Selected Quotations from
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)
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)
No comments:
Post a Comment