UNITED STATES
ATOMIC ENERGY COMMISSION

WASHINGTON 25, D. C.

August 15, 1955

Dear Dr. Lederberg:
Thank you for your letter of August 10.

I see that we have some terminology difficulties, and I mst
confess that they are equally great on my side, since I do not seem
to have a clear idea of what the terms "self-sufficient," "indifferent,"
and "information," that you are using, mean. Doubtless, they are
explained in the other parts of your paper, but since I only saw
a few pages of it, I am confused.

In view of this, it would seem to be best if I described
precisely what my remarks meant. In other words, I will describe
in detail to what sort of construction I am referring.

To be more exact, I have made several constructions which differ
in the models of "parts," "organisms," and the spacial relationships
of these to each other, that they assume. During the last few years,
I have come to believe that one particular procedure is logically
more economical than the others, and I will, therefore, use this in
what follows.

Under this dispensation, then, I mean by the environment M, a
quadratic lattice, as shown in the attached figure* and thought to be
infinitely extended in both dimensions, and in both directions. The
circles in that figure are the basic organs, the lines connecting
them are connections over which impulses can travel. (Please ignore
the area surrounded by a dashed line, shown in the figure, for this
first part of the discussion.) All these basic organs are identical
among each other. Every one has a finite number of states, say N --
in the construction that I used, the N is less than 30. The basic
organ also has a definite scheme of behavior. By this, I mean a
complete set of rules which specify that if an organ is in a state
i (= 1, ..., N), and if its 4 neighbors (enumerated, say, in the
order north, east, south and west) are in the states j,k,1l,n,
respectively, then after the lapse of one time unit, the first
mentioned organ will go over into a specified state jl=F (j,k.1,m).
(Of course, the same happens to its neighbors, with respect to their
own neighbors, and generally to all basic organs in the lattice.)
Thus, the function F is a complete specification of behavior for the

*See last page

 
basic organ. I repeat, all basic organs have the same function F,
i.e., the same behavior. In addition to this, one of the states, say
the state i = 1, to be called the "rest state," has the property,. that
if an organ, as well as all its 4 neighbors, are in this state, then
the first mentioned organ will be in this state a unit time later, too.
(Of course, anyone of its neighbors may itself not be entirely
surrounded by neighbors in the rest state. Therefore, this neighbor
may not be in the rest state after a unit time, and therefore, the
original organ may not be in the rest state after 2 units of time.)
Note, that I am treating time as an integer, i.e., I am only consider-
ing moments of time t = 1,2,3,...

The normal condition of M is one, in which all of its basic
organs are in the rest state. N.

The connecting lines on which, as I said before, impulses are
supposed to be traveling, have no further significance, I am only
using them to indicate that each basic organ is immediately affected
only by the 4 neighbors that I enumerated above, i.e., precisely by
those to which it is directly connected by such lines.

An "organism" A is an area in M, like the one shown on the figure,
surrounded by a dashed line, in which the states of the basic organs
have been prescribed in some definite way -- i.e., in which they are
not necessarily all in the rest state.

Coming to the theorem that I mentioned in my previous letter, the
organisms A and Al are disjunct. The theorem is, that given any A,
I can construct an Al such that if Al is left to itself for a
sufficient length of time, there will appear in M (of course, at
disjunct, and if desired, widely separated, locations in M) the
original Al , plus an additional copy of al (displaced), and a copy A
(also possibly displaced).

Of course, the construction of Al will depend on what A is. To
be more precise, most of Al is the same, no matter what A is; however,
there will be a part of 41 which is determined by the structure of A.
This part of Al, by the way, is not a copy A. It is, in a certain
peculiar notation, a description of A -- i.e., it is related to A in
somewhat the same way as the genetic material determining the structure
of an organism as related to that organism.

I should add, that for all of this to be true, F has to be chosen
in a certain particular way. However, this choice of F is quite
independent of the choice of A (and aly, i.e., it is the same for all
possible A (and al),

 
I would appreciate if you would let me know whether this is
sufficient clarification. I apologize if I have just re-described
things that you had inferred already. I would be mich obliged to you
if you could tell me how this is related to your discussion and ideas.

Sincerely yours,

Gren an Vo nnn

John von Neumann

Dr. Joshua Lederberg
Professor of Genetics
Department of Genetics

The University of Wisconsin
Madison 6, Wisconsin