Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.
The biggest drive towards what we consider the scientific mindset was driven initially by religious ambitions. One who best exemplified this was Peter of Abano, who wanted to take the physical concepts that Aristotle had developed in antiquity and somehow marry them to the ideas in Catholicism, as driven by his Dominican Order. Abano commented on the collective works of Aristotle, not being shy to state when he disagreed with him because man was fallible and prone to making mistakes in his search for the truth (yet he himself was exempt from this). Abano also expanded on some of Aristotle's work, including noting how black objects heat up easier than whiter ones, discussed thermal properties of the sound and noted how sound was a spherical wave emitted from a source. He was the first to theorize how light waves cause rainbows via diffraction, something that would be explored more in the following century (Freely 107-9).
Other areas that Abano covered included kinematics and dynamics. Abano subscribed to the idea of impetus as the driving force behind all things, but its source always being external rather than internal.Objects fell at a faster rate because they were trying to get to their nautral state, according to him. He also discussed astronomy, feeling that the phases of the moon was a property of it and not a result of Earth's shadow. And as for comets, they were stars trapped in Earth's atmosphere (110).
One of Abano's students was Thomas Aquinas, who carried on the work of his predecessor with Aristotle. He published his results in Summa Theologica. In it, he talked about the differences between metaphysical hypotheses (what must be true) and mathematical hypotheses (what corresponds with observations of reality). It boiled down to what possibilities existed for a situation, with only one option belonging to metaphysics and multiple paths belonging to mathematics. In another book of his entitled Faith, Reasoning, and Theology, he delved deeper into the comparisons between science and religion by discussing the realms of exploration both offered (114-5).
One important aspect of science is its ability to stand up to repeated testing of the experiment to see if the conclusion is valid. Albertus Magnus (also a student of Abano) was one of the first to do so. In the 13th century, he developed the notion of repetition of experimentation for scientific accuracy and better results. He also was not too big on believing something just because someone in authority claimed it to be so. One must always test to see if something is true, he contended. His main body of work though was outside of physics (plants, morphology, ecology, entryology, and such) but his concept of the scientific process has proven to be of immense value to physics and would lay the corner stone for Galileo’s formal approach to science (Wallace 31).
Another forefather of the modern scientific frame of mind was Robert Grosseteste, who did a lot of work with light. He described how light was at the beginning of everything (per The Bible) and that this motion outward dragged matter with it and continues to do so, implying that light is the source of all motion. He talked about the progression of light as a set of pulses, extended the concept to sound waves, and how one action determines another and so can stack up and go on forever...a paradox of sorts. A big area of exploration he led was on lenses, at the time a relative unknown topic. He even had some precursor work in the development of a microscope and a telescope, almost 400 years before their formal invention! Now this is not saying that he got everything right, especially his ides on refraction which involved bisectors of different rays with relation to the normal line to the surface of the refractor. Another idea of his was that the colors of the rainbow are determined by the purity of the material, the brightness of the light, and the quantity of the light at the given moment (Freely 126-9).
Petrus Peregrinus de Maricourt was one of the first to explore magnets and wrote about his discoveries in Epistola de magnete in 1269, following scientific procedures his predecessors like Grosseteste did by taking care in order to reduce systematic errors. He talks about many magnetic properties including their north and south poles (attraction and repulsion) and how to distinguish between the two. He even goes into the attractive/repulsive nature of the poles and the role that iron plays in all of this. But the coolest bit was his exploration of breaking up magnets into smaller components. There he found that the new piece wasn’t just a monopole (where it’s just north or south) but in fact acts like a minute version of its parent magnet. Petrus attribute this to a cosmic force permeating in magnets arising from the celestial sphere. He even hints at a perpetual motion using the alternating poles of magnets to spin a wheel – essentially, an electric motor of today (Wallace 32, IET, Freely 139-143)!
In a step towards data analysis, Arnold of Villanova (a student of medicine) hinted at the exploration of trends within data. He tried to show that there was a direct proportion between the sensed benefits of medicine to the quality of the medicine given (Wallace 32).
