Urban design in age of Mars colonization

                      THE DESIGN OF CITIES:
               IN THE AGE OF COLONIZATION OF MARS
               ==================================

                   by Lyndon H. LaRouche,  Jr.
                       (August 24,  1987)

     Planning the colonization of Mars gives deeper meaning to
the ages-old task of rendering man's habitation of unfriendly
natural environments fruitful,   healthy,   and as agreeable as
possible.    We must consider features of the artificial Mars
environment other than merely the molecular-biological
requirements of the human being.  We must take into account the
importance of immunizing the psychological well-being of the
colonists,   against the eerily new kinds of stresses associated
with prolonged exposure to the alien environments of space.

     We must take into account,  in a new way,  both the
physiological and psychological importance of the architectural
design of the local environment in which the explorers and
colonists work,  and perform their normal personal functions away
from the work-place.   Admittedly,  the permanent colonization of
Mars is probably forty years ahead;   yet,  even now,  in the
early stages of planning that colonization,  and during the
coming months and years,   we must set some of the architectural
guidelines for planning the future geometry of the new cities,
the working space,  and the ordinary living space,  in which
space explorers and colonists will work and live.

     Increasing fascination with space-exploration,  especially
among the young,  ensures that whatever we announce as necessary
features of the colonization of the Moon and Mars,  will have an
increasing impact in reshaping the policies governing life here
on Earth.    Even in the stages when only a handful of Earthlings
are actually venturing into space,  increasing portions of the
Earth-bound population will shift the popular sense of human
identity toward the idea of mankind as a space-explorer and
space-colonist.    This will bring about an adjustment in popular
values,  a change in the way human beings think about human
beings.

     During the coming years,  while flights deeper into solar
space are still mainly in the planning and development phases,
more and more people on Earth will look at life here on our home
planet through eyes which are becoming,  in the informed
imagination,  the eyes of the space-explorer.   With ever-greater
frequency,  the suggestion will be made,  that which we can
accomplish in space might point toward the best solution for
problems here on Earth.

     This spill-over of space-planning into practice on Earth,
is a sometimes indispensable,  as well as a likely result of
the growing popularity of space colonization programs.

     Thus,  over the years immediately ahead,  increasing
attention to the design of future cities on Moon and Mars will
lead toward the easier recognition of the urgency of the
establishment of many new cities on this planet,  new cities
designed and built -- not only in the Sahara desert -- in ways
influenced by our thinking about architecture in space.    That
connection is the subject-area within which this report is
situated.

     To bring this matter within the reach of as many laymen-
readers as possible,  I begin with reference to some very
ordinary features of my own adolescent introduction to "human
engineering,"  to show how this led me to uncovering the
scientific principles which should govern proper practice of
architecture in space-colonization.

                       "Human Engineering"
                       -------------------

     My first gainful employment began before my sixteenth
birthday,  in a Summer's job as what is called a "hand-dinker" --
at twenty-five cents an hour -- in a slipper-manufacturing firm.
It represented about as low a level of skill as one might find in
such a place.   My assignment was to stand at a wooden block,
with a die in the left hand and a shoe-cutter's mallet of several
pounds weight in the right,  and to punch out as many of the same
object as I could,  over and over again,  each hour.   At first,
that work seemed to me about as boring as one might imagine.   I
quickly realized that it need not,  and should not be boring.

     My thoughts at that work-bench were on the subject of what
is called "motion-study."  The object of my inquiry,  was to
discover how I could accomplish the maximum of the desired result
with the least effort -- soon,  I added: the least painful after-
effects experienced overnight and the following day.   The mental
image I adopted,  was of the ordinary pendulum of a grandfather's
clock:  to achieve a rythmical movement,  in which my body fought
itself the least in bringing about those motions,  with the
proper force,  to achieve the optimal result.

     My father had secured this lowly employment for me,  as part
of his program for training me as a management consulting in the
shoe-manufacturing industry.   Indeed,  this did help to impel me
toward the consulting profession.   The scientific principle I
confronted in seeking to master that lowly,  repetitive toil,
was an experience which guided my attention to the character and
importance of "human engineering" of the operator's work-place,
and of the traffic-flow of materials and work-in-progress through
the production center locally and the production facility as a
whole.

     No person,  but one who has developed the habit of looking
at every experience in this way,  should be considered qualified
for the profession of "economist."   Do not tell me silly money-
theories of how objects are bought and sold;  tell me exactly how
they are produced and how they are physically distributed.   Tell
me how much labor,  of how many people,  working under what
conditions,  is required to provide an acceptable standard of
market-basket of goods for one household.   Tell me not the
importance of a certain amount of money in a salary or wage;
tell me not merely the money prices of things.    Tell me what
kind of a life a year of a man's labor will,  on the average,
buy for his family household;  tell me how you propose to effect
economies of labor which will help to improve that life.

       Only one who understands the importance of these
questions,  and has acquired the skills for answering them,  is
qualified to become an economist.   These attitudes and skills
are not sufficient,  by themselves,  to qualify a person as an
economist;   but,  no person who lacks these rudimentary skills
will ever be better than useless as an economist.

     In recent decades,  industrial "time-studies" by teams of
so-called "efficiency experts" have become notorious,  as the
higher-priced,  trained industrial engineering was replaced,  by
the cheaper fellow hired off the street for his skill in wearing
in white shirt while using a stop-watch and clip-board on the
factory floor.   Today,  "time studies" are notorious,  because
the drift has been away from capital-intensive investment in
economy of labor,  toward increasing the labor-intensity of the
work-place.   As my own view of "hand-dinking" experience
indicates,  the purpose of industrial engineers' "human
engineering" practice was directly the opposite to policies of
labor-intensification;  the purpose was to achieve greater
productivity and quality with less effort by the operative.

     The benefits of "humanistic engineering" (a better term than
"human engineering") include such obvious economic gains to
employeer and employee as lower rates of industrial accidents,
less cardio-vascular and other illness,  and so on.

     The skilled industrial engineer did not need to refer to a
stop-watch very often.   The norms of movements of eyes and
limbs,  once established,  gave the industrial engineer handy
reference tables of a sort he understood,  because he had learned
to construct such tables as part of his professional education.
He worked essentially as I thought through the best methods for hand-
dinking.   He thought about the physical geometry of the
movements of man,  machine,  and work in progress;  once he had
mapped those qualitative features of the job,   he could assign
allowed times for each required motion with far greater accuracy
than a platoon of time-study boys studying the same work-place.

     As a youth,  I saw this problem expressed in a brutal way
each time I stood in a shoe-manufacturing payroll line-up myself,
or observed the operatives punching-out and leaving the plant at
the end of the day.   I could identify accurately the nature of
the occupation of the older operatives,  merely from observing
their bodily movements as they passed the time-clock.   Their
bodies were distorted by the combination of labor-intensity with
the peculiarities of the organization of the work-place;  so,
one could spot the lasters,  the welters,  and so forth,  from
the posture of their arms,  torsos,  and way they walked.

     Sadly watching that parade,  one recognized the human
importance of making operatives more the masters of their
machinery,  less an increasingly crippled appendage of the
machine.

     For this reason,  I learned to hate technological stagnation
bitterly.   In "humanistic engineering,"  we work to change the
geometry of the work-place,  to the effect of simplifying the
motions,  and reducing the effort required of the operative,
with special emphasis on eliminating the kinds of repetitive
motions which are unhealthful.   We recommend to the employer:
"build this ... change the lighting,  so ... this change in the
tooling of the work-place,"  and so on.   In a climate of
investment in technological progress,  there is gain in profit
and quality by the employer,  and personal and income advantages
to the operative, too.

     Trading so many dollars' worth of unnecessary exertion by
the operative,  against an investment which costs actually less
per unit of output than the amount saved in terms of unnecessary
operative's exertion avoided,  is the normal way in which
productivity increases with gains to the operative as well as the
employer.   This is true up to the point that paid-out dividends
become too large a portion of gross earnings,  or borrowing-costs
for new investments in capital stocks become much too high.

     The humanistic professional might measure his personal
satisfaction from his work,  by reflecting on the image of
twisted bodies of middle-aged operatives parading past the time-
clock.   The personal conscience of the true professional is:
that saddening spectacle,   and everything akin to it,  must be
eradicated systematically from our production.

     The gains effected so,  are not merely physical ones;  the
mental ones are more or less as important.   In the longer time,
it is the mental gains which are of the utmost importance.  The
employer who says to his employee,  "I don't pay you to think,"
is not the genius-laden tycoon he might think himself to be.
The secret of the superior productivity of U.S. labor,  in times
dating from earlier than our recent twenty years of "post-
industrial" drift into technological stagnation,  was precisely
that U.S. farmer's and industrial operative's superior ability to
think while working.

