NONPLUS

S. N. AFRIAT
NONPLUS
— fragments
an accident in biography

Sketch on cover:
the River Cam
Summer 1948
The 4-dimensional
hypercube Logo
and other graphics
are outputs from
QuickBASIC programs
Tentative hardly begun project

NONPLUS—fragments

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 591.
LINEAR DEPENDENCE : Theory and Computation. Kluwer Academic / Plenum
Publishers, 2000. Pp xiii + 169.
The Market : equilibrium, stability, mythology. Foreword by Michael Allingham.
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. Foreword by
Angus Deaton. London & New York: Routledge, 2004. Pp xxx + 421 Routledge
Frontiers of Political Economy, 65.
On the River Non. Foreword by Paolo Vivante. Empoli: Ibiskos di A. Ulivieri, 2006. Pp.
xvi + 33. (Twenty-four poems, a watercolour, graphic outputs from QuickBASIC
programs, and other items.)
Economics and the Price Index. With Carlo Milana. Foreword by Angus Deaton.
London & New York: Routledge, 2008. Pp xx + 263
sul fiume Non / on the River Non. Second edition with translation into Italian by Anna
Maria Cipriani (Italian Embassy, London), translator of Charles Van Doren A
history of knowledge, Past, Present, and Future / Storia della conoscenza. Gli
eventi, le persone e le conquiste fondamentali, Roma: Armando 2006. Siena:
SATOR Siena, 2008. Pp. xxvi + 94.
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

NONPLUS
— fragments
an accident in biography
S. N. AFRIAT

© S. N. Afriat 20??
Piazza dell’Abbadia, 4 53100 Siena, Italy
+39 0577 289322 +39 339 417 8518
s.afriat@gmail.com www.econ-pol.unisi.it/~afriat

Siena , 24 April 20??
BookShop, Galleria S. Pietro 19
tel: 0577 226 594
fax: 0577 219 686
info@bookshopsiena.com
www.bookshopsiena.com
The 4-dimensional hypercube Logo and other graphics
are outputs from QuickBASIC programs by the author

For
Pilù
In her memory
W
e met Summer 1963 in Siena
married 26 November 1965
Pilù died 24 April 2004

Foreword
?
ix

A
late time may be good for
going back to the early time,
and to even before . . .
x

Preface
T
his book may deserve explanation. The original Non—
from on the River Non published by Ibiskos di A.
Ulivieri, 2006—24 poems, a watercolour, graphic outputs from
QuickBASIC programs and other items—has been joined with
a fragmentary Plus, to make NONPLUS—meaning “state
of perplexity, standstill”, according to OED—as puts it all in
perspective in the simplest way to be elaborated now and later
to some extent.
“Impossible!” I always said to recurring suggestions about
doing a biography subsequent to observation about my
scattered life, though I may some time have allowed doing
fragments—something of the sort is what we have now.
People and places are a main stuff of biography, beside
doings that here also have some scatter.
For the additional Plus, the original one watercolour of
Solaia of early 1950s is joined by works starting from time at
school followed by fairly recent products with a Math or
Computer connection.
Then writings representative of different branches of
interests, Math, Econ and Math/Econ, are dealt with. These are
selected for reason of being short, or favourite in some way, in
the case of two.
The third is unfortunately neither short nor a singular
favourite, but declarations for its subject—the “Afriat’s
Theorem” of the recent “Two New Proofs …”—make it
“celebrated”. A celebrated theorem—that’s pretty good! Is
xi

Euclid actually celebrated, or Pythagoras, and how do you
celebrate a theorem? Here we have a go.
For the Math, an early paper in my original concentration
Linear Algebra is included for being elegantly short, and
complete,
Serving for Econ is my favourite “Market & Myth”, also
included in The Market: Equilibrium, Stability, Mythology,
Routledge 2002, representing a chapter of economic teaching
as a hangover from prehistoric culture..
I am aware of several persons who collectively somehow
influenced or brought about the present project. First there is
Marisa Casale who had a new book lying in her workshop and
mentioned another to do with Spannocchia. That touched
familiarity going back decades, to a visit with Pilu to Nando
Cinelli in Detroit in 1965 just after we had married, and visits
to Spannocchia seemingly almost every year after that.
Going to the publisher’s studio and meeting Jennifer
Storey, I bought the book written and illustrated by Pascale
Quiviger then living at Spannocchia, so that prompted a call to
Francesca and Randall and a visit. At which point, I forget
exactly how it happened, I acquired the status, and stimulus, of
being one of Jennifer’s authors—at least for a while! This book
is a descendant of what I started then.
The mentioned poems are the starting point for this
project. These 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 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 in the recent publication. My old friend Paolo
xii

Vivante—the dedication inscribed in the publication of 2000 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 needs no other
purpose. After having discovered that the Sorcerer can write, a
project was needed and here one was. That was 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—surely the command of the Sorcerer!
In a further excavation the title used previously is replaced
by On the River Non, 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 rather from a certain memory of Wad’Noun in the Anti-
Atlas to be expanded here.
The fragments were then joined 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.
The edition which included sketches disappeared, and was
replaced by another without them, done with new printing
facilities. Then came another, with a reproduction in colour of
the watercolour sketch done at Villa Solaia.
The encounter with Jennifer Storey brought forth yet
another edition where poems were joined with the main of
everything in view in the present work. My first pause came
when I understood that—somewhat related to her main
xiii

specialization as a restorer of antique books—her books were
on the side of luxury and splendour, numered, signed, on
special paper, &c, which I felt (and perhaps she felt) did not
suit the freakish disjointed idiosyncratic character of my
material. Also I gathered I would be expected to assist in the
distribution—entirely inconsistent with the view of publication
as abandonment. So the project became put aside. Then the
material was split in two parts, the original poems, with which
it all started and which have now finally been published, and
the remainder, originating the present work. A significant
addition is the section with Memory as heading, perhaps most
interesting for some.
I have to thank Jennifer Storey, of SATOR SIENA, who was
to publish the poems but her printer could not bind a work so
slim, 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,
who published the poems book, and now perhaps this
successor.
F
or a fragment about the author, instead of ramble
without obvious limit unless it be another volume, what
better than the Acknowledgements statement in my
book The Price Index and its Extension: A chapter in
economic measurement, Routledge, 2004, which gives the
thread of a story? Here it is, following added preliminaries.
The uninitiated need to be warned that ‘the true index’ is a
central thing in the subject, theoretically at least. It was at first
to give a name for the book to make it different from “The
Price Index” which I had already published, Cambridge 1977.
Hence the start represents effort at wit not readily appreciated
by the unwarned and uninitiated.
What is that subject that had attention stretched over a
century? Kurt Gödel, whose notorious Theorem nonplussed the
mathematical world—a subject for mourning more than
xiv

celebration—would drop in at the house where I lived when
first in Princeton and once asked me what I was doing. After
my attempt to give an answer he said “That must be awfully
difficult.”
Another attempt is supplied on the half-title page:
“A theft amounting to £1 was a capital offence in 1260,
and a judge in 1610 affirmed the law could not then be
applied since £1 was no longer what it was. Such
association of money with a date is well recognized for its
importance in very many different connections. Thus arises
the need to know how to convert an amount at one date
into an equivalent amount at another date. In other words, a
price index.”
Extensive thought and theory about price indices has
expanded (inflated, one may think) over the decades and a
great number of economists have each contributed a word, or
volume.
To continue with the Acknowledgements quotation:
“For a true index of debts accumulated over half a
century I should make a start at the beginning, with several
persons I should blame for the initiation that has lead to
this volume.
At the very start is J. R. Bellerby, at the Agricultural
Economics Research Institute, Oxford, during 1950-53,
when I had been awarded a Studentship to be his research
assistant in work related to the Agriculture and Industry
Enquiry. I had been a student in mathematics and this was
my first encounter with the economics profession.
A next encounter was with Bob Clower, who came to
see me where I lived in the corner of Wellington Square
the sun never reached with some problem about a matrix.
My thesis was on Matrix Theory and economists were
beginning to have problems with matrices. He said then he
xv

hoped he was not disturbing me and when he turned up
again recently in Siena, more than half a century later, I
told him he had. After that I got to know other students in
economics. About to leave Oxford, I went to say goodbye
to Dr Burckhardt at the Institute of Statistics and, expecting
to take a job in mathematics, mentioned I would be sorry to
give up economics altogether, whereupon he drew my
attention to advertisement of a position at the Department
of Applied Economics (DAE), Cambridge, three days
before closing date.
So the scene changed again to Cambridge where I had
been an undergraduate, and work with Richard Stone, Alan
Brown, and Robin Marris at DAE put me on a path going
towards this book, as also have associations with Angus
Deaton, Terence Gorman and Amartya Sen which began
about that time.
I should also mention Sir Roy Allen for a contact which
though infrequent has been many-sided, including
reviewing each other’s books. I am indebted to him for
getting together with Nuri Jazairi, who had been his
student at LSE and was brought up on my early index
number papers.
Despite that any data I may actually use is more a matter
of form taken out of the air than any record of historical or
other statistics, J. S. G. Simmonds, Codrington Librarian at
All Souls, beside kindness and conviviality during 1981-82
for which I thank him, also provided me with Bishop
William Fleetwood’s Chronicon Preciosum Or, An
Account of English Money, the Price of Corn, and Other
Commodities for the Last 600 Years.
I acknowledge with enduring gratitude friendship with
Oscar Morgenstern begun in 1956 and marked by a
productivity of Research Memoranda of the Econometric
xvi

