Selected Excerpts from
Toward an Explanation
of the Unexplainable",
the New Edition,
by Bob Toben
and Fred Alan Wolf,
Bantum books, 1982,
p. 129 - 130.
"How
does
the universe
do
it?
How
does it
produce
anything
at
all?
No one
really
knows
the answer.
However,
we do know
that the
self-reference
is an important part
of
the process.
The way that it works
in quantum physics,
which underlies
all
of the physical world,
is that
the
quantum wave
flows
between
two events
just like
a river
leaving
a source
and
flowing
to
a sink.
But
then
it
'turns around'
in
space-time
and
flows
back
from the sink
to the source.
The resulting
reinforcement
between
the quantum wave
and its
space-time reflected
image
produces
the
experiences
we call
reality.
In the language
of quantum physics,
we say
that the wave
is
multiplied
by its
'complex-conjugated
self'
to produce
the
probabilities
of the
real world.
This
double-flow
process
occurs
in every
physical
phenomenon.
It is
in this manner
that we
have
self-organization;
self
exists
through
the wave
interacting
with its
space-time mirrored image
in
the same way
that
you
interact
with
your own
mirror image.
Did you
ever notice
that
in order to
notice
yourself
in
a mirror
you
have to
forget
yourself?
And
to forget yourself
you
have to
take note
of
yourself?
By
self-reflection
we
are able
to change
ourselves.
By
observing
ourselves
in
others
we
are able
to
change
each other.
All there is,
is
the one-verse,
the
universe
looking
at
itself
in
itself."
+++
Selections
from
"Russell:
Mathematics:
Dreams
and
Nightmares",
by
Ray Monk,
Phoenix Press,
1997
[on Bertrand Russell,
1872-1970]
"I had been told
that Euclid
proved things,
and
was much disappointed
that he started
with
axioms.
At first
I refused
to accept them
unless my brother
could offer me
some
reason
for doing so,
but he said,
'If you don't accept them
we cannot go on',
and
as I wished to go on,
I reluctantly
accepted them
pro tem.
The doubt
as to the
premises
of
mathematics
which I felt
at that moment
remained with me,
and determined
the course
of my
subsequent work."
[from "The Autobiography
of
Bertrand Russell
1972 - 1914",
1967, p. 36]
(p. 3 - 4)
"For both
Hobbes and Russell,
the
almost erotic delight
they took
in learning
Euclid's geometry
('as dazzling
as first love')
was
aroused
by
the feeling
of
finally
coming to know
something
with
complete certainty.
The beauty
of Euclid's system
is
that
it is axiomatic.
Everything
that it teaches
about circles,
triangles,
squares,
etc.
is not just stated
but
proved;
complicated
and
surprising things
about the relations
between
angles and lengths
and so on
are shown
to be
merely logical consequences
of a few,
simple axioms.
It's
as if a whole,
vast body
of knowledge
has been spun
out of
virtually nothing,
but,
more than that,
this body
of knowledge
is not tentative
or
provisional,
it
does not depend
upon
the contingencies
of
the world,
but rather
can be established
once
and for all.
If one accepts
the axioms,
one
has to accept
the rest;
no further doubt
is possible.
To someone who
wishes,
as Russell
passionately wished,
to find reasons
for their beliefs,
the exhilarating possibility
this opens up
is that
some beliefs
at least
can be provided
with
absolutely
cast-iron foundations."
(p. 4-5)
"... the experience
of discovering
a realm of truth
free from
the vicissitudes
of human existence
was ecstatic
to Russell,
and
it inspired in him
a desire
to found all knowledge
upon
the kind of
rock-solid foundations
provided
by Euclid's
system of geometry."
(p. 6)
"I found
great delight
in mathematics --
much more delight,
in fact,
than in any other study.
I liked to think
of the applications
of mathematics
to the physical world,
and I hoped that
in time
there would be
a mathematics
of human behavior
as precise
as the mathematics
of machines.
