30. IS ANYTHING "RANDOM"? -- "The Cosmic Code: Quantum Physics as the Language of Nature", by Heinz R. Pagels (excerpts)

Selected Quotations from "The Cosmic Code:
Quantum Physics
as the
Language of Nature",
by Heinz R. Pagels,
Bantum  publishers,
1982
 
"It is hard to appreciate
the atomic hypothesis
because atoms are so small
and there are so many of them.
 
For example,
in your last breath
it is almost certain
that you have inhaled
at least one atom
from the dying breath
of Julius Caesar
as he lamented,
'Et tu, Brute'.
 
That is scientific trivia.
 
But the fact is
that a human breath
contains about
one million billion billion
(10 to the 24th power)
atoms.
 
Even if they mix
with the entire atmosphere
of the earth,
the chances are high
that you will inhale
one of them."
(p. 13)
 
"A few years ago
I was walking through
the old city of Jerusalem
with an acquaintance,
an archeologist.
 
Jerusalem
is simply
home
to many people,
but for most visitors
it is a powerful,
holy place.
 
Rationality
counts for little here;
the symbols of faith
are the real currency
of this city.
 
In medieval times,
religious people perceived Jerusalem
as the center of the universe,
the navel of the world
where heaven and earth joined.
 
Here at the center of the world
God spoke to His prophets
and the people of the Book.
 
Jews come to worship
at the wall of their ancient temple
near the Holy of Holies.
Christians follow the steps of their Lord
in His final Passion,
and Muslims worship at the third-holiest place
of Islam, the Dome of the Rock,
upon which the Prophet Mohammed
received the Koran.
 
God may be omnipresent,
but His voice is in Jerusalem.
 
The archeologist remarked
that there was an ancient center
of the old city
marked by a Roman crossroads,
which divided the city
and the earth
into four quadrants --
the fulcrum of medieval geography.
 
The roads has long ago disappeared,
but at each corner of the crossroads
had stood a Roman column
which survives to the present day.
 
As we made our way across the city
to the very center of the ancient universe,
my friend explained
that the Roman columns stood
in the interior of a modern building.
 
Entering the building,
I immediately saw the four columns.
 
And there,
between and around the columns,
stood several pinball machines.
 
Here, at
the very center of the universe,
was the only pinball parlor
in the old city of Jerusalem.
 
I was amazed.
 
According to the Bible
the Lord speaks only to those
who are ready
for His message.
 
The prophecy was not lost --
I had seen a revelation
of the God who plays dice.
 
Major technologies
often enter our civilization
in an innocent
and undemanding way.
 
Some devices,
which eventually become
important material forces,
first appear as toys.
 
Gunpowder was first used
for fireworks entertainment.
 
The use of steam power
in Hellenic Alexandria around A.D. 100
is another good example.
 
The Greeks saw in Hero's steam wheel
only a toy, a novelty,
but centuries later, steam engines
would be used as the motive power
for the first industrial civilizations.
 
The Alexandrian Greeks
were not ready
for that idea.
 
I think pinball machines
are modern examples
of such entertainment devices --
they will eventually take us over.
 
Determinists
think of the universe
as a huge clockwork;
I think it is a pinball machine.
 
Playing pinball
requires total concentration,
the right combination
of skill and chance,
a mastery of indeterminacy
as the ball moves
across the playboard
and interacts
with bumpers and cushions.
 
The machine keeps score
and you can cheat a little
by shaking the machine,
but not too much
lest it tilt.
 
It imitates life's randomness,
rewards skill,
and creates an ersatz reality
which integrates
into the human nervous system
in a remarkable way.
 
Someday such machines
will be combined
with art forms
such as films
and a completely artificial reality
will be created.
 
We are already  a part
of the pinball universe.
 
It is no accident
that pinball machines --
the symbol
of the indeterminate universe --
stand at the center of the world.
 
The quantum theory
implies that to know
the world
we must observe it,
and in the act of observation,
uncontrolled and random processes
are initiated in the world.
 
Also, Bohr's principle of complementarity
implies that knowing everything
at one time about the world --
a requirement of determinism --
is impossible because the conditions
for knowing one thing
necessarily exclude knowledge of others.
 
The quantum theory means that me must
renounce the determinist's dream
that everything can be known.
 
To more deeply appreciate
the indeterminate universe
revealed by the quantum theory,
let us plunge into the world of chaos --
a world first explored by mathematicians.
 
The human mind abhors chaos,
finding order even if there is none.
 
The ancients saw
in the random patterns of the stars
constellations of the figures of myth,
and in the shapes of clouds
animal or human shapes.
 
Tea leaves, in some cultures, foretell the future.
 
The haruspex
finds in the entrails of animals
the destinies of peoples,
and priests consult their gods
by casting bones.
 
The fact of natural randomness
combined with the human disposition
to see patterns in everything
prepares the ground
for heirophany --
an appearance of the sacred.
 
Some people hear
the voice of God
in the rushing wind,
a burning bush,
or a flowing stream."
(p. 82-84)
  
"... we cannot establish whether
a sequence of natural events
is truly random
until we have a mathematical
definition
of randomness.
 
