The Ortega Hypothesis

To wrap things up, I felt that it would be interesting to take a look at The Ortega Hypothesis written by Jonathan R. Cole and Stephen Cole in Science 178. What even is the hypothesis? It is simple: For it is necessary to insist upon this extraordinary but undeniable fact: experimental science has progressed thanks in great part to the work of men astoundingly mediocre, and even less than mediocre. That is to say, modem science, the root and symbol of our actual civilization, finds a place for the intellectually commonplace man and allows him to work therein with success. In this way the majority of scientists help the general advance of science while shut up in the narrow cell of their laboratory, like the bee in the cell of its hive, or the turnspit of its wheel.

Mediocre? Less than mediocre? Harsh words, no doubt, but perhaps it is reassuring to see the importance of the work of these many scientists that don't have their praises sang in articles, on TV, or over the internet.

Except that isn't actually the case, or at least, that wasn't the case back in 1972 when Cole and Cole did this research. Their findings found that most of the discoveries and papers that were cited came from a disproportionate number of "elite" scientists at prestigious institutions. But were those scientists dependent on the mass as Ortega implies? Reading through it, it seems hard for me to accurately say. Cole and Cole seem to not have a definitive stance for sure.

Why does this all matter to students entering physics now though? In all honesty, things may have changed where it doesn't. We would have to look at new research and see what the results are.

The takeaway for this though I think is that you go become a scientist because you have the passion and calling for it. If you have that, does any other consideration matter?

Jonathan Cole and Stephen Cole, "The Ortega Hypothesis," Science, Vol. 178, pages 368-375 (1972)

Reflections on the ideological meanings of modern science from Boyle and Newton to the postmodernists

Jacob's work in exploring the Ideological Meanings of Western Science looks into the interpretations by Latour concerning Hobbes and Boyle and then sketches the outlines of a different interpretation with historical and ideological implications beginning with Boyle, encompassing Newton and the Newtonians, and pointing toward the Enlightenment and modernity.

Reading through this work, there is a lot that I am unable to put a good lens out, and I concede that I do not believe that this would have much use for a new physics student. It is interesting in how it examines motivations and ideologies of the scientists and the times. The world could potentially be a very different place had these ideologies changed to be different from what they are. Changing the interpretation of the time also changes the motivations of the scientists as well, and it brings into question whether or not there was something more that they sought from the work.

Jacob claims that Latour choose to simply ignore key forces that were acting on Hobbes. From this choice springs a cascade effect that alters the interpretation and motivation of Hobbes.

This work shows just how important it is to get the frame of reference correct when looking at historical documents for any reason. By changing that frame, it changes the tones of the work that was done. No longer are things done for the betterment of all, but rather there is some underlying motivation that is not apparent in the other frame.

Thinking about all of this makes me have a headache to be honest. This is most definitely not my milieu, but it is a very well put together argument by Jacob.

Margaret Jacob, "Reflections on the ideological meanings of modern science from Boyle and Newton to the postmodernists," History of Science, Vol. 33, pages 333-357 (1995) 

John Michell and Henry Cavendish: weighing the stars

McCormmach looks into the personal friendship of Michell and Cavendish, their scientific collaboration, and their common Newtonian philosophy.

Michell wanted to weight the stars by the gravitational retardation of their light. He was under the notion that light was something that was also acted on upon gravity, and that this would be measurable. If this were indeed the case, it would be possible to determine how much a star massed based on the amount that the light emitted by it was retarded.

It is interesting to note that they believed that light was affected by gravity. Thanks in part to this work, we know that light is not directly altered by gravity. Thanks to General Relativity, we know that space-time itself is warped by any gravitational field, and the light travels along these fluctuations as if it was still traveling in a straight line.

Going back to the paper at hand, Michell and Cavendish attempted to extend Newton's achievement by following the philosophical path that led to it. They took the force of gravity which was known and sought to deduce new phenomena from it. They looked to new stellar, terrestrial, and optical effects of gravitation.

Michell's early work dealt with the distances to the stars and their real positions in space. This led him to see the correlation between stars and their proximity to one another possibly being due to their mutual gravitation.