Research Program in Princeton 1958-62, in evidence in this
book and all its material.”
Most important is the acknowledgement to my wife Pilù
(Pia Luisa) who saved me from falling off the edge of the
world.
xvii

Fragments
Memory —Morocco and earlier
The Sultan and Queen Victoria
On the River Non
Azharoth
The Burnt Ones
Merchants of the Sultan
Encounter in Marrakesh
Deaf and Dumb
Concerning ‘Afriat’
Bibliography
London and Mogador
Cambridge 1
NPL
Cambridge 2
ARL
Oxford
xi

Cambridge DAE
Jerusalem
Princeton
and North America
Bilkent
Ankara, Buyukada and other
Siena
and Italy …
Math / Econ
Market & Myth
— prehistotic hangover
The Celebrated Theorem
A Tale, and Comment
—Early Pioneer in Citation Analysis
Strange stories
…
…
Story of the Computer
—the Mysterious Word Problem
Story of the Book
—Convoluted Story in
Three Painful Chapters
Finally
xi

NONPLUS—fragments

Memory

A
late time may be good for going back to the early time,
and to even before. In this case the early time was in
Mogador, as we called it, though since departure of the
French it has come to be known more as Essaouira, which is its
Berber or Arab name, meaning “Picture City”. And it was, and still
is, truly a picture city.
Now we are in Siena, no doubt another picture city. And in
between, London and a chain of intermediate locations, ending
lately in an abandoned goat pasture, Bilkent, somewhere outside
Ankara.
And before: on the one hand Spain (rather mother’s side) up to
time of the expulsion by Ferdinand and Isabella, and on the other
hand the legendary Ifrane (or Oufrane) on the River Non
(Wad’Noun) in the Anti-Atlas; before which is Babylon—which is
back far enough.
To tell all that may be encountered in following this thread
one could get extremely confused. Instead, with Mogador as the
unalterable fixed point, we take opportunity for digressions, as
suits the mentality of this writer and perhaps this reader also.
14

The Sultan and Queen Victoria
T
A certain foreign gentleman wanted, ironically, to know if
Mogador belonged to the Sultan or to Queen Victoria. The
response, with hand on heart, was ‘Bijujhum ya señor’—‘To
both, sir’.
R. I. N. Johnston
Morocco: The Land of the Setting Sun
London, 1912. P. 40
hat there has been a French presence in Morocco is well
known. Much less common is awareness of any British
connection, let alone the particular connection celebrated in
Johnston’s story.
To my knowledge this connection is largely a Mogador
phenomenon. And this writer comes out of the heart of it, with
family a pillar of Victorian British civilization on the Barbary
coast throughout the nineteenth century and into the twentieth.
For a start close to home, my mother's mother Miriam
(Corcos) Anahory had her own English school, the only school of
my mother. Her cousin Stella Corcos had another, sponsored by
the Anglo-Jewish association. That English was spoken so much in
Mogador is without doubt connected with the existence of these
two schools.
It happens my father went to neither but to the Rabinical
school, so his English was not so good. My parents always spoke
Arabic together, or perhaps more precisely I suppose, what might
be called Judeo-Arabic, a version that included Hebrew and
Spanish elements, a counterpart of the Ladino spoken by many
Sephardis related to mediaeval Spanish, or the Yiddish of the
Ashkanazis related to mediaeval German. Moreover, I never
learnt that language. And not knowing the language of my parents
was a good start to coming to Italy for over half a century and
being married to an Italian for nearly forty years and not learning
Italian.
15

I share a pattern with grandmother Miriam Anahory, since she
had in fact been born in England of Maghrebi parents. Her mother
a Corcos, and her father a Rabbi imported to England to minister
to the Spanish and Portuguese community. Visiting the ancestral
lands she married a merchant of Mogador, reputed Kabbalisitc
mystic, Moses Anahory whose notable achievement was with the
guitar. Perhaps for support of family she started her own school.
She was well educated in the usual English girls boarding school
fashion, and something of a musician as was transmitted to my
mother. Her old age was spent in Jerusalem, together with her
sister Aida, and I used to have communications from there, though
I never met her. She seemed to be remembered as a distinctly
venerable person by everyone.
The name Anahory, for more recent cases in the last 500
years, is known from pre-Inquisition Spain, and Morocco. The
origins go back 2000 years, to what was then Babylon. It is
Aramaic, not Hebrew, and so unusual in the wider Jewish
community. Rabbis of the Talmud who were considered erudite
were given the name “Anahory” or “Nehorai”, meaning “to
illuminate”.
England used to have interests and be well represented in
Morocco. There was even an issue of stamps from the English Post
Office in Tangier. But there was a withdrawal as a result of the
Treaty of Algeceiras of 1912. By this treaty France gave up
interests in Egypt and in exchange England gave up interests in
Morocco. However, some elements of England got left behind,
especially in Mogador.
There had been pressure on Morocco from colonial powers in
about the middle of the nineteenth century. The granting of
consular protection to individuals served to expand influence and
promote trade. It may also have been meant to promote divisions
in preparation for conquest—but no need now to dwell on politics.
Beside such cases, and additionally picturesque, we have the
children of the British Consul who who had never been elsewhere,
and when he died they got left behind in Mogador, to remain there
all their lives. Beside my visits to her earlier, I remember Emily
16

Broom’s interview on BBC radio just after the war. A particular
interest of it had been that, since she had never been anywhere else
to disturb her from the timewarp, she remained a most perfect
Edwardian.
Mogador is the old port of Morocco and used to be important.
But when Casablanca grew up to the North and Agadir to the
South, it lost its status. That is, were one to forget its rebounding
significance as a station on the Hippy Circuit, like Katmandu and a
few other places. When our house on Rue du Rif was last visited, it
was taken over by a group of hippies. This is the house given us by
the Sultan in the nineteenth century, with the appointment as Royal
Merchants to develop foreign trade, especially with England.
Also, it is celebrated as a mythical city by the once quite well
known song “The Mad Maharaja of Mogador”. And again, as the
setting of the play “Captain Brassbound’s Conversion” by Bernard
Shaw, who got his inspiration from R. B. Cunningham Graham's
Magreb-el-Acksa. Then there is the film of Shakespeare’s
“Othello” made by Orson Wells exploiting the ready-made film
props provided by the city, on the ramparts of the port, among
fortifications with rows of old cannon, and such features.
Though it does have earlier history, Mogador was founded in
1764 by Sultan Sidi Muhammed ben Abdallah, on the Atlantic
coast west of Marrakesh, intended to be Morocco’s main seaport
for trade with Europe.
The name Mogador has a foreign character, is mostly used by
foreigners, and since departure of the French has been largely
given up in favour of the more indigenous name Essaouira,
meaning Picture City, in Berber, or Arabic, or both. There is more
to be said about that, but to continue the pursuit of Mogador, it
could be taken to be just another of the fairly frequent Portuguese
colonial relics found up and down the coast. Along the wide sandy
beach to the South going towards Agadir, after a few kilometers
one comes to a broken up rocky ruin washed around by the sea,
which everyone calls “The Portuguese Fort”. It makes the obvious
turn around point in any excursion on foot, or a horse, along the
beach in that direction, beyond which would seem to go on for
17

ever, and it is very familiar. That contributes to making the
Portuguese idea stick. Possibly there is some place in Portugal
called Mogador, or something like that, and colonials are always
giving the hometown name to places they take over. However,
there is quite another view about how the name happened—more
to do with Scotland than with Portugal!
A familiar landmark of Mogador is the tomb of Sidi Mogdoul,
the local saint. It is said he was a Scottish mariner with name
MacDougal who got wrecked on the coast some centuries ago and
acquired the status—and pronunciation of his name—by which he
is now respected And from Mogdoul to Mogador is just one step!
I am indebted to J. S. G. Simmons, Codrington Librarian at
All Souls, for telling me of Danial Schroeter’s delivery, “Anglo-
Jewry and Essaouira (Mogador), 1860-1900”, that I knew nothing
about though it happened when I was at the College, and
incidentally on Codrington Day. I met Schroeter later in Istanbul,
at the Symposium marking the 500 years since the Ottomans
admitted Jews leaving Spain, and even sent boats to pick them up.
18

