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Mind–body problem

From Wikipedia, the free encyclopedia

See also: Philosophy of mind

René Descartes‘ illustration of mind/body dualism. Descartes believed inputs were passed on by the sensory organs to the epiphysisin the brain and from there to the immaterial spirit.

Different approaches toward resolving the mind–body problem

The mind–body problem is a philosophical problem concerning the relationship between the human mind and body, although it can also concern animal minds, if any, and animal bodies. It is distinct from the question how mind and body can causally interact, since that question presupposes an interactionist account of mind-body relations.[1] This question arises when mind and body are considered as distinct, based on the premise that the mind and the body are fundamentally different in nature.[1]

The problem was addressed by René Descartes in the 17th century, resulting in Cartesian dualism, and by pre-Aristotelian philosophers,[2][3] in Avicennian philosophy,[4] and in earlier Asian traditions. A variety of approaches have been proposed. Most are either dualist or monist. Dualism maintains a rigid distinction between the realms of mind and matter. Monism maintains that there is only one unifying reality, substance or essence in terms of which everything can be explained.

Each of these categories contain numerous variants. The two main forms of dualism are substance dualism, which holds that the mind is formed of a distinct type of substance not governed by the laws of physics, and property dualism, which holds that mental properties involving conscious experience are fundamental properties, alongside the fundamental properties identified by a completed physics. The three main forms of monism are physicalism, which holds that the mind consists of matter organized in a particular way; idealism, which holds that only thought truly exists and matter is merely an illusion; and neutral monism, which holds that both mind and matter are aspects of a distinct essence that is itself identical to neither of them.

Several philosophical perspectives have been developed which reject the mind–body dichotomy. The historical materialism of Karl Marx and subsequent writers, itself a form of physicalism, held that consciousness was engendered by the material contingencies of one’s environment.[5] An explicit rejection of the dichotomy is found in French structuralism, and is a position that generally characterized post-war French philosophy.[6]

The absence of an empirically identifiable meeting point between the non-physical mind (if there is such a thing) and its physical extension has proven problematic to dualism, and many modern philosophers of mind maintain that the mind is not something separate from the body.[7] These approaches have been particularly influential in the sciences, particularly in the fields of sociobiology, computer science, evolutionary psychology, and the neurosciences.[8][9][10][11]

An ancient model of the mind known as the Five-Aggregate Model explains the mind as continuously changing sense impressions and mental phenomena.[12] Considering this model, it is possible to understand that it is the constantly changing sense impressions and mental phenomena (i.e., the mind) that experiences/analyzes all external phenomena in the world as well as all internal phenomena including the body anatomy, the nervous system as well as the organ brain. This conceptualization leads to two levels of analyses: (i) analyses conducted from a third-person perspective on how the brain works, and (ii) analyzing the moment-to-moment manifestation of an individual’s mind-stream (analyses conducted from a first-person perspective). Considering the latter, the manifestation of the mind-stream is described as happening in every person all the time, even in a scientist who analyses various phenomena in the world, including analyzing and hypothesizing about the organ brain.[12]



Mind–body interaction and mental causation[edit]

Philosophers David L. Robb and John F. Heil introduce mental causation in terms of the mind–body problem of interaction:

Mind–body interaction has a central place in our pretheoretic conception of agency… Indeed, mental causation often figures explicitly in formulations of the mind–body problem…. Some philosophers… insist that the very notion of psychological explanation turns on the intelligibility of mental causation. If your mind and its states, such as your beliefs and desires, were causally isolated from your bodily behavior, then what goes on in your mind could not explain what you do… If psychological explanation goes, so do the closely related notions of agency and moral responsibility… Clearly, a good deal rides on a satisfactory solution to the problem of mental causation [and] there is more than one way in which puzzles about the mind’s "causal relevance" to behavior (and to the physical world more generally) can arise.

[René Descartes] set the agenda for subsequent discussions of the mind–body relation. According to Descartes, minds and bodies are distinct kinds of substance. Bodies, he held, are spatially extended substances, incapable of feeling or thought; minds, in contrast, are unextended, thinking, feeling substances… If minds and bodies are radically different kinds of substance, however, it is not easy to see how they could causally interact… Princess Elizabeth of Bohemia puts it forcefully to him in a 1643 letter…

how the human soul can determine the movement of the animal spirits in the body so as to perform voluntary acts—being as it is merely a conscious substance. For the determination of movement seems always to come about from the moving body’s being propelled—to depend on the kind of impulse it gets from what sets it in motion, or again, on the nature and shape of this latter thing’s surface. Now the first two conditions involve contact, and the third involves that the impelling thing has extension; but you utterly exclude extension from your notion of soul, and contact seems to me incompatible with a thing’s being immaterial…

Elizabeth is expressing the prevailing mechanistic view as to how causation of bodies works… Causal relations countenanced by contemporary physics can take several forms, not all of which are of the push–pull variety.[13]— David Robb and John Heil, "Mental Causation" in The Stanford Encyclopedia of Philosophy

Contemporary neurophilosopher, Georg Northoff suggests that mental causation is compatible with classical formal and final causality.[14]

Biologist, theoretical neuroscientist and philosopher, Walter J. Freeman, suggests that explaining mind–body interaction in terms of "circular causation" is more relevant than linear causation.[15]

In neuroscience, much has been learned about correlations between brain activity and subjective, conscious experiences. Many suggest that neuroscience will ultimately explain consciousness: "…consciousness is a biological process that will eventually be explained in terms of molecular signaling pathways used by interacting populations of nerve cells…"[16] However, this view has been criticized because consciousness has yet to be shown to be a process,[17] and the "hard problem" of relating consciousness directly to brain activity remains elusive.[18]

Cognitive science today gets increasingly interested in the embodiment of human perception, thinking, and action. Abstract information processing models are no longer accepted as satisfactory accounts of the human mind. Interest has shifted to interactions between the material human body and its surroundings and to the way in which such interactions shape the mind. Proponents of this approach have expressed the hope that it will ultimately dissolve the Cartesian divide between the immaterial mind and the material existence of human beings (Damasio, 1994; Gallagher, 2005). A topic that seems particularly promising for providing a bridge across the mind–body cleavage is the study of bodily actions, which are neither reflexive reactions to external stimuli nor indications of mental states, which have only arbitrary relationships to the motor features of the action (e.g., pressing a button for making a choice response). The shape, timing, and effects of such actions are inseparable from their meaning. One might say that they are loaded with mental content, which cannot be appreciated other than by studying their material features. Imitation, communicative gesturing, and tool use are examples of these kinds of actions.[19]

— Georg Goldenberg, "How the Mind Moves the Body: Lessons From Apraxia" in Oxford Handbook of Human Action

Neural correlates[edit]

Main article: Neural correlates of consciousness

The neuronal correlates of consciousness constitute the smallest set of neural events and structures sufficient for a given conscious percept or explicit memory. This case involves synchronized action potentials in neocortical pyramidal neurons.[20]

The neural correlates of consciousness "are the smallest set of brain mechanisms and events sufficient for some specific conscious feeling, as elemental as the color red or as complex as the sensual, mysterious, and primeval sensation evoked when looking at [a] jungle scene…"[21]Neuroscientists use empirical approaches to discover neural correlates of subjective phenomena.[22]

Neurobiology and neurophilosophy[edit]

Main articles: Neurobiology and Neurophilosophy

A science of consciousness must explain the exact relationship between subjective conscious mental states and brain states formed by electrochemical interactions in the body, the so-called hard problem of consciousness.[23] Neurobiology studies the connection scientifically, as do neuropsychology and neuropsychiatry. Neurophilosophy is the interdisciplinary study of neuroscience and philosophy of mind. In this pursuit, neurophilosophers, such as Patricia Churchland, [24][25] Paul Churchland[26] and Daniel Dennett,[27][28] have focused primarily on the body rather than the mind. In this context, neuronal correlates may be viewed as causing consciousness, where consciousness can be thought of as an undefined property that depends upon this complex, adaptive, and highly interconnected biological system.[29] However, it’s unknown if discovering and characterizing neural correlates may eventually provide a theory of consciousness that can explain the first-person experience of these "systems", and determine whether other systems of equal complexity lack such features.

The massive parallelism of neural networks allows redundant populations of neurons to mediate the same or similar percepts. Nonetheless, it is assumed that every subjective state will have associated neural correlates, which can be manipulated to artificially inhibit or induce the subject’s experience of that conscious state. The growing ability of neuroscientists to manipulate neurons using methods from molecular biology in combination with optical tools[30] was achieved by the development of behavioral and organic models that are amenable to large-scale genomic analysis and manipulation. Non-human analysis such as this, in combination with imaging of the human brain, have contributed to a robust and increasingly predictive theoretical framework.

Arousal and content[edit]

Midline structures in the brainstem and thalamus necessary to regulate the level of brain arousal. Small, bilateral lesions in many of these nuclei cause a global loss of consciousness.[31]

There are two common but distinct dimensions of the term consciousness,[32] one involving arousal and states of consciousness and the other involving content of consciousness and conscious states. To be conscious of something, the brain must be in a relatively high state of arousal (sometimes called vigilance), whether awake or in REM sleep. Brain arousal level fluctuates in a circadian rhythm but these natural cycles may be influenced by lack of sleep, alcohol and other drugs, physical exertion, etc. Arousal can be measured behaviorally by the signal amplitude required to trigger a given reaction (for example, the sound level that causes a subject to turn and look toward the source). High arousal states involve conscious states that feature specific perceptual content, planning and recollection or even fantasy. Clinicians use scoring systems such as the Glasgow Coma Scale to assess the level of arousal in patients with impaired states of consciousness such as the comatose state, the persistent vegetative state, and the minimally conscious state. Here, "state" refers to different amounts of externalized, physical consciousness: ranging from a total absence in coma, persistent vegetative state and general anesthesia, to a fluctuating, minimally conscious state, such as sleep walking and epileptic seizure.[33]

Many nuclei with distinct chemical signatures in the thalamus, midbrain and pons must function for a subject to be in a sufficient state of brain arousal to experience anything at all. These nuclei therefore belong to the enabling factors for consciousness. Conversely it is likely that the specific content of any particular conscious sensation is mediated by particular neurons in the cortex and their associated satellite structures, including the amygdala, thalamus, claustrum and the basal ganglia.

Historical background[edit]

The following is a very brief account of some contributions to the mind–body problem.

The Buddha[edit]

See also: Gautama Buddha, Buddhism and the body, and Pratītyasamutpāda

The Buddha (480–400 B.C.E), founder of Buddhism, described the mind and the body as depending on each other in a way that two sheaves of reeds were to stand leaning against one another[34] and taught that the world consists of mind and matter which work together, interdependently. Buddhist teachings describe the mind as manifesting from moment to moment, one thought moment at a time as a fast flowing stream.[12] The components that make up the mind are known as the five aggregates (i.e., material form, feelings, perception, volition, and sensory consciousness), which arise and pass away continuously. The arising and passing of these aggregates in the present moment is described as being influenced by five causal laws: biological laws, psychological laws, physical laws, volitional laws, and universal laws.[12] The Buddhist practice of mindfulness involves attending to this constantly changing mind-stream.

Ultimately, the Buddha’s philosophy is that both mind and forms are conditionally arising qualities of an ever-changing universe in which, when nirvāna is attained, all phenomenal experience ceases to exist.[35] According to the anattā doctrine of the Buddha, the conceptual self is a mere mental construct of an individual entity and is basically an impermanent illusion, sustained by form, sensation, perception, thought and consciousness.[36] The Buddha argued that mentally clinging to any views will result in delusion and stress,[37] since, according to the Buddha, a real self (conceptual self, being the basis of standpoints and views) cannot be found when the mind has clarity.


