S. N. AFRIAT on the River Non Il quadrifoglio

S. N. <strong>AFRIAT</strong>
on the River Non
foreword by Paolo Vivante
Il quadrifoglio

On cover:
Watercolour sketch of
Villa Solaia, Siena,
by the author, c. 1955
The 4-dimensional
hypercube Logo
and other graphics
are outputs from
QuickBASIC programs
by the author

on the River Non

By S. N. Afriat
Production Duality and the von Neumann Theory of Growth and Interest.
Meisenheim am Glan: Verlag Anton Hain, 1974. Pp 86. Mathematical
Systems in Economics, 11.
STUDIES IN CORRELATION: Multivariate Analysis and Econometrics (with
Gerhard Tintner and M. V. Rama Sastry). Göttingen: Vandenhoeck and
Ruprecht, 1975. Pp 150. (Contributing Part I: The Algebra and Geometry
of Statistical Correlation. Pp 100). Angewandte Statistik und Ökonometrie.
Combinatorial Theory of Demand. London: Input-Output Publishing Co.,
1976. Occasional Paper No. 1.
THE PRICE INDEX. Cambridge University Press, 1977. Pp xvi + 187
Demand Functions and the Slutsky Matrix. Princeton University Press,
1980. Pp xii + 269. Princeton Studies in Mathematical Economics, 7.
The Ring of Linked Rings. London: Gerald Duckworth & Co Ltd, 1982.
Pp xviii + 126. (Mathematical and computer recreations, theory and
history of Chinese Rings, and its various manifestations, binary dividers,
Lucas’s Tower problem, error correcting code, Dragon Curves, &c.)
Logic of Choice and Economic Theory. Oxford: Clarendon Press, 1987.
Pp xiv + 577.
LINEAR DEPENDENCE : Theory and Computation. Kluwer Academic /
Plenum Publishers, 2000. Pp xiii + 169.
The Market : equilibrium, stability, mythology. London & New York:
Routledge, 2002. Pp xv +128. Routledge Frontiers of Political
Economy, 44.
The Price Index and its Extension—A chapter in economic measurement.
London & New York: Routledge, 2004. Pp xxx + 421 Routledge
Frontiers of Political Economy, 65.
On the latent vectors and characteristic values of products of pairs of
symmetric idempotents. Quart.J. Math. Oxford 2, 7 (1956), 76-8.
The Cube. In Art Has Many Facets, edited by J. MacAgy, Fine Arts
Department, University of St. Thomas, Houston, Texas, 1963.
People and Population. World Politics 17, 3 (1965), 431-9. Japanese
translation, with foreword by Ambassador Edwin O. Reischauer: Japan-
America Forum 11, 10 (October 1965), 1-28.
Graphic A-Mazes. Creative Computing 6, 6 (June 1980), 124-7.
On the constructibility of consistent price indices between several periods
simultaneously. In Essays in Theory and Measurement of Demand: in
honour of Sir Richard Stone, edited by Angus Deaton. Cambridge
University Press, 1981, 133-61.

on the River Non
S. N. <strong>AFRIAT</strong>
foreword Paolo Vivante
Il quadrifoglio

© S. N. Afriat 2006
First Edition April 2006
ISBN 88-7841-215-5
Il quadrifoglio
Stampato dalla Tipografia NUOVA IGE - Empoli
nel mese di aprile 2006 per conto della IBISKOS di A. ULIVIERI
di Alessandra Ulivieri
Sede: Via S. Lavagnini, 40 - C.A.P. 50053 Empoli (FI)
Tel. 0571 79807 (2 linee) - Fax 0571 700633
e-mail: e-mail@ibiskosulivieri.191.it
http://www.ibiskosulivieri.it
Fotocomposizione PHOTOCHROME - Empoli
2006

Siena , 15 April 2006
Bookshop, Via San Pietro, 19
tel: 0577 226 594
fax: 0577 219 686
info@bookshopsiena.com
www.bookshopsiena.com
s.afriat@gmail.com
The 4-dimensional hypercube Logo and other graphics
are outputs from QuickBASIC programs by the author

In memory
Elena de Bosis Vivante
W
atercolour sketch of
Villa Solaia, Siena,
where I visited a few days
every year or two since
soon after the war. Calling
for lunch Elena said
“Leave it, it’s finished—
don’t touch!” and that is
how it remained.

