Almost every serious computer scientist has some knowledge of physics. But the deeper physical background of computer science remains a seldomly addressed issue. (By ``physical background'' we mean an intelligible relationship between the physical properties of a piece of hardware and the computation -- or mathematics -- it delivers.) Nevertheless, almost every computer engineer holds an implicit working hypothesis that this connection is solid. So solid that the hardware does carry out the computation faithfully according to anthropocentric mathematics.
Let us first examine this issue more closely from the stand-point of a mind-matter dualist. The dualist position is a strongly held tenet in the Western tradition since René Descartes. According to the dualist position, matter is an extended and inert substance, while mind's intuition and deduction are the means for mind to understand matter.
Now, an algorithm is a set of abstract procedures devised by computer programmers (applied mathematicians) based on nothing but their knowledge of logic and mathematics. The algorithm is therefore a pure recipe of an intelligent mind. On the other hand, the hardware, although designed by competent engineers, consists of only matter and it works according to physical laws. But, according to Cartesian tenets, matter is independent of the mind of the designer. Now, how can this connection between physical hardware and mental computation be solidly established? Why is the outcome of the calculations as a physical process the same as our mathematical expectation, which is the outcome of a mental process?2.6 To answer these questions, a dualist has to postulate de facto that it is solid. For Descartes, this is attributed to God. In fact, it is difficult for a dualist to establish a genuine solid relation between mind and matter without resorting to some sort of supernatural causes. In a sense, mind is itself supernatural in Cartesian dualism.
Nevertheless, for a naturalist dualist the connection between computation and physics has to be established empirically but not deductively. Thus this connection falls short of the expectation of most mathematicians. And it disproves the working hypothesis of computer programmers in its strongest form.
Here a materialist or an idealist has an upper hand on this issue. For a materialist, human brain consists of matter only. So mind obeys the same laws of physics that matter does. If matter follows the laws of nature, so does its activity -- and this is mind. Thus the connection between mathematics and physics has to be solid. The same argument is valid for an idealist, except that she has to see a piece of hardware as an extension of (her) mind and will argue the other way around.
For many, materialism and idealism are not good alternatives. For, it is argued, to avoid rendering oneself an idealist, in which case one is apt to collapse into solipsism, one has to take a materialist stance. This latter position is implausible for many who take matter as an inert substance that passively obeys the laws of physics. If it were the case, they think, in mathematics all their conscious decisions would have ceased to have any meaning. And indeed, they do not want this to be so. This unwillingness alone is enough for them to refute a materialist stance right from the beginning. This is a crisis of belief lying at the heart of the tension between science/technology and humanities. For a discipline of mind, it seems to me that there can not be any serious new developments without first facing this crisis. In a sense, this is the ``hard-problem'' in disguise. And now it is time to take a look at physics again.