See also: Plato and Theory of forms

Plato (429–347 B.C.E.) believed that the material world is a shadow of a higher reality that consists of concepts he called Forms. According to Plato, objects in our everyday world "participate in" these Forms, which confer identity and meaning to material objects. For example, a circle drawn in the sand would be a circle only because it participates in the concept of an ideal circle that exists somewhere in the world of Forms. He argued that, as the body is from the material world, the soul is from the world of Forms and is thus immortal. He believed the soul was temporarily united with the body and would only be separated at death, when it would return to the world of Forms. Since the soul does not exist in time and space, as the body does, it can access universal truths. For Plato, ideas (or Forms) are the true reality, and are experienced by the soul. The body is for Plato empty in that it can not access the abstract reality of the world; it can only experience shadows. This is determined by Plato’s essentially rationalistic epistemology.[citation needed]


Main article: Aristotle

For Aristotle (384–322 BC) mind is a faculty of the soul.[38][39] Regarding the soul, he said:

It is not necessary to ask whether soul and body are one, just as it is not necessary to ask whether the wax and its shape are one, nor generally whether the matter of each thing and that of which it is the matter are one. For even if one and being are spoken of in several ways, what is properly so spoken of is the actuality.

— De Anima ii 1, 412b6–9

In the end, Aristotle saw the relation between soul and body as uncomplicated, in the same way that it is uncomplicated that a cubical shape is a property of a toy building block. The soul is a property exhibited by the body, one among many. Moreover, Aristotle proposed that when the body perishes, so does the soul, just as the shape of a building block disappears with destruction of the block.[40]

Influences of the religions of "The Book"[edit]

Main articles: Dualism and Gnosticism

In religious philosophy of the people of the book dualism denotes a binary opposition of an idea that contains two essential parts. The first formal concept of a "mind-body" split may be found in the "divinitysecularity" dualism of the ancient Persian religion of Zoroastrianism around the mid-fifth century BC. Gnosticism is a modern name for a variety of ancient dualistic ideas inspired by Judaism popular in the first and second century AD. These ideas later seem to have been incorporated into Galen‘s "tripartite soul"[41] that led into both the Christian sentiments [42] expressed in the later Augustinian theodicy and Avicenna’s Platonism in Islamic Philosophy.


Main article: René Descartes

René Descartes (1596–1650) believed that mind exerted control over the brain via the pineal gland:

My view is that this gland is the principal seat of the soul, and the place in which all our thoughts are formed.[43]

— René Descartes, Treatise of Man

[The] mechanism of our body is so constructed that simply by this gland’s being moved in any way by the soul or by any other cause, it drives the surrounding spirits towards the pores of the brain, which direct them through the nerves to the muscles; and in this way the gland makes the spirits move the limbs.[44]

— René Descartes, Passions of the Soul

His posited relation between mind and body is called Cartesian dualism or substance dualism. He held that mind was distinct from matter, but could influence matter. How such an interaction could be exerted remains a contentious issue.


Main article: Immanuel Kant

For Kant (1724–1804) beyond mind and matter there exists a world of a priori forms, which are seen as necessary preconditions for understanding. Some of these forms, space and time being examples, today seem to be pre-programmed in the brain.

…whatever it is that impinges on us from the mind-independent world does not come located in a spatial or a temporal matrix,…The mind has two pure forms of intuition built into it to allow it to… organize this ‘manifold of raw intuition’.[45]

— Andrew Brook, Kant’s view of the mind and consciousness of self: Transcendental aesthetic

Kant views the mind–body interaction as taking place through forces that may be of different kinds for mind and body.[46]


Main article: Thomas Huxley

For Huxley (1825–1895) the conscious mind was a by-product of the brain that has no influence upon the brain, a so-called epiphenomenon.

On the epiphenomenalist view, mental events play no causal role. Huxley, who held the view, compared mental events to a steam whistle that contributes nothing to the work of a locomotive.[47]

— William Robinson, Epiphenomenalism


Main article: Alfred North Whitehead

A. N. Whitehead advocated a sophisticated form of panpsychism that has been called by David Ray Griffinpanexperientialism.[48]


Main article: Karl Popper

For Popper (1902–1994) there are three aspects of the mind–body problem: the worlds of matter, mind, and of the creations of the mind, such as mathematics. In his view, the third-world creations of the mind could be interpreted by the second-world mind and used to affect the first-world of matter. An example might be radio, an example of the interpretation of the third-world (Maxwell’s electromagnetic theory) by the second-world mind to suggest modifications of the external first world.

The body–mind problem is the question of whether and how our thought processes in World 2 are bound up with brain events in World 1. …I would argue that the first and oldest of these attempted solutions is the only one that deserves to be taken seriously [namely]: World 2 and World 1 interact, so that when someone reads a book or listens to a lecture, brain events occur that act upon the World 2 of the reader’s or listener’s thoughts; and conversely, when a mathematician follows a proof, his World 2 acts upon his brain and thus upon World 1. This, then, is the thesis of body–mind interaction.[49]

— Karl Popper, Notes of a realist on the body–mind problem


Main article: John Searle

For Searle (b. 1932) the mind–body problem is a false dichotomy; that is, mind is a perfectly ordinary aspect of the brain.

According to Searle then, there is no more a mind–body problem than there is a macro–micro economics problem. They are different levels of description of the same set of phenomena. […] But Searle is careful to maintain that the mental – the domain of qualitative experience and understanding – is autonomous and has no counterpart on the microlevel; any redescription of these macroscopic features amounts to a kind of evisceration, …[50]

— Joshua Rust, John Searle

See also[edit]




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Dream argument From Wikipedia, the free encyclopedia The Dream of Life, by unknown Mannerist painter, ca. 1533 T he dream argument is the postulation that the act of dreaming provides preliminary evidence that the senses we trust to distinguish reality from illusion should not be fully trusted, and therefore, any state that is dependent on our senses should at the very least be carefully examined and rigorously tested to determine whether it is in fact reality. Content s 1 Synopsis 2 Hutton’s paradox 3 Simulated reality 4 Critical discussion 5 See also 6 Notes 7 References Synopsis Engra ving of Descartes Part of a series on René Descartes Cartesianism · Rationalism Foundationalism Doubt and certainty Dr eam argument Cogito ergo sum Trademark argument Causal adequacy principle Mind–body dichotomy Analytic geometry Coordi nate system Cartesian circle · Folium Rule of signs · Cartesian diver Balloonist theory Wax argument Res cogitans · R es extensa Works The World Discourse on the Me

Dream argument

From Wikipedia, the free encyclopedia

The Dream of Life, by unknown Manneristpainter, ca. 1533

The dream argument is the postulation that the act of dreaming provides preliminary evidence that the senses we trust to distinguish reality from illusionshould not be fully trusted, and therefore, any state that is dependent on our senses should at the very least be carefully examined and rigorously tested to determine whether it is in fact reality.




Engraving of Descartes
Part of a series on
René Descartes
Cartesianism · Rationalism
Doubt and certainty
Dream argument
Cogito ergo sum
Trademark argument
Causal adequacy principle
Mind–body dichotomy
Analytic geometry
Coordinate system
Cartesian circle · Folium
Rule of signs · Cartesian diver
Balloonist theory
Wax argument
Res cogitans · Res extensa
The World
Discourse on the Method
La Géométrie
Meditations on First Philosophy
Principles of Philosophy
Passions of the Soul
Christina, Queen of Sweden
Baruch Spinoza
Gottfried Wilhelm Leibniz
Francine Descartes

While people dream, they usually do not realize they are dreaming (if they do, it is called a lucid dream). This has led philosophers to wonder whether one could actually be dreaming constantly, instead of being in waking reality (or at least that one cannot be certain, at any given point in time, that one is not dreaming).

In the West, this philosophical puzzle was referred to by Plato (Theaetetus 158b-d) and Aristotle (Metaphysics 1011a6). Having received serious attention in René DescartesMeditations on First Philosophy, the dream argument has become one of the most prominent skeptical hypotheses which clearly has an archetype in elements of Plato’s Allegory of the Cave also.[citation needed]

This type of argument is well known as "Zhuangzi dreamed he was a butterfly" (莊周夢蝶 Zhuāng Zhōu mèng dié): One night, Zhuangzi (369 BC) dreamed that he was a carefree butterfly, flying happily. After he woke up, he wondered how he could determine whether he was Zhuangzi who had just finished dreaming he was a butterfly, or a butterfly who had just started dreaming he was Zhuangzi. This was a metaphor for what he referred to as a "great dream":

He who dreams of drinking wine may weep when morning comes; he who dreams of weeping may in the morning go off to hunt. While he is dreaming he does not know it is a dream, and in his dream he may even try to interpret a dream. Only after he wakes does he know it was a dream. And someday there will be a great awakening when we know that this is all a great dream. Yet the stupid believe they are awake, busily and brightly assuming they understand things, calling this man ruler, that one herdsman—how dense! Confucius and you are both dreaming! And when I say you are dreaming, I am dreaming, too. Words like these will be labeled the Supreme Swindle. Yet, after ten thousand generations, a great sage may appear who will know their meaning, and it will still be as though he appeared with astonishing speed.[1]

One of the first philosophers to posit the dream argument formally was the YogacharaBuddhist philosopher Vasubandhu (fl. 4th to 5th century C.E.) in his ‘Twenty verses on appearance only’. The dream argument features widely in Mahayana Buddhist and Tibetan Buddhist thought.

Some schools of thought in Buddhism (e.g., Dzogchen), consider perceived reality ‘literally’ unreal. As a prominent contemporary teacher, Chögyal Namkhai Norbu, puts it: "In a real sense, all the visions that we see in our lifetime are like a big dream […]".[2] In this context, the term ‘visions’ denotes not only visual perceptions, but appearances perceived through all senses, including sounds, smells, tastes and tactile sensations, and operations on received mental objects.

Hutton’s paradox[edit]

A paradox concerning dreams and the nature of reality was described by the British writer Eric Bond Hutton in 1989.[3] As a child Hutton often had lucid dreams, in which everything seemed as real as in waking life. This led him to wonder whether life itself was a dream, even whether he existed only in somebody else’s dream. Sometimes he had pre-lucid dreams, in which more often than not he concluded he was awake. Such dreams disturbed him greatly, but one day he came up with a magic formula for use in them: "If I find myself asking ‘Am I dreaming?’ it proves I am, for the question would never occur to me in waking life." Yet, such is the nature of dreams, he could never recall it when he needed to. Many years later, when he wrote a piece about solipsism and his childhood interest in dreams, he was struck by a contradiction in his earlier reasoning. True, asking oneself "Am I dreaming?" in a dream would seem to prove one is. Yet that is precisely what he had often asked himself in waking life. Therein lay a paradox. What was he to conclude? That it does not prove one is dreaming? Or that life really is a dream?

Simulated reality[edit]

See also: Simulated reality and Simulation hypothesis

Dreaming provides a springboard for those who question whether our own reality may be an illusion. The ability of the mind to be tricked into believing a mentally generated world is the "real world" means at least one variety of simulated reality is a common, even nightly event.[4]

Those who argue that the world is not simulated must concede that the mind—at least the sleeping mind—is not itself an entirely reliable mechanism for attempting to differentiate reality from illusion.[5]

Whatever I have accepted until now as most true has come to me through my senses. But occasionally I have found that they have deceived me, and it is unwise to trust completely those who have deceived us even once.
— René Descartes[6]

Critical discussion[edit]

In the past, philosophers John Locke and Thomas Hobbes have separately attempted to refute Descartes’s account of the dream argument. Locke claimed that you cannot experience pain in dreams. Various scientific studies conducted within the last few decades provided evidence against Locke’s claim by concluding that pain in dreams can occur but the pain isn’t as severe. Philosopher Ben Springett has said that Locke might respond to this by stating that the agonising pain of stepping in to a fire is non-comparable to stepping in to a fire in a dream. Hobbes claimed that dreams are susceptible to absurdity while the waking life is not.[7]

Many contemporary philosophers have attempted to refute dream skepticism in detail (see, e.g., Stone (1984)).[8] Ernest Sosa(2007) devoted a chapter of a monograph to the topic, in which he presented a new theory of dreaming and argued that his theory raises a new argument for skepticism, which he attempted to refute. In A Virtue Epistemology: Apt Belief and Reflective Knowledge, he states: "in dreaming we do not really believe; we only make-believe."[9] Jonathan Ichikawa (2008) and Nathan Ballantyne & Ian Evans (2010) have offered critiques of Sosa’s proposed solution. Ichikawa argued that as we cannot tell whether our beliefs in waking life are truly beliefs and not imaginings, like in a dream, we are still not able to tell whether we are awake or dreaming.

