1008.4239v1

# Unknown Title ## History of Scientists´ Elimination of Naive Beliefs about Movement - The testing of the theories of Galileo in his lifetime on board of a galley - ## ABSTRACT Throughout the early history of Science the heliocentric world model was refused because it contradicted the thoughts of Aristotle and the medieval 'Impetus' theory of movement. Even Galileo's sky observations did not lead to any acceptance of the heliocentric model, because scientists derived from Aristotle's physics that the earth was static. It was not until 1640 when Gassendi proved the principle of inertia on a moving galley, as well as Galileo's laws of free fall with a giant wheel that 'impetus-physics' which incorporated naive beliefs about movement was abandoned. To understand the methods of calculating movement, novice students can be stitmulaed by using these initial experiments based on the dynamics of a ship movement and not rely on naïve approach. This can help novice students to attain a concept change from naïve to scientific conceptions about movement. Modern students who study movement were found to harbour many of the same naive beliefs as our scientific forefathers. The history behind the elimination of these naive beliefs is presented here in order to help encourage elimination of these naive beliefs. Several studies found these naive beliefs to be held by novice students today. These naive beliefs held in the Science of movement have posed major problems for teaching novice students. Conflicting methods of modelling these movements have been the source of much controversy over time as concepts changed. Considering a conceptual change in history can be helpful in education. ## INTRODUCTION: Concept change In the teaching of Science usually the naive belief of students has to be changed (Chi 1981). For example, the naive belief `there is no motion without a force` should be replaced with the expert belief `there is no acceleration without a force` (diSessa 1998). Literature holds many empirical findings about eliminating naive beliefs (Chi 1994). Concept change is triggered when two concepts are in conflict and the class has to decide which concept best resolved the problem, and sees how the replacement concept explained the demonstration or quantitative problem, for example motion of a dropped object (Kalman 2004). The idea is that the evaluation of a theoretical framework does not occur until there is an alternative to produce the conceptual ecology. The specific failures such as being faced with an anomaly are an important part of this ecology (Posner 1982). Here we demonstrate `teaching approaches in science education in the light of knowledge and understanding of the history of science` (Strike 1982) with a crucial experiment in history, which caused a concept change of scientists. This way recall of historic experiments helps students to eliminate naive beliefs. Context setting of the problem can have a significant influence on students´ reasoning and on concept change (Bao 2002). Concept change to explain the day/night cycle by the rotation of earth rather than a moving sun and a stationary earth is difficult because of students´ ontological and epistemological presuppositions (Vosniadou 1992). In order to achieve conceptual change, the presuppositions have to be subjected to experimentation and falsification (Vosniadou 1994). For example the concept of inertia is tested by the force concept inventory (a ball leaving a circular path), only 5% of all students answered correctly (the path tangential to the circle) independent of distracters in the multiple-choice answers (Rebello 2004, question 7). There are similar results concerning a ball falling from a moving airplane (Rebello 2004, question 14). This is explained by diSessa (1993) by phenomenological primitives used by students (p-prims, diSessa 1998). Since ´both learning and the history of science requires us to understand how conceptions change´ (Strike 1982), we investigate both the concept change from Medieval to Newtonian mechanics as well as the first statement of principle of inertia in this article. ## DATA COLLECTION. Elimination of naive beliefs about movement in history A study is conducted here in which the history behind the elimination of common naive beliefs about movement by scientists is presented in order to help encourage it (Monk 1998). It is demonstrated finally that these naive beliefs are still found to be held by novice students today. Archimedes of Syracuse mentioned in his script 'The Calculator of Sands' that an early Greek astronomer named Aristarch explained the movements in the sky by a theory that the earth circulates around the sun like the other planets do. But no one believed that, because the earth seemed to stand still (Ley 1963). The same happened when Copernicus, who gave his name to the modern heliocentric system, claimed the same thing (Ley 1963). In the time of Galileo science still thought about the world in Aristotle's terms of dichotomy meaning that the planet earth is made up of the elements water, air, fire and earth while the sky, the other planets as well as the stars, are made of aether. Dichotomy was seriously shaken by Galileo's observations of the sky by telescope laid down in his famous script 'Sidereus