Although
I was released from active duty in early November 1945, my nearly
five years service entitled me to terminal leave until February
16,1946, so I didn’t have to find a job immediately. After
selling our house in San Bernardino, we headed East, visiting Mrs.
Chapman in Newport News and settling in with Mother in Hyattsville. I
wanted to return to the Government Printing Office, in order to make
sure my war service would be considered a part of my service there,
and because I needed something to do. It didn’t take me long to
get back my speed of operation, and to pick up the details of the
job. The Printer’s Union dues had been paid for all of us in
service by our local all the time we were gone, so my status as a
union operator was preserved. I didn’t realize then how
valuable that was to be for me in just a few months. The newspapers
published a plan adopted by the Administration to reward the
demobilizing veterans with ‘gangplank promotions', provided
they had accumulated sufficient time in their last war-time grade. My
calculations showed that I just barely qualified for promotion to
full colonel, so I eagerly watched the mail for the notice to come.
In January I got impatient and wrote a letter of inquiry to my
separation center. They responded with the coveted special order,
which had to be rescinded when the one that was already in the mill
came out, as I couldn’t be promoted twice! I could now wear
eagles on my shoulders (see above left), and could hardly wait
to sport them in front of my uncle, Dr. Wilbur Phelps (my mother’s
brother), who had earned his eagles in World War I.
My
involvement with radar and gun-laying directors had convinced me that
I wanted to enter the new field of electronics, but needed to qualify
as an expert by getting a PhD at a university specializing in that
field. Not knowing where that might he, I solicited the advice of my
professors at George Washington, Prof Ames (EE) and Dr. Brown
(Physics). To my surprise they independently recommended Harvard
University, and offered to write testimonial letters for me. I'm sure
those letters were instrumental in my being accepted, as Harvard was
receiving three to four times as many applicants as could be
accommodated. Acceptance was received shortly after the first of the
year, and I was able to arrange my resignation from the GPO and head
for Boston with our little family before the end of January. I can
still remember the frozen streets and snow-piled yards of the houses
we passed. We didn’t see the ground until April.
Post-war Boston was crowded. Finding a place to live was difficult. Fortunately we had a car, so could chase down the few ads for houses for sale and rooms to be rented. We found a two-family house for sale in Brighton (which we bought with our VA guarantee and no down payment), but were dismayed to learn that we would have to wait up to three months for the renter to relocate. Fortunately for us, the upstairs family had no children, as the downstairs family did, and they moved out within the three months allotted. Meanwhile, Mary Charlotte and I had to rent a room in a row house owned by an Irish lady named Mrs. Frame on Green Street, Jamaica Plain, in the southern section of the city. Boston had a fairly good subway system, so getting to Harvard and downtown to work was not too time-consuming. But living in one bedroom, eating all meals in the crummy local restaurants, and having to farm out our children did not make for joyous living. From an ad in the paper, we located a family named Baker in one of the northern suburbs who took Will and Mary Francis. Even after we had moved into our (second floor) home, we decided to leave them with the Bakers, as I had to work at night and sleep in the daytime. The original three months stretched to over two years before we were able to have the kids with us again.
I plunged into
my studies with much gusto, taking five subjects (the normal was
four), and even audited a sixth. When my last Army check had been
spent, I realized that I would have to work. The GI Bill which
Congress had just enacted provided for all my University expenses,
even including books, and $90 a month living costs as well, but that
didn’t even pay for the children’s care. My union card
was a passport to a job, however, and I was first sent to the Rapid
Service Press which had four linotype machines and needed a part-time
night operator. Pay was only $1.35 an hour, the frozen war rate, but
union negotiations had already provided for doubling that, which I
received in due time. I was able to phase my class days and my work
nights to allow an average of six or so hours sleep a night but study
time was hard to come by. One of my courses was electronics lab. The
university had acquired three SCR-584 radar units from the Marine
Corps, and assigned them to our class. We formed teams to study these
units, and physically adjust and align all their circuits, proving
our work by actually tracking airplanes. Having had that excellent
course on these complex devices at the AA School just two years
earlier gave me a real advantage over the other students, and our
team was the only one to get its 584 to track a plane.
Near
the end of the first semester, the school notified me that I would
have to find a professor to sponsor my PhD research, if I wanted to
pursue that degree. The German V2 bomb had shown that space was now
open to man, so I thought a good subject would be the design of an
instrument for spatial navigation. I started out to interview each of
the seven professors in the Department of Engineering Science and
Applied Physics (ESAP) of the Graduate School of Arts and Sciences.