I hoped this
because I liked
demonstrations,
and at most times
this motive
outweighed the desire,
which I also felt,
to believe in
free will."
[from
"Portraits from Memory",
1956. p. 20]
(p. 6)
"Mathematics
is,
I believe,
the chief source
of the belief
in
eternal
and
exact
truth,
as well as
in
a super-sensible
intelligible
world.
Geometry
deals with
exact circles,
but
no sensible object
is exactly circular;
however carefully
we may use our compasses,
there will be
some
imperfections
and
irregularities.
This
suggests the view
that all exact reasoning
applies to
ideal
as opposed to sensible
objects;
it is natural
to go further,
and to argue
that
thought
is nobler
than sense,
and the
objects of thought
more real
than those
of
sense-perception."
[from "History
of Western Philosophy",
1991 p. 55 -56]
(p. 7)
"For a time
I found satisfaction
in a doctrine
derived, with modification,
from Plato.
According to
Plato's
doctrine,
which I accepted
only in a watered-down form,
there is
an unchanging
timeless
world
of ideas
of which
the world presented to our senses
is
an imperfect copy.
Mathematics,
according to this doctrine,
deals with the
world
of ideas
and has
in consequence
an
exactness
and
perfection
which is absent
from the everyday world.
This kind
of mathematical
mysticism,
which Plato
derived
from Pythagoras,
appealed to me."
[from
"Portraits from Memory",
1956, p. 22]
(p. 8)
"I disliked
the real world
and
sought refuge
in a timeless world,
without change
or decay
or
the
will-o'-the-wisp
of
progress."
[from "My
Philosophical Development",
1959, p. 210]
(p. 8)
"As Russell presents him,
Pythagoras
was both
a religious prophet
and
a pure mathematician:
'In both respects
he was
immeasurably influential,
and the two
were not so separate
as they seem
to a modern mind.'
Pythagoras's
religion,
according to Russell,
was
a reformed version
of Orphism,
which was, in turn,
a reformed version
of the worship
of Dionysus.
Central to all three
was the exaltation
of ecstasy,
but
in the cult of Pythagoras,
this ecstasy
is to be achieved
not by
drinking wine
or indulging
in sexual activity,
but rather
by the exercise
of the intellect.
The highest life,
on this view,
is that devoted to
'passionate sympathetic
contemplation',
which Russell
(following F. M. Cornford)
says
was
the original meaning
of
the word
'theory'."
(p. 9)
"For Pythagoras,
the passionate contemplation
was intellectual,
and issued
in mathematical knowledge.
In this way,
through
Pythagoreanism,
'theory'
gradually acquired
its
modern
meaning;
but for all who were inspired
by Pythagoras
it retained an element
of
ecstatic revelation.
To those who have reluctantly learnt
a little mathematics in school
this may seem strange;
but
to those
who have experienced
the intoxicating delight
of
sudden understanding
that mathematics gives,
from time to time,
to those who love it,
the Pythagoras view
will seem
completely natural,
even if untrue.
It might seem
that
the empirical philosopher
is
the slave
of his material,
but
the
pure mathematician,
like the musician,
is
a free creator
of his world
of
ordered beauty."
[from "History
of Western Philosophy",
1991 p. 52 -53]
(p. 9)
"Pythagoras
('as everyone knows',
according to Russell)
believed that
'all things
are numbers'.
Everything
in the world,
whether it be
the building of pyramids,
the things of nature,
the harmonies of music,
or whatever,
expresses a series
of numerical relations,
and can be
described
by those relations.
The tragedy
for the Pythagoreans
(and,
as we shall see,
a similar tragedy
was played out
in Russell's own
philosophical development)
was
that their greatest,
most well-known discovery
was the one
that undermined
this point of view:
namely
the famous
Pythagorean Theorem
concerning
right-angled triangles,
which led immediately
to the discovery
of incommensurables.
According to
the Pythagorean Theorem,
the length of the hypotenuse
of a right-angled triangle
in which the other two sides
are
one unit long
will be equal to
the square root of 2.