Here I see usage similar to applying p-prims when it comes to gravitation. Michell is clearly intrigued by gravity and feels that it can be used to help determine the mass of stellar objects. This is because he knows that gravity affects everything, and particles of light are no different. He had calculated the force with which light must be sent forth, and so he felt he had a great basis to go off of. Cavendish encouraged Michell's work.

Even though Michell was unsuccessful (there was no chance of success, but he did not know that), his methods were sound. It was also from the torsion balance made by Michell that Cavendish was able to determine G.

Michell never got to do the experiment himself, the reality that awaits us all at the end of life finally claiming him, but his work allowed Cavendish to complete it.

There is another great thing to tell to students here in how the work that is started today and passed on can lead to the discoveries of tomorrow; standing on the shoulders of giants as Newton put it.

Russell McCormmach, "John Michell and Henry Cavendish: weighing the stars," British Journal for the History of Science, Vol. 4, pages 126-155 (1968)

A free-fall determination of the Newtonian constant of gravity

In the same issue of Science as the previous article that was discussed is a method that was touched on concern determining G through use of free-fall.

Schwarz, et al took an apparatus that allowed them to measure the trajectory of a test mass in free-fall using laser interferometry. With the introduction of a one-half metric ton source mass, they perturbed this trajectory to allow for the calculation of G.

This is very much a purely scientific article of the modern era, and it is apparent reading it. The importance in reading something like this for a student studying physics is to familiarize them with the methods and style of writing about an experiment that has been conducted.

There is no direct tie to DiSessa that I have been able to find, but for this paper, I did not really expect to find one. If there is one, it would be an example of how advanced understanding can become and almost obscure the existence of the p-prim that could be utilized by a new student.

I do not have much more to say about this article to be honest. 

Joshua P. Schwarz, Douglas S. Robertson, Timothy M. Niebauer, and James G. Faller, "A free-fall determination of the Newtonian constant of gravity," Science, Vol. 282, pages 2230-2234 (1998)

Gravity Measurements Close in on Big G

Continuing on with the discussion of G, Kestenbaum wrote an article in Science that is of direct importance.

It has all really come down to the precision of the tools that are being used to measure the value for G. The value being calculated is so small that any tool has to have precision or reliability in such a way that it is almost a competition of sorts. Where there was original just the method of Cavendish to calculate the value for G, scientists have come up with numerous other methods that can always be used.

This is important to point out to students. One of the beautiful truths about physics in my mind is that there is more than one way to come about a conclusion. If a full understanding exists of what you are researching as far as your methodology is concerned, you can develop multiple experiments that differ in execution but prove the same point.

In the article, the talk about the different methods that they have been using. One group is using the Cavendish method, but they replaced one of the components to allow for more massive objects. Another group has forgone using the torsion balance and is instead dropping an object and using precision timers to detect small fluctuations. Yet another is using massive vats of mercury to influence weights sitting on scales.

All of these different methods will still allow calculation of G. The real beauty is in the agreement that they were having. The error bars are quite large on some of them, but that is also relative to the size of the axis in question. All told, the values were close. 

David Kerstenbaum, "Gravity Measurements Close in on Big G," Science, Vol. 282, pages 2080-2081 (1998)

Resource Letter MNG-1: Measurements of Newtonian Gravitation

Two-hundred and twenty three. That is the number of articles and papers that Gillies collects for listing in his resource letter. All of these papers deal with Newtonian gravitation in some way, shape, or form. There exists, today, even more articles and papers that examine it further. What is the meaning of the startling weakness of the gravitational constant, G? How does that interact with the other fundamental laws?

These questions are all questions that are constantly being asked by scientists the world over. The reason why I wanted to point out this article that is a collection of work is because it shows just how much a single constant in physics can attract attention.

In more recent times, we are all aware of the search for the Higgs. What does the Higgs mean? What can we do with it? There is still a ton of work to be done, but that is something from recent times. The concept of universal gravitation and its corresponding constant date back to the time of Newton!

Getting an accurate and precise measurement for G is extremely difficult. A simple way, at least in setup, would be what Cavendish did to measure the force of gravity between masses, but even then, to get any real accuracy or precision might have your hair going grey if my experience with it is any indication.