Nuncius' (News from New Stars 1610 / 1611, Galileo 1967). However, the scientific world did not accept these findings as proof of the heliocentric system, because science was used to a redesigned kind of physics of Aristotle's called the 'theory of Impetus'(Ibn Sinha 1885/86). This theory claimed the necessity of a `continuous mover` as a cause of every movement (Abu´l Barakat 1939), in modern algebraic language 'velocity is a force divided by resistance', this idea was elaborated on by many a scientist such as Avicenna (965-1039) and Albert of Saxony (1316-1390). However, scientists of antiquity as well as Arabian and Renaissance became aware of contradictions to observations as well as other antiquity theories such as the atomic theory of Epicures. Even simple observations like the trajectory of an arrow caused enormous difficulties within the theory of Impetus. Epicures (341-270 B.C.) described atoms as not infinitely small, invisibly small and continuously in movement. This theory of atoms contradicts Aristotle's physics and the impetus theory. Consequently, atomic theory was abandoned in medieval times as well as in 16 th century physics (Sambursky 1974). In modern physics force is the cause of the change of movement (acceleration), contrarily, impetus calls for a cause for movement at any time based on Aristotle's claims for rest as the privileged and natural state on earth (Brown 2006). Based on these ideas, Aristotle's, Ptolemaist, and Thycho Brahe, amongst many, claimed that, provided the earth rotates in an easterly direction, a stone thrown up would come down in the west as long as earth moved in an easterly direction during the time of the throw, and birds and clouds would drift rapidly in an westerly direction. Since this cannot be observed, it should be reasoned that earth stays still and does not move (Sambursky 1974). Arguing that way the heliocentric ideas of Aristarch from Samos, Copernicus and Galileo have all been rejected. Even Galileo's revolutionary observations of mountains on the moon, of spots on the sun, phases of Venus and four moons encircling Jupiter made by a telescope in 1609 and in 1610 all contradicting the antiquity system of Ptolemaist did not change the situation (Galileo 1957). The seeming stillness of the earth was the major point in both the cases in the courts of inquisition against Galileo in 1516 and 1533, which led to the denouncement of the 'Dialogue concerning the chief world systems' by Galileo. Galileo used the principle of inertia in his arguments in the 'Dialogue'. On the second day of the 'Dialogue' Salviati, who is Galileo's spokesman of the heliocentric system, claims a stone falling down the mast of a moving ship will hit the ground at the foot of the mast and will not drift to the stern as was claimed by Aristotle. Simplicio, Aristotle's spokesman of the Ptolemaic system, does not accept this because that assertion is a claim and has never been proven (Galileo 1967). This dialogue resembles teaching physics to novice students holding naive beliefs about movement. Such an experiment with a moving ship would indeed have been too elaborate for Galileo. In this very situation this crucial experiment with the ship became reality with the help of the French priest and scientist Gassendi. This experiment can help eliminate naive beliefs held by novice students today. Fig. 1 Portrait of Pierre Gassendi 1592-1655, from: Egan , 1964 <details> <summary>Image 1 Details</summary>  ### Visual Description ## Photograph: Portrait of Pierre Gassendi ### Overview The image is a black-and-white engraved portrait of a historical figure, identified as **Pierre Gassendi** (1592–1655), a French philosopher, mathematician, and astronomer. The portrait is framed within an oval border, with a crest at the bottom center. The background is textured with horizontal lines, and the figure is depicted in period attire. ### Components/Axes - **Textual Elements**: - **Name Inscription**: "Pierre Gassendi" is inscribed in cursive script at the bottom of the image, split into two parts: "Pierre" on the left and "Gassendi" on the right. - **Crest**: A shield-shaped emblem at the bottom center features a lion rampant (a heraldic symbol) above a field of stars. No textual labels are present on the crest itself. - **Visual Elements**: - **Subject**: The figure is a middle-aged man with short, curly hair, wearing a dark robe over a light-colored shirt with a high collar. His expression is neutral, and he gazes slightly to the left. - **Border**: The oval frame has a textured, concentric design. </details> Pierre Gassendi was born in 1592 in Champtercier in Provence; he studied theology in Aix-enProvence and Digne (Jones 1981) was consecrated as a priest (minister) in Digne and became a professor in Aix (Detel 1978, Egan 1964). Travelling frequently to Paris he co-operated with the scientific circle (salon) of Mersenne. Since scientific academies had not been founded, this circle of Mersenne was the most important scientific audience at that time. The discussions there caused Gassendi to perform several experiments, such as: - He repeated Pascal's measurement of ambient air pressure, also producing a vacuum renouncing Aristotle's theory of 'horror vacui' - He observed Mercury's eclipse of sun by telescope