language switch

A consideration of how we must do it in order to one day be able to use cad assisted by artificial intelligence.(Part2)


Can you use the terms “double contingency” and “contingency” to describe the oral system and tooth production?

Let me describe the human “jaw system as an entity” in terms of the autopoiesis concept. When the actuation switch, “mandibular movement,” is turned on, a structure and system emerge. When the actuation stops, the system disappears and the “component” becomes a free-way space (interocclusal distance).

# What is a free-way space (interocclusal distance)? In the rest position of the mandible, there is no occlusal contact between the upper and lower teeth. There is a vertical gap of about 2 to 3 mm between the upper and lower jaw teeth at the central incisor. This void is called the free-way space (interocclusal distance), which is a relaxed state in which the oral cavity is not performing any special function.

The mandible operates to create a structure called the “jaw system,” which is distinguished from the structure and the environment. The environment then includes the dentition of the upper and lower jaws, periodontal tissues, tongue, lips, and jaw joints. The “component” is the change in space between the occlusal surfaces. The network of the production process consists of four elements: “action,” “component,” “structure,” and “environment. The network of producing processes produces the “component.” When the mandible ceases to operate, the “component” becomes a resting position void. In other words, when the mandible is activated, the “component” determines the structure.

The question is how contingency and double contingency explain the generation of teeth, but the two create a system. Double contingency is such that it “renounces and changes the status quo, is the only one that is selective, and is also symmetrical, community oriented, and maintained forever by circulation.” Contingency would be such that it “has mercy, continues the status quo, is overwhelmingly selective, and is also relative, collective, and causally oriented, and therefore will eventually disappear.”

Contingency is the element that moves the system forward and keeps it going. And double contingency is the element that changes the system. This is an expression of tooth generation from two standpoints, one from the social sciences and the other from the natural sciences. It is the very mechanism that generates and maintains itself. Luhmann used the double contingency as the basis for the establishment of his social systems theory. In other words, in Luhmann’s system theory, the double contingency is an important component of the system.

It means that contingency and double contingency are the components of the system. These two elements formed an order and formed the current occlusal system including the jaw, joints, and teeth. The “jaw system” as an entity was then created. It also means that the social system, to which man is an emergent entity, is accessible only when he stands at a point where he can divide it into the elements of contingency and double contingency. No other point is sufficiently accessible.

By setting up the pair of contingency and double contingency, we can clarify each other’s meaning, value, and other aspects of existence. The reason why this is possible is that they are both hypothetical and complementary terms created for human beings.

Thus, the concept of autopoiesis is expressed from a standpoint that combines the opposing views of the social sciences and the natural sciences. Social science is a hypothesis about the world from the standpoint of human beings, which can be rewritten through new discoveries. Natural science is also a hypothesis about the world from the standpoint of nature, and may be rewritten in the future due to new discoveries.

The situation in which humans are compelled to be centrally involved in the world will continue as long as humans exist. The social and natural sciences are one way of describing the world, and each exists on its own, in a way that the two separate hypotheses support each other.

This is the idea that when human beings are involved in the world, it is necessary to separate them with the “scalpel of responsibility”. The idea is that by dividing the world into two, we can view the social and natural sciences from that cross-section. The world is never two, but one.

At the present time, I believe that the idea of dividing the world into social and natural sciences is an idea in which humans have great faith, among other hypotheses. Natural science is the half of the world that we have carved out in terms of human responsibility, and that natural science cannot exist independently in the world without human existence and responsibility.

Life forms have a destiny of continuity and change with respect to their existence, and I believe the same is true for the universal common consciousness of human beings. I believe that this subconscious awareness that every human being has to deal with a destiny that is predetermined even before birth has led to the formation of the system of human society. That is social science.

Luhmann considered the world to be a complex system that is structured by meaning. Luhmann’s system theory based on autopoiesis is characterized by the fact that the world and human society are always viewed as a complex system, that the fundamental unit that forms the world and human society is “meaning,” and that everything that processes or edits the “meaning” that humans perceive is derived from the system. This is to say that all the processing and editing of “meaning” as perceived by human beings is derived from the system.

The concept of autopoiesis is a scalpel that separates the black box of the natural world into the natural sciences and the social sciences, requiring reference to both positions. They do not have a side-by-side relationship, but rather a specified relationship, such as (A/non-A) or (system/environment) to each other.

How do you think the teeth came to be in their present form?

Let me refer to the concept of autopoiesis in terms of tooth generation. The concept of autopoiesis includes elements that are not completely manageable by humans. However, it is expressed in a positive sense in the theory. The expression is positive, but I suppose it means that it is something that cannot be determined in one way or another. It may mean that there are things that exist in the real world that we cannot know how and why they came to exist in the way they do today. This was attempted with the special intention of expressing this from a human standpoint. Since teeth are not created by humans, it is probably a natural consequence for the teeth themselves, including the element of evolution, that they have come to exist in their present form.