     Every good industrial manager agrees.    He might inform you
of the steady gains in quality of product and productivity which
industrial firms obtained through the employees' suggestion-box.
He might also instruct you on the subject of increased accident-
proneness among operatives for whom a lower premium is placed on
thinking as integral to the operative's role at the work-place.
A more profound,  more valid general argument could be made:  the
biophysics specialist might suggest that we correlate brain
alpha-wave activity in persons with their ability to sustain
continuing technological progress efficiently -- and to avoid
accidents on the job,  or while driving a motor vehicle.

     In general,  as the level of skill and technology are
increased,  production depends increasingly upon a more active
role by the operator's capacity for effective kinds of problem-
solving innovations,  as an integral part of the work-place.

     Think of space-colonization as what it is:  essentially,
very high levels of skill and technology by every person
involved.

     The chief flaw in the relatively better sort of industrial
engineer practised up to about twenty years ago,  was the lack of
attention to what should have been recognized as the underlying
principles of motion-theory.  Industrial engineering education
should have included at least two years span of study of the
relevant work of Leonardo da Vinci,  Albrecht Duerer,  Raphael,
and Johannes Kepler.   Had such studies been promoted as they
should have been,  a good industrial engineering graduate would
have understood the principles which govern economy of labor.  He
would have mastered also,  the rudiments of applying classical
principles of aesthetics to architecture and urban design,  and
understood these subjects properly from the standpoint of
"humanistic engineering."

                    General Design of A City
                    ------------------------

     At the end of World War II,  significant numbers of the
leading scientists in Germany were gathered into a pool at
Aachen,  awaiting reassignments.   Some of these applied their
skills to planning the reconstruction of the war-ruined Ruhr
district.   Part of their design was implemented.  Other
elements,  if not implemented,  nonetheless influenced thinking
about reconstruction policy.

     Since about 1977,  I had been engaged in studies for the
economic development of Africa,  including the urgent need for
building of cities of a new type in black Africa,  as an
indispensable,  central feature of any successful effort to
develop black Africa in a general way.   My own work in the
latter connection gave my associates an advantageous standpoint
for recent examination of the work of the Aachen circles;
leading features of the Aachen designs coincided on key ponts
with principles of design I had come to view as elementary
through my own work.

     Such is science.   Different groups of investigators,  in
different times and places,  but working from the same general
store of knowledge,  converge on the same result.   The right
principles of design of cities,  are not matters of local tastes;
they are as universal as is the nature of the individual human
being who,  as the inhabitant of the city,  is the measure of its
proper design.   The unchangeable principle governing the proper
design of a city is elementary;  it is the same for a city on
Earth as it is for a permanent colony on Mars.

     The proper design for a city,  is a study of motion of
people,  the goods they use,  and their activities.   The general
scheme for design is therefore the principle of least action --
which I shall describe at a later point in this report.   It is
sufficient,  for the moment,  merely to state as an assertion,
that the definition of least action required for this purpose is
harmonic orderings cohering with those determined by the Golden
Section of the circle.   For reasons to be made clearer,  the
significance of the Golden Section suffices to show that the
general design of a city is implicitly a proposition in Gauss-
Riemann topology.

     I shall develop this theme by stages,  after I have
described the general arrangements.

     The simplest form of result has three features:  1)  The
paradigmatic form,  for approximately level regions,  is
spherical,  with one hemisphere lying above the surface,  and the
other below the surface.   Let us term the circular cross-section
of the sphere at the surface-level the "ecliptic,"  as in the
ecliptic of the solar planetary orbits.   Then,  2)  The harmonic
organization of the ecliptic is analogous to Kepler's arrangement
of the orbits of the Sun and its eight major solar planets,  as
divided by the domain of the shattered ninth planet,  today's
asteroid belt lying between the orbits of Mars and Jupiter.

     The Sun,  tuned to a Keplerian F,  is the central
educational park of the city.   The orbits of Mercury,  Venus,
Earth,  and Mars,  correspond to the administrative and
residential areas of the city.   F#,  the asteroid belt,  is the
boundary between the inner city and the outer,  "industrial"
planets.

     Since the design of the city is based on least-action
movement of human activity  (per-capita,  per-hectare),  it is
the transport-system -- for persons and freight -- which appears
as a delimiting feature of the internal design.   In the modern
form of the city,  this movement is on distinct levels:  walking,
passenger rapid-transit,  sub-surface transit of freight,  sub-
surface transit of activities by utilities.

     Thus,  the sub-surface hemisphere is defined in terms of
sub-surface movements of people and freight,  and in terms of
stores of essential goods:  the density of the sub-surface
structure increases as a function of per-capita motion per-
hectare as we proceed inward from the "asteroid belt" to the
"Sun,"  the educational and classical cultural activities
situated within a large,  educational and recreational park.
So,  within the inner part of the "solar complex,"  the density
of activity increases as we near the "Sun."

     Beyond the asteroid belt,   the per-capita density of
activity per hectare in industrial use,  again increases,
initially relative to the average for the inner portion of the
complex as a whole,  and then diminishes again,  as the eye
travels toward the outermost orbit of these "outer planets."

     Throughout the complex,  the density of movements per-
capita-per-hectare is harmonically distributed as in planetary
orbits:  these are defined in terms of transport-systems,
especially the sub-surface rapid-transit,  freight,  and
utilities.   The spokes and rims of these transport orbits are
cut by a plane self-similar spiral of movement,  radiating from
the "Sun,"  and intersecting the spokes and wheels of the outward
and lateral movements.

     The spokes are twelve in number,  and the inner orbits are
four.    So,  the spokes are named North,  Northeast by North,
Northeast,  Northeast by East,  and so on.   The orbits are named
for musical tones,  Kepler-style.   The spiral-way is known as
the Gaussway.

     This signifies that such a city has a finite maximum
population.   If more population is to be accomodated,  an
additional city must be developed,  linked to others by high-
speed magnetic-levitation rapid-transit links -- at nominal
speeds of about 300 miles per hour.   (Indeed,  magnetic
levitation is used throughout the surface transit systems for
movement of persons and freight.)    How large is that finite
maximum?

     At first glance,  three factors appear to decide this:

1)   The unit-area and volume required by an average person's
mean-free-path motion within the city:  the congestion factor;

2)   The ratio of lapsed-time expended in normal travel by a
person within the city,  to time spent in other activity;

3)   The size of the "Sun."

     These three factors must take two other sets of factors into
account.    The first of those two other sets of factors is,
that each design of a city is delimited by my six primary
constraints for a Riemannian representation of technological
progress:

1)   Level and rate of improvement of per-capita masket-basket
content,  in quality and quantity;

2)   Density and rate of increase of usable energy available per
per-capita unit of per-hectare population-density;

3)   Level and rate of improvement of effective energy-flux
density of modes of applied technology;

4)   Ratio of rural to urban labor-force employment in the region
in which the city is functionally located;

5)   Ratios of employments of the urban labor-force,  in terms of
scientists and kindred professionals per hundred members of the
labor-force employed as operatives,  and in terms of capital-
goods producing to household-goods producing operatives.

6)   The general level and rate of advancement of technology in
practice.

These six factors define the true basis for measuring individual
activity-levels within the city as a whole.

     This is also affected in obvious ways,  by the second
additional set of factors,  the demographic factors centered
around the birth-rate per female of child-bearing age-intervals,
and life expectancies.

     All three sets of factors,  taken together as part of a
single function,  are the primary determinants of the city's
proper choice of maximum population-levels.

     In all these considerations,  the irreducible quantum of
action is the activity-scale required for the average individual.
The individual person's level of activity,  per unit of
population-density,   becomes the definition of scale,  with
respect to which all other measurements are defined.

     A good design for a beautiful city,  is one which will be
durable through a thousand years of technological progress.
This presumes that the city is designed such that it easily
adapts to the effects of technological progress.

     It adapts so,  in terms of increasing of the energy-density
per per-capita unit of population-density.   It adapts so,  in
terms of raising of the level of effective energy-flux density
per square-centimeter cross-section of target-area of work.   It
adapts so,  to related increases in mobility of persons.   It
adapts so,  to increase of the ratio of time expended in creative
leisure,  to that required for labor.

