Mindbody relationship definition math

Correlation and dependence - Wikipedia

mindbody relationship definition math

According to Descartes, these realms are forever separate such that the mind and body cannot influence one another. The problem is that the mind and body obviously do work together. He suggested that the pineal gland in the brain stem was a single point of communication between the. In mathematics, he developed the techniques that made possible of truth; The nature of reality; Mind–body relation; God and error. Mind-Body Relation. The Real Distinction; The Mind-Body Problem In Descartes began serious work on mathematical and mechanical problems under .

Mind–body problem - Wikipedia

Consciousness cannot even be taken as a trivial or necessary feature that is always present in our existence, because we all experience the transition of fading into dreamless sleep and awaking from it tens of thousands of times in the course of a typical life span. The distinction between inner mental content and outer behavioral observables is equally apparent when considering the obvious difference between dreamless sleep and a vivid dream [ 13 ]. Judging from the paralyzed body except for eye movementan external spectator could not even begin to guess the mental state of a dreaming person [ 14 ].

In contrast, we often toss, turn, kick, twitch, mumble, and moan during dreamless sleep [ 15 ]. Here and in the rest of this paper we do not consider the legal or medical definitions of being conscious as opposed to unconscious, because the shared goal of physicians and lawmakers is to evaluate other people rather than themselves.

Thus, they must necessarily take an objective, third-person perspective, that is, one entirely based on behavioral evidence. Similarly, there are clear resemblances between the properties of consciousness and those of attention [ 17 ]. Neuroscience has advanced considerably in the elucidation of the neural mechanisms underlying attentive processes e.

Nevertheless, recent evidence clearly indicates a double dissociation between attention and consciousness [ 19 ]. The challenge of the mind-matter relation, then, is to understand how particular configurations of matter e. Many aspects of conscious experience can be reported explicitly by the subject [ 2223 ] either internally, by inner dialogue or memory rehearsal, or externally, such as by a verbal description or numerical rating.

A defining characteristic of such declarative content of the conscious mind is that it can be communicated. The most common form of communication among human beings is through spoken or written language, but declarative content can also be communicated by other means, such as body gesture, drawings, movies, and many others.

The field of semantics studies meaning and its communication by signifiers. Consider a subject experiencing a certain declarative mental state e. A fascinating facet of declarative communication is that the content intended by the sender is generally not identical to that understood by the recipient e.

We will return to this mismatch at the end of the paper. Spatial and Temporal Patterns of Neural Activity Overwhelming scientific data unequivocally link the conscious mind to the brain, as opposed to matter at large. Available evidence, however, is more specific than generically pointing to the brain as the most relevant organ of the body in relation to the mind.

Particular regions of the brain are more directly and intimately involved with mental activity, including the thalamocortical system [ 25 ] and the hippocampal complex [ 26 ]. Other parts of the central nervous system, such as the cerebellum and the spinal cord, appear less pertinent to the declarative content of the mind.

In fact, those same thalamocortical and hippocampal regions are definitely active even during dreamless sleep, but their activity is different from that during conscious states [ 27 ].

Thus, it is the information process, or computation, carried out by these brain structures, that most closely corresponds to consciousness [ 2829 ]. Implementing that same computation in different mediums, in artificial machines, or in virtual environments, would then in principle also result in conscious experience. Unfortunately, however, what might in fact constitute the essence of this computation, or its neural implementation, is far less clear.

For the purpose of this paper, we do not need to dwell into specific hypotheses, except noting a general consensus supporting spatial-temporal patterns of neural activity as key material correlates of conscious experience. The carriers of neural activity are neurons, biological objects each occupying a physical volume in the brain. Within the particular framework we have chosen to adopt, the key players of the mind-brain relationship can be summarized as the following. On the one hand, each of us has access to the immediate experience of what it feels like to be, in any one moment of our conscious existence and throughout our life span.