What does this all mean for students? For one thing, I think it can be reassuring to them. It shows that there is a lot more to yet learn in physics about stuff that we have known for a considerable amount of time. There are always new theories being proposed and new experiments being designed. That can get them to have some wide-eyed wonder perhaps.

I think it also shows that building upon the p-prim idea allows for this advancement. You can go from the concept of objects attracting each other to describing how and why they do so. Then you can break down to the specifics in the equations used to model the motion of the system. You can explore each constant and variable that you use.

We know a lot and have a lot of ideas about what we aren't sure about yet. Gillies shows us 223 papers worth of information on a single constant. Just imagine how many more will exist in not even three years' time.

G. T. Gillies, "Resource Letter MNG-1: Measurements of Newtonian Gravitation," American Journal of Physics, Vol. 58, pages 525-534 (1990)

Newton's determination of the masses and densities of the Sun, Jupiter, Saturn, and the Earth

Cohen does a wonderful treatment of how Newton went about determining the masses and densities of the planets and our Sun. It is also interesting to me that Newton's quantitative work was plagued with numerical issues, but his qualitative work or symbolical work was spot on. His methods were correct.

The takeaway I feel is that being taught and being able to reproduce the proper method is extremely important. By being able to do that, you are able to refine your result closer and closer to the truth as you gain more understanding. This can be seen between the different releases of Newton where the errors become less and less and the work simpler as a result. Cohen goes into detail for these to show Newton's process of refinement.

For students and teachers, it is very important to get the method correct. A good foundation is required to be able to move forward in understanding of the more advanced topics. With a sufficient methodology, it is possible to move forward and continue to make refinements as you go.

To tie this back to what DiSessa has said on p-prims and their applications, this would probably be akin to choosing the proper p-prim that is being invoked. To simplify it further, it would be like making sure that you are starting at the actual beginning or at least the same area.

Perhaps it would also be reassuring to students to point out that even a great mind like Newton's had to do multiple refinements .

I. Bernard Cohen, "Newton's determination of the masses and densities of the Sun, Jupiter, Saturn, and the Earth," Archive for History of Exact Sciences, Vol. 53, pages 83-95 (1998)

The third law in Newton's mechanics

More focused on the Principia, Home looks further into Newton's justification of the Third Law. Important to note is what Newton meant when he used the words "action" and "reaction." By pulling from Opticks, one would find that Newton is using them in just about the most general terms that there are. An "action" and "reaction" are not limited to accelerative forces, but they can be extended to include any situation in which one thing influences another through some mean.

This raises the interesting notion that we need to be aware as a teacher or lecturer what our students means when they make a statement. If Newton describes something in a certain way and allows for a broader definition than we do, we will miss meaning. The same thing will happen in the classroom.

Home finds that this extension expands Newton's definition of the Third Law to account for numerous different scenarios, and Newton also accounted for non-static cases with an early form of a method later attributed to d'Alembert.

Core to the understanding of the Third Law for Newton was the Laws of Impact, and these are important to use today as well concerning the Third Law. Conservation of Momentum is integral to understanding how happens in a collision, Home holds that the Third Law is not itself an obvious consequence of the principle of conservation of momentum.

I feel that this can in a way be tied back to the concept of p-prims. The benefit of the p-prim concept is that they are as far down as you can reduce a particular concept. That gives a good foundation for moving forward and advancing understanding so that hopefully,  there will be no misunderstandings over language used to describe situations.

R. W. Home, "The third law in Newton's mechanics," British Journal for the History of Science, Vol. 4, pages 39-51 (1968)

Newton's justification of the laws of motion

Newton was very particular when he constructed his laws. Perl points this out and examines it as well to show how Newton justified his laws. Perl makes what I consider to be a good point in how it is of interest to consider Newton's arguments as well as his concepts. In my opinion, it is only through considering both of them together that you get the full impact of what Newton wrote down.

Take for instance the First law. Perl points out that this is a limiting case of the Second Law. It is also put forward that it is possible that the truth of the First Law is taken as evidence for the Third Law in the case of attractions.