     What remains constant is man.   The biology of the person
requires daily about six to eight hours of sleep,  two to three
hours expended in eating.    We know today,  or should know,
that -- for what might be termed pyscho-biological reasons -- no
acceptable substitute for the "nuclear family" as a mode of
development of new individuals will ever be discovered.   We know
that maturation will never be briefer than a span of between
twenty-odd and twenty-five years,  of which at least between
sixteen and eighteen years must be within the setting of the
family household.

     From this,  the design of the dwelling-unit follows.   The
size of sleeping and bathing quarters,   the need for dining
areas and their dimensions,  and so forth,  are defined in an
elementary way.   Improvements in privacy of thoughtful
activities,  and other advances in quality of dwelling-places are
desirable,  and will become more demanded as society progresses.
Yet,  walking through some better-maintained,  older areas of
cities in Europe,  and elsewhere,  and from scholarship in the
same matter,  we see that the elements of design of a good space-
organization of the dwelling-unit have not changed much over
centuries,  even thousands of years.

     If we learn from those studies,  by applying principles of
"humanistic engineering" to what we learn,  we can do much better
today than any preceding generation of mankind,  in building a
city today,  for whose design we will be thanked by its
inhabitants a thousand years into the future.

                     Natural Human Movements
                     -----------------------

     As I stated earlier,  twentieth century industrial
engineering wasted much of its efforts,  and contributed a few
important mistakes,  by neglecting the rigorous study of the
natural movements of the human body associated with such pioneers
as Leonardo da Vinci,  Duerer,  Raphael,  and Kepler.

     Since classical Athens of Plato's time and earlier,  it has
been the central principle of classical aesthetics,  that beauty
of form and movement is limited to those harmonic orderings of
form which are coherent with an harmonic series based upon the
construction of the Golden Section of the circle.   Classical
western aesthetics defines this as a rigorously definable
standard of beauty for the form of music,  poetry,  painting,
sculpture,  and architecture.

     This standard was embedded in western civilization by such
writings of St. Augustine as his "De Musica."   In the wave of
city-building unleashed by Charlemagne,  what were called
"Augustinian principles" were the guide to the development of
cathedral towns around such "Augustinian" works in light,
accoustics,  and form,  as the famous cathedral at Chartres.
Classical aesthetics was defended during the "New Dark Age" by
such influentials as Dante Alighieri and Petrarch,  and became
the central theme of the Golden Renaissance at about the time of
the 1439 Council of Florence.    Brunelleschi's successful
invention in architecture,  completing the construction of the
dome on the cathedral at Florence,  was a signal point of
reference throughout that century.

     The single most influential scientific thinker of that
entire period was Cardinal Nicolaus of Cusa.   Cusa's revolution
in scientific method first appeared in published form in his 1440
theological text,  "De Docta Ignorantia"("Of Learned Ignorance").
This text included a revolution in ideas about geometry and
physics,  solving several classical problems left over from the
work of such as Parmenides,  Plato,  and,  most immediately,
the Archimedes whose work on the quadrature of the circle Cusa
directly corrected in his own 1440 book.

     What Cusa actually accomplished,  was the establishment of a
true "non-euclidean geometry."   Instead of a system of deductive
theorems,  based on a set of axioms and postulates,   Cusa showed
that the physical laws of the universe could be represented by
means of nothing more than geometrical constructions,
constructions all based on no more than a single principle of
physical geometry.   This principle of Cusa's is rightly
described as a "Maximum Minimum Principle."   In geometry,  it is
recognized as including the so-called "isoperimetric theorem of
topology,"  as that was elaborated by Bernouilli and Euler at St.
Petersburg during Benjamin Franklin's lifetime.   In physics,  it
is recognized as the Principle of (Physical) Least Action,  as
this was variously defined,   geometrically,  in various stages,
by Fermat,  Leibniz,  and the work of Carl Gauss and his
successors.

     Following the publication of his "De Docta Ignorantia,"
Cusa devoted a number of other published writings to matters of
scientific method.   Leonardo da Vinci was brought to systematic
study of Cusa's scientific work through Leonardo's Milan
collaborator,  Fra Luca Pacioli,  of "De Divine Proportione"
fame.   From the collaboration between Pacioli and Leonardo,
nearly all of modern science was set into motion,  together with
several revolutions in painting and music.

     Briefly,  to assist the layman in following this,  the part
of Pacioli's and Leonardo's collaboration which is of direct
bearing upon the understanding what we have identified as "the
scale of individual human activity,"  is the following.

     In one of his most influential dialogues,  the "Timaeus,"
Plato presents and discusses the fact,  that in visual space only
five regular solids can be constructed.   These -- the
tetrahedron,  the cube,  octahedron,  the dodecahedron,  and the
icosahedron -- have been known since as "the five platonic
solids,"  or,  simply,  "the platonic solids."  Plato ascribes
the proof of this to a collaborator working at the Cyrenaic
temple of Ammon.

     The importance of the "five platonic solids,"  is that they
are a crucial proof that visual space -- as our eye-brain define
the image of space for us -- is not empty space stretching
infinitely,  in straight lines of Albertian perspective,  to
beyond the furthest imaginable extremes of the very,  very large,
and very,  very small.    What might appear,  wrongly,  to be
empty space and time,  has an efficient geometrical shaping,  and
this in a way which contradicts all of our childish intuitions
about the universality of extension in straight lines.

     Thus,  we say,  physical space-time is self-bounded.   This
does not mean that our universe has some sort of fence around it.
It means what is already clearly stated by the report that,  in
visual space,  the only regular solids which can be constructed,
excepting the sphere,  are the five platonic solids.

     Plato already emphasized this notion of "self-boundedness"
of visual space.    For example,  in his "Republic,"  he supplies
the usually misunderstood reference to what we call today
"Plato's Cave."  He warns that what we imagine ourselves to see,
as images in visual space,  are like shadows cast by firelight
upon the wall of a darkened cave.   Through our senses,  we are
able to know reality,  but what our senses show us directly is
merely the shadow of the reality.

     Today,  after the work of Gauss,  Dirichlet,  Weierstrass,
Riemann,  and so forth,  we say,  "Of course,  that is true."
Today,  as especially in the case of "non-linear" sorts of
electromagnetic processes,  we know that cause and effect occur
outside the limits of our ideas of visual space.   Cause and
effect occur efficiently in what Gauss and Riemann enable us to
define as a fully constructible geometry of the "complex domain."
We can show also that the "shadows" recognized by our senses are
a true,   if distorted reflection,  into "euclidean space,"  of
what actually is occurring within the physically real world of
the complex domain.

     Therefore,  the study of the reasons for the uniqueness of
the "platonic solids" is the most fundamental line of inquiry in
the physical sciences.   What is the reason,  that visual space
should be "self-bounded" in the way this proof demonstrates?   It
should be obvious,  that no amount of interpretation of empirical
evidence,  stated in terms of the physical space-time of
Descartes,  Newton,  LaPlace,  or Maxwell,  is sound physics,
unless we show that our observation of visual space has taken
into account the reasons for the self-boundedness of the visual
representation of physical space-time as a whole.   Competent
physical science begins,  therefore,  with rigorous proof that we
have discovered the reason for this "self-boundedness" of visual
space.

     Pacioli recognized the importance of reconstructing the
proof of the platonic solids.   He succeeded in producing a
model of such proof which was improved upon by scientists such as
Euler and Gauss during later centuries,  but which that more
advanced work shows to have been in the proper direction.
Pacioli's and Leonardo's work shows that they properly grasped
Cusa's contributions to the founding of modern scientific method.
Leonardo,  and Duerer,  Raphael,  and Kepler after him,
established the basis for revolutionizing our approach to
architecture and urban design,  as well as establishing,  in a
related way,  the principles of "humanistic engineering" which
ought to inform the work of the qualified industrial engineer.

     A scientist comes away from a study of Cusa's work as a
whole,  with the sense that the proper descriptive name for
"science" is "an intelligible representation of the lawfulness of
the universe."   This was what study of Cusa's work imparted to
Pacioli and Leonardo,  and Kepler later.    Although our subject-
matter here is,  the principles of architectural form which must
govern the design of new cities,  it is also urgent -- especially
if it is our goal to design cities to endure for a thousand years
-- that we show that those principles are premised upon
unassailable truth.   Therefore,  we should sum up the proper
meaning of "intelligible representation."

     Go to a blackboard.   Draw upon that board all sorts of
shapes of lines,  including the most arbitrarily irregular ones
you are able to produce.    These are "representations."

     Now turn to face the classroom.   Can you meet any challenge
members of the class might pose to you,  on the subject of these
representations?   Can you show under what circumstances each of
those representations might necessarily exist?   In other words,
can you start from a single,  most elementary principle of a
purely constructive geometry?   Can you,  without aid of any
additional assumptions (axioms,  postulates),  and without any
resort to formal deductive reasoning,  show how constructive
geometry generates each and all of those representations you have
drawn?