Norman Malcolm in his monograph "Dreaming" (published in 1959) elaborated on Wittgenstein’s question as to whether it really mattered if people who tell dreams "really had these images while they slept, or whether it merely seems so to them on waking". He argues that the sentence "I am asleep" is a senseless form of words; that dreams cannot exist independently of the waking impression; and that scepticism based on dreaming "comes from confusing the historical and dream telling senses…[of]…the past tense". (page 120). In the chapter: "Do I Know I Am Awake ?" he argues that we do not have to say: "I know that I am awake" simply because it would be absurd to deny that one is awake.

See also[edit]


  1. Jump up^ 莊子, 齊物論, 12. Zhuàngzi, "Discussion on making all things equal," 12. from Zhuàngzi, Burton Watson trans., Chuang Tzu (New York: Columbia University Press, 1996), 43. ISBN 978-0-231-10595-8 [1]
  2. Jump up^ Chögyal Namkhai Norbu Dream Yoga And The Practice Of Natural Light Edited and introduced by Michael Katz, Snow Lion Publications, Ithaca, NY, ISBN 1-55939-007-7, pp. 42, 46, 48, 96, 105.
  3. Jump up^ "Adversaria V," Write Justified, Spring 1989. For Hutton’s definitive statement on the subject see "Hutton’s Paradox," Fortean Times, April 2015, archived online here.
  4. Jump up^ Joseph Barbera, Henry Moller, Dreaming, Virtual Reality, and Presence.
  5. Jump up^ Giuliana A. L. Mazzoni and Elizabeth F. Loftus, When Dreams Become Reality.
  6. Jump up^ René Descartes, Meditations on First Philosophy.
  7. Jump up^ "Dreaming, Philosophy of – Internet Encyclopedia of Philosophy".
  8. Jump up^ Stone, Jim (1984). "Dreaming and Certainty" (PDF). Philosophical Studies. 45 (3): 353–368. doi:10.1007/BF00355443.
  9. Jump up^ Sosa, Ernest (2007). A Virtue Epistemology: Apt Belief and Reflective Knowledge. New York: Oxford University Press. ISBN 978-0-19-929702-3.


Malcolm, N. (1959) Dreaming London: Routledge & Kegan Paul, 2nd Impression 1962.


Philosophical paradoxes (list)



Descartes denied that animals had reason or intelligence. He argued that animals did not lack sensations or perc eptions, but these could be explained mechanistically.92 Whereas humans had a soul, or mind, and were able to feel pai n and anxiety, animals by virtue of not having a soul could not feel pain or anxiety. If animals showed signs of distres s then this was to protect the body from damage, but the innate state needed for them to suffer was absent. Although Des cartes’ views were not universally accepted they became prominent in Europe and North America, allowing humans to trea t animals with impunity. The view that animals were quite separate from humanity and merely machines allowed for the mal treatment of animals, and was sanctioned in law and societal norms until the middle of the 19th century. The publication s of Charles Darwin would eventually erode the Cartesian view of animals. Darwin argued that the continuity between huma ns and other species opened the possibilities

Descartes denied that animals had reason or intelligence. He argued that animals did not lack sensations or perceptions, but these could be explained mechanistically.[92] Whereas humans had a soul, or mind, and were able to feel pain and anxiety, animals by virtue of not having a soul could not feel pain or anxiety. If animals showed signs of distress then this was to protect the body from damage, but the innate state needed for them to suffer was absent. Although Descartes’ views were not universally accepted they became prominent in Europe and North America, allowing humans to treat animals with impunity. The view that animals were quite separate from humanity and merely machines allowed for the maltreatment of animals, and was sanctioned in law and societal norms until the middle of the 19th century. The publications of Charles Darwin would eventually erode the Cartesian view of animals. Darwin argued that the continuity between humans and other species opened the possibilities that animals did not have dissimilar properties to suffer.[93]

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The Pashupatinath Temple (Nepali: पशुपतिनाथ मन्दिर) is a famous, sacred Hindu temple dedicated toPashupatinath and is located on the banks of the Bagmati River 5 kilometres north-east of Kathmandu Valley in the eastern part of Kathmandu, the capital of Nepal. This temple is considered one of the sacred …‎History · ‎Temple complex · ‎Priest · ‎Entry and Darshan












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Pashupatinath Temple

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Pashupatinath Temple, Kathmandu: See 14 reviews, articles, and 18 photos of Pashupatinath Temple, ranked No.86 on TripAdvisor among 188 attractions in Kathmandu.

Pashupatinath Temple – Kathmandu, Nepal – Sacred Destinations

Pashupatinath, or Pashupati, is a Hindu temple on the banks of the Bagmati River in Deopatan, a village 3 km northwest of Kathmandu. It is dedicated to a manifestation of Shiva called Pashupati (Lord of Animals). It attracts thousands of pilgrims each year and has become well known far beyond the Kathmandu Valley.

Kathmandu Pashupatinath Temple Nepal: Transportation,Structure … › Nepal Tibet Tours › Nepal Tours › Kathmandu

Pashupatinath Temple, a world cultural heritage on the banks of the Bagmati River of east Kathmandu is a sacred Hindu temple complex with architectures & cremation ceremony.

Pashupatinath travel – Lonely Planet

Explore Pashupatinath holidays and discover the best time and places to visit. | Nepal’s most important Hindu temple stands on the banks of the holy Bagmati River, surrounded by a bustling market of religious stalls selling marigolds, prasad (offerings), incense, rudraksha beads, conch shells, pictures of Hindu deities and …

Colorful Death: A Day at Pashupatinath Temple in Kathmandu, Nepal ……/colorful-death-pashupatinath-temple-kathmandu-nepal...

Aug 14, 2017 – Pashupatinath is considered to be one of the holiest and most important Hindu places in all of Nepal. After spending a morning there, this is my take on its interesting rituals.

Pashupatinath Temple in Kathmandu – Nepal – YouTube


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Pashupatinath Temple in Kathmandu, Nepal – YouTube


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The Pashupatinath temple complex is located on the holy Bagmati river in Kathmandu, and is the most …

Pashupatinath Temple Hotels, Kathmandu – Book Hotels in ……/pashupatinath_temple-hotels.html

Get the best hotel deals for hotels in Pashupatinath Temple, Kathmandu. ✓ Use coupon code.

About Famous Temple Pashupatinath Temple – Speaking Tree

Apr 15, 2014 – About Famous Temple Pashupatinath Temple – Pashupatinath Temple (Nepali: पशुपतिनाथको मन्दिर) is one of the most significant Hindu temples of Shiva in the world, located on the banks of the Bagmati River in the eastern part of Kathmandu, the capital of Nepal. The temple serves as the seat of …

PASHUPATINATH – Home | Facebook

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PASHUPATINATH, Kathmandu,Nepal. 136K likes. ॐ नम शिवाय। हर हर महादेव !!!!!

The Story that links Kedarnath of India and Pashupatinath of Nepal

Pashupatinath is the guardian spirit and the holiest of all Shiva shrines in Nepal. Pashupatinath Temple is One Part of among one of Dwadash Jyotirlinga of Kedarnath Jyotirlinga Temple. In Chapter 11, titled as ‘Pashupatinath Linga’, of “Koti Rudra Samhita” in Shiva Purana, Pashupatinath has been described as:

Pashupatinath Temple: Of Life and Death | Work the World

Kathmandu has been a Himalayan haven for travellers for decades. The city moves with human life and is famed for its chaotic hustle and bustle. The existence of Pashupatinath crematoria is a reminder that all life eventually comes to an end. Pashupatinath temple is a huge structure that looms over the banks of the …

#Pashupatinath – Twitter Search

22h ago @UjjwalAcharya tweeted: “The life of the dead is placed in the me..” – read what others are saying and join the conversation.

How Did Pashupatinath Temple Survive the Great Earthquake of ……/how-did-pashupatinath-temple-survive-the-great-earth...

May 31, 2015 – Despite the cruel dance of nature in Nepal the age old Pashupatinath still stands strong on the banks of river Bagmati. We take a look at both the scientific.

Pashupatinath Hindu Temple Of Nepal –

One of most popular Hindu pilgrimage sites in the Indian subcontinent, the Pashupatinath temple is located in Kathmandu, Nepal on the banks of the Bagmati River. The temple is associated with centuries of ancient history and culture that amazes all who visit the temple for pilgrimage or tourism. The Hindu supreme deity, …

Pashupatinath Temple, History, Culture,Visiting Timings

Pashupatinath Temple. Located on the banks of river Bagmati River in Kathmandu Valley, Nepal;Pashupatinath got the Grace of God when it went almost unharmed given the range of earthquake hit the roads of valley. Scientific reasons say it happened due to its bricks being held together by strong metal sheets in its roof; …

The 10 Best Pashupatinath Tours & Tickets – Kathmandu | Viator › Nepal › Kathmandu › Attractions

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Pashupatinath – Kathmandu Attractions on

Pashupatinath Temple in Kathmandu Self-Guided Tour – GPSmyCity…/pashupatinath-temple-in-kathmandu-self-guided-tour-...

Pashupatinath Temple is situated near the Tribhuvan International Airport in Kathmnadu. The area in which it is located is truly picturesque – surrounded by virgin jungle. Though you may not be allowed to enter Pashupatinath, you can admire it from the other bank of the river, or you can visit some famous temples situated in …

The Pashupatinath Temple in Kathmandu – Nepal. A sacred site for …

Dec 22, 2014 – Pashupatinath is the most prominent sacred temple for Hindu’s in Nepal . The holy shrine is the greatest place among the Lord Shiva sites. Pashupatinath temple is located in north-east of Kathmandu valley about 5 km away in the bank of Bagmati river. Bagmati is represented as the pious river by religious …

Start of our Nepal Tour at Pashupatinath temple, Kathmandu – Thrilling …

May 19, 2017 – One of the oldest temples, the Pashupatinath temple is a place that every traveler in Kathmandu visits. A travel guide to discovering what makes it special.

Witnessing Open Cremation at Pashupatinath Temple in Kathmandu

Aug 2, 2017 – Read about the open cremation at Pashupatinath temple in Kathmandu, Nepal, which is one of the most visited ancient temples of Nepal & its history.

Babas congregate for Mahashivaratri at Pashupatinath…/babas-congregate-mahashivaratri-pashupatinath/

Feb 13, 2018 – On the eve of the Mahashivaratri festival, which falls today, Sadhus and Babas have started congregating at Pashupatinath temple area.

Pashupatinath temple unharmed in Nepal quake – The Hindu…/article7146853.ece

Apr 27, 2015 – The famous 5th century Pashupatinath Temple in Kathmandu survived the massive 7.9 magnitude earthquake that flattened several World Heritages like iconic Dharhara tower and Darbar Square in Nepal. “The Pashupatinath Temple is safe, we have checked the shrine many times and it has developed …

Go to Pashupatinath And Enjoy Monkey Business | HuffPost…/

Jun 3, 2016 – Have you ever been at Pashupatinath in Kathmandu, Nepal? You would not be allowed to go into all the temples unless you are a Hindu. Only Hindus are allowed to enter inside the main temple of Pashupatinath where a Shiva’s Nandi bull can be seen from the rear. The Pashupatinath Temple, with its …

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A rainbow is a meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of a multicoloured circular arc. Wikipedia

HELLO OLGA AND OBAMA HAPPY HOLI – AND BUBBA -> Descartes also made contributions to the field of optics. He show ed by using geometric construction and the law of refraction(also known as Descartes’ law or more commonly Snell’s l aw) that the angular radius of a rainbow is 42 degrees (i.e., the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow’s centre is 42°).111 He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.112

Descartes also made contributions to the field of optics. He showed by using geometric construction and the law of refraction(also known as Descartes’ law or more commonly Snell’s law) that the angular radius of a rainbow is 42 degrees (i.e., the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow’s centre is 42°).[111] He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.[112]

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René Descartes

From Wikipedia, the free encyclopedia

"Descartes" redirects here. For other uses, see Descartes (disambiguation).