Perhaps most important to take note of in this is the meticulousness with which Newton went about defining and working through his work. It is because of this we have the foundation to move forward.

While the information that Perl goes over is interesting to me, I have to admit defeat in finding useful tidbits to give to students and utilize in the classroom or lecture hall as I have been able to do for previous works that I have gone over. That is not to say that it does not exist, but I am unable to glean significance with my current understanding of how classrooms operate and what may or may not be beneficial to teachers and students alike.

M. R. Perl, "Newton's justification of the laws of motion," Journal of the History of Ideas, Vol. 27, pages 585-592 (1966)

By their properties, causes and effects: Newton's scholium on time, space, place and motion

The scholium that follows the eight opening definitions of the Principia concerns Newton's views on absolute time, space, place, and motion and contains discussion of the bucket with water that is being spun around and two spheres connected to each other that are spinning about their center of mass. Rynasiewicz brings attention to the points of contention that exist due to translation.

The Principia never had an English translation during Newton's lifetime. It was until after he had passed on that it was translated, and it has been refined since. One thing of note, similar to what was made in a previous post, is that the meanings of words in old languages, especially Latin, change or morph as time goes on. Being certain of a translation is important in understanding what is trying to be argued or posited.

In this case, it is the adjacency of "determine" and "define." When the sentences in question read with the word "determine," we see that to mean that we are unable to achieve a result, but rather, if we replace the word with "define," it takes on a new meaning. An undefined system or property is similar to that of an undetermined one in that we aren't getting a result on the surface, but if you are to dive down into it, you will see that an undefined result is a result itself. For Newton's work in the scholium, he is saying that absolute time, space, place, and motion cannot be defined by their relation to their relative counterparts. If we are to borrow mathematical understanding here, we can say that something so defined would not be unique, and a uniquely defined situation is what we require for the absolute cases.

Newton goes on to discuss the importance of the difference between relative and absolute, but I feel that for the purposes of this, they are not important in fine detail. The broader concept is more of what we are interested in, and Rynasiewicz does a wonderful job of allowing for an understanding of both the fine and coarse in the article.

This paper is further reinforcement for the clarity of language when delivering information to students. As a lecturer, it is our duty to being clear and concise so as to avoid as many misunderstandings as we can. We cannot claim to be able to avoid them all, as I feel this paper shows with how people have viewed the scholium over the years, but we can certainly do our best.

Robert Rynasiewicz, "By their properties, causes and effects: Newton;s scholium on time, space, place and motion," Studies in History and Philosophy of Science, Vol. 26, pages 133-153, 295-321 (1995)

Uniform acceleration, space, and time

The concept of uniform acceleration, space, and time is an intriguing one if you look at how readily we accept it in modern times. The same can be said for a lot of our concepts and theories of course, but Drake explores whether or not Galileo had this understanding.

A central point to the argument that had to be cleared up was the translation of the original notes. These are notes that were not a part of any of Galileo's other work, so they do not have that context to help them. What is important to also understand is that translations from old languages can change over time. Whether or not that is a good thing is another discussion, but Drake holds that mistakes are made in more recent translations when compared to older ones and guessing as to what Galileo was implying.

Galileo also makes his argument for uniform acceleration without the usage of any diagram. It is strictly what could be considered a verbal argument. This makes the translations even more important as there are no diagrams to compare to as drawn by Galileo. If the translations have errors, the conclusions that are drawn have errors. It is something that propagates through.

Why is this important? I think it highlights the understanding that is required in exploring theories and concepts. A student has to be sure of what they are being taught if they are going to be able to be confident in using that knowledge they are gaining. As luck would have it, we have a country that speaks English and holds classes in English. All citizens learn English as that is the language of the country. The same could be said for China if you replace English with Chinese, or for Japan, France, Germany, etc.

We are not having to teach students material from a language that is not their own (internationals are a special case), but there is still a concern about the clarity of the language that is used. Drake brings attention to the differences in the plural and singular form for double in the original text. If you read it as "double," it has one meaning. If you read it as "doubles," it has another meaning. Again, this is translation causing issues, but as said above, it highlights proper word choice being significantly important.

