research Needed: Conic Sections, Apollonius of Perga, Algebraic Geometry, Johannes Kepler, Sir Isaac Newton, Bayesianism, (Bayesian inference), Edwin Jaynes, Stephen Hawking

But first, my ...

Next blog entry: "Galileo Dropped the Ball".