The trouble
is that the square root of 2
is
incommensurable;
that is,
it cannot be expressed
as the relation
between two numbers,
or,
to put it another way,
it is
'irrational'.
It follows
that there is
at least
one thing
in the world
which is
not
the expression
of a numerical relation.
Others, of course,
followed;
the best known of which
is pi,
the relation
between
the circumference
and
the diameter
of
a circle.
To the ancient Greeks,
this suggested
that geometry,
not arithmetic,
was the surest source
of exact knowledge,
which is one reason
for the pre-eminence
given to Euclid's Elements.
The Pythagorean Dream
of showing everything
to be reducible
to arithmetic
was, it seemed,
over."
(p. 10)
"The problem
of incommensurables,
however,
continued
to haunt those
who looked
to mathematics
for
perfect rigor
and
exactitude.
Quantities like
the square root of 2
and pi
were included
in the domain
of 'real' numbers,
though
no satisfactory definition of them --
or, therefore, of the notion
of a 'real number' in general --
was yet available.
And, indeed,
the new techniques
brought with them
further problems
which
opened up the science
of mathematics
to the charge
of
being riddled
with
inconsistencies.
Three fundamental notion
in mathematics --
infinity,
the
infinitesimal,
and
continuity --
seemed
inherently
paradoxical.
The paradoxes
of infinity
and continuity
had been known
since ancient times,
but they acquired
a new importance
as
the power of mathematics
to represent
continuous
and
infinite sequences
grew."
(p. 10 - 11)
"... the notion
of
an infinitesimal ...
[...]
What are
these 'evanescent Increments'
used
in the calculus?
Berkeley sneered.
'They are neither
finite
Quantities,
nor Quantities
infinitely small
nor yet
not
nothing.
May we not call them
the Ghosts
of departed Quantities?'
Anyone
who could
accept
such a notion,
Berkeley suggested,
ought to have
no qualms
in
accepting
the mysteries
of Christianity,
for
do not mathematicians
have
their own mysteries,
'and
what is more,
their repugnancies
and
contradictions?'
(p. 13)
"Those who taught me
the
infinitesimal Calculus
did not know
the valid proofs
of
its fundamental theorems
and tried to
persuade me
to accept
the official sophistries
as an
act of faith.
I realized that
the calculus works
in practice,
but I was at a loss
to
understand
why
it should do so.
However
I found
so much pleasure
in the acquisition
of technical skill
that
at most times
I forgot my doubts."
[from "My Philosophical
Development",
1959, p. 35 - 36]
(p. 14)
"... The mathematical teaching
at Cambridge
when I was an undergraduate
was definitely bad."
[from "My Philosophical
Development",
1959, p. 37]
(p. 14)
"The 'proofs'
that were offered
of mathematical theorems
were
an insult
to
the logical intelligence.
Indeed,
the whole subject
of mathematics
was taught
as a set
of clever tricks
by which
to pile up marks [...]
The effect
of all this
upon me
was
to make me
think mathematics
disgusting.
When I
had finished [...]
I sold
all
my
mathematical books
and
made a vow
that I
would never look
at a
mathematical book
again.
And so,
in my fourth year,
I plunged
with whole-hearted delight
into the
fantastic world
of
philosophy."
[from "My Philosophical
Development",
1959, p. 37 - 38]
"Kant concluded
that Euclidean geometry
describes
not the world as it is
in itself,
but the world
as it appears to us.
The world
does not have to be
as Euclid describes it,
but we
have to see and imagine it
as such.
We look at the world,
so to speak,
through Euclidean spectacles.
Or,
to put it into
Kantian jargon,
what
Euclidean geometry
describes
is
our
'form of intuition'
with regard
to space.
That is why
the theorems
of
Euclidean geometry
look to us
as if
they were
necessarily true,
as if,
like the principles
of logic,
their
truth
was
guaranteed
by
the
nature of reason
itself."
