The curvature of spacetime is a probability distribution, corresponding to a UNIVERSAL MINDSCAPE.
Each event in space-time has its own intrinsic measure of the "present moment" which is the separation of past and future, with the future as an uncertainty.
Why not represent the present moment of an arbitrary observer as the inward collapse of the "past" light-cone to the present moment and the outward expanse of the future light-cone into the uncertain future.
A 2-dimensional "cross-section" of the present moment, or proper time, of an observer, p:
[<-[->[<-[p]->]<-]->]
Now it appears that the past moments are cumulative and are increasing in density? as a cumulative stacking of present moments. Since the laws of physics are time invariant, the uncertain future is beholden to the action principle.
uncertainty is a necessary condition, in order for free will to exist.
God is a psychometric eigenvector?
The eigenvector plane of symmetry, becomes an interactive -
spatio-temporally stratified display screen, in the holographic
universe.
Humans become observer participants in the co-creation OF reality
itself.
Here is a quote of Richard Feynman:
Quote:
"I can live with doubt and uncertainty and not knowing. I think it's
much more interesting to live not knowing than to have answers which
might be wrong. I have approximate answers and possible beliefs and
different degrees of certainty about different things, but I'm not
absolutely sure of anything. "
Feynman appears to be expressing a mathematical paradox, basically in
the form of a statement:
We can ONLY be CERTAIN that we are NOT-CERTAIN
X if and only if not-X
Conclusion?
Perfection is the hypothetical limit of removing imperfections or
"perterbations" that break the perfect symmetry.
Perfection can exist at the end of an infinite series of operations
Perfection is transfinite
Imperfection is finite
Perfection becomes a necessary and sufficient, abstraction
The abstract contains the concrete
Reality is MIND
In simplest terms:
Universal Mind = Universal Eigenvector
In general relativity, there is a formulation called configuration
space, i.e. the superspace, of the geometrodynamics formulation, where
the wavefunctions will be functions over the abstract spaces that
define space itself. The spaces are generally covariant and
"coordinate spaces" are just a convienient modeling tool. There is an
independence of coordinate systems; the classical geometrodynamics constitutes an algorithm for constructing a leaf history of foliations through superspace in a background independent-interlocking of three geometries.
Coordinates are a convienient means of mathematical modeling, ...but
reality actually defines itself with "events". Events don't happen in
a fixed absolute background of space, or time; events characterize the
evolution OF "space-time".
"The boundary condition of the universe is that it has no boundary",
to quote S. Hawking.
The basic feature of cognitive functions appears to be the simulation
of possible future scenarios via a self modeling process. Memory
corresponds to a simulation of past to present to future plans, with
predictions to the simulation of ever further future scenarios. The
thermodynamic arrow of time shows how time gives a reliable simulation
of the past via repeatable experiments/memories, such, that it is so
reliable that one speaks of actual memories rather than predictions of
the past. The possible nonuniqueness of the classical spacetime and
related classical nondeterminism suggests a possible origin for the
simulatory aspects of consciousness built in to the geometric
structure OF ...space-time.
A person's mind and personality is equivalent to their "software",
that is, to the programming of their brain.
Any software structure can be coded by some large set of natural
numbers.
Every set of numbers exists eternally as a mathematical abstraction
independent of the physical universe.
Therefore each individual's personality is immortal.
According to Mach's principle, a single particle in a bleak void of a
universe, has ZERO inertial mass. An infinitesimally small force
accelerates it - energy is zero because inertial mass is zero, so that
potential energy, mgh and kinetic energy, 1/2 mv^2 are each zero.
Einstein emphasized that a single particle in a void could not have
inertia, for there can be no inertia of matter against space, only
inertia against other matter.
It seems that coordinate independence must hold, and artificial
coordinate "patches" are not really necessary. So a defined "point" in
space-time, must really be an ...event?
There would only be events, related to other events. But all observers
would observe everything else to be in a past moment due to the finite
propagation speed, of light. Proper time would be the only "real time"
So if Einstein says that "the train arrives here at ten o'clock" he
means that the pointing of the small hand of his clock to the ten and
the arrival of the train are "simultaneous events"... where the clock
and the event, are in close proximity.
So a certain definition of time appears to be OK when defining time
for the place where the clock is located, but it is insufficient for defining
time for a series of events at different locations, i.e. to evaluate
times of events occurring at locations remote from the clock.