in 1630 - He was the first to draw a map of the moon to scale; a crater was named 'Gassendi' in memory of this, - He observed the growth as well as the solution of crystals through a microscope deriving existence of atoms from the persistence of angles in crystals (Detel 1978, Fisher 2005). . - He discovered of the rings of Saturn before Huygens did so, describing Saturn's view through the telescope as elongated and wrinkled with handles. He had exchanged letters with Galileo since 1625 (Detel 1978). After his death in Paris in 1655 his work about logic was printed in Tours in 1658 (Jones 1981), mentioning his experiments on a ship. ## DATA COLLECTION AND ANALYSIS. Reconstruction of the experiments aboard a galley 1640 which proved the principle of inertia and eliminated naive beliefs about motion An understanding of the history of Science regarding motion can promote student understanding of important concepts through the process of conceptual change. The argument is that there are similarities between student naive beliefs and the early naive beliefs of motion held by scientists. Gassendi´s straightforward ship experiments demonstrated the effectiveness of inertial explanation of motion. The students themselves in an appropriate conceptual change teaching environment could perform similar experiments. Before recapping these historical events it should be noted that in 1610 Galileo published Sidereus Nuntius with discoveries of the moons of Jupiter, mountains on the moon and suns´ spots. In 1616 the inquisition forced him to mention the heliocentric system of Copernicus only as a hypothesis rather than a fact. Galileo's´ Dialogue Concerning the Two Chief World Systems comparing the heliocentric system of Copernicus with the Ptolemaic earth centred world system in a dramatic dialogue was published in Italian in 1632 but censored by the Roman Inquisition in 1633. The translation into Latin was published in 1636 in Strasbourg in protestant oriented central Europe, ignoring censorship. The 2 nd Latin edition was improved by Galileo in 1641; it became his last major work and was released all over Europe (Galileo 1957, 1967). Since Galileo exchanged letters with Gassendi (Taussig 2004) it can be conjectured that Galileo knew the ship experiments when he was working on the 2 nd edition. Several ship experiments performed by Pierre Gassendi in 1640 decided whether Galileo's theoretical experiment on the movement of bodies in a cabin of a ship was correct. This question was evidently answered by Gassendi positively. This episode documents the importance of access to proper experimental equipment in the testing of mechanical hypotheses, and of the necessity of political support in the present case, in which expensive military hardware was required. The friend and sponsor of Gassendi Louis Emanuel of House Valois became governor of Provence in 1638 and so he was in charge of the French fleet. Thus it became possible to conduct the experiment with a moving ship as proposed by Galileo. This experiment was described in his letter 'De motu impresso epistolae due', Paris, 1640 / 1642 (Gassendi 1642) in articles V and VIII superficially. Data collected from the Bavarian State Library as well as the 'Musée de la Marine' in Paris was analysed to give a report of the valid construction of Gassendi´s experiments to prove Galileo's theories. By these means the experiments can be reconstructed as follows. Ships sailing are exposed to waves and heel over and thus are not suited to perform these experiments, small rowing boats have no masts. For testing Aristotle's claims regarding motion large military galleys are required to which Galileo had no access. The experiments could be done with Louis Emanuel of House Valois and his access to the French fleet at Marseilles. The galleys of the French fleet at 1640 had a length of about 40m, the masts were about 20 m high, and attained the speed of modern sports rowing boats, about 5m/s (Mondfeld 1972). At this time Galleons of the French fleet presented two masts as shown in figures 2 and 3. Fig. 2 French Galley in 1675, 'Musée de la Marine', Paris, from: Mondfeld 1972 <details> <summary>Image 2 Details</summary>  ### Visual Description ## Diagram: Sailboat Rigging and Structure ### Overview The image is a black-and-white technical diagram of a sailboat, labeled "La Dracene" with the author "Sauvageau, 1 juin 1803" and "Tome 1" (Volume 1). It depicts the hull, masts, sails, rigging, and deck in a simplified, schematic style. The diagram includes a scale (0–5 meters) and labels for key components. ### Components/Axes - **Labels**: - "La Dracene" (top-left corner, likely the vessel's name). - "Sauvageau, 1 juin 1803" (author and date, in French). - "Tome 1" (Volume 1, in French). - "Spar" (horizontal support for the mast). - "Mast" (vertical structure for sails). - "Hull" (main body of the boat). - "Sail" (triangular fabric for propulsion). - "Rigging" (network of lines and pulleys). - "Deck" (flat surface of the boat). - **Scale**: A linear scale labeled "Mètre" (meter) from 0 to 5, positioned near the bottom-left. - **Legend**: No explicit legend, but labels are directly embedded in the diagram. ### Detailed Analysis - **Hull**: A long, rectangular shape with a small cabin at the bow (front). - **Masts**: