Here is the Ellis Paul track I played in class called "Did Galileo Pray?", a song that considers to what extent a convicted heretic himself may have been spiritual.
The next track is more like a poem set to music. Tim Minchin's "Storm" is the tale of a scientifically-minded man trying to avoid making a scene as he debates with a new-age woman at a dinner party. Explicit language.
Saturday, April 13, 2013
Wednesday, April 10, 2013
Scientific Revolutions
Aristotle and Ptolemy believed in a universe that was divided into two parts. On the one hand was the earth, with water, fire and air. On the other hand, beyond the moon was a fifth element, called ether. In this realm of ether, things moved eternally in perfect circles. The original four elements, including earth, were thought to be stable and fixed. The movement of earthly bodies was thought of as a disruption from its natural state and the body's subsequent tendency to get back to this natural state. For example, since a stone is made of earth, it is supposed to be on the ground. A stone moves only when this natural state is disrupted, such as when it is thrown or kicked.
Dr. Bencivenga emphasizes the symbolism of Galileo's gesture of turning a telescope, which had been used only to look at the earth, to the heavens. Such a gesture indicates looking at the earth in a similar way to how we look at the other heavenly bodies. This is exactly the shift in scientific thinking that occurred when Galileo hypothesized that the earth is in motion just as other heavenly bodies are in motion.
Dr. Bencivenga notes that the common idea of modern science is that a super-human intelligence should be able to explain the movement of the entire universe with a single formula. It is only because human intelligence is limited that we cannot know everything. An unlimited intelligence could know everything. Dr. Bencivenga also notes that this conception of science is not faithful to current practice. Our next text, from Werner Heisenberg, will focus on the ways that science has changed in the last few hundred years.
In order to understand Heisenberg, we must understand the scientific context in which he was writing. Newton was very influential into the 18th century. Newton thought that the movement of light could be explained by particles. His system (Newtonian Mechanics) characterized physics for decades. At the outset of the 19th century, a famous experiment seemed to prove him wrong.
Thomas Young performed the two slit experiment. The experiment involves a source of light that goes through one screen with two slits onto a second blank screen. If light is made of particles, then some of these particles should go through either slit and hit the back screen. We would expect that the back screen will be illuminated by two spheres of light that overlap with a bright patch. But what we actually see is a series of strips, some brighter, some darker. This suggests that light is not made of particles but of waves. If waves travel through a slit, they can interfere with one another and either amplify or minimize the intensity of the light. The resulting display of light is an interference pattern.
Another change in science in the last couple hundred of years is how we conceive of motion. Aristotle, for example, thought that all motion is continuous. To travel from point A to point B means to travel on a continuous path between the two points, where all points on the path are met along the way. Max Planck thought that energy must travel in units of energy called quanta (or photons for light). Rather than moving in a continuous manner, energy makes giant leaps. Rather than passing by all points on a path, energy travels quantitative jumps from one place or value to another place or value.
Experiments about light in the early part of the 20th century seemed to indicate that both theories about light had some support in empirical evidence.
Heisenberg suggested that rather than conceiving of mechanical laws as equations for positions and velocities of electrons but for the frequencies and amplitudes. Frequencies themselves are the complex mixture of many different frequencies that occur at once. The extent to which a frequency is composed of other frequencies can be indicated with weighted measures. For example, a certain frequency, F, may be made of up 1/4 fA, 1/4 fB and 1/2 fC. So the equations are not fixed numbers but their value shifts depending on the complex event that is being described.
Dr. Bencivenga emphasizes the symbolism of Galileo's gesture of turning a telescope, which had been used only to look at the earth, to the heavens. Such a gesture indicates looking at the earth in a similar way to how we look at the other heavenly bodies. This is exactly the shift in scientific thinking that occurred when Galileo hypothesized that the earth is in motion just as other heavenly bodies are in motion.