Jordanus Nemorarius and members of his school explored statics as they looked into the lever that Aristotle and Archimedes had developed in order to see if they could understand the deeper mechanics. Looking at the lever and the concept of the center of gravity, the team developed “positional gravity” with parts of a force (hinting at the eventual development of vectors by Newton’s era) being distributed. They also used virtual distance (really an indivisible-like small distance) as well as virtual work to help develop a proof for the lever law, the first to ever do so. This led to the axiom of Jordanus: "motive power that can lift a given weight a certain height can lift a weight k times heavier to 1/k times that prior height, where k is any number." He also extended the lever law ideas to a system of weights and pulleys on different inclines (Wallace 32, Freely 143-6).
Gerard of Brussels in his De motu tried to show a way to relate “curvilinear velocities of lines, surfaces, and solids to the uniform rectilinear velocities of a moving point.” While that is a bit wordy, it foreshadows the mean-speed theorem, which shows how different “rotational motion of a circle’s radius can be related with a uniform translational motion of its midpoint.” Which is also wordy (Wallace 32-3).
Theodoric of Freiberg shifted the focus from mechanics to optics when he studied prisms and discovered that rainbows are the result of the reflection/refraction of light. These findings were published in De iride in 1310. He uncovered this by experimenting with different light angles as well as blocking out selective light and even trying different types of materials such as prisms and containers with water to represent raindrops. It was this last field that gave him the leap he needed: Just imagine each raindrop as a part of a prism. With enough of them in a vicinity, you can get a rainbow to form. He found this to be true after he experimented with the height of each container and found he could get different colors. He tried to explain all those colors but his methods and geometry were not sufficient to accomplish that, but he was able to talk about secondary rainbows as well (Wallace 34, 36; Magruder).
Thomas Bradwardine, a fellow of Norton College, wrote Treatise on the ratios of velocities in motion, in which he used speculative arithmetic and geometry to examine said topic and see how it extended to relations between forces, velocities, and resistance to motion. He was spurred to work on this after discovering a problem in Aristotle’s work where he claimed velocity was directly proportional to force and inversely proportional to resistance of motion (or v = kF/R). Aristotle had then claimed that velocity was zero when the force was less than or equal to the resistance of motion (thus being unable to overcome the inherent resistance). Thus, v is a finite number expect for when the force is zero or when the resistance is infinite. That did not jive well with Thomas, so he developed the “ratio of ratios" to solve what he felt was a philosophical problem (for how can anything be unmovable). His “ratio of ratios” eventually led to the (not right) idea that velocity is proportional to the log of the ratios, or that v=k*log(F/r). Our buddy Newton would show this is just plain wrong, and even Thomas offers no justification for its existence other than it removes the aformanetioned case of the finite/infinite dichotomy because of logarithm properties pertaining to log(0). He most likely didn't have access to the necessary gear to test out his theory, but some of Thomas’ footnotes discuss the calculations of his equation and hints at the idea of an instantaneous change, an important bedrock of calculus, versus an average change and how they approach one another as the differences shrink. He even hinted at the idea of taking a bit of infinity and still having infinity. Richard Swinehead, a contemporary of Bradwardine, even went through 50 variations of the theory and in said work also has those hints of calculus (Wallace 37-8, Thakker 25-6, Freely 153-7).
John of Dumbleton also made headway into the field of physics, when he wrote Summa logical et philosophiae naturalis. In it, rates of change, motion, and how to relate them to scale were all discussed. Dumbleton was also one of the first to use graphs as a means of visualizing data. He called his longitudinal axis the extension and the latitudinal axis the intensity, making the velocity the intensity of motion based off the extension of time. He used these graphs to provide evidence for the direct relation between strength of a shining object and the distance one is from it and also as evidence for an indirect relation between "the density of the medium and the distance of action (Freely 159)."
Even thermodynamics was given the time of day for research during this time period. People such as William of Heytesbury, Dumbleton, and Swineshead all looked at how heating non-uniformly affected the heated object (Wallace 38-9).