Two vertical masts, one larger (main mast) and one smaller (foremast), connected by rigging. - **Sails**: Two triangular sails, one on each mast, with lines and pulleys (rigging) extending from the masts to the deck. - **Rigging**: A complex network of lines and pulleys, including a "Spar" (horizontal support) and "Mast" (vertical structure). - **Deck**: A flat surface with a small cabin and a mast at the stern (rear). - **Scale**: The 0–5 meter scale is positioned near the bottom-left, but no specific measurements are labeled on the diagram. ### Key Observations - The diagram emphasizes the **rigging system**, with lines and pulleys connecting the masts to the deck. - The **sails** are triangular, typical of traditional sailing vessels. - The **hull** and **deck** are simplified, with no detailed features beyond the cabin and mast. - The **scale** (0–5 meters) is present but not used to label specific dimensions. ### Interpretation This diagram appears to be a **technical illustration** of a historical sailboat, likely from the early 19th century (as indicated by the date "1 juin 1803"). The focus on **rigging and sail structure** suggests it was created for educational or archival purposes, possibly to document the design of "La Dracene." The absence of a bowsprit (a horizontal spar at the bow) may indicate a specific design choice for stability or maneuverability. The diagram’s simplicity prioritizes clarity over realism, making it useful for understanding the basic mechanics of a sailing vessel. The French text ("Sauvageau, 1 juin 1803") and "Tome 1" imply it is part of a larger collection or publication, possibly a technical manual or historical record. **Note**: The image contains no numerical data or trends, as it is a schematic diagram rather than a chart. All textual information has been transcribed, with French terms translated for clarity. </details> The heights of the mast were approximately 25 m of which 20 m were accessible, thus the free fall from the mast lasted approximately 2 seconds while the ship was swiftly rowed a distance of about 10m. Thus the falling stone would be carried away 10m towards the stern. Gassendi wrote in his letter, however, that the impact of the stone was right at the foot of the mast - a very impressive contradiction to the movement theories of Aristotle as well as 'impetus' and thereby a major defeat for the entire medieval scholar system of 'Scholasticism'. Today, discussion of this experiment can be a way to help students to eliminate naive belief about movement. Fig. 3 Galley of French fleet 1692, 'Musèe de la Marine', Paris , from: Mondfeld 1972 <details> <summary>Image 3 Details</summary>  ### Visual Description ## Technical Diagram: Traditional Sailing Ship ### Overview The image is a black-and-white line drawing of a traditional sailing ship, depicted in profile view. It emphasizes the ship's structural components, including the hull, masts, sails, deck, and rigging. No textual labels, legends, or numerical data are present. ### Components/Axes - **Hull**: The elongated, tapered body of the ship, shown with a central keel and side planking. - **Masts**: Two vertical masts are positioned along the ship's centerline, with rigging lines connecting them to the hull. - **Sails**: Multiple triangular sails are attached to the masts, with lines extending to the deck for control. - **Deck**: A flat surface spanning the ship's width, with a small cabin structure near the stern. - **Rigging**: Horizontal and diagonal lines connecting masts to the hull, indicating structural support. ### Detailed Analysis - **Hull**: The hull is divided into sections by horizontal lines, suggesting deck levels or structural reinforcement. - **Masts**: The masts are evenly spaced, with the main mast slightly taller than the foremast. - **Sails**: Sails are depicted with dotted lines, possibly indicating furling mechanisms or sail folds. - **Rigging**: Rigging lines are shown in parallel and crisscross patterns, emphasizing their role in stabilizing the masts. ### Key Observations - The ship's design prioritizes symmetry, with masts and sails evenly distributed along the centerline. - No text, scale, or annotations are present to provide context (e.g., ship name, dimensions, or historical period). - The absence of color or shading limits interpretation of material properties (e.g., wood grain, sail fabric). ### Interpretation This diagram likely serves an educational or engineering purpose, illustrating the basic anatomy of a traditional sailing vessel. The lack of textual details suggests it may be a schematic for instructional use, focusing on structural relationships rather than specific historical or operational data. The simplicity of the line drawing implies it could be used to teach principles of naval architecture or sailing mechanics. ## Notes - **Language**: English (no non-English text detected). - **Data Absence**: No numerical values, trends, or categorical data present. - **Spatial Grounding**: All elements are centered in the image, with no legends or axis markers to indicate spatial relationships beyond the ship's own structure. </details> Gassendi performed other experiments aboard the moving ship. He let bowls down the deck once from the stern and once from the bow of the ship