by Richard Frazier
For nearly a decade I have challenged my students (grades 7-9) to answer the question, "How did the Cartesian Diver get its name?" The students who have taken up this challenge have returned with little more than a description of the device and a conviction that the name is eponymous, that "Cartesian" is derived from the name of the French mathematician and philosopher Rene Descartes (1596-1650). Never has a student found a documented link between the diver and Descartes although some science activity books suggest Descartes was the inventor (Vilenkin in Kikoin, 1980). We have recently made a more concerted effort to pursue the question and have posted queries by electronic and regular mail to science educators, to researchers at science museums, and to historians and philosophers of science. We have examined works about and by Descartes but have not yet uncovered any direct connection. Several of our scholarly contacts have very generously provided suggestions, references, and even speculations. What we have concluded up to now is that a description of the diver is quite difficult to find in Descartes' main body of work. If a connection does exist, it must be extremely obscure. One of our early references speaks, however, as if the device (called a Cartesian Devil) were well known (Triewald, 1731). Descriptions of hydrostatic phenomena and designs for diving apparatus (such as diving bells) did appear in Descartes' era (Damerow et al, 1992, Marx, 1990, Tokaty, 1971). Hydrostatics did provide important analogies for thinkers like Galileo in the development of concepts of free fall (Damerow et al, 1992). Descartes contributed important ideas to the debate about motion before the development of Newtonian mechanics and would have certainly been in a position to reflect upon the many phenomena illustrated by the diver (Damerow et al, 1992, Garber, 1992, Shea, 1991). However, it is one of Galileo's students, Raffaelo Maggiotti, who is given credit for first describing the Cartesian diver or devil in writing (Rose, 1970). In a short pamphlet Maggiotti (1648, reprinted in Targioni-Tozzetti, Giovanni , 1780) speaks of the device as "my invention" ("L'invention mia non consiste nel caldo, o ned freddo; ma nella Renitenza all Compressione "). The diver has been falsely ascribed to Descartes (Damerow, 1994). The French do not refer to the diver as Cartesian but rather as ludion, a word derived from the Latin meaning actor, jester, wandering entertainer (Feral, 1994).
As a teacher, I am intrigued by the obscure beginnings of such a well-known object in classroom science. I have often wondered how many other classic demonstrations, experiments, and pieces of apparatus live on in schools as taken-for-granted rituals and relics of scientific knowledge. The nearly obsessive quest this year for the diver's origin has tempted me with digression into the many dilemmas of how best to promote children's learning of science. It is my students' best guess, however, as to why the toy was named for Descartes that suggests one route out of that quandary and that provides the focus of this article. Their answer, in a historically naive way, is a very good answer and may, after all, connect us with the very best of reasons for using philosophical toys in schools.
" The diver is named after a great philosopher because it makes us think." "Think about what?" "About explanations and evidence and about weight, pressure, movement and matter, water, gravity, floating and sinking, and forces and a vacuum."
In contrast to its hesitant appearance in the history of science, the Cartesian diver is nearly ubiquitous in science teaching. Two articles on the toy graced the pages of The Science Teacher within six months of each other in 1993 (Penick, Berg). Another article attesting to the pedagogical richness of the system was published in the same journal over a decade ago (Roberts, 1981). Within my personal library, I have found descriptions of the diver in a diverse set of "how-to" books of science activities (Barrett, 1963, Cherrier, 1978, Ehrlich, 1990, Marson, 1978, Van Cleave, 1985, Zubrowsky, 1981). At least one middle school science program, Foundational Approaches to Science Teaching (FAST) (Pottenger and Young, 1992), uses the diver as a central piece in activities devoted to building students' ideas about the relationship between buoyancy and density. With so much already said about the diver in science education, what more could be added? As Penick (1993) and Berg (1993) each expressed so well in their respective Science Teacher articles, the simple "Closed System" of the Cartesian diver is actually a rich and elaborate system, open and inviting to the practice of scientific investigation. At the same time, it is easy to take the diver for granted, to assume that correct explanations lie simply behind anomalous events, that the diver is, in fact, only a toy.
Toy or not, the diver never fails to fascinate middle schoolers. I usually provide them first with a simple version. These first versions we employ are constructed from 1.5 liter plastic soft drink bottles. For the divers themselves, we use inverted test tubes, medicine droppers, and small syringes fitted with a small lead sphere as ballast. (The syringe design appears in FAST 1 (Pottenger and Young, 1992)). The divers can be "tuned" so that they respond readily once they are in the bottles. It is easiest to adjust the buoyancy of the divers in a large open container of water before putting them in the bottles. The bottles need to be filled with water, the divers inserted open end down without losing the "adjusted" amount of water, and the lids tightened. The first time I give students the divers, they are all operational. I usually offer a brief introduction, including a speculation about the name and also some outrageous explanation for what is happening with the diver. For example, I might claim to demonstrate psychokinesis by driving the diver down with my thoughts; I actually squeeze the bottle imperceptibly. While the students can hardly wait to get their hands on the system, I assign two tasks. One is to describe and explain the behavior of the diver or divers as completely as possible; the other is to learn to construct and operate all forms (test tube, medicine dropper, syringe) of the device. I encourage students to draw pictures to accompany their descriptions and explanations.