All the aforementioned people were members of Merton College, and it is from there that others worked on the mean-speed theorem (or the Merton rule, after Heytesbury’s work on the subject was heavily read), which was first developed in the early 1330s and worked on by said group in the 1350s. This theorem is also wordy but gives us a glance into their thought process. They found that a
“uniformly accelerated motion is equivalent, so far as the space traversed in a given time is concerned, to a uniform motion whose velocity is equal throughout to the instantaneous velocity of the uniformly accelerating body at the middle instant of the period of acceleration.”
That is, if you are accelerating at the same rate throughout a given period, then your average speed is simply how fast you were going at the midpoint of your journey. The Mertonians, however, failed to consider the application of this with a falling object nor were they able to come up with what we would consider a real-life application of this. But, to a student of calculus this finding is critical (Wallace 39-40, Thakker 25, Freely 158-9).
Another Mertonian piece of work was impetus, which would eventually evolve into what we call inertia. Biblically, impetus meant a push towards one goal and some of that meaning stayed with the word. Many Arabs had used the term to talk about projectile motion and the Mertonians worked with it in the same context. Franciscus de Marcha talked about impetus as a lingering force on projectiles caused by its launch. Interestingly, he says the projectile leaves behind a force as it is launched, then said force catches up to the projectile and gives it impetus. He even extends inputs when referencing how sky objects move in a circular fashion (Wallace 41).
John Buridan took a different viewpoint in his Questions on Aristotle's Physics and Metaphysics, feeling that impetus was an inherent part of the projectile and not something exterior to it. Impetus, he claimed, was directly proportional to velocity as well as the matter in motion and was a "quantity of matter" times velocity, aka momentum as we know it today. In fact, impetus would be an everlasting quantity if it weren’t for other objects impeding the path of the projectile, a major component of Newton's 1st law. John also realized that if the mass was constant then the force acting on an object had to be related to a changing velocity, essentially discovering Newton's 2nd law. Two out of the three big motion laws attributed to Newton had their roots here. Finally, John argued for impetus being responsible for falling objects and therefore gravity as well, stacking up in its full effect (Wallace 41-2, Freely 160-3).
In a follow-up, Nicole Oresine, one of Buridan's students, found that impetus was not a permanent fixture of the projectile but instead is a quantity that is used up as the object moves. In fact, Nicole postulated that acceleration was somehow connected to impetus and not at all to uniform motion. In his Fractus de configurationibus quantitatum et motuum, Oresine gave a geometrical proof for the mean speed theorem that Galileo ended up using also. He employed a graph where velocity was the vertical axis and time on the horizontal. This gives us slopes values of acceleration. If that slope is constant, we can make a triangle for a given time interval. If acceleration is zero, we could instead have a rectangle. Where tho two meet is the location of our mean speed, and we can take the upper triangle we have just created and past it below to fill in that empty space. This was further evidence for him that velocity and time were indeed proportional. Additional work by him established falling objects tend to fall onto a sphere, another precursor to Newton. He was able to calculate the spin rate of the Earth rather well but didn't readily release the results because of his fears for contradicting doctrine. He even pioneered mathematics, with a "proportional parts to infinity" summation happening, aka converging and diverging series (Wallace 41-2, Freely 167-71)!
But others studied falling objects and had their own theories as well. Albert of Saxony, another student of Buridan, found that the velocity of a falling object was directly proportional to the distance of the fall and also to the time of the fall. That, dear audience, is the basis of kinematics, but the reason why Albert isn’t remembered is because his work defended the claim that distance was an independent quantity and so it was therefore not a valid finding. Instead, he tried to break up little bits of velocity and see if it could be attributed to a set time interval, set distance, or set space amount. He did predict correctly that an object, if given a horizontal motion, should continue in that direction until the impetus of gravity overcomes the vertical distance required to get to the ground state (Wallace 42, 95; Freely 166).