On the River Non
The Jews of Oufrane have conserved, up to the present,
another old tradition in support of the belief that their
ancestors had come at the time of the deportation of the ten
tribes and established themselves in the country. After many
generations they founded a kingdom of their own and subdued
all the native peoples of the said region. Their first monarch
was called Abraham Ha-Ephrati, of the tribe of Ephraim, from
whom are descended all the succeeding kings who bore the
name of the Ephratim. And it happened that when they were
invited by Esdras the scribe to return to Jerusalem, they
refused to respond to his call. Due to this transgression his
kingdom declined, until the enemy took it over and dispersed
his people. And henceforth they were obliged to change the
name of their family, Ephrati, for that of Afriat, which is the
name held by the family living in the said town today.
Rabbi Jacob Moshe Toledano
Sepher Ner-Ha-Ma’arav
Jerusalem, 1910
W
hen the conquering Arabs reached “Al Maghreb Al
Aksa”—the Land of the Farthest West—in the 7th
century, Jews had been there many centuries. Some had
arrived after the first destruction of the temple in Jerusalem by the
Babylonian King, Nebuchadnezzar II, in 586 BC. There they met
the other early inhabitants of Morocco, the Berbers, whose origins
are unknown.
From evidence of discoveries in the Anti-Atlas and the Draah
valley, it appears that Jews had come to Morocco still earlier. And
there is the legend of Ifrane, on “Wad’Noun”, or River Non, in the
province of Tiznit in the Anti-Atlas—told by Rabbi Toledano in
the passage quoted above. This is in the South of Morocco, in the
Souss region, near Goulamime on the edge of the Sahara, where
one meets the Touaregs, the Blue Men of the Atlas. Their
characteristic flowing blue robes might in the more recent times
20

have been spun in Manchester, dyed with indigo brought from
Pondicherry in India, and imported to Morocco by A Afriat & Co
of London and Mogador.
According to the tradition, Ifrane was populated at the time of
deportation of the ten tribes by the Assyrians around 715 BC.
These are the fabled ‘Lost Ten Tribes’, which included the tribe of
Ephraim. The community on the island of Djerba off the coast of
Tunisia has a similar history, at least going back to the Babylonian
dispersion, if not to the Assyrian. These must be among the oldest
communities in the World.
21

Azharoth
Azharoth of the 11th century poet, talmudist, and dayyan Isaac
b. Reuben al-Barceloni at Denia. He was one of the ancestors
of Nachmanides and much praised by Moses b. Ezra and
Alcharisi.
The ‘azharoth’ were used in most North-African liturgies.
A commentary was written by Moses Mnatti, which was
published, Zimron, 1655. The date is on the title-page [… ] …
… , psalm VI, 7, which should be read … . That date agrees
with one given on the last folio: Monday, 1st Iyyar 5423 =
1663.
On the title-page an “explanation of the words” by ‘Amram
b. Mas‘od of Ophran (Morocco) is mentioned.
My learned neighbour
Wellington Square, Oxford, 1953
T
he antique manuscript book shown in the illustrations was
found, with other materials, in an old cardboard box in the
house in Mogador. No one there knew anything about it; I
took charge of it and brought it to England.
The quotation above transcribes the report on the book given
me by a learned Rabbi who was my neighbour in Wellington
Square, Oxford, during 1950-53, whose name I forget. I was in
No. 42, the corner the sun never reached, next to Peat’s lodging
house at the end of St John's street, where lived Ricardo Caminos,
Egyptologist of my college, near Geach and Anscombe where
Wittgenstein stayed, as did, for that matter, George Kreisal and
Teddy Goldsmith. I thought that was where Wittgenstein died, on
testimony I believe from Goldsmith, though Brian McGuinness
assures me he had returned to Cambridge. I had heard him before
in Cambridge, at meetings of the Moral Science Club in Kings
College, which he dominated. I was told he had been asked to
leave because no one could get a word in, but then no one had
anything to say so he was asked to come back. An expression of
22

agony accompanied anything he said even when it seemed, to
more ordinary minds, rather simple.
In those days the Salvation Army band would play in the
Square every Sunday morning. My landlady was Mrs De Arteaga,
widow of the Professor of Spanish whose famous library had been
kept in the room I occupied, quite unchanged with labels still on
the shelves, Cervantes, Lopez de Vega, Calderon de la Barca, …,
except that the books themselves were no longer there. As also
was the distinguished Sherry they had at one time gone to provide.
“I'm no ordinary landlady” she had explained to me in reference to
the refined taste which had been one bequest and had consumed
the distinguished collection which was the only other, so that
giving rooms for rent became necessary.
The other tennant was Bruce M. Goldie, tutor in Latin, on the
top floor, who seldom appeared in person though flocks of
students would clatter up the stairs.
Robin Chanter came sometimes, not to see me personally but
to show my room to someone—he said it reminded him of “Great
Expectations”.
The learned Rabbi was on the side of the square diametrically
opposite. On short notice, after a quick look through the book, he
scribbled out the report I have transcribed, which is reproduced on
the next page.
23

The Burnt Ones—Nesrafim
Rabbi Ichia Ben Rab Jacob Sabat
Mogador, October 20, 1953.
Translation from the Hebrew:
Story of the Afriat Family—Oufrane
THE ALLIANCE ISRAELITE of Paris requested of the Jews of
Mogador to find out from the children of JACOB AFRIAT..
SOLOMON NAFTALI.. and SALAM living in Mogador, to give
them a copy of any information they had about the cemetery in
OUFRANE who is buried there... The following is the record of
information:
Rabbi Joseph Baibison
..... buried in 1158
Rabbi Eli Galilee
..... it was said that he came from France
and that he quarrelled with Solomon Ezaby.
The 50 Tombs of those who were burned to death
..... 202 years ago
Rabbi Jacob Ben Sabat
..... original name was Levi... he is
supposed to have gone to the Sahara with a company.. and
when he refused to travel on the Sabbath.. they changed his
name to Levi He remained alone in the Sahara, observing
the Sabbath .. an angel came, and said that he would no
longer be called Levi .. but BEN SABAT.. this happened
333 years ago .. and the proof of it is, that in TETUAN
they have the family Levi Ben Sabat.
Rabbi Joseph Ben Sabat
... buried 301 years ago
Rabbi Solomon Aflalo
... buried 208 years ago
27

Rabbi Samuel Ben Jacob ben Sabat
... buried 351 years ago
Rabbi Yahesh Ben Mosche
... buried 274 years ago
Rabbi Solomon Ben Abo
... no date
… They say that one day he was passing,
and as he was a very handsome man, a Moorish woman
called to him from her window, and asked him to come up
to her. When he refused, she spat upon him, at which
moment two great horns sprung from her head so that she
could not get back out of the window. A great crowd
gathered before her window … and she related what had
happened to her. They begged the Rabbi to forgive her and
remove the horns. The Rabbi said a prayer, the horns
disappeared..and from that day on, the Moors were in awe
of the Rabbi … and held him in high estimation ..
Rabbi Shushan Ben Amram … family Siboni
..... no date
Rabbi Judah Ben Naftali Afriat
.....it was he who stood by to see that the
family of 50 persons, who, with his encouragement had
made the decision to be burned alive rather than accept
conversion to Moslemism.....did not waver from their
decision. He decided to see them all burned first, since he
thought that some..fearing..might change their minds. After
the 50 were burned..he made ready for his own death in the
same way...He asked a negro who was standing nearby, to
bring him a pail of water so that he could wash himself.
The negro asked for money before he would bring it. As he
had no money he tore from his ear the gold earing, and
gave it to the negro instead of money..the Rabbi washed
himself..said his prayers..and then burned himself.
28

After all of the Afriat family were burned, the people
standing by, saw a pidgeon fly out of the fire. Later, that
night, a fire sprung out of another place..and the Moors
thought it was an act of God, and were frightened, and
refused to burn the rest who had been brought to suffer the
same fate of being burned alive. And that explains how
these were saved.
Rabbi Salom Ohayon...his son named Rabbi Maklond
.... no date
No one has the right to enter the cemetery as it is a
sanctified place. Anyone who goes near the place, and tries
to enter starts to tremble. They only look at it from afar..
And it is said that anyone who did enter the Cemetery to
see what was there, did not live to the end of the year
The final statement of the record by the writer of the account
above
The righteousness which the Israelites earned by this great
sacrifice for their religion, is shared by others as Rabbi Rabbino
Shlomo Ishahi (renowned all over the world..who was called
Rachi..came from Paris) Rabbi Chaim Joseph David Azulai..also
called Chida..and Rabbi Jacob Ben Sabat of Mogador..and Rabbi
Ben Walid..of Tetuan
These Rabbis agree with what Rabbi Afriat did … and the others
who sacrificed their lives for the sake of their religion. These
Rabbis say, that the page which tells the story of the great sacrifice
which these people made by being burned to death, should be
written and hung in every home so that everyone in the family,
from the smallest on will know the story and be reminded of the
meaning of their religion.. and be guided by it.
Signed by
ICHIA BEN RAB JACOB SABAT du MOGADOR
This is the Rabbi who recorded these events as above
October 20, 1953
29

