Harold R. (Hal)
Foster’s Prince Valiant
© Respective
copyright/trademark holders.
The class which has no
members is called the "null-class," and is denoted by "A." Any propositional
function which is always false determines the null-class. One such function is
known to us already, namely "x
is not identical with x," which
we denote by "x ≠ x." Thus
we may use this function for defining L,
and put
L =
x^(x ≠ x) Df.
The class determined by a
function which is always true is called the universal
class, and is represented by V;
thus
V = x^(x
= x) Df.
Thus L
is the negation of V.
We have
┝ .
(x) . x Î V,
i.e. " 'x is a member
of V'
is always true "; and
┝ .
(x) . x ~ Î L,
i.e. " 'x is a member of L'
is always false." Also
┝ :
a = L .
º . ~ ∃ !
a,
i.e. "a
is the null-class" is equivalent to "a
does not exist." For relations, we use similar notations, lacking equivalent font symbols, relations are expressed here as ∃, L, V, etc. here this color denoting the symbol relation. We put
∃ !
R . = . (∃x,y) . xRy,
i.e. " ∃ !
R"
means that there is at least one couple x, y between which the relation R
holds. L
will be the relation which never holds, and V the relation which always holds. V
is practically never required; L will be the relation x^y^(x
≠ x . y ≠ y). We have
┠
. (x,
y) . ~(x L
y),
and ┠
:
R = L .
º ~∃ ! R.
There
are no classes which contain objects of more than one type. Accordingly there
is a universal class and a null-class proper to each type of object. But these
symbols need not be distinguished, since it will be found that there is no
possibility of confusion. Similar remarks apply to relations.
Descriptions.
By a "description" we mean a phrase of the form "the
so-and-so" or of some equivalent form. For the present, we confine our
attention to the in the singular. We
shall use this word strictly, so as to imply uniqueness; e.g. we should not say "A is the son of B"
if B
had other sons besides A. Thus a description of
the form "the so-and-so" will only have an application in the event
of there being one so-and-so and no more.
Hence
a description requires some propositional function φx^ which is satisfied by one value of x and by no other values; then "the x which satisfies φx^"
is a description which definitely describes a certain object, though we may not
know what object it describes. For
example, if y is a man, "x is the father of y" must be true for one, and only one, value of x. Hence "the father of y" is a description of a certain
man, though we may not know what man
it describes. A phrase containing "the" always presupposes some
initial propositional function not containing "the"; thus instead of
"x is the father of y" we ought to take as our initial
function "x begot y"; then "the father of y" means the one value of x which satisfies this propositional
function.
If φx^ is a
propositional function, the symbol "(ɿx)(φx)" is used in
our symbolism in such a way that it can always be read as "the x which satisfies φx^." But we do not define "(ɿx)(φx)" as standing
for "the x which satisfies φx," thus
treating this last phrase as embodying a primitive idea.
David Mazzuccheli’s Asterios Polyp © Respective copyright/trademark
holders
(Text in this font lifted from Wikipedia for illustration and I understand it, and believe it to be accepted and correct for my purpose here.) General relativity is a theory of gravitation
developed by Einstein in the years 1907–1915. The development of general
relativity began with the equivalence principle,
under which the states of accelerated motion and being at rest in a gravitational
field (for example when standing on the surface of the Earth) are
physically identical. The upshot of this is that free fall
is inertial
motion; an object in free fall is falling because that is how
objects move when there is no force being exerted on them, instead of this being due to the
force of gravity
as is the case in classical mechanics. This is incompatible with
classical mechanics and special relativity because in those theories inertially
moving objects cannot accelerate with respect to each other, but objects in
free fall do so. To resolve this difficulty Einstein first proposed that space-time
is curved.
In 1915, he devised the Einstein field equations which relate the
curvature of space-time with the mass, energy, and momentum within it.
Some of the consequences of general relativity are:
- Clocks
run more slowly in deeper gravitational wells. This is called gravitational time dilation.
Taking pursuit of game, the
stress of combat, or the initial instigation if important interpersonal contact
as examples of gravitational time dilation we may observe that when there is a
vital interest at stake, we experience a heightened state of perception and a
slowing of and expansion of our awareness of the passage of time. This affects
and is experienced disjunctively in the conscious and subconscious aspect of
our mind as a function of as yet described action of human brain chemistry.
Every person has experienced the essential effect of a gravitational well in
building up the courage to approach a person of their target gender who they
really like, for the first time.
- Orbits precess in a way unexpected in Newton's theory of gravity. (Newton
described the attraction between one object and another. It is one of the
fundamental forces of nature applicable to all objects. It is usually used
to describe the gravitational attraction exerted by the core of the Earth.)
Precess, in our example, means we slowly circle both
physically and emotionally; slowly around our target in a closing spiral or conical
manner, approaching at last our desired and by this time not unsuspecting intention.
Rays of light are
generally perceived as a constant spectrum of equations or named colors. The
light of the sun or a flashlight or a candle are analogues to themselves and
also to human spectrums including perception, intention or desire.
- Rotating masses "drag along" the space-time around them; a phenomenon termed "frame-dragging".
Individuals in groups of
diverse persons interacting together will inevitably observe and attract a disjunction
of the attention and perceptions of interested and not interested persons. Frame-dragging
can be viewed as the gravitational analog of electromagnetic induction, or the
human attraction of a lover by means of personal electricity of appearance and/or
appearance. Cash, power or position, not really large variables in this
equation, although never fully discounted in some subjects.
- The Universe is expanding,
and the far parts of it are moving away from us faster than the speed of light.
The universe containing
any human being is only that of her perception. The means of a human’s
perception is her brain and its chemical and electrical function. To postulate that
the universe extends infinitely in all directions from our planet may be true
of false, but this may only be imagined through the working of human brain
function. Human beings stand in the same physical proximity to the universe as
our canine companions, but it may be observed that a dog is generally more
comfortable in and the master of their than most human beings can hope become.
Technically, general relativity is a theory of gravitation
whose defining feature is its use of the Einstein field equations. The solutions of
the field equations are metric tensors which
define the topology
of the space-time and how objects move inertially.
Special relativity
1.
The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity).
As a factor of personal, social or cultural human interaction, this axiom
may be seen to be a disjunction of truth and falsehood as determined by the
construction of each combination of propositional equations in individual human
personality.
2.
The speed
of light in a vacuum is the same for all observers,
regardless of their relative motion or of the motion of the source of the light.
This aspect may be seen as the practical personal application one each
person’s obvious external assets those hidden unseen talents by extension or by
inference.
***
I am now considering the construction of a reflective equation to make this assertion
more apparently applicable to Evident Relativity within my contribution to our
system. My point is to show the connected nature of the universe, and the
handicap one takes on in isolating one field from all others in consideration.
i.e. Science separate from art, separate
from metaphysics, separate from industry, economics, consumption, philanthropy,
public bureaucracy, legislation, statecraft, etc.; this extensive and
exponential separation does not allow right perception of each individual variable
and causes resulting equations to be out of balance skewing perceptions of
perhaps all individuals in dominant culture to some extent. Indians could command this total
balance in the equations of their own personal and tribal universe first because
their lives excluded the concept of money as a function rather than a tool.
Such is the essential disjunction
that is the success and equally the failure of dominant cultural perception. As
a result of this, Indians lived closer to nature and largely without most
technology that feeds and distracts our culture and economy.
 |
| Gus Arriola’s Gordo © Respective copyright/trademark holders. |
Harold R. (Hal)
Foster’s Prince Valiant
© Respective
copyright/trademark holders.
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