JF Ptak Science Books *Quick Post*

John von Neumann contributed a major piece of prescient thinking in the 1949 volume of* Proceedings/Computation Seminar*, December 1949, assembled by Cutherbert Hurd of the IBM Applied Science Department. [The entire contents of the volume is available here.] Von Neumann (1903-1957)--perhaps the most advanced mind of the 20th century, a man whose work made the other advanced minds say "how did he do that?"--was a staggering polymath who made contributions in many fields, not the least of which was in the creation of the modern computer. His one-page contribution to this volume was a deep insight into the possibilities of the machine. In 1949. Check out this terrific piece by the great Claude Shannon, "John von Neumann's Contributions to Automata Theory" here.

"The Future of High-Speed Computing" by John von Neumann of the Institute for Advanced Study (Princeton):

A major concern which is frequently voiced in connection with very fast computing machines, particularly

in view of the extremely high speeds which may now be hoped for, is that they will do themselves out of business rapidly; that is, that they will out-run the planning and coding which they require and, therefore, run out of

work. I do not believe that this objection will prove to be valid in actual fact. It is quite true that for problems of those sizes which in the past~and even in the nearest past have been the normal ones for computing machines..[continued in full below]

1. ...[continued] planning and coding required much more time than the actual

solution of the problem would require on one of the hopedfor,

extremely fast future machines. It must be considered,

however, that in these cases the problem-size was dictated

by the speed of the computing machines then available.

In other words, the size essentially adjusted itself automatically

so that the problem-solution time became longer,

but not prohibitively longer, than the planning and coding

time.

For faster machines, the same automatic mechanism

will exert pressure toward problems of larger size, and the

equilibrium between planning and coding time on one

hand, and problem-solution time on the other, will again

restore itself on a reasonable level once it will have been

really understood how to use these faster machines. This

will, of course, take some time. There will be a year or

two, perhaps, during which extremely fast machines will

have to be used relatively inefficiently while we are finding

the right type and size problems for them. I do not believe,

however, that this period will be a very long one, and

it is likely to be a very interesting and fruitful one. In

addition, the problem types which lead to these larger sizes

can already now be discerned, even before the extreme

machine types to which I refer are available.

Another point deserving mention is this. There will

probably arise, together with the large-size problems which

are in "equilibrium" with the speed of the machine, other

and smaller, "subliminal" problems, which one may want

to do on a fast machine, although the planning and programming

time is longer than the solution time, simply

because it is not worthwhile to build a slower machine for

smaller problems, after the faster machine for larger

problems is already available. It is, however, not these

"subliminal" problems, but those of the "right" size which

justify the existence and the characteristics of the fast

machines.

Some problem classes which are likely to be of the

"right" size for fast machines are of the following:

1. In hydrodynamics, problems involving two and three

dimensions. In the important field of turbulence, in particular,

three-dimensional problems will have to be primarily

considered.

2. Problems involving the· more difficult parts of compressible

hydrodynamics, especially shock wave formation

and interaction.

3. Problems involving the interaction of hydrodynamics

with various forms of chemical or nuclear reaction

kinetics.

4. Quantum mechanical wave function determinations

-when two or more particles are involved and the problem

is, therefore, one of a high dimensionality.

In connection with the two last-mentioned categories of

problems, as well as with various other ones, certain new

statistical methods, collectively described as "Monte Carlo

procedures," have recently come to the fore. These require

the calculation of large numbers of individual case histories,

effected with the use of artificially produced "random

numbers." The number of such case histories is necessarily

large, because it is then desired to obtain the really

relevant physical results by analyzing significantly large

samples of those histories. This, again, is a complex of

problems that is very hard to treat without fast, automatic

means of computation, which justifies the use of machines

of extremely high speed.

2. Some of the contetns of the volume:

JOHN VON NEUMANN The Future of High-Speed Computing

RICHARD W. HAMMING Some Methods of Solving Hyperbolic and Parabolic

EVERETT C. YOWELL Partial Differential Equations

HARRY H. HUMME Numerical Solution of Partial Differential Equations

PAUL E. BISCH An Eigenvalue Problem of the Laplace Operator

KAISER S. KUNZ A Numerical Solution for Systems of Linear Differential

BONALYN A. LUCKEY Equations Occu"ing in Problems of Structures

JOHN P. KELLY Matrix Methods

FRANZ L. ALT Inversion of an Alternant Matrix

JOHN LOWE Matrix Multiplication on the IBM Card-Programmed Electronic Calculator

CECIL HASTINGS, JR. Machine Methods for Finding Characteristic Roots of a Matrix

PAUL HERGET Solution of Simultaneous Linear Algebraic Equations

STUART L. CROSSMAN Using the IBM Type 604 ElectronicCa/culating Punch

EVERETT KIMBALL, JR Rational Approximation in High-Speed Computing

F. N. FRENKIEL The Construction of Tables

H. POLACHEK A Description of Several Optimum Interval Tables

MARK KAC Table Interpolation Employing the IBM Type 604

M. D. DONSKER Electronic Ca/lculating Punch

Po C. JOHNSON An Algorithm for Fitting a Polynomial through n Given Points

F. C. UFFELMAN The Monte Carlo Method and Its Applications

-EVERETT C. YOWELL A Punched Card Application of the Monte Carlo Method (presented by EDWARD W. BAILEY)

GILBERT W. KING A Monte Carlo Method of Solving Laplace's Equation

JOHN W. TUKEY Further Remarks on Stochastic Methods in Quantum Mechanics

ROBERT J. MONROE Standard Methods of Analyzing Data

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