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Brain Computation as Hierarchical Abstraction

Computational Neuroscience
Terence J. Sejnowski and Tomaso A. Poggio, editors
For a complete list of books in this series, see the back of the book and http://mit-
press.mit.edu/Computational_Neuroscience

Brain Computation as Hierarchical Abstraction
Dana H. Ballard
The MIT Press
Cambridge, Massachusetts
London, England

© 2015 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form by any
electronic or mechanical means (including photocopying, recording, or information
storage and retrieval) without permission in writing from the publisher.
MIT Press books may be purchased at special quantity discounts for business or sales
promotional use. For information, please email special_sales@mitpress.mit.edu.
This book was set in ITC Stone Serif Std by Toppan Best-set Premedia Limited, Hong
Kong. Printed and bound in the United States of America.
Library of Congress Cataloging-in-Publication Data
Ballard, Dana H. (Dana Harry), 1946– author.
Brain computation as hierarchical abstraction / Dana H. Ballard.
p. ; cm. — (Computational neuroscience)
Includes bibliographical references and index.
ISBN 978-0-262-02861-5 (hardcover : alk. paper)
I. Title. II. Series: Computational neuroscience.
[DNLM: 1. Brain—physiology. 2. Mental Processes—physiology. 3. Models,
Neurological. 4. Nerve Net—physiology. 5. Neural Networks (Computer)
6. Neurons—physiology. WL 337]
QP357.5
612.8’23343—dc23
2014021822
10 9 8 7 6 5 4 3 2 1

Contents
Series Foreword ix
Preface xi
Acknowledgments xiii
Part I Setting the Stage 1
1 Brain Computation 3
1.1 Introducing the Brain 7
1.2 Computational Abstraction 13
1.3 Different than Silicon 21
1.4 The Brain’s Tricks for Fast Computation 25
1.5 More Powerful than a Computer? 30
1.6 Do Humans Have Non-Turing Abilities? 34
1.7 Summary 38
2 Brain Overview 41
2.1 Spinal Cord and Brainstem 44
2.2 The Forebrain: An Overview 54
2.3 Cortex: Long-Term Memory 60
2.4 Basal Ganglia: The Program Sequencer 63
2.5 Thalamus: Input and Output 68
2.6 Hippocampus: Program Modifications 70
2.7 Amygdala: Rating What’s Important 76
2.8 How the Brain Programs Itself 78
2.9 Summary 80
Part II Neurons, Circuits, and Subsystems 81
3 Neurons and Circuits 83
3.1 Signaling Strategies 85
3.2 Receptive Fields 89
3.3 Modeling Receptive Field Formation 95

vi Contents
3.4 Spike Codes for Cortical Neurons 102
3.5 Reflexive Behaviors 109
3.6 Summary 112
3.7 Appendix: Neuron Basics 113
4 Cortical Memory 127
4.1 Table Lookup Strategies 128
4.2 The Cortical Map Concept 135
4.3 Hierarchies of Maps 139
4.4 What Does the Cortex Represent? 146
4.5 Computational Models 154
4.6 Summary 160
5 Programs via Reinforcement 163
5.1 Evaluating a Program 168
5.2 Reinforcement Learning Algorithms 173
5.3 Learning in the Basal Ganglia 177
5.4 Learning to Set Cortical Synapses 186
5.5 Learning to Play Backgammon 192
5.6 Backgammon as an Abstract Model 199
5.7 Summary 200
Part III Embodiment of Behavior 201
6 Sensory-Motor Routines 203
6.1 Human Vision Is Specialized 204
6.2 Routines 210
6.3 Human Embodiment Overview 214
6.4 Evidence for Visual Routines 219
6.5 Changing the Agenda 230
6.6 Discussion and Summary 232
7 Motor Routines 235
7.1 Motor Computation Basics 238
7.2 Biological Movement Organization 240
7.3 Cortex: Movement Plans 248
7.4 Cerebellum: Checking Expectations 253
7.5 Spinal Cord: Coding the Movement Library 255
7.6 Reading Human Movement Data 263
7.7 Summary 272
8 Operating System 275
8.1 A Hierarchical Cognitive Architecture 279
8.2 Program Execution 283
8.3 Humanoid Avatar Models 289
8.4 Module Multiplexing 293

Contents vii
8.5 Program Arbitration 298
8.6 Alerting 305
8.7 Program Indexing 307
8.8 Credit Assignment 309
8.9 Implications of a Modular Architecture 313
8.10 Summary 316
Part IV Awareness 319
9 Decision Making 321
9.1 The Coding of Decisions 322
9.2 Deciding in Noisy Environments 325
9.3 Social Decision Making 330
9.4 Populations of Game Players 341
9.5 Summary 345
10 Emotions 349
10.1 Triune Phylogeny 351
10.2 Emotions and the Body 354
10.3 Somatic Marker Theory 361
10.4 The Amygdala’s Special Role 366
10.5 Computational Perspectives 369
10.6 Summary 373
11 Consciousness 377
11.1 Being a Model 378
11.2 Simulation 392
11.3 What Is Consciousness For? 402
11.4 Summary 406
Notes 411
References 413
Index 435

Series Foreword
Computational neuroscience is an approach to understanding the develop-
ment and function of nervous systems at many different structural scales,
including the biophysical, the circuit, and the systems levels. Methods
include theoretical analysis and modeling of neurons, networks, and brain
systems and are complementary to empirical techniques in neuroscience.
Areas and topics of particular interest to this book series include compu-
tational mechanisms in neurons, analysis of signal processing in neural
circuits, representation of sensory information, systems models of senso-
rimotor integration, computational approaches to biological motor con-
trol, and models of learning and memory. Further topics of interest include
the intersection of computational neuroscience with engineering, from
representation and dynamics, to observation and control.
Terrence J. Sejnowski
Tomaso Poggio

Preface
The 1950s saw a huge step in the development of computers with the intro-
duction of the IBM 701, the FORTRAN programming language, and the
integrated circuit, but arguably the major landmark in their promotion as a
model of human information processing came with Lindsay and Norman’s
seminal book in 1972.1
Nonetheless, the idea of a computer being a model
for human thought was not greeted with enthusiasm by the biological
community, and indeed the general reaction was very negative. The main
impediment was that conceptualizations of computation were grounded in
the ways that silicon computing approached them, and the animal brain is
nothing like a silicon computer in implementation.
Change in this perspective was given a major impetus in 1982 with
the publication of David Marr’s Vision,2
which promoted the distinction
between the computational problems that the brain was faced with and
its neural implementation of solutions. The computational problem now
could be studied in the abstract without having knowledge of the detailed
workings of the very complex cellular and molecular underpinnings.
Nonetheless, an ultimate account of brain functioning has to address
the primary signaling method of the voltage spike in nerve cells. A major
step forward in this direction was and Churchland and Sejnowski’s Com-
putational Brain,3
which addressed computation with respect to the brain’s
overall complexity, particularly its organization at multiple spatial scales.
But there is still the issue of computational abstraction. Even though the
signaling in the brain is all about spikes, their myriad of different functions
is unlikely to be interpretable without the concept of computation at dif-
ferent spatial and temporal scales. To appreciate this point, we can cross
over to silicon computing. Silicon computer architectures depend crucially
on the abstraction of the low-level realization of computation in hardware
through an elaborate succession of more abstract descriptions of the same
in levels of software. Without these levels, there would be no computers in

xii Preface
their present form. In this context, it is surprising that thinking about brain
computation tends to eschew computational hierarchical descriptions.
Thus, while it is true that the voltage spike is the basic way neurons com-
municate with each other, the contexts of spikes can be so different that it
is extremely unlikely that they can ever be interpreted without understand-
ing their hierarchical venues.
For the brain, increasing abstraction levels buy a crucial survival advan-
tage: the ability to predict the future at ever larger spatial and temporal
scales. In addition, the complexities surrounding brain computation spec-
tacularly can be reduced if the entirety of the computation can be factored
into different levels of abstraction. This book focuses on these issues. After
the two introductory chapters of part I, the book is organized into three
main parts: neural, embodiment, and social. Each of these is similarly fac-
tored into composite abstraction levels. The aim is to show that there is
a natural correspondence between the computational issues and the ana-
tomic levels of organization in the brain.
It is a wonderful time to be thinking about a comprehensive picture of
brain computation, as there is a constant flood of new insights both from
the experimental and theoretical sides. Nonetheless, the dynamic nature of
this boon introduces challenges for a book of this kind. As a consequence,
the book is an admixture of models that are generally believed to be settled
and other models that are very speculative. Without the more speculative
parts, it would be impossible to paint a coherent picture, as they provide
helpful scaffolds for discussing problems that the brain has to solve. I have
tried to indicate wherever things are on the edge.
In the modern scientific arena, research progress in developing both
computational and biological understanding is racing ahead at breakneck
speed, with the result that in any subject, one quickly enters territory acces-
sible only to the specialist. Nonetheless, to paint a picture in a single book,
many important details have to be abstracted away, from both the compu-
tational and biological sides. The net result is that the descriptions of either
side may disappoint the specialist, but the focal intent is to point out con-
nections that may promote new understanding.

Acknowledgments
This book developed over the course of many years, and as a result there are
many people and institutions to thank. Sometime in 1982, at lunch with
my mentor Jerry Feldman and colleague Chris Brown at the University of
Rochester’s faculty club, the topic of really big unsolved problems came
up, and when the brain made a short list of three, I decided that was a lot
more interesting than the biomedical image processing I was doing. I had a
leave to study anatomy in cortical hierarchies with Paul Coleman and was
hooked. A few years afterward, the field of machine learning was born, or
reborn to some, and a plethora of new statistically driven algorithms such
as reinforcement learning, backpropagation, and support vector machines
suddenly appeared on the scene to provide new ways of thinking about
brain computation. It has taken a while, but these algorithms have since
matured to the point where the connections between them and the brain’s
underlying complexity are being made rapidly.
The idea and impetus for the book started at the University of Rochester.
The scale of the university makes it ideal for researchers from different fields
to interact, and umbrella structures such as the Center for Visual Science
and umbrella funding from the National Center for Research Resources of
the National Institutes of Health made it normal for researchers from differ-
ent disciplines to interact on a daily basis. I will always be grateful for the
conversations with Jerry, Chris Brown, Robbie Jacobs, Dave Williams, Dick
Aslin, Peter Lennie, Tania Pasternak, Ed Freidman, Charley Duffy, Daeyeol
Lee, Marc Schieber, and Gary Paige.
In the course of a move to the University of Texas at Austin in 2006, I
spent 6 months on leave at the University of Sydney where most of the
book took shape. It assumed its current form with another semester leave
in 2011 at the Queensland Brain Institute in Brisbane, and I am grateful
for help I received there from my sponsor Mandayam Srinivasan and host

xiv Acknowledgments
Peter Bartlett, as well as Jason Mattingly, Ada Kritikos, Judith Reinhard,
Charles Claudianos, Janet Wiles, and Geoff Goodhill.
The University of Texas at Austin’s Center for Perceptual Systems,
directed by Bill Giesler, has provided a wonderfully stimulating intellectual
setting for testing the book’s ideas. I am grateful for feedback from Bill
as well as colleagues Alex Huk, Jonathan Pillow, Larry Cornack, and Eyal
Seidemann as well as Nicholas Priebe and Ila Fiete from Neuroscience.
I have been extremely fortunate to have worked with many extraor-
dinarily talented PhD students and Postdocs whose creativity appears
throughout the book. Special thanks go to Joseph Cooper, Rahul Iyer, Dmi-
try Kit, Rajesh Rao, Polly Pook, Justinian Rosca, Garbis Salgian, Virginia
DeSa, Xue Gu, Constantin Rothkopf, Nathan Sprague, Weilie Yi, Chen Yu,
Andrew McCallum, Michael Swain, Steven Whitehead, Shenghuo Zhu, Jan-
neke Jehee, Greg Zelinsky, and Jochen Treisch.
In fall 2012, the book was polished off during participation in the ZiF
program on Attention at the University of Bielefeld. I very much appreciate
the helpful discussions I had with Helge Ritter, Wolfgang Einhuser-Treyer,
Gernot Horstman, and Werner Scheider.
Most of all I am grateful for my longtime collaboration with Mary
Hayhoe.
The book would not have been possible without the leaves, and I am
most grateful to the Department of Computer Science of the University of
Texas for, particularly to the Chair Bruce Porter, who has been an unfailing
supporter of this work.
I am very grateful to my editor at MIT Press, Bob Prior, who was hugely
encouraging toward the idea of a book with a hierarchical perspective, and
also to Chris Eyer for his essential help with all aspects of its production.
Katherine Almeida and her copyediting staff did a fantastic editing job,
with the result that the book is enormously more polished.
Ultimately, what makes research possible is funding, and in the process
I have been generously supported by the National Science Foundation and
by the National Institutes of Health through National Eye Institute grants
and, particularly at Rochester, through a National Center for Research
Resources grant, which, together with startup funds from the University of
Texas at Austin, funded the technological developments described in the
book.