The reason for this is that, with very great probability, teeth, regardless of race or ethnicity, have a similar shape in the same area, even if there are some individual and racial/ethnic differences. We know the conclusion, but we do not know the process by which it was made. Thus, I think this concept is necessary to understand the nature of tooth shape.

I believe that Japan needs a dynamical systems theory with the concept of autopoiesis as an element. If you advocate “Japan is a manufacturing power,” I would like you to deal with this issue.

The autopoiesis concept, in part, allows us to hypothesize about the process of tooth and dentition formation. The hypothesis would allow for human involvement in the generation of teeth. If it is found to be useful, it would mean that the hypothesis has some validity. This “process of formation” does not mean that we can explain the process of tooth development and gradual formation in the fetus. It is very difficult to say how the teeth formed into their current shape.

From an archaeological perspective, apes, which are thought to be the ancestral relatives of the hominids, have jaws and teeth similar in structure to those of present-day humans. The basic structure of the “jaw system as an entity” existed long before humans acquired language as we know it today.

Apes today are also highly intelligent and lead social lives. Although their language is less sophisticated than human language, they communicate and share emotions and intentions through vocalizations and pronunciations. It is thought that the ancestors of humans were similarly intelligent. Since apes are vertebrates and have vocal cords, it is likely that our ancestors also had the functions of mastication, vocalization, and pronunciation at the same time.

This is the independence of multiple systems in the autopoiesis concept. The “mastication system” and the “speech and pronunciation system” are duplicated in the same “jaw system as an entity.

Today, I believe we have not only this “masticatory system” and “speech and pronunciation system” but also an “aesthetic system”. Using the system theory based on the autopoiesis concept, we can hypothetically express “how the tooth shape was formed into its present shape” in terms of the system, albeit roughly and partially.

What factors could have caused the tooth to be produced?

When the autopoiesis concept is used to explain tooth generation, there are two terms as communication codes responsible for functional differentiation, and they are extremely important. One is called contingency and the other is called double contingency. Contingency is a very important word, yet its meaning is very difficult to understand.

Once again, this image of “dependence” is often translated as “possibility of another kind” or “functional equivalence,” or explained as “contingency,” “contingency,” or “inherent contingency,” but this is not clear. There are two semantic constructions of “contingency” in the Anglo-Saxon tradition.

One is “contingency,” which in everyday terms means “depending on something.” The other is “contingency” in the sense that other things are possible, thus as a negation of impossibility and necessity. This is one of the key terms for systems theory expressed in the concept of autopoiesis.

Therefore, everything that is uncertain or indeterminate for human beings is also implied as contingent. Furthermore, the possibilities that may arise are also considered contingent. Contingency involves the “inherent contingency” that exists in everyday life, and it also involves the “nature of occurrence” of things.

First, let us use the term contingency to describe the fact that the shape of the teeth was determined as it is now. The contingent is the sequence of events that accompanies the fact that the universal shape of the teeth has been determined as it is now, by a contingent event.

This is a representation that is created because it expresses an event in which humans are not involved, such as the generation of teeth, from a human standpoint. A sudden incident or accident is expressed as “I didn’t expect this to happen to a contingent.

To be contingent means, first of all, to be aware of coincidences and contingencies. It means being aware of their existence. It means that the occurrence of change in the state of continuity and its response are required, and that one’s own projection is directed toward the direction of progress.

From the standpoint of the tooth, the tooth perceives the contingencies and coincidences that have occurred to it, its origin, and where it is going. It edits anew all the events, information, perceptions, and contemplations that come in and out of that contingent occasion. This is what it means to be contingent.

Let me try to describe it simply. The forerunner of teeth, which at some point realizes that it is forced to exist in the world, becomes aware of these things through anxiety, looks at its current situation, and from there, reassesses its own shape and structure anew. From there, I think it can be expressed as starting to form a new shape and structure.

We believe that the present tooth shape was generated by this repetition. Of course, teeth are not supposed to have a mind or consciousness, but since there is no appropriate way to describe them, we have put ourselves in the shoes of the teeth. The approach is still one that appeals only to physical and chemical laws of nature, without the help of supernatural forces or principles.

Another term used in Luhmann’s systems theory is double contingency. Combining this term with contingency makes it self-referential and can further explain the generation of teeth.

By defining the state of reality as the result of what has been done by chance, it means that the operation of the autopoiesis system is entirely by chance. In other words, it is open to chance. The term “double contingency” was originally coined by Parsons and used in Parsons’ social systems theory, but Luhmann changed Parsons’ double conditional dependence to his own interpretation.

Luhmann is similar to Parsons in the cycle in which what one does is a precondition for what the other does, and vice versa. Unlike Parsons’ “based on shared values,” however, Luhmann sought the basis for the establishment of a social system on the basis of dual conditional dependence.

It is a model in which two parties face each other, both with their own requirements and viability. One depends on the other’s way of doing things, and the other depends on this one’s way of doing things. In other words, the instability of the “if you do what I want, I will do what you want” cycle, a situation that is not determined by any of the systems involved, creates a self-referential and autonomous functional differentiation.