Merchants of the Sultan
Afriats — first capitalists
This is the heading on a page of Daniel Schroeter’s Merchants of
Essaouira (1988), the chapter on “Merchants of the Sultan”
We touched the subject already, and the book gives a full and
authoritative account, not now to be repeated beyond this simple
line.
The photograph is part of Schroeter’s 1982 delivery in
London.
30

Encounter in Marrakesh
It was 1937 or 38, when I was at a prepschool, Downsend in
Leatherhead near Ashstead, Surrey, at the beginning of
Summer holidays, when as usual we went to the house in
Mogador. I had been having trouble with my chronic asthma
problem and my father decided to take me to Marrakesh for the
dry air. We went to stay at the Hotel Mamounia, then new though
already famous.
Going round the large and dense garden we encountered an
Indian alone seated on a bench, who spoke to us in English. He
said immediately, though we had said nothing, that we were there
for my health, and prescribed some rigmarole involving flowers.
Returning to the hotel, arriving at the clearing in front, I heard
a voice say “There’s Churchill!”, and saw someone standing not
far away, dressed in riding clothes and carrying a crop, and
speaking with others, in a way that made a marked impression on
me as being not ordinary at all. At that time I knew nothing about
Churchill. I was told he frequently went to Marrakesh, and
painting was one of his pursuits there.
Later I learnt that El Glaoui, Pasha of Marrakesh, was staying
at the hotel and, becoming aware of my father’s presence there,
had been in touch and we were to meet
The meeting took place that afternoon and included El
Glaoui’s companions at the hotel: Churchill, Lloyd George, and
Thompson, Lloyd George’s secretary. For an extra dimension of
coincidence, Malcolm Thompson immediately told us he already
knew we were in Morocco—from his son who was at my school!
31

That might have been a link that woke up El Glaoui to our being at
the hotel.
Lloyd George was more my size and I was seated next to him
on one of the benches so, though still slight, I had more
communication with him than the others.
It needs to be appreciated that the Marrakesh region is almost
a separate country, more Berber than Arab. It is among tribal
territories that had been governed by war lords without allegiance
to the Sultan.
Without comparison with the hereditary right and Chereefian
(title for a descendant of the Prophet) Majesty of the Sultan, the
Glaoui had effectively eliminated opposition and ruled by no other
right.
Another observation is that Berbers and Jews had lived
together in Morocco since long before arrival of the Arabs, they
knew each other very well. When Thami El Glaoui, mindful of
political compromising ambiguities, removed himself from
Morocco during the Rif War and took himself to London, he spent,
I gather, just about every day with my father, who gave him the
latest news. Hence this encounter in Marrakesh was animated by
old friendship.
An anecdote I recall is that one day a secretary of El Glaoui
came to my father’s office (I suppose 21 Mincing Lane in the City
where I used to be dragged, near Tate and Lyle), and asked if care
could be taken of a parcel he had with him. It was some time,
perhaps years, later a secretary turned up again and, stirring up
recollection of the parcel, asked if he could be permitted to take
charge of it. He was about to leave in possession of the parcel
when my father asked, out of understandable curiosity, what was
the nature of the contents. It was explained that the parcel
contained valuables that could be useful for incidental needs while
on a journey, as it were like travellers checks, which of course at
that time had not been invented. In other words, gold, silver,
precious stones … imagination is in overload to picture the
contents.
32

Gavin Maxwell, Lords of the Atlas: Adventure, Mystery, and
Intrigue in Morocco, 1893-1956; The Rise and Fall of the
House of Glaoua. The Lyons Press, New York, 2000.
Marvin Rintala, Lloyd George and Churchill: How Friendship
Changed Politics. Madison Books, 1995 (I came across this
interesting book at the same time as my search for the Lloyd
George biography by Thomson.)
Daniel J. Schroeter, “The Jews of Essaouira (Mogador) and the
Trade of Southern Morocco.” In M. Abitbol (1982), pp. 365-
90.
— , “Anglo-Jewry and Essaouira (Mogador), 1860-1900: the
social implications of philanthropy.” Transactions of the
Jewish Historical Society of England, sessions 1981-1982,
Volume XXVIII & Miscellanies Part XIII, 1984. Paper
presented to the Society on 28 April 1982 (see earlier
reference).
— , Merchants of Essaouira: Urban society and imperialism in
southwestern Morocco, 1844-1886. Cambridge University
Press, 1988. Cambridge Middle East Library.
Malcolm Thomson, with the collaboration of Frances, Countess
Lloyd-George of Dwyfor, David Lloyd George: The Official
Biography. London, Hutchinson. (Thomson was his secretary
1925 to 1940, I met both in Marrakesh 1937 or 38, I recently
got this together with the Rintala 1995 book about Lloyd
George and Churchill.)
33

Concerning “Afriat”
Provided by Dina Binyamin, Tel Aviv, concerning ‘Afriat’,
obtained from:
Beth Hatefutsoth – Communities and Family Names – Tel Aviv
Afriat is a toponymic surname (i.e. derived from a place of origin
or residence), associated with the King of Ifrane, Sous, in
Morocco, and of the Sous tribe descended from his family.
According to the Jewish inhabitants of the fertile alluvial region of
Ifrane, Sous, in Morocco, their ancestors came to this area after the
deportation of the ten tribes from Eretz Israel.
Their first king was “Abraham the Ephramite”/“Abraham
Hephrati”, a descendant of the tribe of Ephraim, and all his
successors were called “Ephrati”. Following the fall of their
powerful kingdom, the Ephrati changed their name to
“Afriat/Aferiat” [written without vowels in Hebrew or Arabic it
could be pronounced either way]
Rabbi Yudah ben Naftali Afriat was the leader of a group martyrs
burned alive at Oufran, Morocco, in 1775.
Afriat is recorded as a Jewish family name in the following cases:
At the end of the 18 th century, Messod Afriat was Chief Rabbi of
Marrakech, Morocco.
The merchant Joseph Afriat was born in Oufran, settled in
Mogador, Morocco in 1792, and moved to London in 1809. His
nephews, Jacob Aron and Sellam Afriat, opened in London the
most important Moroccan commercial enterprise of the City
dealing in tea, the “Atay Afriat” tea [the second brought my
Father, the junior nephew, to London]
Other distinguished bearers of the Jewish surname Afriat include
Frank Afriat, a 20
34
th century leader of the Sephardi community in
London, England, elected several times member of the “Maamad”.

Comment by S. N. (Sydney Naftali) Afriat, Siena, Italy
Sellam, uncle of my father M. N. (Messod Naftali) Afriat, adopted
the name Sydney in place of Sellam when he was in England. It
was he who brought my father, his junior nephew, to
England.(needed for his knowledge of Morocco, the languages,
and communication with different elements) who later inherited
from him the family company A. Afriat & Co.
With my names I was named after him, and also, like my father,
after the Rabbi of Oufrane/Ifrane, on the River Non (Wad’Noun)
in the Sous region of Morocco, in the Anti-Atlas.
35

I came across the following note, without statement of source:
Ofran (Ifran) in the Anti-Atlas region of S. W. Morocco, according
to Judeo-African tradition, is regarded as the first site of Jewish
settlement in Morocco. Many legends have been created about the
ancient community of Ofran, whose first members are said to have
arrived from Erez Israel before the destruction of the first Temple
in Jerusalem.
A Jewish kingdom was set up there which was governed by
the Afriat family—then named Efrati. The Jews of this kingdom
are said to have belonged to the tribe of Ephraim—one of the lost
Ten Tribes of Israel. Indeed.in the modern era the Afriat family
administered the affairs of the community of Ofran and of all the
communities of the region.
The Jewish cemetery of Ofran is very old, and there are many
tombstone inscriptions dating from the Middle Ages. Local
tradition ascribes some of them to thc first century B.C.E.
Pilgrimages were made from every part of Morocco to this
cemetery, which contains the remains of revered rabbis and
martyrs.
According to local traditions there was a terrible persecution
following the destruction of the community by thc Byzantine
Christians (sic). Other persecutions have been historically proven,
the last of which took place in 1792 when the pretender
Bou-Hallais, who sought to be proclaimcd sultan, arrived in Ofran.
He seized 50 Jewish notables and gave them the alternative of
converting to Islam or death by fire. Under the guidance of their
leader Judah Afriat, they jumped one after the other into the huge
furnace which had been lit for the occasion. Judah Afriat remained
to the end in order to encourage those who faltered. The remains of
these martyrs, known as the Nisrafim (“Burnt Ones”), were piously
gathered and interred in the cemetery of Ofran.
The account of their martyrdom was copied on parchment and
circulated throughout the country. A popular etymology explains
the name Ofran as a combination of efer (“the ashes of ”) and the
letter nun (= 50). Their descendants were greatly esteemed and to
36