rolling one time in and the other time against the movement of the vessel. They arrived at the same time. The galleys of the French fleet in 1640 had 1- to 36 - pound cannons aboard. The deck was elevated at both ends (stern 1972, Risch 2007). If you let a cannonball roll from either side, it would attained the speed of about 2.5 m/s taking into account the energy of rotation, this is less than the speed of the boat of about 5m/s. If Aristotle's theories about movement and the 'impetus' theory were right, then the cannonball released at the stern would not even move toward amidships, but move away towards the stern. This again was an impressive contradiction to the Aristotle and 'impetus' theories of movement and thereby a major defeat for all medieval physics as well as a demonstration today helping novice students to eliminate naive beliefs. and bow) about 0.5m with respect to amidships, along a length of 17 m respectively (Mondfeld Having completed experiments aboard the moving ship, Gassendi has written the principle of inertia for the first time as it is used today in article XVI of his first 'de motu' letter: 'You will ask in passing what would happen to that stone which I claimed could be imagined in empty space if it were roused from its state of rest and impelled by some force. I answer that it is probable that it will move indefinitely in a uniform fashion, slowly or rapidly, depending on whether a small or great impetus had been imparted on it. I take my proof from the uniformity of the horizontal motion I have already explained since it would apparently not stop for any other reason than then influence of perpendicular motion... would not be accelerated or slowed down, and therefore would never stop.' (Detel 1978, Fisher 2005). The first two 'de motu' letters were addressed to Pierre Dupui in Paris in November and December 1640 and were published in 1642 (Brush 1972). Galileo's name is used today with the principle of inertia; he claimed this principle before for rotary motions alone (Galileo 1967, Brown 2006). High expenses for the ship's experiments with French state galleys and more than one hundred participants including persons of importance gave these refusals of Aristotelian physics and scholastic teachings credibility and public focus far beyond the borders of France (Taussig 2004). Due to expenses, the number of participants and high prestige of galleys, which had been involved in state races (Rambert 1931); this can be called the first 'big Science' experiment. This paved the way for wide acceptance of Galileo's findings and the heliocentric model as well as scientific revolution. These experiments can be used to eliminate naive beliefs about movement found to be held by novice students. ## METHODOLOGY. Free fall experiments to eliminate naive beliefs about movement The 'de mute' letters took away the strongest objection against the heliocentric model by disproving Aristotelian physics. However, rejection of the findings of Galileo did not cease. Especially the 'Dialogue Concerning the Two Chief World Systems', and his experiments about free fall were still rejected. The naive beliefs about free fall kept at those times are found to be held by novice students today (Bar 1994). With his inclined plane (shown in figure 4), Galileo proved the law of odd numbers, claiming distances passed in consecutive times behave like odd numbers; in today's words, speed increases proportionally with time. Fig. 4 Galileo's inclined plane, reconstruction in the Deutsche Museum, Munich, Germany. <details> <summary>Image 4 Details</summary>  ### Visual Description ## Photograph: Historical Classroom/Laboratory Interior ### Overview The image depicts a black-and-white photograph of a historical academic or scientific workspace, likely from the 18th or 19th century. The room features a checkered floor (black and white tiles), a central wooden table with scientific instruments, a globe on a stand, a fireplace with a mantel, and a chair with a cushion. Windows with shutters and exposed ceiling beams are visible. The atmosphere suggests a blend of educational and experimental use. ### Components/Axes - **Central Table**: Wooden, with a dark finish. Positioned at the center of the room. - **Instruments**: Includes a telescope mounted on a tripod, a microscope on a stand, and other unidentifiable apparatus (possibly glassware or mechanical devices). - **Globe**: Spherical, mounted on a three-tiered stand. Located to the right of the table. - **Fireplace**: Stone or brick construction with a decorative mantel. Positioned on the left wall. - **Chair**: Wooden, with a cushion. Situated near the fireplace. - **Windows**: Tall, rectangular, with wooden shutters. Allow natural light into the room. - **Ceiling**: Exposed wooden beams, suggesting a traditional architectural style. ### Detailed Analysis - **Textual Elements**: No legible text, labels, or axis markers are visible in the image. The fireplace mantel appears to have inscriptions, but they are too small or blurred to decipher. - **Spatial Layout**: - The central table is the focal point, flanked by the globe (right) and fireplace (left). - The chair is positioned near the fireplace, facing the table. - Windows are evenly spaced along the back wall, with shutters partially open. - **Material and Design**: - The checkered floor uses alternating black and white tiles, creating a geometric pattern. - The table and instruments reflect a utilitarian design, prioritizing function over ornamentation. ### Key Observations 1. **Historical Context**: The room’s design (fireplace, wooden furniture, globe) aligns with pre-industrial or early industrial-era educational institutions. 