Luhmann held that such emergent occurrences point the way to the formation of social systems. I think what Luhmann has in mind here is the emergent property of a system, which is a structural property of the system. I believe the same is true for tooth generation.

What is the virtual kinematic axis method?

In order to experiment, I have built a special articulator in which the motion of the left and right mandibular head can be represented by a curve. For this purpose, I have to obtain data on mandibular motion according to that method. One method is to use a pantograph to obtain curve data, but here I used two check bites on each side during lateral movement. This articulator was not made for use in clinical cases. Therefore, it cannot be used in clinical cases.

One method for determining the amount and direction of mandibular motion is to use a check bite. Normally, one check bite is taken for each lateral movement. In the case presented here, however, two check bites are taken on one lateral movement.

In the case of the method using a single check bite, the movement of the mandibular head on the working side is ignored. This method has been used for semi-adjustable articulators. However, the two check bite methods introduced here handle the working side differently. The Bennett movement of the working side will also be reproduced with a curve.

Semi-adjustable articulators have no adjustment mechanism for the working side of the condylar path, and its path of motion is predetermined by the intention of the articulator designer. The adjustment mechanism of only the non-working side cannot accurately reproduce mandibular motion. The Bennett movement, which is the movement of the working side, has been ignored as a slight blur, and the adjustment mechanism of the condyle path of the non-working side only has been used.

The method of using two check bites, presented here, allows the correct reproduction of mandibular motion in the articulator, with the same response to the movement of the mandibular head on the working side as on the non-working side. With one on one side, the path of motion is a straight line, but by using two on one side, the path can be curved. Also, while anterior and lateral movements of the mandible are usually required to create a dental prosthesis, posterior movements could be incorporated into the creation of the condylar path if you so desire.

Two check bites are used per unilateral lateral movement; the first check bite is occluded between the maxillary and mandibular dental models. The mandibular momentum is measured by measuring the movement of the left and right condylar balls of the experimental articulator and the tip of the incisal pin. The amount of movement of the condylar ball is measured by measuring the gap between the condylar ball and the inner, posterior, and upper walls with a gap gauge. The amount of movement of the tip of the incisal pin is measured by measuring the amount of movement of the incisal table and the tip of the incisal pin. after the measurement of the first check bite is completed, a second check bite is occluded and measured in the same way.

The data just measured is applied to an experimental articulator reconstructed in CAD to reproduce mandibular motion. In this case, we used four check bites for lateral movement on the left and right sides and one check bite for anterior movement. A total of five check bites were used.

Traditional mechanical and electronic pantographs have been used to measure mandibular movement. This method is too loaded for a dental technologist to mention, and if one wishes an explanation of how to use such an instrument, the dentist should be in charge of the explanation.

The transfer of data from the body to the articulator requires very careful handling when using such a measuring device. The positional relationship from the body to the articulator must be strictly transferred and reproduced on the articulator so that the relationship between the body and the reference plane is the same as the relationship between the articulator and the reference plane. It may also be necessary to reproduce the distance between the left and right mandibular condyles of the body on the articulator.

Actually measuring the distance between the left and right mandibular condyles of the body is a difficult task. Careful attention must be paid when transferring the maxillary model to the articulator. This is because any error in this process will render the physically precise measurement of the angle of the condyle paths meaningless. The angle between the reference plane and the condylar path as measured by the pantograph is input into the adjustment mechanism of the articulator, but it is essential that the reference plane set on the body be accurately reproduced on the articulator.

Thus, when measurements are made by the conventional pantograph method, strict instrument handling is required.

Here is one of the features of the virtual motion axis method. When reproducing mandibular motion with an articulator, even if the distance between the left and right mandibular condyles on the body and the distance between the condyles on the articulator are different, the difference in distance does not cause accuracy problems in the reproduction of motion.

The usual check bite method uses the change in position of the mandibular dentition relative to the maxillary dentition to obtain the motion path of the condyle ball of the articulator. Since there is only one check bite, the motion path is a straight line. In the mechanical or electronic pantograph method, the change in the position of the condyle head is measured with the reference plane as “0” and calculated as the condylar guidance inclination. The measurement principle is different from the check bite method.

The method using two check bites takes advantage of the change in position of the mandibular dentition relative to the maxillary dentition to obtain the motion path of the lower condylar ball of the articulator. Since two check bites are used, the path of motion is curved.

Adding another check byte adds a midpoint to the motion path of the condyle ball. The motion path of a condyle ball is represented by a curve. Usually, the curves are circular arcs, which are easy to handle in CAD. I wanted to realize this example, so I built a special articulator to obtain the curved path of motion of the condylar ball needed for the experiment. And I made a video of it.

What kind of articulator is born from the category of uniqueness and diversity, a new way of thinking, and which employs the virtual kinematic axis method?

In conventional articulators, a mechanical adjustment mechanism similar to a condyle path is created and set on either side of the upper part of the articulator. It is the mechanism that allows the lower part of the articulator to rotate and slide.

