Showing posts with label Bertrand Russell. Show all posts
Showing posts with label Bertrand Russell. Show all posts

Tuesday, December 6, 2011

92. DO YOU WONDER WHY PEOPLE CAN'T THINK CLEARLY? -- Excerpts from "The Functions of a Teacher", by Bertrand Russell

Excerpts
from

"Unpopular Essays",

by
Bertrand Russell,

Simon and Schuster,
New York,
1950,
pages  112 - 123.


Chapter Eight

The Functions of a Teacher


Teaching,
more even
than most other professions,
has been transformed
during the last hundred years
from a small,
highly skilled profession
concerned
with a minority
of the population,
to
a large and important branch
of
the public service.
 
The profession
has
a great and honorable tradition,
extending
from the dawn of history
until recent times,
but
any teacher in the modern world
who allows himself
to be inspired
by the ideals of his predecessors
is likely to be made
sharply aware
that
it is not his function
to teach what he thinks,
but to instill
such beliefs
and prejudices
as are thought useful
by his employers.

In former days
a teacher was expected
to be
a man
of exceptional knowledge
or wisdom,
to whose words
men
would do well to attend.
 
In antiquity, teachers
were not
an organized profession,
and
no control was exercised
over what they taught.

It is true that they were
often punished afterwards
for their subversive doctrines.
 
Socrates
was put to death
and
Plato
is said to have been
thrown into prison,
but
such incidents
did not interfere
with
the spread of their doctrines.
 
Any man
who
has the genuine impulse
of the teacher
will be more anxious
to survive
in his books
than
in the flesh.
 
A feeling
of
intellectual independence
is essential
to the proper fulfillment
of the teacher's functions,
since it is his business
to instill what he can
of knowledge
and
reasonableness
into
the process
of
forming public opinion.
 
In antiquity
he performed the function
unhampered
except
by
occasional spasmodic
and
ineffective interventions
of tyrants
or mobs.
 
In the middle ages
teaching became
the exclusive prerogative
of the church,
with the result
that
there was little progress
either
intellectual
or social.
 
With the Renaissance,
the general respect
for learning
brought back
a very considerable
measure of freedom
to the teacher.

It is true
that the Inquisition
compelled Galileo
to recant,
and
burned Giordano Bruno
at the stake,
but
each of these men
had done his work
before being
punished.
 
Institutions
such as
universities
largely remained
in the grip of the dogmatists,
with the result
that
most of the best intellectual work
was done
by independent men of learning.
 
In England, especially,
until near the end
of the nineteenth century,
hardly any
men of first-rate eminence
except Newton
were connected with universities.
 
But the social system was such
that this interfered little
with their activities
or their usefulness.
 
In our
more highly organized world
we face a new problem.
 
Something
called
education
is given to everybody,
usually by the state,
but
sometimes by the churches.

The teacher
has thus become,
in the vast majority of cases,
a civil servant
obliged to carry out the behests
of men
who have not
his learning,
who have
no experience
of dealing with the young,
and
whose only attitude
towards education
is that of
the propagandist.

It is not very easy
to see
how,
in these circumstances,
teachers
can perform the functions
for which
they are specially fitted.
 
State education
is obviously necessary,
but
as obviously
involves certain dangers
against which
there ought to be safeguards.
 
The evils to be feared
were seen
in their full magnitude
in Nazi Germany
and
are still seen
in Russia [1950].
 
Where these evils prevail
no man can teach
unless he subscribes
to a dogmatic creed
which
few people of free intelligence
are
likely to accept
sincerely.
 
Not only must he
subscribe to a creed,
but
he
must condone abominations
and
carefully abstain
from speaking his mind
on current events.

So long as he is teaching
only
the alphabet
and
the multiplication table,
as to which
no controversies arise,
official dogmas
do not necessarily
warp his instruction;
but even while he
is teaching these elements
he is expected,
in totalitarian countries,
not to employ the methods
which he thinks
most likely
to achieve the scholastic result,
but
to instill fear,
subservience,
and
blind obedience
by demanding
unquestioned submission
to his authority.
 