Over the years, I have come to expect certain typical explanations. The fact that many of the same ideas are repeated again and again, in class after class, makes me think the concepts are worthy of some scrutiny. This year we used a portion of our diver activity with parents at a science forum. Three of the consistently offered explanations of students appeared as well with parents. It is not my intention to examine these "theories" here in regard to their position within the alternative conceptions research. I do think it is noteworthy that similar sets of explanations have been espoused in ten year's worth of science classes, an approximate total of one thousand three hundred students. I do want to outline each explanation carefully and will use the most recent set. The fun really begins once we articulate the theories. Each has been named to make discussion easier.
The Theories of How the Cartesian diver Works
The Heaviness Theory: Squeezing the bottle forces water into the diver. More water makes the diver heavier and causes it to sink. Releasing the bottle allows the compressed air trapped in the diver to push the excess water out. The diver becomes light enough to float again.
The Air Theory: Air makes things float. When the air by volume of an object is reduced to a certain point, there's not enough air to hold the object up and the object sinks. The diver works because squeezing the bottle compresses the air to the point where it cannot hold up the diver. When the bottle is released, the air expands again to the point where it can hold the diver up.
The Pressure-Current Theory: Squeezing the bottle puts pressure on the water inside. The water tries to go up out of the mouth of the bottle. This can be seen when squeezing the bottle without a lid. When the lid is on, the water rebounds and carries the diver down. Releasing the bottle reverses this current.
The Pressure-Force Theory: Squeezing the bottle puts pressure on the water inside. Because the force of squeezing cannot move the water since it is enclosed, the force is transmitted to the diver and pushes it down. This transmitted force disappears when the squeezing stops and the diver returns to a floating position.
The Volume-Displacement Theory: Floating and sinking involves a relationship between the weight of an object and the weight of the water it displaces. For floaters, the weight of the floating object is equal to the weight of the water displaced. For sinkers, the weight of the sinking object is greater than the weight of the water displaced. The diver uses the pressure to cause different amounts of water to be displaced and thus change back and forth from being a floater to a sinker. The different amounts of displaced water seem to go in and out of the diver.
Depending on the year or the class, one theory or another may be most popular. Sometimes the explanations have nearly equal numbers of adherents. A few students want to combine the theories. A few think all the explanations are reasonable. Generally, the more standard the explanation (using density/constant mass/variable volume), the less likely it will be most popular. Most of the students offering explanations have already begun an investigation of buoyancy phenomena. Some may even have heard the story of Archimedes. The Heaviness Theory is typically very popular. In fact, five of the six "how-to" references mentioned earlier claim that adding water to the diver by squeezing makes it heavier. The FAST 1 Teacher's Guide (Pottenger and Young, 1992) treats the Heaviness Theory as a matter of definition. If water is included as a constituent part of the diver, then the Heaviness Theory is reasonable. The Pressure-Current Theory often precedes the Pressure-Force Theory. After testing students often abandon the Current theory, but the concept of pressure producing an effect does persist in some cases. Interestingly, the Pressure theories are often depicted with identical diagrams.
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Figure 1. Diagram produced for Pressure-Current and Pressure-Force Theories.
Lines of current or force are drawn from the points of squeezing up to the top and along the curve of the bottle. These lines then curve down upon the diver. In the past two years only one student (out of one hundred twenty) each year has offered a theory based on Achimedean principles. I suspect that the Pressure-Current and Pressure-Force proponents do not see the diver system as an example of buoyancy phenomena. The Heaviness Theory does invoke gravity as the source of the sinking force. The Air Theory has the fanciful hint of natural motion to the proper place; air goes up.
Once the theories are stated, clarified, and consolidated, I assign the students the task of testing each theory. They are to find new evidence for or against each theory. This evidence should be gathered by explicitly testing the consequences arising from each theory. Students eventually present their evaluations of the various explanations to the class. A variety of approaches are taken. Some students interrogate each theory vigorously as if they were trying to disprove each one. Some students hang on to their original idea; they cannot envision how it could not be true. Other theories present no problem. Some students are troubled by the fact that the theories are of different kinds. The Pressure-Force Theory invents a new cause while the Volume-Displacement Theory simply describes a comprehensive relationship. Some students are excited by discovering a new facet of the diver; others are unsettled by comprehending that they have evidence against a theory that still seems good.