The improvement is that the motion path can be freely machined from a resin block, or a 3D printer can be used to form the motion path. In other words, it is free from the mechanical adjustment mechanism that the articulator’s designers had in mind. The guide surfaces can be created any way the operator thinks fit. The most important thing is that the path of motion of the condylar path can be expressed as a curve. It is also possible to reproduce the Bennett movement on the working side.

The operator can add elements to the path of motion that would otherwise be omitted due to chance in the operation of the measurement. The ease of customization by the user is an advantage of the method of machining from a resin block or using a 3D printer. If the motion pathway is simple, the left and right condyle and incisor pathways can be formed as in the conventional method.

The category of uniqueness and diversity means that the user can arbitrarily choose a motion path from among the many mandibular motion paths acquired. As with the body’s mandibular motion, it is not possible to reproduce a number of motion paths in an entity’s articulator. The motion paths to be given to the articulator should be those that are necessary to produce a dental prosthesis. The CAD system can reproduce all of the motion paths that have been obtained, and it can also reproduce the movement of the mandible during opening and closing, which has not been done in the past.

In view of the fact that dentists are inconvenienced, dental technologists have created a theory of occlusion!

I am a dental technologist and I see and hear messages about dental technology from dentists fragmented from published cases in professional journals and at lectures. It is now common practice for dental technologists to reconstruct these messages to fit the individual cases of dental laboratory work that is their practice. However, there is no guarantee that this method will produce a prosthetic that is satisfactory for both the patient and the dentist!

The reason for this is that the dental technologist has no contact with the patient and may not be able to fully fulfill his/her responsibilities if entrusted with the task without sufficient information. I would greatly appreciate it if the dentist would integrate the problems that exist in each individual case, optimize them for that case, and present them to the dental technologist as a concrete image. Optimization also means that it is important to be able to fully explain to the patient how the prosthesis will be made, and it is not enough to just say that the prosthesis has been “optimized”. It is not sufficient to think that what is not bad is good, or that if it is not bad, it is good. This is a recommendation for dentists who want to put their own ideas into dental prosthetics.

Recognizing changes in the space between the occlusal surfaces of the upper and lower molars

It is difficult to come up with a plausible answer to the question of why teeth were created in the mouth, and we cannot go beyond the realm of hypothesis. Or is it safe to assert that teeth were indeed created for biting, and that they are based on such an assumption? The issue here is not whether or not biology as a philosophy, such as evolution, is correct. When human beings become aware of themselves, when they recognize that there are things that exist without being directly visible, and when they try to manage and maintain these things, it is necessary to consider things that are not directly visible.

When we consider purpose and means, the purpose is what we cannot see, and what we can see is the means. In order to do this, tools that have not been used in the past, such as computer aided engineering (CAE), are necessary, and without such tools, it would not be possible to carry out the project. The shape and structure of teeth are created by the laws of nature. How can human beings use these laws and how can they be involved? There are not many systems theories that go beyond the conceptual level of the laws of nature, and can refer to specific mechanisms. I suggest that we adopt a systems theory called autopoiesis.

Autopoiesis recommends considering from which perspective (1) overlapping functions, (2) supporting outcome media, (3) types of codes, and (4) classification of programs. There are binary codes that humans should check in advance because they are performed by humans, and here we will focus on doing dental work and making dental prosthetics.

For prosthetics that have been designed and optimized by the dentist down to the last detail

Even today, I believe that basically anything approved by a dentist and set in the mouth can be considered an optimized dental prosthesis. In other words, the definition of “optimization” is a concept and method that is in line with the concept of autopoiesis. So what are some specific examples of optimization?

As for the complex cases of the natural world, I believe that we need a method that is appropriate to the subject we are dealing with. Science can expand the range of what we can refer to the natural world by increasing the options of possibilities that humans can think and think about. Complexity reduction means that humans will be able to handle complexity. It means changing the levels and channels of human thought at will. To handle complexity, we must acquire a way to understand and operate it. Anyway, the natural world is very complex, and the more we know about it, the more complex it is waiting for us. We can say that optimization is to make sure that humans have sufficient management control over their objectives.

I say “full area reproducibility articulator system” and “cad assisted by artificial intelligence” because it seems to me to be an application of a symmetrical concept and an example of its practical application.

I am a dental technologist. I believe that the dental technologist was requested to speak on the creation of dental prosthetics, which is not the dentist’s point of view.

If ideas based on conventional ideas from dentistry, “solely for the purpose of advancing dental care,” were required, I believe that it could have been done by dentists in the name of their central position in dental care and their responsibility regarding dental care. Japanese universities should have a system for such research, so it could have been done at a suitable research institution without having to be done by an individual like myself.