the present day they commemorate the anniversary of the event
(the 17th of Tishri) by refraining from lighting fires in their homes.
The community of Ofran was prominent and wealthy and a
large part of thc trans-Sahara trade passed through its hands. After
1792 its members dispersed. They played an important role in the
community of. Mogador, especially the members of the Afriat
family, and during the 19th century they established a commercial
house in London. For more than 50 years the Afriat house was the
most important family in Anglo-Moroccan trade. …
Mogador (Souirah), Moroccan port on the Atlantic Ocean, a
kilometer distant from the island of Cerne which in antiquity was a
commercia! base of the Phoenicians and Carthagenians and where,
under King Juba II (23 C.E.) thc famous purple of Getulia was
manufactured. From the Middle Ages until the 17th century there
were sugarcane refineries in thc vicinity of Mogador, and the sugar
trade was concentrated in the hands of the Jews. The activity of
Mogador, which was brought to a halt between 1650 and 1760,
started anew when Sultan MuhAmmad ibn Abdallah decided to
build a city and a port through which the greater part of the
international commerce of his kingdom would bc conveyed. The
most important Jewish families of the country sent some of their
members there. The sultan chose ten of them; and conferred upon
them the title of tâjir al-sultân (“merchant of the king”), together
with the duties and prerogatives attached to it. …
37

I should add the following from my old friend J. R. T. Hughes,
Economic History, Queen’s College, Oxford, and Northwestern
University, USA
10 December,1969
Dear Sidney
In Volume I, of Henry Mayhew’s book (recently issued again in
paperback and hardcover), London Labour and the London Poor,
first published in 1851 there is, beginning.page 452 an account of
street sellers of rhubarb and spices. They come from Mogadore.
There is a picture of one. The account runs like this (exerpts from
p.453)
“De people were Mahomedans in Mogadore, but we were Jews,
just like here, you see ……… All de rhubarb-sellers was Jews.
Dere was anoder called Ben Aforiat, and two broders; and anoder,
his name was Azuli. One of Aforiat's broders used to stand in
St Paul’s …… ”
Interested? I’ve been meaning to write this for a year but never got
around to it. I ran onto this when I was reading Mahew for a
review.
The man being interviewed is not an "Aforiat'. He tells how things
were in Marocco for the Jews, in Gibralter, Portugal, London. It is
a very touching account. But he must be talking about Afriats. His
language is taken down as it sounded to Mayhew..
38

Bibliography
Michel Abitbol (ed.), Communautés juives des marges
sahariennes du Maghreb. Jerusalem, 1982.
— , Temoins et acteurs: Les Corcos et l’histoire du Maroc
contemporaine. Jerusalem:, Institut Ben Zvi, 1977
Tahar Ben Jelloun, “Haïm Zafrani, souvenir d'une culture judéomusulmane.”
Le Monde, Vendredi 7 Juin 1996.
Robert Boutet, “Notes sur le Judaism dans l’extreme-sud
Marocain” L’Avenir Illustre 1930, 30/4/1936, 31/3/1936
David Corcos, Studies in the History of the Jews of Morocco.
Jerusalem, 1976. (My mother’s cousin)
Sidney S. Corcos, “The Corcos family: Spain-Morocco-
Jerusalem”, Sharsheret Hadorot—Journal of Jewish
Genealogy Vol. 14 No. 2 (Winter 2000), The Israel
Genealogical Society. (Son of David Corcos and main
historian of the Corcos family)
R. B. Cunninghame Graham, Mogreb-el-Acksa: A Journey in
Morocco. London, 1898. Reprinted by the Viking Press, NY,
1930, and the Marlboro Press, Vermont, 1985.
Elias Canetti, Die Stimmen von Marrakesh.
Ernest Gellner, Saints of the Atlas. Chicago and London, 1969.
— and C. Micaud (eds.), Arabs and Berbers. London, 1972.
Walter B. Harris, France, Spain and the Rif. London: Edward
Arnold & Co., 1927
Ibn Khaldun, The Muqaddimah, trans. by F. Rosenthal, 3 vols.
New York, 1958.
39

James Grey Jackson, Esq., An Account of the Empire of
Morocco, and the District of the Suse; compiled from
miscellaneous observations made during a long residence in,
and various journeys through, these countries. To which is
added, an accurate and interesting account of Timbuctoo, the
great emporium of Central Africa. London, 1809. (Original
edition presented to me and inscribed by Elias Canetti.)
R. I. N. Johnston, Morocco: The Land of the Setting Sun. London,
1912.
Mourad Kusserow, “Erbe und Zukunft von Marokkos Juden.”
Neue Zürcher Zeitung, 15/16 February 1997.
Abraham Laredo, Les Noms des Juifs du Maroc. Madrid, 1978.
Bernard Lewis, The Jews of Islam. Princeton, 1984.
Stephen Lister, By the Waters of Babylon. Peter Davies, London,
1944. (a novel)
Gavin Maxwell, Lords of the Atlas: Adventure, Mystery, and
Intrigue in Morocco, 1893-1956; The Rise and Fall of the
House of Glaoua. The Lyons Press, New York, 2000.
Henry Mayhew, London Labour and the London Poor, first
published 1851, recently issued again in paperback and
hardcover. P. 452 ff.
Marvin Rintala, Lloyd George and Churchill: How Friendship
Changed Politics. Madison Books, 1995 (I came across this
interesting book at the same time as my search for the Lloyd
George biography by Thomson.)
Daniel J. Schroeter, “The Jews of Essaouira (Mogador) and the
Trade of Southern Morocco.” In M. Abitbol (1982), pp. 365-
90.
— , “Anglo-Jewry and Essaouira (Mogador), 1860-1900: the
social implications of philanthropy.” Transactions of the
Jewish Historical Society of England, sessions 1981-1982,
Volume XXVIII & Miscellanies Part XIII, 1984. Paper
40

presented to the Society on 28 April 1982 (see earlier
reference).
— , Merchants of Essaouira: Urban society and imperialism in
southwestern Morocco, 1844-1886. Cambridge University
Press, 1988. Cambridge Middle East Library.
Henri Terrasse, History of Morocco, trans. by Hilary Tee.
Editions Atlantides, Casablanca, 1952.
Malcolm Thomson, with the collaboration of Frances, Countess
Lloyd-George of Dwyfor, David Lloyd George: The Official
Biography. London, Hutchinson. (Thomson was his secretary
1925 to 1940, I met both in Marrakesh 1937 or 38, I recently
got this together with the Rintala 1995 book about Lloyd
George and Churchill.)
Rabbi Jacob Moshe Toledano, Sepher Ner-Ha-Ma’arav.
Jerusalem, 1910.
Joseph Toledano, Une histoire de familles; les noms de famille
Juifs d’Afrique du Nord. Jerusalem, 1998.
Edward Westermarck, Ritual and Belief in Morocco, 2 vols.
London, 1926.
Haïm Zafrani, Les Juifs du Maroc. Paris, 1969.
— , Juifs d'Andalousie et du Maghreb. Ed. Maisonneuve et
Larose, 1996.
41

Econ
Market & Myth
F
or an Econ item without Math my favourite is the essay
“Market & Myth” included as a chapter in my book The
Market: Equilibrium, Stability, Mythology, Routledge 2002, and
suits this situation for an exhibition.
42

Market & Myth
In speech of today a single being, the Market, is at the centre of
existence. It is the self-created, self-regulated, unquestioned
measure of everything. The textbooks teach that, but for
objectionable intrusions, or ‘imperfections’, its rule would be
optimal!
It has been remarked that every age has its myth, proclaimed as
the higher truth; here we have ours. It permeates every sphere—
which could perhaps interfere with visibility. As a movement in the
immediate present it is on a gallop with fresh energy, commanding
submission everywhere.
In history this myth, and the reality which would go with it
where the human factor is something like an accident, seems in some
way new. Now it is propagated by endlessly repeated teaching, and
bolstered by interests, and inertia. A first impulse for present
objections came simply from encounter with the textbook teaching,
and being struck by its thorough absurdity, and deceptive use of
language. This is unaltered by the mathematical dress given to it, and
enunciation of portentous theorems. While such presentation may
give it all an aura of lofty science and unassailable truth, it is
anything but that.
Such a concern might appear simply scholastic, a field of sport
for any with the training and inclination and otherwise of no account,
like many another. Faults with the teaching have been pointed out
many times, but this appears to make no difference. As
indoctrination it has a now ominous persistence. With inheritance
from the 19th century based on inchoate notions from France in the
17th, we are approaching the 21st. Instead of being rudely awakened,
as happened lately on another side, it could still be asked whether
43