     If you can succeed in meeting that challenge,  in the
fullest of its implications,  you have met,  in that degree,  the
challenge of "intelligible representations,"  as distinct from
mere "representations."   The most troublesome question you must
face,  is the very first question:  What is the correct choice of
"most elementary principle"?   If you grasp what that question
implies,  you are prepared to appreciate the genius of Cusa's
work.

     Two examples which I have frequently employed,  over the
years,  bring the idea of "elementary intelligible
representation" to bear with full force.   I challenge you,  to
supply me an intelligible representation of two terms,
"creation" and "life."   These are terms common in our
vocabulary,  especially the latter.   In modern civilization,
all serious thinkers have recognized that these two terms have a
connected meaning.   Yet,  I challenge you:  If you can put such
a word into your mouth,  can you also supply me with an
intelligible representation of what you mean by that word,  or
even any representation at all?

     If you use as system of reasoning such as that of Euclid's
Elements,  these two words correspond to ideas for which you have
no possible representation,  and certainly no intelligible
representation.    Yet,  already,  Cusa did have an intelligible
representation of both,  and,  Pacioli,  Leonardo,  and Kepler,
a more elaborated such representation.   This representation is
the fundamental idea underlying a modern form of the science of
classical aesthetics,  and underlying the principles of
functional form for design of new cities.

     In formal logic,  "creation" does not occur; it is merely
asserted to have occurred.   "Creation" is implicitly situated
between two successive moments of existence,  such that something
which does not exist in the first,  exists in the second.   There
is no representation of that which occurs between the two
moments.

     Perhaps the most famous case of use of formal logic to deny
the existence of "creation,"  is that expressed by Immanual Kant,
most emphatically in his "Critique of Judgment."   Kant asserted
that no intelligible representation of creative mental action,
such as that responsible for fundamental scientific or artistic
discoveries,  is possible.   Kant did not assert that "creation"
does not exist;  he argued,  that since the human mind is,
according to his view,  incapable of providing an intelligible
representation of an act of creation,  mankind can not know
"creation" as an idea.

     Kant's argument is absurd,  with one qualification.   In
deductive logic,  it is axiomatically impossible to provide even
a representation of the idea of "creation,"  and certainly not an
intelligible representation.

     The word "life" encounters exactly the same difficulties as
the representation of the word "creation."   In formal logic,  or
in molecular biology,  it is impossible to provide even a
representation of "life" per se,  let alone an intelligible
representation.

     Today,  intelligible representations of "creation" are
available to us even in mathematical physics,  as the case of the
Riemann Surface illustrates this most directly and simply.    The
same Gauss-Riemann physics,  applied to a more advanced
representation of the work of Pacioli,  Leonardo,  and Kepler,
permits us to provide an intelligible representation of "life"
per se,  as molecular biology can not.    Moreover,  in the same
context,  we can show that both notions,  "creation" and "life,"
are of the same characteristic.

     This is no digression from the principal subject-matter of
the present report.   A correct understanding of these two terms
is essential for a rigorous definition of what architecture must
measure as "human activity,"  for the work of designing cities
which will be of durable worth for a thousand years yet to come.
That connection will become clearer as we progress.

     Functionally,  there is only one platonic solid,  the
dodecahedron,  each of whose equal twelve facets is a regular
pentagon;  the other four,  the tetrahedron,  the square,  the
octahedron,  and icosahedron,  are simply and directly derived
from the dodecahedron,  rather than the proof of their existence
being derived separately from that for the dodecahedron.   So,
we must say that the dodecahedron expresses adequately the self-
boundedness of visual space.

     The construction of both the regular pentagon,  and the
dodecahedron,  depends upon the prior construction of the Golden
Section of the circle.   So,  the construction of the Golden
Section represents the self-boundedness of visual space.   In
other words,  the limit of constructibility of intelligible
representations in visual space is constructions dependent upon
the construction of the Golden Section.

     This point is traced to its elementary root by aid of Cusa's
solution to the problem of the intelligibility of the problem of
attempting to square the circle,  a solution whose result is
reflected in a central way within his 1440 "De Docta Ignorantia."
Cusa implicitly eliminates the use of deductive method in
geometry and in physics,  and also eliminates all need to base
geometry and physics on an initial set of axioms and postulates.
From this point on,  in the history of development of modern
physical science along a pathway of progress,  through the work
of Leonardo,  Kepler,  Leibniz,  Gauss,  and Riemann,  circular
action is the only elementary conception upon which geometry and
physics are premised.

     Circular action is defined,  topologically,  as the least
amount of perimetric action required to generate the relatively
largest area or volume.   Since volume exists,  circular action
must be understood as acting upon circular action in every
interval,  reciprocally.   For purposes of identification,  we
call this "doubly-connected circular action."   The analysis of
possible constructions in visible space requires us to employ the
notion of "triply-connected circular action."

     That is the definition of the term "least action,"  not only
in constructive (or,  "synthetic") geometry.   It is also the
basis for definition of "least action" in the physics of Kepler,
Fermat,  and Leibniz.   It is the point of derivation for the
work of Gauss,  Riemann,  et al.,  in defining the form of least
action in the complex domain:  multiply-connected,  (conical)
self-similar-spiral action.    Understanding of the way in which
the two definitions of physical (multiply-connected) least action
are connected,  is the mathematical-physics premise for those
measurements of human activity central to proper architectural
designs.

     Pacioli and Leonardo already knew this universality of
(circular) least action from the work of Cusa.   For that reason,
it was possible for Pacioli to elaborate a most respectable
approximation of the stricter proof for the uniqueness of the
platonic solids.    If universal cause-effect action is
representable as multiply-connected circular action,  all action
in visual space is fundamentally underlain by this form of
physical least action.   Hence,  the self-boundedness of visual
space,  as shown by the platonic solids,  must be a constructible
"property" of universal least action of this form.   Hence,  the
Golden Section of least action,  a construction itself derivable
from nothing but this form of least action,  is a sufficient
demonstration of the necessary characteristic of the self-
boundedness of visual space.

     The most famous immediate application of this result,  by
both Pacioli and Leonardo as collaborators,  was their definition
of the form of life:  all living processes are distinguished from
ordinary non-living ones,  in respect to morphology of growth and
function,  in the respect that that form is ordered as an
harmonic series consistent with the harmonic series defined by
the Golden Section.

     Today,  we qualify that discovery.   Between the limits of
the very,  very large (astrophysics),  and of the very, very
small (microphysics),  any process which is harmonically ordered
in congruence with the Golden Section is either a living process,
or is a special class of work done by a living process.   Kepler,
who based his founding of a comprehensive mathematical physics
chiefly upon the combined work of Cusa and Pacioli-Leonardo,  was
the first to prove that the universe as a whole is governed by
the same harmonic ordering.    Some leading scientists among the
writer's collaborators,  are proving that a Gauss-Riemann
correction for Keplerian laws of astrophysics also rules on the
scale of organization of atoms and smaller scales of physics.
With that qualification,  Pacioli's,  Leonardo's,  and Kepler's
geometrical (least action) definitions of living processes,  is
conclusively demonstrated today to be fully as accurate as
Pacioli represented this to be at the beginning of the sixteenth
century.

     Thus,  all of the movements and related functions of the
human physiology are harmonically ordered least-action-based
movements of this sort.

     This standpoint governed several aspects of the work of
Leonardo.    In anatomy,  he explored the Golden Section
harmonics of the physiology of persons,  horses,  birds,  and so
on.   In pioneering the principles of design of machinery,  and
the design and use of weapons,  the same principles predominated.
He revolutionized the science of perspective,   by emphasis upon
anomalies of visual space associated with the periphery of
vision,  rather than an Albertian,  linear vanishing-point.  This
we note in viewing the originals of such master works of Raphael
as the famous murals in the papal apartment,  and the
"Transfiguration" on display in the Vatican museum.

     It can also be shown,  that his general approach to
application of hydrodynamics to not only water movements but also
phenomena of electromagnetic radiation (including propagation of
sound!),  is based on the same principles of constructive
geometry.

     Thus,  must "humanistic engineering" be reformulated in
terms consistent with these principles of human physiology.
Thus,  must the design of new cities be adapted.