We can communicate that experience to each other, and our mental states are altered by receiving those messages. On the other hand, the brain is a dynamical information processing system, consisting of a large number of neurons, each characterized at any one time by the spatial distribution of its electrochemical state. Within a brain, neurons continuously exchange signals with each other, mutually affecting their spatially distributed electrochemical state.

In this framework, the mind-brain problem can be formulated as a simple question. Why and how do certain spatio-temporal patterns of neural dynamics relate to declarative mental states?

What Would Count as an Explanation? Many relationships are routinely observed in the course of everyday life, such as how the weight of bodies relates to their size or how satisfying it feels to drink when thirsty. Why is the mind-brain relationship so different as to constitute a problem? Brains and minds are so different from each other as to inspire several kinds of dualist philosophies in the course of time.

This fundamental difference has been considered challenging by scientists and philosophers alike, from confronting possible inconsistencies in temporal dynamics [ 34 ] through a retreat to the acceptance of limited explanations [ 35 ], to overt calls for giving up scientific accounts altogether [ 36 ].

The more extreme positions maintaining that there is no solution to the mind-brain problem have been refuted both on philosophical [ 37 ] and scientific grounds [ 38 ]. The key issue is in fact to understand what would count as a solution. In other words, if the mind-brain relationship can be explained, what type of explanation is being sought?

To answer this central question, it is useful to consider previous scientific breakthroughs that resulted in satisfactory understanding of relationships that had been considered difficult to explain before. More than one hundred years later the first comprehensive treaty on thermodynamics was published [ 41 ], describing the relationship between heat, energy, temperature, and what was later called entropy.

While both mechanics and thermodynamics were and still are recognized as landmark advancements of scientific progress, they seemed to describe phenomena of different kinds.

Yet, some relationships, discovered earlier by the likes of Gay-Lussac, Avogadro, and Boyle [ 42 ], consistently crossed that divide, such as the proportionality of gas pressure a mechanical attribute and temperature a thermodynamic one in a container of fixed volume. Specifically, temperature relates to the average quadratic velocity of a large number of microscopic particles and pressure to their momentum. Entropy is related to the number of possible states a system can be in, which clarifies why disorder tends to increase in the absence of other constraints.

The demonstration of the equivalence between thermodynamics and mechanics is as convincing and direct as the derivation of the corresponding thermodynamic and mechanical laws. Furthermore, this link solved the mystery of the lower bound of temperature: Notably, the kinetic theory also led to the famous Einsteinian explanation of Brownian motion recounted in [ 45 ]. Yet the properties of mirrors and the passage of light through various media such as air and water seem so different from the phenomena of electric current and magnetic dipoles.

Other illustrations of the same relationships are the quantum physics foundation of chemistry, the genomics bases of genetics, and the explanation of neuronal firing in terms of voltage-dependent sodium and potassium channels [ 46 ]. When Mendeleev compiled the first draft of the Periodic Table of the Elements, there was no physical justification of the observed proportions of chemical reactions: Thus his corrections, required to describe then-available data parsimoniously, de facto predicted the atomic number nearly half a century prior to its actual discovery.

Today we readily accept that many chemical phenomena e. Is there a common thread in these seemingly disparate, if illustrious, precedents? We purport that the illusion of mystery at one level e. Here we surmise that the content and meaning of mental states, the most inescapable yet ineffable puzzle of human cognition, will eventually be understood as a direct reflection, if not simply an aspect, of brain computation, much like thermodynamics is statistical mechanics.

The principle of what would count as an explanation, however, remains the same: We are not simply proposing mental properties to be probabilistically supervenient on brain properties, that is, that they can be inferred statistically from brain measures within any given error rate [ 47 ]. On the contrary, we are asserting the possibility of a formal equivalence between the two, through all temporal scales and plastic changes [ 48 ]. The explanatory power of mathematical theory in neuroscience is recognized in principle [ 49 ], but the extent of its reach has not yet been fully realized, and the path forward has never been chartered before.

