Skip to Main Content
Have library access? Log in through your library
The Computer and the Brain

The Computer and the Brain

Copyright Date: 1986
Published by: Yale University Press
Pages: 136
  • Cite this Item
  • Book Info
    The Computer and the Brain
    Book Description:

    In this classic work, one of the greatest mathematicians of the twentieth century explores the analogies between computing machines and the living human brain. John von Neumann, whose many contributions to science, mathematics, and engineering include the basic organizational framework at the heart of today's computers, concludes that the brain operates both digitally and analogically, but also has its own peculiar statistical language.

    In his foreword to this new edition, Ray Kurzweil, a futurist famous in part for his own reflections on the relationship between technology and intelligence, places von Neumann's work in a historical context and shows how it remains relevant today.

    eISBN: 978-0-300-18808-0
    Subjects: Technology, Psychology

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-x)
    (pp. xi-xxxii)
    Ray Kurzweil

    Information technologies have already transformed every facet of human life from business and politics to the arts. Given the inherent exponential increase in the price-performance and capacity of every form of information technology, the information age is continually expanding its sphere of influence. Arguably the most important information process to understand is human intelligence itself, and this book is perhaps the earliest serious examination of the relationship between our thinking and the computer, from the mathematician who formulated the fundamental architecture of the computer era.

    In a grand project to understand the human brain, we are making accelerating gains in...

    (pp. xxxiii-xliv)
    Paul M. Churchland and Patricia S. Churchland

    This innocent-looking little book lies at the eye of a hurricane. It represents a locus of clarity and calm at the center of a vast vortex of powerful arguments and competing research programs. And it is all the more singular for having been written in 1956, at the very beginning of the recent explosion in electronic computer technology, an explosion that will forever define the second half of the twentieth century. What John von Neumann attempted to provide in his final lecture series—here published as a single book—was a balanced assessment of the brain’s possible computational activities, seen...

    (pp. xlv-lii)
    Klara von Neumann
    (pp. 1-2)

    Since I am neither a neurologist nor a psychiatrist, but a mathematician, the work that follows requires some explanation and justification. It is an approach toward the understanding of the nervous system from the mathematician’s point of view. However, this statement must immediately be qualified in both of its essential parts.

    First, it is an overstatement to describe what I am attempting here as an “approach toward the understanding”; it is merely a somewhat systematized set of speculations as to how such an approach ought to be made. That is, I am trying to guess which of the—mathematically guided—...


    • The Analog Procedure
      (pp. 3-6)

      In an analog machine each number is represented by a suitable physical quantity, whose values, measured in some pre-assigned unit, is equal to the number in question. This quantity may be the angle by which a certain disk has rotated, or the strength of a certain current, or the amount of a certain (relative) voltage, etc. To enable the machine to compute, i.e. to operate on these numbers according to a predetermined plan, it is necessary to provide organs (or components) that can perform on these representative quantities the basic operations of mathematics.

      These basic operations are usually understood to...

    • The Digital Procedure
      (pp. 6-10)

      In a decimal digital machine each number is represented in the same way as in conventional writing or printing, i.e. as a sequence of decimal digits. Each decimal digit, in turn, is represented by a system of “markers.”

      A marker which can appear in ten different forms suffices by itself to represent a decimal digit. A marker which can appear in two different forms only will have to be used so that each decimal digit corresponds to a whole group. (A group of three two-valued markers allows 8 combinations; this is inadequate. A group of four such markers allows 16...

    • Logical Control
      (pp. 11-22)

      Beyond the capability to execute the basic operations singly, a computing machine must be able to perform them according to the sequence—or rather, the logical pattern—in which they generate the solution of the mathematical problem that is the actual purpose of the calculation in hand. In the traditional analog machines—typified by the “differential analyzer”—this “sequencing” of the operation is achieved in this way. There must be a priori enough organs present in the machine to perform as many basic operations as the desired calculation calls for—i.e. enough “differential gears” and “integrators” (for the two basic...

    • Mixed Numerical Procedures
      (pp. 22-25)

      These remarks should suffice to give a picture of the flexibility which is inherent in these control modes and their combinations.

      A further class of “mixed” machine types that deserve mention is that where the analog and the digital principles occur together. To be more exact: This is a scheme where part of the machine is analog, part is digital, and the two communicate with each other (for numerical material) and are subject to a common control. Alternatively, each part may have its own control, in which case these two controls must communicate with each other (for logical material). This...

    • Precision
      (pp. 25-28)

      Let me, first, compare the use of analog machines and of digital machines.

      Apart from all other considerations, the main limitation of analog machines relates to precision. Indeed, the precision of electrical analog machines rarely exceeds 1:10³, and even mechanical ones (like the differential analyzer) achieve at best 1:10⁴ to 10⁵. Digital machines, on the other hand, can achieve any desired precision; e.g. the twelve-decimal machine referred to earlier (for the reasons to be discussed further below, this is a rather typical level of precision for a modern digital machine) represents, of course, a precision 1:1012. Note also that increasing...

    • Characteristics of Modern Analog Machines
      (pp. 29-29)

      The order of magnitude of the number of basic-operations organs in the largest existing analog machines is one or two hundred. The nature of these organs depends, of course, on the analog process used. In the recent past they have tended uniformly to be electrical or at least electromechanical (the mechanical stage serving for enhanced precision, cf. above). Where an elaborate logical control is provided (cf. above), this adds to the system (like all logical control of this type) certain typical digital action organs, like electromechanical relays or vacuum tubes (the latter would, in this case, not be driven at...