Dr. Bencivenga notes that the common idea of modern science is that a super-human intelligence should be able to explain the movement of the entire universe with a single formula. It is only because human intelligence is limited that we cannot know everything. An unlimited intelligence could know everything. Dr. Bencivenga also notes that this conception of science is not faithful to current practice. Our next text, from Werner Heisenberg, will focus on the ways that science has changed in the last few hundred years.
In order to understand Heisenberg, we must understand the scientific context in which he was writing. Newton was very influential into the 18th century. Newton thought that the movement of light could be explained by particles. His system (Newtonian Mechanics) characterized physics for decades. At the outset of the 19th century, a famous experiment seemed to prove him wrong.
Thomas Young performed the two slit experiment. The experiment involves a source of light that goes through one screen with two slits onto a second blank screen. If light is made of particles, then some of these particles should go through either slit and hit the back screen. We would expect that the back screen will be illuminated by two spheres of light that overlap with a bright patch. But what we actually see is a series of strips, some brighter, some darker. This suggests that light is not made of particles but of waves. If waves travel through a slit, they can interfere with one another and either amplify or minimize the intensity of the light. The resulting display of light is an interference pattern.
Another change in science in the last couple hundred of years is how we conceive of motion. Aristotle, for example, thought that all motion is continuous. To travel from point A to point B means to travel on a continuous path between the two points, where all points on the path are met along the way. Max Planck thought that energy must travel in units of energy called quanta (or photons for light). Rather than moving in a continuous manner, energy makes giant leaps. Rather than passing by all points on a path, energy travels quantitative jumps from one place or value to another place or value.
Experiments about light in the early part of the 20th century seemed to indicate that both theories about light had some support in empirical evidence.
Heisenberg suggested that rather than conceiving of mechanical laws as equations for positions and velocities of electrons but for the frequencies and amplitudes. Frequencies themselves are the complex mixture of many different frequencies that occur at once. The extent to which a frequency is composed of other frequencies can be indicated with weighted measures. For example, a certain frequency, F, may be made of up 1/4 fA, 1/4 fB and 1/2 fC. So the equations are not fixed numbers but their value shifts depending on the complex event that is being described.
Vocab for Heisenberg
An interference pattern is the pattern that results from when two waves interfere with one another. If two crests meet, the waves become amplified. If a high point on a wave meets a low point on another wave, the wave becomes interrupted and de-intensified.
Quanta are small units of energy in Quantam Mechanics. Photons are small units of light energy. These can be contrasted with particles, which are thought to be basic units of energy in the system of Newtonian Mechanics. Particles were thought to move in a continuous manner, whereas quanta move in large jumps (quantum jumps).
Fourier Expansion was used to explain the movement of heat through a surface. The idea was that the movement of heat cannot be explained in one general theory but must be explained by appealing to explanations of the different parts of the larger event.
A parameter is a feature of a body that can be measured, such as velocity and location.
Superposition is a state in which a body has many values for any given parameter such as velocity, location, etc. In this state, there are many overlapping and co-existing values for each parameter. This is the state of things before we observe them. For example, before we observe an electron, there is no given fact about the position of the electron. The electron is rather co-located at many different positions.
Quanta are small units of energy in Quantam Mechanics. Photons are small units of light energy. These can be contrasted with particles, which are thought to be basic units of energy in the system of Newtonian Mechanics. Particles were thought to move in a continuous manner, whereas quanta move in large jumps (quantum jumps).
Fourier Expansion was used to explain the movement of heat through a surface. The idea was that the movement of heat cannot be explained in one general theory but must be explained by appealing to explanations of the different parts of the larger event.
A parameter is a feature of a body that can be measured, such as velocity and location.
Superposition is a state in which a body has many values for any given parameter such as velocity, location, etc. In this state, there are many overlapping and co-existing values for each parameter. This is the state of things before we observe them. For example, before we observe an electron, there is no given fact about the position of the electron. The electron is rather co-located at many different positions.