this is the way to face the now well recognized and already well
advanced, developing and encircling realities.
The question requires a regard for the market teaching which has
importance from its influence, and apart from that is an exhibition of
self-deception—a spectacle to make the power of reason as much of
a myth as what it pretends to offer. Of course we know reason has its
intermittences; and F. A. Hayek has spoken well about authority in
economics and the transmission of mistakes, how they are handed
down with uncritical acceptance simply because of the prestige of
their perpetrators.
Without the barriers that not long ago always prevailed, when
markets were auxiliaries, subordinate to life in a locality, the market
dictatorship would most likely impose itself anyway, by its own law,
regardless of what anyone should say or think about it. As well
accepted, liberty requires a constant defense. Now the absolute rule
is fostered by absurd reasoning of scholastics, joined with zealous
belief of creatures of the days of innocence which are no longer with
us.
We have a concern with the Maximum Doctrine of Perfect
Competition which is central to the dominant ‘neoclassical’
economics. It appears to have originated in the seventeenth century
with François Quesnay and the Physiocrats, and was imported from
France into the United States by Dupont. For perfect competition
there are the well known conditions, and the conclusion—which for
the Physiocrats was nothing but self-evident—is that under these
conditions the economy achieves an optimum. This is the “social
maximum” alluded to by Kenneth J. Arrow in motivating his theory
of Social Choice and Individual Values:
“If we continue the traditional identification of rationality with
a maximization of some sort, then the problem of achieving a
social maximum derived from individual desires is precisely
the problem which has been central to the field of welfare
economics.”
What is the criterion by which one can know the better and the
worse and hence what is best, or the optimum? Nobody knows.
Without a knowledge of this what we have been told must be quite
44

empty. There could be cause for an abandonment of the whole idea,
and surprise at how it is accepted without a tremor by the multitude
of the faithful.
To be free, and yet a good slave—put that way it sounds
ridiculous, though it should strike one the teaching is just like that.
First there is the individual freedom in the self-regulated order, the
market. Then as if here is not enough to the system, and in further
praise of it, it is submitted that the overall result is efficient, as an
obedient slave performing some precise duty to the utmost. It is a
relief one never is told what the duty is. The social objective it is
taken to exist and to govern because it is talked about. With more
known about it there would be a better position to verify whether or
not it is at a maximum. For some the loose end is put out of the way
as the Aggregation Problem, but should anyone ever get to that
problem they would not know what it is.
We are faced with a phenomenon appreciated in another case,
the famous “happiness” formula, known as a Marxist slogan though
it has an earlier origin. P. P. Wiener attributes it to Frances
Hutchison, the teacher of Adam Smith. Its classic attribution is to the
Utilitarians, and Marxists must have borrowed it from them.
According to I. Philips:
“John Bowring says in his Deontology [1834, p.100] that
Jeremy Bentham recalled how on a visit to Oxford in 1768 he
had first come across the phrase ‘the greatest happiness of the
greatest number’, in Joseph Priestley’s Essay on the first
principles of Government, published in that year, 1768. “It was
from that pamphlet [Bentham said] … that I drew the phrase,
the words and import of which have been so widely diffused
over the civilized world. At the sight of it, I cried out, as it
were in an inward ecstasy like Archimedes on the discovery of
the fundamental principle of hydrostatics, Eurhka”.
We should try to find out what the stirring formula could
possibly mean. Since “widely diffused” without any qualification, we
may look for its import in a simple possible world, one where a cake
is distributed over a number n and happiness is the size h of the slice
45

anyone gets. Then the greatest h for the greatest n is wanted. To put
all this mathematically, with the size of a slice measured by its angle
in radians, so the whole cake is 2p we have the constraint hn £ 2p
and have to maximize h and n simultaneously. Let anyone try!
Economics students receive the notion that if no one can have
more, unless someone has less, then we have an “optimum”. It is
tagged with Pareto’s name. It is just like with the cake, so apparently
you can distribute it around to everyone any way you please, it’s
always optimal. Good news for the party host as for the economics
catechism. Since everyone wants more, this would have to be a case
of “Multi-objective Optimization”—the title of a lecture I once saw
announced. But there can be no such thing. If you have one objective
then you cannot at the same time also have another—you just have to
make up your mind!
Impressive absurdities on the same model had occurred
previously, for instance Quesnay’s Economic Principle “greatest
satisfaction with the least labour-pain”, and he must have drawn
inspiration from Leibniz whose “best of all possible worlds”
provided the greatest good at the cost of the least evil. The
precedents give a reminder of Hayek’s remark about the transmission
of mistakes.
Obviously if you choose to maximize one thing, then you cannot
at the same time make a free choice of another. You may be lucky,
for instance if (x, y) is subject to x £ 1, y £ 1 and you want to
simultaneously maximize x and y, this is provided by (1, 1). But we
do not have a case like this in dealing with the “happiness” formula,
or the cake; for when n is made large h is forced to be small, and vice
versa.
It may be wondered how anyone, whose respected output is
supposed to be rational (in an ordinary sense), can make such
remarks, and how they can then have acceptance, even be awarded
prizes. On submitting about wrong reasons to Chalongphob
Sussangkarn, on a visit with a Thai trade delegation, he gave a
healthy answer: “We have the right thing—never mind those
reasons!”
46

Here is another thought bright with free market devotion, from
Robert Heilbroner in The Worldly Philosophers:
“Edgeworth's pleasure machine assumption bore wonderful
intellectual fruit … it could be shown—with all the
irrefutability of the differential calculus—that in a world of
perfect competition each pleasure machine would achieve the
highest amount of pleasure that could be meted out by society.”
Enjoyment of the wonderful fruit should in this case be spoilt by
a suspicion of worms. What is “all the irrefutability of the differential
calculus”? Is it irresistible authority of the Chain Rule; or final truth
in the Infinitesimal unphased by digital diversions; or the
incomprehension and boredom of all those readers who give a
passing glance at the exhibition of machinery and then get on with
the text?
We should do that first since the outer skin of this fruit is not
without blemishes. We are faced once more with the Leibnizian
nonsense, expanded into n dimensions. That ought to be a relief since
now there should really be no need to go back to that skipped-over
calculus after all. However, belief that there is complete relief is
feeble optimism—a dream of rationality. The particular calculus
turns up in countless textbooks—at least now we may perhaps know
where it started.
For a separate matter where there is a striking inconsistency,
something like in the “happiness” formula, Mr. James Baker the
erstwhile U.S. Secretary of State toured the newly independent
republics of Central Asia, speaking with their leaders and submitting
what is expected of them: “democratic government and free-market
economics”. The principle of such government must include some
independence. In allowing that, how can it also be laid down what
they should decide? A people could wish to maintain competition
internally to brace up performance and exploit local capacities,
perhaps on the side of basics for people and territory, without putting
these at the mercy of a noisy global competition for which they are
thoroughly ill-prepared—in other words, settle for living happily
with their comparative disadvantage. Instead of doubling their
population in thirty years or so they might even choose to limit
47

themselves—and pursue “greatest happiness” for their steady
number! After all, if one couple have three children its an appalling
50% expansion in one generation, draining away surplus for
improvements, if any. Human rights which get eager attention and
have been listed at Helsinki are no doubt good. Nonetheless it is not
always clear where the rights come from, and whether people in a
chaotically crowded world have any rights at all. How about
obligations, and shouldn’t they come first? The signatories of the
accord could then form a truly well-considered trading block.
There is a strong tide in favor of knocking down trade barriers
and fostering growth, but also a rising opposition coming out of
concerns with ecology, resources, demographics, environment and
the like, and deteriorations throughout the world. At an earlier time
the collision was rather between economic and social factors. Karl
Polanyi (1944) gives an account. Now a completely new era has
arrived in which hanging over everything are broad questions of
survival with a rather short time horizon. Near the threshold of
subsistence there are no margins, and with a tight global competition,
in a great part divorced from local attachments, there are none either.
That covers the most numerous and also the most rich and powerful
elements. So where is the will or strength to alter the current course?
This is the question dealt with provocatively by Richard Falk in his
Explorations at the Edge of Time.
J. M. Keynes reviewed the accounts and gave a reconsideration
of usual wisdom about trade in his 1933 article on “National Selfsufficiency”.
He was perhaps thinking about other things, but what
he had to say may cut better now than it could at that time.
The Earth is not a remote abstraction but a patchwork of
localities, each quite immediate to whoever happens to be there. Nor
is humanity, which consists of actual people all living somewhere.
Beside the currently topical global outlook, if there is a relationship
that has priority it is that between people and where they live. The
place is a first base for life and sustenance of inhabitants, who are its
custodians; all that goes with it is their care and responsibility, and if
they make a disaster of it, it is mainly their hardship and their own
fault. Such a severe view seems in harmony with remarks of Keynes,
48