René Descartes
Frans Hals - Portret van René Descartes.jpgPortrait after Frans Hals, 1648[1]
Born 31 March 1596
La Haye en Touraine, Kingdom of France
Died 11 February 1650 (aged 53)
Stockholm, Swedish Empire
Nationality French
Education Collège Royal Henry-Le-Grand(1607–1614)
University of Poitiers (LL.B., 1616)
University of Franeker
Leiden University
Era 17th-century philosophy
Region Western philosophy
School Rationalism
Main interests Metaphysics, epistemology, mathematics, physics, cosmology
Notable ideas Cogito ergo sum
Method of doubt
Method of normals
Cartesian coordinate system
Cartesian dualism
Mathesis universalis
Folium of Descartes
Dream argument
Evil demon
Conservation of momentum(quantitas motus)[2]
Wax argument
Trademark argument
Firma Descartes.svg
Engraving of Descartes
Part of a series on
René Descartes
Cartesianism · Rationalism
Doubt and certainty
Dream argument
Cogito ergo sum
Trademark argument
Causal adequacy principle
Mind–body dichotomy
Analytic geometry
Coordinate system
Cartesian circle · Folium
Rule of signs · Cartesian diver
Balloonist theory
Wax argument
Res cogitans · Res extensa
The World
Discourse on the Method
La Géométrie
Meditations on First Philosophy
Principles of Philosophy
Passions of the Soul
Christina, Queen of Sweden
Baruch Spinoza
Gottfried Wilhelm Leibniz
Francine Descartes

René Descartes (/ˈdeɪˌkɑːrt/;[9] French: [ʁəne dekaʁt]; Latinized: Renatus Cartesius; adjectival form: "Cartesian";[10] 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist. Dubbed the father of modern western philosophy, much of subsequent Western philosophy is a response to his writings,[11][12] which are studied closely to this day. A native of the Kingdom of France, he spent about 20 years (1629–49) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces. He is generally considered one of the most notable intellectual representatives of the Dutch Golden Age.[13]

Descartes’ Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes’ influence in mathematics is equally apparent; the Cartesian coordinate system (see below) was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the scientific revolution.

Descartes refused to accept the authority of previous philosophers. He frequently set his views apart from those of his predecessors. In the opening section of the Les passions de l’âme, a treatise on the early modern version of what are now commonly called emotions, Descartes goes so far as to assert that he will write on this topic "as if no one had written on these matters before". His best known philosophical statement is "Cogito ergo sum" (French: Je pense, donc je suis; I think, therefore I am), found in part IV of Discours de la méthode (1637; written in French but with inclusion of "Cogito ergo sum") and §7 of part I of Principles of Philosophy (1644; written in Latin).[14]

Many elements of his philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like Augustine. In his natural philosophy, he differed from the schools on two major points: first, he rejected the splitting of corporeal substance into matter and form; second, he rejected any appeal to final ends, divine or natural, in explaining natural phenomena.[15] In his theology, he insists on the absolute freedom of God’s act of creation.

Descartes laid the foundation for 17th-century continental rationalism, later advocated by Baruch Spinoza and Gottfried Leibniz, and opposed by the empiricist school of thought consisting of Hobbes, Locke, Berkeley, and Hume. Leibniz, Spinoza[16] and Descartes were all well-versed in mathematics as well as philosophy, and Descartes and Leibniz contributed greatly to science as well.




Early life[edit]

The house where Descartes was born in La Haye en Touraine

Graduation registry for Descartes at the University of Poitiers, 1616

René du Perron Descartes was born in La Haye en Touraine (now Descartes, Indre-et-Loire), France, on 31 March 1596.[17] His mother, Jeanne Brochard, died soon after giving birth to him, and so he was not expected to survive.[17] Descartes’ father, Joachim, was a member of the Parlement of Brittany at Rennes.[18] René lived with his grandmother and with his great-uncle. Although the Descartes family was Roman Catholic, the Poitou region was controlled by the Protestant Huguenots.[19] In 1607, late because of his fragile health, he entered the JesuitCollège Royal Henry-Le-Grand at La Flèche,[20][21] where he was introduced to mathematics and physics, including Galileo’s work.[20][22] After graduation in 1614, he studied for two years (1615–16) at the University of Poitiers, earning a Baccalauréatand Licence in canon and civil law in 1616[20], in accordance with his father’s wishes that he should become a lawyer.[23] From there he moved to Paris.

In his book Discourse on the Method, Descartes recalls,

I entirely abandoned the study of letters. Resolving to seek no knowledge other than that of which could be found in myself or else in the great book of the world, I spent the rest of my youth traveling, visiting courts and armies, mixing with people of diverse temperaments and ranks, gathering various experiences, testing myself in the situations which fortune offered me, and at all times reflecting upon whatever came my way so as to derive some profit from it.

Given his ambition to become a professional military officer, in 1618, Descartes joined, as a mercenary, the Protestant Dutch States Army in Breda under the command of Maurice of Nassau[20], and undertook a formal study of military engineering, as established by Simon Stevin. Descartes, therefore, received much encouragement in Breda to advance his knowledge of mathematics.[20] In this way, he became acquainted with Isaac Beeckman[20], the principal of a Dordrecht school, for whom he wrote the Compendium of Music (written 1618, published 1650). Together they worked on free fall, catenary, conic section, and fluid statics. Both believed that it was necessary to create a method that thoroughly linked mathematics and physics.[24]

While in the service of the Catholic Duke Maximilian of Bavaria since 1619,[25]Descartes was present at the Battle of the White Mountain outside Prague, in November 1620.[26]


According to Adrien Baillet, on the night of 10–11 November 1619 (St. Martin’s Day), while stationed in Neuburg an der Donau, Descartes shut himself in a room with an "oven" (probably a Kachelofen or masonry heater) to escape the cold. While within, he had three dreams[27] and believed that a divine spirit revealed to him a new philosophy. Upon exiting, he had formulated analytical geometry and the idea of applying the mathematical method to philosophy. He concluded from these visions that the pursuit of science would prove to be, for him, the pursuit of true wisdom and a central part of his life’s work.[28][29] Descartes also saw very clearly that all truths were linked with one another so that finding a fundamental truth and proceeding with logic would open the way to all science. Descartes discovered this basic truth quite soon: his famous "I think, therefore I am".[24]


In 1620 Descartes left the army. He visited Basilica della Santa Casa in Loreto, then visited various countries before returning to France, and during the next few years spent time in Paris. It was there that he composed his first essay on method: Regulae ad Directionem Ingenii (Rules for the Direction of the Mind).[24] He arrived in La Haye in 1623, selling all of his property to invest in bonds, which provided a comfortable income for the rest of his life.[30] Descartes was present at the siege of La Rochelle by Cardinal Richelieu in 1627.[31] In the fall of the same year, in the residence of the papal nuncio Guidi di Bagno, where he came with Mersenne and many other scholars to listen to a lecture given by the alchemist Nicolas de Villiers, Sieur de Chandoux on the principles of a supposed new philosophy,[32] Cardinal Bérulle urged him to write an exposition of his own new philosophy in some location beyond the reach of the inquisition.[33]


In Amsterdam, Descartes lived on Westermarkt 6 (Descarteshuis, on the left).

Descartes returned to the Dutch Republic in 1628.[27] In April 1629 he joined the University of Franeker, studying under Adriaan Metius, living either with a Catholic family, or renting the Sjaerdemaslot, where he invited in vain a French cook and an optician.[citation needed] The next year, under the name "Poitevin", he enrolled at the Leiden University to study mathematics with Jacobus Golius, who confronted him with Pappus’s hexagon theorem, and astronomy with Martin Hortensius.[34] In October 1630 he had a falling-out with Beeckman, whom he accused of plagiarizing some of his ideas. In Amsterdam, he had a relationship with a servant girl, Helena Jans van der Strom, with whom he had a daughter, Francine, who was born in 1635 in Deventer.

Unlike many moralists of the time, Descartes was not devoid of passions but rather defended them; he wept upon Francine’s death in 1640.[35] "Descartes said that he did not believe that one must refrain from tears to prove oneself a man." Russell Shortopostulated that the experience of fatherhood and losing a child formed a turning point in Descartes’ work, changing its focus from medicine to a quest for universal answers.[36]

Despite frequent moves,[37] he wrote all his major work during his 20+ years in the Netherlands, where he managed to revolutionize mathematics and philosophy.[38] In 1633, Galileo was condemned by the Catholic Church, and Descartes abandoned plans to publish Treatise on the World, his work of the previous four years. Nevertheless, in 1637 he published part of this work[39] in three essays: "Les Météores" (The Meteors), "La Dioptrique" (Dioptrics) and "La Géométrie" (Geometry), preceded by an introduction, his famous Discours de la méthode (Discourse on the Method).[39] In it, Descartes lays out four rules of thought, meant to ensure that our knowledge rests upon a firm foundation.

The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgment than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.

In La Géométrie, Descartes exploited the discoveries he made with Pierre de Fermat, having been able to do so because his paper, Introduction to Loci, was published posthumously in 1679.[40] This later became known as Cartesian Geometry.[40]

Principia philosophiae, 1644

Descartes continued to publish works concerning both mathematics and philosophy for the rest of his life. In 1641 he published a metaphysics work, Meditationes de Prima Philosophia (Meditations on First Philosophy), written in Latin and thus addressed to the learned. It was followed, in 1644, by Principia Philosophiæ (Principles of Philosophy), a kind of synthesis of the Discourse on the Method and Meditations on First Philosophy. In 1643, Cartesian philosophy was condemned at the University of Utrecht, and Descartes was obliged to flee to the Hague, and settled in Egmond-Binnen.

Descartes began (through Alfonso Polloti, an Italian general in Dutch service) a long correspondence with Princess Elisabeth of Bohemia, devoted mainly to moral and psychological subjects. Connected with this correspondence, in 1649 he published Les Passions de l’âme (Passions of the Soul), that he dedicated to the Princess. In 1647, he was awarded a pension by the Louis XIV of France, though it was never paid.[41] A French translation of Principia Philosophiæ, prepared by Abbot Claude Picot, was published in 1647. This edition Descartes also dedicated to Princess Elisabeth. In the preface to the French edition, Descartes praised true philosophy as a means to attain wisdom. He identifies four ordinary sources to reach wisdom and finally says that there is a fifth, better and more secure, consisting in the search for first causes.[42]


René Descartes (right) with Queen Christina of Sweden (left)

The rear of the "von der Lindeska huset" on Västerlånggatan 68

By 1649, Descartes had become famous throughout Europe for being one of the continent’s greatest philosophers and scientists.[39] That year, Queen Christina of Sweden invited Descartes to her court in to organize a new scientific academy and tutor her in his ideas about love. She was interested in and stimulated Descartes to publish the "Passions of the Soul", a work based on his correspondence with Princess Elisabeth.[43] Descartes accepted, and moved to Sweden in the middle of winter.[44]

He was a guest at the house of Pierre Chanut, living on Västerlånggatan, less than 500 meters from Tre Kronor in Stockholm. There, Chanut and Descartes made observations with a Torricellian barometer, a tube with mercury. Challenging Blaise Pascal, Descartes took the first set of barometric readings in Stockholm to see if atmospheric pressure could be used in forecasting the weather.[45][46]


The tomb of Descartes (middle, with detail of the inscription), in the Abbey of Saint-Germain-des-Prés, Paris

His memorial, erected in the 1720s, in the Adolf Fredriks kyrka

Descartes apparently started giving lessons to Queen Christina after her birthday, three times a week, at 5 a.m, in her cold and draughty castle. Soon it became clear they did not like each other; she did not like his mechanical philosophy, nor did he appreciate her interest in Ancient Greek. By 15 January 1650, Descartes had seen Christina only four or five times. On 1 February he contracted pneumonia and died on 11 February.[47] The cause of death was pneumonia according to Chanut, but peripneumonia according to the doctor Van Wullen who was not allowed to bleed him.[48] (The winter seems to have been mild,[49] except for the second half of January which was harsh as described by Descartes himself; however, "this remark was probably intended to be as much Descartes’ take on the intellectual climate as it was about the weather."[43])

In 1996 E. Pies, a German scholar, published a book questioning this account, based on a letter by Johann van Wullen, who had been sent by Christina to treat him, something Descartes refused, and more arguments against its veracity have been raised since.[50] Descartes might have been assassinated[51][52] as he asked for an emetic: wine mixed with tobacco.[53][dubious ]

As a Catholic[54][55][56] in a Protestant nation, he was interred in a graveyard used mainly for orphans in Adolf Fredriks kyrka in Stockholm. His manuscripts came into the possession of Claude Clerselier, Chanut’s brother-in-law, and "a devout Catholic who has begun the process of turning Descartes into a saint by cutting, adding and publishing his letters selectively."[57] In 1663, the Pope placed his works on the Index of Prohibited Books. In 1666 his remains were taken to France and buried in the Saint-Étienne-du-Mont. In 1671 Louis XIV prohibited all the lectures in Cartesianism. Although the National Convention in 1792 had planned to transfer his remains to the Panthéon, he was reburied in the Abbey of Saint-Germain-des-Prés in 1819, missing a finger and skull.[58] His skull is on display in the Musée de l’Homme in Paris.[59]

Philosophical work[edit]

Further information: Cartesianism

Initially, Descartes arrives at only a single principle: thought exists. Thought cannot be separated from me, therefore, I exist (Discourse on the Method and Principles of Philosophy). Most famously, this is known as cogito ergo sum (English: "I think, therefore I am"). Therefore, Descartes concluded, if he doubted, then something or someone must be doing the doubting, therefore the very fact that he doubted proved his existence. "The simple meaning of the phrase is that if one is sceptical of existence, that is in and of itself proof that he does exist."[60]

Descartes concludes that he can be certain that he exists because he thinks. But in what form? He perceives his body through the use of the senses; however, these have previously been unreliable. So Descartes determines that the only indubitable knowledge is that he is a thinking thing. Thinking is what he does, and his power must come from his essence. Descartes defines "thought" (cogitatio) as "what happens in me such that I am immediately conscious of it, insofar as I am conscious of it". Thinking is thus every activity of a person of which the person is immediately conscious.[61] He gave reasons for thinking that waking thoughts are distinguishable from dreams, and that one’s mind cannot have been "hijacked" by an evil demon placing an illusory external world before one’s senses.[62]

And so something that I thought I was seeing with my eyes is in fact grasped solely by the faculty of judgment which is in my mind.