Monday, April 8, 2013
Scientific Method Pt II: Another Application and Critical Comments
Today, before we turn to criticisms of the scientific method, we will first look at another application of Galileo's method. Consider arguments about the daily, or diurnal, movement of the earth. One might wonder why we feel no wind from the movement of the earth. Or one might wonder why gravity pulls things straight down rather than at an angle. Indeed, these considerations seem to show that the earth is stationary. It does not seem as if the motion of the earth has an impact on the physical laws that govern the movement of things on this planet.
Galileo responds with an analogy. Imagine standing high on the mast of a ship. If you were to drop a stone, it would land directly below where you had dropped it--even though the ship is moving just as the earth is moving! This analogy is not yet conclusive, however. The scientific method requires that there be a causal explanation of the movement of objects. One explanation for why we feel no wind from the movement of the earth is that the atmosphere of the earth rotates with the earth. This is a causal explanation for why we feel no wind from the movement of the planet. Also, consider the movement of a stone that is dropped. At the time that the stone is dropped, it is already moving at the velocity of the earth. As it falls to the ground, it maintains this motion, which is why it falls directly below where it is dropped. Both the stone and the ground below it have the same motion, so it appears as if they stay in the same location in relation to one another.
Dr. Bencivenga notes that the scientific method does not prevent Galileo himself from making serious mistakes. He notes two important mistakes in particular. First, Galileo thinks that stars and planets move in perfectly circular motions. A contemporary thinker, Thomas Kepler, was correct to theorize that the planets move in an elliptical shape. Second, Galileo was very invested in his explanation of the tides. He thought that because the earth moves on a rotation around its own axis as well as around the sun, this creates a very irregular motion that causes the waters of the oceans to slosh around.
Another criticism of the method is that it does not help us to make a choice between two opposing theories. Both the view of Ptolemy and the view of Galileo are able to provide a causal account for the evidence. Both can provide Ultimately, Galileo claims that his view is better because it is more natural. Specifically, he appeals to a notion of simplicity in justifying the truth of his own view. He thinks that it is simpler to explain the apparent motion of the heavens if me hypothesize that the earth rotates around the sun rather than other planets rotating around the earth. He also thinks that his explanations are more elegant. Another notion that he appeals to is a notion of proportionality between causes and effects. In short, little things have little causes and big things have big causes. According to this principle, it seems silly to think that the earth (which is relatively small in the cosmos) could cause the heavens (relatively large compared to the earth) to move. Proportionality, elegance and simplicity are three intuitive principles that Galileo appeals to. None of the three are themselves justified by the scientific method.
In short, Galileo thinks that the Copernican system is more credible and reasonable. Dr. Bencivenga questions why we should think that the universe is organized according to credible and reasonable principles? Indeed, Galileo himself at certain points notes that we should not think that the universe operates only in ways that we are able to understand clearly. The actual events that happen in the universe are not limited simply by what we find to be reasonable and credible.
The upshot of all of this is that there is no single method that can be used infallibly to find the truth. Mistakes will be made when searching for the truth. Trial and error are both important in the quest for knowledge. Galileo thinks that we must accept that our searches for knowledge may not always yield knowledge. We must have intellectual courage in the face of this daunting fact. Not only do we need courage but also freedom in order to perform science. Freedom is necessary in order to pursue alternative explanations and to try to explain things in new ways.
Galileo responds with an analogy. Imagine standing high on the mast of a ship. If you were to drop a stone, it would land directly below where you had dropped it--even though the ship is moving just as the earth is moving! This analogy is not yet conclusive, however. The scientific method requires that there be a causal explanation of the movement of objects. One explanation for why we feel no wind from the movement of the earth is that the atmosphere of the earth rotates with the earth. This is a causal explanation for why we feel no wind from the movement of the planet. Also, consider the movement of a stone that is dropped. At the time that the stone is dropped, it is already moving at the velocity of the earth. As it falls to the ground, it maintains this motion, which is why it falls directly below where it is dropped. Both the stone and the ground below it have the same motion, so it appears as if they stay in the same location in relation to one another.