(p. 16)
"This also
threatens
the thought
that had
excited
the eleven-year-old
Bertrand Russell,
the
thought
that
we can know,
a priori
and with
complete certainty
and
exactitude,
the
spatial relations
that exist
in
the
physical world."
[p. 16]
"Whatever
real
physical space is like,
Russell maintained,
it cannot be
like the surface
of an egg.
Unfortunately
for this view,
the space
of relativity theory
is
like
the surface
of an egg,
its curvature
varying
with respect to
varying degrees
of
mass gravitational force.
Russell's
earliest published
philosophical theory,
therefore,
is
now regarded
as
one of the few
philosophical theories
capable
of
conclusive
scientific
refutation."
(p. 17)
"'...all reality
is
rational
and
righteous...
the
highest object
of
philosophy
is
to indicate to us
the
general nature
of
an ultimate harmony,
the
full content of which
it has not yet
entered into our hearts
to
conceive'.
'All
true
philosophy',
[J.M.E.]
McTaggart
declares,
'must be
mystical,
not indeed
in its methods,
but
in
its
final
conclusions.'"
(p. 19)
+++
Selected Quotations
from
"The Cosmic Code:
Quantum Physics
as the
Language of Nature",
by Heinz R. Pagels,
Bantum publishers,
1982
"Grasping
quantum reality
requires
changing
from
a reality
that can be seen
and felt
to
an
instrumentally detected
reality
that
can be perceived
only
intellectually."
(p. xiii)
"Quantum
reality
is
rational
but not
visualizable."
(p. xiii)
"... the space
of our universe
is
non-Euclidean;
it is not
flat."
(p. 31)
was
a bohemian
and
a rebel
who
identified
himself
with
the highest
and
best
in
human thought."
(p. 22)
+++
"As far as
the
laws of mathematics
refer to
reality,
they
are
not certain;
as far as
they are
certain,
they
do not
refer
to
reality."
( -- Albert Einstein,
found online at:
Toward an Explanation
of the Unexplainable",
the New Edition,
by Bob Toben
and Fred Alan Wolf,
Bantum books, 1982,
p. 129 - 130.
"How
does
the universe
do
it?
How
does it
produce
anything
at
all?
No one
really
knows
the answer.
However,
we do know
that the
self-reference
is an important part
of
the process.
The way that it works
in quantum physics,
which underlies
all
of the physical world,
is that
the
quantum wave
flows
between
two events
just like
a river
leaving
a source
and
flowing
to
a sink.
But
then
it
'turns around'
in
space-time
and
flows
back
from the sink
to the source.
The resulting
reinforcement
between
the quantum wave
and its
space-time reflected
image
produces
the
experiences
we call
reality.
In the language
of quantum physics,
we say
that the wave
is
multiplied
by its
'complex-conjugated
self'
to produce
the
probabilities
of the
real world.
This
double-flow
process
occurs
in every
physical
phenomenon.
It is
in this manner
that we
have
self-organization;
self
exists
through
the wave
interacting
with its
space-time mirrored image
in
the same way
that
you
interact
with
your own
mirror image.
Did you
ever notice
that
in order to
notice
yourself
in
a mirror
you
have to
forget
yourself?
And
to forget yourself
you
have to
take note
of
yourself?
By
self-reflection
we
are able
to change
ourselves.
By
observing
ourselves
in
others
we
are able
to
change
each other.
All there is,
is
the one-verse,
the
universe
looking
at
itself
in
itself."
+++
Selections
from
"Russell:
Mathematics:
Dreams
and
Nightmares",
by
Ray Monk,
Phoenix Press,
1997
[on Bertrand Russell,
1872-1970]
"I had been told
that Euclid
proved things,
and
was much disappointed
that he started
with
axioms.
At first
I refused
to accept them
unless my brother
could offer me
some
reason
for doing so,
but he said,
'If you don't accept them
we cannot go on',
and
as I wished to go on,
I reluctantly
accepted them
pro tem.