2. **Scientific Focus**: The presence of a telescope and microscope indicates a dual emphasis on astronomy and microscopy, common in 18th-century natural philosophy. 3. **Ambiguity in Text**: The mantel’s inscriptions remain unreadable, leaving the room’s specific institutional purpose (e.g., university, observatory) open to interpretation. ### Interpretation The room likely served as a multipurpose space for teaching and experimentation. The globe and instruments suggest a curriculum centered on natural sciences, while the fireplace and seating imply a lecture or discussion environment. The absence of modern equipment (e.g., electrical devices) reinforces its historical context. The unreadable text on the mantel could denote the institution’s name or a motto, but without clearer imagery, this remains speculative. The spatial arrangement prioritizes accessibility to tools and natural light, critical for observational and experimental work. **Note**: No numerical data, charts, or diagrams are present. The image provides contextual clues about historical pedagogy and scientific practice but lacks quantifiable metrics. </details> This is in contrast to medieval scholastic physics claiming speed would increase in equal steps with distance deriving this from the writings of Aristotle. This would yield to an exponential increase of distance with time. Having no modern clock, Galileo probably used his heartbeat or a water clock as a measure of time (Crawford 1996). Such poor accuracy could not clearly distinguish scholastic teaching from Galileo's law of free fall. Galileo himself describes precisely a comparison of time intervals of free fall in his 'Dialogue Concerning the Two Chief World Systems': He drops ammunition for a musket as well as a cannonball from the inclined tower of Pisa, both hit at ground the same time (Galileo 1967). It is not clear if he really performed this experiment. For a final proof of Galileo's law of free-fall, Gassed replaces measurement of time by time difference in his shrewd wheel of free fall (figure 5). This treadmill wheel with almost 4m diameter contained three glass tubes, which guided three bodies falling simultaneously. They arrived the same time proving Galileo's law of free fall. Since the wheel represents Thales´ circle, force accelerating the bodies as well as distance are diminished by the same factor (cosine) resulting in the same time of fall, provided Galileo's law holds. The time would not be the same if speed would increase proportionally with distance, as was claimed by scholastic theory. Fig. 5, Gassendi´s wheel of free fall with three glass tubes G1 to G3 <details> <summary>Image 5 Details</summary>  ### Visual Description ## Diagram: Wooden Wheel Structure ### Overview The image depicts a simplified technical diagram of a wooden wheel. The wheel is circular with a gray outer rim and a white inner hub. Three radial spokes labeled **G1**, **G2**, and **G3** divide the wheel into three uneven sections. The text "Wooden wheel" is positioned at the top-left corner of the diagram. ### Components/Axes - **Wheel Structure**: - **Outer Rim**: Gray circular band. - **Inner Hub**: White circular area. - **Spokes**: Three radial lines labeled **G1**, **G2**, and **G3**. - **Labels**: - **G1**: Vertical spoke on the right side. - **G2**: Diagonal spoke from top-right to bottom-left. - **G3**: Diagonal spoke from top-left to bottom-right. - **Text**: "Wooden wheel" (top-left corner). ### Detailed Analysis - **Spoke Placement**: - **G1** is positioned vertically at the 3 o’clock position. - **G2** spans from the 1 o’clock to 7 o’clock position. - **G3** spans from the 11 o’clock to 5 o’clock position. - **Color Coding**: - The outer rim is uniformly gray. - The inner hub is white, with no additional shading or gradients. - **Textual Elements**: - "Wooden wheel" is in black, sans-serif font, left-aligned. - Labels **G1**, **G2**, and **G3** are in bold black text, placed near their respective spokes. ### Key Observations 1. The spokes are not evenly spaced, suggesting a non-symmetrical design. 2. The labels **G1**, **G2**, and **G3** are unambiguous and directly associated with their spokes. 