One after another, they all turned me down. Finally I was sent to Dr.
Howard Aiken, a tall, austere man, who upon hearing my proposal
answered, "I am not interested in that; but if you want to study
the application of this computer to the social sciences, I’ll
sponsor your research." The only thing I heard him say was "I’ll
sponsor your research." In my entire university career I had
taken only one social science course, economics. "This computer"
turned out to be Mark I, a monster machine Aiken had designed and IBM
engineers had built for Harvard for which Aiken was pictured on the
cover of Time magazine as the "father of the automatic computer"
some months later. Upon my immediate assent, Prof. Aiken turned me
over to Grace Hopper, one of the two or three programmers assigned to
the Computation Laboratory. She provided me with some reading
material on the machine, and I spent as much time as I could during
the summer months learning how to program this computer.
I
took three more courses during the summer term, qualifying for the MA
degree in electronics. The extra work at Rapid Service Press dried
up, so I shifted to the newspapers, first the Boston Herald, and then
the Boston Globe. Several factors were in my favor: (1) The end of
price control and rationing had released the stores to offer
merchandise long in short supply, and they were making a mint,
advertising more and more; (2) the newspaper had to hire whomever the
union endorsed as qualified; and (3) the regular journeymen had to
hire substitutes as available to "burn" up their overtime
hours, a union requirement. Thus I was able to get as much work as I
wanted, and on almost any night I wanted. All I had to do was to turn
my name-slug to show my name, and some regular would put it on the
time-board in place of his own, signifying that I was to work his
shift, and receive his pay. When I didn’t want to work, I kept
my name-slug turned to the blank side. Since everything was done by
seniority, I soon worked my way up to the top of the sub board. When
this happened, I was eligible to be hired as a regular, and this
happened early in 1947.
Mary Charlotte wanted to work, and
plenty of work was available. She first tried a laundry clerk
position, but soon gave that up, as she didn’t like to handle
the filthy clothing that was brought in. Then she tried assembling
hearing aids, and later making rubber boots. In both cases, the firms
offered high wages to trainees, but as soon as their training time
was over, their pay was piece-work. Not being very fast at the work,
Mary Charlotte’s pay dropped to less than half as soon as her
training time was over, so she quit. Eventually she got a job in the
Harvard Widener Library, and kept it for the rest of my time as
student there.
We saw the children every week-end, either
visiting them at the Bakers, or bringing them to our home in Brighton
for a few hours. We also attended church in nearby Brookline, when
permitted by a rare non-working Saturday night. Week-ends were my
only opportunity to catch up on my sleep, often only four hours per
24, and to do the many assignments my courses required. Mary
Charlotte would prepare a set of snacks for me and place them at my
elbow as I was working on my assignments. I would eat the snacks
without even knowing it! I also did a lot of reading on the subway
between Brighton and Cambridge. We sold our car, as I had decided I
couldn’t afford the compulsory insurance, which had the highest
cost in the entire country. Ironically, our home in Brighton (part of
the city of Boston) was just a block from Brookline, in which the
insurance rate was less than half that for Boston.
During the autumn of 1946, I had
two course credits entitled "research time." This work was
programming the Mark I. Dr. Aiken had decided that my research should
be a major computation needed by one of the University economics
professors, Wassily Leontief, who became a member of my doctoral
committee. Dr. Leontief was pioneering an economic theory entitled
"Input-output", which essentially said that the economy of
a country could be subdivided into interdependent sectors. If the
dollar amount of goods and services passing between one sector and
each of the others could be determined, it would be possible to
calculate the increase in performance of each sector needed to meet
some national goal, such as a war effort, a building boom, or any
other major change desired in the levels of production. The
calculations required, however, were completely beyond the
capabilities of then existing calculating machines, and that is why
Dr. Aiken wanted me to figure out how to get his new computer to do
the job. I started out with a model of a 10-sector economy, for which
I had to find the levels of production for each sector for a
hypothetical national goal. Mathematically speaking, this entailed
the specific solution of a 10x10 matrix. A full matrix of that size
had never before been calculated. The engineers had just finished
installing a new set of hardware devices, called subsequence units
(ten of them). I made use of them to solve this problem, as well as
to enable the engineers to check out their work. It took Mark I about
24 hours to finish the calculation (after I finally got all the bugs
out of the program), using just about every register and calculating
unit it had. Aiken and Leontief were delighted. Incidentally, it was
about this time that a malfunction in the computer was discovered to
have been caused by a moth getting into a relay — hence the
term "bugs" in a computer or program. Grace Hopper helped
me with a number of problems in setting up the program, and I was
grateful for her help and suggestions.