And as soon as he
passes beyond
the bare elements,
he is obliged to take
the official view
on
all controversial questions.

The result is
that
the young
in Nazi Germany became,
and
in Russia become,
fanatical bigots,
ignorant of the world outside
their own country,
totally
unaccustomed to free discussion,
and
not aware
that their opinions
can be questioned
without wickedness.

This state of affairs,
bad as it is,
would be less disastrous
than it is
if the dogmas instilled
were,
as in medieval Catholicism,
universal
and
international;
but
the whole conception
of
an international culture
is denied
by the modern dogmatists,
who preached
one creed in Germany,
another in Italy,
another in Russia,
and yet another
in Japan.
 
In each of these countries
fanatical nationalism
was what was
most emphasized
in
the teaching of the young,
with the result
that
the men of one country
have no common ground
with
the men of another,
and that
no conception
of a common civilization
stands in the way
of warlike ferocity.
 
The decay of cultural internationalism
has proceeded
at a continually increasing pace
ever since
the First World War.
 
When I was in Leningrad
in 1920,
I met
the Professor
of Pure Mathematics,
who was familiar
with
London,
Paris,
and
other capitals,
having been
a member
of various international congresses.
 
Nowadays [1950]
the learned men
of Russia
are very seldom permitted
such excursions,
for fear
of their drawing comparisons
unfavorable to their own country.
 
In other countries
nationalism in learning
is less extreme,
but everywhere
it is far more powerful
than it was.
 
There is a tendency
in England
(and I believe,
in the United States)
to dispense with
Frenchmen and Germans
in
the teaching
of French and German.
 
The practice
of
considering a man's nationality
rather than his competence
in appointing him to a post
is damaging to education
and
an offense against the ideal
of international culture,
which was a heritage
from the Roman Empire
and
the Catholic Church,
but
is now being submerged [1950]
under a new barbarian invasion,
proceeding
from below
rather than
from without.
 
In democratic countries
these evils have not yet reached
anything like
the same proportions,
but
it must be admitted
that there is grave danger
of similar developments
in education,
and
that this danger
can only be averted
if those who believe
in liberty of thought
are
on the alert
to protect teachers
from intellectual bondage.

Perhaps the first requisite
is a clear conception of the services
which teachers can be expected to perform
for the community.
 
I agree
with the governments of the world
that the imparting
of definite
uncontroversial information
is
one of the least
of the teacher's functions.
 
It is, of course,
the basis
upon which the others
are built,
and
in a technical civilization
such as ours
it has
undoubtedly
a considerable utility.

There must exist
in a modern community
a sufficient number of men
who possess the technical skill
required
to preserve
the mechanical apparatus
upon which
our physical comforts depend.
 
It is, moreover,
inconvenient
if any large percentage
of the population
is
unable to read and write.
 
For these reasons
we are
all in favor
of
universal compulsory education.
 
But governments
have perceived
that it is easy,
in the course of giving instruction,
to instill beliefs on controversial matters
and
to produce habits of mind
which may be convenient
or
inconvenient
to those in authority.
 
The defense
of the state
in all civilized countries
is quite as much
in the hands of teachers
as
in those of
the armed forces.
 
Except
in totalitarian countries,
the defense of the state
is desirable,
and
the mere fact
that education
is used for this purpose
is not
in itself
a ground of criticism.
 
Criticism
will only arise
if
the state
is defended by
obscurantism
and
appeals
to
irrational passion.
 
Such methods
are quite unnecessary
in the case
of
any state worth defending.
 
Nevertheless,
there is
a natural tendency
towards
their adoption
by those
who have
no first-hand knowledge
of education.
 
There is
a widespread belief
that
the nations are made strong
by
uniformity of opinion
and
by the suppression of liberty.
 
One hears it said
over and over again
that
democracy weakens a country in war,
in spite of the fact [in 1950]
that in every important war
since the year 1700
the victory
has gone to
the more democratic side.
 