3. No numerical values, scales, or additional annotations are present. ### Interpretation This diagram likely represents a conceptual or schematic representation of a wooden wheel, emphasizing its structural components rather than functional dynamics. The labels **G1–G3** may denote specific stress points, load-bearing elements, or assembly instructions in an engineering context. The absence of numerical data or motion indicators suggests the diagram is static, focusing on geometry rather than performance metrics. The uneven spoke spacing could imply a custom or non-standard wheel design, requiring further context for precise interpretation. **Note**: The image contains no numerical data, trends, or quantitative information. All descriptions are based on visible textual and structural elements. </details> This experiment could be repeated everywhere improving acceptance of Galileo's laws of free fall. In our times it can still serve as an impressive demonstration for students. The simultaneous arrival of three falling bodies is more convincing to novice students than digital readouts of computers or counters as it is used in many present day classroom experiments about free fall. Discussing free fall in his 'de mutu' letter, Gassendi draws a parabolic curve of throw claiming that speed is diminished as a body is thrown up the same way as it increases falling down following Galileo's law of odd numbers ('reciproce', 'de motu' article VII). Fig. 6. Parabolic path of body thrown, possibly the first drawing of physics in a modern coordinate system, from Gassendi, 1642. <details> <summary>Image 6 Details</summary>  ### Visual Description ## Parabolic Curve Diagram: Labeled Points and Segments ### Overview The image depicts a parabolic curve with labeled points and segmented vertical divisions. The curve is plotted on a coordinate system with labeled axes (x-axis: K to A; y-axis: J to B). The curve is divided into distinct segments by vertical dashed lines, and key points along the curve are labeled with uppercase letters (e.g., Z, X, T, Q, O, M). The curve peaks at points T and Q, then slopes downward toward M. ### Components/Axes - **X-axis (Horizontal)**: Labeled with uppercase letters from **K** (leftmost) to **A** (rightmost). - **Y-axis (Vertical)**: Labeled with uppercase letters from **J** (top) to **B** (bottom). - **Curve**: A parabolic shape with a dotted line, peaking at **T** and **Q**, then declining to **M**. - **Vertical Segments**: Dashed lines divide the curve into regions labeled with letters (e.g., **I**, **H**, **G**, **F**, **E**, **D**, **C**). ### Detailed Analysis - **Curve Labels**: - **Z**: Leftmost point on the curve, near the x-axis. - **X**: First labeled point on the ascending slope. - **T**: Peak of the curve (highest point). - **Q**: Second peak (slightly lower than T). - **O**: Point on the descending slope after Q. - **M**: Rightmost point on the curve, near the x-axis. - **Vertical Segments**: - Segments are labeled **I**, **H**, **G**, **F**, **E**, **D**, **C** (from left to right). - Each segment corresponds to a vertical division between the curve and the x-axis. ### Key Observations 1. **Symmetry**: The curve appears symmetric around the midpoint between T and Q. 2. **Peaks**: T and Q are the highest points, suggesting a bimodal distribution or dual maxima. 3. **Decline**: The curve slopes downward sharply after Q, ending at M. 4. **No Numerical Data**: The axes and curve lack numerical values, relying solely on alphabetical labels. ### Interpretation - The diagram likely represents a conceptual or categorical relationship rather than a quantitative one, given the absence of numerical scales. - The labels (e.g., Z, X, T, Q, O, M) may correspond to variables, categories, or stages in a process. - The vertical segments (I, H, G, etc.) could denote intervals or thresholds between key points on the curve. - The parabolic shape suggests a non-linear relationship between the x-axis (K to A) and y-axis (J to B) variables. - The absence of a legend or numerical data limits quantitative analysis, but the structure implies a focus on qualitative or categorical distinctions. ## Notes - **Language**: All text is in English. - **Missing Elements**: No numerical values, units, or legends are present. - **Assumptions**: The curve’s shape and labels are interpreted as abstract or symbolic rather than empirical data. </details> This graphic representation (Figure 6) of Galileo's law of odd numbers is possibly the first visualisation of a law of physics in a modern co-ordinate system. His arguments, which reciprocate Galileo's law of diminishing odd numbers when a body is thrown up, imply invariance of physics laws with respect to time variance. After his death the 'Institutio Logica' (Jones 1981) was published in Tours trying to simplify Aristotle's logic by a new scheme. The fourth part concerns methods of logic arguing and in its fourth canon he stresses logical implications of his experiments on a moving ship. Canon four conjectures that both reason and senses have to be taken into account arguing logically. The senses, however, have to be trusted more than reason, because 'there is the possibility that the reasoning is an inaccurate estimate or surface explanation only, the true reason for the phenomenon appearing to the senses as it does remaining hidden. For instance, although reason would at first persuade us that an arrow fired from the stern of a moving ship would fall not upon the same stern but into the sea some distance away, the ship having moved forward in the meantime, yet reason must give way to the senses, because experience shows us that it turns out differently and in actuality motion is imparted to the arrow not only by the bow but also by the ship itself (Jones 1981).' This example contradicts Aristotle. It is also a description of conceptual background naive beliefs held by many novice students today. The next example of Gassendi´s is based on Aristotle: '...People who used to