                   The Form of Mental Activity
                   ---------------------------

     This is also true of the most characteristic form of human
mental life,  the aspect of human mental life which absolutely
separates mankind from the beasts.   The form of design of the
city must be agreeable to the form of this aspect of human mental
behavior,  as well as the functional requirements of form imposed
by human physiology otherwise.   It happens that the form of
mental behavior is also congruent with the harmonics of the
Golden Section.    We must make clear the most relevant points
involved.

     Man is the only living creature who is capable of willfully
changing the form of his species' behavior for the better,  and
does this through creative discoveries bearing upon laws of
nature.   Scientific and technological progress are but the
paradigmatic expressions of human existence.

     Today,  we know how to construct an intelligible
representation of the creative mental processes involved in
either scientific discovery or valid works of classical forms of
art.   However,  there is no principle in this (Riemannian)
branch of mathematical physics to this effect,  which was not
already stated in another way by the dialogues of Plato.
Looking at the socratic method retrospectively,  in examples of
such dialogues from the pens of Plato and Leibniz,  the work on
representation of non-linear functions by Gauss,  Dirichlet,
Weierstrass,  Riemann,  and Cantor,  permits us to show that
socratic method is such a non-linear method.

     The reason that creativity is not an intelligible idea in
formal logic -- Kant's argument,   is readily illustrated by
reference to the case of any scientific discovery of a new
principle.

     If the previous state of scientific belief is represented in
a deductive way,  there is no way that the new discovery can be
represented as a deductive action in those terms of reference.
A new deductive schema,  representing scientific belief
consistent with the discovered new knowledge,  can be
constructed;  however,  there is no deductive method by which the
transition from the first to second deductive schema can be
represented.   This is Kant's problem.

     If we compare the two deductive schemas directly with one
another,  a crucial difference is exposed.   There is a
difference among one or more of the postulates of the two arrays.
The act of creative thought is reflected in the form of the
changes in postulates which have occurred.

     That is the characteristic of the socratic method.   In that
method,  every proposition considered is driven to deeper and
deeper levels of critical examination,  until the exposure of the
axiomatic basis underlying the proposition is exposed.   An
inappropriate,  or otherwise false postulate is exposed to light,
and the appropriate change in postulate effected.    The correct
proposition is then constructed on this new basis.

     The two cases,  the case of the deductive mathematical
representation of two successive schemas,  and the alteration of
underlying postulates of propositions in socratic method,  are
equivalent.   The changes so encountered,  in both cases,  can
not be made intelligible,  or even represented directly,   in
deductive method;  they have the form of a mathematical
discontinuity.   By definition,  formal logic does not permit the
construction of a continuous function which includes such a kind
of discontinuity.   Kant's problem.

      For such cases,  we require continuous "non-linear"
functions of a sort which exist only in the mathematical physics
of Gauss,  Dirichlet,  Weierstrass,  Riemann,  et al.   Consider
as much explanation of this as bears directly on the scope of
this report.

     Like the physics-thinking of Cusa,  Leonardo,  Kepler,  and
Leibniz,  the physics of Gauss and Riemann is not based on the
methods of deductive geometry or algebra.   It is based on the
method of constructive geometry.   We may say,  that it differs
from earlier forms of synthetic geometry because it is the
constructive geometry of the complex domain,  rather than of
visible space.   However,  although that statement is an accurate
one,  we must restate it differently,  for our purposes here.

     The difference is,  that the mathematics of visible space's
(shadow) images is based upon multiply-connected circular action,
while Gauss-Riemann physical space-time is represented by a
constructive geometry based upon multiply-connected (conic) self-
similar-spiral action.   A doubly-connected form of least action,
in the latter case,  immediately defines continuous functions
which generate discontinuities without losing their quality of
being continuous.    Such functions are the minimal precondition
for representing intelligibly notions corresponding to "creation"
and "life" per se.

     This implies immediately the question,  where does the
Golden Section fit within Gauss-Riemann physical space-time?
The answer is elementary.   To illustrate this in the simplest
way,  project the image of a cone's self-similar-spiral onto a
flat surface,  enclosing that spiral within a circle
corresponding to the perimeter of the cone's base.   Divide the
circle into twelve equal sectors by radii.   Then,  observe how
these radii divide the lengths of the spiral's arm,  and also how
the spiral arm divides the length of the radii.   The divisions
are those corresponding to the Golden Section.

     Since creative mental activity,  as typified by the
generation and assimilation of fundamental scientific discovery
is the characteristic form of human mental activity to be
considered in the design of cities,   what we have identified as
the principle of measurement for human physiology,  is also the
principle of measurement for human psychology.

                     Why Keplerian Harmonics
                     -----------------------

     I have reported earlier,  that the design of the city is  
based upon Keplerian harmonics,  with the qualification that we 
must employ the correction of Kepler's calculations supplied by 
Gauss-Riemann physics.    Since nearly all university textbook 
and classroom instruction on the subject of Kepler's work,  is 
rather savagely incompetent,  that matter must be cleared up 
immediately,  before indicating how Keplerian harmonics apply to 
the design of cities.

     Kepler informs us that his solar hypothesis was built 
entirely around two central sets of notions,  those of Cusa and 
those of Pacioli and Leonardo.   The hypothesis around which the   
entirety of his work was organized, was Cusa's solar hypothesis 
as amplified by the work of Pacioli and Leonardo to which I made   
reference above.

     Whether Kepler had access to the relevant sermons of Cusa,    
as well the works of Cusa printed for publication during the 
sixteenth century,  I can not say at present.   He certainly knew     
very well the work of Archimedes to which Cusa referenced his own 
discovery of what we term today the isoperimeric theorem.   In 
crucial parts of his construction of the solar system,  Kepler 
worked as if he knew how Cusa had treated the problem stated by     
Archimedes' theorems on the quadrature of the circle,  as a  
maximum-minimum problem.

     Kepler applied to Cusa's solar hypothesis the work, and  
associated theological,  cosmogonical standpoints represented   
(chiefly) in Pacioli's "De Divine Proportione."  Hence,  the 
Golden Section was central in his work,  and the role of the  
platonic solids subsumed by the Golden Section. Kepler's system    
gives us nine orbits for the principal planets:  four inner 
planets,   four outer planets,  and a ninth planetary orbit lying   
between the two sets.

     Gravitation occurs in Kepler's astrophysics as a 
characteristic of the self-bounded character of the visual form   
of physical space-time.    So,  Kepler's laws implicitly state 
the mathematical function for universal gravitation,  which he
links to electromagnetism as defined by Gilbert's "De Magnete."
If we examine this feature of his physics from the standpoint of
the later work of Gauss,  Riemann,  et al.,  Kepler's gravitation
is not as a force acting between physical bodies,  but the
physical effect of the geometry of least action in self-bounded
physical space-time.

     In other words,  Kepler's space is not empty space,  not
mere distance between interacting bodies;  it is not the space of
Descartes,   Newton,  or LaPlace.   Kepler's space-time is an
efficient agency.   Indeed,  looking at Kepler's construction of
his three laws with the eyes of Gauss or Riemann,  there is no
distinction among matter,  space,  and time in Kepler's physics.
Matter is physical space-time.   In that specific sense,  but
only that sense,  we may say that space-time acts directly on
matter.    We continue to relate our references to Kepler's work
as that work would be explained from the standpoint of a student
of Gauss and Riemann.

     All of the seventeenth and eighteenth century opponents of
Kepler's methods and results were proven to be incompetent
through the work of Gauss at approximately the beginning of the
nineteenth century.    Since these opponents of Kepler based the
fundamental principles of their physics on the same premises used
to attack Kepler,  Gauss's proof showed not only that Kepler's
physics was correct,  relative to the erroneous arguments of
Galileo,  Descartes,  and Newton;  this proved also that the
entire physics of Galileo,  Descartes,  and Newton was
axiomatically wrong throughout.

     The center of Gauss's empirical proof for Kepler,  and
against Galileo,  Descartes,  and Newton,  was the case of the
asteroid's orbits.

     Kepler had insisted,  that a planet had once existed between
the orbits of Mars and Jupiter.   Kepler had given both the
location and harmonic-orbital values for this planet.   The fact
that,  until the end of the eighteenth century,  no rubble from a
destroyed planet was found in such an orbit,  was considered
evidence of Kepler's error.    Indeed,  if it could have been
proven that no planetary body had ever occupied that position,
this would have shown a pervasive flaw in Kepler's work as a
whole.

     In each case,  following the discovery of Pallas and Ceres,
Gauss recognized that these were fragments of Kepler's missing
planet.   He used Kepler's orbital values for that planet to
predict the next relevant appearance of each asteroid.   This
successful prediction vindicated the entirety of Kepler's work on
principle;  after that,  there was no scientific basis for
continuing to regard the work of Galileo,  Descartes,  and Newton
as competent physics.