I Setting the Stage
The vast differences between silicon circuitry and the brain’s neural cir-
cuitry can easily lead to the conclusion that they have nothing in com-
mon; however, not only is this not the case, but also computational tools
turn out to be essential for understanding brain function. The hierarchical
organization of the brain finds many parallels in the hierarchical organiza-
tion of silicon. What chapter 1 stresses most is that to be comprehensible,
the computation done by the brain must be organized into functional hier-
archies, as is done in silicon.
The staggering complexity of the brain itself can be daunting, but the
enormous research focus on the brain in recent times has crystallized an
overview of its function. This overview has many lacunae, where pieces
are missing or still not completely understood, but nonetheless, a broad
picture is emerging, which is characterized in chapter 2. At the level where
the brain is organized into its major subsystems, the interactions between
them are increasingly well-defined.

1 Brain Computation
To say the brain is a computer is correct but misleading. It’s really a highly special-
ized information-processing device—or rather, a whole lot of them. Viewing our
brains as information-processing devices is not demeaning and does not negate
human values. If anything, it tends to support them and may in the end help us to
understand what from an information-processing view human values actually are,
why they have selective value, and how they are knitted into the capacity for social
mores and organization with which our genes have endowed us.
—David Marr, Vision (W. H. Freeman, 1982, p. 361)
The human brain is a candidate for the most complex structure of any
kind in the universe. It is a truly remarkable information-processing device
that can learn the structure of the world, including intricate social inter-
actions with other intelligent agents necessary to build and execute suc-
cessful plans for survival and procreation. It is also the most complicated
part of the body. Although the brain represents only about 2% of total
body weight, it is estimated that 40% of the human genome is used in
putting the brain together. How are we to understand the brain? And what
would it mean to understand the brain? The emergent thinking is that this
enormous capability and complexity can be made comprehensible through
computational science.
The acceptance of the brain as a computational device is recent. With
the explosion of computer technology in the 1950s came suggestions that
the brain is some kind of computer, and these suggestions were not greeted
with enthusiasm. At that time, the National Institutes of Health had no
explicit study section to address computation in the brain. However in the
modern day, the situation has changed dramatically. The field of compu-
tational neuroscience has been born and endorsed. Dozens of scientific
meetings worldwide are devoted to computational brain models, and the
number is growing rapidly.

4 I Setting the Stage
If the brain is a computer,a
it is almost certainly unlike any one we’ve
seen before, and so even the computer expert has to be open to very unusual
and radical ways of getting things done. We are only just beginning to
understand how these kinds of differences are handled, but enough has
been learned to offer a coherent framework. Thus, the thrust of this book
is to show how the kinds of things that we associate with thinking all have
computational and neural underpinnings, and the thrust of this chapter is
to get started by outlining the main issues, of which there are three.
1. Hierarchies The hierarchical structure of the brain can be related to the
hierarchical organizing principle of computation. We now know that the
brain evolved in layered structures and that later layers usefully exploit
the structure of the earlier layers to great advantage. This observation leads
directly to the principle of computational abstraction hierarchies, which com-
poses the essential organizing backbone of computers. So important is
this principle for understanding brain function that it dictates the central
organizational structure of this book. In part I, chapter 1 introduces the
computational issues, and chapter 2 provides an overview of brain func-
tion, focusing on the mammalian forebrain. Later chapters are organized
in a sequence of increasing computational abstraction. In part II, chapter
3 describes basic neuron function, with a focus on timing issues. Chapter
4 describes the cortex, the forebrain’s essential memory system that makes
everything else possible.b
Chapter 5 describes the basal ganglia, a collec-
tion of brain subsystems that can be very loosely thought of as analogous
to a parallel processor. With part III we jump abstraction levels. Chapter
6 shows how behavioral programs can use the basic brain architecture to
interrogate the world for crucial information. Chapter 7 shows how motor
programs can use this information to act in the world to achieve goals.
Chapter 8 shows how the crucial ability of multiplexing can be handled,
wherein the brain can manage different programs simultaneously, each try-
ing to achieve different objectives. With part IV we jump abstraction levels
again. Chapter 9 focuses on properties that can be experienced by the user,
starting with decision making. Chapter 10 focuses on emotions. Finally
with all this structure in place, we can consider properties of consciousness
in chapter 11, which is the final chapter.
2. Slow circuitry The brain must have very ingenious ways of coping with
its tardy neural circuit responses, which are more than a million times
slower than switching times in silicon circuits. Consequently, it is a huge
mystery how the brain can accomplish all of its cognitive tasks fast enough
to act successfully in the world. In this chapter, we introduce in outline the

main tricks the brain uses, and the details will come later. Each chapter will
have to deal with the timing issue in some way. But even understanding
these will not settle the issue completely. Our understanding of how the
brain compensates for its slow circuitry remains a work in progress.
3. The enterprise This issue, which will be touched upon lightly in this
chapter, concerns the enterprise of a computational brain theory itself.
Assertions of great progress do not move skeptics. They allow that although
computation can be a model of the brain, and a poor one at that, it cannot
truly be the ultimate description of brain function because human brains
operate outside of the computational realm. To counter this negativity, we
will have to touch on the very nub of the issue, and that is: What is com-
putation? There are ways of deciding what is computation and what is not,
even though, because they appeal to abstract issues involving infinities,
they aren’t very interesting to the computational convert. Nonetheless,
because anticomputational arguments have been widely circulated,4, 5
they
need to be addressed.
Given the surge in focus on brain computing, what kinds of explana-
tory power can we expect? Current computation is far from predicting, and
probably will never be able to predict, individual acts such as Michelangelo
carving the Pieta—although it would have more to say about Romeo woo-
ing Juliet—but for a broad theoretical understanding of why we think the
way we do and why we feel the way we do, computation is rapidly becom-
ing the best alternative. It’s not that we will ever be able to predict exactly
what we’ll do in any situation, but we will be able to predict the kinds of
things we are likely to do under different circumstances with an increasing
fidelity.
Computational descriptions of humans make us uneasy in a way that
descriptions by other disciplines are spared. We don’t rail against physicists
or chemists for their models of us. Perhaps the main reason that computa-
tion is singled out is that it is associated with mindless robotic behavior,
the very antithesis of the rich tapestries of affect and contemplation asso-
ciated with being human. However, this connection is an overinterpreta-
tion that takes the instances of current computers to be coextensive with
the umbrella discipline of computational science. It is true that conven-
tional robots can be driven by silicon-based computers, but computation
has much deeper things to say, in particular some stunning things, about
how brains work. It may well be that ultimately the best way to understand
our collection of human traits, such as language, altruism, emotions, and
consciousness, is via an understanding of their computational leverage. We

shouldn’t worry that this understanding will preclude us celebrating all our
humanness in the usual ways. We will still fall in love and read Shakespeare
with this knowledge, just as knowing a chair is made up of atoms doesn’t
preclude the joy of a comfortable sit down.
The job of understanding the brain has been characterized as one of
reverse engineering.6
There are brains galore sitting in front of us; we just
have to deduce what makes them work. This in turn involves figuring out
what the parts are and how they interact with each other. What makes the
task daunting is that the brain exhibits complexity that is nothing short
of staggering. Somewhere from 10 billion to 100 billion brain cells act in
ways unlike any other cells in the body, forming tangled networks of inter-
connections, and each of these cells is itself a small factory of thousands
of proteins that orchestrate a myriad of internal functions. Faced with all
these webs of interconnected detail, reverse engineers have the enormous
challenge of breaking the overall system into manageable pieces. To meet
this challenge, computation proves an extremely useful tool. Evolution is a
great tinkerer, always ready to exploit a solution to a problem that appears
anywhere in the dynamics of life, but with the result that, in retrospect,
the solutions can be hard to anticipate or analyze from a first-principles
perspective. Computation, being very abstract, has the great versatility of
being able to fit many different settings once the appropriate identifica-
tions are established. Thus to use a crude analogy, an abstract level might
be described in terms of a high-level programming language, whereas a
lower level of abstraction might look more like an assembly-level language.
The job of the computationally minded reverse engineer is to posit these
kinds of distinctions and splice them together.
Most of the time, the researchers doing computational sleuthing would
take their models for granted and not spend much time wondering what
other possibilities there could be. The fact is, to date we do not have any
good alternatives to thinking about the brain other than as doing computa-
tion, particularly when we focus on accounting for behavior. The central
construct of computer science is the algorithm,7
expressed in very rich sym-
bolic languages that have constructs that are analogous to those of a recipe
in a cookbook. An algorithm’s steps can be repeated a certain number of
times (e.g., “stir until thickened”) until a test is satisfied, partial results
can be saved and combined (e.g., “add the marinade to the mixture”), and
steps can be conditional (e.g., “if you are allergic to cow’s cheese add goat’s
cheese at this point and continue”). Mathematics and especially physics
have at times competed with computation with rival explanations of brain
function, so far without result because they do not have the construct of

the programming language. The parts of mathematics and physics that are
accessible and useful turn out to be the parts that readily can be specified by
algorithms. In the same way, chemistry and especially biology and molecu-
lar biology have emerged as essential descriptive constructs, but when we
try to characterize the aspects of these disciplines that are important for
cognition, more and more often we turn to algorithmic constructs. The
main factor is that the primitives we need to describe brain function that
involve the direction of physical and mental behaviors naturally seem to
fit onto the algorithmic notions of iteration, decision making, and memory
that compose the essence of computation.
The central thrust of this book is about computation, but at this cru-
cial introductory juncture we must emphasize an extremely important
point. While we argue that computation will ultimately prove necessary
in understanding the brain, it will never displace the extraordinary experi-
mental and analytical work that leads to the discovery of the fundmental
descriptions and workings of the brain’s basic biology. The mere thought
of the magnitude of this enterprise, which involves chemistry, biology, and
physics and includes many other ancillary disciplines, can be daunting and
overwhelming. The deepest hope is that the essential inclusion of compu-
tational principles will play a complementary and important role in the
drive to understand the most complex device nature ever created.
1.1 Introducing the Brain
The tropical pitcher carnivorous plant has an astonishing design. Insects
drawn to it by its fragrant nectar slip on its sides, fall into a slippery pit,
and cannot get out. The plant can then digest them at leisure. Think about
this for a moment. Is the plant doing computation or not? The sequence
of operations that lead to an insect’s demise are well suited to a symbolic
description, but perhaps the line has to be drawn here. The realization that
we come to is that it is animals that do the computation characterized by
brains. Animals move, and to avoid pitfalls they necessarily have to sense
aspects of the environment and change direction to improve their survival
chances. Tiny bacilli have flagella to follow sensed gradients left by nutri-
ents but can spin randomly in the absence of these to try and stumble into
another nutrient cache. So it’s animals that have the brains, and they use
them to navigate dynamic environments.
Our focus is the human brain, and it has a very specialized architecture
compared to other brains of a much earlier evolutionary heritage. Its basic
brain architectural plan starts with its vertebrate heritage, but humans are

mammals and mammals represent a radical point of departure in brain
design. While the brains of other animals have precursor elements, mam-
mals have a very integrated forebrain that contains specialized subparts for
creating and using new programs. The mammalian forebrain itself is an
exquisitely complex structure that has evolved over millennia to perform
an enormous number of very specific new functions related to animal sur-
vival and procreation. The mammalian forebrain is a breakthrough system
that is very complex, and it is likely that its workings will only be properly
understood by studying its features from many different vantage points.
Here let us sketch the largest anatomic viewpoint, and that is how the
forebrain is situated with respect to antecedent structures and what proper-
ties they confer on its overall organization. Figure 1.1 will serve to orient
the reader. What the figure makes immediately obvious is that the fore-
brain has the largest percentage of the total brain volume. The functions of
the various parts of the forebrain will be dissected in the next chapter, but
collectively they perform in large part the basic sophisticated planning and
Figure 1.1
A cutaway view of the brain showing a major division between the forebrain (F),
which handles simulation, planning, and acting, and the lower brain structures that
handle basic life support functions. Midbrain (M): basic drives. Pons and cerebel-
lum (P and C): sensorimotor calibration. Medulla oblongata (mO): management of
body organs and life support operations. Spinal cord (S): motor functions and organ
regulation circuitry.