A real financial blow
came in January 1947, when the Veterans Administration terminated my
$90 a month living allowance, and demanded my return of that
allowance for the past five months! Because of some abuses of the GI
Bill, Congress had passed an amendment denying living allowance to
persons receiving pay for their schooling. The language was vague,
however, and the VA representative at Harvard assured me that I would
not be affected. However, when I had to submit a form on which to
show any employment, the bureaucrats decided that I was affected, and
was not entitled to the allowance from the date of the change. Since
I had been working just enough to make ends meet, I told the VA man I
could not repay the $450. Two months later, I received word that I
had been eligible for a dividend from my GI insurance, but the VA had
taken it to satisfy my debt to them. The amount of the dividend?
$450! This loss of income required me to increase my hours of work
and to accept the full-time job when offered.
Work as a linotype operator at the Boston Globe
was an experience in itself. The machines were crowded into a corner
of the top floor of the newspaper building, which must have been
fifty years old. We composed nearly all the reading matter printed,
including that in many of the ads. The classifieds, the neighborhood
movie ads, and the sports columns constituted most of my work. I soon
knew every movie being shown and every actor in each of them, often
having to correct the erroneous copy. I got to know the name of every
horse on every track in the country, and every player of the
baseball, football, soccer, basketball, curling, and you-name-it
sports in eastern USA and Canada. My interest in sports has been zero
ever since! Ever so often we had to do the "Set and Kill."
Where the advertiser supplied his own matrix for the ad, union
regulations required that the operators set up the reading matter in
those ads, even though it was not to be printed. Many times the
volume of work was more than we could get done in the regular shift,
and we would have overtime — one, two, or four hours. If this
was the beginning of a school day, this time came right out of my
sleeping time. The overtime pay, however, enabled me to cut back on
total work hours, so I welcomed it.
When told I would have to
take the full-time job or go to the bottom of the sub-board, I
decided that I had better take it. I had classes on Monday,
Wednesday, and Friday mornings, with computer lab work in the
afternoons. If I could get the night shift which gave me Sundays and
Thursdays off, I would have only one night a week with a short
sleeping time. The foreman said he didn’t think I could have
it, as shift assignment was by seniority, but I did get it, and that
enabled me to survive that very full semester at school and still
work nearly full time (I had to put on a sub when over-time hours
accumulated). The full-time job also provided hospitalization
insurance coverage for my family and me, so Mary Charlotte and I
decided that Will and Mary Francis should have their tonsils taken
out. When we told them they were going to the hospital, they were all
excited and eagerly looked forward to it. We felt like hypocrites
when we visited them immediately after the operation, as they had the
longest faces we had ever seen on them.
I managed to wrap up
all the course requirements for my PhD by the end of the spring term
of 1947, leaving only my thesis, my oral exams, and my language
qualification tests to be completed during the next school year.
However, I just squeaked by in the course in Applied Mathematics —
a major course taught by a French import, Dr. Brillouin. This man had
developed a theory of integration called the saddle-point theory, by
which one could integrate mathematical expressions not otherwise
possible. He had dwelt on this theory in class, but no one expected
him to make it the sole part of the final examination. He gave us
four formulas to integrate by this method, right out of the back of a
mathematics handbook. I got the first one done in one hour. The
second I bogged down on after five minutes, so put it aside. The
third took another hour, as did the fourth, allowing me just enough
time to finish it before time was called. There was a fifth question
from Dr. Aiken, on a lecture he had given which I had not attended,
due to overtime work, and which I had overlooked in studying my notes
from another student. I went home, read my notes and worked the
bypassed problem and Dr. Aiken’s problem in an hour each. Three
out of five gave me 60% — hardly a passing grade. This exam was
the only measure of competence, and a grade less than B in one’s
major field meant OUT, no second chance. I had just about given up
all hope of getting my doctorate, when the grades were distributed; I
got a B-! Praise the Lord! I learned how it happened just by chance
(?) several months later when Dr. Aiken was talking about the
examination to someone else. It seems that Dr. Brillouin was called
back to France for a consultation, and had Dr. Aiken mark the papers.