The doubt
as to the
premises
of
mathematics
which I felt
at that moment
remained with me,
and determined
the course
of my
subsequent work."
[from "The Autobiography
of
Bertrand Russell
1972 - 1914",
1967, p. 36]
(p. 3 - 4)
"For both
Hobbes and Russell,
the
almost erotic delight
they took
in learning
Euclid's geometry
('as dazzling
as first love')
was
aroused
by
the feeling
of
finally
coming to know
something
with
complete certainty.
The beauty
of Euclid's system
is
that
it is axiomatic.
Everything
that it teaches
about circles,
triangles,
squares,
etc.
is not just stated
but
proved;
complicated
and
surprising things
about the relations
between
angles and lengths
and so on
are shown
to be
merely logical consequences
of a few,
simple axioms.
It's
as if a whole,
vast body
of knowledge
has been spun
out of
virtually nothing,
but,
more than that,
this body
of knowledge
is not tentative
or
provisional,
it
does not depend
upon
the contingencies
of
the world,
but rather
can be established
once
and for all.
If one accepts
the axioms,
one
has to accept
the rest;
no further doubt
is possible.
To someone who
wishes,
as Russell
passionately wished,
to find reasons
for their beliefs,
the exhilarating possibility
this opens up
is that
some beliefs
at least
can be provided
with
absolutely
cast-iron foundations."
(p. 4-5)
"... the experience
of discovering
a realm of truth
free from
the vicissitudes
of human existence
was ecstatic
to Russell,
and
it inspired in him
a desire
to found all knowledge
upon
the kind of
rock-solid foundations
provided
by Euclid's
system of geometry."
(p. 6)
"I found
great delight
in mathematics --
much more delight,
in fact,
than in any other study.
I liked to think
of the applications
of mathematics
to the physical world,
and I hoped that
in time
there would be
a mathematics
of human behavior
as precise
as the mathematics
of machines.
I hoped this
because I liked
demonstrations,
and at most times
this motive
outweighed the desire,
which I also felt,
to believe in
free will."
[from
"Portraits from Memory",
1956. p. 20]
(p. 6)
"Mathematics
is,
I believe,
the chief source
of the belief
in
eternal
and
exact
truth,
as well as
in
a super-sensible
intelligible
world.
Geometry
deals with
exact circles,
but
no sensible object
is exactly circular;
however carefully
we may use our compasses,
there will be
some
imperfections
and
irregularities.
This
suggests the view
that all exact reasoning
applies to
ideal
as opposed to sensible
objects;
it is natural
to go further,
and to argue
that
thought
is nobler
than sense,
and the
objects of thought
more real
than those
of
sense-perception."
[from "History
of Western Philosophy",
1991 p. 55 -56]
(p. 7)
"For a time
I found satisfaction
in a doctrine
derived, with modification,
from Plato.
According to
Plato's
doctrine,
which I accepted
only in a watered-down form,
there is
an unchanging
timeless
world
of ideas
of which
the world presented to our senses
is
an imperfect copy.
Mathematics,
according to this doctrine,
deals with the
world
of ideas
and has
in consequence
an
exactness
and
perfection
which is absent
from the everyday world.
This kind
of mathematical
mysticism,
which Plato
derived
from Pythagoras,
appealed to me."
[from
"Portraits from Memory",
1956, p. 22]
(p. 8)
"I disliked
the real world
and
sought refuge
in a timeless world,
without change
or decay
or
the
will-o'-the-wisp
of
progress."
[from "My
Philosophical Development",
1959, p. 210]
(p. 8)
"As Russell presents him,
Pythagoras
was both
a religious prophet
and
a pure mathematician:
'In both respects
he was
immeasurably influential,
and the two
were not so separate
as they seem
to a modern mind.'
Pythagoras's
religion,
according to Russell,
was
a reformed version
of Orphism,
which was, in turn,
a reformed version
of the worship
of Dionysus.