acting that we associate with being human. The crucial point to note here
is that they depend on the parts of the brain that evolved before them, and
those subsystems of the brain evolved to keeping us alive and kicking. The
brain’s evolutionarily earlier functionality comprises a huge network of pri-
mordial structures that are heavily optimized for a myriad of life-support
functions that relate both to its internal structures and the external world.
If certain parts of these are damaged, the consequences can be dire. But to
return to the main point, in order to think about what the forebrain does
computationally, it helps to understand what its predecessor structures do.
Let’s start from the periphery and work our way inward.
Reflexes in the Spinal Cord
One of the most important of the lower brain functions is the reflex that
connects sensory information to motor actions. Figure 1.2 shows the basic
features of a reflex. Sensory information is almost directly connected to
efferent (meaning “conducting away” as opposed to afferent, “conducting
toward”) neurons for a fast response. This means that the neural response
is not dependent on adjudication by the forebrain, a long way away in
space and time. Although we might be tempted to think (recalling experi-
ences of withdrawing a hand from a hot plate or being whacked on the
knee’s patella by a well-meaning physician) that reflexes are simple, they
are not, and they represent coordinated muscle patterns.8
Concatenations
of such circuitry can produce oscillatory patterns that are the basis of an
animal’s library of complicated posture changes. In experiments with cats
without a forebrain, the basic spinal cord circuits are enough for the cat to
walk and run, with only slight assistance in support. Moreover, the cat’s
feet will retract from encounters with small obstacles and step over them
unaided. The sensory motor systems of the human spinal cord are even
more sophisticated and have many additional capabilities that allow the
ready programming of complex movements.
Reflexes can get an animal a long way. A praying mantis can get dinner
by snapping at another unsuspecting insect as can a frog. In each case,
some visual feature of the stimulus is enough to set off the reflexive snap.
Primitive robots have demonstrated that a variety of behaviors can be pack-
aged to generate useful behaviors. IRobot’s Roomba vacuum cleaner makes
extensive use of a reflexive level of behavior.
Life Support in the Medulla Oblongata
At the next level, proceeding from the spinal cord toward the forebrain,
is the medulla oblongata. The primary function of this cell complex is to
regulate vital internal processes such as heart rate, breathing, and the many

Figure 1.2
A basic sensorimotor reflex. Transmission through banks of neurons is sufficiently
slow that the brain uses “hard-wired” circuits to achieve fast computation that can-
not be done with the forebrain in the control path. Withdrawing a finger from a
heat source is a very familiar reflex, but there are many others that are essential that
control the body’s complicated dynamic systems in a timely way. Reprinted with
permission from http://encyclopedia.lubopitko-bg.com/.

steps in digestion. If this area is damaged, then some functions can be
taken over by machinery in a hospital’s intensive care unit, but, if the
patient does not recover, these functions cannot be duplicated in the long
term.
Sensorimotor Calibration in the Pons and Cerebellum
Next to the medulla oblongata are the pons and cerebellum, which are in
charge of sensory motor calibration. An easy way to understand the impor-
tance of this function is to focus for a moment on infant development. As
an infant grows, the body size changes drastically, but the visual system’s
optics is relatively invariant. This means that the number of steps needed
to reach a distant object, as measured by the visual system, is continually
changing. So the connections between the visual measurements and the
motor output system have to be continually adjusted. Another example
is when, as an adult, you carry a heavy backpack. The effective mass of
your upper body has changed, and so the forces needed to balance have
to be recalculated. It is not inaccurate to think of the cerebellum as a huge
sensorimotor input-output table that, for every sensory stimulus, registers
the appropriate parts of the motor system to innervate. Thus, the cerebel-
lum is the first stage that realizes a very important evolutionary step: a
map of the body’s sensorimotor parts that is an abstraction of the body’s
more concrete neuromusculature. In effect it is a kind of regulatory model
of the more concrete structures. In sensorimotor calibration, the adjust-
ments are made to the model and then signaled to the spinal cord. It’s as
if evolution discovered a programmable “patch panel.” Rather than signal
an enormous number of changes throughout the body, they can be made
far more succinctly within a more local programmable circuit that uses
abstractions of the body’s parts.
Unlike the medulla oblongata, damaging your cerebellum is not fatal,
but there can be very substantial costs. An adult without one loses the
exquisite ability to readjust to different loads, and even simple sensorimo-
tor coordination such as touching one’s nose with a forefinger becomes
very laborious.
Chemical Regulation in the Midbrain
The medulla oblongata is a command center for regulating body function.
Given the notion of an abstraction for sensorimotor control in the cerebel-
lum, why not have one for the body functions as well? The midbrain does
this via an armamentarium of neurotransmitters, chemicals that can modify
circuit function, of which five are crucially important and have elaborate

private circuits covering large parts of the forebrain. Imagine for a moment
the issue of regulating all the different body systems, each with its own pre-
ferred setpoint and mechanism. Would it not be better to summarize these
with a small set of neural mechanisms that code the optimal setpoints for
each of the group of systems? Evolution discovered a general way of regu-
lating the state of the body with chemical signals.
Programs in the Forebrain
All the previous structures are an enormous benefit for the forebrain, as
they provide a set of sophisticated primitives as well as contexts that can be
used as part of a neural “programming language” to realize very complex
behaviors. The forebrain is all about making and storing programs, and
compared to other animal brains, the mammalian brain has by far the most
sophisticated neural machinery for doing this.
When thinking about the virtues of human intelligence, there is often
a tendency to jump to its more exotic capabilities such as understanding
calculus, but even the simplest ordinary behaviors are a huge advance over
reflexive behavior. Suppose you are ready to make a peanut butter and jelly
sandwich. The plate is empty, and it is time to get two slices of bread. So
the next thing to do is to get them. You can effortlessly distinguish this
state of affairs from the state you’d have been in if the slices were already
on the plate. For either of these states, you know what to do next. Further-
more, you know how to sequence through a set of actions that will produce
the sandwich. You can handle frequent errors (such as spilling jelly on the
table) as well as the unexpected (the jelly jar lid is especially difficult to
remove). And you would not repeat a step that you had already carried out.
After a series of such steps, the sandwich is ready. You have just exhibited a
dexterity beyond any current robot.
You probably were not aware that in making the sandwich, you have
executed a complex program with many features that can be described as
computation. Specifically:
• There has to be a way of defining the state of affairs, or state. Even though
the sandwich construction that has jelly on the bread might seem obvi-
ously different than without, defining the notion of state succinctly in gen-
eral turns out to have many subtleties.
• There has to be a way of transiting between states. To make a sandwich,
coordinated actions consisting of coordinated movements have to be car-
ried out.
• There has to be a way of assembling these states and action transitions
into programs. The sandwich recipe has to be remembered as a unit.

The core computations of all these tasks are done by the forebrain, the
focus of the next chapter. Furthermore, sandwich making is just one of
millions of things you know how to do. And the way most of these are
encoded are in the forebrain’s “memory” system that in many ways is much
closer to the computer concept of memory than what we mean by human
memory colloquially. When we describe how this neural memory func-
tions later on, we will see that one way of compensating for the very slow
neural circuitry is to remember how to do enormous numbers of things—
basically all of the things you do—more or less exactly.
1.2 Computational Abstraction
A good way to start thinking about computational abstraction is to intro-
duce the enormous contribution of David Marr, who made seminal contri-
butions in defining the enterprise of computational neuroscience. He and
Poggio showed how the perception of depth in random-dot stereograms
could be explained in purely geometric and computational terms.9
But per-
haps more importantly, Marr pointed out that the study of computation
could be factored into three parts (see ref. 2):
• the formal statement of the problem that needed to be solved;
• an algorithm for solving it; and
• the implementation of that algorithm in the brain’s neural circuits.
Thus, Marr’s triage is a series of constraints. The formal problem statement
is defined at a logical level and ignores the methods for solving it. The
algorithm is defined at the computational level and ignores the biological
details of implementing it. The implementation level takes up the problem
of making correspondences between abstractions in the algorithm and cor-
responding biological mechanisms.
This tri-part factorization of a computational problem continues to
prove enormously helpful in thinking about the brain’s algorithms, par-
ticularly because at this point in time, as we move toward more abstract
problems, there are still huge gaps in our knowledge of how the nervous
system carries them out. At the time, this triage was a breakthrough as it
opened up thinking about the brain’s computation in abstract algorithmic
terms while postponing the reconciliation with biological structures, and
this mode of thinking remains extremely useful for at least two reasons.
One is that there are many areas of brain function where we still do not
have enough information to make satisfying detailed connections. A sec-
ond reason is that despite such a gulf, the abstract properties of an algo-
rithm can suggest new ways of thinking about biological data.

It is important to keep in mind that the Marr triage is a prescription to
help reverse engineers organize their thoughts. In effect, it is a sequence of
specifications on the way to a detailed theory. But there is another way to
think hierarchically, and it is to that way we now turn. Basically, there is
only one known way to design large complex systems, as pointed out by
Alan Newell10
and his long-time colleague Herb Simon, and that is to intro-
duce hierarchical organization, where each higher level in the hierarchy
is successively more abstract. Let’s make sure we have properly drawn the
distinction between the Marr hierarchy and the intrinsic hierarchy inher-
ent in complex systems. A simple example from programing languages will
get us started. Let’s multiply two numbers together in the language Python
(where * stands for multiplication):
z = x * y.
Because Python is a high-level language, we do not have to worry about the
details, but some part of the computer does. Before the computation can be
carried out, it has to be translated into a lower-level assembly language that
is closer to the machine’s architecture. So we might have
LOAD x, A
MULT A, y
STORE A, z
At the higher level, we did not have to worry about where the multi-
plication happens, but the lower level knows that the multiplication
only works for data in special registers, such as the one here denoted by
A. The crucial point here is that the two descriptions are equivalent in
a strong sense in that the higher-level description can be translated into
the lower-level description. You can immediately see that the Newell
and Simon hierarchies are a very different way of characterizing hierar-
chies than that of Marr. Note that the Marr strategy can be used at any
level.
To gain further purchase in the brain’s management of program com-
plexity, it helps to set the stage by visiting other examples of hierarchies,
so let’s take another look at hierarchies in the brain’s anatomy, hierar-
chies in silicon computer organization, and then introduce a hierarchy for
human behavior. Given the state of knowledge, this last hierarchy should
be regarded as very provisional. Nonetheless, we hope to give it some cre-
dence by enfleshing its parts with experimental data as well as algorithms
in later chapters. Let’s elaborate on these points.

Anatomic Levels of Abstraction
You have already been introduced to the brain’s top level of abstraction,
whereby the brain is divided into major anatomic and functional subdi-
visions. Now let’s move inside the forebrain’s cerebral hemispheres. At
the scale of a few centimeters, there is a predominantly two-dimensional
organization of “maps” consisting of repetitions of very characteristic cir-
cuits,11
wherein subdivisions of cells have identifiable roles. For example,
there will be several areas responsible for computing different aspects of
visual motion across the visual field of view that have their own map. At
an abstraction level below that, subdivisions within these maps represent
circuits of cells responsible for motion computations in a small area of the
visual field. Such circuits, in turn, are made up of different varieties of neu-
rons, each of which has an elaborate set of connections to other nearby
neurons. Going to an even smaller scale, the connections to an individual
neuron are defined by synapses that regulate the charge transfer between
cells. Figure 1.3, from reference 3, summarizes this information. The differ-
ent anatomic levels are easy to appreciate because they have a characteristic
physical appearance that can readily be captured by various imaging tech-
niques that operate at different scales.
Levels of Abstraction for Silicon
Now let’s cross over to the idea of brain computation needing and using
levels of abstraction. This is first easiest to appreciate by seeing how com-
putational abstraction is essential in silicon computers. The basic levels
are summarized in table 1.1. At the top, any standard computer has an
operating system. This is the program that does the overall management
of what computation happens when. It determines when jobs are sent to
the printer, when input is read in, and when to clean up the memory after
a bunch of running programs have left it in disarray (unsurprisingly this
is called “garbage collection” in the jargon). But among all these jobs, the
operating system runs the program you may have written—the user pro-
gram. Your program contains instructions of things to do, but to the operat-
ing system these are just data, and when it determines your program’s turn,
the instructions are carried out systematically by the computer’s processor.
Of course, when you wrote such a program, you would not have used a
language that the lowest level of the machine understands, but instead you
would have chosen a high-level language such as Java or C. The reason is
that the lower-level instructions are too detailed, being appropriate for the
minutiae of the machine. The instructions you program with are translated
into two lower levels: first of all, as we just saw, assembly language, which

Figure 1.3
The organization of the brain into units at different spatial scales. The scale for the
neuron characterizes its central body, or soma. Its other parts project over much
larger distances. Subsystems have well-defined roles in behavior. For example, the
hippocampus is responsible for new memories. Each such subsystem tends to have
very characteristic large-scale organization, usually organized with respect to body
topology. These subsystems also have characteristic circuits. Neurons also exhibit
specialized types such as basket cells for short-range inhibition and pyramidal cells
for long-range excitation. Messages are sent to individual cells through thousands of
contacts termed synapses. Reprinted from Churchland and Sejnowski (1992).

Table 1.1
Basic levels of computational abstraction of a standard computer
Description Function
Operating system Control the running of other programs; manage input
and output
User program A particular program with a specialized objective;
written in a high-level language
Assembly language The translation into basic machine instructions that
are for the most part hardware independent
Microcode Machine instructions that can be interpreted by a
particular machine’s hardware
Circuits Adding, shifting, etc.
Gates Basic logical operations; e.g., AND and OR
Note: The standard computer uses many levels of abstraction in order to manage the
complexity of its computations. Its hardware levels also can be divided into abstrac-
tion levels consisting of circuits that are composed of basic switches, or gates.
addresses elemental operations but postpones the details of how these are
done, and then finally microcode, a language that can be understood by
the machine’s hardware, which in turn uses hierarchical levels that start
with circuits composed of logic gates. The bottom line is that just to run
your program, many different levels are needed, and indeed it is almost
impossible to see how the resultant complexity could be handled if they
were dispensed with.
From a historical perspective, computer software was designed from the
bottom up. Original computer instructions were in the form of an assem-
bly language, and the more abstract user program languages were added
later, as were the constructs used by modern operating systems. An old saw
declares that it takes the same time to debug 10 lines of code no matter
what language it is written in. It is easy to understand why almost everyone
writes in the highest-level language possible: you get the most leverage.
Nonetheless, everything the computer does ultimately is carried out by the
logic gates at a low hardware level of abstraction.
Although at first encounter, the idea that the computations of cogni-
tion have to be organized this way might seem to be eccentric, reading
pioneers Simon and Newell one concludes that there is unlikely to be a
non-hiearchical alternative. Like almost any strong statement, however,
this one needs to be tempered, and perhaps the most important caveat is
the following.