I have continued to prioritize this project above all else because it seemed to me that the request to put “full area reproducibility articulator system” and “cad assisted by artificial intelligence” out into the world by all means was a request from “Almighty God.” Had I not felt that way, I would not have become a Christian, nor would I have created such a thing. Continuing to do so would only cost me money and gain me nothing. Also, if a dental technologist proposes a “definition concerning the centric relation”, he will be called a “very naive or innocent person” and no one will take him up on it. (Reference URL:

Nevertheless, I continued to do so because I had the feeling that there was a strong request working from “God Almighty” for me to express dental technology in a new way and to modify the conventional method.

That is, “The only way that the Japanese can build the future that they themselves desire is to make something practical out of a symmetrical concept in the real world, and show us the process of doing so.” This is what I mean. I think it is to propose a “definition concerning the centric relation” from a new point of view that has not existed before, and to show the technological results concerning it.

I believe that by not being involved in treatment or diagnosis, dental technologists can speak to a perspective on tooth shape, etc. that has never been seen before.

Is it true that the uneven occlusal surfaces of the molars were created for biting things?

Is it a new discovery to find a reason for the formation of teeth around the mouth, or is it one of the hypotheses that can be drawn from a number of facts? Is it a natural selection of individuals that accidentally formed tooth-like hard objects around the mouth but remained as they are because they are very good for getting food into the body? I have never seen a dental treatise that makes such a sweeping statement as “the uneven occlusal surfaces of the molars were created for biting”. Perhaps this is because their origin is not considered particularly problematic for dentistry. I think it means that at the moment it is treated as a hypothesis.

By the way, Newton recognized that the phenomenon of an apple falling when you let go of your hand was special, and he named it gravitation and discovered its law. It is not necessary to mention it now, but the phenomenon of falling actually means that objects are attracted to each other. Newton, an English physicist, discovered that all objects with mass have an “attractive force”.

This phenomenon is named “universal gravitation.” The universal gravitation between two objects is proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them. The tides in the ocean are also caused by the “universal gravitation” between the earth and the moon. If we simply take it for granted that an object will fall out of our hands, it will not be a subject of special interest and will be treated as a phenomenon that we dare not mention.

The reason why Newton was able to recognize it was because he recognized it as uniqueness in “falling. Newton experimentally formulated and proved that universal gravitation is a force that occurs in all things with mass as a mathematical formula. It has been pointed out that he made a great achievement in systematizing universal gravitation through experiment and theory.

The discovery of gravitational attraction and the discovery that “the bumps on the occlusal surface are there to make it easier to bite” are essentially the same thing. These are both created by nature. They were not created by humans. However, chewing with teeth is something that not only humans but also other animals do on a daily basis, so there is nothing to say now about the reason for the existence of teeth. In using them for dental technology in dentistry, I will try to express them again.

The idea that there is some objective reason in nature and that a mechanism based on that reason created teeth around the mouth is an idea that arises from the categories of necessity and chance. It is very difficult to discover the reason. It would be an extremely difficult task to try to think about or explain the generation of teeth in this way. We have to start not with the occlusion of monkeys, but with an earlier generation.

By using the categories of uniqueness and diversity here and combining natural and social sciences, we can begin our research with the human generation. Since the purpose of the research is human occlusion, it serves the purpose. It is my opinion that if we gradually work our way bottom up by building up from a natural science standpoint, we will never get to the bottom of why the unevenness of the occlusal surface of the molars was created. It seems to me that since it was created naturally, natural science should be able to solve everything, but apparently that is not the case.

I believe that humans need a pair of natural and social sciences to understand the world. Living organisms are not created by humans. I believe that we need access to both sides to understand and unravel the whole mechanism of such things.

I think the answer to the question of why this is so is that the traditional bottom-up method of accumulation did not work, so we invented other methods, which led us to the idea of autopoiesis. I think it is extremely difficult to explain organisms in an orderly manner from their development, in other words, to explain how the mechanisms of organisms came to be the way they are from the beginning, as in the case of evolutionary theory.

There are many aspects of how organisms work that are not explained by Darwin’s theory of evolution. In particular, it is said that there is no mention of the development of organisms. I think that the way to access the mechanisms of the human oral cavity is to access the presently recognizable oral cavity from both the natural and social sciences to get at the objective. I do not think it is necessary to “go back in time” on an archaeological level.

I believe that the natural and social sciences are paired, but never in opposition to each other. Therefore, I believe that incorporating the two sciences into the same subject does not create a contradiction; when dynamical systems theory is applied to one subject and the question of priority is asked, the natural science takes precedence over the social science. The dynamical systems theory presented here is also called emergent dualism, and it gives priority to the contingency side over the double contingency.

By the way, crowns, inlays and ceramic frames are designed using general purpose CAD (Solidworks). Creating and editing tooth geometry in this general-purpose CAD is a very time-consuming and labor-intensive process by hand, even if the number of teeth is small. If you use a dental-specific CAD system, it may be easy to operate because it has dedicated commands. However, it is quite difficult to operate a dental CAD system with a general-purpose CAD system. When editing the outline of a crown, the basic shape is first read in, and then the outline is deformed by moving the edit points according to the case. Particularly difficult is the editing of inlays. It is very difficult to create a surface just for the missing part of the occlusal surface of a molar. General-purpose CAD does not have such dedicated commands. It is not impossible, but it is difficult. Examples of these creations are shown in the video later in the text.