Dr. Bencivenga notes that the scientific method does not prevent Galileo himself from making serious mistakes. He notes two important mistakes in particular. First, Galileo thinks that stars and planets move in perfectly circular motions. A contemporary thinker, Thomas Kepler, was correct to theorize that the planets move in an elliptical shape. Second, Galileo was very invested in his explanation of the tides. He thought that because the earth moves on a rotation around its own axis as well as around the sun, this creates a very irregular motion that causes the waters of the oceans to slosh around.
Another criticism of the method is that it does not help us to make a choice between two opposing theories. Both the view of Ptolemy and the view of Galileo are able to provide a causal account for the evidence. Both can provide Ultimately, Galileo claims that his view is better because it is more natural. Specifically, he appeals to a notion of simplicity in justifying the truth of his own view. He thinks that it is simpler to explain the apparent motion of the heavens if me hypothesize that the earth rotates around the sun rather than other planets rotating around the earth. He also thinks that his explanations are more elegant. Another notion that he appeals to is a notion of proportionality between causes and effects. In short, little things have little causes and big things have big causes. According to this principle, it seems silly to think that the earth (which is relatively small in the cosmos) could cause the heavens (relatively large compared to the earth) to move. Proportionality, elegance and simplicity are three intuitive principles that Galileo appeals to. None of the three are themselves justified by the scientific method.
In short, Galileo thinks that the Copernican system is more credible and reasonable. Dr. Bencivenga questions why we should think that the universe is organized according to credible and reasonable principles? Indeed, Galileo himself at certain points notes that we should not think that the universe operates only in ways that we are able to understand clearly. The actual events that happen in the universe are not limited simply by what we find to be reasonable and credible.
The upshot of all of this is that there is no single method that can be used infallibly to find the truth. Mistakes will be made when searching for the truth. Trial and error are both important in the quest for knowledge. Galileo thinks that we must accept that our searches for knowledge may not always yield knowledge. We must have intellectual courage in the face of this daunting fact. Not only do we need courage but also freedom in order to perform science. Freedom is necessary in order to pursue alternative explanations and to try to explain things in new ways.
Wednesday, April 3, 2013
Galileo's Scientific Method
The most basic feature of Galileo's method is that we must rely on data and evidence. We cannot judge without evidence and facts. We must first take notice of data before we can judge. Science should not be based on a priori principles, meaning that science should not be based on principles that we have before we actually get evidence. Science should be done in an a posteriori manner, meaning that science should be based on evidence and experience. In short, sciences should be empirical. Also, a scientist should not just cherry-pick evidence that already confirms the beliefs that she or he holds. Recalcitrant evidence, or evidence that seems to go against one's presuppositions, is the most important evidence. Scientists should not be concerned with confirming presuppositions but they should want to explore all of the evidence and let the data itself determine the progress of the sciences.
Once we have the data, scientists should provide a causal account. For example, we can explain the movement of billiard balls by explaining how forces are transferred between two entities when they come in contact with one another. The scientist aims to identify necessary and universal links that explain the relationship between causes and effects. A ball moves because it is hit by a cue or by another ball. If this is truly a discovery of cause and effect, then it must be the case that in general, all balls will move when hit by a cue or another ball. Scientific principles thus seek to provide general truths that apply to a broad class of events and occurrences. The power of such principles is that we can use them to predict the motion of, for example, billiard balls or constellations in the sky. Because sciences identify universal truths, they can predict the future.
Causal accounts should be represented in mathematical form. Effects should be calculated from causes. If we formulate causal principles in mathematical form, then we can deduce certain effects. For example, if we know that f = ma, and we know the mass and acceleration of a certain object, then we can calculate the force of that object. Not only can the sciences predict, but they do so with mathematical certainty. Galileo thought that humans can have perfect knowledge of mathematical truths. Indeed, he thought that our perfect knowledge of mathematical truths was comparable to God's knowledge of mathematical truths.
