When I learned that I was to give a seminar on RMT™ technologies at Tufts University, I rushed to my bookshelf and pulled down one of my well-worn engineering textbooks. The economist in me needed to do some homework on the mechanics of materials.
After reading the second page of the text, I was relieved. I realized that engineering and economics are very similar. From long experience, I knew that economics is essentially metaphysics. By the second page of the textbook, it occurred to me that materials engineering is essentially applied metaphysics. It was the assumptions that convinced me.
The Concept of Stress
"Stress" was the momentous heading on the second page of the text.1 The author began the section by explaining that obtaining the distribution of force of internal loading is one of the major problems in mechanics of materials. He said to solve this problem it will be necessary to study how a body deforms under load, since each internal force distribution will deform the material in a unique way. "Before this can be done, however," he said, "it is first necessary to develop a means for describing each of the internal forces at all points on the sectioned area (author's emphasis) [see Figure (a)]. To do this will establish the concept of stress."
As the author instructed, I noticed that the sectioned area of Figure (a) was divided into a smaller area in Figure (b). The author explained that "…the force distribution will become more uniform as the area gets smaller and smaller." He said, "As we reduce the area in this manner, however, we must make two assumptions regarding the properties of the material." The author explained:
We will consider the material to be continuous, that is, to consist of a continuum or uniform distribution of matter having no voids, rather than being composed of a finite number of distinct atoms and molecules. Furthermore, the material must be cohesive, meaning that all portions of it are connected together, rather than having breaks, cracks, or separations (author's emphasis).
From this, I concluded that the basic element of materials engineering is a glob, albeit a continuous and cohesive glob. A glance at the body pictured in Figures (a) and (b) confirmed that a glob was at the heart of the matter (pun aside). Fortunately, I knew enough not to confuse the glob with an 
agglomeration of Newtonian particles, since there can be no voids in a glob.
"Now, as the subdivided area of this continuous-cohesive material is reduced to one of infinitesimal size," the author continued, "the distribution of force acting over the entire sectioned area will consist of an infinite number of forces, each acting at a specific point on the area" (author's emphasis). He explained that a typical finite yet very small force acting on its subdivided area will have a unique direction. "But," he said, "for further discussion we will replace it by two of its components, which are taken normal and tangent to the area respectively."
Of course, "infinitesimal" and "infinite" are familiar concepts. So, I thought I could imagine how there could be an infinite number of forces each acting at specific points on respective subdivided areas of infinitesimal size on the sectioned area of a glob. The author summed it all, by explaining that as the sectioned area becomes smaller and smaller, and approaches zero, so do the force and its components; however, the quotient of the force and area will, in general, approach a finite limit. "This quotient," he said, "is called stress, and it describes the intensity of the internal force on a specific plane passing through a point" (author's emphasis).
continued 
1 R. C. Hibbeler, Statics and Mechanics of Materials, eds. David Johnstone and John Griffin (New York, Macmillan Publishing Company, 1993) p. 342. Quoted text appears on the second page of the second volume of this text (click here to see text).