(a) Mathematics has become, then, in certain of its embodiments, the life-space of an intelligence so spiritualized as to be totally incorporeal, the niche and cradle of its existence, its element.
(b) 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.
(c) It is only through reasoning that we are in touch with mathematics, only through abstract thought that we experience it whereas the personoids live in it; it is their air, their earth, clouds, water and even bread - yes, even food, because in a certain sense they take nourishment from it.
(d) 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 mathematical substance, the protoplasm of a universum, fed into the machine.
(e) So they are imprisoned, hermetically locked inside the machine, solely from our point of view; just as they cannot work their way out to us, to the human world, so conversely and symmetrically, a man can in no way enter the interior of their world, so to exist in it and know it directly.
(f) To declare that the personoids are handicapped with respect to us, in as much as they do not see or hear as we do, is totally absurd, because with equal justice one could assert that it is we who are deprived with respect to them – unable to feel with immediacy the phenomenalism of mathematics, which we know only in a cerebral, inferential fashion.