One example of this method in Galileo's work is his discussion of the surface of the moon. Aristotle, for example, thought that the moon was made of ether, or an unchanging substance. The moon was popularly thought to have a smooth, glassy surface that was unchanging. Galileo, using a telescope, saw that the moon's surface was actually rough and included many features. This was evidence that directly contradicted Aristotelian physics. Dr. Bencivenga notes that Galileo's knowledge of techniques used in perspective painting may have allowed him to correctly "read" the combinations of color and shadows on the moon as evidence of mountains and other features. To show that the moon had a rough surface, the characters in the dialogue show how the rough surface of a wall reflects light in a more uniform way than a mirror does. With a mirror, light is reflected in a very directed way. With a rough wall, light is reflected in many directions, creating a more uniform appearance of light. Rough and irregular surfaces have many different angles off of which light can be reflected. This means that no matter the angle from which one is viewing the surface, light will be equally reflected. On a smooth surface, in contrast, light is only reflected at one certain angle. Here we see how Galileo 1) used empirical evidence to 2) challenge presuppositions and then 3) theorized about how the evidence can be explained.
Another point that Galileo made about the moon is that the light that comes from the moon is actually a reflection off of the earth.
Once we have the data, scientists should provide a causal account. For example, we can explain the movement of billiard balls by explaining how forces are transferred between two entities when they come in contact with one another. The scientist aims to identify necessary and universal links that explain the relationship between causes and effects. A ball moves because it is hit by a cue or by another ball. If this is truly a discovery of cause and effect, then it must be the case that in general, all balls will move when hit by a cue or another ball. Scientific principles thus seek to provide general truths that apply to a broad class of events and occurrences. The power of such principles is that we can use them to predict the motion of, for example, billiard balls or constellations in the sky. Because sciences identify universal truths, they can predict the future.
Causal accounts should be represented in mathematical form. Effects should be calculated from causes. If we formulate causal principles in mathematical form, then we can deduce certain effects. For example, if we know that f = ma, and we know the mass and acceleration of a certain object, then we can calculate the force of that object. Not only can the sciences predict, but they do so with mathematical certainty. Galileo thought that humans can have perfect knowledge of mathematical truths. Indeed, he thought that our perfect knowledge of mathematical truths was comparable to God's knowledge of mathematical truths.
One example of this method in Galileo's work is his discussion of the surface of the moon. Aristotle, for example, thought that the moon was made of ether, or an unchanging substance. The moon was popularly thought to have a smooth, glassy surface that was unchanging. Galileo, using a telescope, saw that the moon's surface was actually rough and included many features. This was evidence that directly contradicted Aristotelian physics. Dr. Bencivenga notes that Galileo's knowledge of techniques used in perspective painting may have allowed him to correctly "read" the combinations of color and shadows on the moon as evidence of mountains and other features. To show that the moon had a rough surface, the characters in the dialogue show how the rough surface of a wall reflects light in a more uniform way than a mirror does. With a mirror, light is reflected in a very directed way. With a rough wall, light is reflected in many directions, creating a more uniform appearance of light. Rough and irregular surfaces have many different angles off of which light can be reflected. This means that no matter the angle from which one is viewing the surface, light will be equally reflected. On a smooth surface, in contrast, light is only reflected at one certain angle. Here we see how Galileo 1) used empirical evidence to 2) challenge presuppositions and then 3) theorized about how the evidence can be explained.
Another point that Galileo made about the moon is that the light that comes from the moon is actually a reflection off of the earth.
Monday, April 1, 2013
Intro to Humanity & Nature
Science is the method through which we encounter the third "other" with which we can compare and contrast humanity: nature. Dr. Bencivenga is providing an introduction into the modern conception of science. This interpretation will be coming from the sciences itself. Specifically, we will be looking at Galileo and Heisenberg.