If for a location A of space, there is a clock, with an observer, and
the observer at A can determine the time values of events in the
immediate proximity of A by observing the positions of the hands of
the clock which are simultaneous with the events at location A.
If at another location in space, point B, with an identical clock, the
observer at B can determine the time values in the immediate proximity
of B. But the time of an event at A cannot compare to the time of an
event at B since a common time for both A and B is yet to be defined.
According to Einstein, the time it takes a ray of light to travel from
A to B equals the time it takes the ray to travel from B to A. Let the
ray of light start at the A time "TA" from A to B, it arrives at the B
time "TB" and is reflected back in the direction of A, where it
arrives at the A time "T'A".
TB - TA = T'A - T'B
A "synchronous" definition of time is arrived at?
2AB/[T'A - TA] = c,
the speed of light in vacuum.
Distance is a property between objects in space. Duration is a
distance between events in time. Spacetime is a relational structure;
The structure of space is possibly a distributive lattice. A lattice
is a partially ordered set, closed under least upper and greatest lower
bounds.
The geometric view of physics means that the laws of physics are the
same in every Lorentz reference system. Local Lorentz invariance. But
since the universe has no exterior reference frame, and it must refer
to itself, such, that its overlapping geometry is a computational self
configuration, parameterized by time. The quantized-evolution of
spacetime dictated by GR and QM, means that the past history of then
universe is carried along with the present, for the universe. A
geometric stacking of space like slices, parameterized by t, The
universe is a function of itself. Spacetime becomes relativistically "compressed". As the time evolution proceeds in the thermodynamic direction of t, the space like sheets continually increase in density. The information storage of space time.
(<-(->(<-(U)->)<-)->)
This increasing refractive spacetime density must be background
independent. The increasing density functions are, in a sense,
equivalent to the non-Euclidean geometry of Riemann and Einstein.
Matter-energy is a form of "event density" where the distribution of
matter-energy determines the geometry of space-time. If there is no
matter energy, that is to say "events", then there is no geometry.
Therefore a body in an otherwise empty universe would have no
intertial properties. Even though Einstein's theory of general
relativity can describe universes that contain no matter, possibly
leading one to believe that GR is not relational - because there can
be space without matter, and there are no material relations that
serve to define space, it is incorrect to make such an assumption. GR
is a theory of fields, and fields vary continuously over space,
forming networks of interactive relations[events].
[1.] Nothingness is a difficult concept, or rather a difficult
"non-concept" since it is ...nothing.
[2.] To say that nothingness exists is to create a contradiction,
since nothingness is non-existence. Nothingness "non-exists".
[3.] Nothingness is non-existence; therefore nothingness is
non-relational. Nothingness has no distinctiveness in and of itself,
hence nothingness cannot be recognizable.
[4.] Being-ness means basically "to be", and to exist. Being-ness
exists.
[5.] Take any two distinct quantities-attributes of existence:
A<------P------>B
A and B perceive each other to be different with perception P. That is
to say A is perceived to be different from B and B is perceived to be
different from A.
A and B are different elements of a larger picture, but they
also[must] share certain common attributes of the larger reality
including them. From that perspective A and B are the same, because
aspects of A transform into B and aspects of B transform into A. At a
higher level of generality and symmetry, A cannot be distinguished
from B, and B cannot be distinguished from A. For example, dogs and
cats are distinctively different, yet dogs and cats are the same from
the perspective that both are "mammals".
[6.] Following this premise, it stands to reason that all attributes &
aspects of reality can be transformed into each other, and hence they
have no distinctions from each other[at continually higher and higher
levels of symmetry].
[7.] Therefore, it follows, that at a top[infinite?] level of
symmetry, everything is nothing.
QED.
Is it possible to develop warp drive technology? or more correctly,
warp drive ..."trek" nology?
http://arxiv.org/abs/gr-qc/0204012
The universal constants are precisely balanced, such, that carbon
based life could not exist otherwise.
Now take those finely tuned constants out hundreds, thousands,
millions, billions ...trillions, quadrillions of decimal places.
Slight, almost infinitesimal differences between the constants of each
universe, which are actually resonances of a quantum "multiverse",
mean that each resonance is unique.
http://www.cs.unc.edu/~barman/HT96/P43/pictura.htm
Riemann's cuts are analogous to spatio-temporal holes connecting to an
almost exactly identical parallel reality[phase resonance-frequency].