Nations have been
brought to ruin
much more often
by insistence upon
a narrow-minded
doctrinal uniformity
than
by
free discussion
and
the
toleration
of
divergent opinions.
 
Dogmatists the world over
believe that
although the truth
is known to
them,
others
will be led
into false beliefs
provided they are allowed
to hear the arguments
on
both sides.
 
This is a view
which leads
to one or another
of two misfortunes:
either
one set of dogmatists
conquers the world
and
prohibits all new ideas,
or,
what is worse,
rival dogmatists
conquer different regions
and
preach the gospel of hate
against each other,
the
former
of
these evils
existing
in the middle ages,
the
latter
during the wars of religion,
and
again
in the present day [1950].
 
The first
makes civilization
static,
the second
tends
to destroy it completely.
 
Against both,
the teacher
should be
the main safeguard.
 
It is obvious
that organized party spirit
is
one of the greatest dangers
of our time [1950].

In the form
of
nationalism
it leads to
wars between nations,
and
in other forms
it leads to
civil war.
 
It should be
the business of teachers
to stand outside
the strife of parties
and
endeavor
to instill into the young
the
habit of impartial inquiry,
leading them
to judge issues
on their merits
and
to be on their guard
against accepting
ex parte
[partisan;
for one side only]
statements
at their face value.
 
The teacher
should not be expected
to flatter the prejudices
either
of the mob
or
of officials.
 
His professional virtue
should consist
in
a readiness
to do justice to all sides,
and
in an endeavor
to rise above controversy
into a region
of
dispassionate
scientific investigation.
 
If there are people
to whom
the results of his investigation
are inconvenient,
he should be
protected against their resentment,
unless it can be shown that
he has lent himself
to
dishonest propaganda
by the dissemination
of
demonstrable untruths.

The function of the teacher,
however,
is
not merely
to mitigate the heat
of current controversies.
 
He has
more positive tasks
to perform,
and
he cannot be
a great teacher
unless he is
inspired by
a wish to perform
these tasks.

Teachers are
more than any other
class
the guardians
of
civilization.
 
They should be
intimately aware
of what civilization is,
and
desirous
of imparting
a civilized attitude
to their pupils.
 
We are thus
brought
to the question:
what constitutes
a civilized community?
 
This question
would
very commonly
be answered
by pointing
to merely
material tests.
 
A country is
civilized
if it has
much machinery,
many motor cars,
many bathrooms,
and
a great deal
of rapid locomotion.
 
To these things,
in my opinion,
most modern men
attach
much too much
importance.
 
Civilization,
in the more important
sense,
is
a thing of the mind,
not
of material adjuncts
to
the physical side
of living.
 
It is a matter
partly of knowledge,
partly
of emotion.
 
So far as
knowledge
is concerned,
a man should be aware
of
the minuteness of himself
and
his immediate environment
in relation
to the world
in time
and space.
 
He should see
his own country
not only as
home,
but
as one
among
the countries of the world,
all
with an equal right
to live
and think
and feel.

He should
see his own age
in relation
to the past
and
the future,
and be aware
that its own controversies
will seem
as strange to future ages
as those of the past
seem to us now [1950].
 
Taking
an even wider view,
he should be
conscious
of
the vastness
of
geological epochs
and
astronomical abysses;
but
he should be aware of all this,
not as a weight
to crush the individual human spirit,
but
as a vast panorama
which enlarges the mind
that contemplates it.
 
On the side of the emotions,
a very similar
enlargement from the purely personal
is needed
if a man is
to be truly civilized.
 
Men pass from birth to death,
sometimes happy,
sometimes unhappy;
sometimes generous,
sometimes grasping and petty;
sometimes heroic,
sometimes cowardly and servile.
 
To the man who views
the procession as a whole,
certain things stand out
as
worthy of admiration.
 
Some men have been inspired
by love of mankind;
some
by supreme intellect have
helped us to understand
the world in which we live;
and some
by exceptional sensitiveness
have created beauty.