If a lecturer is talking about force, they have to be mindful of when they say force or forces. It is known that an object can have many forces acting on it, but it will only have one resultant force. This clarity is required to be able to progress in the solution of the equations of motion for the system.

Stillman Drake, "Uniform acceleration, space, and time," British Journal for the History of Science, Vol. 5, pages 21-43 (1970)

Catholic astronomers and the Copernican system after the condemnation of Galileo

Russell examines the impact on Catholic astronomers and the Copernican system after Galileo was condemned by the Church. In short, they did not notice it much beyond the borders of the Papal states as the power of the inquisitors was next to nothing in other sovereign lands despite the supposed ability to practice their own law in the nations that were followers of the Church.

It is intriguing that nothing happened to the Copernican system until Galileo came about. Kepler had already published his works, and the Church paid him little mind. It is posited that this could be because Kepler was keen to harmony and peace. He did not want to antagonize those that did not agree with him. The same apparently cannot be said for Galileo. He wanted to bring things to a head; him and his opponents both.

So what did this do? It caused the Holy Office to become involved and make a judgment. They condemned the immobility of the sun more so than the mobility of the earth. A distinction that it is unknown why they made it, but made it they did. They also privately admonished Galileo and told him to abandon his opinion and not teach it.

From there, the Congregation of the Index was informed, and they released a general condemnation of the Copernican system that amounted to saying it was false and contrary to scripture. Only three books were specifically mentioned in a prohibition of Copernican works.

It is well taught that Galileo did end up facing a trial. This trial did not happen until 1633, fourteen years after the last official action took place in 1619. It was at this trial that the Copernican system was ultimately openly labeled as heretical in nature.

Where the decree did not have much of an impact to the following of the Copernican system, the condemnation of Galileo certainly did. It stayed the hand of a number of astronomers when it came to publishing their work. They did end up eventually publishing, but it took time for it to happen.

The takeaway I think is that the suppression of knowledge is dangerous. Not only is it ultimately not going to work, people will find a way to publish, it is going to put a certain air to the information that is being published. This is something that is apparent in today's society. People see to view things that are considered taboo or off limits to be of a high inherent interest.

For students, I think it is important to reinforce the concept that ideas are meant to be shared freely and without fear of being condemned by an institutional or governmental body. This does not mean that your peers cannot shout you down, they can and some of them undoubtedly will, but it is not the job of higher powers that be to silence its citizens.

John L. Russell, "Catholic astronomers and the Copernican system after the condemnation of Galileo," Annals of Science, Vol. 46, pages 365-386 (1989)

Impetus mechanics as a physical argument for Copernicanism: Copernicus, Benedetti, Galileo

Copernicanism is interesting to me in how it came about and what was used to argue its validity. It required a physical theory that Copernicus was unaware of, but his system demanded its existence. It is from this requirement that it is possible to move from the realm of impetus mechanics to inertial mechanics.

This to me shows the morphing and growing of an idea and understanding of the world as more is learned and understood. More questions get asked and answered which refines what came before it. Luckily, it also leads us to yet more questions that we deem worth asking.

Wolff pieces together how Copernicus, Benedetti, and Galileo used impetus mechanics to explain what they saw and how this becomes inertial mechanics because it has no other choice if it is to work. The Earth itself has to be able to rotate about its own axis for the Copernican system to work, and the argument was put forth that it does so because it is spherical. That is what spheres are able to do. The universe is made out of spheres, so the Earth is able to rotate.

Building from that is the concept of forced and natural motions. Forced motions are motions that require an external force to act upon a body. Natural motions are simple motions and suit the "nature" of simple bodies. Spheres are considered to be simple bodies, and their simplicity is realized by their form and their motion.

I will be honest in saying that wrapping my head around the mental gymnastics that are being used to justify all of this is giving me a slight headache as it all seems a bit much, but then again, our understanding has advanced from what Copernicus had to work with when he made his statements.

For students, it is very important to show how theories and ideas evolve over time. They can be morphed or outright discarded. Parts of a discarded theory can come find new meaning after a new discovery. It could be said that the world of science is ever evolving, but perhaps it would be better to say that we're just becoming better at describing what it is that we have seen all along.