In this manner, Descartes proceeds to construct a system of knowledge, discarding perception as unreliable and, instead, admitting only deduction as a method.[63]


Further information: Mind-body problem and Mind-body dualism

L’homme (1664)

Descartes, influenced by the automatons on display throughout the city of Paris, began to investigate the connection between the mind and body, and how the two interact.[64]His main influences for dualism were theology and physics.[65] The theory on the dualism of mind and body is Descartes’ signature doctrine and permeates other theories he advanced. Known as Cartesian dualism, his theory on the separation between the mind and the body went on to influence subsequent Western philosophies. In Meditations on First Philosophy Descartes attempted to demonstrate the existence of God and the distinction between the human soul and the body. Humans are a union of mind and body,[66] thus Descartes’ dualism embraced the idea that mind and body are distinct but closely joined. While many contemporary readers of Descartes found the distinction between mind and body difficult to grasp, he thought it was entirely straightforward. Descartes employed the concept of modes, which are the ways in which substances exist. In Principles of Philosophy Descartes explained "we can clearly perceive a substance apart from the mode which we say differs from it, whereas we cannot, conversely, understand the mode apart from the substance". To perceive a mode apart from its substance requires an intellectual abstraction,[67] which Descartes explained as follows:

"The intellectual abstraction consists in my turning my thought away from one part of the contents of this richer idea the better to apply it to the other part with greater attention. Thus, when I consider a shape without thinking of the substance or the extension whose shape it is, I make a mental abstraction."[68]

According to Descartes two substances are really distinct when each of them can exist apart from the other. Thus Descartes reasoned that God is distinct from humans, and the body and mind of a human are also distinct from one another.[69] He argued that the great differences between body and mind make the two always divisible. But that the mind was utterly indivisible, because "when I consider the mind, or myself in so far as I am merely a thinking thing, I am unable to distinguish any part within myself; I understand myself to be something quite single and complete."[70]

In Meditations Descartes discussed a piece of wax and exposed the single most characteristic doctrine of Cartesian dualism: that the universe contained two radically different kinds of substances – the mind or soul defined as thinking, and the body defined as matter and unthinking.[71] The Aristotelian philosophy of Descartes’ days held that the universe was inherently purposeful or theological. Everything that happened, be it the motion of the stars or the growth of a tree, was supposedly explainable by a certain purpose, goal or end that worked its way out within nature. Aristotle called this the "final cause", and these final causes were indispensable for explaining the ways nature operated. With his theory on dualism Descartes fired the opening shot for the battle between the traditional Aristotelian science and the new science of Kepler and Galileo which denied the final cause for explaining nature. Descartes’ dualism provided the philosophical rationale for the latter and he expelled the final cause from the physical universe (or res extensa). For Descartes the only place left for the final cause was the mind (or res cogitans). Therefore, while Cartesian dualism paved the way for modern physics, it also held the door open for religious beliefs about the immortality of the soul.[72]

Descartes’ dualism of mind and matter implied a concept of human beings. A human was according to Descartes a composite entity of mind and body. Descartes gave priority to the mind and argued that the mind could exist without the body, but the body could not exist without the mind. In Meditations Descartes even argues that while the mind is a substance, the body is composed only of "accidents".[73] But he did argue that mind and body are closely joined,[74] because:

"Nature also teaches me, by the sensations of pain, hunger, thirst and so on, that I am not merely present in my body as a pilot in his ship, but that I am very closely joined and, as it were, intermingled with it, so that I and the body form a unit. If this were not so, I, who am nothing but a thinking thing, would not feel pain when the body was hurt, but would perceive the damage purely by the intellect, just as a sailor perceives by sight if anything in his ship is broken.[75]

Descartes’ discussion on embodiment raised one of the most perplexing problems of his dualism philosophy: What exactly is the relationship of union between the mind and the body of a person?[76] Therefore, Cartesian dualism set the agenda for philosophical discussion of the mind–body problem for many years after Descartes’ death.[77] Descartes was also a rationalistand believed in the power of innate ideas.[78] Descartes argued the theory of innate knowledge and that all humans were born with knowledge through the higher power of God. It was this theory of innate knowledge that later led philosopher John Locke(1632-1704) to combat the theory of empiricism, which held that all knowledge is acquired through experience.[79]

Descartes on physiology and psychology[edit]

In The Passions of the Soul written between 1645 and 1646 Descartes discussed the common contemporary belief that the human body contained animal spirits. These animal spirits were believed to be light and roaming fluids circulating rapidly around the nervous system between the brain and the muscles, and served as a metaphor for feelings, like being in high or bad spirit. These animal spirits were believed to affect the human soul, or passions of the soul. Descartes distinguished six basic passions: wonder, love, hatred, desire, joy and sadness. All of these passions, he argued, represented different combinations of the original spirit, and influenced the soul to will or want certain actions. He argued, for example, that fear is a passion that moves the soul to generate a response in the body. In line with his dualist teachings on the separation between the soul and the body, he hypothesized that some part of the brain served as a connector between the soul and the body and singled out the pineal gland as connector.[80] Descartes argued that signals passed from the ear and the eye to the pineal gland, through animal spirits. Thus different motions in the gland cause various animal spirits. He argued that these motions in the pineal gland are based on God’s will and that humans are supposed to want and like things that are useful to them. But he also argued that that the animal spirits that moved around the body could distort the commands from the pineal gland, thus humans had to learn how to control their passions.[81]

Descartes advanced a theory on automatic bodily reactions to external events which influenced 19th century reflex theory. He argued that external motions such as touch and sound reach the endings of the nerves and affect the animal spirits. Heat from fire affects a spot on the skin and sets in motion a chain of reactions, with the animal spirits reaching the brain through the central nervous system, and in turn animal spirits are sent back to the muscles to move the hand away from the fire.[82]Through this chain of reactions the automatic reactions of the body do not require a thought process.[83]

Above all he was among the first scientists who believed that the soul should be subject to scientific investigation. He challenged the views of his contemporaries that the soul was divine, thus religious authorities regarded his books as dangerous. Descartes’ writings went on to form the basis for theories on emotions and how cognitive evaluations were translated into affective processes. Descartes believed that the brain resembled a working machine and unlike many of his contemporaries believed that mathematics and mechanics could explain the most complicated processes of the mind. In the 20th century Alan Turing advanced computer science based on mathematical biology as inspired by Descartes. His theories on reflexes also served as the foundation for advanced physiological theories more than 200 years after his death. The Nobel Prize winning physiologist Ivan Pavlov was a great admirer of Descartes.[84]

Three types of ideas[edit]

There are three kinds of ideas, Descartes explained: Fabricated, Innate and Adventitious. Fabricated ideas are inventions made by the mind. For example, a person has never eaten moose but assumes it tastes like cow. Adventitious ideas are ideas that cannot be manipulated or changed by the mind. For example, a person stands in a cold room, they can only think of the feeling as cold and nothing else. Innate ideas are set ideas made by God in a person’s mind. For example, the features of a shape can be examined and set aside, but its content can never be manipulated to cause it not to be a three sided object.[85]

Descartes’ moral philosophy[edit]

For Descartes, ethics was a science, the highest and most perfect of them. Like the rest of the sciences, ethics had its roots in metaphysics.[63] In this way, he argues for the existence of God, investigates the place of man in nature, formulates the theory of mind-body dualism, and defends free will. However, as he was a convinced rationalist, Descartes clearly states that reason is sufficient in the search for the goods that we should seek, and virtue consists in the correct reasoning that should guide our actions. Nevertheless, the quality of this reasoning depends on knowledge, because a well-informed mind will be more capable of making good choices, and it also depends on mental condition. For this reason, he said that a complete moral philosophy should include the study of the body. He discussed this subject in the correspondence with Princess Elisabeth of Bohemia, and as a result wrote his work The Passions of the Soul, that contains a study of the psychosomatic processes and reactions in man, with an emphasis on emotions or passions.[86] His works about human passion and emotion would be the basis for the philosophy of his followers, (see Cartesianism), and would have a lasting impact on ideas concerning what literature and art should be, specifically how it should invoke emotion.[87]

Humans should seek the sovereign good that Descartes, following Zeno, identifies with virtue, as this produces a solid blessedness or pleasure. For Epicurus the sovereign good was pleasure, and Descartes says that, in fact, this is not in contradiction with Zeno’s teaching, because virtue produces a spiritual pleasure, that is better than bodily pleasure. Regarding Aristotle‘s opinion that happiness depends on the goods of fortune, Descartes does not deny that this good contributes to happiness but remarks that they are in great proportion outside one’s own control, whereas one’s mind is under one’s complete control.[86] The moral writings of Descartes came at the last part of his life, but earlier, in his Discourse on the Method he adopted three maxims to be able to act while he put all his ideas into doubt. This is known as his "Provisional Morals".

Descartes on religious beliefs[edit]

René Descartes at work

In the third and fifth Meditation, he offers an ontological proof of a benevolent God (through both the ontological argument and trademark argument). Because God is benevolent, he can have some faith in the account of reality his senses provide him, for God has provided him with a working mind and sensory system and does not desire to deceive him. From this supposition, however, he finally establishes the possibility of acquiring knowledge about the world based on deduction and perception. Regarding epistemology, therefore, he can be said to have contributed such ideas as a rigorous conception of foundationalism and the possibility that reason is the only reliable method of attaining knowledge. He, nevertheless, was very much aware that experimentation was necessary to verify and validate theories.[63]

In his Meditations on First Philosophy Descartes sets forth two proofs for God’s existence. One of these is founded upon the possibility of thinking the "idea of a being that is supremely perfect and infinite," and suggests that "of all the ideas that are in me, the idea that I have of God is the most true, the most clear and distinct."[88]Descartes considered himself to be a devout Catholic[54][55][56] and one of the purposes of the Meditations was to defend the Catholic faith. His attempt to ground theological beliefs on reason encountered intense opposition in his time, however: Pascal regarded Descartes’ views as rationalist and mechanist, and accused him of deism: "I cannot forgive Descartes; in all his philosophy, Descartes did his best to dispense with God. But Descartes could not avoid prodding God to set the world in motion with a snap of his lordly fingers; after that, he had no more use for God," while a powerful contemporary, Martin Schoock, accused him of atheist beliefs, though Descartes had provided an explicit critique of atheism in his Meditations. The Catholic Church prohibited his books in 1663.[41][89]

Descartes also wrote a response to External world scepticism. Through this method of scepticism, he does not doubt for the sake of doubting but to achieve concrete and reliable information. In other words, certainty. He argues that sensory perceptionscome to him involuntarily, and are not willed by him. They are external to his senses, and according to Descartes, this is evidence of the existence of something outside of his mind, and thus, an external world. Descartes goes on to show that the things in the external world are material by arguing that God would not deceive him as to the ideas that are being transmitted, and that God has given him the "propensity" to believe that such ideas are caused by material things. Descartes also believes a substance is something that does not need any assistance to function or exist. Descartes further explains how only God can be a true “substance”. But minds are substances, meaning they need only God for it to function. The mind is a thinking substance. The means for a thinking substance stem from ideas.[85]

Descartes and natural science[edit]

Descartes is often regarded as the first thinker to emphasize the use of reason to develop the natural sciences.[90] For him the philosophy was a thinking system that embodied all knowledge, and expressed it in this way:[63]

Thus, all Philosophy is like a tree, of which Metaphysics is the root, Physics the trunk, and all the other sciences the branches that grow out of this trunk, which are reduced to three principals, namely, Medicine, Mechanics, and Ethics. By the science of Morals, I understand the highest and most perfect which, presupposing an entire knowledge of the other sciences, is the last degree of wisdom.