The language-translation view could easily be misconstrued as imply-
ing that the higher-level abstraction, when translated to the level below,
can account for all the lower-level representation. The opposite is true,
as typically the lower level has details (such as particular registers in our
earlier example) that are suppressed when abstracting. In biology, this
feature is compounded many times, as there may be many housekeeping
details needed to make the circuitry viable that are unnecessary at the more
abstract levels. This points to the virtue of the abstractions, as trying to
understand a composite of high-level functions and low-level functions
can easily be too demanding a task if confined to the lowest level.
Neural Computation Levels of Abstraction
If people had not designed the computer in the first place and kept track
of the addition of its hierarchies, it would be an enormous job to figure out
what it did just by looking at its outputs at the gate level, yet that daunting
vista magnified is just what is facing us in understanding the brain. Despite
the fact that so much has been learned, most of the important issues as to
how computation is accomplished remain unsettled. Even the basic out-
put of neurons has still to be satisfactorily decoded. Nonetheless, the con-
cept of processing hierarchies provides the reverse engineer with enormous
leverage. So much so that you probably are guessing correctly what comes
next. We will use these insights about hierarchies from anatomy and com-
putation as constraints with which to formulate neural computation levels
of abstraction.
Just by looking at table 1.1, you can intuit why we are unlikely to under-
stand the brain without a similar triage of functions into computational
levels of abstraction. We can understand the machinery that generates a
voltage spike (the main signaling mechanism) in a neuron, as well as how
networks of neurons might use those spikes. However, we cannot really
understand them together. For clarity, we have to keep them separate. And
when we come to model something several levels more abstract, such as
altruistic behavior, we have to ignore all this low-level machinery entirely
and model an entire brain as a small number of key parameters. We should
not think of this technique of using abstraction levels as a disadvantage
at all. Instead, it is a tremendous benefit. By telescoping through different
levels, we can parcellate the brain’s enormous complexity into manageable
levels.
To make these points more concrete, let’s reconsider the job of making
a peanut butter and jelly sandwich. In the typical kitchen, peanut butter
and jelly would be found in their respective jars, and bread would come

presliced. You might be tempted to think that making the sandwich is a
trivial task, but its relative straightforwardness belies the complex of neural
computations that are needed to put things together. Thus, this task can be
used to illustrate the different kinds of computational levels that the brain
must address. Working from the bottom to the top, one needs to appreciate
that the raw visual and motor information extracted is essentially unusable
by the brain’s programs as it is too unstructured. The visual information
extracted at the retina is summarized into about a million spatial samples
of lightness and color that have no explicit indication of what object the
samples come from. This kind of information must be extracted in the
forebrain, which creates elaborate visual data indexes that allow the fast
identification of image samples. Similarly, the peripheral motor codes con-
tain a huge number of signals for the contraction of muscle fibers, with no
explicit indication of the total coordination patterns necessary for purpo-
sive movement. These are also created in the forebrain’s elaborate indexing
structure, which has special partitions devoted to motor representations.
Neither of these representations, along with companion representations
of other sense information, comes for free, but instead must be created
through elaborate computation at what table 1.2 calls the data abstraction
level.
Table 1.2
Levels of computational abstraction
Description Abstract Function Example Function
Evaluation Strategic decisions Evaluate current task suite. Hungry?
What are the nourishment options?
Scheduler Multitask management Regulate different sandwich-making
programs. Jelly jar lid off now?
Programs Solve a single task Spread peanut butter on bread.
Peanut butter is viscous and spreads
easily.
Routines Individual fixations used
to guide posture changes
Find location of bread slice. Vision
locates the bread loaf.
Data
abstraction
World sensory data
coded to emphasize
intrinsic organization
Compact codes for sensorimotor
signals: Activate codes for color and
texture of bread.
Note: To manage complexity, the brain also has to resort to different levels of com-
putational abstraction. While the ultimate abstraction has not been precisely deter-
mined, we can describe tentative organization based on the tasks that the brain has
to direct.

Having elaborate indexes for sensory input and motor output is a big
step forward, but a crucial but subtle step is to process this data structure
to obtain vital information. Consider filling a cup with coffee. The sensory
system can represent the coffee cup and the coffee going into the cup, but
how do we know when the cup is full? There are several available cues such
as the increased weight of the cup and the closeness of the fluid level to the
cup brim, but the point is that these must be tested to ascertain the cup’s
fullness. So what is needed here is another computational abstraction level
that takes the sensed data measurement system for granted and interro-
gates its results. Let us term this the routines level.
At this point in the discussion, we have defined an elemental data
abstraction level and another level to test that data, so the next step is to
compose these tests into sequences. Consider putting the peanut butter on
the bread. The knife goes in the jar for a glob of peanut butter, removes
it, and then it is spread on the bread; if there is still not enough peanut
butter on the bread, then the brain sends the knife back for more, and so
on. We have just defined another abstraction level, the programs level. At
this level, we can take the details of the tests for granted and worry about
how they are melded together into an action sequence that accomplishes
a larger goal.
When you start to think along these lines, you quickly realize that there
are many more possible abstraction levels above the program level, but in
this illustration let us stop at two more. The particular program for spread-
ing peanut butter can be defined at the program level, but what of multi-
tasking? Perhaps you were boiling water for tea to go with the sandwich,
so that the kettle is on. At the same time, the phone rings. Should you stop
what you are doing and answer it or let it go to the message recorder? You
only have one body, so somehow you must juggle its position in space and
time to make the best use of its resources. The need to manage motivates
another computational abstraction, the scheduler, which takes programs as
primitives and manages their execution. The various steps in each program
can be scheduled in an efficient way to get everything done.
There are other levels to think about, but for the moment let’s intro-
duce one more, the evaluation level. Is the current task suite of making a
meal the most important or is there a more pressing demand? To catch a
bus, perhaps the sandwich should go in the fridge for later. To make these
kinds of judgments, the brain needs some kind of scoring function so that
the adjudication can be managed systematically. This is not the only com-
putational taxonomy one can think of, and one can debate the necessity
of any aspect of the hierarchy of table 1.2. But the point is that if we take

the lessons of biology and silicon computers to heart, we are unlikely to
get away with a “flat” neural computation description. The far more likely
arrangement is that the brain is composed of many more abstract neural
networks that leverage the results of less abstract networks in the process of
getting things done. And if we do not acknowledge and address the need
for such hierarchies, then the overall neural organization is likely to appear
very confusing.
1.3 Different than Silicon
The brain is nothing like a conventional computer and is staggeringly more
complex, even though at an abstract level the brain has to solve some of
the same kinds of problems. Nonetheless, the huge number of differences
between silicon circuits and neurobiological structures means that the bio-
logical solutions must be of a hugely different character. Let’s introduce
some fundamental characteristics that show just how shockingly different
brain computation must be.
The major factor separating silicon and cells is time. The switching
speed of silicon transistors, which limits the speed at which a processor can
function, is in the nanosecond regime. In contrast, neurons send messages
to each other using voltage pulses or, in the jargon, “spikes.” Neurons can
send these spikes at a top speed of several hundred spikes per second, but
in the main processing areas the average rate is 10 spikes per second, with
100 spikes per second regarded as a very high rate. Figure 1.4 shows some
typical representative spike sequences. For a long time, it was thought that
a spike was a binary pulse, but recent experiments suggest ways in which it
C
B
A
Figure 1.4
Three spike trains from an integrate and fire neuron model show the characteristic
low firing rate behavior with random inter spike intervals. Such features can pose
additional challenges in explaining the control real time behaviors. Courtesy of Liz
Stuart, University of Plymouth Visualization Laboratory.

could signal an analog value, so let’s assume that its message is of the order
a byte per pulse. Even with this assumption, nerve cells communicate 10
million times slower that silicon transistors. Given 1011
nerve cells, only
about 1010
are sending spikes at 10 Hz. It would be easy to compress these
data by a factor of 10, so that roughly 103
seconds of your brain’s neural
firing (more than enough for a thought or two) could be saved on 10 tera-
bytes of storage. The task for brain scientists is to break this code.
Code breaking will ultimately require a collection of many different
insights, but to introduce just one as an example, let’s bring to mind the
metaphor of a old-fashioned player piano. Such a piano uses special sheet
music in the form of thick paper with perforations. As the drum rotates,
the perforations depress pistons pneumatically, causing piano keys to be
struck. Think of the piston depressions as “spikes.” In an analogous way,
the neural spike code can be a sparse discrete code; the body makes the
music.
The slow communication rate is sandwiched from above by the time for
the fastest behavior. Evidence from behavioral experiments suggests that
essential computations take about 200 to 300 milliseconds. This means
that the average neuron has to get its computation done with two to three
spikes. From these analyses, the consensus is that the way the brain must
do it is to have most of the answers precomputed in some tabular format
so that they just have to be looked up. Evidence in favor of this view comes
from the rich connectivity between nerve cells. Each neuron connects to
about 10,000 other neurons, compared to a gate’s connectivity to just a
handful of gates on a silicon chip. As shown in figure 1.5, the size of the
gates in silicon are comparable to the processes of a living cell. It is the neu-
ron’s huge connectivity that gives it one of its biggest advantages.
Another factor that the brain uses to overcome the speed handicap
is the power of nerve cells themselves. The exact computing power of
a neuron is unknown, but a good guess is that it is at least much more
powerful than a transistor. The synapses that connect it to other cells are
closer to transistors, but again more powerful as their action can be modi-
fied by neurotransmitters. Thus, the neuron itself has been likened to a
microprocessor, albeit a specialized one. Because the brain has approxi-
mately 100 billion nerve cells—much less than the U.S. fiscal debt in 2004
dollars, but still a lot—that can work simultaneously, the parallel comput-
ing power is obviously one source of compensation for the brain’s slow
circuitry.
With the incredibly slow circuitry, there is no hope of implementing the
strategies used by the billion times faster silicon circuitry. In fact, even the

basic ways of measuring silicon performance have to be thrown out the
window. To understand this provocative claim, we have to take a look at
how the standard algorithm’s accounting is done.
Even if you have no training in computer science, it’s easy to understand
what an algorithm can do because, as noted earlier, it is very much like
a recipe in cooking. There are standard steps, and it’s important to remem-
ber where you are in the process. You may have to repeat operations, as
in stirring, and you may have to test something to see if you are done
and keep going if you are not. Recipes can be thought of as algorithms for
cooking.
Let’s introduce the silicon computer’s traditional bookkeeping method-
ology for counting the steps in a recipe. On serial silicon computers, most
algorithms are dominated by the size of the input. For example, consider
sorting a list of n numbers. Here is a recipe: Go through the list and move
Figure 1.5
An exotic electron micrograph of a neuron artificially grown on a silicon wafer re-
veals the comparable scales of the two technologies. The raised clump is the neuron’s
body, or soma. One of the spidery processes coming out of the soma is its axon,
which connects it to an average of 10
4
other cells. In contrast, silicon transistor con-
nections between gates are limited to a handful. Figure courtesy of Peter Fromherz,
Max Planck Institute.