Just as I have found the theories of the diver predictable over the years, I have found the tests of the divers incredibly innovative. Every year I learn something new, see a new piece of evidence or an old piece in a new light. The air of discovery and debate takes over the science class during this theory testing time. New ideas are borrowed freely; new techniques are invented and revised. Some of the tests have been so unique, they must be described. Few of these tests have been described in any of the references I have ever seen. Most have been developed by middle school students.
Tests of the Theories of How the Cartesian diver Works:
According to the Heaviness Theory, a diver closed to the water should not work since water cannot enter to make it heavier. A test tube with a balloon stretched over the mouth can be adjusted to operate as a diver. In fact, a slightly inflated balloon with a marble or lead fishing weight stuffed inside can operate as a diver.
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Figure 2. Photograph of student operating a "closed" diver made from a balloon with a small fishing weight stuffed inside. Balloon floats inside water-filled plastic soft drink bottle until the bottle is squeezed.
The ability of a closed diver to sink and float is considered by most to be a serious threat to the Heaviness Theory. Closed divers are useful in other tests because the bottles can be turned upside down, dropped, and spun. Some strict proponents of the Heaviness Theory will argue that the closed divers operate along different principles than the open classic Cartesian divers.
According to the Heaviness Theory, a syringe should get heavier when more water is added. When a syringe is attached by a piece of thread to a sensitive spring scale and water is added the syringe does get heavier when the weighing is done in air. For a syringe that is in the sinking state and is weighed under water, adding more water does not appear to change the weight. This is an ambivalent test for some since the syringe has crossed the buoyancy threshold when the underwater weighing is performed.
A series of tests can be carried out in a vacuum chamber with the balloon diver described above. The balloon and weight should sink when placed in water at atmospheric pressure. When the chamber is evacuated, balloon should inflate and float. If a graduated container is used inside the vacuum bell, the displaced water can be measured when the balloon is both a sinker and a floater. A small spring scale can be placed inside the vacuum bell to see how the weight is affected by inflating and deflating the balloon. These tests support the Volume-Displacement theory and challenge the heaviness theory in that the weight cannot be observed to change. The two Pressure Theories do not seem helpful in these cases since the pressure change does not come from a particular direction. The Air Theory is usually seen to be supported by the balloon diver in the vacuum chamber. Some proponents of the Air Theory see it as very similar to the Volume-Displacement Theory.
A balloon diver and a floater made of some other material (a toy plastic animal) are placed in a squeeze bottle. The bottle is flipped end over end or is spun on a table. Currents of water carry the two objects around the inside of the bottle along similar paths. The bottle is then squeezed and only the balloon sinks. Currents can move floating objects around in the bottle, but squeezing cannot produce a detectable current.
The most exciting tests involve trying to operate the diver during free fall. The two Pressure Theories and the Air Theory seem to invoke causes other than gravity for the diver's movement. Most students agree that if the Pressure Theory is true, whether the bottle falls or not is irrelevant; only the squeezing is important. At the school pool students practice jumping off the diving board while operating the divers. The following situations are produced. The student jumps and squeezes the Cartesian diver bottle. The student squeezes and jumps. The student squeezes, jumps, and then releases the pressure. The student squeezes, jumps, and releases the bottle. The freely falling diver gives nearly everyone, including adults, a pause for reflection. Is the Cartesian diver an example of buoyancy phenomena? Do floating and sinking involve gravitational force?
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Figure 3. Student jumping from a diving board and operating a Cartesian diver system. The balloon diver works well with diving board experiments because they will operate even when the bottle is turned upside down.
The most clever test I ever saw of the Air Theory involved the subtle use of a vacuum. A student took a fifty cubic centimeter syringe with the plunger in, fitted it with a rubber hose and clamp, and attached a solid plastic cylinder. The whole assembly was made to sink in a large container of water. The student then removed the syringe from the water, pinched the hose, and clamped it shut. She then pulled the plunger open and wedged the plastic cylinder between the end of the plunger and the edge of the barrel to prevent the plunger from closing in response to atmospheric pressure. The student demonstrated that the space inside the syringe did not behave like air by opening the hose under water and allowing water to fill the syringe. She emptied the syringe of water, then locked the plunger open again, and placed the assembly in the water. The syringe floated even though no air was added. The student was able to change the buoyancy of a device similar to the Cartesian diver without changing the weight or adding air. The ensuing discussion about the rationality of the vacuum would perhaps have even impressed Descartes.
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Figure 4. Diagram of a diver to test the Air Theory. A syringe that is held open against atmospheric pressure still floats even though no air has entered the diver.
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Figure 5. With no air and with no vacuum and with no change in mass the syringe can be made to sink.
