Modern philosophy is full of the discussion of dualism, the belief that somehow the mind is separate from the physical body. However, dualism is not just a problem of the philosophy of mind, it is also a fundamental problem in physics.
Cartesian Dualism arose because Renee Descartes found that although light could be traced to the eye and the excitation of the retina could be traced to the brain he could find no physical process or theory by which a pattern in the brain could be converted into a view containing the world such as exists in our minds. He was forced to suggest that there was a supernatural phase to perception where an image laid out in the brain became the image in our minds.
If we retrace Descartes' reasoning in his "Meditations" and "Treatise on Man" we discover that he describes perception in terms of the transfer of material signals from place to place. Light goes from things to the eyes and "animal spirits" (what we now call electricity) travel through the brain. Signals travel from place to place but Descartes cannot say that it is physically possible for these material signals to all end up at a point from which they are seen, he has to resort to a supernatural, non-extended place that he calls the "res cogitans" to act as the viewing point. He can only obtain, or model, the spatial form of the mind by abandoning material signals. Historians of science may be intrigued to know that Aristotle, in his book "On the Soul", mentions this problem almost two millennia before Descartes.
Descartes describes material signals going from place to place but when he actually wants the signals to be themselves he ends up with a geometrical point. The dualism here is between information as an arrangement of things in space and time and the observation of this arrangement which would have to occur at a physically impossible point.
This problem of the impossibility of a point observation is created by the concept of space and the concept of material object or signal. What is space? We cannot actually measure space - what we call a spatial measurement always ends up as a comparison of material marks. What is a material object? When we probe material objects we find that they are mostly composed of space and we can only interact with these objects by virtue of "fields" of "virtual particles" that cannot be isolated. In fact it is only the brash overconfidence of school physics that would allow us to conclude that Descartes MUST be wrong because the world is simply lumps of stuff flowing from place to place. Perhaps material objects are not simple lumps in 3D space and perhaps space is not an instantaneous container for lumps of stuff.
Personally, I do not believe that Descartes was right. Certainly he was right to notice that there is a problem modelling the form of the mind using primitive materialism but he was wrong to abandon physics. He should have said "I don't know how a pattern in the brain becomes a mind, maybe people in a thousand years time will figure out how a pattern in space and time can also be at a point".
Another form of dualism has been proposed in more recent years. This is "property dualism". Property dualism holds that the mind could indeed be a ghost in the machine of the brain, such ghosts being possible counterparts of ordinary matter that do not get involved in ordinary physical interactions. This is no more than an acceptance that erroneous nineteenth century materialism describes the world coupled with the obvious fact of the existence of mind. A sort of bizarre combination of "folk physics" with empirical truth.
Descartes, R. (1641). Meditations on First Philosophy. http://oregonstate.edu/instruct/phl302/texts/descartes/meditations/Meditation1.html
Descartes, R. (1664) "Treatise on Man". Translated by John Cottingham, et al. The Philosophical Writings of Descartes, Vol. 1 (Cambridge: Cambridge University Press, 1985) 99-108. http://lrc.csun.edu/~battias/454/descartes/