the biggest number to the top. Then go through the n − 1 remaining num-
bers and pick the second largest and move it to the penultimate position.
After you get down to fixing the last two elements, you are done. This is
called “bubble sort” because the larger numbers bubble up to the top. This
basic algorithm would take
n n
( 1)
2
+
steps because the total number of steps is the sum of the numbers from 1 to
n. In practice, we don’t sweat the factor of 1/2 or the 1, and we say “of the
order” or O(n2
) operations.c
Of course, computer science majors all know that there is a faster algo-
rithm that takes advantage of the fact that two sorted lists of length n can be
merged in O(n) steps. Here is the algorithm that uses the merging property:
Sort(List)
if List has one element
return the resultant list
else if a List has two elements
Sort them
return the resultant list
else Merge(Sort(Front-of-List),Sort(Back-of-List))
You start out with the original list and contract to merge its two sorted sub-
lists. Of course, they too need to be handled in the same way, but the key
is that they are only half as long as the original list. For each list of more
than two elements, an IOU is created. These IOUs are resolved when we get
down to two- or one-element lists. Once this happens, the many outstand-
ing merging processes that need sorted sublists can be completed, resulting
in a sorted list. To see the idea, try it on a piece of paper with small lists of
say four to six numerical elements.
A careful accounting shows that this only requires, in the notation, O(n
log n) operations, which of course is better than the easier-to-understand
O(n2
) algorithm that was considered first. Why is all this analysis impor-
tant? Because basically if the number of operations in an algorithm is
known, along with the time each operation takes, the total time an algo-
rithm takes can be calculated. Carrying such calculations through, most
of the best algorithms that are fine for silicon computers working at clock

speeds of 1 GHz, or a billion operations per second, are not possible for
the brain’s much slower neural circuits. The clever sorting algorithm just
described is the best that can be done but still won’t do for a model of brain
computation. The main reason is that the neurons that are the candidates
for the principal computing elements are very slow, more than a million
times slower than silicon. A reasonable size for n is 1 million for human
vision, and if we assume neurons are computing at 10 binary “bits” per
second, you can see why an O(n log n) algorithm could not be a candidate.
An algorithm that had to poll each of these cells serially would take an
impractical 100,000 seconds.
From the perspective of naively counting steps as we did with the silicon
computing examples, it would seem that the situation is hopeless. Given
the number of steps in simple algorithms and the slowness of executing
steps with neurons, there seems to be no way that computations can finish
in time. But the brain has very powerful tricks up its sleeve.
1.4 The Brain’s Tricks for Fast Computation
If the brain is doing computation, then at some point we have to be able to
explain how that computation gets done in time to direct our daily activi-
ties. In computational science, this question has to be resolved by coming
up with the brain’s specific algorithms. Of course, our main point is that an
overarching hierarchical structure of brain computation makes the compu-
tation at each level easier to specify. But there is still the issue of describing
what computation goes on.
Although we still do not quite know how to specify the brain’s proces-
sors in detail, we suspect that nerve cells will be at the center of the answer.
So the method is to define models of neurons that represent best guesses
of what is important about them and then define algorithms that use these
abstractions. When one starts to do this, one quickly finds out that the
brain’s algorithms must be very unlike those for conventional silicon com-
puters. This difference is most apparent when considering the standard
way of evaluating algorithms, and that is to see how long they take to
complete. But even this measure must be changed for brain algorithms.
For silicon processing, the traditional way of counting operations is called
“worst case.” We want to guarantee that the algorithm will take no longer
than some temporal bound. But the brain doesn’t care about the worst case
because it is always under time pressure. If something is taking too long,
there is always the option of giving up and moving on. And in this spirit,

the brain also uses lots of dramatic economies. Let’s introduce the main
ones.
1. Parallel computation The nerve cell can be thought of as the brain’s basic
computing unit, with the result that the brain has at least an astonishing
1010
processors. If there was some way of exploiting this huge capability
for simultaneous processing, then the brain could compete with silicon
speeds. Fortunately for much of the sensory and motor circuitry, this paral-
lelism is possible. For example, in visuomotor processing, raw image data
flows in parallel through banks of neurons, where each bank is able to com-
pute a successively more abstract representation. Thus, a moving black and
yellow stimulus becomes, after less than 10 of these banks, a neural code
for “tiger,” which can immediately be passed on to banks of motor circuits
elaborating a “flight” response.
2. Using probability The O(n log n) algorithm for sorting is provably the
best there is. It can sort any sequence in its allotted time. But this is not the
case for all problems. For some algorithms, such as finding the best round-
trip route through a set of cities, getting the shortest possible path is very
expensive. You have to examine all of the paths, and that is exponentially
many. Naturally, this is prohibitively expensive for humans.
But although humans can get themselves end-played in fatal situations,
in the vast majority of cases that does not happen. The normal environ-
ments we inhabit are very rich in alternatives, and as a consequence, if
we just want a reasonably good solution, this can be had at a reasonable
cost. Thus, one of the main ways of speeding things up is to use prob-
ably, approximately correct (PAC) algorithms. The PAC way of accounting
was pioneered by Valiant12
and is standard issue for thinking about brain
computation.
It turns out that probability is enormously helpful in coming up with
fast estimates even when it uses not very reliable data. Suppose that you
are wondering if a coin you have is fair. You flip it five times and observe
HTHHT. Based on these data, you can’t be very sure. But if you flip the coin
200 times and observe 70 heads and 130 tails, then you can be extremely
sure the coin is biased. As we will see, the brain has vast networks that allow
approximate estimates of individual nerve cells to be pooled quickly. This
kind of probabilistic reasoning allows questions to be answered incredibly
quickly.
3. Oscillations at different frequencies Although one can be more confident
of the bias upon seeing a head-to-tail total coin flips ratio of 70:130, the
computation has used up a lot of time. Take another gander at figure 1.4

and count the spikes to determine the spike rate. You can come up with
an estimate, but you have used almost half a second on the figure. A much
faster, and at this point controversial, way to do this would be to code the
estimate as the delay from the zero phase point of a reference frequency. To
unpack the last sentence, let’s go back to figure 1.4 and, focusing on one of
the traces, superimpose a grid on the timescale with ticks 20 milliseconds
apart. No draw a short line rightward from each tick to the nearest spike.
The idea is that this short interval could be a number. So using this con-
vention, the ratio can be sent in one spike! Of course, the accuracy of this
coding strategy depends on the ability of the brain to time spikes with great
precision, but this is something the brain can do.
Not only can the brain achieve the requisite timing, but also accumulat-
ing evidence suggests that it can do this for a number of distinct frequency
ranges, and these ranges have specific computational functions, as reported
in table 1.3.
There is a lot to be said about the particulars of how these different
frequencies are used, and the full appreciation for their functional prop-
erties is still a work in progress, nonetheless we will paint a precis of the
situation here.13, 14
One difficult problem the brain has is to slice and dice
the continuous nature of sensory motor commerce into a form that can be
interpreted by internal codes. The frequency that demarcates the begin-
ning and end of such an episode is the θ (theta) frequency. For humans,
the length of an episode can be arbitrary, say as in planning a long trip. For
more near-term behaviors that involve real-time control of the body, such
as reaching for a coffee cup on a nearby table, evidence suggests that the β
(beta) frequency is used.
Table 1.3
Oscillation frequencies associated with computational functions in the brain
Frequency Range (Hz)
θ 4–7
α 8–12
β 13–39
γ 40–90
Note: Recent evidence is revealing that different temporal frequencies of oscillation
created by neurons have computational roles. Oscillations in the brain have long
been known, but their involvement in computation has only much more recently
been appreciated.

The jury is still out on the use of the α (alpha) frequency. Some evidence
suggests it has a role in the timing of behavior. Another idea, perhaps a
minority view, suggests that it has a role in maintaining calibration in fore-
brain circuitry. The circuits are never “off,” and when they are not actively
involved in a computation, α might be used to calibrate their dynamic
range.
When thinking about brain circuitry, should we think of the neurons
in one huge holistic computation or is there a way that the computation
is broken down into more or less independent parts? Parsimony favors the
compositional view because, if it were true, the brain could achieve enor-
mous diversity in composing different collections of component parts. To
appreciate a problem, at least for the discussion, adopt the cloak of a com-
positionalist and imagine one of the circuits that is essential among the
huge network of the rest of the brain circuitry. How does it keep its func-
tion separate? There have been various ways suggested to do this, but they
all require some technical artifice. One is to assume that the circuit can
somehow be tuned to a distinct frequency in the γ (gamma) range. This
idea is relatively new, but evidence is accruing for the importance of γ in
this role.
4. Bounded input and output sizes In the analysis of sorting algorithms on
silicon computers, the assumption is that the dominant factor is the size
of the input. Where the size of the input can grow arbitrarily, this is the
correct analysis. For example, suppose we pick a give cost for bubble sort so
that now there is no “Big O,” but instead we know that the cost is exactly
1,000n2
on a given computer. Now your colleague gets a computer that
is 1,000 times faster so that the cost is exactly n2
. You have to use the old
computer but can use the merge-sort algorithm. So now even though you
have the better algorithm, your colleague wins when
1,000 n log n > n2
.
Thus, the standard “Big O” analysis breaks down for biological systems as
the number of inputs and outputs are for all practical purposes fixed. When
this happens, it pays to optimize the hardware. To pursue the example of
vision, suppose now that each image measurement could be sampled in
parallel. Now you do not have to pay the 1,000,000 factor. Furthermore
suppose that you wanted to use this parallel “bus” of image measurements
to look something up. Now you only need O(log n) measurements. Further-
more, the brain ameliorates this cost as well by using a pipeline architec-
ture so that the log factor is amortized quickly over a series of stages. Each

stage can be thought of as answering one of 20 questions so that by the
time the process exits, the answer has been determined.
5. Special-purpose sensors and effectors The design for the light-sensing pho-
toreceptors used by vision is believed to have started with the properties of
sea water. It turns out that the visible spectrum is especially good at pen-
etrating water and so could be exploited by fish. Once the hardware was
discovered, it worked on land as well.
In the same way, the human musculoskeletal system is especially
designed for the human ecological niche. We cannot outrun a cheetah,
but we can climb a tree slightly better, and for manual coordination it’s
no contest. The niche is even more sharply illustrated by current robotics.
Although silicon computers can easily out-calculate humans, the design
of robotic bodies is still very much inferior to that of human bodies. Fur-
thermore, the general problems that these human bodies solve seemingly
effortlessly are still very much superior to their robotic counterparts except
in a few special cases. To appreciate this further, try wearing gloves and
going about your normal everyday activities. You will quickly find that you
are frustrated in nearly every situation that requires detailed hand coordi-
nation. If this does not convince you, put on boxing gloves! You will still be
better off than a robot with a parallel-jaw gripper robot arm.
Of course, there are difficult situations that can overwhelm a human
body, such as staring into the Sun or trying to jump a canyon on a motor-
cycle. But these situations are for Darwin Award contestants. For almost all
the problems of everyday existence, the human body is an exquisite design
that works just fine.
6. Amortized computation One contributing factor to fine motor coordina-
tion that we have just discussed is the design of the physical system. To
date, no robot can even come close to the strength-to-weight capabilities
of the human musculoskeletal system. But there is another factor, too,
which is that the process of designing the control algorithms that work
so well happens over many years. Babies learn to control their arms sequen-
tially. They’ll lock all the outboard joints and try movements. When the
nervous system has a model of this reduced system, they’ll unlock the
next more distal joint and try again. The new system has fewer variables
than it would if starting from scratch. Naturally, it is essential to have
parents that patiently care-take while this process is happening, but the
essential feature is that the computation is amortized over time. A wonder-
ful analogy is Google. To make fast Web searches, overheated warehouses

of server computers crawl the Web around the clock to find and code
its interesting structure. The coded results are what makes the response
to your query lightning fast. In the same way, efficient motor behavior
reflects a multiyear process of coding the way the body interacts with
its physical surroundings. The result is that reaching for a cup is fast
and effortless, and carrying it upstairs without spilling its liquid contents
is a snap.
Combinations of all these tricks, plus others that await discovery, are
what allows the brain to do its job fast enough to keep up with real-time
behavioral demands. The chapters ahead use the computational abstrac-
tion formalism to index the different collections of tricks used at different
levels. For the moment, we will turn to take a look at some of the pessimis-
tic views.
1.5 More Powerful than a Computer?
Is the brain just a computer or is it somehow much more powerful? Many
readers would be agnostic to the answer to this question, but it is funda-
mental. Is computation a superb theory, to use Penrose’s term (see ref. 4), or
is it just a useful engineering model that produces helpful answers some
of the time? To answer this question as to whether or not the brain could
be a computer, we must first understand computation in the abstract. This
is because the popular notion of computing is irretrievably tied to silicon
machines. Furthermore, these machines have evolved to augment human
needs rather than exist on their own and as such have not been made to
exhibit the kinds of values inherent in biological choices. Thus, an immedi-
ate reaction to the idea that brains are kinds of computers is to reject the
idea as baseless, with the rejection based on the limitations and peculiari-
ties of modern silicon computers. To counter such intuitions will take a bit
of work starting with a formal characterization of computation. We need
to describe what a computer is abstractly so that if a brain model can be
shown to be incompatible or compatible with this description, then the
issue is settled. It could turn out that brains are unreachably better than
formal computation. I don’t think so for a moment, but the crucial point is
to frame the question correctly.
In framing the question, one has to put one’s reverse engineer hat aside
and ask a fundamental question: Can computation be the root of a theory
of brain function? As Penrose points out, there are many grades of theory,
Newtonian mechanics and quantum mechanics being graded by him as
superb theories for their enormous predictive scopes. Could computation

wind up being a superb theory also? The jury is still out. One way to settle
the question would be to show that humans have abilities that are more
powerful than those of computers. If this could be done, then of course
computation would lose its potential for a superb rating. So let’s take a brief
look at formal computation to sketch the prospects.
Turing Machines
What is computation? Nowadays, most of us have an elementary idea of
what a computer does, so much so that it can be difficult to imagine what
the conceptual landscape looked like before its advent. In fact, the inven-
tion or discovery of formal computation was a remarkable feat, astonish-
ing in retrospect. Enter Alan Turing, a brilliant mathematician who led
the team that broke the German Enigma code during World War II. Tur-
ing’s approach, which resulted in the invention of formal computation,
was constructive: He tried to systematize the mechanisms that people went
through when they did mathematical calculations. The result was the Tur-
ing machine, a very simple description of such calculations that defines
computation (box 1.1). Although there have been other attempts to define
computation, they have all been shown to be equivalent to Turing’s defi-
nition. Thus, it is the standard: If a Turing machine cannot do it, it’s not
computation.
The steps a Turing machine (TM) goes through in the course of accom-
plishing even simple calculations are so tedious that they challenge our
intuitions when we are confronted with its formal power: Any computa-
tion done by any computer anywhere can be translated into an equivalent
computation for a TM. Of course, it could easily be the case that the TM
would not finish that computation in your lifetime, no matter how young
you are, but that is not the point. The computation can be simulated.
Box 1.1
TURING MACHINE
All computation can be modeled on a universal machine called a Turing
machine (TM). Such a machine has a very simple specification, as shown
in the figure below. The machine works by being in a “state” and reading a
symbol from linear tape. For each combination of state and tape symbol, the
machine has an associated instruction that specifies a triple consisting of the
new state, a symbol to write on the tape, and a direction to move. Possible
motions are one tape symbol to the left or right. Although the TM operation
appears simple, it is sufficiently powerful that if a problem can be solved by
any computer, it can be solved by a TM.