These men have produced
something of positive good
to outweigh
the long record
of
cruelty,
oppression,
and superstition.
 
These men have done
what lay in their power
to make human life
a better thing
than
the brief turbulence
of
savages.

The civilized man,
where he cannot admire,
will aim rather
to discover
and
remove
the impersonal causes of evil
than to hate
the men
who are in its grip.
 
All this
should be
in the mind and heart
of the teacher,
and
if it is in his mind and heart
he will convey it
in his teaching to the young
who are in his care.
 
No man can be
a good teacher
unless he has
feelings of warm affection
towards his pupils
and
a genuine
desire to impart to them
what he himself believes
to be of value.

This is
not the attitude
of the propagandist.

To the propagandist
his
pupils
are
potential soldiers
in
an army.
 
They
are to serve purposes
that lie outside
their own lives,
not
in the sense in which
every generous purpose transcends self,
but
in the sense
of ministering to unjust privilege
or
to despotic power.

The propagandist
does not desire
that
his pupils should survey
the world
and
freely choose a purpose
which
to them
appears of value.
 
He desires,
like a topiarian artist,
that their growth
shall be trained
and twisted
to suit the gardener's purpose.
 
And
in
thwarting their natural growth
he is apt to destroy in them
all generous vigor,
replacing it
by
envy,
destructiveness,
and cruelty.
 
There is no need
for men to be cruel;
on the contrary,
I am persuaded
that
most cruelty results
from
thwarting
in early years,
above all
from
thwarting what is good.
 
Repressive
and
persecuting passions
are very common,
as the present [1950]
state of the world
only too amply proves.
 
But
they are
not an inevitable part
of
human nature.
 
On the contrary,
they are,
I believe
always the outcome
of
some kind of unhappiness.
 
It should be
one of the functions
of
the teacher
to open vistas
before his pupils
showing them
the possibility of activities
that will be
as
delightful
as they are
useful,
thereby letting loose
their kind impulses
and
preventing
the growth of a desire
to rob others of joys
that they
will have missed.
 
Many people
decry
happiness as an end,
both
for themselves
and
for others,
but
one may suspect them
of sour grapes.
 
It is one thing
to forgo personal happiness
for a public end,
but
it is quite another
to treat
the general happiness
as a thing
of no account.
 
Yet this is often
done in the name
of some supposed heroism.
 
In those who take
this attitude
there is generally
some vein of cruelty
based probably
upon an unconscious envy,
and
the source of the envy
will usually be
found
in childhood
or youth.

It should be
the aim of the educator
to train adults
free from
these psychological misfortunes,
and
not anxious
to rob others of happiness
because they themselves
have
not been robbed
of it.
 
As it stands
today [1950],
many teachers
are unable to do
the best
of which
they are capable.
 
For this
there are a number of reasons,
some
more or less accidental,
others
very deep-seated.
 
To begin with the former,
most teachers are overworked
and
are compelled to prepare
their pupils
for examinations
rather than
to give them
a liberalizing mental training.
 
The people
who are
not accustomed to teaching --
and this
includes
practically all educational authorities --
have no idea
of the expense
of spirit
that it involves.
 
Clergymen
are
not expected to preach sermons
for several hours every day,
but the analogous effort
is demanded
of teachers.
 
The result is
that
many of them
become harassed and nervous,
out of touch
with recent work
in
the subjects that they teach,
and
unable
to inspire their students
with a sense
of
the intellectual delights
to be obtained
from
new understanding
and
new knowledge.

This, however,
is
by no means
the gravest matter.
 
In most countries
certain opinions
are
recognized as correct,
and others
as dangerous.
 
Teachers
whose opinions
are not correct
are expected to keep silent
about them.
 
If they mention their opinions
it is propaganda,
while
the mentioning of correct opinions
is considered to be
merely
sound instruction.
 