and invites consideration as a response to ruinations that take place.
In any case, there is unrest in being dependent for vital needs on
trade with others with whom no steadier bond exists.
Since every era has something like its own economics,
dissatisfaction with what we now have may reflect a transition. But
to what? Some say a “new paradigm” without suggestion of its
nature or what should be done about it. Propensities in the
neoclassical and Marxist phases give visions of another heady round
of ‘theory’. The neoclassical outlook originated from the time of
Newton and the euphoria over his mechanics, and the ‘Optimism’ of
Leibniz. The economy had then to be approached as a machine, not
well understood because nobody around had made it or had the plan.
Hence the models economists play with, and the cult of the
optimum—“the best is enemy of the good” may be recalled at this
point. Marx under the spell of fashionable Hegel took on his notions
helplessly, and adopted Ricardo’s theory of value without noticing
the actual arithmetic is impossible. What could be next?
Documentation of happenings to the globe such as State of the World
reports of the Worldwatch Institute, or The Ecologist, suggest things
are going to be different. They cannot be the better—let alone
optimal, if that myth can be dispelled—simply by submitting to
government by the self-regulating machine and giving anxious
attention to its ups and downs that dominate the news. There must no
doubt be withdrawal from that foolishness, though there cannot be a
ready-made design for an era with unprecedented features—and
touch of finality.
BIBLIOGRAPHY
Afriat, S. N. (1965). People and Population. World Politics 17, 3, 431-9.
Japanese translation, with foreword by Edwin O. Reischauer: Japan-
America Forum 11, 10 (October), 1-28.
— (1972). Reservations about Market Sovereignty: four notes. In Mundell
(1972).
49

— (1980). Demand Functions and the Slutsky Matrix. Princeton University
Press, Princeton Studies in Mathematical Economics, 7.
— (1987a). Economic Optimism. Economics Department, Stanford
University, 21 April.
— (1987b). Logic of Choice and Economic Theory. Oxford: Clarendon
Press.
— (1988). Optimism from Leibniz to Modern Economics. Sophia
University, Tokyo, 27 April.
— (1994). On Trade, and Self-sufficiency. Institute of Economics and
Management Science, Kobe University, 22 April 1988. Research
Paper No. 326 (April 1989), School of Economic and Financial
Studies, Macquarie University, New South Wales.
Arrow, K. J. (1951). Social Choice and Individual Values. New York: John
Wiley. 2nd edition 1963.
Brecher, Irving and Donald J. Savoie (Eds.) (1993). Equity and Efficiency
in Economic Development: Symposium in honour of Benjamin
Higgins. Montreal: McGill-Queen's University Press.
Bell, Daniel and Irving Kristol (1982). The Crisis in Economic Theory.
New York: Basic Books.
Braudel, Fernand (1981). Civilization and Capitalism. New York: Harper
and Rowe.
Cassidy, John (1996). The Decline of Economics. The New Yorker,
December 2. Pp 50-60.
Deane, Phyllis (1978). The Evolution of Economic Ideas. Cambridge
University Press.
Falk, Richard (1992). Explorations at the Edge of Time: The Prospects for
World Order. United Nations University Press, Tokyo, and Temple
University Press, Philadelphia.
Goldsmith, Edward (1992). The Way: An Ecological World View. London:
Rider.
Hansen, Bent and Girgis A. Marzouk (1965). Development and Economic
Policy in the UAR (Egypt). Amsterdam: North-Holland.
50

Hayek, F. A. (1974). The Pretence of Knowledge. Nobel Memorial
Lecture, Stockholm, 11 December. In Hayek (1978), Chapter 2.
— (1978). New Studies in Philosophy, Politics, Economics and the History
of Ideas. University of Chicago Press.
Heilbroner, Robert (1972). The Worldly Philosophers. New York: Simon
and Schuster.
Higgins, Benjamin (1989). Equity and Efficiency in Development: basic
concepts. In Brecher and Savoie (1992), Chapter 1.
Hutchison,T. W. (1977). Knowledge and Ignorance in Economics.
University of Chicago Press.
Keynes, J. M. (1933). National Self-Sufficiency. The New Statesman and
Nation, 8 and 15 July; The Yale Review, Summer; Collected Writings
edited by D. Moggridge. London: Macmillan (1982), Vol. XXI, 233-
246.
Leijonhufvud, Axel (1968). Keynesian Economics and the Economics of
Keynes. New York: Oxford University Press.
— (1973). Life among the Econ. Western Economic Journal 11, 3
(September).
Morowitz, Harold (1981). Entropy, a New World View by Jeremy Rivkin
and Ted Howland. Discover, January, 83-5.
Mundell, R. A. (Ed.) (1972). Policy Formation in an Open Economy.
Proceedings of the conference at the University of Waterloo.
Waterloo, Ontario: Waterloo Research Institute.
Polanyi, Karl (1944). The Great Transformation: the political and
economic origins of our time. New York: Rinehart & Co. Inc. (and
Boston: Beacon Press, 1957).
Samuelson, Paul A. (1970). Maximum Principles in Analytical Economics.
Nobel Memorial Lecture, Stockholm, 11 December. In Les Prix Nobel
en 1970. Amsterdam and New York: Elsevier.
Shubik, Martin (1970). A Curmudgeon's Guide to Microeconomics.
Journal of Economic Literature 18, 2.
Soros, George (1997). The Capitalist Threat. The Atlantic Monthly,
February, 45-58.
51

Symons, Michael (1987). In Adelaide, the collapse of the free market.
Sydney, NSW: Times on Sunday, 3 May, p. 35.
Tarascio, Vincent J. (1986). The Crisis in Economic Theory: a Sociological
Perspective. Research in the History of Economic Thought and
Methodology 4, 283-95.
Ukai, Yasuharu (1987). Cycles of Isolationism and Foreign Trade—a case
study of Japan. Kansai University Review of Economics and Business
16, 1 (September), 61-74.
Worldwatch Institute (2000). State of the World 2000. New York and
London: W. W. Norton & Co.
52

Math-Econ
The Celebrated Theorem
It is impressive to find three distinguished senior professors at
leading American Universities with grants from NSF and ONR
have published a paper on “Two new proofs of Afriat’s
theorem”. Moreover, from the Abstract, it’s “celebrated”!
A “celebrated theorem”—that’s pretty good! Is Euclid actually
celebrated, or Pythagoras, and how do you celebrate a theorem? Here
we have a go.
I remember Herbert Scarf, one of the three authors, getting me to
give a talk at Cowles in 1964 when I was Visiting Fellow there. I
thank him for the appreciation and attention to the theorem which he
has taught generations of students since then.
Instead of my own paper “The construction of utility functions
from expenditure data”, Cowles Foundation Discussion Paper No.
144 (October 1964) delivered at First World Congress of the
Econometric Society, Rome, September 1965 and published in
International Economic Review, 8 (1) (1967), 67-77, which is of
some length and is in any case provided as an appendix to my book
just now published by Routledge, I reproduce the Introduction of the
“Two new proofs …” paper, Cowles Foundation Discussion Paper
No. 1415 (May 2003) now published in Economic Theory 24, 1 (July
2004), 211-9.
I thank Paul Streeten who was the first to tell me about the “Two
new proofs …”, and Martin Shubik who was the second.

The Tale, and Comment
Ihesitated dealing with this item for its objectionable features. But then
it is itself a further tale where I had particular satisfaction in the
outcome, and in my contributed comment. Hence I have been rough
enough, with the inclusion of due treatment for presumed villains, to want
to include it. I just hope it is not too boring for others.
PS
I included this item on my page, and confess to satisfaction
having it there, but then removed it because my son repeatedly
expressed disapproval at the advertisement of academic
organized crime (experienced by many and no joke), and making a festival
out of it.
But then a visitor came from Rome, with family, to talk about
something. At mention of the removal there came an expression of surprise
and regret, and of euphoric enthusiasm for the piece, on the part of all,
including the assistant who had got left behind in Rome and sent a
message..
I was somewhat—though not altogether—surprised at the change of
atmosphere giving comfort to conscience, and promptly—now without
interference from son—promised restoration, which I have already carried
out as anyone now acessing the Page will notice.
I may as well mention that the visitor, who I never had met before,
became moreover a collaborator, and we are now writing a paper together,
not unrelated to a not entirely dissimilar issue.
I can add—I can only assume it is because of the astronomical “black
hole” treatment—I am invited to contribute (should it be this actual piece?)
to SkyWatcher, magazine of Unione Astrofili Senesi (UAS), also noted
especially for Gastronomy—whose Webmaster, or Webmistress, got me
started with my Home Page.