In his Discourse on the Method, he attempts to arrive at a fundamental set of principles that one can know as true without any doubt. To achieve this, he employs a method called hyperbolical/metaphysical doubt, also sometimes referred to as methodological scepticism: he rejects any ideas that can be doubted and then re-establishes them in order to acquire a firm foundation for genuine knowledge.[91] Descartes built his ideas from scratch. He relates this to architecture: the top soil is taken away to create a new building or structure. Descartes calls his doubt the soil and new knowledge the buildings. To Descartes, Aristotle’s foundationalism is incomplete and his method of doubt enhances foundationalism.[62]

Descartes on animals[edit]

Descartes denied that animals had reason or intelligence. He argued that animals did not lack sensations or perceptions, but these could be explained mechanistically.[92] Whereas humans had a soul, or mind, and were able to feel pain and anxiety, animals by virtue of not having a soul could not feel pain or anxiety. If animals showed signs of distress then this was to protect the body from damage, but the innate state needed for them to suffer was absent. Although Descartes’ views were not universally accepted they became prominent in Europe and North America, allowing humans to treat animals with impunity. The view that animals were quite separate from humanity and merely machines allowed for the maltreatment of animals, and was sanctioned in law and societal norms until the middle of the 19th century. The publications of Charles Darwin would eventually erode the Cartesian view of animals. Darwin argued that the continuity between humans and other species opened the possibilities that animals did not have dissimilar properties to suffer.[93]

Historical impact[edit]

Emancipation from Church doctrine[edit]

Cover of Meditations

Descartes has often been dubbed the father of modern Western philosophy, the thinker whose approach has profoundly changed the course of Western philosophy and set the basis for modernity.[11][94] The first two of his Meditations on First Philosophy, those that formulate the famous methodic doubt, represent the portion of Descartes’ writings that most influenced modern thinking.[95] It has been argued that Descartes himself didn’t realize the extent of this revolutionary move.[96] In shifting the debate from "what is true" to "of what can I be certain?," Descartes arguably shifted the authoritative guarantor of truth from God to humanity (even though Descartes himself claimed he received his visions from God) – while the traditional concept of "truth" implies an external authority, "certainty" instead relies on the judgment of the individual.

In an anthropocentric revolution, the human being is now raised to the level of a subject, an agent, an emancipated being equipped with autonomous reason. This was a revolutionary step that established the basis of modernity, the repercussions of which are still being felt: the emancipation of humanity from Christian revelational truth and Church doctrine; humanity making its own law and taking its own stand.[97][98][99] In modernity, the guarantor of truth is not God anymore but human beings, each of whom is a "self-conscious shaper and guarantor" of their own reality.[100][101] In that way, each person is turned into a reasoning adult, a subject and agent,[100] as opposed to a child obedient to God. This change in perspective was characteristic of the shift from the Christian medieval period to the modern period, a shift that had been anticipated in other fields, and which was now being formulated in the field of philosophy by Descartes.[100][102]

This anthropocentric perspective of Descartes’ work, establishing human reason as autonomous, provided the basis for the Enlightenment‘s emancipation from God and the Church. According to Martin Heidegger, the perspective of Descartes’ work also provided the basis for all subsequent anthropology.[103] Descartes’ philosophical revolution is sometimes said to have sparked modern anthropocentrism and subjectivism.[11][104][105][106]

Mathematical legacy[edit]

A Cartesian coordinates graph, using his invented x and y axes

One of Descartes’ most enduring legacies was his development of Cartesian or analytic geometry, which uses algebra to describe geometry. He "invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c". He also "pioneered the standard notation" that uses superscripts to show the powers or exponents; for example, the 4 used in x4 to indicate squaring of squaring.[107][108] He was first to assign a fundamental place for algebra in our system of knowledge, using it as a method to automate or mechanize reasoning, particularly about abstract, unknown quantities. European mathematicians had previously viewed geometry as a more fundamental form of mathematics, serving as the foundation of algebra. Algebraic rules were given geometric proofs by mathematicians such as Pacioli, Cardan, Tartaglia and Ferrari. Equations of degree higher than the third were regarded as unreal, because a three-dimensional form, such as a cube, occupied the largest dimension of reality. Descartes professed that the abstract quantity a2 could represent length as well as an area. This was in opposition to the teachings of mathematicians, such as Vieta, who argued that it could represent only area. Although Descartes did not pursue the subject, he preceded Gottfried Wilhelm Leibniz in envisioning a more general science of algebra or "universal mathematics," as a precursor to symbolic logic, that could encompass logical principles and methods symbolically, and mechanize general reasoning.[109]

Descartes’ work provided the basis for the calculus developed by Newton and Leibniz, who applied infinitesimal calculus to the tangent line problem, thus permitting the evolution of that branch of modern mathematics.[110] His rule of signs is also a commonly used method to determine the number of positive and negative roots of a polynomial.

Descartes discovered an early form of the law of conservation of mechanical momentum (a measure of the motion of an object), and envisioned it as pertaining to motion in a straight line, as opposed to perfect circular motion, as Galileo had envisioned it. He outlined his views on the universe in his Principles of Philosophy.

Descartes also made contributions to the field of optics. He showed by using geometric construction and the law of refraction(also known as Descartes’ law or more commonly Snell’s law) that the angular radius of a rainbow is 42 degrees (i.e., the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow’s centre is 42°).[111] He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.[112]

Influence on Newton’s mathematics[edit]

Current opinion is that Descartes had the most influence of anyone on the young Newton, and this is arguably one of Descartes’ most important contributions. Newton continued Descartes’ work on cubic equations, which freed the subject from the fetters of the Greek perspectives. The most important concept was his very modern treatment of independent variables.[113]

Contemporary reception[edit]

Although Descartes was well known in academic circles towards the end of his life, the teaching of his works in schools was controversial. Henri de Roy (Henricus Regius, 1598–1679), Professor of Medicine at the University of Utrecht, was condemned by the Rector of the University, Gijsbert Voet (Voetius), for teaching Descartes’ physics.[114]


Handwritten letter by Descartes, December 1638

Principia philosophiae (1685)

  • 1618. Musicae Compendium. A treatise on music theory and the aesthetics of music written for Descartes’ early collaborator, Isaac Beeckman (first posthumous edition 1650).
  • 1626–1628. Regulae ad directionem ingenii (Rules for the Direction of the Mind). Incomplete. First published posthumously in Dutch translation in 1684 and in the original Latin at Amsterdam in 1701 (R. Des-Cartes Opuscula Posthuma Physica et Mathematica). The best critical edition, which includes the Dutch translation of 1684, is edited by Giovanni Crapulli (The Hague: Martinus Nijhoff, 1966).
  • 1630–1631. La recherche de la vérité par la lumière naturelle (The Search for Truth) unfinished dialogue published in 1701.
  • 1630–1633. Le Monde (The World) and L’Homme (Man). Descartes’ first systematic presentation of his natural philosophy. Man was published posthumously in Latin translation in 1662; and The World posthumously in 1664.
  • 1637. Discours de la méthode (Discourse on the Method). An introduction to the Essais, which include the Dioptrique, the Météores and the Géométrie.
  • 1637. La Géométrie (Geometry). Descartes’ major work in mathematics. There is an English translation by Michael Mahoney (New York: Dover, 1979).
  • 1641. Meditationes de prima philosophia (Meditations on First Philosophy), also known as Metaphysical Meditations. In Latin; a second edition, published the following year, included an additional objection and reply, and a Letter to Dinet. A French translation by the Duke of Luynes, probably done without Descartes’ supervision, was published in 1647. Includes six Objections and Replies.
  • 1644. Principia philosophiae (Principles of Philosophy), a Latin textbook at first intended by Descartes to replace the Aristotelian textbooks then used in universities. A French translation, Principes de philosophie by Claude Picot, under the supervision of Descartes, appeared in 1647 with a letter-preface to Princess Elisabeth of Bohemia.
  • 1647. Notae in programma (Comments on a Certain Broadsheet). A reply to Descartes’ one-time disciple Henricus Regius.
  • 1648. La description du corps humain (The Description of the Human Body). Published posthumously by Clerselier in 1667.
  • 1648. Responsiones Renati Des Cartes… (Conversation with Burman). Notes on a Q&A session between Descartes and Frans Burman on 16 April 1648. Rediscovered in 1895 and published for the first time in 1896. An annotated bilingual edition (Latin with French translation), edited by Jean-Marie Beyssade, was published in 1981 (Paris: PUF).
  • 1649. Les passions de l’âme (Passions of the Soul). Dedicated to Princess Elisabeth of the Palatinate.
  • 1657. Correspondance (three volumes: 1657, 1659, 1667). Published by Descartes’ literary executor Claude Clerselier. The third edition, in 1667, was the most complete; Clerselier omitted, however, much of the material pertaining to mathematics.

In January 2010, a previously unknown letter from Descartes, dated 27 May 1641, was found by the Dutch philosopher Erik-Jan Bos when browsing through Google. Bos found the letter mentioned in a summary of autographs kept by Haverford College in Haverford, Pennsylvania. The College was unaware that the letter had never been published. This was the third letter by Descartes found in the last 25 years.[115][116]

















In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.

Analytic geometry is widely used in physics and engineering, and also in aviationrocketryspace science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraicdifferentialdiscrete and computational geometry.

Usually the Cartesian coordinate system is applied to manipulate equations for planesstraight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space (three dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes’ numerical definitions and representations. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.




Ancient Greece[edit]

The Greek mathematician Menaechmus solved problems and proved theorems by using a method that had a strong resemblance to the use of coordinates and it has sometimes been maintained that he had introduced analytic geometry.[1]

Apollonius of Perga, in On Determinate Section, dealt with problems in a manner that may be called an analytic geometry of one dimension; with the question of finding points on a line that were in a ratio to the others.[2] Apollonius in the Conics further developed a method that is so similar to analytic geometry that his work is sometimes thought to have anticipated the work of Descartes by some 1800 years. His application of reference lines, a diameter and a tangent is essentially no different from our modern use of a coordinate frame, where the distances measured along the diameter from the point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates. He further developed relations between the abscissas and the corresponding ordinates that are equivalent to rhetorical equations of curves. However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori. That is, equations were determined by curves, but curves were not determined by equations. Coordinates, variables, and equations were subsidiary notions applied to a specific geometric situation.[3]


The eleventh century Persian mathematician Omar Khayyám saw a strong relationship between geometry and algebra, and was moving in the right direction when he helped to close the gap between numerical and geometric algebra[4] with his geometric solution of the general cubic equations,[5] but the decisive step came later with Descartes.[4]

Western Europe[edit]

Analytic geometry was independently invented by René Descartes and Pierre de Fermat,[6][7] although Descartes is sometimes given sole credit.[8][9] Cartesian geometry, the alternative term used for analytic geometry, is named after Descartes.