    • Characteristics of Modern Digital Machines
      (pp. 29-38)

      The organization of large digital machines is more complex. They are made up of “active” organs and of organs serving “memory” functions—I will include among the latter the “input” and “output” organs, although this is not common practice.

      The active organs are the following. First, organs which perform the basic logical actions: sense coincidences, combine stimuli, and possibly sense anticoincidences (no more than this is necessary, although sometimes organs for more complex logical operations are also provided). Second, organs which regenerate pulses: restore their gradually attrited energy, or simply lift them from the energy level prevailing in one part...


    • Simplified Description of the Function of the Neuron
      (pp. 40-40)

      The most immediate observation regarding the nervous system is that its functioning isprima faciedigital. It is necessary to discuss this fact, and the structures and functions on which its assertion is based, somewhat more fully.

      The basic component of this system is thenerve cell, the neuron, and the normal function of a neuron is to generate and to propagate anerve impulse. This impulse is a rather complex process, which has a variety of aspects—electrical, chemical, and mechanical. It seems, nevertheless, to be a reasonably uniquely defined process, i.e. nearly the same under all conditions; it...

    • The Nature of the Nerve Impulse
      (pp. 40-52)

      The nerve cell consists of abodyfrom which originate, directly or indirectly, one or more branches. Such a branch is called anaxonof the cell. The nerve impulse is a continuous change, propagated—usually at a fixed speed, which may, however, be a function of the nerve cell involved—along the (or rather, along each) axon. As mentioned above, this condition can be viewed under multiple aspects. One of its characteristics is certainly that it is an electrical disturbance; in fact, it is most frequently described as being just that. This disturbance is usually an electrical potential of...

    • Stimulation Criteria
      (pp. 52-61)

      I can now turn to the discussion of the idealizations and simplifications contained in the description of nerve-action as it was given further above. I pointed out there that these existed and that their implications are not at all trivial to evaluate.

      As pointed out before, the normal output of a neuron is the standard nerve pulse. This can be induced by various forms of stimulation, including the arrival of one or more pulses from other neurons. Other possible stimulators are phenomena in the outside world to which a particular neuron is specifically sensitive (light, sound, pressure, temperature), and physical...

    • The Problem of Memory within the Nervous System
      (pp. 61-68)

      The discussions up to this point have not taken into account a component whose presence in the nervous system is highly plausible, if not certain—if for no other reason than that it has played a vital role in all artificial computing machines constructed to date, and its significance is, therefore, probably a matter of principle rather than of accident. I mean thememory. I will, therefore, turn now to the discussion of this component, or rather subassembly, of the nervous system.

      As stated above, the presence of a memory—or, not improbably, of several memories—within the nervous system...

    • Digital and Analog Parts in the Nervous System
      (pp. 69-70)

      Having pointed out in the above the deep, fundamental, and wide-open problems connected with the memory aspect of the nervous system, it would seem best to go on to other questions. However, there is one more, minor aspect of the unknown memory subassembly in the nervous system, about which a few words ought to be said. These refer to the relationship between the analog and the digital (or the “mixed”) parts of the nervous system. I will devote to these, in what follows, a brief and incomplete additional discussion, after which I will go on to the questions not related...

    • Codes and Their Role in the Control of the Functioning of a Machine
      (pp. 70-74)

      Let me now pass on to the questions involving other aspects than those of memory. By this I mean certain principles of organizing logical orders which are of considerable importance in the functioning of any complicated automaton.

      First of all, let me introduce a term which is needed in the present context. A system of logical instructions that an automaton can carry out and which causes the automaton to perform some organized task is called a code. By logical orders, I mean things like nerve pulses appearing on the appropriate axons, in fact anything that induces a digital logical system,...

    • The Logical Structure of the Nervous System
      (pp. 74-77)

      At this point, the discussion is best redirected toward another complex of questions. These are, as I pointed out previously, not connected with the problems of the memory or with the questions of complete and short codes just considered. They relate to the respective roles of logics and arithmetics in the functioning of any complicated automaton, and, specifically, of the nervous system.

      The point involved here, one of considerable importance, is this. Any artificial automaton that has been constructed for human use, and specifically for the control of complicated processes, normally possesses a purely logical part and an arithmetical part,...

    • Nature of the System of Notations Employed: Not Digital but Statistical
      (pp. 77-81)

      As pointed out before, we know a certain amount about how the nervous system transmits numerical data. They are usually transmitted by periodic or nearly periodic trains of pulses. An intensive stimulus on a receptor will cause the latter to respond each time soon after the limit of absolute refractoriness has been underpassed. A weaker stimulus will cause the receptor to respond also in a periodic or nearly periodic way, but with a somewhat lower frequency, since now not only the limit of absolute refractoriness but even a limit of a certain relative refractoriness will have to be underpassed before...

    • The Language of the Brain Not the Language of Mathematics
      (pp. 81-83)

      Pursuing this subject further gets us necessarily into questions oflanguage. As pointed out, the nervous system is based on two types of communications: those which do not involve arithmetical formalisms, and those which do, i.e. communications of orders (logical ones) and communications of numbers (arithmetical ones). The former may be described as language proper, the latter as mathematics.

      It is only proper to realize that language is largely a historical accident. The basic human languages are traditionally transmitted to us in various forms, but their very multiplicity proves that there is nothing absolute and necessary about them. Just as...