This is in stark contrast to the third simulation-based leg of scientific progress complementary to experiments and theorywhich is blossoming into maturity in computational neuroscience and cognitive modeling alike [ 50 ] and in the study of consciousness in particular [ 5152 ].

Neural Connectivity as the Most Informative Constraint in the Brain To explain the equivalence of brain and mind by mapping them onto each other, it is essential to identify the relevant levels of analysis in order to define proper mathematical formalisms for their quantitative description.

We start from the brain in this section and tackle the mind in the next. Nervous systems are gigantic networks of intercommunicating neurons. From the computational point of view, it matters relatively little that neurons are electrical devices.

Instead, brain signal processing is fundamentally dependent on circuit connectivity [ 53 ]. Specifically, how neurons are connected to each other constrains network dynamics [ 54 ] and therefore determines the possible flow of information transmission [ 55 ]. Because real brains are wired to a certain degree according to stereotypical principles [ 57 ], the actual number of connectivity patterns that could be found in any one human brain is undoubtedly lower.

However, brain circuitry is neither random nor regular, and the information content of a single human brain remains far greater than the number of fundamental particles in the whole universe, let alone just the complete biochemical specification of that individual brain.

Thus network connectivity is necessarily more informative than the entire molecular profile of each of all of its neurons, including the expression of every gene and protein constituting the biophysical machinery at the basis of neuronal electrophysiology.

While neuroanatomy provides the foundational roadmap of information transmission in nervous systems, neural activity is itself characterized by chaotic dynamics [ 58 ] typical of complex systems [ 5960 ]. As these aspects are particularly relevant to conscious brain function [ 61 ], a full understanding of the brain as it relates to mental content will have to integrate adequate accounts of both neural dynamics and connectivity [ 62 — 64 ].

Nevertheless, the network architecture specification is absolutely central to the assumed correspondence between spatial-temporal patterns of neural spiking and mental states. The former is further distinguished in the dense reconstruction of the entire synaptic matrix and the statistical potential of synaptic connectivity, both highly relevant to computational processing [ 71 — 73 ]. In contrast, the much coarser description of regional connectivity has less direct implications for a mechanistic understanding of brain cognition.

However, this latter approach is also substantially more realistic to achieve in the near future, using existing histological techniques in animal models [ 7475 ] or noninvasive imaging in humans [ 7677 ].

mindbody relationship definition math

But couldn't Descartes somehow be mistaken about his clear and distinct ideas? Given the existence of so many non-thinking bodies like stones, there is no question that bodies can exist without minds. So, even if he could be mistaken about what he clearly and distinctly understands, there is other evidence in support of premise 2.

But can minds exist without bodies? Can thinking occur without a brain? This veridical guarantee is based on the theses that God exists and that he cannot be a deceiver. These arguments, though very interesting, are numerous and complex, and so they will not be discussed here. Moreover, Descartes claims that he cannot help but believe clear and distinct ideas to be true.

However, if God put a clear and distinct idea in him that was false, then he could not help but believe a falsehood to be true and, to make matters worse, he would never be able to discover the mistake. Since God would be the author of this false clear and distinct idea, he would be the source of the error and would, therefore, be a deceiver, which must be false.

However, if it turns out that God does not exist or that he can be a deceiver, then all bets are off. There would then no longer be any veridical guarantee of what is clearly and distinctly understood and, as a result, the first premise could be false.

Consequently, premise 1 would not bar the possibility of minds requiring brains to exist and, therefore, this premise would not be absolutely certain as Descartes supposed. Notice that mind and body are defined as complete opposites. This means that the ideas of mind and body represent two natures that have absolutely nothing in common. And, it is this complete diversity that establishes the possibility of their independent existence.

To answer this question, recall that every idea of limited or finite things contains the idea of possible or contingent existence, and so Descartes is conceiving mind and body as possibly existing all by themselves without any other creature.

Since there is no doubt about this possibility for Descartes and given the fact that God is all powerful, it follows that God could bring into existence a mind without a body and vice versa just as Descartes clearly and distinctly understands them.