Michael Wolff, "Impetus mechanics as a physical argument for Copernicanism: Copernicus, Benedetti, Galileo," Science in Context, Vol. 1, pages 215-256 (1987)

Galileo on the telescope and the eye

Brown takes a look at Galileo and his use of the telescope to make his observations. It is very important that we have an understanding about the tools and methods that we employ to study the different phenomena that interest us. Other scientists of Galileo's times felt that the usage of the telescope introduced illusions that did not exist in naked eye observation. These observations were largely because manufacturing methods were not sufficiently advanced to the task of producing reliable lenses or mountings for them.

Galileo was particularly sensitive to all of these considerations, and he worked at getting reliable observations from his tools after learning their peculiarities. The importance of this is that similar considerations exist today if not in as advanced of a state.

Proper knowledge to use a research tool to characterize a material, observe a phenomenon, or calculate a value is extremely important in any advanced science education. There are long training sessions for the advanced equipment used in a research school. There are safety briefings on what can and cannot harm a tool or a user. All of these considerations exist to use the tool most effectively to get reliable results.

The benefit that we have today is that there exists a strong manufacturing method for creating precision scientific equipment. While Galileo was unable to benefit from such a thing existing, he did show that one could work with subpar tools to great success.

I think it is also important to note that Galileo took into considerations the phenomena that our eyes observe in general when observing light. He saw how light interacted to change what we perceived whether it be a diffuse image due to something being far away or out of focus to the affect that the atmosphere plays on observations to something as simple as the tear content or squinting of the eye.

The takeaway for students I think should be to understand your equipment. We ask questions on error in measurements in the measurements lab that students take, but we do not revisit it all that much beyond that until you make it to the advanced lab course in my experience.

Harold I. Brown, "Galileo on the telescope and the eye," Journal of the History of Ideas, Vol. 46, pages 487-501 (1985) 

Kepler's ‘Distance Law’ - Myth not Reality

Davis carried out a reworking of chapter 32 of Kepler's Astronomia Nova in order to explore the so called "distance law." Davis finds there is no foundation for such a law there or subsequently. Instead, Davis shows that Kepler's innovative approached allowed for a consideration of the component of the velocity which is precisely perpendicular to the Sun-planet line which is the exact equivalent of the area law according to modern standards. Davis holds that no other interpretation would have been compatible with Kepler's Aristotelian principles.

What I find interesting in the work for this chapter of Kepler is the treatment of time and how it differs from that of Newton. For Newtonian time, it is easy to arrange it to vary uniformly, but Keplerian form has it straightforward to be represented geometrically. I see this as being a very key feature for making Kepler's laws appear. What is really nice is that it is possible to transition between both styles.

It is from this treatment of the times and ellipses that it is possible to derive the area law, and it is what Davis does. It flows cleanly in a way that any student that is versed in calculus II would be able to follow.

For students and to help them with this, I think it is important to focus on where Davis talks about the exactitude and usage of approximations. Choosing when to be exact and when to be approximate is very important for a physicist trying to model the world. To me, this screams of a time when intuition needs to be properly trained so that it is properly employed; an understanding of something along the lines of when it is viable to use the small angle approximation or to keep it exact. Based on the problem at hand, choosing one will simplify it while the other will bog down any calculations and deny an analytical solution.

Further touching on Davis's astonishment that the existence of a so called "distance law," it is interesting that such persisted. This reinforces my feeling that understanding exactly what an article or textbook says is very important for the budding physicist because gaining a false notion can be detrimental to the development of their tailored intuition.

Davis*, A. E. L. (1992), Kepler's ‘Distance Law’ - Myth not Reality. Centaurus, 35: 103–120. doi:10.1111/j.1600-0498.1992.tb00872.x

Johannes Kepler in the light of recent research

Aiton takes a look at Johannes Kepler in light of recent research that became available back around 1976. It seems that Aiton holds key to understanding Kepler is that Kepler should be considered as a single individual that rationally lived and developed thoughts of both the physical and metaphysical world rather than embracing the physical work that he did and casting off the metaphysical as flights of fancy.