Foreword
T
he writing of poetry is not a profession. It
cannot be closely identified with a certain
vocation or activity, and need not be an occupation
to be consistently pursued through a lifetime. The
poetical faculty is at the roots of feeling and thought,
and will show itself in unaccountable moments, and
find its own modes of expression.
The poems of Mr Afriat seem to be proof of this
principle. He is a mathematician and scientist. He
does not keep up with literary currents or fashions,
though certainly he is familiar with the language of
this age. He simply has an embracing sense of life,
and his poems are expressions of that awareness and
sensibility.
Troubles of youth, the sensation of morning
light, or revelations of a sleepless night; the world as
a bare strand, cradled by the baffling hand of space,
or overswept by the flux of the ages; the charm of
intellectual thought, that would fain extract a form or
meaning from the elusive sediments of reality; the
spell of a silent fleeting encounter—these are some
of the motives of Afriat’s poems.
In no form but that of poetry can there be
expression of these feelings, thoughts, ideas,
rendered as they are in their essential simplicity,
ix

stripped of accidental contours, bared of extraneous
matter. For instance in the poem—
Where is the end to sadness?
There is no end.
It blows through the world
Like a cold wind,
Set in motion
On the friendless frontiers
Of existence,
Where death and life
Confront each other
Out of their solitudes.
each line sets in with a native rhythm of its own,
with the cadence which must run through a selfcontained
sentence no less than in a lonely word. We
might say this is the rhythm of the thought itself.
Brief as they are, these poems have a wide
range. They seem to branch into a whole life
experience. The dates and factual occasions in which
they were written are forgotten but the moments
stand out and rebound in time.
In these poems, sharp sadness goes with the
vision of beauty. What is that vision since no theory
explains its striking vivifying power? Especially
from time to time it is gathered in lines of poetry;
Keats tells us about it in the opening of Endymion
and Shelley in his Spirit of Delight Wallace
Stevens in Susan and the Elders. Those feel it best
who also have the tragic sense. Afriat, in his own
way, tells us why.
Austin, Texas P. Vivante
1963
x

Preface
T
hese items go back to schooldays and about
twenty years after. Nothing was done with them
except they were looked at occasionally from an
ever increasing distance. They were not thrown
away, and of course one may wonder why not. Now
the distance is such that, though I once knew the
author quite well, he has become a bit of a stranger,
like a friend or an enemy one has not seen for a long
time.
The last addition was made in Houston, Texas,
in the 1960’s. Stirred by this and thought of the
dedication, I put them together much as they are
now. My old friend Paolo Vivante—the dedication
is to his mother—was in Austin at the time and
wrote the foreword. Then it all joined a heap packed
for travel, from which it hardly came out of since.
A cause of excavation was arrival of one of
those early PCs, the Exidy Sorcerer, 1979. That
computers are useful has an ordinary acceptance,
and for some they are just that. But there is another
community in which a different government
prevails, where means have some confusion with
ends. Working with the gadget is self-sustaining and
requires no other purpose. After having discovered
xi

that the Sorcerer can write, a project was needed and
here one was.
This is the result. WP is commonplace now, but
then it seemed amazing that a single ‘command’
could cause everything to be printed from first page
to last!
January 1982
PS This is the second excavation, where the title
used previously is replaced by another, which may
stand well, even best, without comment or
explanation. However, though this is not to limit it in
any way, it does have one of sorts. It could be from
the sticker that occurs on apples in Italy that says
“Val di Non”, and if there is a valley quite likely
there is a river. Or it could be from a certain memory
of Wad’Noun in the Anti-Atlas.
The fragments are joined this time with graphic
items, in a way counterparts, arbitrary survivors
located in, or on, odd envelopes, the back of a bus
ticket, or propped up somewhere.
May 1990
PPS The edition which included sketches
disappeared, and here is another without those, done
with new printing facilities.
January 1995
PPPS Another, now with a reproduction in colour of
the watercolour sketch done at Villa Solaia.
April 2004
xii

PPPPS Book-design features encountered with two
of my books published recently have given this work
a new look.
I have to thank Jennifer Storey, of SATOR
SIENA, who was to publish this work but her printer
could not bind a work so slim the way wanted, on
the model of a similarly slim work I had from
Margherita Sergardi, who now also is thanked for
leading us to her publisher, and now also very much
is Alessandra Ulivieri.
March 2006
xiii