The result is
that
the inquiring young
too often
have to
go outside the classroom
to discover
what is being thought
by
the most vigorous minds
of their own time.
 
There is
in America
a subject called Civics,
in which,
perhaps more than in any other,
the teaching
is expected to be misleading.
 
The young are taught
a sort of copy-book account
of how public affairs
are supposed to be conducted,
and are
carefully shielded from all knowledge
as to how
in fact they are
conducted.
 
When they grow up
and discover the truth,
the result is
too often
a complete cynicism
in which
all public ideals are lost;
whereas
if they had been taught
the truth
carefully
and with proper comment
at an earlier age
they might have become men
able to combat evils
in which,
as it is,
they acquiesce with a shrug.
 
The idea
that falsehood
is
edifying
is one of the besetting sins
of
those who draw up educational schemes.
 
I should not
myself
consider
that
a man could be
a good teacher
unless he had made a firm resolve
never
in the course of his teaching
to conceal truth
because it is what is called
"unedifying."
 
The kind of
virtue
that can be produced
by
guarded ignorance
is frail
and
fails at the first touch
of
reality.
 
There are,
in this world,
many men
who deserve admiration,
and
it is good
that the young should be taught
to see the ways
in which
these men are admirable.
 
But it is not good
to teach them to admire
rogues
by concealing their roguery.
 
It is thought
that
the knowledge of things as they are
will lead to cynicism,
and
so it may do
if the knowledge comes suddenly
with a shock of surprise
and horror.
 
But if it comes gradually,
duly intermixed
with a knowledge of what is good,
and
in the course of a scientific study
inspired
by
the wish
to get at the truth,
it will have
no such effect.
 
In any case,
to tell lies to the young,
who have
no means
of checking what they are told,
is morally indefensible.
 
The thing,
above all,
that
a teacher should endeavor to produce
in his pupils,
if democracy is to survive,
is the kind of tolerance
that springs from
an endeavor
to understand
those
who are different from ourselves.
 
It is
perhaps
a natural human impulse
to view with horror and disgust
all manners
and customs
different
from
those to which we are used.
 
Ants and savages
put strangers to death.
 
And those
who have never traveled
either
physically
or
mentally
find it difficult
to tolerate the queer ways
and
outlandish beliefs
of other nations
and other times,
other sects
and
other political parties.
 
This kind of ignorant intolerance
is
the antithesis of a civilized outlook,
and is
one of the gravest dangers
to which
our overcrowded world
is exposed.
 
The educational system
ought to be designed
to correct it,
but
much too little is done
in this direction
at present [1950].

In every country
nationalistic feeling
is encouraged,
and
school children are taught,
what they are
only too ready to believe,
that
the inhabitants of other countries
are morally
and intellectually
inferior
to those
of the country in which
the school children
happen to reside.

Collective hysteria,
the most mad
and cruel
of all human emotions,
is encouraged
instead of being discouraged,
and
the young are encouraged
to believe
what they hear frequently said
rather than
what
there is some rational ground
for believing.
 
In all this
the teachers
are not to blame.
 
They are not free
to teach
as they would wish.
 
It is they who know
most intimately
the needs
of the young.
 
It is they
who
through daily contact
have come to care for them.
 
But
it is not they
who decide
what shall be taught
or
what
the methods of instruction
are to be.
 
There ought to be
a great deal more freedom
than there is
for the scholastic profession.
 
It ought to have more
opportunities
of self-determination,
more independence
from
the interference of bureaucrats
and bigots.
 
No one would consent
in our day [1950]
to subject
the medical men
to
the control
of non-medical authorities
as to
how they should treat their patients,
except of course
where they depart
criminally
from the purpose of medicine,
which is
to cure the patient.
 
The teacher
is a kind of
medical man
whose purpose
is to cure the patient
of childishness,
but
he is not allowed
to decide for himself
on the basis of experience
what methods
are
most suitable
to this end.
 
A few great historic universities,
by the weight of their prestige,
have secured virtual self-determination,
but
the immense majority
of
educational institutions
are
hampered
and
controlled
by men who do not understand
the work
with which they are interfering.
 