As I recall his words he said, "One guy got 100, the next was
80, and the grades ranged from there down to 10. I decided to accept
60 as passing." I have wondered since if my being his only
research student had any bearing on his decision. Without any extra
effort on my part other than to apply for it, I was awarded a new
degree, along with seven others, called Master of Engineering
Science. I believe it was instituted to provide a recognition for two
years’ graduate work when a PhD was not obtained. The degree
was discontinued two years later.
Even with all the pressure
of school and work, I had not neglected my military career. Since I
was already in Boston when my terminal leave expired (when I reverted
to inactive status), I quickly affiliated with an Active Reserve unit
there. I attended a few of its meetings, hoping to learn something
about the rocket principle behind the German V-2 rocket bombs.
Instead I was assigned to give a lecture on the subject, and had to
dig the principle out for myself. Opportunity for a refresher course
for officers, to be held at Fort Benning GA in June, was just down my
alley, and I applied and was accepted. Those two weeks have
contributed to my military pension for over 32 years now.
Although I had no formal courses during the
summer, I found it expedient to spend a good deal of time at the
Computation Lab. Dr. Aiken and Dr. Leontief had decided that my
thesis subject was to be the inversion of a matrix of order 38. What
this means is that my thesis would be the result of programming and
computing the general solution to a set of 38 simultaneous linear
equations, each representing the annual contribution of one of the
sectors of the US economy to the other 37 sectors. The term "general"
meant that my computation would generate the coefficients of the 38
unknowns in each equation which, when any set of specific values of
the outputs was given, the unknowns (each representing needed
production of one sector) could be calculated. Dr. Aiken and his
hardware staff had been deeply involved in developing a new computer,
to be known as Mark II, more than ten times faster than Mark I, and
my computation would be used as the guinea pig to check out the
hardware of this computer. Mark II was actually two identical relay
computers, with a check register that continuously compared the
results from each unit, stopping computation instantly if a
disagreement was detected in the two values. Dr. Leontief and his
colleagues at the University had put in an enormous amount of work in
generating the numbers they supplied me, representing the 38x38
"inputs" to our national economy. I knew nothing of that
work or even the theories on which it was based. I just took the
numbers and carefully punched them into paper tape to be used as
input for my program. Although the decisions were made during the
summer, construction of the computer was slow, and I didn’t get
down to the initial checking of my programs until well into the
autumn, and actual computation did not begin until January
1948.
Meanwhile Dr. Aiken decided that I should teach a
laboratory course on computation and programming, as part of my
training for the doctorate. So Harvard hired me as a lab instructor
at $180 per month. They only paid me $125, however, as that was the
most a veteran could earn and still get his living allowance of $90.
The bureaucrats were most unhappy to learn that I got no living
allowance, and that they would have to pay me the full $180. This lab
course took a great deal of my time, but it was worthwhile. For the
first semester’s work, Dr. Aiken had obtained about 50 old
Marchant calculators, on which my students had to work out by hand
the solution to a variety of mathematical problems. One poor student
just could not get the right numbers into the machine, and he took
two to three times as much time on the course as the others. The
second semester was devoted to the programming and running on Mark I
of a series of small programs. I believe that was the very first
programming course ever conducted in the US. Not having classes to
attend in the morning (the lab work was all in the afternoon), my
sleeping hours were much more reasonable. However, all my time on the
Mark II had to be done at night, as the engineers had the machine
every day. This competed with my work at the Boston Globe, but I
managed to get enough work to pay our bills. Just before Christmas, a
notice was given at the Reserve Officers meeting of a 2-month
opportunity for a qualified Reserve Officer to be Assistant PMS&T
(professor of military science and tactics) at Boston College —
in AA gun gunnery. I applied for the job and was interviewed by the
Regular Army colonel who was the PMS&T, but did not know AA
gunnery. He objected to my service as almost exclusively automatic
weapons, until I pointed to my superior rating at an AA gun gunnery
course I had taken in Hawaii while waiting to come home, and to my
radar course. I got the job, and became the second Protestant on the
staff of this Roman Catholic institution. Now I had three full-time
jobs — student, linotype operator, and professor. My seniority
at the Globe had caused me to be transferred to the Day Side (better
hours, same pay), which I could not handle, so I had put a sub on and
left him there. On my next visit to work the one day a month I had to
work to maintain my active status in the union, the union secretary
told me I would either have to give up my regular job or come to
work. I gave up the job.