Contents
Foreword ........................................................... ix
Preface ................................................................ xi
This morning .................................................. 1
Where is the end ............................................ 2
Encounter ........................................................ 3
Image .............................................................. 4
Awake ............................................................ 5
Luna ............................................................... 6
Taking stock ................................................... 7
Aftermath ....................................................... 8
Purpose ........................................................... 9
A place to stand ............................................ 10
Jerusalem ...................................................... 11
Business Machines ....................................... 12
The Program ................................................. 13
Mathematics ................................................. 14
Remember ..................................................... 15
Question the Rose ........................................ 16
The Thorn ..................................................... 17
Moon City .................................................... 18
Travel note ................................................... 19
The Beast ..................................................... 20
Apocalypse ................................................... 21
Meeting ........................................................ 22
Free dream days ........................................... 23
Elena ............................................................ 24
xv

on the River Non

This morning
T
his morning, waking early,
A curtain was awry,
To show the sudden radiance
Which was the edge of dawn.
Which with frames of shifting grey
Set the rimmed blue sky,
And with blades of shaded gold
Split the colour’s edge,
And sparkled the green dark throng of rustling leaves
With running silver.
While birds, with slow exchange,
Lowly rang the air
With their first song.
42 Wellington Square Oxford 1951
1

Where is the end ?
W
here is the end to sadness?
There is no end.
It blows through the world
Like a cold wind,
Set in motion
On the friendless frontiers
Of existence,
Where death and life
Confront each other,
Out of their own solitudes.
2

Encounter
I
am grieved to madness
Since we met,
In that distance,
Speaking just an empty word
For no other would do.
We had reluctantly smiled,
And were surely acquainted.
Then as we separated without will,
From the rending of peace
In the tremor of your turning,
I knew we were bound
By those hidden cords,
That tear in the parting.
And now I am bleeding.
3

Image
M
ad one,
What enchantment
Stung your wits
And made you a toy
Of torments.
White flame
Shed radiance,
Radiance streamed
And flooded the world.
But where there seemed warmth
Was found a thoughtless stone,
Where walking adult gods,
The mere twisted corpses of men.
And before the sublime
Was glass.
In laughter,
Hard silence
The singing on the rack.
With broken images
Sinks one existence,
But in some way
Is a certain rebirth.
4

Awake
T
orn in what dim centres,
Last night I had a revelation
Of childhood memories.
A dark ocean rose, and flooded,
And it seemed it was to sink me
To a deep of soundless sleep.
So it seemed.
But then turning,
Quickly the tide ebbed,
And I was left staring
Into the hard night,
Wondering for a sorrow
I could not understand.
5

Luna
O
uter sun once balming the inward eye,
Burning radiance shifts its flux,
Darkness now darkens outer light,
Inner moon shines in the outward eye.
Source in satellite mind eclipsed,
In kaleidoscopic spread transforms,
Where clarity might have straightly ruled
Is throned the tortuous law of hell.
Bound in drives of failing will,
Thought unfolds a giddy orbit,
On creaking fibres of sickened nerves
Supporting insupportable executions.
Tautness in a languid frame,
And joints in jangling disjoint,
A subtle spring is wound up tight,
And all a searing lassitude.
While just faintly stirring to reach
Where earth and rebirth are all cut out,
Into the floorless tomb of the unborn,
The reverberating catacomb
Where, in the inner circle,
The final centre,
A sinking gyroscope
Heaves, and spins.
6

Taking stock
S
ee the closeness to the stars
Spread in deep of darkness shining;
Silent words of greater worlds
Than words can fill.
Take stock of the stars and,
Through their serene indifference, fall
Each sickened thought to sleep,
And in the laughter of space,
Let flicker with their radiance
The faltering will.
7

Aftermath
O
n the roving globe, the wrinkled Earth,
Where runs the twisted course of memory,
There could be found a certain coast,
Set against sea, welcoming spreading sky.
Soaring pillars of rock surround its aspects,
And on its shore myriad varied creatures,
Winding shells, and old and shapely stones,
Sprinkle a carpet, lacing pools and crevices,
Glittering, and casting multifarious hues.
In a cavern there, murmuring with the commotion,
Old Man dwells still, and spells the passing ages.
8