Galileo is regarded as the founder of modern science, including the scientific method. Dr. Bencivenga will introduce this method and critique it, as well. We will also be looking at a dialogue between two important theories about the universe. These two views are coming from Ptolemy and Copernicus.
When encountering nature, some of the most basic phenomena that we observe are the sun, moon, stars and planets. Each night and each year, we see shifting patterns in these phenomena. The sun moves in the same direction all the time, but sometimes it appears as if the stars move in an opposite direction. The earth, however, seems to remain still. Based on this most basic data, then, it was commonly thought that the earth was the center of the universe.
Three Ancient Views: Aristotle thought that the entire universe was spherical. Indeed, he thought that it was a series of concentric spheres. The innermost sphere was made of the four basic elements: earth, water, wind, and fire. This allows for things to live, die and change. Beyond the moon, everything is made of ether, an unchanging substance. Ptolemy explained the motions of heavenly bodies by appealing to eccentrics and epicycles. Eccentricity means that the earth is not exactly at the center of the universe. An epicycle is a circle that is centered on the perimeter of another circle. He hypothesized that planets and stars did not merely travel in a circular pattern, but that they traveled in a circle around the perimeter of another circle. Copernicus, in contrast to these other two views, thought that the sun (rather than the earth) is the center of the universe.
The Players: Gallileo's dialogue includes three figures, but the author himself never directly speaks. Simplicio is named after a commentator of Aristotle and he represents the Aristotelian/Ptolemic view. Salviati is the spokesman for Gallileo and Copernicus. Sagredo is a neutral and intelligent observer, but we also see that he ends up sympathizing with Salviati and he straightens the Copernican view. The dialogue takes place over four days. The first day is about Aristotelian physics. The second is about the daily rotation of the earth around the sun. The third is about the yearly rotation around the sun and the fourth is about the tides.
Practical Rhetoric: Dr. Bencivenga notes that the dialogue is meant to be somewhat leisurely and playful, so as to allow for transgressions. He also reminds us of the danger of addressing such issues at the time. It was considered heresy to claim that the earth revolved around the sun. Indeed, one could be executed for such crimes. Galileo himself was tried in 1616 and was forced to recant his views. The dialogue is thus an attempt to distance himself from his own claims. He distances himself from the views he represents in order to try to avoid persecution. His attempt was unsuccessful, however. It took two years for The Church to grant permission to publish the book, which was then revoked. Galileo was then tried and shown the instruments of torture, after which he recanted his views again and was then sentenced as a heretic.
Galileo is regarded as the founder of modern science, including the scientific method. Dr. Bencivenga will introduce this method and critique it, as well. We will also be looking at a dialogue between two important theories about the universe. These two views are coming from Ptolemy and Copernicus.
When encountering nature, some of the most basic phenomena that we observe are the sun, moon, stars and planets. Each night and each year, we see shifting patterns in these phenomena. The sun moves in the same direction all the time, but sometimes it appears as if the stars move in an opposite direction. The earth, however, seems to remain still. Based on this most basic data, then, it was commonly thought that the earth was the center of the universe.
Three Ancient Views: Aristotle thought that the entire universe was spherical. Indeed, he thought that it was a series of concentric spheres. The innermost sphere was made of the four basic elements: earth, water, wind, and fire. This allows for things to live, die and change. Beyond the moon, everything is made of ether, an unchanging substance. Ptolemy explained the motions of heavenly bodies by appealing to eccentrics and epicycles. Eccentricity means that the earth is not exactly at the center of the universe. An epicycle is a circle that is centered on the perimeter of another circle. He hypothesized that planets and stars did not merely travel in a circular pattern, but that they traveled in a circle around the perimeter of another circle. Copernicus, in contrast to these other two views, thought that the sun (rather than the earth) is the center of the universe.
