The fact that we can see colours and smell smells is often used as an argument against the idea that the world is physical. It is held that redness or rancidness are qualities that transcend the physical nature of the brain. This intuition is really just another version of Aristotle's regress argument because if we have "red" in the brain then what sees this "red"? Another bit of "red" in another part of the brain? (See Time and conscious experience for more on regress).
Some philosophers have claimed that the problem of explaining conscious experience shows that there is a problem with the whole enterprise of science, for instance there is an entire "Knowledge Argument" (Jackson 1982) industry in philosophy that deals with a "super scientist" called Mary who has never seen the colour red. It is asked if she could ever know the colour red even if she knew everything that science and physical theory could tell her about red and redness. It is declared that if science does not include the experience called "red" then there is "knowledge" that is forever outside of scientific knowledge.
To answer this conundrum we need to know a bit more about science. Science gathers information about the world and uses physical information to embody theories about future changes in information about the world.
Information is simply a change in state induced in a system that can have more than one state. This allows us to create descriptions of the world in terms of information. For instance I can tabulate the observations of a moving body by changing the state of ink on a sheet of paper. It also allows us to process information, for instance I could tabulate observations as patterns of holes on a paper tape and also tabulate potential relationships between these holes. Having done this I could run the tape through a Turing machine (a simple computer that uses marks on tapes) and produce predictions for future observations. Mathematical theories of the world are just advanced forms of this sort of processing and can be reduced to computational forms that use paper tapes.
The successions of state changes that are equivalent to the operation of physical theories are obviously different from the original physical events that these theories describe. The fact that Mary cannot see red if she just reads books about it or sees paper tapes about it does not mean that science is false. Science is a description of how the world works, it is not the world itself. So, the introduction of science into this debate about whether knowledge can cause Mary to see red is a red herring, a category mistake, because scientific knowledge is not identical to the events that science describes. Scientific knowledge is marks on a medium, it includes instructions on how to observe events but is not those events itself. Science is a set of descriptions, it is not the things it describes so maintaining that "science is wrong" because a theory of the motion of a ball is not the same as a ball itself is just a crazy non-sequitur.
The "superscientist" part of Jackson's example is clearly irrelevant but the central issue of whether or not the redness in Mary's mind is physical remains. Her "red" is a changed state in her mind and so is a form of information. This suggests that a signal in the world, such as a photon of red light has changed the state of Mary's brain. Whether she is a super scientist or not has got nothing to do with this changed state but the existence of the change suggests a physical connection between the world and the mind. Is it possible to have a scientific theory about this "red" in Mary's mind? Basically this is Aristotle's conundrum - is it possible to have a sense that is self aware? (See Perceiving perception and seeing seeing). Can we have a scientific theory of self awareness, a description that describes how self awareness occurs?
If red is a physical state then it is an arrangement of things in the various directions in which these things can exist. If the things just exist in space and do not move then there is no physical theory that could turn this fixed arrangement into "red". If the things can move then information can be processed but there is still nothing about a moving collection of electrons or carrots or steel balls or other physical things that would imply "redness". Perhaps the part of the brain that has "red" is arranged in more than space and time, who knows? Unfortunately, until we know a lot more about states of things in the physical brain the answer to the problem of the nature of the "red" in our experience is unknown.
There have been many attempts to define physicalism. As an example, Stoljar(2001) uses "theory based", or "t-physical", properties for the extrinsic properties of things that are known by their relations and "object based", or "o-physical", properties to describe the intrinsic properties of things. Others have used similar ideas such as "token" and "type" physicalism. These distinctions revolve around the simple fact that physical theories are not the objects of those theories. When I write E=mc2 on a blackboard I do not vaporize the tutorial group! In the case of Mary this means she can do science but cannot be science.
In the sense that we can have a theory about how electrons flow in ammonia or in a superconductor even when no-one has seen an electron we can have a physical theory about conscious experience even though no-one can measure subjective "red" with an instrument. The theory will be tested by its predictions. However, even if we do eventually obtain a description of the state that is "red" the description will not be the state itself. (See There is no information without representation).
Jackson 1982. Epiphenomenal qualia. Philosophical Quarterly 32: 127–136.
Stoljar, D. (2001). Two conceptions of the physical. Philosophy and Phenomenological Research