Purpose
O
n the long shore,
Where the wide ocean rushes
On warmed sands,
There linger traces:
—how creatures came from the formless depths
And, enthralled by a distant music,
Entered a new sea.
They forgot their
Fish-like character,
Swimming though they were
In a sea of questions.
They contained themselves
In dreams which they called purpose,
As in strong ships
Afloat in darkness,
Riding filament currents of the boundless flux
—for a moment
9

A place to stand
G
ive me a place to stand
And I shall move the Universe
—said Archimedes
in comment on his
Principle of the Lever
While Prophet Moses
standing by the Law he submitted
moved Man
10

Jerusalem
C
ity of longing,
On earth
And among the stars,
Where was set forth
The crystal of the law,
And the veil was rent
On a new age.
Dwelling
Drenched in time,
Melted in eternity.
In construction,
Fragile,
Like other cities.
In destruction
At the summit of transformation,
Irreducible.
11

Business Machines
I
n the multiblink of machines
Transferring checks,
Computing margins,
In the strict march
Of perfect competition,
The fountain of play beyond purpose
Dies.
Now, each and all alone,
All arrayed against each,
Each set against all,
Step to the dance
Of interdependent markets.
Silence in the wayward streets,
Gardens are empty,
All are intent, reduced
In the ultimate multiplicity
Of single optimality.
And lubricated by smiles,
Friction fades,
As men are logically digested
To meticulous functions.
Spare parts all,
With the terror of every spare part
—that it be replaced.
Houston, Texas, 1964
12

The Program
DATA It might be really pointless
DATA To list a page or two of primes.
DATA But there are compulsions to continuations,
DATA The next that is always to be had,
DATA The right libration of a machine,
DATA The reappearance by which we know a name,
DATA The daily round, the beat of clocks,
DATA The programmation of all that exists
—Keep Going!
13

Math
W
rought in thought,
Severe ravishment of scheme,
Immutable flowers
Of intellectual dream.
Set in symmetry,
Cast in the wide
Wordless matrix,
Cool impregnation
Of combination’s empty form.
Imponderable lattice where to
Play an unknown game
And for duality with death’s power
Life’s canonic form explain
14

Remember
R
emember the pain of youth,
Caught in the wilds of longing—
One would see fair forms in distant clouds,
And hear the trumpet falter in the wind
Summoning endurance
15

Question the Rose
Q
uestion the Rose
Witness of the ages
In whom the first dawn glows
And whose truth no time assuages
16

The Thorn
W
hen first I struck your beauty
I did not see the thorn,
And touching so was torn.
And thus learnt I love's levity
In love's long sought felicity
—and yet still not to mourn
17

Moon City
H
ighway turns
A ribboned elegance,
Wheels’ steady singing hiss
On sustained hardness,
Machine flocks
Clockwork recurrent surge
To complex signals,
Trim signs composing fantasia,
Feeding, filtering, loop
The loop.
Parking lots winding the skies
Immersed in a sea ablaze
In advertising voltage.
Streets bare of human tumbling.
Towers of glass and steel
Are majesty,
Profit the holy ghost.
The Moon invested
In a corporation.
Through the door
The old Beast,
Feeling the cold,
Is not so sanguine,
And much more mean
18

Travel Note
B
erber maidens, with dark tresses,
And brightly coloured, flower covered dresses,
Move like queens of the countryside,
Stepping quickly, with a gay stride,
Eyes deep with passion, and laughter—
Rather striking the wayward stranger
Travelling the road to Taroudant
19

The Beast
N
ow the old blind Beast roams near,
Gentleness lies a crushed flower,
Love is melted in a tear
And Wisdom gone to her tower.
How the wind runs through empty shrouds,
Heavy with Time’s calumny.
Joy remains locked in clouds
Until fails the Beast's tyranny
20

Apocalypse
M
ankind dissolves,
There stands each alone,
All arrayed against each
Each set against all.
Perhaps in the last debris
Shines just a ray,
A fire to rush through the tortured realm
All alight with a united longing,
Pain to be swallowed up in
Universal expectation
21