Okay, so we have talked about the concepts people were thinking of, but how did they notate it? Confusingly. Bradwardine, Heytesbury, and Swinehead (our Mertonians) used something akin to function notation, with:
- -U(x) = constant velocity over a distance x
- -U(t) = constant velocity over a time interval t
- -D(x) = changing velocity over a distance x
- -D(t) = changing velocity over a time interval t
- -UD(x) = uniform change over a distance x
- -DD(x) = difform change over a distance x
- -UD(t) = uniform change over a time interval t
- -DD(t) = difform change over a time interval t
- -UDacc(t) = uniform accelerated motion over a time interval t
- -DDacc(t) = deform accelerated motion over a time interval t
- -UDdec(t) = uniform decelerated motion over a time interval t
- -DDdec(t) = difform decelerated motion over a time interval t
Yikes! Rather than realize a sign convention would result in familiar kinematic concepts, we have under the Mertonian system 12 terms! (Wallace 92, Freely 158)
We can clearly see that the eventual arrival of classical mechanics and much of the background for other branches of science was taking root, and it was during this century that many of those plants began to sprout out of the ground. The Mertonians and Bradwardine’s work was especially critical, but none of them ever developed the idea of energy. It was during this timeframe that the concept began to sneak in (Wallace 52).
Motion was being thought of a ratio that had existence outside of a particular circumstance at the Aristotelians contended was the case. To the Mertonians, motion wasn’t even a point of reality but rather an objectification of it and didn’t bother with the distinction between violent (man-made) and natural motion, as the Aristotelians did. However, they did not consider the energy aspect of the situation. But Albert and Marsilius of Ingham were the first to split the broad concept of motion into dynamics and kinematics, which was a step in the right direction as they sought to provide a real-world explanation (53-5).
It was with this in mind that Gaelano de Theine picked up the baton and continued on. His goal was to make bare the distinction between uniform and non-uniformed motion as well as methods for measuring uniform motion, hinting at kinematics. To demonstrate this as a real world application, he looked at spinning wheels. But once again, the energy aspect did not enter the picture as de Theine was focused on the magnitude of the motion instead. But he did create a new notation system which was also messy like the Mertonians:
- -U(x)~U(t) (constant velocity over a distance x and not over a time interval t)
- -U(t)~U(x) (constant velocity over a time interval t and not over a distance x)
- -U(x) · U(t) (constant velocity over a time interval t and over a distance x)
- -D(x)~D(t) (changing velocity over a distance x and not over a time interval t)
- -D(t)~D(x) (changing velocity over a time interval t and not over a distance x)
- -D(x) · D(t) (changing velocity over a distance x and over a time interval t)
Alvano Thomas would also create a similar notation. Note how this system doesn’t address all the possibilities that the Mertonians did and that U(t)~U(x) = D(x)~D(t), etc. Quite a bit of redundancy here (55-6, 96).
Many different authors continued this study of the distinctions of different motions. Gregory of Rimini contended that any motion can be expressed in terms of the distance covered while William of Packham held that old viewpoint of motion being inherent to the object itself. Where he differed was his critique of the notion that motion was something that could exist one moment and the not the exist. If something exists, it has a measurable quality to it but if at any point it doesn’t exist then you cannot measure it. I know, it sounds silly but to the scholars of the 16th century this was a huge philosophical debate. To resolve this existence issue, William contends that motion is just a state-to-state transference with nothing truly at rest. This in of itself is a big leap forward but he goes on to state the causality principle, or that “whatever is moved is moved by another,” which sounds very similar to Newton’s Third Law (66).
Paul of Venice did not like that and used a continuity paradox to illustrate his displeasure. Otherwise known as Zeno’s paradox, he argued that if such a state-to-state were true then one object would never be in a single state and thus would never move. Instead, Paul claimed that motion had to be continuous and ongoing within the object. And since local motion is a real phenomenon, some cause had to exist so why not the object itself (66-7).
We can see that people were getting key components of the ideas right, but what about some of the math that we take for granted? Those who took a nominalistic approach felt that if motion was related to the space the object was moving in, then mathematical models should be able to predict the outcome of the motion. Sounds like kinematics to me! Those nominalists looked at velocity as a ratio relating itself to space and time. Using that, they could look at motion as a cause and effect scenario, with the cause being some force applied and the effect being the distance traveled (hence where the motion comes in). But though many tried to think about how the resistance to motion might appear here, they did not think it was a physical cause (67).
But some didn’t care for the by-the-numbers approach and instead wanted to discuss the “reality” behind the motion, like Paul. But there was even a third group that took an interesting position to both sides, realizing that some good ideas were present with both. John Majors, Jean Dullaert of Ghent, and Juan de Celaya were but a few who tried to look at the pros and cons objectively and develop a hybrid between the two (67-71).