It is most likely true that when a massive star collapses to form a
"black hole", instead of creating a singularity, it transforms into a
type of "Bose Einstein Condensate", also known as "gravastar theory"
If space is constructed of discrete units, and a smallest possible
volume of space is quantized, then how can a "singularity" exist?
According to Lee Smolin, empty space could be a type of colour
electric superconductor, which could explain why quarks are confined.
Some nostalgic "Conan the Barbarian":
Does Crom exist?
Shades of Nietzsche?
Conan: Crom, I have never prayed to you before. I have no tongue for
it. No one, not even you, will remember if we were good men or bad.
Why we fought, and why we died. All that matters is that today, two
stood against many. Valor pleases you, so grant me this one request.
Grant me revenge! And if you do not listen, ...the HELL with you!
[...]
Mongol General: We have won again. That is good! But what is best in
life?
Mongol Warrior: The open steppe, fleet horse, falcon on your wrist,
wind in your hair!
Mongol General: Wrong! ...Conan, what is best in life?
Conan: To crush your enemies, see them driven before you, and to hear
the lamentation of the women!
Mongol General: That is good.
The psychometric matrix corresponds to the Einstein tensor:
X axis = motor-sensory
Y axis = Right-Left hemispheres
Z axis = stem-limbic-cortex
The 3 neuropsychological divisions correspond to the 3
psychometric dimensions of E,N,P
E = motor-sensory
N = Sperrian Lateralization
P = Neuraxial cleavage
Two of these dimensions are real, the other dimension along with all
possible compactified dimensional manifolds, are virtual.
A primary aspect of "science" is the development and construction of
theories leading to the verification of a correspondence between
observed data and an abstract model, formulated to represent the data.
Conventional psychometrics utilizes statistical models via probability
distributions, to describe, the results of mental tests. The degree of
correspondence between empirical observations and those predicted
through the operation of the model is a "fit" between the data and
the model. Of course, the scientists endeavor to formulate an exact a
fit as possible.
The psychometric matrix is the result of a probability distribution.
In terms of quantum gravity, the curvature of "space-time" is a
Gaussian probability distribution.
Quantum gravity controls brain growth. The quantum gravity in the
brain at the subatomic level controls elemental processes of the
brain, which includes brain growth itself. Therefore, the curvature
of space-time is a direct causative factor of the statistical
curvature in the Psychological metric.
A metric field can be defined by the primary substratum of events.
Thus the intrinsic geometrical structure of spacetime is predicated on
the pseudo-Riemannian spaces via the affine relationships — all
physical events are fully reducible to manifestations of the
substratum i. e. the metric field.
Stochastically speaking, gravity is must be taken beyond the limits of
classical reality, where the mean value of the stress energy tensor of
quantum fields also has fluctuations as a source of stochastic
Einsteinian vacuum equations. Such is the necessary foundation for
neo-classical gravity for the viability of inflationary cosmology
based on the vacuum energy dominated phase. Metric fluctuations and
spacetime foams form a chaotic substrate.
Yes, the shortest distance between two points is a straight line;
energy is conserved.
Form a space-time triangle with vertices A,B,C, of three lines - two
null and one spacelike line, such that the triangle "spans" the
timelike plane.
Because of the one-to-oneness of the mapping, the image of the
triangle with the vertices A,B,C , "spans" the transformed plane as
different points are mapped onto different points. Therefore, the
three lines forming the transformed triangle must be coplanar. In
general, the images of all lines lying in a time-light plane must be
coplanar. Thus, timelike planes map into planes.
Any time light-cone line, is the intersection of two time-light
planes. Since timelike planes are mapped onto planes, they intersect
into a line. Thus, any timelike line is mapped into a line.
Basically, all three types of lines - lightlike(null), spacelike, and
timelike, are mapped onto lines.
The uncertainty principle and gravity are related to the same
mathematical properties. The proof of the uncertainty relation
involves the Cauchy Schwartz inequality. The triangle inequality
follows from the Cauchy Schwartz.
1. With a little earnest thought, one realizes that the concept of
"ultimate randomness" is logically absurd.
2. The laws of physics are time independent. They hold for all frames
of reference.
3. Also, even if ...physical randomness is true, physical randomness
would not exist without time, or "change" - from one state to the
next.
4. If the physical laws are time independent then the physical laws,
by definition, did not arise "randomly".
5. The laws of physics are a set of organizing principles.
6. The only true example we have of an organizing principle is that of
a "MIND"
7. The universe came from a MIND
Each event in space-time has its own intrinsic measure of the "present moment" which is the separation of past and future, with the future as an uncertainty.