Descartes made significant progress with the methods in an essay titled La Geometrie (Geometry), one of the three accompanying essays (appendices) published in 1637 together with his Discourse on the Method for Rightly Directing One’s Reason and Searching for Truth in the Sciences, commonly referred to as Discourse on Method. This work, written in his native French tongue, and its philosophical principles, provided a foundation for calculus in Europe. Initially the work was not well received, due, in part, to the many gaps in arguments and complicated equations. Only after the translation into Latin and the addition of commentary by van Schooten in 1649 (and further work thereafter) did Descartes’s masterpiece receive due recognition.[10]

Pierre de Fermat also pioneered the development of analytic geometry. Although not published in his lifetime, a manuscript form of Ad locos planos et solidos isagoge (Introduction to Plane and Solid Loci) was circulating in Paris in 1637, just prior to the publication of Descartes’ Discourse.[11][12][13] Clearly written and well received, the Introduction also laid the groundwork for analytical geometry. The key difference between Fermat’s and Descartes’ treatments is a matter of viewpoint: Fermat always started with an algebraic equation and then described the geometric curve which satisfied it, whereas Descartes started with geometric curves and produced their equations as one of several properties of the curves.[10] As a consequence of this approach, Descartes had to deal with more complicated equations and he had to develop the methods to work with polynomial equations of higher degree. It was Leonhard Euler who first applied the coordinate method in a systematic study of space curves and surfaces.


Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: (2,3) in green, (−3,1) in red, (−1.5,−2.5) in blue, and the origin (0,0) in purple.

In analytic geometry, the plane is given a coordinate system, by which every pointhas a pair of real number coordinates. Similarly, Euclidean space is given coordinates where every point has three coordinates. The value of the coordinates depends on the choice of the initial point of origin. There are a variety of coordinate systems used, but the most common are the following:[14]

Cartesian coordinates (in a plane or space)[edit]

The most common coordinate system to use is the Cartesian coordinate system, where each point has an x-coordinate representing its horizontal position, and a y-coordinate representing its vertical position. These are typically written as an ordered pair (xy). This system can also be used for three-dimensional geometry, where every point in Euclidean space is represented by an ordered triple of coordinates (xyz).

Polar coordinates (in a plane)[edit]

In polar coordinates, every point of the plane is represented by its distance r from the origin and its angle θ from the polar axis.

Cylindrical coordinates (in a space)[edit]

In cylindrical coordinates, every point of space is represented by its height z, its radius r from the z-axis and the angle θ its projection on the xy-plane makes with respect to the horizontal axis.

Spherical coordinates (in a space)[edit]

In spherical coordinates, every point in space is represented by its distance ρ from the origin, the angle θ its projection on the xy-plane makes with respect to the horizontal axis, and the angle φ that it makes with respect to the z-axis. The names of the angles are often reversed in physics.[14]

Equations and curves[edit]

In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation, or locus. For example, the equation y = x corresponds to the set of all the points on the plane whose x-coordinate and y-coordinate are equal. These points form a line, and y = x is said to be the equation for this line. In general, linear equations involving x and y specify lines, quadratic equations specify conic sections, and more complicated equations describe more complicated figures.[15]

Usually, a single equation corresponds to a curve on the plane. This is not always the case: the trivial equation x = x specifies the entire plane, and the equation x2 + y2 = 0 specifies only the single point (0, 0). In three dimensions, a single equation usually gives a surface, and a curve must be specified as the intersection of two surfaces (see below), or as a system of parametric equations.[16] The equation x2 + y2 = r2 is the equation for any circle centered at the origin (0, 0) with a radius of r.

Lines and planes[edit]

Lines in a Cartesian plane or, more generally, in affine coordinates, can be described algebraically by linear equations. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form:

{\displaystyle y=mx+b\,}


m is the slope or gradient of the line.

b is the y-intercept of the line.

x is the independent variable of the function y = f(x).

In a manner analogous to the way lines in a two-dimensional space are described using a point-slope form for their equations, planes in a three dimensional space have a natural description using a point in the plane and a vector orthogonal to it (the normal vector) to indicate its “inclination”.

Specifically, let {\displaystyle \mathbf {r} _{0}} be the position vector of some point {\displaystyle P_{0}=(x_{0},y_{0},z_{0})}, and let {\displaystyle \mathbf {n} =(a,b,c)} be a nonzero vector. The plane determined by this point and vector consists of those points {\displaystyle P}, with position vector {\displaystyle \mathbf {r} }, such that the vector drawn from {\displaystyle P_{0}}to {\displaystyle P} is perpendicular to {\displaystyle \mathbf {n} }. Recalling that two vectors are perpendicular if and only if their dot product is zero, it follows that the desired plane can be described as the set of all points {\displaystyle \mathbf {r} } such that

{\displaystyle \mathbf {n} \cdot (\mathbf {r} -\mathbf {r} _{0})=0.}

(The dot here means a dot product, not scalar multiplication.) Expanded this becomes

{\displaystyle a(x-x_{0})+b(y-y_{0})+c(z-z_{0})=0,}

which is the point-normal form of the equation of a plane.[17] This is just a linear equation:

{\displaystyle ax+by+cz+d=0,{\text{ where }}d=-(ax_{0}+by_{0}+cz_{0}).}

Conversely, it is easily shown that if abc and d are constants and ab, and c are not all zero, then the graph of the equation

{\displaystyle ax+by+cz+d=0,}

is a plane having the vector {\displaystyle \mathbf {n} =(a,b,c)} as a normal.[18] This familiar equation for a plane is called the general form of the equation of the plane.[19]

In three dimensions, lines can not be described by a single linear equation, so they are frequently described by parametric equations:

{\displaystyle x=x_{0}+at\,}

{\displaystyle y=y_{0}+bt\,}

{\displaystyle z=z_{0}+ct\,}


xy, and z are all functions of the independent variable t which ranges over the real numbers.

(x0y0z0) is any point on the line.

ab, and c are related to the slope of the line, such that the vector (abc) is parallel to the line.

Conic sections[edit]

In the Cartesian coordinate system, the graph of a quadratic equation in two variables is always a conic section – though it may be degenerate, and all conic sections arise in this way. The equation will be of the form

{\displaystyle Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0{\text{ with }}A,B,C{\text{ not all zero.}}\,}

As scaling all six constants yields the same locus of zeros, one can consider conics as points in the five-dimensional projective space {\displaystyle \mathbf {P} ^{5}.}

The conic sections described by this equation can be classified using the discriminant[20]

{\displaystyle B^{2}-4AC.\,}

If the conic is non-degenerate, then:

  • if {\displaystyle B^{2}-4AC<0}, the equation represents an ellipse;

    • if {\displaystyle A=C} and {\displaystyle B=0}, the equation represents a circle, which is a special case of an ellipse;

  • if {\displaystyle B^{2}-4AC=0}, the equation represents a parabola;

  • if {\displaystyle B^{2}-4AC>0}, the equation represents a hyperbola;

Quadric surfaces[edit]

quadric, or quadric surface, is a 2-dimensional surface in 3-dimensional space defined as the locus of zeros of a quadratic polynomial. In coordinates x1x2,x3, the general quadric is defined by the algebraic equation[21]

{\displaystyle \sum _{i,j=1}^{3}x_{i}Q_{ij}x_{j}+\sum _{i=1}^{3}P_{i}x_{i}+R=0.}

Quadric surfaces include ellipsoids (including the sphere), paraboloidshyperboloidscylinderscones, and planes.

Distance and angle[edit]

The distance formula on the plane follows from the Pythagorean theorem.

In analytic geometry, geometric notions such as distance and angle measure are defined using formulas. These definitions are designed to be consistent with the underlying Euclidean geometry. For example, using Cartesian coordinates on the plane, the distance between two points (x1y1) and (x2y2) is defined by the formula

{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}},\!}

which can be viewed as a version of the Pythagorean theorem. Similarly, the angle that a line makes with the horizontal can be defined by the formula

{\displaystyle \theta =\arctan(m),}

where m is the slope of the line.

In three dimensions, distance is given by the generalization of the Pythagorean theorem:

{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}},\!},

while the angle between two vectors is given by the dot product. The dot product of two Euclidean vectors A and B is defined by[22]

{\displaystyle \mathbf {A} \cdot \mathbf {B} {\stackrel {\mathrm {def} }{=}}\|\mathbf {A} \|\,\|\mathbf {B} \|\cos \theta ,}

where θ is the angle between A and B.


a) y = f(x) = |x|       b) y = f(x+3)       c) y = f(x)-3       d) y = 1/2 f(x)

Transformations are applied to a parent function to turn it into a new function with similar characteristics.

The graph of {\displaystyle R(x,y)} is changed by standard transformations as follows:

  • Changing {\displaystyle x} to {\displaystyle x-h} moves the graph to the right {\displaystyle h}units.

  • Changing {\displaystyle y} to {\displaystyle y-k} moves the graph up {\displaystyle k} units.

  • Changing {\displaystyle x} to {\displaystyle x/b} stretches the graph horizontally by a factor of {\displaystyle b}. (think of the {\displaystyle x} as being dilated)

  • Changing {\displaystyle y} to {\displaystyle y/a} stretches the graph vertically.

  • Changing {\displaystyle x} to {\displaystyle x\cos A+y\sin A} and changing {\displaystyle y} to {\displaystyle -x\sin A+y\cos A} rotates the graph by an angle {\displaystyle A}.

There are other standard transformation not typically studied in elementary analytic geometry because the transformations change the shape of objects in ways not usually considered. Skewing is an example of a transformation not usually considered. For more information, consult the Wikipedia article on affine transformations.

For example, the parent function {\displaystyle y=1/x} has a horizontal and a vertical asymptote, and occupies the first and third quadrant, and all of its transformed forms have one horizontal and vertical asymptote,and occupies either the 1st and 3rd or 2nd and 4th quadrant. In general, if {\displaystyle y=f(x)}, then it can be transformed into {\displaystyle y=af(b(x-k))+h}. In the new transformed function, {\displaystyle a}is the factor that vertically stretches the function if it is greater than 1 or vertically compresses the function if it is less than 1, and for negative {\displaystyle a} values, the function is reflected in the {\displaystyle x}-axis. The {\displaystyle b} value compresses the graph of the function horizontally if greater than 1 and stretches the function horizontally if less than 1, and like {\displaystyle a}, reflects the function in the {\displaystyle y}-axis when it is negative. The {\displaystyle k} and {\displaystyle h} values introduce translations, {\displaystyle h}, vertical, and {\displaystyle k} horizontal. Positive {\displaystyle h} and {\displaystyle k} values mean the function is translated to the positive end of its axis and negative meaning translation towards the negative end.

Transformations can be applied to any geometric equation whether or not the equation represents a function. Transformations can be considered as individual transactions or in combinations.

Suppose that {\displaystyle R(x,y)} is a relation in the {\displaystyle xy} plane. For example,

{\displaystyle x^{2}+y^{2}-1=0}

is the relation that describes the unit circle.

Finding intersections of geometric objects[edit]

For two geometric objects P and Q represented by the relations {\displaystyle P(x,y)} and {\displaystyle Q(x,y)} the intersection is the collection of all points {\displaystyle (x,y)} which are in both relations.[23]

For example, {\displaystyle P} might be the circle with radius 1 and center {\displaystyle (0,0)}{\displaystyle P=\{(x,y)|x^{2}+y^{2}=1\}} and {\displaystyle Q} might be the circle with radius 1 and center {\displaystyle (1,0):Q=\{(x,y)|(x-1)^{2}+y^{2}=1\}}. The intersection of these two circles is the collection of points which make both equations true. Does the point {\displaystyle (0,0)} make both equations true? Using {\displaystyle (0,0)} for {\displaystyle (x,y)}, the equation for {\displaystyle Q} becomes {\displaystyle (0-1)^{2}+0^{2}=1} or {\displaystyle (-1)^{2}=1} which is true, so {\displaystyle (0,0)} is in the relation {\displaystyle Q}. On the other hand, still using {\displaystyle (0,0)} for {\displaystyle (x,y)} the equation for {\displaystyle P} becomes {\displaystyle 0^{2}+0^{2}=1} or {\displaystyle 0=1} which is false. {\displaystyle (0,0)} is not in {\displaystyle P} so it is not in the intersection.

The intersection of {\displaystyle P} and {\displaystyle Q} can be found by solving the simultaneous equations:

{\displaystyle x^{2}+y^{2}=1}

{\displaystyle (x-1)^{2}+y^{2}=1.}

Traditional methods for finding intersections include substitution and elimination.

Substitution: Solve the first equation for {\displaystyle y} in terms of {\displaystyle x} and then substitute the expression for {\displaystyle y} into the second equation:

{\displaystyle x^{2}+y^{2}=1}

{\displaystyle y^{2}=1-x^{2}}.