(A) A Turing machine program for the very simple function of erasing a series
of 1’s on the tape. (B) The program can be represented by a table that shows
what to do for each state and input. (C) Equivalently, a TM program can be de-
scribed by a state transition diagram in which the nodes of a graph are states,
and arcs are labeled by the symbol read, the direction of motion, and the sym-
bol written. Despite the extreme modesty of its structure, a TM is sufficiently
powerful to be able to emulate all the operations of any other computer, albeit
much less efficiently.
Box 1.1
(continued)

An important point that cannot be overstressed is the breakthrough of
the TM architecture that makes explicit the utility of thinking about pro-
grams in terms of a collection of states and actions that can be taken when
“in” a state. In terms of everyday behavior, if you are making a cup of tea
and you are in a state where {the kettle is nearby and empty}, then presum-
ably the next action is to {put water in the kettle}. The power of thinking in
this way cannot be overestimated. In chapter 5, when we describe ways
of formalizing the brain’s programs, it will be in terms of the state, action
terminology.
To return to the formal computational theme, TMs are not without con-
troversy, as they do have limitations. In general, a TM cannot tell whether
the program of another arbitrary TM will halt or keep going forever. Of
course, it can for some TMs but not in general. Furthermore, TM calcula-
tions cannot use random numbers because the very definition of a random
number is that a TM cannot decide whether it is random or not. And it
This example shows a very simple program for erasing a block of contigu-
ous 1’s. The head is moved along the tape serially, replacing each 1 with a 0.
When the end symbol is encountered, the program terminates. You can define
any number of auxiliary symbols to help write the program or alternately find
ways around using them. Here, for example, you could avoid the # symbol just
by terminating after you see the second 0. For more of a challenge, try to add
two numbers together, and then for even more of a challenge, try to multiply
two numbers together. Remember that they are in a unary representation, just
like that used by convicts marking jail time. To get you started, think of the
initial tape as containing, for example,
0000#1111#000#111#0000#000000000
Your program will probably find a 1, replace it with a 0, and then go and put
it in the answer region, repeating the process until all the 1’s were used up. For
multiplication, the answer would be
0000#1111#000#000#0000#11111111111100
This program will require even more sawing back and forth on the tape.
As you try to write more complex programs, you will quickly be over-
whelmed by the tedium associated with the low-level description used by the
TM. But the point is that in principle, any program in any computer language
has a TM equivalent.
Box 1.1
(continued)

cannot use real numbers either because there are infinitely many more real
numbers than TMs. Experienced programmers know that when they have
randomness in their programs, the program is using pseudo-random num-
bers; that is, numbers that behave enough like random numbers to get use-
ful answers to programs that need them. Similarly, programs use integers
to sample the space of real numbers, again getting numbers close enough
to the real thing for the calculations to have meaning. Finally, as we will
elaborate in a moment, a TM cannot use everyday formal logic either with-
out some form of limitation, as if it tries to prove a theorem that is not true,
there is a possibility that the program will run forever and not halt.
The question is: Are these limitations important or do we need a more
powerful model such as physics? What are the prospects for a physics-based
computing? Some scientists think big, and one is Seth Lloyd.15
He calcu-
lated the operations that would be needed to simulate the universe since
its inception. The estimate is that you need no more than 10120
operations
on 1090
bits for the memory. These numbers are more than the accessible
universe has, but that is because any simulation will have some overhead.
Also, you might not get the same universe if you started with a different
random number seed; indeed, if the process depended on truly random
numbers, you might not get our universe at all. One important take-home
message from this vantage point is that to the extent that the universe can
be described in terms of computation, then presumably our small brains
can, too! But a larger point is that perhaps there is a prospect of harnessing
quantum computing to solve difficult problems. Potentially many solu-
tions could be coded as probabilistic quantum states in a machine that
could then pick the best one. While this is intriguing, the technical prob-
lems in making this work at any useful scale are enormous. For an introduc-
tion, see Lloyd’s book (see ref. 15).
1.6 Do Humans Have Non-Turing Abilities?
Given that real numbers and random numbers are the death knell for TMs,
one quick way to distance humans and machines would be to show that
in fact humans have the ability to use either or both. This is a tricky task
because one has to show that the infinite precision of real numbers is real-
ized by the humans. An intriguing way station toward this task shows that
a neural-like model that can use real numbers is in fact more powerful than
Turing computation, as is done by Selgelmann16
in a model where model
neurons have the ability to realize real numbers as input. However, a cru-
cial next step would be to show that real neurons can in fact do this. The

real world is riddled with noise sources that limit the precision of analog
signals.
A more pessimistic view of computational prospects is represented by
Roger Penrose, who has written three books with the theme that TMs are
too weak a model to encompass the brain (see ref. 4; Penrose also holds out
hope for the quantum computation and proposes a way in which it might
be utilized by cells that is wildly speculative). But what of his arguments
that TMs do not have sufficient power? One of Penrose’s main arguments
settles around Gödel’s theorem.
Penrose argues that as humans understand this theorem that points to
a fundamental weakness of logic (in proving statements about arithmetic),
but computers are forced to use logic, ergo humans think out of the logical
box and are more powerful than TMs. However, if we understand a proof, it
has to be logical. The trick is that the referents of the proof are highly sym-
bolic sentences. Gödel’s brilliant insight, wonderfully described by Nagel
and Newman,17
was that when these were about mathematics, they could
be reduced to arithmetic. Hence, the referents of the logical statements are
regularized, and no special machinery is necessary. We are not saying it is
easy; after all there has only been one Kurt Gödel! However, any gradu-
ate student in computer science or mathematics can easily understand the
logic of the proof.
One central, potentially confusing issue that Gödel’s theorem addresses
successfully and that we touched upon when discussing hierarchies earlier
is that of managing concepts at different levels of abstraction. When work-
ing a given level, one has to be careful to stay within that level to have
everything make conceptual sense. You can switch levels but you have to
be careful to do the bookkeeping required to go back and forth (see ref. 10).
The failure to do this can lead to “strange loops” and the delight in experi-
encing the ambiguity that comes with it.18
However, keeping this straight
diffuses the alleged mystery in understanding Gödel’s theorem. If we take
the vantage point of the coded formula, the proof is such that anyone with
advanced training in logic can understand it. It is only when we simul-
taneously try to entertain consequences of the uncoded logical formulas
together with statements at a different level of abstraction that use their
coded form that things get confusing.
Turing Machines and Logic
At this point, there might be one last puzzling question in your mind. For
one thing, the standard computer is constructed with network logic gates,
each of which implements an elementary logic function such as the logical

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CHAPTER X.
BARNEY’S DISAPPEARANCE—FIGHT WITH
BEARS.
As far as the eye could reach all was one vast snow bank. The wind
rioting had twisted the loose material into all sorts of fantastic
shapes.
The snow had now ceased falling and the air was crisp and clear.
Leaving the airship’s deck the voyagers walked boldly out upon the
huge drifts.
The snowshoes prevented their sinking into the white depths,
perhaps over their heads.
Frank Reade, Jr., led the way to the highest point accessible and
from this a good view of the surroundings could be had.
It was a bleak, desolate and forbidding region spread to view.
Yet the white country had its peculiar beauty and charms. Like
crystal palaces the bergs of clearest ice glistened in the rarefied air.
“Grand!” cried Professor Gaston. “Where will you ever see the likes
again?”
“Begorra, I wish I had a toboggan!” cried Barney, pointing to an icy
slope near.
“Yo’ don’ need nuffin’ ob dat kind, sah!” cried Pomp. “Jes’ slide down
on yo’ feet an’ stiddy yo’se’f wif a pike.”

All the party had long pike poles with iron tips to prevent sliding into
any hole or dangerous pit.
Barney was just in a mood to refute any dare that Pomp might offer,
so he cried:
“Bejabers, I’ll go ye!”
“A’right, I’ish!”
Away went the two jokers at full speed across the snow. They
reached the slope a few moments later.
The slide was fully a hundred yards in length, and was quite steep
and slippery. Frank looked anxious.
“I fear they are rash,” he said. “If one of them should fall he might
break some bones.”
But Professor Gaston laughed.
“Have no fear,” he said. “They will make it all safely. It is fun for
them.”
The two jokers were now on the brow of the descent. They were
chaffing each other in a friendly manner.
“Am yo’ ready, I’ish?” cried Pomp.
“Begorra, I am!”
“Then jes’ follow me!”
With their pikes thrust deep into the ice behind, and acting both as
rudder and support, they began the slide.
The surface seemed as smooth as polished glass. Down they shot at
lightning speed.
It required but a few brief seconds to cover the distance.
But before it was covered a thrilling incident occurred. Suddenly, and
when half way down, there was a crackling sound, and Barney threw
up his arms and disappeared.

Pomp went on down to the end of the slide.
A cry of horror burst simultaneously from the lips of Frank Reade, Jr.,
and Professor Gaston.
“My soul!” cried the young inventor. “My fears are realized! Barney is
lost!”
They lost no time, but started at once for the spot.
Reaching the foot of the slide, Frank saw the explanation of Barney’s
disappearance.
There, in the surface of the slide, was a yawning hole. The ice in this
spot was thin and had covered a pit, into which the unlucky Celt had
fallen.
With the aid of his pike, Frank crawled to the edge of the hole and
looked in.
What he beheld gave him an awful, horrified chill.
“My God!” he cried, wildly, “Barney has gone to his death!”
“Don’t say that!” cried Gaston. “Can we not pull him out of that
awful hole?”
“No,” replied Frank, sadly. “Barney is beyond earthly aid!”
By this time Pomp and Gaston were by Frank’s side. A glance into
the hole was enough.
It was a deep, circular opening, extending downward for twenty
feet. At its bottom was a surging, boiling mass of icy waters.
It was into the ocean that Barney had dropped.
Doubtless before this he had been carried under the vast field of ice
and was beyond earthly aid.
For a moment the three explorers looked at each other in utter
horror.
Then Pomp began to wail in sorrow.

“Fo’ de good Lor’, am de I’ishman done gone an’ dronwed?” he
cried. “Den dis chile am lef’ all alone. Boo, hoo, hoo! He was jes’ de
bes’ frien’ I eber had. Wha’ am I gwine to do now?”
Indeed, all were deeply affected. Pomp was inconsolable.
Watch was kept at the hole for a reasonable time in the faint hope
that the Celt would reappear.
But he did not.
Sorrowfully the three explorers now returned to the airship. But
before they reached it they were confronted with new and startling
incidents.
The Dart was half buried in the snow at the foot of the big berg. As
Frank and his companions came in sight of the Dart they paused.
Clambering over the deck were a number of fur-clad forms.
At first the explorers thought them human beings, but a closer
glance showed that they were huge white bears.
Six of the monsters were boarding the airship in the coolest possible
manner.
“Great heavens!” exclaimed Professor Gaston. “What does that
mean, Frank?”
“It looks as if the bears had taken possession of our property,”
declared the young inventor.
“Can they do any harm?”
“Certainly. We must tackle them at once.”
The prospect of tackling the six monsters was by no means a
pleasant one.
The white bear is known as a powerful and savage beast and not
easily handled.
But there was no alternative for the adventurers.

They must certainly regain the airship. It was not easy to say how
long the bears would remain on board or what damage they might
do.
“Forward!” cried Frank. “Reserve your fire until at close quarters.”
This command was obeyed.
When near the rail fire was opened with the Winchesters. One of the
bears tumbled in a heap with three bullets in his carcass.
Frank’s plan was to tackle one bear at a time and fire at him until he
succumbed. This would have been all very well had the bears
remained inactive.
But this they did not seem disposed to do. At sight of the white men
they came to the attack at once.
The white bear is a huge, unwieldy monster, but nevertheless supple
and quick in action.
The five remaining bears started for the explorers pell mell. They
were evidently hungry and regarded them as lawful prey.
“Look out!” shouted Frank. “Separate and fire as rapidly as you can.”
These instructions were followed.
Pomp retreated as fast as his legs could carry him with two of the
bears after him. On even ground the darky might have distanced
them.
But on the snowshoes he found it hot work to keep out of reach of
their paws. Once overtaken, his fate would be sealed.
Knowing this, he sped on with all speed. There was no chance to
turn and fire until he had gained at least a reasonable distance.
The darky was all pluck, however, and kept on at a rapid pace.
Finally he managed to gain a pinnacle of ice which projected upward
from the plain.
This he believed was his opportunity.