After the Air Theory students have the most trouble finding ways to test the Volume-Displacement Theory. Some try to check the Archimedean relationship by weighing objects and the water they displace. When only a few middle schoolers perform such a test, the results are equivocal; variation in measurement can be large. Some groups feel the variation in their results challenges the theory; some feel that the other theories have so much against them, that the Displacement-Volume Theory must be correct. Still other students completely ignore the Displacement-Volume Theory, perhaps because it fails to offer a cause even though a comprehensive pattern is described.
A class of twenty four usually tries about ten to fifteen different tests in a three day period. At the end of that time, each group presents their findings and their choice of the most workable theory. Though all the theories have been tested and each theory has someone who thinks it discredited, each theory still retains some support. We compile all the supporting and all the challenging evidence and then try to evaluate which theory has best survived our intense scrutiny. It is interesting to watch students engage in a discourse about explanations and evidence. Students take a variety of positions as they discuss and negotiate a class evaluation of the theories. Not all evidence speaks for itself; there are times when the same observed effect is interpreted in opposite ways. For those students who feel that there must be some authoritative answer, we look at a range of references. Even published works may propose an explanation we have discredited, may conflate explanations, or may propose a detail we have never observed or considered.
We often extend the discussion to the diver in disguised forms such as the swim bladders of certain fish (Lerman, 1986) or a piece of vacuum technology, the Dubrovin gauge (Roth, 1982). We have also encountered new puzzles in trying to develop more elaborate tests of the students explanations of the variable buoyancy of the Cartesian Diver.
One of these demonstrations involves the introduction of a new factor, temperature, which produces a seemingly complicated effect. . The buoyancy of an inverted test tube with the end left open is adjusted so that it just sinks in ice water. A small vial with a rigid, watertight cap is adjusted so that it barely floats. Water, lead shot, or sand can be used to adjust the buoyancy of the vial. The two objects, one floating and one sinking, are placed in the same container filled with ice water. The water is then warmed; at some point during the warming, the two objects will swap positions. The floater becomes a sinker and the sinker, a floater. With care, the initial buoyancies can be adjusted so that the test tube and vial shift places simultaneously. The variable buoyancy of a rigid, closed object soon brings back a cousin of the Pressure-Current Theories where the new effect is attributed to temperature. The Heaviness Theory claims the concept of heat as substance; some students think the vial gets heavier when heated. The fact that the two objects go in opposite directions under the same conditions definitely reinforces the idea that complacent understanding does not always last with scientific theory-making.
The other demonstration is puzzling precisely because a test tube in a bottle appears to reverse the behavior of the Cartesian diver An inverted test tube containing an amount of air insufficient to keep it floating is dropped into a 1.5 liter plastic soft drink bottle. The test tube should have enough air so that it remains vertical with mouth down on the bottom of the bottle. The sides of the bottle are then struck vigorously with a stick or the sides of the hands. The blows need to be sharp enough to propel the tube upward. Blows can be repeated with a frequency that keeps the tube suspended in the bottle. Some students see the blows as analogous to the squeezing of the Cartesian diver bottle but as producing an opposite effect; these students often argue from contraries. A sinking tube will rise when the bottle is struck; a floating tube will sink when the bottle is squeezed. I have seen several students encounter this event independently, but no one has ever tried to develop a complete explanation. The "drum" diver remains as an unincorporated anomaly in our knowledge of the Cartesian diver.
Students reach a level of tentative certainty in their knowledge of the Cartesian diver, unsettled with the idea that it may not be possible to find the book where the final truth is written but invigorated with the accomplishment of having thoroughly investigated a compelling physical system. Toy that it is, the Cartesian diver does live up to its Philosophical designation.
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Damerow, Peter, (1994), personal communication, e-mail: "I can tell you, that the Cartesian diver was first described 1648 and later erroneously (?) ascribed to Descartes."
Damerow, Peter, Gideon Freudenthal, Peter McLaughlin, and Juergen Renn, (1992), Exploring the Limits of Preclassical Mechanics, Springer-Verlag, New York.
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Feral, Isabelle, (1994), personal communication. Miss Feral writes from the Conservatoire National des Arts et Metiers in Paris.
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List of Figures to accompany "A Philosophical Toy"
Figure 1 -- A diagram often produced by students trying to explain either the Pressure-Current or the Pressure-Force Theory.
Figure 2 -- Photograph of student operating a "closed" diver made from a balloon with a small fishing weight stuffed inside. Balloon floats inside water-filled plastic soft drink bottle until the bottle is squeezed.
Figure 3 -- Student jumping from a diving board and operating a Cartesian diver system. The balloon diver works well with diving board experiments because they will operate even when the bottle is turned upside down.
Figure 4 -- Diagram of a diver to test the Air Theory. A syringe that is held open against atmospheric pressure still floats even though no air has entered the diver.
Figure 5 -- With no air and with no vacuum and with no change in mass the syringe can be made to sink.