We then substitute this value for {\displaystyle y^{2}} into the other equation and proceed to solve for {\displaystyle x}:

{\displaystyle (x-1)^{2}+(1-x^{2})=1}

{\displaystyle x^{2}-2x+1+1-x^{2}=1}

{\displaystyle -2x=-1}

{\displaystyle x=1/2.}

Next, we place this value of {\displaystyle x} in either of the original equations and solve for {\displaystyle y}:

{\displaystyle (1/2)^{2}+y^{2}=1}

{\displaystyle y^{2}=3/4}

{\displaystyle y={\frac {\pm {\sqrt {3}}}{2}}.}

So our intersection has two points:

{\displaystyle \left(1/2,{\frac {+{\sqrt {3}}}{2}}\right)\;\;\mathrm {and} \;\;\left(1/2,{\frac {-{\sqrt {3}}}{2}}\right).}

Elimination: Add (or subtract) a multiple of one equation to the other equation so that one of the variables is eliminated. For our current example, if we subtract the first equation from the second we get {\displaystyle (x-1)^{2}-x^{2}=0}. The {\displaystyle y^{2}} in the first equation is subtracted from the {\displaystyle y^{2}} in the second equation leaving no {\displaystyle y} term. The variable {\displaystyle y} has been eliminated. We then solve the remaining equation for {\displaystyle x}, in the same way as in the substitution method:

{\displaystyle x^{2}-2x+1+1-x^{2}=1}

{\displaystyle -2x=-1}

{\displaystyle x=1/2.}

We then place this value of {\displaystyle x} in either of the original equations and solve for {\displaystyle y}:

{\displaystyle (1/2)^{2}+y^{2}=1}

{\displaystyle y^{2}=3/4}

{\displaystyle y={\frac {\pm {\sqrt {3}}}{2}}.}

So our intersection has two points:

{\displaystyle \left(1/2,{\frac {+{\sqrt {3}}}{2}}\right)\;\;\mathrm {and} \;\;\left(1/2,{\frac {-{\sqrt {3}}}{2}}\right).}

For conic sections, as many as 4 points might be in the intersection.

Finding intercepts[edit]

One type of intersection which is widely studied is the intersection of a geometric object with the {\displaystyle x} and {\displaystyle y} coordinate axes.

The intersection of a geometric object and the {\displaystyle y}-axis is called the {\displaystyle y}-intercept of the object. The intersection of a geometric object and the {\displaystyle x}-axis is called the {\displaystyle x}-intercept of the object.

For the line {\displaystyle y=mx+b}, the parameter {\displaystyle b} specifies the point where the line crosses the {\displaystyle y} axis. Depending on the context, either {\displaystyle b} or the point {\displaystyle (0,b)} is called the {\displaystyle y}-intercept.

Tangents and normals[edit]

Tangent lines and planes[edit]

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that “just touches” the curve at that point. Informally, it is a line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c on the curve if the line passes through the point (cf(c)) on the curve and has slope f‘(c) where f is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.

As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is “going in the same direction” as the curve, and is thus the best straight-line approximation to the curve at that point.

Similarly, the tangent plane to a surface at a given point is the plane that “just touches” the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space.

Normal line and vector[edit]

In geometry, a normal is an object such as a line or vector that is perpendicular to a given object. For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.

In the three-dimensional case a surface normal, or simply normal, to a surface at a point P is a vector that is perpendicular to the tangent plane to that surface at P. The word “normal” is also used as an adjective: a line normal to a plane, the normal component of a force, the normal vector, etc. The concept of normality generalizes to orthogonality.

See also[edit]

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sig?u=a_mishraAjay Mishra

My Latest Gig


From: Alumni Association, IIT Kanpur <alumni>
Date: Wed, Feb 28, 2018 at 7:17 PM
To: ajayinsead03

Dear Ajay Mishra,

Thank you for the response and voting for the amendment to the constitution so far.

Further to the recommendations to the amendments shared with you earlier we have received feedback and suggestions.

Incorporating the same we are sharing a) updated amendment, b) the rationale behind the proposal and c) changes with a comparison table.

Further, we are extending the polling for few more days, Polling shall continue till Midnight of 4th March based on US West-coast time.

Please follow the below link to peruse and vote on the same.


Pradeep Bhargava
Alumni Association, IITK

Someone just viewed: YEH KUCH BATA PAYENGE ? :) TO BATAO ?






From: Streak <notifications>
Date: Wed, Feb 28, 2018 at 5:38 PM
Subject: Someone just viewed: YEH KUCH BATA PAYENGE ? :) TO BATAO ?
To: ajayinsead03

Someone just viewed your email with the subject: YEH KUCH BATA PAYENGE ? :) TO BATAO ?
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where is KANSAS ?





From: Streak <notifications>
Date: Wed, Feb 28, 2018 at 5:39 PM
To: ajayinsead03

Device: PC
Location: independence, ks


How Empathy Sparks Innovation

sig?u=a_mishraAjay Mishra
My Latest Gig

From: Knowledge@Wharton <knowledge>
Date: Wed, Feb 28, 2018 at 5:43 PM
Subject: How Empathy Sparks Innovation
To: ajayinsead03

The Wharton School
February 28, 2018
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What Xi Jinping’s Longer-term Rule Will Mean for China’s Economy

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Ajay, להיות מי שאני או מי שאני רוצה להיות? *ספיישל פורים *

From: DIB Coaching <info>
Date: 2018-02-28 17:26 GMT+05:30
Subject: Ajay, להיות מי שאני או מי שאני רוצה להיות? *ספיישל פורים *
To: ajayinsead03

different is the NEW better – מגזין מס’ 128
אימון שהופך את מה שאחר בך ליתרון שלך!
הי Ajay,

חג פורים שמח!!
נכון…אנחנו כבר לא ילדים ויש סיכוי שבחרת לא להתחפש בשנים האחרונות…
יחד עם זאת, במגזין DIB ה-128 אני שולח לך תובנות אימוניות עדלאידע :-)
הרי אתם יודעים שנושא התחפושות והמסכות הוא לא נחלתו היחידה של פורים.

למעשה זה משהו שאנחנו עושים ונמצאים איתו בדיאלוג מדי יום.
ממש עושים חשבון נפש עם עצמנו על עד כמה אנחנו אמיתיים או אותנטים.
בינינו לבין עצמנו, בזוגיות שלנו, ואפילו מול הקריירה או העסק שלנו.

זאת בדיוק הסיבה שהמילה ‘פורים’ לקוחה מהמילה ‘כיפורים’.
נכון ששני החגים האלו הם ‘דיפרנט’. האחד שקט וכבד והשני שמח ומבדח.
ויחד עם זאת הם דומים במהות שלהם.

בתהליכי אימון אישי או עסקי בשיטת DIB מתרחשים שני מהלכים מקבילים –

1. קבלת ה’דיפרנט’ שלי.

המתאמנים שלי לומדים להיות מודעים למה ש’אחר’ בהם.
הם עושים תהליכים של קבלה ואהבה עצמית.
מצליחים להפוך את מה ש’אחר’ בהם ליתרון בדרך להצלחה.
לאהוב את מי שהם בדיוק כמו שהם.

2. לחשוב, להרגיש, לעשות את ה’דיפרנט’.

המתאמנים שלי נדרשים לקבל אחריות על המחשבה, רגש והמעשים שלהם.
מתבקשים להיות אפקטיביים ולפעול בדרכים שמשרתות את הרצונות שלהם.
לצאת מאזור הנוחות, למתוח את הגבולות שלהם ולייצר שינויים מרחיקי לכת.
לשחרר קביעות ואמונות מגבילות על עצמם והדרך בה הם תופסים את העולם.

על פניו אלו מהלכים שעשויים להיתפס כסותרים או מנוגדים, נכון Ajay?

המתאמנים שלי בתחילת תהליכי אימון אישי או עסקי לפעמים מעלים את הנושא.
איך זה שדווקא המאמן שמדבר על להיות ‘דיפרנט’
הוא זה שכביכול מבקש מהם לעשות דברים שמנוגדים למי שהם?

חשוב להבין שתהליכי שינוי הם דבר מורכב מאוד.
זאת בדיוק הסיבה שחשוב ללכת לאיש מקצוע עם ניסיון עשיר ויכולות יוצאות דופן.
יש לדייק בין ה‘דיפרנט’ שמייחד את האדם והופך אותו למי שהוא…
לבין המקומות בהם יש לעשות את ה’דיפרנט’ כי הבן אדם פוגע ומגביל את עצמו,
בין אם הוא עושה זאת במודע או שלא במודע.

אז מה במגזין DIB השבועי?
מחקר חדש מגלה שאנחנו אותנטים דווקא כשאנחנו עושים דברים שלא מתאימים לנו, פוסט חגיגי עם טיפים ותובנות אימוניות וגם דוגמנית הפלאס סייז ריי שגב,
למדה לקבל את עצמה כמו שהיא וגם לעשות את ה’דיפרנט’, ממליצה על DIB.

אז הנה התכנים ה’דיפרנט’ שהכנתי לך במגזין DIB ה-128
(מעבר לתכנים המלאים בתחתית המייל וניתן לגלול אליהם)

את הבלוג ה-1 כתבתי בהשראת מחקר התנהגותי מאונ’ בארה"ב שנחשפתי אליו
כנסו עכשיו לקרוא ממצאים מפתיעים בנוגע למה גורם לנו להיות נאמנים לעצמנו
ואיך עשיית ה’דיפרנט’ ופעולה בניגוד לדפוס התנהגות מחזקת את האותנטיות

בבלוג ה-2 ספיישל פורים עם תובנות אימוניות ו’דיפרנט’ עדלאידע בהשארת החג
למה אני חושב ‘דיפרנט’ ומעודד להתחפש ולשים מסיכות בכל ימי השנה?
מה מסתירה אסתר? האם פורים זה יום כי-פורים בתחפושת? כנסו עכשיו לקרוא

ולסיום סרטון בו ממליצה הדוגמנית ריי שגב לכל מי שאיכפת מעצמו להגיע אלי!
כנסו לצפות בדוגמנית הפלאס סייז המצליחה מספרת כיצד "הכל השתנה!"
ועל ההישגים האישיים והעסקיים שהשיגה בתהליך אימון בליווי שלי, כנסו לצפות

Ajay, עזור לי להעביר את המסר ש-different is the NEW better.
תוכל להזמין אותי להרצאה או סדנה בארגון, חברה או חוג בית שלך. צור קשר כאן
להצטרפות לתהליך אימון אישי או עסקי יסודי בשיטת DIB, לחץ

שיהיה פורים ‘דיפרנט’ ו’בטר’,
וזכרו ש’מה שאחר בכם זה היתרון שלכם להצלחה!
שלכם, עדי פרבר – ליווי ואימון בשיטת DIB
אשמח אם תשתפו את המגזין עם החברים בפייסבוק או במייל

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מחקר מפתיע על אותנטיות ועשיית הדיפרנט – לחץ
בלוג חדש המבוסס על מחקר מאונ' לפסיכולוגיה בארה"ב שמוכיח שדווקא פעולה בניגוד לדפוסי ההתנהגות המוכרים לנו היא זאת שמחזקת את תחושת האותנטיות! לחץ כאן למעבר לבלוג המלא
בלוג לפורים עם תובנות אימוניות עדלאידע – לחץ
בלוג מיוחד בהשראת חג פורים עם תובנות אימוניות על מסיכות, תחפושות ואסתר המלכה :-) לחץ כאן למעבר לבלוג
דוגמנית הפלאס סייז ריי שגב על אימון DIB – לחץ
דוגמנית הפלאס סייז המובילה בישראל שכיכבה לאחרונה על שער מגזין בלייזר ועשתה היסטוריה - ממליצה על אימון אישי ועסקי בלייוי שלי בשיטת DIB! לחץ כאן כדי לצפות בריי
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ותמיד תזכרו ש… different is the NEW better


hello and hOWDY


From: Streak <notifications>
Date: Wed, Feb 28, 2018 at 2:12 PM
To: ajayinsead03

Someone just viewed your email with the subject: ABOUT OLGA SHULMAN LEDNICHENKO AND CLINTON :)
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