The only way
to prevent totalitarianism
in our highly organized world
is
to secure a certain degree of independence
for bodies performing useful public work,
and
among such bodies
teachers deserve a foremost place.
 
The teacher,
like the artist,
the philosopher,
and
the man of letters,
can only perform his work
adequately
if he feels himself to be
an individual
directed by an inner creative impulse,
not
dominated
and
fettered
by an outside authority.

It is very difficult
in this modern world
to find a place
for
the individual.

He can subsist at the top
as a dictator
in a totalitarian state
or
a plutocratic magnate
in a country
of large industrial enterprises,
but
in the realm of the mind
it is becoming
more and more difficult
to preserve
independence of
the great organized forces
that control the livelihoods
of men and women.
 
If the world
is not to lose the benefit
to be derived from its best minds,
it will have to find some method
of allowing them
scope and liberty
in spite of organization.

This involves
a deliberate restraint
on the part
of those who have power,
and
a conscious realization
that
there are men
to whom
free scope must be afforded.
 
Renaissance Popes
could feel in this way
towards Renaissance artists,
but
the powerful men of our day
seem to have more difficulty
in feeling respect
for exceptional genius.
 
The turbulence
of our times
[1950]
is
inimical
to the fine flower of culture.
 
The man in the street
is full of fear,
and
therefore
unwilling to tolerate freedoms
for which he sees
no need.
 
Perhaps
we must wait for quieter times
before the claims
of civilization
can again override the claims
of party spirit.
 
Meanwhile, it is important
that some at least
should continue to realize
the limitations
of what can be done
by organization.
 
Every system
should allow loopholes and exceptions,
for
if it does not
it will
in the end
crush all that is best in man.
 
+++

Wednesday, October 19, 2011

32. "TWENTY-FIVE STARTING POSITIONS FOR AGREEMENT" (Some Conclusions linked to 3 recent Posts)

These Synthetic Results
are
based on some
recently blogged
Scientific Assumptions --
they are
for those
who have read
the following
three
blog entries:

#29. "Mathematics:
     Dreams and Nightmares",

#30. IS ANYTHING
     "RANDOM"?,

and

#31. "To Live
     is to Suffer".

The following
are statements
that
can be considered
TRUE
[BY MOST OF US!]
based on
the
scientifically
accepted
accuracy
of
the information
posted
in these 3
most recent blog entries
(#29, #30, and #31,
listed above).

1. Belief in the Accuracy of Mathematics is clearly a MATTER OF FAITH, based on the PROOF-LESS state of its very foundations, in terms of demonstrable Logic.

2. Accepted "Axioms" underlie all of Mathematics; Skeptics are prevented from entering the lofty realms of abstract Mathematics because of these very MATTERS OF FAITH which must be accepted to facilitate travel therein.

3. Unlike "most" objects in the Observable Universe, certain REAL objects within Space-Time -- objects called the "incommensurables" (such as the ever-abbreviated concept of "pi" in geometry) -- are NOT  capable of expression as a finite number sequence  or even as the expression of a known relationship between finite numbers.

4. "Irrational Numbers" have not been satisfactorily defined by Mathematicians.

5.  "Rational Numbers" too have not been satisfactorily defined by Mathematicians.

6. "Chaos" or "Randomness" has never received an INTRINSIC definition from Mathematicians, only an OPERATIONAL DEFINITION (such as: "randomness is unbeatable", a belief useful for PROFITABLE BUSINESSES, such as the Gambling Industry and the Insurance Industry.

7. Likewise, "Probability" has never received an INTRINSIC definition from Mathematicians, only an OPERATIONAL DEFINITION.

8. Geometry shares the Bastard Status of Mathematics, but goes on to utilize points so small and immaterial that they have been ridiculed as the "Ghosts of Departed Quantities" (by Berkeley).