For when I consider the mind, or myself in so far as I am merely a thinking thing, I am unable to distinguish any parts within myself; I understand myself to be something quite single and complete….

By contrast, there is no corporeal or extended thing that I can think of which in my thought I cannot easily divide into parts; and this very fact makes me understand that it is divisible.

This one argument would be enough to show me that the mind is completely different from the body…. I understand the mind to be indivisible by its very nature. I understand body to be divisible by its very nature. Therefore, the mind is completely different from the body. Notice the conclusion that mind and body are really distinct is not explicitly stated but can be inferred from 3. What is interesting about this formulation is how Descartes reaches his conclusion. He does not assert a clear and distinct understanding of these two natures as completely different but instead makes his point based on a particular property of each.

So, here Descartes is arguing that a property of what it is to be a body, or extended thing, is to be divisible, while a property of what it is to be a mind or thinking thing is to be indivisible. First, it is easy to see that bodies are divisible. Just take any body, say a pencil or a piece of paper, and break it or cut it in half. Now you have two bodies instead of one. Second, based on this line of reasoning, it is easy to see why Descartes believed his nature or mind to be indivisible: Therefore, the body is essentially divisible and the mind is essentially indivisible: Here it should be noted that a difference in just any non-essential property would have only shown that mind and body are not exactly the same.

For two things could have the same nature, for example, extension, but have other, changeable properties or modes distinguishing them. Hence, these two things would be different in some respect, for example, in shape, but not completely different, since both would still be extended kinds of things. Consequently, Descartes needs their complete diversity to claim that he has completely independent conceptions of each and, in turn, that mind and body can exist independently of one another.

Descartes can reach this stronger conclusion because these essential properties are contradictories. On the one hand, Descartes argues that the mind is indivisible because he cannot perceive himself as having any parts. On the other hand, the body is divisible because he cannot think of a body except as having parts. Hence, if mind and body had the same nature, it would be a nature both with and without parts. Yet such a thing is unintelligible: Notice that, as with the first version, mind and body are here being defined as opposites.

This implies that divisible body can be understood without indivisible mind and vice versa. Accordingly each can be understood as existing all by itself: However, unlike the first version, Descartes does not invoke the doctrine of clear and distinct ideas to justify his premises. But if removed from this apparatus, it is possible that Descartes is mistaken about the indivisibility of the mind, because the possibility of the mind requiring a brain to exist would still be viable.

This would mean that, since extension is part of the nature of mind, it would, being an extended thing, be composed of parts and, therefore, it would be divisible. As a result, Descartes could not legitimately reach the conclusion that mind and body are completely different.

This would also mean that the further, implicit conclusion that mind and body are really distinct could not be reached either. The Mind-Body Problem The real distinction of mind and body based on their completely diverse natures is the root of the famous mind-body problem: Their concern arises from the claim at the heart of the real distinction argument that mind and body are completely different or opposite things.

The complete diversity of their respective natures has serious consequences for the kinds of modes each can possess. It makes no sense to ascribe such modes to entirely extended, non-thinking things like stones, and therefore, only minds can have these kinds of modes.

Conversely, it makes no sense to ascribe modes of size, shape, quantity and motion to non-extended, thinking things. For example, the concept of an unextended shape is unintelligible. Therefore, a mind cannot be understood to be shaped or in motion, nor can a body understand or sense anything. The arm moving upward is the effect while the choice to raise it is the cause.

The crux of their concern was that in order for one thing to cause motion in another, they must come into contact with one another as, for example, in the game of pool the cue ball must be in motion and come into contact with the eight-ball in order for the latter to be set in motion.

Accordingly, the mind does not have a surface that can come into contact with the body and cause it to move. So, it seems that if mind and body are completely different, there is no intelligible explanation of voluntary bodily movement. Again, since the mind is incapable of having motion and a surface, no intelligible explanation of sensations seems possible either.