believe that there were no people living in the Antipodes did so on the grounds that if there were they would fall downwards into the sky, but now that they have been discovered to indeed exist, this reasoning obviously loses its validity in the light of experience...' ## DISCUSSION. Consequences from Gassendi´s experiments to teaching physics Gassendi´s experiments are important for modern psychology of perception and also for teaching. Teaching movement of earth is still a difficult task today (Parker 1998). In many investigations about perception of movement, people believed that bodies lose their speed instantaneously and stop as soon as the force driving ceases. The psychologist McCloskey found that most students believe a ball dropped while running will fall down not in a parabolic fashion but abruptly and straightaway to ground (McCloskey 1980, Caramazza 1981). This phenomenon is called 'intuitive physics' (McCloskey 1980, Krist 1993). Similarly, Clement (1982) found that most students believe a rocket drifting in space will retain its speed before ignition (figure 7) when engines stop. Fig. 7 Rocket path question to investigate intuitive physics. <details> <summary>Image 7 Details</summary>  ### Visual Description ```markdown ## Diagram: Physicist's Answer vs. Typical Incorrect Answer ### Overview The image contains two schematic diagrams labeled **(a) Physicist's Answer** and **(b) Typical incorrect Answer**. Both diagrams depict a sequence of points (A → B → C) with directional arrows, suggesting motion or flow between these points. The diagrams differ in the trajectory from point B to point C. ### Components/Axes - **Labels**: - Points labeled **A**, **B**, and **C** in both diagrams. - Arrows indicate directionality: - **A → B**: Horizontal arrow in both diagrams. - **B → C**: - Diagram (a): Diagonal arrow (downward-right). - Diagram (b): Horizontal arrow (rightward). - **Text**: - Top diagram: "Physicist's Answer" (above the diagonal arrow). - Bottom diagram: "Typical incorrect Answer" (above the horizontal arrow). - **No axes, scales, or legends** are present. ### Detailed Analysis - **Diagram (a)**: - The path from **B → C** is diagonal, implying a change in direction (e.g., a vector with both horizontal and vertical components). - The arrow is annotated with 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</details> College students were asked about an object dropped from a mast of a moving ship, most students answered the object will fall and strike the deck behind the foot of the mast rather than at the foot of the mast (Whitaker 1983). Though 'intuitive physics' ignores the principle of inertia and follows Aristotelian physics and the false idea of impetus, it has been found in many investigations about students (Reif 1987, Clement 1989, Adey 1992, DiStefano 1996a, 1996b, Gautreau 1997). It is a serious pitfall when teaching beginner's classes in physics, therefore testing scores of students in physics remain low (Driver 1989, Licht 1990). ## CONCLUSION. Possible ways to improve concept change in teaching and learning. Beginner's difficulties in physics can be eased by the discussion of Gassendis´ experiments and repetition of these by students' observing for example falling bodies in a moving vehicle such as a car, a bus, a lorry or a boat as an out- of- school experience (Mahoy 1997). This kind of experience has been shown to improve learning (Donnelly 1998). To ease elimination of naive beliefs about movement, each individual can recall the long way mankind took to overcome these naive beliefs. Even a single experiment can induce a concept change in students; most efficient are hands-on experiments (Abbott 2000). Individual naive belief in physics is sometimes a recapitulation of a historic naive belief (Chi 1994). Approach to concept change is easier `in the light and understanding of the history of science` (Strike 1982). For example, computer simulation of Galileo's historic experiments with the inclined plane and water clock helped understanding of physics concepts (Borghi 1992). Suspense stories like ' Galileo and the inquisition ' raise emotions improving memory and attendance thus easing concept change, according to results of psychological research (Cahill 1994, Erk 2003). ## REFERENCES - Abbott, D. E., Saul, J. M., Parker, G. W., Bleichner, R. J., 2000. Can one lab make the difference? Physics Education Research. American Journal of Physics Suppl., 68 (7), 560561. - Abu`l Barakat, 1939. Hibatallah ibn ´Ali al-Baghdadi, al-Kitab al Mu´tabar . 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Journal Phys. , 51, 352-357. ## FIGURE CAPTIONS Fig. 1 Portrait of Pierre Gassendi1592-1655 Fig. 2 French Galley in 1675, 'Musèe de la Marine', Paris, (Mondfeld 1972) Fig. 3 Galley of French fleet 1692, 'Musèe de la Marine', Paris (Mondfeld 1972) Fig. 4 Galileo's inclined plane, reconstruction in the Deutsche Museum, Munich, Germany. Fig. 5, Gassendi´s wheel of free fall with three glass tubes G1 to G3 Fig. 6. Parabolic path of body thrown, possibly the first drawing of physics in a modern coordinate system Fig. 7 Rocket path question to investigate intuitive physics. ## KEY WORDS Galileo Gassendi Free fall Galley Principle of inertia STICHWORTE Galilei Gassendi Freier Fall Galeere Trägheitsprinzip