Central to all three
was the exaltation
of ecstasy,
but
in the cult of Pythagoras,
this ecstasy
is to be achieved
not by
drinking wine
or indulging
in sexual activity,
but rather
by the exercise
of the intellect.
The highest life,
on this view,
is that devoted to
'passionate sympathetic
contemplation',
which Russell
(following F. M. Cornford)
says
was
the original meaning
of
the word
'theory'."
(p. 9)
"For Pythagoras,
the passionate contemplation
was intellectual,
and issued
in mathematical knowledge.
In this way,
through
Pythagoreanism,
'theory'
gradually acquired
its
modern
meaning;
but for all who were inspired
by Pythagoras
it retained an element
of
ecstatic revelation.
To those who have reluctantly learnt
a little mathematics in school
this may seem strange;
but
to those
who have experienced
the intoxicating delight
of
sudden understanding
that mathematics gives,
from time to time,
to those who love it,
the Pythagoras view
will seem
completely natural,
even if untrue.
It might seem
that
the empirical philosopher
is
the slave
of his material,
but
the
pure mathematician,
like the musician,
is
a free creator
of his world
of
ordered beauty."
[from "History
of Western Philosophy",
1991 p. 52 -53]
(p. 9)
"Pythagoras
('as everyone knows',
according to Russell)
believed that
'all things
are numbers'.
Everything
in the world,
whether it be
the building of pyramids,
the things of nature,
the harmonies of music,
or whatever,
expresses a series
of numerical relations,
and can be
described
by those relations.
The tragedy
for the Pythagoreans
(and,
as we shall see,
a similar tragedy
was played out
in Russell's own
philosophical development)
was
that their greatest,
most well-known discovery
was the one
that undermined
this point of view:
namely
the famous
Pythagorean Theorem
concerning
right-angled triangles,
which led immediately
to the discovery
of incommensurables.
According to
the Pythagorean Theorem,
the length of the hypotenuse
of a right-angled triangle
in which the other two sides
are
one unit long
will be equal to
the square root of 2.
The trouble
is that the square root of 2
is
incommensurable;
that is,
it cannot be expressed
as the relation
between two numbers,
or,
to put it another way,
it is
'irrational'.
It follows
that there is
at least
one thing
in the world
which is
not
the expression
of a numerical relation.
Others, of course,
followed;
the best known of which
is pi,
the relation
between
the circumference
and
the diameter
of
a circle.
To the ancient Greeks,
this suggested
that geometry,
not arithmetic,
was the surest source
of exact knowledge,
which is one reason
for the pre-eminence
given to Euclid's Elements.
The Pythagorean Dream
of showing everything
to be reducible
to arithmetic
was, it seemed,
over."
(p. 10)
"The problem
of incommensurables,
however,
continued
to haunt those
who looked
to mathematics
for
perfect rigor
and
exactitude.
Quantities like
the square root of 2
and pi
were included
in the domain
of 'real' numbers,
though
no satisfactory definition of them --
or, therefore, of the notion
of a 'real number' in general --
was yet available.
And, indeed,
the new techniques
brought with them
further problems
which
opened up the science
of mathematics
to the charge
of
being riddled
with
inconsistencies.
Three fundamental notion
in mathematics --
infinity,
the
infinitesimal,
and
continuity --
seemed
inherently
paradoxical.
The paradoxes
of infinity
and continuity
had been known
since ancient times,
but they acquired
a new importance
as
the power of mathematics
to represent
continuous
and
infinite sequences
grew."
(p. 10 - 11)
"... the notion
of
an infinitesimal ...
[...]
What are
these 'evanescent Increments'
used
in the calculus?
Berkeley sneered.
'They are neither
finite
Quantities,
nor Quantities
infinitely small
nor yet
not
nothing.
May we not call them
the Ghosts
of departed Quantities?'
Anyone
who could
accept
such a notion,
Berkeley suggested,
ought to have
no qualms
in
accepting
the mysteries
of Christianity,
for
do not mathematicians
have
their own mysteries,
'and
what is more,
their repugnancies
and
contradictions?'