Therefore, the completely different natures of mind and body seem to render their causal interaction impossible. The consequences of this problem are very serious for Descartes, because it undermines his claim to have a clear and distinct understanding of the mind without the body.

For humans do have sensations and voluntarily move some of their bodily limbs and, if Gassendi and Elizabeth are correct, this requires a surface and contact. Since the mind must have a surface and a capacity for motion, the mind must also be extended and, therefore, mind and body are not completely different. Descartes has not included anything in the argument to ward off the possibility that he, as a thinking thing, is in fact a complex material system.

He has merely relied on the fact that he can doubt the existence of matter to conclude that matter is distinct from mind. This argument is clearly inconclusive. From the fact that the Joker cannot, at a certain moment, doubt the existence of Batman because he is with himbut he can doubt the existence of Bruce Wayne who might, for all the Joker knows, have been killed by the Joker's henchmenit does not follow that Bruce Wayne is not Batman.

In fact, he is Batman. The Joker is merely ignorant of that fact. In the Meditations, Descartes changed the structure of the argument. In the Second Meditation, he established that he could not doubt the existence of himself as a thinking thing, but that he could doubt the existence of matter. However, he explicitly refused to use this situation to conclude that his mind was distinct from body, on the grounds that he was still ignorant of his nature 7: Then, in the Sixth Meditation, having established, to his satisfaction, the mark of truth, he used that mark to frame a positive argument to the effect that the essence of mind is thought and that a thinking thing is unextended; and that the essence of matter is extension and that extended things cannot think 7: He based this argument on clear and distinct intellectual perceptions of the essences of mind and matter, not on the fact that he could doubt the existence of one or the other.

This conclusion in the Sixth Meditation asserts the well-known substance dualism of Descartes. That dualism leads to problems. As Princess Elisabeth, among others, asked: This problem vexed not only Descartes, who admitted to Elisabeth that he didn't have a good answer 3: It seems that, somehow, states of the mind and the body must be brought into relation, because when we decide to pick up a pencil our arm actually moves, and when light hits our eyes we experience the visible world.

But how do mind and body interact? Some of Descartes' followers adopted an occasionalist position, according to which God mediates the causal relations between mind and body; mind does not affect body, and body does not affect mind, but God gives the mind appropriate sensations at the right moment, and he makes the body move by putting it into the correct brain states at a moment that corresponds to the volition to pick up the pencil.

Other philosophers adopted yet other solutions, including the monism of Spinoza and the pre-established harmony of Leibniz. In the Meditations and Principles, Descartes did not focus on the metaphysical question of how mind and body interact.

Rather, he discussed the functional role of mind—body union in the economy of life. As it happens, our sensations serve us well in avoiding harms and pursuing benefits.

Pain-sensations warn us of bodily damage. Pleasure leads us to approach things that usually are good for us. Our sense perceptions are reliable enough that we can distinguish objects that need distinguishing, and we can navigate as we move about.

René Descartes (1596—1650)

They are not perfect. Sometimes our senses present things differently than they are, and sometimes we make judgments about sensory things that extend beyond the appropriate use of the senses.

In discussing the functioning of the senses to preserve or maintain the body, he explained that God has arranged the rules of mind—body interaction in such a manner as to produce sensations that generally are conducive to the good of the body. Nonetheless, in each case, errors occur. In various circumstances, our judgments may be false often, about sensory thingsjust as, more broadly, human beings make poor moral choices, even though God has given them a will that is intrinsically drawn to the good 1: In addition, our sense perceptions may represent things as being a certain way, when they are not.

Sometimes we feel pain because a nerve has been damaged somewhere along its length, and yet there is no tissue damage at the place in which the pain is felt. Amputees may feel pain in their fingers when they have no fingers Princ. Descartes responded to these problems differently. He explained cognitive and moral errors as resulting from human freedom.

God provides human beings with a will, and wills are intrinsically free. In this way, there is no difference in degree in freedom between God and man. But human beings have finite intellects. And because they are free, they can choose to judge in cognitive or moral situations for which they do not have clear and distinct perceptions of the true or the good. If human beings restricted their acts of will to cases of clear and distinct perception, they would never err.