The Tale of Two Research Communities: The Diffusion of Research on
Productive Efficiency. By Finn R. Førsund, Department of Economics,
University of Oslo, Norway, and Nikias Sarafoglou, Department of
Economics, Mid-Sweden University, Sweden. April 2004.
Abstract. The field of theoretical and applied efficiency analysis is
pursued both by economists and people from operational research and
management science. Each group tends to cite a different paper as the
seminal one. Recent availability of extensive electronically accessible
databases of journal articles makes studies of the diffusion of papers
through citations possible. Research strands inspired by the seminal paper
within economics are identified and followed by citation analysis during
the 20 year period before the operations research paper was published. The
first decade of the operations research paper is studied in a similar way and
emerging differences in diffusion patterns are pointed out. Main factors
influencing citations apart from the quality of the research contribution are
reputation of journal, reputation of author, number of close followers;
colleagues, “cadres of protégés”, Ph.D. students, and extent of network
(“invisible college”). Such factors are revealed by the citing papers. In
spite of increasing cross contacts between economics and operations
research the last decades co-citation analysis reveals a relative constant
tendency to stick to “own camp” references.
(The above is included only for reference in the present document.)
Attachment to the Quaderno starts here.

This paper by Finn R. Førsund and Nikias Sarafoglou is a
development of one presented at the IFORS conference, Athens,
1999, and is to be published in the International Journal of
Production Economics.
Professor Sarafoglou gave a lecture based on it at the University of
Siena, 25 November 2004, at which time he conferred with several
members. Sydney Afriat had communication with him before and was
already familiar with the paper. The paper has been offered for the
Quaderno (Working Paper) series, in conjunction with a Comment
prepared by Afriat.
Comment by Sydney Afriat. At about the time of the lecture I was able to
supply Nikias Sarafoglou with a copy of the 1971 paper of Charles Geiss,
which he had requested but after a lapse of over three decades had proved
hard to find. I added that this key paper and the one of J. Richmond
(1974), both of which are linked to my own of 1971, are without citations
that are due to them in the subsequent literature. I asked that attention be
drawn to these papers, and to the statement that involves them in my book
of 2002 listed below.
Geiss, Charles (1971). Computations of critical efficiencies and the
extension of Farrell’s method in production analysis. Department of
Economics, University of North Carolina at Chapel Hill, mimeograph.
Presented at Summer Meeting of the Econometric Society, Boulder,
Colorado, September.
Richmond, J. (1974). Estimating the efficiency of production. International
Economic Review 15, 515-21.
Afriat, S. N. (1971). Efficiency Estimation of Production Functions.
Presented at Summer Meeting of the Econometric Society, Boulder,
Colorado, September. International Economic Review 13, 3 (October
1972), 568-98.

—— (2002). The Market: equilibrium, stability, mythology. London &
New York: Routledge, 2002. Routledge Frontiers of Political
Economy No. 44. Remark on p. xiv and then Note 4, Historical note
on “Data Envelope Analysis”: Frontier and stochastic-frontier
production functions, pp. 119-22.
The unsuitability of submitting to investigators of citation statistics
two items which each have citation frequency zero then occurred to me.
There must be many such items that do not figure among the ones that get
cited and can be picked up by investigators using the newly available
computer resources.
It therefore seemed reasonable that these two papers should not feature
in the statistical work. But that left the outstanding question: Considering
their demonstrable importance derived from positions of priority on key
issues, why had they not been cited? It occurred to me (with an image from
astronomy) that bright stars had fallen into a black hole so that others could
shine.
In ordinary language, credit that was due to them had been taken by
others. That is certainly true, as will be elaborated—though there can still
be curiosity about the black hole!
At this point I will deal with Geiss, Richmond, Afriat and Farrell (and
then some others) and their relationships, by quoting from the above
mentioned Note 4.
In giving account of the frontier production function to an economics
graduate student class at UNC Chapel Hill, when dealing with the case
where there is imposition of constant-returns, Charles Geiss, a member of
the class, declared that obtaining production efficiences by such means was
another way of representing the method proposed by M. J. Farrell (1957).
That was confirmed, and Geiss (1971) recomputed and extended Farrell’s
results, using the same data. He developed computer programs for carrying
out test of various production models, defined by restrictive properties, and
the corresponding efficiency determinations.

A constant returns function is determined by a single isoquant, and
Farrell dealt with the unit isoquant instead of the function graph. However,
when dealing with the function graph, instead of taking the monotone
convex conical closure—a kind of “envelope”— of the data points,
yielding an equivalent of Farrell, one can just as well drop the conical, or
constant-returns, imposition, to get something different from Farrell, with
which we had started, these procedures being among those proposed in
Afriat (1971). Since the values of a ‘frontier’ function were immediately
given by a linear programming (LP) formula, there was no issue about
computational procedure.
So with reference to Farrell, Afriat and Geiss we have the early history
of the frontier production function, which comprises the main ideas of
what is now called ‘data envelopment analysis’. My entry to the subject
came directly from demand analysis, and Geiss introduced me to Farrell’s
work.
The stochastic-frontier production function is something completely
different, the idea having been proposed by Afriat (1971). Computations
with data were first carried out by J. Richmond (1974).
Credits for first computations, or basic ideas, due to Geiss, Richmond,
or Afriat, have all been given to or claimed by others. After all, we have
been told:
If we should ever encounter a case where a theory is named for the
correct man, it will be noted.
George J. Stigler
The Theory of Price (3rd edition), 1966, p.77
Stigler may have marked, if not just ignorance, a prevalence of ritual
citations by separate individuals that amount to nothing more than
greetings to friends. Such a phenomenon is consistent with “The Tale of
Two Research Communities” and the tendency observed there to “stick to
‘own camp’ references”. But still, he need not have touched a matter as
dreaful as we now have, where collaborating individuals have acted

together to mislead everyone, serving their own interests while damaging
others, and with full awareness about it all.
Førsund and Sarafoglou deal most especially with statistics of citation
occurrences, but they do sometimes deal with citations also for their
absence:
“… the special form of a ... model set up in Banker, Charnes and
Cooper was actually introduced already in Afriat … ”
“But Afriat … also contributed ... [to Farrell’s model]… by
formulating the model with variable returns to scale. This was later
referred to as the BCC model (Banker, Charnes and Cooper, 1984)
by the OR/MS community (without reference to Afriat).”
I suppose the Charnes, Cooper and Rhodes (1978) (CCR model) paper
has a similar significance.
After-conference drinks found Cooper and myself by chance in a
proximity, and Cooper said “Do you mind?”, as if I should know what he
was talking about. I raised my glass slightly and moved attention
elsewhere. 2000 citations later more can be said, and quite likely will be.
At the time of my paper I was puzzled by the interest shown in it. For
want of an appropriate communication environment, or absorption in other
things, I had been not aware, or concerned, that a promising application
field was undergoing expansion. It was promising in financial terms, to be
an abundant provider of well-funded projects. It certainly turned out to be
that, on a great scale. A “scientific revolution” affecting efficiency
measurement has been proclaimed. It was valuable for a consultant to be a
much cited authority, and even better, to be an acknowledged originator
and pioneer of the revolution. For profit, the control of publications, and
with that the control of citations, was important. Hence the seizure of a
journal that had, from that point of view, been in unreliable hands.
Concerning the Journal of Productivity Analysis, the obvious target,
Ali Dogramaci had been founder and first Editor-in-Chief; and I was a
Member of the original Advisory Board. It was taken over (hijacked)
forcibly, that is, without agreement or consultation with the management,
by individuals who must have made a direct approach to the publisher with

appearance of good-faith so they would be accepted without question.
There followed a ‘purge’ or ‘cleansing’ of unwanted elements, in which
the Editor-in-Chief was replaced; and I was ejected from the Advisory
Board. Since I no longer received copies of the journal, I have been unable
to follow what happened thereafter. I always thought that Members of the
Advisory Board of a journal were, ordinarily, fixtures. However, the new
management were serious and determined people, not to be deterred by
custom.
That journal take-over always has in my mind something to do with
the black hole I spoke about.
In contemplation of production efficiency measurement history I go
back to Richmond, and to Charles Geiss, like Richmond an absolute first
for a most important type of computation. Our papers were presented at the
same meeting in 1971. When I left UNC Chapel Hill I thought Geiss was
the only person there who had anything to do with efficiency measurement.
I had not been aware that any Professor shared the interest at all. However,
Geiss, the Student, completely disappeared (into the black hole), and a
Professor emerged as a new shining star (Editor-in-Chief-to-be and black
hole manager) with priority claims belonging properly to Geiss, Richmond
or myself (more specifically, Richmond and myself; Cooper took over
credits due to Geiss and myself in the division of black hole spoils).
.
Attachment to the Quaderno ends here.
The Quaderno consisting of the paper with this attachment should be
available on-line at http://www.econ-pol.unisi.it/quaderni.html.

Finally

Sydney Afriat graduated in Mathematics from
Pembroke College, Cambridge, with a period at
the National Physical Laboratory, Teddington,
during World War II, after which he did 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 Visiting Fellow in Economics at Yale.
Beside teaching spells 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 he was at Bilkent
University, Ankara, before becoming associated with the
University of Siena. He is author of several books and
many articles to do with Mathematics and Economics,
beside scattered accidentals for computer programmer,
painter, and poet.
112

“… 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

“… 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 € 15,00
(IVA compresa)

*
NONPLUS
fragments