9. Even at Cambridge and other institutions of Higher Learning, Mathematics has often been taught "badly" and for reasons of "technical wizardry" alone, as if it amounted to nothing more than a series of "clever tricks" based on a sort of "logic" that, under careful scrutiny, sometimes insults the intelligence.

10. Before abandoning Mathematics for a less mythological subject (Philosophy) Bertrand Russell went "on record" with a statement he thought was as true as the light shining across the heavens to the earth -- he declared that Euclid's geometry would find space "flat", and not warped differently in one area than in another.  He was proven conclusively wrong on that topic a short time later, when Einstein's work with Relativity showed that the fabric of Space-Time is warped and stretched proportionately by the massive objects (such as galaxies, stars, and planets) within it.

11. "Space-Time" appears to require us (at this "point" in "time") to approach it using Non-Euclidian Geometry.

12. The Quantum Universe is rational, but not visualizable.  Even Einstein's Relativity had pushed us far beyond the realm of the visualizable, in areas such as the "overlapping" warping(s) of so-called "empty" space BETWEEN two massive objects, such as a planet and its moon.

13.  The Quantum Universe is detectable only through complex instrumentation -- it is revealed to the mind through the objects of thought, and not through our sense perceptions.

14. Mystics and Scientist appear to agree that the Objects of Thought are MORE "REAL" SOMEHOW than the objects apprehended by our senses.

15. "Reality" as we perceive it involves a mirror reflection of Quantum Waves forward and backward ("simultaneously") in Time to allow us the near-endless opportunities to choose between Possible Future Worlds.

16. Our "selves" are complex conjugations of "decisive" quantum "events", echoed to the Source instantly, and leaving a trail in Space-Time for all Out-of-Time Observers to Witness.

17.  Even by simply looking towards the Universe, beholding it, and Observing it, we are continually CHANGING the Universe, and helping to "create" the History of it, as it expands into each new virtual opportunity.

18.  By seeing ourselves IN A REFLECTION, we are free to change ourselves.

19.  By sensing ourselves IN EACH OTHER, we are destined to change each other.

20. We stare at the vastness of Creation dumbfounded, in a state of shock -- but without us to WITNESS these moments, the Universe itself would be "blind" to its own reflection in Space-Time (formed by combinations of Matter/Energy, and governed by Laws of Physics, such as "E" [Energy]is equal to the "M" [the Mass] times "C" -- the speed of light, that is, yielding a very large number which is then squared).

21. There are enough known inconsistencies and contradictions in Mathematics and Geometry for both areas of investigation to be known as "Mystical Sciences" -- not the sort to be PROVEN CONCLUSIVELY  without ARTICLES OF FAITH which first must be accepted without PROOF.

22.  All forms of "logic" which require the action of RANDOM PROCESSES or CHANCE EVENTS are not capable at this time of definitive PROOF.

23.  Even in the absence of Facts and Truth, the Human Mind will hunger to weave some kind of "meaning" from the perceived environment and the inscrutable motions of "Fate" or "Destiny".

24.  Some believe that "God" knows EVERYTHING all at the same time, and that He does not "play dice" or "gamble" with the Fate of the Universe.  Others believe that "God" has NO OTHER OPTION BUT TO THROW THE DICE, and that HE can't always even see the result.

25.  "Determinism" as a guiding principle for the Physical Cosmos has been discredited, along with the stubborn old notions of a Clockwork Universe; the "Randomness" we thought we "perceived" in what passes for "Chaos" here (until we learn more), and the attendant notion of "Probability" have been shoved aside by even more stubborn "fact-like" observations, and Mathematical "Proofs" of several varieties have been exposed as Products of Complacent and Unquestioning minds.

+++

With these 25
new STARTING POSITIONS
FOR AGREEMENT,
LET US CONTINUE
TOGETHER
WITH
OUR SYNTHESIS
OF INFORMATION.

Many more places of AGREEMENT
can likewise be derived
from these 3
recently blogged documents.

I hope you will ADD
to our findings at your leisure!

Peace to you!

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:

 
+++