If these tasks were performed directly by humans, they would be time-consuming, labor-intensive, and impractical. To perform these tasks efficiently, we would definitely like to take advantage of the capabilities of artificial intelligence. Doing them manually is nothing short of a painful process.

Deep learning 3D polygon mesh representation learning determines the most important high-level features that describe how a group of meshes are displayed so that any point in that feature space is a qualified spatial representation.

New representations created by manipulating the values of features in the feature space have a higher probability of looking like real teeth when transformed back into the original polygon mesh region than if a human attempted to manually manipulate individual meshes directly. These can be represented by mathematical formulas or programmatically.

On Descartes’ Theory of Biomechanics

 (Descartes’ philosophy and the problem of theory of biomechanics, Eitaro Honda, bulletin of the faculty of foreign studies, Aichi Prefectural University, No. 38, Language and Literature, “This text is excerpted and additionally edited from the PDF version”)

Descartes’ role in the history of the quest for scientific knowledge is undeniable. His mechanical world theory can be applied to various fields and, according to the traditional division of worldviews, is deeply relevant not only to the macrocosm, which is the universe, but also to the microcosm, which is the living organism. We should not look for the significance of the scientific revolution of the 17th century only in its physical achievements, but also in the fact that in Harvey and Descartes the human being became the subject of serious medical and physiological research. Descartes’ unfinished book on physiology, “Description of the Human Body,” which he was working on in his later years, describes the following.

# William Harvey (1578-1657) was an anatomist and physician in England and the English Republic. While honing his skills as a physician and rising to the rank of court physician, he also studied anatomy and advocated the theory of blood circulation.

One of the important achievements of Hippocrates medicine was to separate it from primitive superstition and witchcraft and to develop it into an empirical science that emphasizes clinical practice and observation. Descartes’ philosophy of the living body is not the kind of medicine that preserves the health of the human body, cures disease, and expels it, as in Hippocratic medicine. The distinctive feature of Descartes’ philosophy of the living body, which is medicine, is that it remains in the realm of physiology, the full description of healthy human nature, which is the first division of its basic sciences.

It was Descartes who most clearly presented human and animal mechanism on the basis of a mechanistic view of nature, and given the magnitude of his influence, we are compelled to consider this issue in Descartes’ terms. The characteristic feature of Descartes’ idea of biomechanics is that the natural and the mechanical are homogeneous, since they can be interpreted by mathematics when illuminated from the viewpoint of natural science.

The central issue of natural science in the modern era may be considered to be the problem of motion of objects. In this case, two worlds are traditionally considered. One is the macroscopic world. It is the world of infinitely addable, decomposable, and thus open to infinity and infinitesimals. The other is the micro world of living organisms. It is a spatially limited and closed world whose underlying principle motion can be understood.

The former is the motion of celestial bodies, rooted in the principle of inertia that led to Galileo Galilei, Descartes, and Newton. The latter is the “perpetual circulatory motion” of the blood represented by Harvey’s physiology. Thus, if we take the two motions as images, we can think of the motion of each world as represented by a straight line and a circle, respectively. The inertial motion of an object in a celestial body is a straight line. And the circulatory motion of blood in a living body is a circular motion. In this case, which seeks the principle model of mandibular motion in the field of dentistry from Descartes’ biomechanics, the circulatory motion of blood in a living body is irrelevant, so I will not mention it here.

Descartes states that the motion of living bodies and the motion of machines are the same, so they do not require special principles, but are under the laws of the mechanics of objects, which are rooted in the law of inertia. The motion of living bodies and the motion of machines are continuous. We are entering the realm of mechanics, a point about as far removed from physiology or biology as we can be from the organism. Descartes, however, does not believe that this way of understanding the living organism lacks scientific verification and rigor.

Descartes’ theory of living organisms is characterized by many references to machines. Descartes made many references to machines while relying on anatomy. Descartes relied on anatomy, but made many references to machines because he wanted to place the motion of living organisms in a mathematical dimension. This is because natural science is strictly the study of mathematics, and mathematics is the foundation on which mechanics is based.

The investigation of the motion of living organisms should not be thought of as an object of knowledge inquiry based on some unknown principle unrelated to the rigor of mathematics, since its object is a living object, i.e., life as an object that moves automatically. Descartes believed that anatomy and mechanics would reveal the direction of knowledge in the study of living organisms. The sure inference of the essential identity of the machine and the organism is disassembly in the case of the machine and anatomy in the case of the organism. Descartes attempted to elucidate the motion of living organisms from a mechanistic point of view, supported by an experimental spirit. Descartes’ thought should not be easily judged as an argument that begins with dogmatic definitions and principles based on hypotheses.