(p. 13)
"Those who taught me
the
infinitesimal Calculus
did not know
the valid proofs
of
its fundamental theorems
and tried to
persuade me
to accept
the official sophistries
as an
act of faith.
I realized that
the calculus works
in practice,
but I was at a loss
to
understand
why
it should do so.
However
I found
so much pleasure
in the acquisition
of technical skill
that
at most times
I forgot my doubts."
[from "My Philosophical
Development",
1959, p. 35 - 36]
(p. 14)
"... The mathematical teaching
at Cambridge
when I was an undergraduate
was definitely bad."
[from "My Philosophical
Development",
1959, p. 37]
(p. 14)
"The 'proofs'
that were offered
of mathematical theorems
were
an insult
to
the logical intelligence.
Indeed,
the whole subject
of mathematics
was taught
as a set
of clever tricks
by which
to pile up marks [...]
The effect
of all this
upon me
was
to make me
think mathematics
disgusting.
When I
had finished [...]
I sold
all
my
mathematical books
and
made a vow
that I
would never look
at a
mathematical book
again.
And so,
in my fourth year,
I plunged
with whole-hearted delight
into the
fantastic world
of
philosophy."
[from "My Philosophical
Development",
1959, p. 37 - 38]
"Kant concluded
that Euclidean geometry
describes
not the world as it is
in itself,
but the world
as it appears to us.
The world
does not have to be
as Euclid describes it,
but we
have to see and imagine it
as such.
We look at the world,
so to speak,
through Euclidean spectacles.
Or,
to put it into
Kantian jargon,
what
Euclidean geometry
describes
is
our
'form of intuition'
with regard
to space.
That is why
the theorems
of
Euclidean geometry
look to us
as if
they were
necessarily true,
as if,
like the principles
of logic,
their
truth
was
guaranteed
by
the
nature of reason
itself."
(p. 16)
"This also
threatens
the thought
that had
excited
the eleven-year-old
Bertrand Russell,
the
thought
that
we can know,
a priori
and with
complete certainty
and
exactitude,
the
spatial relations
that exist
in
the
physical world."
[p. 16]
"Whatever
real
physical space is like,
Russell maintained,
it cannot be
like the surface
of an egg.
Unfortunately
for this view,
the space
of relativity theory
is
like
the surface
of an egg,
its curvature
varying
with respect to
varying degrees
of
mass gravitational force.
Russell's
earliest published
philosophical theory,
therefore,
is
now regarded
as
one of the few
philosophical theories
capable
of
conclusive
scientific
refutation."
(p. 17)
"'...all reality
is
rational
and
righteous...
the
highest object
of
philosophy
is
to indicate to us
the
general nature
of
an ultimate harmony,
the
full content of which
it has not yet
entered into our hearts
to
conceive'.
'All
true
philosophy',
[J.M.E.]
McTaggart
declares,
'must be
mystical,
not indeed
in its methods,
but
in
its
final
conclusions.'"
(p. 19)
+++
Selected Quotations
from
"The Cosmic Code:
Quantum Physics
as the
Language of Nature",
by Heinz R. Pagels,
Bantum publishers,
1982
"Grasping
quantum reality
requires
changing
from
a reality
that can be seen
and felt
to
an
instrumentally detected
reality
that
can be perceived
only
intellectually."
(p. xiii)
"Quantum
reality
is
rational
but not
visualizable."
(p. xiii)
"... the space
of our universe
is
non-Euclidean;
it is not
flat."
(p. 31)
"The young
Einsteinwas
a bohemian
and
a rebel
who
identified
himself
with
the highest
and
best
in
human thought."
(p. 22)
+++
"As far as
the
laws of mathematics
refer to
reality,
they
are
not certain;
as far as
they are
certain,
they
do not
refer
to
reality."
( -- Albert Einstein,
found online at:
+++
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