     Thus,  it was proven experimentally,  that our universe is
not organized on the basis of "forces" through which bodies act
upon one another at a distance.    It was proven that our
universe is not made up of separate qualities of matter,  space,
and time;  only physical space-time exists,  and to the effect
that it must appear to our senses as if the geometry  of empty
space acted efficiently on ponderable,  discrete bodies within
it.

     There are three features of Kepler's work which have the
greatest relevance for the design of cities.

1)   Although Kepler's calculations for orbits are not precisely
accurate,  his three laws are.   These laws apply to the orbits
of lunar bodies,  and to modern discoveries in astrophysics in
other matters.     Kepler's discoveries were all essentially
sound,  if imperfected ones,  and his general hypothesis is
correct.   The Gauss-Riemann corrections in Kepler's physics
point the way to refining the laws and the calculations.

2)   Physical space-time is harmonically ordered according to a
universal principle of least action,  rather than organized by
means of action-at-a-distance interactions through forces.   The
correct measurement of least action for visible space is the
projection of Gauss-Riemann least action's effects upon the
manifold of visible space.

3)   The universe as a whole is "negentropic,"  not "entropic."

     It is the latter of the three points listed to which we turn
our attention immediately.

     All functions which have an harmonic ordering consistent
with the Golden Section represent reflections of multiply-
connected self-similar-spiral action occurring in the domain of
the complex manifold.   These occur only in two kinds of cases
within our universe.   Either they are the products of action by
living processes,  or they represent least-action as expressed at
the extremes of astrophysics and microphysics.

     All processes which are harmonically ordered in a way
congruent with the Golden Section belong to a single class of
phenomena.   They are processes which statistical thermodynamics
classes as "negentropic."   Unfortunately,  although we can
explain,  on the basis of Gauss's constructive-geometric basis
for probability,  why such processes should appear to be
"statistically negentropic,"  the usual statistical analysis of
such processes is intrinsically an incompetent one.

     Curiously,  Isaac Newton was one of the first to warn of the
incompetent results which result from attempting to explain
fundamentals of physics from the deductive standpoint in
mathematics,  on which the statistical methods of LaPlace,
Boltzmann,  et al. are based.   The superimposition of a
deductive mathematical schema upon the analysis of phenomena,
will seem to show that our universe is running down,  in the
sense of a mechanical time-piece.   This fact,  of which Newton
warned the readers of his work,  is the simplest,  adequate
definition of what statistical thermodynamics call "entropy."

     It is assumed,  on such a statistical basis,  that our
universe is running down.   It is widely assumed, that this is
proceeding to such effect,  that the increase of the universe's
entropy as a whole is both the direction and ultimate,  natural
measurement of the passage of time.

     That assumption of "universal entropy" is directly contrary
to the astrophysical evidence,  as the construction of Kepler's
three laws proves the case.

     We must measure "negentropy" and "entropy" in a different
way.   We must discard deductive mathematics,  statistical
methods included.   We must employ the only available
alternative,  constructive geometry.   In the latter case,  we
have the following relevant results:

1)   The sense of "negentropy" is supplied as processes
undergoing harmonically ordered growth congruent with the Golden
Section's ordering of the visible manifold.

2)   This means that "negentropy" can be measured in terms of the
increasing number of discontinuities generated by the continuing
process of such harmonically ordered growth.   Mathematically,
this is expressed in the form of Cantor's transfinite functions,
as an harmonically ordered increase of the density of
discontinuities within some arbitrarily small interval of action
adopted as a unit of measurement.

3)   This means that "entropy" must be measured as reversed
"negentropy."   As life is the paradigm of "negentropy," death
and decomposition are the paradigm of entropy.  Yet,  entropy is
harmonically occurs in different geometric ordering than for
negentropic processes.

     That is sufficient description of the background to permit
us to proceed to the matter of applications to the design of new
cities.

                 Cities As "Negentropy Machines"
                 -------------------------------

     Successful economic processes belong to the class of
negentropic processes.

     On first examination of its physical characteristics,  a
successful economic process is typified by a continuous process
of increase of the combined quality and quantity of the standard
market-basket of physical goods consumed per capita.   This
presumes a corresponding increase of output by the operatives
producing these physical goods.   It presumes technological
progress's causing such increases of the productive powers of
labor,  and improvement of the varieties and qualities of
products.

     It is also an improved mastery of land-area.   This occurs
to the effect that less land-area per-capita is required to
sustain a population in a higher standard of living,  than the
land-area required to produce a relatively poorer standard of
living at an earlier time.

     So,  the proper mathematical function in the science of
physical economy is expressed in terms of rate of increase of the
population's potential population-density.   This function is
elaborated in terms of the set of set constraints identified
earlier.   It is a "non-linear,"  continuous function of the
general form of a Riemann Surface function.

     Assume that a city satisfying this function's requirements,
has reached the limit of population-growth built into that city's
design.    Let us consider the "equilibrium condition" so
defined.

     First,  as to population.

     The fecundity remains constant,  at the same rate after the
population-limit is reached,  as earlier.    So,  the limit of
population-growth is expressed in terms of the number of
households,  and the number of persons limited only by the number
of households comprising the total census of households.   The
"excess population" is deployed to populate new cities,
including some on Mars.

     Second,  as to employment.

     The labor-force is defined as a function of the total
population of labor-force age.   Of this,  initially,  on Earth,
about half should be employed as operatives employed in
production of household goods,  producers' goods,  or
development,  maintenance and operation of basic economic
infrastructure (transportation,  water-management,
communications,  production and distribution of energy-supplies,
and basic urban sanitation).   About one-tenth or more are
employed as scientists,  engineers,   in direct management of
production as such,  medical professionals,  or in teaching of
the young.   Unemployed members of the labor-force,  and persons
in other occupations,  combined,  are kept within the limit of
less than forty percent of the total labor-force,  preferably
less than thirty-five percent.

     Within this composition of employment,  several interrelated
shifts occur as both the level and rate of technological progress
are advanced.   A smaller percentile is employed in production of
households' goods,  relative to growth in the ration employed in
the production of producers' goods.    In production of
producers' goods,  there is increased emphasis on employment in
the machine-tool class of production.    The ratio of scientists
and related professionals to the total size of the labor-force
rises.   Gradually,  there is a shift of employment from
operatives' categories into science categories.

     In social life.

     As technology advances,  the average school-leaving age
rises in the direction of equivalence to a terminal degree in
physical sciences.   As the working-day is shortened,  the
leisure so generated is consumed largely in adult education;
this is aimed significantly at upgrading the technological
competencies of the labor-force as a whole,  but also for the
enriched development of the character of the adult individual,
through scientific "leisure hobbies" and participation in the
life of classical forms of art,  in addition to travel.

     Hence,  the "Sun" of our city is at the city's center,  a
complex of facilities for secondary and higher education,  for
conduct of classical fine art,  and similar activities,  situated
in a park and garden zone in the center of the city.   Knowledge
in the form of science and fine art are the heart of the city,
the driving-force of the city's development.    By affirming
this,  in such a fashion,  we make the development of the
character of the citizen to the fullest of its potentials the
mainspring of life within the city.

     Such design of the city,  defines a knowledge-intensive
society,  and knowledge-intensity as the driving force of the
city's maintenance,  growth,  and economic as well as cultural
development.    The energy driving the city,  is produced in the
outer orbit of the "outer planetary" region.   This supply of
energy is constantly increasing,  per-capita and per-hectare,
for the city as a whole.   The effective energy-flux density with
which this energy is applied to the target-areas of work,  is
also increasing.   Yet,  these energy-supplies,  their growth,
and the shaping of their application,  are always under the
conntrol of knowledge radiating from the city's "Sun."

     The administration and commercial functions of the city are
most proximate to the central park.   Here,  the density of land-
usage,  per-capita unit of human activity,  is at the highest,
and the structures,  correspondingly,   generally the tallest.

     As we move outward,  the density of movement per-square
hectare attenuates harmonically.

     Beyond the F# orbit separating the inner from outer city,
we reach first the orbit of densest land-use by the labor-force's
productive activities.   The three further orbits each represent
a less-dense employment per unit of productive activities,
including the power-generating complex for the city.

     Beyond the last orbit,  there is permanent agricultural,
forest,  and related uses of land,  until the outer boundaries of
the next city or township is encountered.   No suburban sprawl is
to be permitted,  for ecological reasons,  as well as economic
ones.

