97
“submultiple” numbers.
4
As biological facets of the infinite heaps of the life force
increasingly dawn upon our species, two phases of passing importance become
clear. The species drifts in one direction, while its individuals have every random
reason to veer somewhere else. These two geographic migrations are as varied as
the personal parts. Biographies coalesce or seek out alienation, exile, what the
Desert Fathers prescribed as a prelude to ultimate union with their Holy Father, a
topic the authors have dealt with in some depth in The Theoretical Individual.
5
10.2 Paradoxical Sub-sets
Like all empirical evidence, we reclaim in every act of perception a different version
of the sorites paradox, or heap-of-sand enigma. At what point have enough grains
been removed so that it is no longer a verifiable “heap”?
6
A second paradox also
confronts us. Sand may be initially laid claim to in the words of “a heap of sand.”
But we are presuming many things about each granule. They are not the same size
or weight. Moreover, each has multitudes of organisms attached. A tiny heap contains, easily, some ten thousand Loricifera, one of the most recently discovered of
all known phyla of life (out of approximately 40): Meiofauna (meiobenthos) are
vast swathes of invertebrate animalia whose discoverers include Reinhardt Mobjerg
Kristensen and Robert Higgins. Higgins calls them bibliocryptozoans. Relatively
simple tools of the naturalist’s profession can discern them: “a homemade sieve
fashioned out of a nylon mesh net fastened over a funnel; a spray bottle for rinsing
it out; a petri dish to place the samples in; and a stereomicroscope of at least 25
times magnification.” Like a pair of binoculars, the human interest in Others
explodes with so many newly perceived neighbors that, of course, our position
standing on a Florida beach with a bucket of sand is not what it appears. Gulls and
countless other seabirds eyeing us, we are strange members of a vast community.
The gulls are teeming with their own life forms. And even those meiofauna are
additionally inhabited by yet others, who are also each inhabited, and so on until we
are lost in a black hole of biological numbers.
7
There are approximately 137 species
of Loricifera (most have not yet been studied) and unknown numbers of species that
inhabit them. We earlier recognized in the Russell’s Paradox or Antinomy, a set of
sets, sub-sets of sub-sets, until is theorized a set that cannot be a member of itself,
although that Self is the very set of sets it cannot by definition be party to. While
numerous equations have since been proposed that bypass the apparent contradiction in the numbers game, ecologists remain confounded by the essential truth
4 See André Weil’s book, Number Theory – An approach through history From Hammurabi to
Legendre, Birkháuser, Boston, Basel, Stuttgart, 1984, pp. 52–53.
5 Tobias/Morrison, Springer, 2018.
6 Sorensen, Roy A. (2009). “sorites arguments”. In Jaegwon Kim; Sosa, Ernest; Rosenkrantz, Gary
S. A Companion to Metaphysics. John Wiley & Sons, p. 565.
7 See “Life On A Grain Of Sand,” by Virginia Morell, Discover, April 1, 1995.
10.2 Paradoxical Sub-sets
“submultiple” numbers.
4
As biological facets of the infinite heaps of the life force
increasingly dawn upon our species, two phases of passing importance become
clear. The species drifts in one direction, while its individuals have every random
reason to veer somewhere else. These two geographic migrations are as varied as
the personal parts. Biographies coalesce or seek out alienation, exile, what the
Desert Fathers prescribed as a prelude to ultimate union with their Holy Father, a
topic the authors have dealt with in some depth in The Theoretical Individual.
5
10.2 Paradoxical Sub-sets
Like all empirical evidence, we reclaim in every act of perception a different version
of the sorites paradox, or heap-of-sand enigma. At what point have enough grains
been removed so that it is no longer a verifiable “heap”?
6
A second paradox also
confronts us. Sand may be initially laid claim to in the words of “a heap of sand.”
But we are presuming many things about each granule. They are not the same size
or weight. Moreover, each has multitudes of organisms attached. A tiny heap contains, easily, some ten thousand Loricifera, one of the most recently discovered of
all known phyla of life (out of approximately 40): Meiofauna (meiobenthos) are
vast swathes of invertebrate animalia whose discoverers include Reinhardt Mobjerg
Kristensen and Robert Higgins. Higgins calls them bibliocryptozoans. Relatively
simple tools of the naturalist’s profession can discern them: “a homemade sieve
fashioned out of a nylon mesh net fastened over a funnel; a spray bottle for rinsing
it out; a petri dish to place the samples in; and a stereomicroscope of at least 25
times magnification.” Like a pair of binoculars, the human interest in Others
explodes with so many newly perceived neighbors that, of course, our position
standing on a Florida beach with a bucket of sand is not what it appears. Gulls and
countless other seabirds eyeing us, we are strange members of a vast community.
The gulls are teeming with their own life forms. And even those meiofauna are
additionally inhabited by yet others, who are also each inhabited, and so on until we
are lost in a black hole of biological numbers.
7
There are approximately 137 species
of Loricifera (most have not yet been studied) and unknown numbers of species that
inhabit them. We earlier recognized in the Russell’s Paradox or Antinomy, a set of
sets, sub-sets of sub-sets, until is theorized a set that cannot be a member of itself,
although that Self is the very set of sets it cannot by definition be party to. While
numerous equations have since been proposed that bypass the apparent contradiction in the numbers game, ecologists remain confounded by the essential truth
4 See André Weil’s book, Number Theory – An approach through history From Hammurabi to
Legendre, Birkháuser, Boston, Basel, Stuttgart, 1984, pp. 52–53.
5 Tobias/Morrison, Springer, 2018.
6 Sorensen, Roy A. (2009). “sorites arguments”. In Jaegwon Kim; Sosa, Ernest; Rosenkrantz, Gary
S. A Companion to Metaphysics. John Wiley & Sons, p. 565.
7 See “Life On A Grain Of Sand,” by Virginia Morell, Discover, April 1, 1995.
10.2 Paradoxical Sub-sets