Descartes’ work may not be sufficient as a scientific truth, but it still holds great potency in the direction of the study of the physiology of the living body. As long as man is considered as an object of natural science, the functions of the body can be explained essentially on the basis of the laws of mechanics.

Descartes describes the difference between living organisms and machines as follows. “Man is capable of building many different kinds of automatic machines, moving machines that resemble animals. But the machines that imitate animals use very few parts compared to the multitude of bones, muscles, nerves, arteries, veins, and all the other parts of the living body. Since the human body is made by the hand of God, it may be regarded as a machine that has order and motion in it that is incomparably more orderly and marvelous than any machine that could be invented by man. We can think of the difference between a machine made by the hand of God and a machine made by the hand of man not as an intrinsic difference, but as a quantitative difference in degree of complexity.”

What Gnathology Left Behind

From this heading, gnathology is already being described as a forsaken concept, but as a dental technologist, I don’t think I am qualified to make a statement. What I am trying to say here is that gnathology was a discipline that aimed to study and treat the maxillofacial system as a functional unit, and it set the direction regarding subsequent dental treatment. As a matter of fact, in a report titled “Reconsidering the centric relation (Theory)” in the special issue of the July 2022 issue of Shikai Tenbo, it is reported that “Today, few clinicians record the terminal hinge axis.”

Here I have tried to introduce the concept of autopoiesis into dental technology, although it is of course impossible to think about it without knowledge of dental technology. This is not something that I started by coming up with in my clinical experience in dental technology. Hence, I thought that dental technologists, not dentists, could make some reference to gnathology. The concept of autopoiesis is not specifically related to dentistry. Descartes’ theory of biomechanics is not specifically related to dentistry, but American dentists introduced it and created gnathology. I think that the introduction of the concept of autopoiesis into dental technology is similar to the introduction of Descartes’ biomechanics.

Gnathology is a discipline proposed by American dentists Harvey Stallard (1888-1974) and Beverly B. McCollum (1883-1968) that aims to restore oral and maxillofacial function, primarily through occlusal reconstruction of the dentulous jaw.

Let us consider the definition of an ideal bite. Ideal occlusion is the bite state assumed to be most appropriate for humans. Descartes does not mention the state of the human jaw or bite, but he states that the human body was created by the hand of God. If Descartes did mention the state of occlusion, he would have assumed that it was physically created in an ideal state. I tried to imagine how Descartes would have described it.

The human body is ideal, perfect and impeccable because it was created by God. Therefore, the human bite is also ideal. God created the human “design”. However, the actual human bite, made of matter, was not directly created by God.

What does God’s design look like? The upper and lower rows of teeth are ideally aligned. Furthermore, the occlusion of the upper and lower dentition is also ideal. When the mandible begins to open, the mandibular head initially moves in a pure rotational motion without any blurring. The ideal occlusion is one in which the mandibular head gradually moves forward and downward as the degree of opening of the mandible increases. However, we will not go into the specifics of how the individual teeth are aligned and how the upper and lower meshing is constructed.


What is the difference between “the real biological jawbone and dentition” and “the ideal jawbone and dentition designed by God?” Let us borrow a concept from Descartes’ biomechanical theory to express the definition of centric relation.

When the mandible opens in the ideal state created by God, the mandibular head of the mandible undergoes a pure rotational motion with no blurring at all in the initial state of the opening motion. However, it is inconceivable that the mandibular head of the real jaw would rotate in a pure, unshakeable manner. I do not think that a pure hinged axis exists in a living organism. There are six degrees of freedom in a kinematic rigid body. Therefore, the mandible also has 6 degrees of freedom. Although a kinematically pure hinge axis exists in the mandible, I do not think that muscles can actually make the mandible do only geometrically pure hinge axis motion.

The centric relation can be described as the positional relationship between the condyle head of the mandible and the mandibular fossa of the maxilla when the upper and lower dentition are in the central occlusal position, which is the ideal state created by God. What is the difference between the ideal state created by God and the actual positional relationship between the condyle of the mandible and the mandibular fossa of the maxilla in the actual living organism?

I think the difference is whether the tissues around the joint head of the mandible, including the muscles and other driving systems that move the mandible, are optimized by the organism itself, or whether the tissues around the joint head of the mandible are built by God.

However, since the ideal state is God’s design, humans cannot know what exactly it is like. The only example that can be used as a reference is the state of the tissues of similar parts of a healthy human being. This is the closest we can get to God’s design. The ideal state is specifically unknown. Since God’s design is an ideal, even an optimized version of reality may be slightly different from the original ideal state. The question is whether God’s design and optimization in reality are congruent.

How have humans optimized their dentition, jaw bones, tissues around the mandible head, etc. during periods of physical growth and completion, etc.? In my opinion, perhaps the organism has a kind of divine blueprint and grows to match it. However, this may change depending on the individual’s living environment and lifestyle. The meshing of the human dentition and the positional relationship between the condyle head of the mandible and the maxilla within the mandibular fossa/articular fossa would be expected to have gradually established a relationship as the body grew. Therefore, even if the centric relation must be determined in a short period of time for treatment, it will have to be done by trial and error.