Quick as a flash he dodged behind it. Then he drew aim at almost
point-blank range and fired at the first bear.
The bullet took effect in the brute’s brain, through the eye. It
staggered back and then dropped in a heap.
A yell of pleasure escaped the darky’s lips. He was about to draw
back the hammer and throw a second cartridge into the rifle barrel
when he saw, with horror, that there was not another cartridge in
the chamber of the repeater.
He had just time to dodge the surviving bear around the ice
pinnacle.
Round and round he went, the bear at his heels. The predicament
was a comical as well as a serious one.
“Golly! wha’ am I gwine to do?” reflected the darky. “I kain’t keep
dis sort of fing up fo’ebber.”
The bear was enraged at his futile effort to capture his prey. Pomp
eluded him every time.
Then a daring idea occurred to the darky. He broke away and made
a dash for the airship.
If he could reach it and gain an entrance to the cabin he would be
saved. Unarmed as he was it was certain death to face the bear.
Swift as he could, Pomp ran toward the Dart. The bear was howling
close at his heels.
Indeed, when the Dart’s rail was reached the monster was hardly
three yards behind. A dozen yards more and Pomp would certainly
have been captured.
Over the rail at a leap went the darky. The next moment he reached
the cabin door.
He threw his weight against it and it gave way. Into the cabin he
sprang. The bear paused at the door.

While the brute seemed to be meditating upon the feasibility of
entering, Pomp procured an elephant rifle.
This threw a deadly explosive shell of Frank Reade, Jr.’s own
invention. Pomp took steady aim at the brute.
Then he fired.
The shell struck the bear in the chest. It was instantly fatal,
penetrating the heart. Pomp had won.
Then the victorious darky thought of his companions.
“Golly! I done fink Marse Frank am habin’ a hard time!” he cried.
This was indeed true.
Professor Gaston was dodging his bear behind an ice column as
Pomp had been. But Frank was in hand-to-hand conflict with the
remaining two bears.
The young inventor had fired three bullets into the body of one of
the bears. But though somewhat crippled, the beast was yet in
fighting trim.
And both had come to close quarters with Frank.
He had drawn his long hunting-knife and was slashing at the brutes,
but it was a moral certainty that he would have been soon
overpowered had it not been for the opportune coming of Pomp.
The darky rushed up at this moment and cried:
“Jes’ yo’ hol’ on, Marse Frank. I’se here, an’ I’se gwine to sabe yo’.”
Placing his elephant rifle close against the body of one of the bears
Pomp pulled the trigger. The effect was fatal.
The brute’s vitals were literally destroyed, and it sank dying upon the
snow. The other bear Frank quickly finished with his knife.
Then the two victorious hunters went to the rescue of Professor
Gaston.

This sole remaining bear was easily dispatched and the battle was
over.
Beyond a few scratches and cuts the party was uninjured. But all
realized what good reason there was for self-congratulation.
“By Jove!” cried Frank. “Six bears to three men! That is the biggest
luck for one day’s hunting that I have ever seen.”
“If we had been hunting for such game we could never have found it
in such numbers,” declared Professor Gaston.
“I don’t know about dat!” said Pomp, dubiously. “Dar am a heap ob
dem critters in dese regions!”
“Well,” cried Frank, cheerily, “let us remove their pelts and keep
them as trophies of our prowess, anyhow.”

CHAPTER XI.
AT THE NORTH POLE.
This was quickly done.
Pomp was an adept at the business, and soon the six pelts were
stored away on board the airship.
Then it was decided to ascend and continue the journey to the Pole.
“We ought to locate that very-much-sought spot in two days more,”
declared Frank; “then we are homeward bound.”
Somehow the sound of the words “homeward bound” had begun to
have a powerful charm for the explorers.
The time they had been absent and the thrilling experiences which
had been theirs were certainly sufficient to satisfy the most
fastidious seeker of wild adventure.
“Surely it will seem good to see home once more,” declared Gaston,
warmly. “And think of the honor which awaits us!”
Pomp now lacked the co-operation of Barney in clearing the snow
from the deck of the airship and its rigging.
But Frank and Gaston lent their services in this. Soon the deck was
quite clear and ship-shape.
Then the rotascope was raised and the wings expanded.
The machinery was tried to see that no harm had come to it. Then
all was in readiness for the start.

But just as Frank was about to enter the pilot-house a wild cry
escaped Pomp’s lips.
“Fo’ de Lor’ sakes, Marse Frank!” he screamed, “jes’ cast yo’ eye
ober yender!”
Frank did so. The sight which rewarded his gaze was a thrilling one.
Painfully clambering over an icy ridge near were two men. As they
reached its summit and were in full view of the airship one of them
shouted:
“Help! Help!”
“Great heavens!” was Frank’s wild cry, “that is Barney!”
“Barney!” gasped the professor.
“Yes, back from the dead!”
“Massy sakes, it am his ghostis!” cried Pomp, in terror. “Don’ go ober
dere, Marse Frank!”
“Don’t be a fool!” cried Frank, angrily. “Come along, both of you!”
Gaston followed Frank instantly.
Barney it was, and but just alive. The Celt was covered with a
coating of ice.
The man with him was shrunken to a shadow, with pale, cadaverous
features. He could hardly creep along and blood marked his course
over the snow.
“Barney!” cried Frank, rushing up to the spot. “Thank God you are
alive! How did you come here, and who is this?”
“Begorra, Misther Frank, it’s a long swim I had!” replied Barney. “An’
it’s nigh dead I am wid me wet clothes. Shure, we’ll tell yez all about
it whin we get warm!”
“Help us, for the love of God!” said the pallid wretch in a whisper.
Nothing more was said until the two exhausted men were helped
aboard the airship.

Then Barney was undressed and thawed out, and both were given
hot drink and food.
The Celt’s story was brief and succinct.
“Shure, whin I fell into that hole,” he declared, “fer toime me head
was under wather. Then I cum up into the air an’ all was dark.
“I felt mesilf being carried along by the current, an’ thin all became
loight agin an’ I kem out into daylight wanst more. I was carried
about a moile below here, to a big, open basin av wather. I cloimbed
out, an’ shure there in the ice I saw the hull av a big ship.
“Masts nor riggin’ there was none, only the hull. An’ whin I wint up
to it this gintleman crawled out an’ spoke to me. Shure, he kin tell
his story betther than me.”
“Golly! but I am done glad fo’ to see yo’ safe agin, I’ish!” cried
Pomp, with glistening eyes.
“Shure, an’ it’s glad I am to be wid yez wanst again!” replied Barney.
The Arctic refugee now began, in a weak, quavering voice to tell his
story.
“Three years I have passed in thus cursed clime!” he declared. “All
has been solitude like unto death. Oh, God! the horror of that time!
“Three years ago our brig, the Valiant, in command of Captain
Alexander Bent, was nipped by the ice and drifted hither, after many
months of futile attempt to liberate her.
“I was the first mate, James Spencer, and I am to-day the only
survivor. Within six months from the nipping of the ship every
member of the crew of twelve men, save myself, were dead.
“A fearful disease struck us and all had it but me. I prayed to have it,
but fate ordered otherwise.
“I buried them all, one by one, in the ice. Then I was left in solitude.
For three years I lived on the stores of the ship.

“But last week the last biscuit gave out. I had no longer strength to
hunt. I had given myself up to die when this man appeared before
me. Even now it seems as if I must be dreaming.”
“No,” replied Frank, cheerily, “you are not dreaming. Cheer up, my
good man, for you are sure of getting back home.”
“What!” cried the castaway. “Do not mock me. You are cast away
here like me?”
“No; this is our ship.”
“Ah, but you will never sail it home. This ice will never break up.”
“You are wrong!” cried Frank. “This is an airship. We sail in the air.”
“An airship!” the poor fellow passed his hand across his brow in a
troubled manner. “No, no; it is really a dream! I shall soon awake, as
I have many times before.”
Then he lapsed into a revery.
“Let him be!” said Frank, compassionately. “Poor fellow, his brain is
weak. He will be stronger soon.”
Barney was soon himself again and as chipper as ever. There was no
reason now why the journey should not be continued.
Spencer, the castaway, was asleep. The airship was soon aloft in the
air and speeding on its way.
Frank, as well as possible, took his bearings.
“Barely two days more!” he declared. “Then we shall reach the North
Pole!”
“We have heard much of the open Polar sea,” declared Professor
Gaston. “Now we shall have a chance to prove it.”
“Right!” cried Frank. “And it is really in existence!”
“You know that?”
“Yes, I do.”

The airship sped on for hours. As Frank had predicted, just two days
were occupied in reaching the Pole.
In the meantime Spencer had come to himself and was
overwhelmed with amazement at his position.
“An airship!” he exclaimed. “The impossible has come to pass! I
really cannot realize that I am going home!”
Then great joy became his. Truly it was not to be wondered at, for
he might regard it as being almost equivalent to being brought back
from death to life.
When the exact locality of the Pole was reached all were
disappointed.
It was a cold, blustering spot; a sort of elevation among hills of
rugged rock, now, however, heavily coated with ice and snow.
“Now for home!” cried Frank. “Our journey is near its end!”
The mention of home had a magic sound. But thrilling events were
yet in store.
The course taken by Frank was a straight line for the Arctic Islands
and Hudson’s Bay.
For days the airship kept steadily on this course.
Baffin’s Land and many of the small islands in the Gulf of Bothnia
were passed over in the flight.
Then the waters of Hudson’s Bay burst upon the view of the
voyagers.
It was truly a wonderful sight.
The course was along the east shore of Hudson’s Bay. When near
James Bay and at the mouth of the Great Whale River an astounding
thing happened.
Suddenly and without warning the airship began to fall.
“Great heavens!” cried Professor Gaston. “What has happened?”

“Something is wrong!” cried Frank Reade, Jr., “the machinery has
failed us!”
However this was it was certain that the airship was bound to reach
the earth. The rotascope and wings seemed to have lost their power.
Barney, who was in the pilot-house, steered the Dart to a good
landing place just in the verge of a forest of firs.
The waters of the bay were not one hundred yards distant.
Had the airship fallen into them the result would have been serious
enough. It would have meant death.
But fortunately they were to alight on shore. Down settled the
airship until it struck the earth.
Then Frank went over the machinery critically. He found the defect
as he had believed he should in the machinery.
He located the break and then said to his anxious companions:
“It can be repaired, but it will require a couple of days to do it in.”
This meant a delay, and just at a time when all were anxious to
reach home. Yet no demur was made.
The anchors were put out and then work was begun.
As Frank had predicted there was a couple of days’ work on the
machinery. The job was pushed forward as rapidly as possible and
had been nearly completed when an exciting incident occurred.
Suddenly in the water of the bay there appeared a number of the
peculiar Esquimau canoes, known as kayaks.
In each was an Esquimau equipped for seal hunting.
They landed and approached the airship. Short and squatty in figure
they were, with greasy countenances. A more villainous-looking set
had never been seen by the voyagers.
They conversed with Frank for a while in broken English, and then
went away. As they disappeared Frank said, with conviction:

“Do you know I do not believe we have seen the last of them. I feel
sure that we shall have trouble.”
“You may be sure of that!” declared Spencer. “I know something
about their race, and I tell you they are a bad lot.”
“Begorra, ther’s enough av us to whip them!” averred Barney.
“That may be true,” agreed Frank, “but it will put us to the
unpleasant necessity of killing a few of them.”
That night a careful guard was kept. Barney and Pomp watched
alternately. But it was not until the next day, that the real trouble
came.

CHAPTER XII.
THE PROFESSOR’S ADVENTURE.
Then Frank Reade, Jr.’s premise proved correct. However, no open
attack was made upon the Dart.
But it happened in as bad a way, in fact, much worse. Professor
Gaston was out upon an exploring tour.
The professor was enriching his collection of rare fossils, and was
about a quarter of a mile from the airship when attacked.
Suddenly and without warning he found himself surrounded by the
Esquimaux. He blew his whistle.
The professor’s Winchester was under his arm. He could have shot a
couple of them, but he knew that it would mean his instant death.
“White man gib gun to Eskimo!” said the leader. “Come along! Be
prisoner. Mebbe so he live, mebbe not so, he die!”
“Hold on!” said the shrewd scientist. “Just wait until I return and I
will bring you some more guns.”
“No! White man stay. Mebbe no come back. Stay here!”
Gaston saw that he was in for it. Yet he did not believe for a
moment that his life was as yet in special danger.
He ransacked his brain in vain for a subterfuge by which to foil the
Esquimaux. But each time he was disappointed.
Finally he was led away into the fir forest. A few moments more of
delay and he would have been rescued by his friends.