The first to publish such a position was Domingo de Soto. He claimed that not only was there compromise but that many of the differences between the nominalists and the realists was just a language barrier. Motion itself is removed but yet related to the object as it stems from a cause and effect scenario. The velocity is a product of the effect, like for example a falling object, but can also come from the cause, like a hammer strike. De Soto was also the first to related the mean speed theorem to the distance an object falls and the time it takes for it to fall (72-3, 91)
With much of this clarified, the focus shifted to how a force causes motion but is not within the object itself. Aristotle had claimed that nature itself was the “cause of motion” but in 1539 John Philiiponus disagreed. He wrote that “nature is a kind of force that is diffused through bodies, that is formative of them, and that governs them; it is a principle of motion and of rest.” That is, nature was the source of motion and not the cause of motion, a subtle but important distinction. This caused people to ponder about the internal nature of force and how it applied to the world (110).
John’s work is just one example of the ideas that were coming out of Collegio Romano at the time. Like Merton College, this institution would see many gifted minds grow and develop new ideas that would expand into many disciplines. In fact, evidence exists for many of their works being in Galileo’s procession, for he references this view on nature without justifying it. We have our possible first direct link to an inspirational source for Galileo (111).
Another one of these authors was Vitelleschi, who was definitely aware of John’s work and expanded upon it. Nature, Vitelleschi claimed, gives each object its own type of motion from within, a “natural motive power.” This hints at what medieval minds called vis, or an external cause. Now, Vitelleschi went a step further and discussed what happens when a moving object causes other objects to move as well. He attributes this new motion to the original object being an “efficient cause” or an object bringing about changes in objects other than itself (111-2).
Content with hat explanation, the author went on to talk about “natural motion” which arises from the object and how it relates to a falling body. He simply states that it falls because of a quality from within it and thus not because of vis nor because of an efficient cause but more of a passive cause especially if because of an efficient cause. In such instance, he would describe the now falling object as having “violent motion” which is similar to both vis and an efficient cause but unlike them the violent motion doesn’t add anything to the force of the object (112).
Clearly, we can see how the wordiness begins to murk up Vitelleschi’s ideas, and it doesn’t get any better when he moves on to gravity. He figured it was a passive cause but wondered if it had an active component and if it was external or internal. He figured that something akin to iron being attracted to magnets was happening here, where an object contained some force that caused it to respond to gravity. The makeup of the falling object is what made gravity “an instrumental principle of the body’s fall.” But is it an efficient cause? It seemed so because it was bringing about change, but was it changing itself? Was gravity an object? (113)
Vitelleschi needed to become clearer, so he refined his definition of an efficient cause into two types. The first was what we have already discussed (known by the author as proprie efficiens) while the second is when the cause works only on itself, creating the motion (dubbed efficiens per emanationem). With this, Vitelleschi came up with three major theories from gravity. He felt it was:
- “potency to the substantial form by a generator.”
- “motion that follows on the form” by the removal of what would normally impede it.
-motion which leads to a natural state by, “the substantial form of the element as the acting principle form from which the motive quality flows.”
They sure did have a way with words, didn't they? (Ibid)
Freely, John. Before Galileo. Overlook Duckworth, New York. 2012. Print. 107-10, 114-5, 126-9, 139-146, 153-63, 166-171.
IET. “Archive Biographies: Pierre de Maricourt.” Theiet.org. Institute of Engineering and Technology, Web. 12 Sept. 2017.
Magruder, Kerry. “Theodoric of Freiberg: Optics of the Rainbow.” Kvmagruder.net. University of Oklahoma, 2014. Web. 12 Sept. 2017.
Thakker, Mark. “The Oxford Calculators.” Oxford Today 2007: 25-6. Print.
Wallace, William A. Prelude to Galileo. E. Reidel Publishing Co., Netherlands: 1981. Print. 31-4, 36-42, 52-6, 66-73, 91-2, 95-6, 110-3.
© 2017 Leonard Kelley
Darquavius on April 20, 2018:
Pretty good writing