But the vicissitudes of life may require judgments in less than optimal circumstances, or we may decide to judge even though we lack a clear perception. In either case, we may go wrong. Matters are different for the errors of sensory representation. The senses depend on media and sense organs and on nerves that must run from the exterior of the body into the brain. God sets up the mind—body relation so that our sensations are good guides for most circumstances.

But the media may be poor the light may not be goodcircumstances may be unusual as with the partially submerged stick that appears as if bentor the nerves may be damaged as with the amputee.

In these cases, the reports of the senses are suboptimal. Since God has set up the system of mind—body union, shouldn't God be held accountable for the fact that the senses can misrepresent how things are? Here Descartes does not appeal to our freedom not to attend to the senses, for in fact we must often use the senses in suboptimal cognitive circumstances when navigating through life.

Rather, he points out that God was working with the finite mechanisms of the human body 7: In fact, the distinction between these two types of error, cognitive error and sensory misrepresentation, is not completely clear-cut in Descartes.

In the case of the amputee, the pain seems to be in fingers that are not there. That appears to be a clear case of sensory misrepresentation: Similarly with the partially submerged stick. It may look bent. In these cases, even if we use our intellects to interpret the illusions or sensory misrepresentations so as to avoid error by withholding judgment or even by judging correctly 7: In other cases, however, Descartes describes the senses as providing material for error, but it remains uncertain whether he assimilates such error to what has been labelled cognitive error or to sensory misrepresentation.

He offers as an example the idea of cold: Accordingly, this case should be assimilated to sensory misrepresentation: Material falsity would be a matter of misrepresentation. But Descartes also offers a different gloss on the obscurity of sensory ideas. Accordingly, sensory ideas are not misrepresentations, they are simply so obscure and confused that we cannot tell what their representational content might be by considering their experienced character, such as the phenomenal character of cold or of color.

Metaphysics and natural philosophy are needed to tell us what our color sensations obscurely represent: On this interpretation, Descartes is saying that the resemblance thesis arises not because the sensory ideas of cold or of color misrepresent those qualities in objects, but because we make a cognitive error, stemming from the prejudices of childhood as mentioned in Sec.

The issues surrounding the notion of material falsity in Descartes are intricate and cut to the core of his theory of mind and of sensory representation. The interested reader can gain entrance to literature through Wee and Hatfield More generally, Copernicus had, in the previous century, offered a forceful argument for believing that the sun, not the earth, is at the center of the solar system. Early in the seventeenth century, Johannes Kepler announced new results in optics, concerning the formation of images, the theory of lenses, and the fact that the retinal image plays a central role in vision.

By the early s, Descartes was aware 1: Descartes himself contributed some specific new results to the mathematical description of nature, as co-discoverer of the sine law of refraction and as developer of an accurate model of the rainbow. Special physics concerned actually existing natural entities, divided into inanimate and animate. Inanimate physics further divided into celestial and terrestrial, in accordance with the Aristotelian belief that the earth was at the center of the universe, and that the earth was of a different nature than the heavens including the moon, and everything beyond it.

Animate terrestrial physics concerned the various powers that Aristotelians ascribed to ensouled beings, where the soul is considered as a principle of life possessing vital as well as mental or cognitive powers. In the simplest textbooks, the powers of the soul were divided into three groups: Descartes' ambition was to provide replacements for all the main parts of Aristotelian physics.

In his physics, there is only one matter and it has no active forms. Thus, he dissolved the boundary that had made the celestial and the terrestrial differ in kind. His one matter had only the properties of size, shape, position, and motion. The matter is infinitely divisible and it constitutes space; there is no void, hence no spatial container distinct from matter. The motions of matter are governed by three laws of motion, including a precursor to Newton's law of inertia but without the notion of vector forces and a law of impact.