Frank was in the engine-room when he heard the whistle of alarm.
“Quick, then!” cried Frank. “Pomp, you stay with the airship.”
Barney and Spencer grabbed their rifles and followed Frank. Soon
they had reached the spot where the professor had been seized by
the Esquimaux.
Their tracks were seen and understood at once by Frank.
All search was of no avail. It was known that the professor was in
the hands of the Esquimaux and that was all.
Back to the airship the three men went and to work.
Meanwhile the professor was having some thrilling experiences.
As the party tramped on the professor could not help wondering
what his fate was to be.
He was not left long in doubt.
Suddenly the party came out of the fir forest and were in sight of a
long, level plain extending down to the sea.
And near the water’s edge were a number of huts made of brush
and bark. This was the manner of habitation used by the Esquimaux
of this region in lieu of ice.
Perhaps there were a hundred or more of these huts.
A vast throng of Esquimaux came out to meet them.
The prisoner was surrounded by a howling mob. Some of them
seemed disposed to do him harm.
But the leader of the band kept them back in his persuasive way, by
swinging his battle-club about him.
The prisoner was led down into the Esquimau settlement. His arms
and legs were bound with thongs, and he was unceremoniously
tumbled upon the ground.
As he lay in the midst of his foes thus, the professor fell to
wondering if his whistle of alarm had been heard at the airship.

If it had there was good reason to believe that he might expect help
and perhaps rescue.
But as time passed and his friends did not appear he began to give
up hope.
His position was becoming unendurable, when suddenly the
Esquimau chief appeared and gave some orders to his men.
The prisoner was lifted and the thongs which bound his feet being
severed he was commanded to stand up.
Then the Esquimau chief said, in broken English:
“White man mebbe live. He gib Eskimo man more gun and more fire
dust. See?”
The professor grasped the situation.
“All right,” he said; “let me go and I’ll get the guns for you.”
But the chief smiled in a leering way.
“Eskimo no fool! White man go, mebbe stay. No come back, Eskimo
be big fool.”
“Well, then, how am I to get the guns for you?” argued the
professor.
“Mebbe see.”
The chief beckoned to one of the tribe, a muscular fellow, who came
forward.
“He go tell you people he want gun, see! You tell him.”
Gaston was not disposed to be reckless.
He saw at once that if he could not gain all the pie at least a piece
would be better than nothing at all.
He realized that if his friends were thus notified of his predicament
they would adopt some speedy plan for his rescue.
So he said:

“Very well, chief. Send your man to my friends. They will give you
guns, and then you shall set me free.”
The Esquimaux now all seemed to be waiting for the return of their
courier.
Frank had just finished his job of repairing the machinery when the
Esquimaux’ messenger arrived.
“Well, you greasy rascal, what do you want?” he asked.
“Heap gun!” was the reply. “Mebbe you give me, mebbe no kill you
man. See?”
“Ah!” said Frank, with comprehension. “You have got one of our men
in your clutches, eh?”
“Yep!” replied the Esquimau.
“Come aboard this airship and I’ll go with you.”
But this did not strike the wretch’s fancy.
“No, mebbe not,” he said, shaking his head violently. “Mebbe gib me
guns!”
“Mebbe I won’t,” said Frank, sternly. “Come over, or die!”
He aimed a revolver at the villain. The Esquimau knew what that
meant and began to beg.
“Mebbe no kill me. Sabe white man. He live, no kill me!”
“You diabolical shark, you!” cried Frank, grabbing the miscreant’s
collar. “Come aboard here, and no fooling!”
And Frank pulled him over the rail where he lay cowering upon the
deck.
“Now, Barney,” he cried, “send her up!”
Barney needed no second command.
The airship sprang into the air. She was as steady once more as a
humming top.

Over the fir forest she sped. It was hardly ten minutes before the
Esquimau village was in sight.
The natives at sight of the airship seemed imbued with terror.
They retreated with dismay into their bough huts.
Frank allowed the airship to descend right on the verge of the
settlement. Then he picked up the shivering wretch on the deck and
hurled him over the rail.
“Go tell your chief I want to see him,” he said.
In a few moments the Esquimau chief sullenly appeared.
As he stood with folded arms by his bough hut Frank addressed him:
“You greasy scoundrel! You thought to make a treaty with me and
force me to give you firearms, did you? Why, I’ve a mind to
annihilate the whole tribe of you!”
The Esquimau flashed a leering, contemptuous glance at Frank and
replied:
“White man mebbe fly in air; but Eskimo man no ’fraid ob him.”

CHAPTER XIII.
THE END.
Frank was amazed at the cool nerve and effrontery of the wretch.
For a moment the young inventor was silent.
Then he said:
“You have one of our men in captivity here. I want him.”
The chief shook his head sullenly.
“What?”
“Mebbe no.”
“Mebbe, yes!” cried Frank, angrily. “Come, I’ll blow you to perdition if
you don’t give him up!”
“No can do dat.”
“Why?”
“White man killed!”
For a moment Frank reeled as if given a terrific blow. He turned
ghastly pale. Then Gaston was dead.
“That is awful!” he thought.
But something in the Esquimau chief’s face caused him to start. He
grasped the situation at once.
“You are lying!” he hissed, leaning over the rail. “Give him up, or I’ll
kill you and all your cowardly crew!”

The Esquimau chief laughed scornfully, and gave a peculiar cry. In a
moment the vicinity was thronged with armed natives.
Frank saw that the crisis had come. There was no use in dallying
further.
He picked up a bomb brought him by Barney and hurled it fairly into
the midst of the murderous horde.
In a flash there was a frightful explosion. Heaps of dead and dying
Esquimaux lay upon the ground.
The survivors fled wildly. Frank leaped from the airship’s deck. He
rushed into the nearest bough hut.
There was Gaston bound hand and foot.
“Thank God! you have come to save me!” cried the scientist. “You
are none too soon!”
“But there is yet danger!” cried Frank. “Follow me quickly!”
To the airship they rushed. The Esquimaux were recovering and
seemed ready to fight. But though he could have annihilated the
whole gang, Frank did not wait for their attack.
Up into the air sprang the airship.
The course was at once set to the southward and for a week was
firmly held. Then evidences of civilization appeared.
Canada was passed over, Lake Erie and then the United States was
once more beneath the aerial voyagers.
Home again! There was an indescribable charm in the words.
The airship descended into Readestown one evening. The next
morning every daily paper in the world was recording the return of
the travelers from zone to zone.
James Spencer returned to his home where he was happily
welcomed.

Professor Gaston took the first train to New York and reported to the
committee of the scientific society.
The much-mooted question of the two Poles was settled forever.
Professor Gaston was instantly made honorary member in every
scientific society in the world.
Indeed, the honors thrust upon him were most burdensome.
Barney and Pomp were pleased to once more return to their duties
in quiet old Readestown.
“I don’ fink I want berry much to do wif dem Arctic countries!” Pomp
declared. “Dey am a pooty po’ place fo’ a live man.”
“Bejabers, I’m wid yez, naygur!” cried Barney. “Hurroo fer ould
Oireland an’ Afriky!”
“And hurrah for America, the queen of all nations!” cried Frank
Reade, Jr., with a laugh, for he had overheard them.
The Dart was at once taken to pieces. The strain of her long voyage
would preclude any possibility of ever using her again.
But the young inventor had plenty of other plans to develop.
For many a day the famous trip of Frank Reade, Jr., and his airship,
the Dart, from zone to zone, rang through the country.
But though this was certainly a most extraordinary feat, the young
inventor had even mightier projects on hand, some of which the
reader may hear of at a later day.
THE END.

Read “FRANK READE, JR., AND HIS ELECTRIC CRUISER OF THE
LAKES; OR, A JOURNEY THROUGH AFRICA BY WATER,” which will
be the next number (14) of “Frank Reade Weekly Magazine.”
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SPORTING.

No. 21. HOW TO HUNT AND FISH.—The most complete hunting and
fishing guide ever published. It contains full instructions about guns,
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No. 26. HOW TO ROW. SAIL AND BUILD A BOAT.—Fully illustrated.
Every boy should know how to row and sail a boat. Full instructions
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No. 48. HOW TO BUILD AND SAIL CANOES.—A handy book for boys,
containing full directions for constructing canoes and the most
popular manner of sailing them. Fully illustrated. By C. Stansfield
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HYPNOTISM.
No. 81. HOW TO HYPNOTIZE.—Containing valuable and instructive
information regarding the science of hypnotism. Also explaining the
most approved methods which are employed by the leading
hypnotists of the world. By Leo Hugo Koch, A.C.S.
FORTUNE TELLING.
No. 1. NAPOLEON’S ORACULUM AND DREAM BOOK.—Containing the
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No. 23. HOW TO EXPLAIN DREAMS.—Everybody dreams, from the
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No. 28. HOW TO TELL FORTUNES.—Everyone is desirous of knowing
what his future life will bring forth, whether happiness or misery,
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No. 76. HOW TO TELL FORTUNES BY THE HAND.—Containing rules
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ATHLETIC.
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No. 10. HOW TO BOX.—The art of self-defense made easy.
Containing over thirty illustrations of guards, blows, and the different
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No. 51. HOW TO DO TRICKS WITH CARDS.—Containing
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card tricks; of card tricks with ordinary cards, and not requiring
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No. 72. HOW TO DO SIXTY TRICKS WITH CARDS.—Embracing all of
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tricks, containing full instruction on all the leading card tricks of the
day, also the most popular magical illusions as performed by our
leading magicians; every boy should obtain a copy of this book, as it
will both amuse and instruct.
No. 22. HOW TO DO SECOND SIGHT.—Heller’s second sight
explained by his former assistant, Fred Hunt, Jr. Explaining how the
secret dialogues were carried on between the magician and the boy
on the stage; also giving all the codes and signals. The only
authentic explanation of second sight.
No. 43. HOW TO BECOME A MAGICIAN.—Containing the grandest
assortment of magical illusions ever placed before the public. Also
tricks with cards, incantations, etc.
No. 68. HOW TO DO CHEMICAL TRICKS.—Containing over one
hundred highly amusing and instructive tricks with chemicals. By A.
Anderson. Handsomely illustrated.
No. 69. HOW TO DO SLEIGHT OF HAND.—Containing over fifty of
the latest and best tricks used by magicians. Also containing the
secret of second sight. Fully illustrated. By A. Anderson.
No. 70. HOW TO MAKE MAGIC TOYS.—Containing full directions for
making Magic Toys and devices of many kinds. By A. Anderson. Fully

illustrated.
No. 73. HOW TO DO TRICKS WITH NUMBERS.—Showing many
curious tricks with figures and the magic of numbers. By A
Anderson. Fully illustrated.
No. 75. HOW TO BECOME A CONJUROR.—Containing tricks with
Dominos, Dice, Cups and Balls, Hats, etc. Embracing thirty-six
illustrations. By A. Anderson.
No. 78. HOW TO DO THE BLACK ART.—Containing a complete
description of the mysteries of Magic and Sleight of Hand together
with many wonderful experiments. By A. Anderson. Illustrated.
MECHANICAL.
No. 29. HOW TO BECOME AN INVENTOR.—Every boy should know
how inventions originated. This book explains them all, giving
examples in electricity, hydraulics, magnetism, optics, pneumatics,
mechanics, etc., etc. The most instructive book published.
No. 56. HOW TO BECOME AN ENGINEER.—Containing full
instructions how to proceed in order to become a locomotive
engineer; also directions for building a model locomotive; together
with a full description of everything an engineer should know.
No. 57. HOW TO MAKE MUSICAL INSTRUMENTS.—Full directions
how to make a Banjo, Violin, Zither, Æolian Harp, Xylophone and
other musical instruments: together with a brief description of nearly
every musical instrument used in ancient or modern times. Profusely
illustrated. By Algernon S. Fitzgerald, for twenty years bandmaster of
the Royal Bengal Marines.
No. 59. HOW TO MAKE A MAGIC LANTERN.—Containing a
description of the lantern, together with its history and invention.
Also full directions for its use and for painting slides. Handsomely
illustrated. By John Allen.
No. 71. HOW TO DO MECHANICAL TRICKS.—Containing complete
instructions for performing over sixty Mechanical Tricks. By A.

Anderson. Fully illustrated.
LETTER WRITING.
No. 11. HOW TO WRITE LOVE-LETTERS.—A most complete little
book, containing full directions for writing love-letters and when to
use them; also giving specimen letters for both young and old.
No. 12. HOW TO WRITE LETTERS TO LADIES.—Giving complete
instructions for writing letters to ladies on all subjects, also letters of
introduction, notes and requests.
No. 24. HOW TO WRITE LETTERS TO GENTLEMEN.—Containing full
directions for writing to gentlemen on all subjects; also giving
sample letters for instruction.
No. 53. HOW TO WRITE LETTERS.—A wonderful little book, telling
you how to write to your sweetheart, your father mother, sister,
brother, employer, and, in fact, everybody and anybody you wish to
write to. Every young man and every young lady in the land should
have this book.
No. 74. HOW TO WRITE LETTERS CORRECTLY.—Containing full
instructions for writing letters on almost any subject; also rules for
punctuation and composition; together with specimen letters.
WORK AND WIN.
The Best Weekly Published.
ALL THE NUMBERS ARE ALWAYS IN PRINT.
READ ONE AND YOU WILL READ THEM ALL.
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