Once we have such a definition,
then we have the additional empirical problem
of determining whether real events correspond
to such a definition.
 
For example,
we can mathematically define a triangle
in Euclid's geometry.
 
But it is a separate, empirical question
whether physical triangular configurations
actually correspond
to such a definition.
 
Here we run into the first problem:
Mathematicians have never succeeded
in giving a precise definition of randomness
or
the associated task of defining probability.
 
If you go to a math library
you will find lots of books on probability.
 
How is it possible to have so much written
about a topic that has not been precisely defined?
 
What stands in the way
of a precise definition?
 
In part the problem of precisely defining
randomness,
or more specifically
a random sequence of integers,
is that if you succeed in giving an exact definition
the sequence may no longer be random.
 
Being able to say precisely
what randomness is
denies the very nature of randomness,
which is utter chaos --
how can you be precise about chaos?"
(p. 84-85)
 
"For any finite sequence
of integers,
I can always find a rule
that tells me
exactly how
to construct the sequence.
 
But the rule
may be very complicated."
(p. 86)
 
"A precise mathematical definition
of randomness for finite sequences
simply does not exist.
 
So there you have it:
Mathematicians don't know
what randomness is!"
(p. 87)
 
"... even if a sequence of numbers
passes all tests
we cannot be certain
that it is random --
someone may invent a new test
and it might fail."
(p. 87)
 
"... we do not have an intrinsic
definition of randomness.
Perhaps it is impossible to give one --
randomness
may be
absolutely undefinable.
 
So how do the mathematicians
write all those books without
defining randomness or probability?
 
They get away with it
by becoming operationalists --
they give an operational definition
of randomness and probability
as that which obeys the theorems
they derive about it.
 
The mathematical theory
of probability begins
after
probabilities have been assigned
to elementary events.
 
How probability is assigned
to the elementary events is not discussed,
because that requires an intrinsic definition
of the randomness of events --
which is not known.
 
This operational approach
if applied to geometry
would be like proving all sorts of theorems
about triangles
without actually precisely defining
what is a triangle.
 
An operational definition of "triangle"
is simply the logical object
that obeys all these theorems.
 
One asks only for consistency,
not for definition.
 
You can really go very far
with this approach,
and that is what is in
all those probability books."
(p. 87)
 
"... what we may think
is a random number
really isn't -- it is related to other numbers
which are specified by a simple rule.
 
How can you be sure
a number is truly random?
 
You can't --
the most you can do is establish
if the number is not random
if it fails one test for randomness."
(p. 88)
 
"...two random sequences
can be correlated --
each is individually chaotic
but if properly compared
by using some rule [...]
then a nonrandom pattern appears."
(p. 89)
 
"... the information
is in the cross-correlation."
(p. 89)
 
"A teacher of mathematics
in postrevolutionary Iran
began his lecture on probability theory
by holding up a die
which he was going to use
in a demonstration.
 
Before he could begin,
an Islamic fundamentalist student
cried out,
'A satanic artifact!' --
referring,
of course,
to the die.

The teacher lost his job
and almost his life.
The notion of probability
is antithetical
to those interpretations of Islam
which maintain
that God knows everything --
there is no place for chance
for many religious fundamentalists.
 
Had the teacher
been permitted to give his lecture,
we can imagine
what he would have told the students.
 
He may have emphasized
the application of probability theory
to the real world
and begun
with the operational definition
of probability.
 
This kind of definition
is required
because we do not have
an intrinsic definition
of randomness [...].

We cannot determine whether
or not
an actual process is truly random."
(p. 90)
 
"Real randomness
is unbeatable.

This practical definition
of randomness
is good for the real world.
 
Gambling houses
and
insurance companies
all use it.

And because randomness
is unbeatable
and they base their business
on that fact,
they always win."
(p. 91)
 
"The quantum
probability distributions,
the invisible hands
at the atomic level,
are actually responsible
for the chemical forces
that bind atoms together."
(p. 93)
 
"Individual chaos
implies
collective determinism."
(p. 94)
 
"The die
when it is thrown
may 'think' it has freedom,
but whatever it does
it is part of a probability distribution;
it is being influenced
by the invisible hand.
 
We cannot act
without being part of a distribution --
it is like being in an invisible prison
held by invisible hands.
 
Even the very act of trying to escape
is again
part of a new distribution,
a new prison.
 
Perhaps this is why
real creativity is so difficult --
thousands of invisible hands
hold us
to our conventional acts
and ideas.
 
There seem to be
two kinds of people
in this world,
who
in their extreme forms
are
those who see
everything in the world
as caused
and meaningful
and those
who believe
that God plays dice
and that truly random
occurrences happen."
(p. 95)

29. "Mathematics: Dreams and Nightmares", Bertrand Russell, Albert Einstein, Heinz Pagels, Fred Allen Wolf, Bob Toben and Science AT THE EDGE

Selected Excerpts from "Space-Time and Beyond:
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

Einstein
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:

http://www.spaceandmotion.com/mathematical-physics/famous-mathematics-quotes.htm )

 

+++