     Agriculture is at the verge of a fundamental revolution,
and the agricultural needs of permanent colonies on Mars will be
a goad to more rapid advancement in these directions.   The
amount of agricultural product per hectare is about to increase
by an order of magnitude,  through methods which popular opinion
today would,  somewhat inaccurately,  associate with large,
multi-story "hydroponics" factories.    The social system which
has served the United States so well,  family- and intra-family-
operated entrepreneurial farming,  should be protected and
preserved,  thus ensuring the best rate of improvement of quality
of product,  together with the highest rates of effective
innovation.

     Yet,  we know that the maintenance of highly productive
biomass,  in the forms of crops,  pasturage,  water-management,
and well-managed woodlands,  is essential to maintaining the
general environment.    The best way in which to accomplish this,
is to entrust this work to entrepreneurial farmers,  counting
this maintenance of cultivate farm,  pasture,  and forest land as
part of the necessary cost of agricultural production as a whole.

     It must be our object to break the pattern of suburban
sprawl,  driven only by speculative gains,  which is destroying
so much of the land-area of the United States today.   We can
effect all the qualities of beauty,  privacy,  and function,
which might be sought through modes of surburban sprawl,  in
well-designed new cities,  designed to remain viable for up to a
thousand years or more.    The initial investment per cubic meter
of volume of dwelling constructed,  will be much higher (at
first),  but the average annual cost of possession, in terms of
maintenance and amortization combined,  with be much less.

     The judicious channelling of very low-cost public credit,
loaned through the banking system and governmental capital-
improvements agencies and authorities,  will make this change in
construction policy feasible.   The accelerated demand for the
new types of materials and other products used for such
construction,  will expand the turnover and investment-rates in
such industries to the point of fostering a rapid rate of
technological advancement in those industries.   This increase in
productivity,  in a large sector of the economy as a whole,  will
rapidly lower the effective average physical costs of
construction,  for the city-building and kindred programs as a
whole;  the expansion of investment in advanced technologies in
that sector,  will spill over into the economy more generally.
Within less than a generation,  perhaps,  the costs of housing
and other construction for new cities' designs will fall to
levels of per-capita social cost below those of today.

     The heaviest increment of cost in the building of the city,
will be the emphasis upon building the deep sub-structure first,
and then putting the upper portion of the city upon that prepared
substructure.   This is the cheapest way of building sub-
structure of a city.   With the proper designs,  and use of the
proper materials,  this substructure will be cheaper to
maintain,  and to improve technologically,  than present
alternatives.    The combined cost of amortization and
maintenance of this substructural investment will drop to below
that of what is presently considered a conventional city.

     The utilities built into the city will last for centuries,
and will be cheap to maintain for per-capita unit of activity
which those utilities support.    The savings in movements of
persons and goods will be greater than the apparent added initial
costs of amortization of the investment,  with none of the costs
which the cities and their inhabitants of today endure in the
forms of street-traffic congestion,  pollution,  time delays,
and costs.

     It is not necessary,  in this location,  to detail the
technologies involved in building the city.   We know that such
things can be done with technologies existing or in sight today.
It is sufficient to supply the architects and their fellow-
professionals the set of criteria to be met,  and leave it to
such professionals to do what they do best.

     We know,  with a fair degree of certainty,  the general
nature of the scientific advances likely to occur during the next
hundred years.    A glance at some of the leading facts this
involves,  guides our attention to those principles which show
why our new city should endure in its original design for a
thousand years,  or perhaps even two or more thousands.

     For the coming fifty years,  inorganic physics will be
dominated by the development of controlled thermonuclear fusion
as mankind's new energy-source,  and by increasing use of the
technologies of "non-linear" electromagnetic radiation.   During
the first half of the next century,  the new levels of technology
will be associated with per-capita increases in energy-
consumption by up to a thousand times that of today:  space-
colonization will write "terawatts" for power-units,  where the
largest power-producing units today measure output in
"gigawatts."   Technologies of production will increase the
energy-flux density of process-applications to the levels of
coherent gamma-ray pulses,  and coherent "particle-beam"
radiation in the direction shown by the "free-electron" laser:
effective energy-flux density will increase more rapidly than the
quantity of energy consumed per capita.

     For thousands of years to come,  biological science will be
dominated by the presently emerged new science of optical
biophysics.   By the middle of the next century,   mankind shall
leap beyond the limitations of fusion energy,  to more powerful
technologies based upon what are now termed "matter/anti-matter"
reactions.    Gigantic "radio telescopes,"  many miles in
effective aperture,  placed in or near Mars' orbit during the
middle of the coming century,  will enable astrophysicists to
explore the most anomalous astronomical objects within our galaxy
and beyond,  and to assist thus in proving the discovery of new
physical principles,  previously unknown to physical science.

     Powerful fusion engines will enable mankind to reach any
destination within the region of the inner planets within days of
flight.   However,  even the extraordinary efficiency of fusion
power involves a delimiting factor of fuel-load on spacecraft.
Special tricks would permit limited forms of manned exploratory
flight into the region of the outer planets,  and development of
deeper-space terminals based on the logistics of the Mars colony
would assist the exploration of the outer region of the solar
system.    Yet,  manned deep-space flights beyond the solar
system must wait upon the development of a more powerful,  more
efficient propulsion system.    The mastery of what we call the
"matter/anti-matter" reaction,  is the visible pathway for
developing techniques for deeper-space explorations.

     So,  the next hundred years technological progress can be
summed up as shaped by two successive singularities in the
continuous development of improved "energy technologies."   This
implies,  as I stress now,  that there exists a "non-linear"
continuous function,  through aid of which we can project,
beyond a third and a fourth singularity,  into hundreds of years
yet to come,  and might do this with as much accuracy as would be
of any practical use to us in the coming decades' planning of the
design of new cities to be built within our solar system.

     With that in view,  one can return attention now to the
subject matter of forseeable changes in the life of our new city,
as a result of such technological progress.

     We know two things:

1)   We know that the definition of man,  as man is properly
defined by knowledge up to the present time,  will not change.
Through aid of optical biophysics' mastery of the spectroscopy of
the mitotic process,  we will be enabled to improve greatly the
maintenance and repair of the human organism,  to control the
aging of tissue to significant degree,  as well as achieving
early conquest of cancer,  and the most challenging kinds of
viral infections.   The increase of mean life-expectancies to the
age of 120 years or more,  and kindred extension of the upper-age
limit for defining the active labor-force,  are likely changes.
However,  no forseeable change would change the required mean
free-pathway of the motions of human beings.    The nuclear
family household must persist,  unchanged,  for thousands of
years to come.

     For such reasons,  the spatial organization of the new city
need not be changed from those specifications of spatial
organization which are optimal for today's technologies.

2)   Presently developed levels of knowledge in the Leibnizian
science of physical economy,  enable us to forsee how the
forseeable directions of advance in technology will introduce
modifications of technologies integral to the functioning of the
city as such.     The six constraints,  cited above,  for the
LaRouche-Riemann function in physical economy,  permit us to
forsee these changes with as much accuracy as is required for the
design of the new city.

     Essentially,   the spatial requirements of organization of
the city will not change.   What will change is the per-capita
(and per-square-meter,  and per-cubic-meter) quantity of energy
consumed,  and the effective energy-flux density of the use of
that flow of energy-supplies.

     Think of the spatial structure of the new city as the basic
structure of a machine.   This does not change.   Think of the
changes introduced as analogous to alterations of the tools
developed for attachment to that machine,  in company with rather
continual increases in energy-flows into the machine as a whole.

     All of the changes will take the form of a combined,
interdependent increase of energy-density and energy-flux density
per-cubic-meter in the volume of structure represented by the new
city as a unified machine for living.

     In designing the new city today,  the architects must think
clearly of both the kinds of modifications to be introduced to
the city's spatial organization of structure over the coming
centuries,  and think also of how we can ensure that the needed
kinds of improvements in energy- and energy-flux densities can be
installed with the least time and effort.

     Consider again, some things that will not change.   The
physical-geometrical function of a chair,  a bed,  a table,  and
of personal "space for mean-free-action" by persons,  in all
functions,  will not change.    The amount of fresh water
required will not exceed the proper design-limits specified for a
new city today,  even though there may be qualitative changes in
the technology of fresh-water management.   The amount of air
required will not change,  although cleaner air will be achieved
by aid of qualitative changes in technologies.