When treatment requires occlusal reconstruction, a new centric relation must be determined. Conventional thinking, in order to understand Descartes’ biomechanical theory in terms of the categories of “necessity and chance,” has led dentists to dogmatically determine the position of the mandibular head as a matter of necessity.

I believe that “optimization” arising from autopoiesis, which I introduced, embodies the original Cartesian idea of biomechanics, rather than a dentist’s dogmatic determination of the centric relation.

The centric relation is the kinematic reference position for the biomechanical theory. I think that the application of the dynamical systems theory of “variety and uniqueness” suits Descartes’ biomechanical theory. When the ideal becomes reality, it is considered to be optimized by the organism itself, even if it does not coincide with the ideal for various reasons.

The terms “centric relation” and “terminal hinge-axis” are similar concepts, but I believe that “terminal hinge-axis” is the very “centric relation” designed by God in Descartes’ biomechanical theory. I believe that the positioning of the upper and lower jaws in the centric occlusion of a healthy human being is referred to as the “centric relation”. Descartes would have thought of it this way.

This is my opinion, but I think that conventional gnathology is an idea derived from Descartes’ biomechanical theory, and that meaning is made in a theoretical system from the combined categories of necessity and chance. I think conventional gnathology is one way of expressing biomechanical theory in dentistry. The treatment from the combined categories of necessity and chance has been reworked into the problem of determining the position of the “centric relation”. Although the term “inevitability” and “contingency” are used, the strict rules of inevitability and the ambiguity of contingency are so closely intertwined that it is difficult to separate them accurately in practice. It seems that Japanese dentists have had quite a bit of trouble with this. Some dentists took it seriously, but others were not interested in this kind of thing.

I first learned the word gnathology more than 40 years ago. It was some time after I became a dental technologist. What I learned then was that the human mandible has a purely rotational axis, like a robot’s jaw. I thought, “This is a curious story.” Other than that, I thought it made a reasonable amount of sense. But then again, this is all about diagnostics. It would be valuable to know where the “centric relation” is if the dentist himself were actually doing the dental work. However, I also thought that it would be meaningless for a dental technologist who specializes in making prosthetics to study such things.

The reason for this is that the dental technologist actually makes the dental prosthesis, but basically has no access to the patient in question. In difficult cases such as these with occlusal reconstructions, it is quite troublesome to try waxing up the dental prosthesis and ask the dentist for his/her opinion and correction at that time, due to the discretionary power regarding the fabrication of dental prosthetics. In addition, the dental technologist cannot see the result of the treatment. So, although it may not be a waste of time to think about this and that, it was tedious and I wondered how it would be done.

In fact, where the axis of rotation is located is a diagnostic matter and is not relevant to the dental technologist. Wherever it is, it is the dentist’s own problem and does not directly concern the dental technologist. If it matters to the dental technologist, misalignment of the axis can lead to greater adjustment of the fabricated dental prosthesis and, in the worst case, possible remanufacturing.

Why was gnathology applied in this way to the movement of the mechanical human mandible, despite the fact that gnathology is about the movement of the human mandible? I found it very unnatural. I now wonder again if gnathology was not a starting point from the viewpoint of Descartes’ theory of biomechanics, rather than dental medicine as preached from clinical experience in dentistry. The definition of the determination of the mandibular position, the central position associated with the terminal hinge axis, has changed many times over the course of time.

By the way, this is what I think now, that the gnathologists who first devised it asked the people of the world how to interpret the terminal hinge axis. I propose a way to use the “virtual kinematic axis” to address the first invented gnathologists’ question that emerges from that deeper reading. The purpose of this is to urge that more consideration should have been given to metaphysical concepts rather than to the relationship between the real world and materialistic worldviews. In the real natural world, few things about motion have a purely rotational and translational component that is separate, and I believe that the motion of the mandible is no exception to this rule.

I believe that conventional gnathology has contributed to binding together the fragmented pieces of dental knowledge. In other words, it means to think of dentistry as a system. It also means treating not only the teeth but also the entire oral cavity, including the jaw joints, as a single unit.

# Metaphysics is a field of study or philosophy that considers the world beyond the senses and experience to be true existence and attempts to recognize the universal principles of the world through rational thought (or Logos). It considers things that transcend the senses, such as the reasons for the fundamental origins of the world (the root causes of the world) and the reasons and meanings for the existence of things and people. From Wikipedia

# Examples of interpenetration of necessity and chance

If you line up 10 steel cubes with 10 mm on a side and measure their dimensions, they will probably be 100.1 mm or 99.9 mm, and they will rarely be exactly 100 mm. In mathematical or arithmetic terms, 10mm times 10 = 100mm. This is in an ideal world, and the reality is that even very small errors, invisible to the eye, can become unwieldy when added up. 10,000, 100 million, or 10 billion pieces would be more significant.

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