Why not represent the present moment of an arbitrary observer as the inward collapse of the "past" light-cone to the present moment and the outward expanse of the future light-cone into the uncertain future.
A 2-dimensional "cross-section" of the present moment, or proper time, of an observer, p:
[<-[->[<-[p]->]<-]->]
Now it appears that the past moments are cumulative and are increasing in density? as a cumulative stacking of present moments. Since the laws of physics are time invariant, the uncertain future is beholden to the action principle.
uncertainty is a necessary condition, in order for free will to exist.
God is a psychometric eigenvector?
The eigenvector plane of symmetry, becomes an interactive -
spatio-temporally stratified display screen, in the holographic
universe.
Humans become observer participants in the co-creation OF reality
itself.
Here is a quote of Richard Feynman:
Quote:
"I can live with doubt and uncertainty and not knowing. I think it's
much more interesting to live not knowing than to have answers which
might be wrong. I have approximate answers and possible beliefs and
different degrees of certainty about different things, but I'm not
absolutely sure of anything. "
Feynman appears to be expressing a mathematical paradox, basically in
the form of a statement:
We can ONLY be CERTAIN that we are NOT-CERTAIN
X if and only if not-X
Conclusion?
Perfection is the hypothetical limit of removing imperfections or
"perterbations" that break the perfect symmetry.
Perfection can exist at the end of an infinite series of operations
Perfection is transfinite
Imperfection is finite
Perfection becomes a necessary and sufficient, abstraction
The abstract contains the concrete
Reality is MIND
In simplest terms:
Universal Mind = Universal Eigenvector
In general relativity, there is a formulation called configuration
space, i.e. the superspace, of the geometrodynamics formulation, where
the wavefunctions will be functions over the abstract spaces that
define space itself. The spaces are generally covariant and
"coordinate spaces" are just a convienient modeling tool. There is an
independence of coordinate systems; the classical geometrodynamics constitutes an algorithm for constructing a leaf history of foliations through superspace in a background independent-interlocking of three geometries.
Coordinates are a convienient means of mathematical modeling, ...but
reality actually defines itself with "events". Events don't happen in
a fixed absolute background of space, or time; events characterize the
evolution OF "space-time".
"The boundary condition of the universe is that it has no boundary",
to quote S. Hawking.
The basic feature of cognitive functions appears to be the simulation
of possible future scenarios via a self modeling process. Memory
corresponds to a simulation of past to present to future plans, with
predictions to the simulation of ever further future scenarios. The
thermodynamic arrow of time shows how time gives a reliable simulation
of the past via repeatable experiments/memories, such, that it is so
reliable that one speaks of actual memories rather than predictions of
the past. The possible nonuniqueness of the classical spacetime and
related classical nondeterminism suggests a possible origin for the
simulatory aspects of consciousness built in to the geometric
structure OF ...space-time.
A person's mind and personality is equivalent to their "software",
that is, to the programming of their brain.
Any software structure can be coded by some large set of natural
numbers.
Every set of numbers exists eternally as a mathematical abstraction
independent of the physical universe.
Therefore each individual's personality is immortal.
According to Mach's principle, a single particle in a bleak void of a
universe, has ZERO inertial mass. An infinitesimally small force
accelerates it - energy is zero because inertial mass is zero, so that
potential energy, mgh and kinetic energy, 1/2 mv^2 are each zero.
Einstein emphasized that a single particle in a void could not have
inertia, for there can be no inertia of matter against space, only
inertia against other matter.
It seems that coordinate independence must hold, and artificial
coordinate "patches" are not really necessary. So a defined "point" in
space-time, must really be an ...event?
There would only be events, related to other events. But all observers
would observe everything else to be in a past moment due to the finite
propagation speed, of light. Proper time would be the only "real time"
So if Einstein says that "the train arrives here at ten o'clock" he
means that the pointing of the small hand of his clock to the ten and
the arrival of the train are "simultaneous events"... where the clock
and the event, are in close proximity.
So a certain definition of time appears to be OK when defining time
for the place where the clock is located, but it is insufficient for defining
time for a series of events at different locations, i.e. to evaluate
times of events occurring at locations remote from the clock.
If for a location A of space, there is a clock, with an observer, and
the observer at A can determine the time values of events in the
immediate proximity of A by observing the positions of the hands of
the clock which are simultaneous with the events at location A.