I am in agreement with this treatment of Kepler as we must consider a person as a whole to begin to truly understand whatever motivations that might have in moving forward in work. There are many examples of men and women driven to science to affirm their Faith and bring glory to God through their remarkable research that have added to the panoply of knowledge that we now have today. Were it not for their conviction, it is possible such works would not have been completed.

For Kepler, he wanted to bring rationality to astrology. He wanted to make it more scientific and what I consider to be "hard." He didn't believe that the signs and portents directly affected us, rather, he felt that they resonated with our soul to influence us. This thought process also allowed him to develop a method of meteorological forecasting.

Kepler felt that God was praised by his work in astronomy. It was an extension of his Faith and Theology to do great works to advance the realm of astronomy. All told, Kepler sought harmony, and this seems to be a very strong desire for him that borders on the divine.

Rather than continue to make a point-by-point recounting of the article as I have almost done to this point, I am going to move on from here to think about how this can be used in a classroom.

Understanding the motivation of a student when they think about a problem is extremely important in my eyes. The reason why they choose to invoke certain laws or rules can give glimpses into their thought process so that we can better educate them and train them to think similar to that of a physicist. We see in this article that taking Kepler as a whole person, all of his aspects in his thoughts, help to illuminate even more his motivating factors. He is far from a student in the sense of what we are discussing, but I would say that he saw himself as a true student of God and wanted to unravel the mysteries that he saw to bring glory to Him.

To reiterate, knowing the motivations of the student will allow the instructor to better tailor their lectures to resonate and advance understanding.

E. J. Aiton, "Johannes Kepler in the light of recent research," History of Science, Vol. 14, pages 77-100 (1976)

Science and Selection: Essays on Biological Evolution and the Philosophy of Science

The discussion on the examination of Hull to study the study of science scientifically is sadly not going to take place because the copy that I had became corrupted and does not have the entire article. I am also unable to reacquire it due to unforeseen circumstances.

David L. Hull, "Science and Selection: Essays on Biological Evolution and the Philosophy of Science," pages 222-238, Cambridge: Cambridge University Press. (2001)

Magnetism and the anti-Copernican polemic

Baldwin explores the arguments of the anti-Copernicans that sought to bolster their astronomical claims by appealing to the science of magnetism that was also being used by the heliocentrists.

Kepler and Galileo both applied magnetism to their astronomical physics as being agents that explained aspects of planetary motions. The elliptical orbits of the planets that had been observed were said to be because of the magnetic force. The constancy of the polar tilt of the Earth was due to the magnetic force. These were things that could be seen using a spherical lodestone as Gilbert did in his original work, and I can understand why that would hold so much weight because we as people like being able to see something to tell whether or not it is true. The use of an analogous system is powerful in that way for teaching physics.

Cabeo was a Jesuit that took issue with the Copernican notion of a heliocentric system, and he wrote a full treatise on magnetism. He conceded that the whole Earth participated in magnetic virtue, but he did not hold that the Earth was a big magnet itself. He felt this way because of how weak the magnetic field was measured to be, and that if the Earth were such a large magnet, the minor (by comparison) lodestones that were used to study magnetism would have negligible effect on compass needles. Cabeo felt that the role of the magnetic force of the whole Earth was that of an  emergency force used to correct the rotation and position of the heavens should they become dislodged.

Continuing to read through the works that Baldwin has collected, it is apparent how the choices of the Church played heavily into the usage of the magnetic force in astronomy. In the end, the subject was dropped altogether as having impact on astronomy, but it seems to have essentially fizzled out as scientists went on to study other phenomena that were unfettered by ecclesiastical debates.

Tying this in with DiSessa, I can see a pitfall that students would fall into that is illustrated by the Copernicans and anti-Copernicans. The magnetic force was a hot topic item when Gilbert penned his work on it. The usage of it in the astronomies to describe the different motions is fair evidence to that fact. We know now today that things are the way they are due to gravitational attraction and the physics governing bodies in such a system as our Solar system, but they were unaware of that. Students, upon learning a new concept to build upon and advance the p-prims that they have, will possibly be anxious to make use of that knowledge in new ways that they find. I feel that it is important to make sure that they understand the when for making use of this new knowledge just as much as the how. 