Finally Mark II was ready for my
computation. There was no internal or disk memory in these early
computers. All data had to be fed in from punched paper tape at 10
characters per second (modern computers operate at millions of
characters per second), and intermediate values had to be punched out
on paper tape and then read back in when needed. I had already
punched up the primary data tapes with the 1,444 industry
input-output values on them, and also the program tape. In addition
to the 38 columns of numbers in each of the 38 rows, I used a 39th
column (originally the sum of the 38) as a check column, receiving
the same operations as each of the 38. The computer compared this
check value when reached with the running sum of the preceding 38
values to insure that there was equality. Any discrepancy signaled an
error. About 10% into the calculation, the computer fouled up on the
current check number, and we had to compute it by hand before
continuing the main computation. As I had to go to work at the time,
Art Katz (a student friend) calculated it for me, and got the Mark II
back into operation. Three weeks later I got a phone call while at
the Globe from the chief engineer saying that the check number had
"blown up" and would I come to the Computation Lab to take
care of it. There were at the time 12 bushel baskets full of paper
tape rolls. Which one of the thousands of numbers was responsible?
The thought came to me [from God?] that perhaps Art had made an error
in computing that check number three weeks earlier. I immediately set
about to recompute that value. It took me all day, but I got it done
just before the night shift of engineers came on duty. The next day
brought the confirmation that the new number was okay, and the
computation ran to completion — taking only six weeks! The
chief engineer, who had hardly looked at me before, now thought I was
a genius, as he thought we would surely have to start all over
again.
The final values had to be typed up by hand and
presented to Dr. Leontief. Twenty-five years later he would be
awarded a Nobel prize for this and subsequent work in Input-Output
Theory. The inverse could readily be proved by multiplying itself by
the input matrix, which should give the unit matrix, just as
multiplying any number by its inverse gives one. The result showed a
precision (accuracy) of our numbers to over 9 decimal places. Unknown
to me, one of the Nation’s foremost mathematicians, Dr. John
von Neumann, had been wrestling with the theoretical considerations
of the very calculation I had undertaken. He published his results in
the Journal of the American Mathematical Society early in 1948. Using
very involved advanced mathematical concepts, he had come to the
conclusion that the accumulated round-off error in a computation of a
matrix inversion of any large magnitude would greatly erode the
accuracy of the results. (Round-off error is experienced when the
full span of digits obtained from multiplication, which is the sum of
the digits in the inputs to the multiplication, is truncated to the
number of places carried by the computer.) An even greater hazard in
this particular type of computation is the loss of precision when two
nearly equal values are differenced, particularly if the resulting
difference is used as a divisor. Since this sequence of steps is an
integral part of the matrix inversion process, the loss of accuracy
could be catastrophic. In a table in the appendix to his paper, Dr.
von Neumann estimated that in the inversion of a 38x38 matrix with a
computer carrying ten-place values (my situation), the results could
be depended on for only three places of the ten. When my work was
completed, it tested correct to over nine places of the possible ten!
Dr. Aiken was so pleased to be able to refute the great von Neumann
that he strongly recommended I be granted my degree. Without that
incentive, I might still be at Harvard trying to produce something
sufficiently unique and worthwhile to be rewarded with a PhD from
Harvard.
With the thesis work done, I dug into the task of
preparing the thesis document itself, which occupied most of March
and April. I also had to pass my orals and the two language
competence tests (French and German). Since the degree requirements
involved one major field (in my case numerical analysis) and three
minor fields (I chose antennas, vacuum tubes, and traveling wave
tubes), my orals covered all these fields. Prof. Mimno gave me the
hardest time, in his questions on traveling wave tubes, in which he
was the University expert. I had had only one course in them (under
him), and was by no means an expert. His questions got more and more
specific, and I was struggling to describe the phenomena in terms of
voltage changes until I realized that I was over my depth, and
thought, "This is the end." Almost as an afterthought [from
God?] in the last answer I said, "Of course, one can describe
these phenomena in terms of current variations also." He stopped
at once. That was what he had been trying to get me to say.