Meeting
N
ow that they have met
They can go together,
From the lonely road without end
Through the changing weather
Departing from that road
To the garden under the sky,
Where no dark cloud weighs its load
Nor cruel bird sends its cry
22

Free dream days
T
hose long free dream days,
Shining skies of unbroken youth,
Before there gleamed the smile
To loose the slender line of truth.
Then blows struck in what mad contest,
How the leaves scatter,
Spreads the clouding grief of sorrows protest
23

Elena
E
lena,
How could you,
Such to us who know you
As a brightness of our kind,
Beautiful as an austere tree
Straight and slender,
Whose branches murmur with
Perpetual currents,
Whose sense is a blade
Edged with knowledge,
Shimmered with subtle wit,
Of metal that is
One with kindness
Gentle as the wind,
How could you,
Heroic as an ever present star,
Ever cease to be with us
24

S
ydney Afriat graduated in Mathematics from
Pembroke College, Cambridge, with a period at
Aerodynamics Division, National Physical
Laboratory during World War II, after which a
D.Phil. at Queen’s College, Oxford. Work with
Richard Stone in the Department of Applied
Economics, Cambridge, 1953-56, initiated his activity
in Economics. Following time as Lecturer and
Research Fellow in Mathematics at the Hebrew
University, Jerusalem, 1956-58, the years 1958-62
were in Princeton. He then taught in Economics and
Mathematics at Rice University, Houston, and was a
Visiting Fellow in Economics at Yale. Beside
teaching at Purdue, North Carolina, Waterloo and
Ottawa, subsequent years include intervals as
Member of the Mathematical Sciences Research
Institute, Berkeley, Visiting Fellow at All Souls
College, Oxford, Izaak Walton Killam Memorial
Fellow, Canada, Academic Visitor at the London
School of Economics, Visiting Fellow at Macquarie
University, NSW, Visiting Professor at the Institute
of Social and Economic Research, Osaka, and Jean
Monnet Fellow at the European University Institute,
San Domenico di Fiesole/Firenze. Most recently at
Bilkent University, Ankara, before becoming
associated with University of Siena. Author of books
and articles to do with Mathematics and Economics,
beside scattered other items.
28

The Tower Puzzle

“Brief as they are, these poems have a wide range.
They seem to branch into a whole life experience.”
P. Vivante
Austin, Texas, 1963
“… his work is a classic illustration of how much we
learn from new ways of thinking.”
Angus Deaton
Dwight D. Eisenhower Professor
of International Relations
Professor of Economics
Princeton University, USA
“Sydney Afriat belongs to that select group of
economic theorists who have become a legend in
their own times. There is such a thing as “Afriat’s
Theorem”, which has become part of the staple for
students of microeconomic theory. … Moreover, he
may belong to another select group of prose stylists
who are also masters of some aspects of the
mathematical method and its philosophy.”
K. Vela Velupillai
Journal of Economics, March 2004

English SOLITAIRE: In eighteen
The game called Solitaire pleases me much
… I like to do it backwards …
Gottfried Wilhelm Leibnitz
17 th January 1716

Stampato dalla Tipografia NUOVA IGE - Empoli
nel mese di aprile 2006 per conto della IBISKOS di A. ULIVIERI
di Alessandra Ulivieri
Sede: Via S. Lavagnini, 40 - C.A.P. 50053 Empoli (FI)
Tel. 0571 79807 (2 linee) - Fax 0571 700633
e-mail: e-mail@ibiskosulivieri.191.it
http://www.ibiskosulivieri.it
Fotocomposizione PHOTOCHROME - Empoli

“Brief as they are, these poems have a
wide range. They seem to branch into
a whole life experience.”
P. Vivante
Austin, Texas, 1963
“… his work is a classic illustration of
how much we learn from new ways of
thinking.”
Angus Deaton
Dwight D. Eisenhower Professor
of International Relations
Professor of Economics
Princeton University, USA
“Sydney Afriat belongs to that select
group of economic theorists who have
become a legend in their own times.
There is such a thing as “Afriat’s
Theorem”, which has become part of
the staple for students of microeconomic
theory… Moreover, he may
belong to another select group of
prose stylists who are also masters of
some aspects of the mathematical
method and its philosophy.”
K. Vela Velupillai
Journal of Economics
March 2004
Prezzo € 12,00
(IVA compresa)

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