If at another location in space, point B, with an identical clock, the
observer at B can determine the time values in the immediate proximity
of B. But the time of an event at A cannot compare to the time of an
event at B since a common time for both A and B is yet to be defined.
According to Einstein, the time it takes a ray of light to travel from
A to B equals the time it takes the ray to travel from B to A. Let the
ray of light start at the A time "TA" from A to B, it arrives at the B
time "TB" and is reflected back in the direction of A, where it
arrives at the A time "T'A".
TB - TA = T'A - T'B
A "synchronous" definition of time is arrived at?
2AB/[T'A - TA] = c,
the speed of light in vacuum.
Distance is a property between objects in space. Duration is a
distance between events in time. Spacetime is a relational structure;
The structure of space is possibly a distributive lattice. A lattice
is a partially ordered set, closed under least upper and greatest lower
bounds.
The geometric view of physics means that the laws of physics are the
same in every Lorentz reference system. Local Lorentz invariance. But
since the universe has no exterior reference frame, and it must refer
to itself, such, that its overlapping geometry is a computational self
configuration, parameterized by time. The quantized-evolution of
spacetime dictated by GR and QM, means that the past history of then
universe is carried along with the present, for the universe. A
geometric stacking of space like slices, parameterized by t, The
universe is a function of itself. Spacetime becomes relativistically "compressed". As the time evolution proceeds in the thermodynamic direction of t, the space like sheets continually increase in density. The information storage of space time.
(<-(->(<-(U)->)<-)->)
This increasing refractive spacetime density must be background
independent. The increasing density functions are, in a sense,
equivalent to the non-Euclidean geometry of Riemann and Einstein.
Matter-energy is a form of "event density" where the distribution of
matter-energy determines the geometry of space-time. If there is no
matter energy, that is to say "events", then there is no geometry.
Therefore a body in an otherwise empty universe would have no
intertial properties. Even though Einstein's theory of general
relativity can describe universes that contain no matter, possibly
leading one to believe that GR is not relational - because there can
be space without matter, and there are no material relations that
serve to define space, it is incorrect to make such an assumption. GR
is a theory of fields, and fields vary continuously over space,
forming networks of interactive relations[events].
[1.] Nothingness is a difficult concept, or rather a difficult
"non-concept" since it is ...nothing.
[2.] To say that nothingness exists is to create a contradiction,
since nothingness is non-existence. Nothingness "non-exists".
[3.] Nothingness is non-existence; therefore nothingness is
non-relational. Nothingness has no distinctiveness in and of itself,
hence nothingness cannot be recognizable.
[4.] Being-ness means basically "to be", and to exist. Being-ness
exists.
[5.] Take any two distinct quantities-attributes of existence:
A<------P------>B
A and B perceive each other to be different with perception P. That is
to say A is perceived to be different from B and B is perceived to be
different from A.
A and B are different elements of a larger picture, but they
also[must] share certain common attributes of the larger reality
including them. From that perspective A and B are the same, because
aspects of A transform into B and aspects of B transform into A. At a
higher level of generality and symmetry, A cannot be distinguished
from B, and B cannot be distinguished from A. For example, dogs and
cats are distinctively different, yet dogs and cats are the same from
the perspective that both are "mammals".
[6.] Following this premise, it stands to reason that all attributes &
aspects of reality can be transformed into each other, and hence they
have no distinctions from each other[at continually higher and higher
levels of symmetry].
[7.] Therefore, it follows, that at a top[infinite?] level of
symmetry, everything is nothing.
QED.
Is it possible to develop warp drive technology? or more correctly,
warp drive ..."trek" nology?
http://arxiv.org/abs/gr-qc/0204012
The universal constants are precisely balanced, such, that carbon
based life could not exist otherwise.
Now take those finely tuned constants out hundreds, thousands,
millions, billions ...trillions, quadrillions of decimal places.
Slight, almost infinitesimal differences between the constants of each
universe, which are actually resonances of a quantum "multiverse",
mean that each resonance is unique.
http://www.cs.unc.edu/~barman/HT96/P43/pictura.htm
Riemann's cuts are analogous to spatio-temporal holes connecting to an
almost exactly identical parallel reality[phase resonance-frequency].
It is most likely true that when a massive star collapses to form a
"black hole", instead of creating a singularity, it transforms into a
type of "Bose Einstein Condensate", also known as "gravastar theory"
If space is constructed of discrete units, and a smallest possible
volume of space is quantized, then how can a "singularity" exist?