The
language tests brought on another miracle. The German test was tough,
but I was reasonably well prepared for it, with my background of
Scientific German at George Washington Univ. The French was something
else. The secretary of the Computation Lab had been a French major,
and she had had great difficulty in passing the test there at
Harvard. When she learned of my pitifully weak background in French,
she was aghast, and urged me to spend full time boning up for the
exam. That was impossible, as I was up to my ears in completing the
thesis and handling my lab students. When the date for the French
exam was posted, it conflicted with my lab class. I asked Dr. Aiken
what I should do, and he said he would arrange for me to take a
make-up, which he did. The make-up test was "duck-soup", a
paragraph from a French mathematics paper that anyone knowing the
math could have understood, even if he never studied French. That
hurdle was passed! Praise the Lord, who most certainly must have
arranged it.
Commencement exercises were scheduled for the morning of June 11th, 1948, with an address at the Harvard Club in the afternoon by General Marshall, now Secretary of State. Mother, Dad, Marion, and Mrs. Chapman had flown up from Washington to observe the ceremony. Mary Charlotte and I had driven up from Glen Cove, Long Island, where I had already started on my new job as professor of engineering at the Webb Institute of Naval Architecture. Each graduate had two tickets for General Marshall's address, and as Mary Charlotte was anxious to get back to Glen Cove, I gave my tickets to Mother and Marion. I didn't know then that history was in the making, as that was where the famous Marshall Plan for Europe's recovery from World War II was unveiled. As I drove out of Harvard Yard, I realized that another page in my life had been turned. Henceforth I would be addressed as DOCTOR Mitchell.
I cannot pass by this period in my life without acknowledging
God’s omnipotence in controlling all factors of a complex
situation. This whole episode was one miracle after another. First,
the choice of Harvard was completely outside my control. Even with my
acceptance, how is it that Mary Charlotte, who had never before or
since been willing to live in New England, was willing to go there at
this time? Next, my acceptance when only one in three or four was
admitted must have been a work of God Himself. Third, our support was
never lacking, with income from the VA, from the printing trade, from
the Army, from Mary Charlotte’s earnings, and finally from the
University enough to meet our needs. We did not borrow throughout all
this time. Fourth, the choice of my PhD research was completely the
Lord’s — I did not know who Dr. Aiken was. I had never
heard of his computer, and I certainly would never have chosen a
project from the social sciences if he had not made it mandatory. As
I look back on that incident and realize what that choice has meant
to me — it has affected every period of my life since — I
am overwhelmed with the realization that truly the Lord looks after
fools and the simple minded. Fifth, the simultaneous occurrence of my
need for access to a computer and the engineers’ need for a
guinea-pig computation to prove their work —- both on Mark I
and on Mark II — is still one more case of the Lord’s
orchestration. Sixth, the Lord’s guidance to the cause of the
blow-up in the computation at the half-way point was essential to the
successful completion of the work. It is problematical if I would
have been allowed the computer time to complete the calculation, if
it had been necessary to start over, as the engineers were through
with their check at about the same time as my problem was completed.
I could easily have spent several weeks trying to find the source of
that error — if I ever could find it — if the Lord had
not led me right to it. Seventh, my preparation for the oral
examination was inadequate — particularly in the three
collateral areas required for the doctorate, and I could easily have
been flunked out, particularly by Dr. Mimno, if the Lord had not
given me the inspiration to satisfy him. Eighth, my passing the
French examination was in some ways the greatest miracle of all, for
I made absolutely no preparation for it. If a text like any one of
the three presented on the German examination had been required, I
would have been hopelessly lost. Ninth, the passing of the course in
applied mathematics with only 60% on the final exam could only have
come about by Dr. Aiken’s substitution for Dr. Brillouin —
the latter would cheerfully have flunked two-thirds of the class! But
the greatest miracle of all was the concurrence of the publishing of
Dr. von Neumann’s study of the instability of the matrix
inversion calculation (essentially saying in a 125-page treatise in
the Journal of the American Mathematical Society that the calculation
on which I was engaged would almost certainly be riddled with
round-off error) with my results of almost complete accuracy. The
only reason for that accuracy was the tedious and careful compilation
of the industry coefficients for the input matrix by Dr. Leontief and
his coworkers. Had this computation been done in some other field, or
if the input data had not been so carefully and accurately compiled,
my results would have been as inaccurate as Dr. von Neumann’s
paper predicted. And I had absolutely nothing to do with these
factors. I was indeed the fool who rushed in where angels fear to
tread. Yes, although I had to work hard and faithfully for those
2-1/2 years, nevertheless my doctorate was a gift from the Lord
Himself.
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