Martha Baldwin, "Magnetism and the anti-Copernican polemic," Journal for the History of Astronomy, Vol. 16, pages 155-174 (1985)

Saving the Phenomena

In Saving the Phenomena: The Background to Ptolemy's Planetary Theory, Goldstein explores the usage of the term "phenomena." He claims that it is important to understand what was being referred to at the time of Ptolemy when he penned the Almagest.

Ptolemy did an unprecedented act when he took data that had been collected earlier by people making observations of the heavens above. The meticulous data that was taken allowed Ptolemy to create a planetary model that was derived explicitly by geometric techniques - the first of its kind. The observations used covered more than 800 years including observations made by the Babylonians.

Goldstein points out that Ptolemy reduces his models to tables. The means the tables are constructed are explicitly given, and they show a heavy appeal to geometry, not arithmetic schema. Luckily, through Ptolemy's desire to be explicit in all that he did for his work, the observations that he used are noted in detail and how they are used as well. I would draw a parallel to modern research articles that we, as a community, to be of great merit; the kind of articles that you can look at and reproduce what the authors did because it is well documented.

Goldstein also points out how Ptolemy's work got taken as gospel of just how everything was believed to be by ancient and modern scholars as commonplace among his predecessors rather than the unique work that it actually was. Goldstein feels that this may be because Ptolemy did not stress his innovations beyond releasing them.

To tie this back with DiSessa, I see the usage of the observations by the Babylonians and Ptolemy's predecessors to be how we want to build up students from a groundwork. If you have a solid foundation upon which to work, p-prims or detailed observations, it will simplify things moving forward as you don't have to account for the lack of such a thing. All told, I found this an interesting article.

Bernard R. Goldstein, "Saving the phenomena: The background to Ptolemy's planetary theory," Journal for the History of Astronomy, Vol. 28, pages 1-12 (1997)

Dutka examines Erastothenes’ measurement and calculation of the Earth with a focus on surveying methods that were in practice at the time. There is debate, even in modern times, about what exactly the equivalent modern measurement of a stade is. Various values have been proposed and supported by their champions, but as Erastothenes’ original work has been lost to the ages, it is all a best guess based on what information we can find for measurements of distances that are still fully support by documentation that dates back to the era in question. 

Another thing that complicates matters is the lack of a standardized unit of measurement that holds between all of the different regions. The value for a stade could differ between neighboring regions or even within the region itself.  

I also find it interesting that the idea is put forth that Erastothenes used his position at the Library of Alexandria to collect data that was helpful in his determination of the circumference of the Earth. I feel importance in this as it shows that the practice has been around for a long time; that people responsible for repositories of knowledge not only curated the vast tomes and collections of information but developed their own conclusions and theories from those collections. We see today the work that is done around museums and universities. The former being a collection of such knowledge of antiquity and the latter being able to obtain recorded information from nearly any source required.  

Another interesting thing was that the method of Erastothenes was similar to that which had been done in the past, but it differed in a key point: the use of the gnomon. By working off of the assumptions that he did - parallel rays and so on – he was able to get an accurate measurement through means that most people could understand without having to use specialized equipment or measurement techniques.  

To tie this work back to DiSessa, I find that all of the experiments that were done have a core point that ties them together. They are equating a change in distance on the Earth with changes in the night sky. These projections and relations are then allowing them to posit circumferences for the Earth. As understanding advanced and measurement techniques became more refined, they were able to provide more accurate and precise information into the relationship to determine a better value.  

I feel the connection here is how we build students a repertoire of techniques and understanding to help them as they advanced through their physics learning journey. In early courses, we give them equations that become more refined as they go on. The form of the equations themselves don’t so much change as the information put into them does. Take for instance Newton’s work. We go from F=ma to the differential form. They mean the same thing, but one is more advanced and, perhaps, more powerful than the other. 

Jacques Dubka, "Eratosthenes' measurement of the Earth reconsidered," Archive for History of Exact Sciences, Vol. 46, pages 55-66 (1993)