According to Lee Smolin, empty space could be a type of colour
electric superconductor, which could explain why quarks are confined.
Some nostalgic "Conan the Barbarian":
Does Crom exist?
Shades of Nietzsche?
Conan: Crom, I have never prayed to you before. I have no tongue for
it. No one, not even you, will remember if we were good men or bad.
Why we fought, and why we died. All that matters is that today, two
stood against many. Valor pleases you, so grant me this one request.
Grant me revenge! And if you do not listen, ...the HELL with you!
[...]
Mongol General: We have won again. That is good! But what is best in
life?
Mongol Warrior: The open steppe, fleet horse, falcon on your wrist,
wind in your hair!
Mongol General: Wrong! ...Conan, what is best in life?
Conan: To crush your enemies, see them driven before you, and to hear
the lamentation of the women!
Mongol General: That is good.
The psychometric matrix corresponds to the Einstein tensor:
X axis = motor-sensory
Y axis = Right-Left hemispheres
Z axis = stem-limbic-cortex
The 3 neuropsychological divisions correspond to the 3
psychometric dimensions of E,N,P
E = motor-sensory
N = Sperrian Lateralization
P = Neuraxial cleavage
Two of these dimensions are real, the other dimension along with all
possible compactified dimensional manifolds, are virtual.
A primary aspect of "science" is the development and construction of
theories leading to the verification of a correspondence between
observed data and an abstract model, formulated to represent the data.
Conventional psychometrics utilizes statistical models via probability
distributions, to describe, the results of mental tests. The degree of
correspondence between empirical observations and those predicted
through the operation of the model is a "fit" between the data and
the model. Of course, the scientists endeavor to formulate an exact a
fit as possible.
The psychometric matrix is the result of a probability distribution.
In terms of quantum gravity, the curvature of "space-time" is a
Gaussian probability distribution.
Quantum gravity controls brain growth. The quantum gravity in the
brain at the subatomic level controls elemental processes of the
brain, which includes brain growth itself. Therefore, the curvature
of space-time is a direct causative factor of the statistical
curvature in the Psychological metric.
A metric field can be defined by the primary substratum of events.
Thus the intrinsic geometrical structure of spacetime is predicated on
the pseudo-Riemannian spaces via the affine relationships — all
physical events are fully reducible to manifestations of the
substratum i. e. the metric field.
Stochastically speaking, gravity is must be taken beyond the limits of
classical reality, where the mean value of the stress energy tensor of
quantum fields also has fluctuations as a source of stochastic
Einsteinian vacuum equations. Such is the necessary foundation for
neo-classical gravity for the viability of inflationary cosmology
based on the vacuum energy dominated phase. Metric fluctuations and
spacetime foams form a chaotic substrate.
Yes, the shortest distance between two points is a straight line;
energy is conserved.
Form a space-time triangle with vertices A,B,C, of three lines - two
null and one spacelike line, such that the triangle "spans" the
timelike plane.
Because of the one-to-oneness of the mapping, the image of the
triangle with the vertices A,B,C , "spans" the transformed plane as
different points are mapped onto different points. Therefore, the
three lines forming the transformed triangle must be coplanar. In
general, the images of all lines lying in a time-light plane must be
coplanar. Thus, timelike planes map into planes.
Any time light-cone line, is the intersection of two time-light
planes. Since timelike planes are mapped onto planes, they intersect
into a line. Thus, any timelike line is mapped into a line.
Basically, all three types of lines - lightlike(null), spacelike, and
timelike, are mapped onto lines.
The uncertainty principle and gravity are related to the same
mathematical properties. The proof of the uncertainty relation
involves the Cauchy Schwartz inequality. The triangle inequality
follows from the Cauchy Schwartz.
1. With a little earnest thought, one realizes that the concept of
"ultimate randomness" is logically absurd.
2. The laws of physics are time independent. They hold for all frames
of reference.
3. Also, even if ...physical randomness is true, physical randomness
would not exist without time, or "change" - from one state to the
next.
4. If the physical laws are time independent then the physical laws,
by definition, did not arise "randomly".
5. The laws of physics are a set of organizing principles.
6. The only true example we have of an organizing principle is that of
a "MIND"
7. The universe came from a MIND
that an exact correspondence between the infinitely symmetrical modular forms, and elliptic curves was discovered. Elliptic curves are modular