Earth, air, fire, and water were simply four among many natural kinds, all distinguished simply by the characteristic sizes, shapes, positions, and motions of their parts. Although Descartes nominally subscribed to the biblical story of creation, in his natural philosophy he presented the hypothesis that the universe began as a chaotic soup of particles in motion and that everything else was subsequently formed as a result of patterns that developed within this moving matter.

Thus, he conceived that many suns formed, around which planets coalesced. On these planets, mountains and seas formed, as did metals, magnets, and atmospheric phenomena such as clouds and rain.

The planets themselves are carried around the sun in their orbits by a fluid medium that rotates like a whirlpool or vortex. Rather, they are driven down by the whirling particles of the surrounding ether.

Descartes insisted that all cases of apparent action at a distance, including magnetism, must be explained through the contact of particle on particle. He explained magnetism as the result of corkscrew-shaped particles that spew forth from the poles of the earth and flow from north to south or vice versa, causing magnetized needles to align with their flow Princ.

To explain magnetic polarity, Descartes posited that the particles exiting from the south pole are threaded in one direction and those from the north are threaded oppositely like the oppositely threaded spindles on bicycle pedals. Descartes also wanted to provide an account of the formation of plants and animals by mechanical causes, but he did not succeed during his lifetime in framing an account that he was willing to publish so that only portions of his physiology were revealed in the Discourse, Dioptrics, Meditations, Principles, and Passions.

In writings that were published only posthumously but were read by friends and followers during his lifetime, e. In mechanizing the concept of living thing, Descartes did not deny the distinction between living and nonliving, but he did redraw the line between ensouled and unensouled beings.

In his view, among earthly beings only humans have souls. He thus equated soul with mind: Descartes regarded nonhuman animals as machines, devoid of mind and consciousness, and hence lacking in sentience.

Although Descartes' followers understood him to have denied all feeling to animals, some recent scholars question this interpretation; on this controversy, see Cottingham and Hatfield Consequently, Descartes was required to explain all of the powers that Aristotelians had ascribed to the vegetative and sensitive soul by means of purely material and mechanistic processes These mechanistic explanations extended, then, not merely to nutrition, growth, and reproduction, but also to the functions of the external and internal senses, including the ability of nonhuman animals to respond via their sense organs in a situationally appropriate manner: In the Treatise on Man and Passions, Descartes described purely mechanical processes in the sense organs, brain, and muscles, that were to account for the functions of the sensitive soul.

The brain structures that mediate behavior may be innate or acquired. Descartes ascribed some things that animals do to instinct; other aspects of their behavior he explained through a kind of mechanistic associative memory. He held that human physiology is similar to nonhuman animal physiology, as regards both vegetative and some sensitive functions—those sensitive functions that do not involve consciousness or intelligence: Now a very large number of the motions occurring inside us do not depend in any way on the mind.

These include heartbeat, digestion, nutrition, respiration when we are asleep, and also such waking actions as walking, singing, and the like, when these occur without the mind attending to them.

When people take a fall, and stick out their hands so as to protect their head, it is not reason that instructs them to do this; it is simply that the sight of the impending fall reaches the brain and sends the animal spirits into the nerves in the manner necessary to produce this movement even without any mental volition, just as it would be produced in a machine.

The fact that Descartes offered mechanistic explanations for many features of nature does not mean that his explanations were successful. Indeed, his followers and detractors debated the success of his various proposals for nearly a century after his death. His accounts of magnetism and gravity were challenged. Leibniz challenged the coherence of Descartes' laws of motion and impact. Newton offered his own laws of motion and an inverse square law of gravitational attraction.

His account of orbital planetary motions replaced Descartes' vortexes. Others struggled to make Descartes' physiology work. There were also deeper challenges. Some wondered whether Descartes could actually explain how his infinitely divisible matter could coalesce into solid bodies. Why shouldn't collections of particles act like whiffs of smoke, that separate upon contact with large particles? Indeed, how do particles themselves cohere? Such problems were real, and Descartes' physics was abandoned over the course of the eighteenth century.