The Players: Gallileo's dialogue includes three figures, but the author himself never directly speaks. Simplicio is named after a commentator of Aristotle and he represents the Aristotelian/Ptolemic view. Salviati is the spokesman for Gallileo and Copernicus. Sagredo is a neutral and intelligent observer, but we also see that he ends up sympathizing with Salviati and he straightens the Copernican view. The dialogue takes place over four days. The first day is about Aristotelian physics. The second is about the daily rotation of the earth around the sun. The third is about the yearly rotation around the sun and the fourth is about the tides.
Practical Rhetoric: Dr. Bencivenga notes that the dialogue is meant to be somewhat leisurely and playful, so as to allow for transgressions. He also reminds us of the danger of addressing such issues at the time. It was considered heresy to claim that the earth revolved around the sun. Indeed, one could be executed for such crimes. Galileo himself was tried in 1616 and was forced to recant his views. The dialogue is thus an attempt to distance himself from his own claims. He distances himself from the views he represents in order to try to avoid persecution. His attempt was unsuccessful, however. It took two years for The Church to grant permission to publish the book, which was then revoked. Galileo was then tried and shown the instruments of torture, after which he recanted his views again and was then sentenced as a heretic.
Vocab List for Galileo
Data, in its most basic sense, is what is given. Data is the sensory information provided to us by phenomena.
Phenomena are just what we experience. A phenomenon is an appearance, or the way a thing appears to us.
Retrograde motion is what happens when the stars appear to move in a direction opposite of the trajectoryin which the sun appears to move.
Concentric means sharing the same center. Concentric circles are circles that have the same center point. Larger and smaller circles can be organized around the same point.
Quintessence or ether, is a theoretical construct of an absolutely unchanging substance.
The deferent circle is the circle that is centered on a single point.
Eccentricity means that the earth is not exactly at the center of the universe.
An epicycle is a circle that is centered on the perimeter of another circle.
A priori means before evidence or before experience. An a priori principle does not depend on experience in order to show its truth.
A posteriori means after experience. An a posteriori principle is based upon evidence and experience in the world.
Extensive knowledge is having knowledge about a broad range of things. In comparison to God, Galileo thinks that we know a finite number of things compared to God knowing an infinite number of things.
Intensive knowledge is having in depth knowledge about one thing. In comparison to God, we can know some things, such as mathematical principles and proofs, perfectly.
Diurnal means daily. To talk about the diurnal movement of the earth means to talk about the daily movement of the earth, or the movement of the earth in a 24 hour period.
Dogma is a set of doctrines taken as an authority. Einstein praised Galileo for going against scientific dogma.
Phenomena are just what we experience. A phenomenon is an appearance, or the way a thing appears to us.
Retrograde motion is what happens when the stars appear to move in a direction opposite of the trajectoryin which the sun appears to move.
Concentric means sharing the same center. Concentric circles are circles that have the same center point. Larger and smaller circles can be organized around the same point.
Quintessence or ether, is a theoretical construct of an absolutely unchanging substance.
The deferent circle is the circle that is centered on a single point.
Eccentricity means that the earth is not exactly at the center of the universe.
An epicycle is a circle that is centered on the perimeter of another circle.
A priori means before evidence or before experience. An a priori principle does not depend on experience in order to show its truth.
A posteriori means after experience. An a posteriori principle is based upon evidence and experience in the world.
Extensive knowledge is having knowledge about a broad range of things. In comparison to God, Galileo thinks that we know a finite number of things compared to God knowing an infinite number of things.
Intensive knowledge is having in depth knowledge about one thing. In comparison to God, we can know some things, such as mathematical principles and proofs, perfectly.
Diurnal means daily. To talk about the diurnal movement of the earth means to talk about the daily movement of the earth, or the movement of the earth in a 24 hour period.
Dogma is a set of doctrines taken as an authority. Einstein praised Galileo for going against scientific dogma.
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