     Within the city,  and in travel to nearby population
centers,  a maximum speed of about 300 miles per hour achievable
with magnetic levitation,  will remain acceptable specification
for generations yet to come.   It is probably the case,
especially on Mars,  but also probably on Earth,  that supersonic
or even hypersonic speeds of continental travel of pressurized
cabins through long reaches of evacuated,  sub-surface tube may
appear during the next century.   This will not affect the
internal and nearby requirements for the new city itself.

     The spatial-design impact of the changes is forseeable.
Today's architects must simply leave room for installation of
such changes within initial structures,   and must provide the
ready access needed for effecting such installations with the
relatively greatest economy of labor.

     The harmonics of the design will never change.   What will
change is the level and rate of increase of effective negentropy,
per-capita,  and per-cubic-meter.

                        A Beautiful City
                        ----------------

     The general requirement must be,  that wherever each
function of human activity is to be served,  the form of design
employed shall be the principle of harmonic ordering congruent
with the Golden Section.

     This includes the proportions of rooms,  the relative scales
of the rooms of a dwelling-place,  the relations of windows to
room-sizes,  and everything else blended into an harmonic unity.
Here,  the architect must became at once a composer of classical
polyphony,  a painter with the informed eye of a Leonardo,  a
Raphael,  a Rembrandt,  and a physicist in the spirit of Kepler.

     Such harmonic composition will coincide with the optimal
agreement with the physiology of human least action.   It will
provide the optimal accoustics,  the optimal distribution of
light,  of air movement,  and so forth.   The physiological
requirements,  so addressed,  are consistent with the
psychological ones.

     Contrary to the cults of Romanticism and Modernism which
have spoiled our great western european tradition of classical
art,  nothing is beautiful unless it is consistent with harmonic
orderings based on the Golden Section.   Such is the beauty
inherent in all living animals and plant life.   Art must emulate
the principle of life on this account,  but it is not art unless
it does something more than that.

     The composer of classical fine art must start with
principles of beauty,  and must never conclude with any result
which is not congruent with beauty.   Yet,  this defines the
character of the particular medium in which the artist works;  it
does not suffice to define the stirring of that medium of beauty
as art.    Art is not a business of selecting by mere intuition
those random stirrings of the medium seen to have the pleasing
quality of beauty.

     Beautiful art is art because it is composed by an
accomplished artist.   What defines such a composer of art is the
exact same mental quality which defines the accomplished
scientific discoverer:  the development of the composer's
creative powers of mind,  together with the composer's moral
character.   The composer of great art works in the medium of
beautiful harmonic orderings as the scientific discovery works in
his or her medium.   The same powers of mind,  perfected to such
work in the one medium,  or the other,  are at work.

     It is this creative endeavor,  in the medium of beauty,
which defines great art.

     For that reason,  the general quality which all great art
shares in common,  in whatever artistic medium,  is that it
contains nothing not fully susceptible of intelligible
representation,  as I have identified "intelligible
representation" above.   Furthermore,  the entire composition is
itself susceptible of such intelligence representation,  to such
effect that the uniquely creative features of the development of
the composition are the kernel of the artistic idea.

     There is never anything arbitrary,  "romantic,"  in
classical art.   It is always delimited by the principles of
harmonics associated with the Golden Section in visual space,
and perfect well-tempering in classical musical composition.   No
principle contrary to that definition of classical beauty,  no
deductive sort of arithmetic principle (e.g., the twelve-tone
system of the musical "modernists),  must be tolerated.   The
"idea" associated with classical art is never akin to what we
encounter so often in the romanticist "program notes"  of the
concert program,  record jackets,  or art exhibition.   The idea
of a classical artistic composition is the elaboration of the
specifically creative feature of the composition's development.

     A great architect,  like a great classical painter -- such
as Leonardo or Raphael -- is thus a professional who might have
become a great musical composer or performer,   who applies the
same intelligible creative principles to a different medium.
The architect's medium is the humanistic science of physical
economy expressed as art,  governed by the same principles as
great classical art.

     We must free ourselves of the heritage of both Kant's
"Critique of Judgment" and the evil Professor Karl Savigny's
arbitrary,  irrationalist separation of science
("Naturwissenschaft) from the arts ("Geisteswissenschaft").  This
means,  inclusively,  that in architecture,  there is no proper
distinction between "art" and "function."   It means,  as I have
stressed throughout this report,  that the principles of
classical artistic composition are always in implicit agreement
with the best solution to a problem of function,  so much so,
that wherever a purported functional design deviates from the
rigorous standards for classical beauty in artistic composition,
the deviation represents an elementary error in the principles of
functional design adopted.

     All architecture is a machine for use by human beings.  It
must agree with the requirements of the whole human being.   This
wholeness is expressed by human activity in its wholeness.  All
human activity is activity directed by the self-developmental
characteristics peculiar to the human mind.   As I have shown as
a matter of principles,  both the physiology of individual mean-
free-pathway least action,  and the characteristic human creative
mental activity,  are forms harmonically ordered in congruence
with the Golden Section in visual space.   That architecture
which is defective as classical art,  is therefore also defective
in function.

     Reference Johannes Kepler's famous dissertation on the
subject of the snowflake.   Focus,  within that paper,  on the
discussion of the constructions by the bees,  constructions which
are excellent for bees,  but not for human beings.   The
construction is not harmonically ordered in congruence with the
Golden Section.   This case illustrates an absolute separation in
principle,  from architecture for lower forms of life,  and for
humanity.

     The most sensitive architects and students of classical
painting are more notably aware of the fact,  that the
experiencing of the visual space in which persons' activity
occurs,  has an important psychological effect upon the persons
experiencing that organized space.   Leonardo and Raphael are of
outstanding importance in any systematic study of this matter,
particularly so because their own recognition and use of this
principle is so directly,  immediately situated with respect to
the underlying principles involved.

     In the experiencing of the organization of visual space,
our minds draw upon the same kinds of powers of judgment we
experience in the beauty of well-performed classical polyphony.
Today,  because of important researches into the organization of
the relationship between the eye and the visual cortex of which
it is functionally an integral part,  we can understand the
validity of Leonardo's principles of hemispherical perspective in
a refined way.   Although,  to the extent of my present
knowledge,  the study of the accoustical functions of the brain
are less well-mapped than those for the visual cortex,  we know
that Riemann's approach to the physiology of hearing was sound on
principle;  and,  from knowledge of well-tempered polyphony,  we
know that the principles adduced for vision are congruent with
those for the sense of beauty in hearing.

     So,  we know,  that the same principles of creative
composition expressed by such as Bach,  Mozart,  Beethoven,
Schubert,  Chopin,  Schumann,  Verdi,  and Brahms -- although not
those of Romantics such as Lizst and Wagner -- express in a
musical medium the same underlying,  proper principles of a great
architectural composition.   We should speak,  without a sense
that we might be indulging ourselves with mere metaphor or even
hyperbole,  of architects as composers.  We should say this with
an eye cast directly toward Leonardo and Raphael,  but also with
a sense that the musical reference is not merely analogy.

     The standard should be: "intelligible representation of a
beautifully artistic fulfilment of nothing but the functional
purpose of the construction."   The architect must start with
function.   By applying "Keplerian" harmonics to the
understanding of that human function as an integrated whole,  the
problem to be solved,  function,  is stated also,  and by no
accident,  in precisely the form which transforms a science of
architecture into a practice of classical artistic composition,
without moving one millimeter from science.

     The creative solution is always in response to a problem
posed in terms of satisfying the need of a human function,
rather than decoration superimposed,  as a kind of flamboyance,
upon the structural "cake."   No arbitrary sort of "pleasing
effect" is to be sought as mere decoration.

     Since the architect is a human being,  as the great
classical composer is a musician,  the architect designs by aid
of travelling in his imagination through each mean-free-pathway
activity of the persons inhabiting the city.   He visualizes,  in
this imagination,  using each part of the city for one or another
of the functions of which the totality of their lives are each
composed.   He does this with a refined eye,  doing from his more
advanced standpoint in professional knowledge,  more or less what
I first learned to do in economic science standing,  still at the
age of fifteen,  at the dinker's bench in that slipper
 "function."   It means,  as I have
stressed throughout this report,  that the principles of
classical artistic composition are always in implicit agreement
with the best solution to a problem of function,  so much so,
that wherever a purported functional design deviates from the
rigorous standards for classical beauty in artistic composition,
the deviation represents an elementary error in the principles of
functional design adopted.

     All architecture is a machine for use by human beings.  It
must agree with the requirements of the whole human being.   This
wholeness is expressed by human activity in its wholeness.  All
human activity is activity directed by the self-developmental
characteristics peculiar to the human mind.   As I have shown as
a matter of principles,  both the physiology of individual mean-
free-pathway least ac