This point, all but inaccessible to the nonmathematician, Dobb attempts to explain by adducing simple facts, the sort generally learned in school. It is possible, as we know, to construct a geometrically regular three-dimensional solid—say, a cube—which in the real world possesses a counterpart in the form of a die; and it is equally possible to create geometrical solids of four, five, n dimensions (the four-dimensional is a tesseract). These no longer possess real counterparts, and we can see this, since in the absence of any physical dimension No. 4 there is no way to fashion genuine four-dimensional dice. Now, this distinction (between what is physically constructible and what may be made only mathematically) is, for personoids, in general nonexistent, because their world is of a purely mathematical consistency. It is built of mathematics, though the building blocks of that mathematics are ordinary, perfectly physical objects (relays, transistors, logic circuits—in a word, the whole huge network of the digital machine).
As we know from modern physics, space is not something independent of the objects and masses that are situated within it. Space is, in its existence, determined by those bodies; where they are not, where nothing is—in the material sense—there, too, space ceases, collapsing to zero. Now, the role of material bodies, which extend their "influence," so to speak, and thereby "generate" space, is carried out in the personoid world by systems of a mathematics called into being for that very purpose. Out of all the possible "maths" that in general might be made (for example, in an axiomatic manner), the programmer, having decided upon a specific experiment, selects a particular group, which will serve as the underpinning, the "existential substrate," the "ontological foundation" of the created universum. There is in this, Dobb believes, a striking similarity to the human world. This world of ours, after all, has "decided" upon certain forms and upon certain types of geometry that best suit it—best, since most simply (three-dimensionality, in order to remain with what one began with). This notwithstanding, we are able to picture "other worlds" with "other properties"—in the geometrical and not only in the geometrical realm. It is the same with the personoids: that aspect of mathematics which the researcher has chosen as the "habitat" is for them exactly what for us is the "real-world base" in which we live, and live perforce. And, like us, the personoids are able to "picture" worlds of different fundamental properties.
Dobb presents his subject using the method of successive approximations and recapitulations; that which we have outlined above, and which corresponds roughly to the first two chapters of his book, in the subsequent chapters undergoes partial revocation—through complication. It is not really the case, the author advises us, that the personoids simply come upon a readymade, fixed, frozen sort of world in its irrevocably final form; what the world will be like in its specificities depends on them, and this to a growing degree as their own activeness increases, as their "exploratory initiative" develops. Nor does the likening of the universum of the personoids to a world in which phenomena exist only to the extent that its inhabitants observe them provide an accurate image of the conditions. Such a comparison, which is to be found in the works of Sainter and Hughes, Dobb considers an "idealist deviation"—a homage that personetics has rendered to the doctrine, so curiously and so suddenly resurrected, of Bishop Berkeley. Sainter maintained that the personoids would know their world after the fashion of a Berkeleyan being, which is not in a position to distinguish "esse" from "percipi"—to wit, it will never discover the difference between the thing perceived and that which occasions the perception in a way objective and independent of the one perceiving. Dobb attacks this interpretation of the matter with a passion. We, the creators of their world, know perfectly well that what is perceived by them indeed exists; it exists inside the computer, independent of them—though, granted, solely in the manner of mathematical objects.
And there are further clarifications. The personoids arise germinally by virtue of the program; they increase at a rate imposed by the experimenter—a rate only such as the latest technology of information processing, operating at near-light speeds, permits. The mathematics that is to be the "existential residence" of the personoids does not await them in full readiness but is still "in wraps," so to speak—unarticulated, suspended, latent—because it represents only a set of certain prospective chances, of certain pathways contained in appropriately programmed subunits of the machine. These subunits, or generators, in and of themselves contribute nothing; rather, a specific type of personoid activity serves as a triggering mechanism, setting in motion a production process that will gradually augment and define itself; in other words, the world surrounding these beings takes on an unequivocalness only in accordance with their own behavior. Dobb tries to illustrate this concept with recourse to the following analogy. A man may interpret the real world in a variety of ways. He may devote particular attention—intense scientific investigation—to certain facets of that world, and the knowledge he acquires then casts its own special light on the remaining portions of the world, those not considered in his priority-setting research. If first he diligently takes up mechanics, he will fashion for himself a mechanical model of the world and will see the Universe as a gigantic and perfect clock that in its inexorable movement proceeds from the past to a precisely determined future. This model is not an accurate representation of reality, and yet one can make use of it for a period of time historically long, and with it can even achieve many practical successes—the building of machines, implements, etc. Similarly, should the personoids "incline themselves," by choice, by an act of will, to a certain type of relation to their universum, and to that type of relation give precedence—if it is in this and only in this that they find the "essence" of their cosmos—they will enter upon a definite path of endeavors and discoveries, a path that is neither illusory nor futile. Their inclination "draws out" of the environment what best corresponds to it. What they first perceive is what they first master. For the world that surrounds them is only partially determined, only partially established in advance by the researcher-creator; in it, the personoids preserve a certain and by no means insignificant margin of freedom of action—action both "mental" (in the province of what they think of their own world, of how they understand it) and "real" (in the context of their "deeds"—which are not, to be sure, literally real, as we understand the term, but are not merely imagined, either). This is, in truth, the most difficult part of the exposition, and Dobb, we daresay, is not altogether successful in explaining those special qualities of personoid existence—qualities that can be rendered only by the language of the mathematics of programs and creational interventions. We must, then, take it somewhat on faith that the activity of the personoids is neither entirely free—as the space of our actions is not entirely free, being limited by the physical laws of nature—nor entirely determined—just as we are not train cars set on rigidly fixed tracks. A personoid is similar to a man in this respect, too, that man’s "secondary qualities"—colors, melodious sounds, the beauty of things—can manifest themselves only when he has ears to hear and eyes to see, but what makes possible hearing and sight has been, after all, previously given. Personoids, perceiving their environment, give it from out of themselves those experiential qualities which exactly correspond to what for us are the charms of a beheld landscape—except, of course, that they have been provided with purely mathematical scenery. As to "how they see it," one can make no pronouncement, for the only way of learning the "subjective quality of their sensation" would be for one to shed his human skin and become a personoid. Personoids, one must remember, have no eyes or ears, therefore they neither see nor hear, as we understand it; in their cosmos there is no light, no darkness, no spatial proximity, no distance, no up or down; there are dimensions there, not tangible to us but to them primary, elemental; they perceive, for example—as equivalents of the components of human sensory awareness—certain changes in electrical potential. But these changes in potential are, for them, not something in the nature of, let us say, pressures of current but, rather, the sort of thing that, for a man, is the most rudimentary phenomenon, optical or aural—the seeing of a red blotch, the hearing of a sound, the touching of an object hard or soft. From here on, Dobb stresses, one can speak only in analogies, evocations.