Nonetheless, it provided a conception for a comprehensive replacement of Aristotelian physics that persisted in the Newtonian vision of a unified physics of the celestial and terrestrial realms, and that continued in the mechanistic vision of life that was revived in the latter part of the nineteenth century. This was especially true for what came to be known as the secondary qualities in the terminology of Robert Boyle and John Locke.

mindbody relationship definition math

The secondary qualities include colors, sounds, odors, tastes, and tactile qualities such as hot and cold. A red thing possesses the quality red in just the same way it possesses a shape: He rendered light as a property of particles and their motions: When light strikes an object, the particles that constitute light alter their rotation about their axis.

When particles with one or another degree of spin interact with the nerves of the retina, they cause those nerves to jiggle in a certain way. This jiggling is conveyed to the brain where it affects the animal spirits, which in turn affect the mind, causing the mind to experience one or another color, depending on the degree of spin and how it affects the brain.

Color in objects is thus that property of their surface that causes light particles to spin in one way or another, and hence to cause one sensation or another.

There is nothing else in the surface of an object, as regards color, than a certain surface-shape that induces various spins in particles of light.

Descartes introduced this new theory of sensory qualities in the first six chapters of the World. There, he defended it by arguing that his explanation of qualities in bodies in terms of size, shape, and motion are clearly understood by comparison with the Aristotelian qualities Subsequently, in the Meditations and Principles, he defended this account by appeal to the metaphysical result that body possesses only geometrical modes of extension.

Real qualities are ruled out because they are not themselves instances of size, shape, or motion even if patches of color have a size and a shape, and can be moved about. In addition to a new theory of sensory qualities, Descartes offered theories of the way in which the spatial properties—size, shape, distance, and position—are perceived in vision. It had been an area of inquiry since antiquity. Euclid and Ptolemy had each written on optical problems. During the Middle Ages, the Arabic natural philosopher Ibn al-Haytham produced an important new theoretical work in which he offered an extensive account of the perception of spatial properties.

The theoretical terrain in optics changed with Kepler's doctrine that vision is mediated by the retinal image and that the retina is the sensitive body in the eye.

Descartes accepted Kepler's result and framed a new theory of spatial perception. Some of his theorizing simply adapted Ibn al-Haytham's theories to the newly discovered retinal image.

Thus, Ibn al-Haytham held that size is perceived by combining the visual angle that a body subtends with perception of its distance, to arrive at a perception of the true size of the object. Visual angle is formed by the directions from a vantage point to a seen-object for a given fixation, e. In al-Haytham's scheme, visual angle is registered at the surface of the crystalline humor. Descartes held that size is perceived by combining visual angle with perceived distance, but he now treated visual angle as the extent of an object's projection onto the retina.

In Ibn al-Haytham's account, if the size of an object is known distance may be perceived through an inference; for a given size, an object's distance is inversely proportional to its visual angle. Descartes recognized this traditional account, depending as it does on past experience of an object's size and on an inference or rapid judgment that combines perceived visual angle with known or remembered size. Descartes held that these rapid judgments are habitual and happen so quickly that they go unnoticed.

Further, the sensations that present the objects in accordance with visual angle also go unnoticed, as they are rapidly replaced by visual experiences of objects at a distance. Ibn al-Haytham also explained that distance can be perceived by an observer's being sensitive to the number of equal portions of ground space that lie between the observer and a distant object. Descartes did not adopt this explanation.

However, Descartes used his mechanistic physiology to frame a new account of how distance might be perceived, a theory different from anything that could have been found in Ibn al-Haytham. In Kepler's new theory of how the eye works, an image is formed on the retina as a result of refraction by the cornea and lens. For objects at different distances, the focal properties of the system must be changed, just as the focal length of a camera is changed.

He then theorized that this change in the shape of the lens must be controlled by muscles, which themselves are controlled by nerve processes in the brain. Descartes realized that the central nervous state that controls accommodation would vary directly in proportion to the distance of objects.