SOME UNECONOMICAL ROBOTS
109
An outside observer (one unable to lift up the hood) could not
predict the exact path of such a robot and might attribute to it some
freedom of the will.
If some memoryless robots were constructed to destroy each
other, it is clear that one built deterministically could be badly taken
advantage of by those with properly weighted probabilistic responses.
A probabilistic behavior strategy can be simulated without in
serting any unreliable elements if we use cycles. In Figure k the cells
fire successively and each fires once every 4 time units. (The non-positive
threshold on C1 eliminates any problem about getting the cycle started
and also allows it to start up again spontaneously after recovering from
any accidental power failure or other stoppage.) It is clear that the
period of each cell equals the number of cells in the cycle.
Let Pr{x,y] be the probability that y fires at t + 1 if x
fires at t. In general we may interrelate x, y and a cycle so as to
simulate any given rational value of this probability as follows. If
Pr(x,y] = a/p then
(1) let x have one excitatory bulb on y
(2 ) let 0 on y equal 2
(3 ) let exactly a members in a cycle of £ cells each have one
excitatory bulb on y.
Since exactly a cycle members contact y the probability that
any one of them fires at t equals a/p . Hence Pr(x,y) = a/p. For ex
ample, in Figure 5 there are 7 cycle members (the inhibitory bulbs on
C1 are not shown) and 3 of them contact y 1. Hence Pr(x,y] = 3/7 .
For example, in Figure 5 there are 7 cycle members (the inhibitory bulbs
on C1 are not shown) and 3 of them contact y 1 . Hence Pr(x,y.j) = 3/7;
also, as shown, Pr(x,y2) = 2/7 and Pr(x,y^) = 2/7. The cycle is a kind
of neurological roulette wheel, so to speak, determining whether or not
the impulse is to pass through the synapse.
FIGURE k FIGURE 5
The possible input-output specifications for a probabilistic
memoryless robot are not limited to (2 M )2n since for each receptor 3et
and each effector set, we may assign any probability we want — the firm.;
1 10
CULBERTSON
of the former cause the firing of the latter. Using these "roulette"
cycles, however, it is easy to show in detail how to construct a memoryless
robot satisfying any given probabilistic input-output specifications [2 ].
The more difficult but, no doubt, more practical reverse problem of getting
deterministic behavior from unreliable elements has been worked out by von
Neumann [ 5 ] .
COMPLETE ROBOTS
Unlike deterministic memoryless robots, humans and animals do not
react always the same way to a given spatial input. The way they respond
may be influenced by inputs from the past — often the remote past. The
way Professor Emeritus Jones behaves in the presence of ladies may depend
on something that happened to him when he was four years old.
Human beings learn, they remember, and their behavior is modified
by experience in various other ways. They ingeniously solve problems,
compose symphonies, create works of art and literature and engineering, and
pursue various goals. They seem to exhibit extremely complex behavior.
The problem arises in constructing robots which would exhibit behavior of
this kind.
In this section we will describe a general method for designing
robots with any specified behavioral properties whatsoever. They can be
designed to do any desired physically possible thing under any given cir
cumstances and past experience, and certainly any naturally given "robot,"
such as Smith or Jones, can do no more. Remember, of course, that we are
assuming, quite contrary to fact, that all the neurons we want are available,
that they are small enough, etc., and that we have enough mechanical dex
terity and enough time to assemble them.
We have examined robots with no memory at all; now let us go to
the other extreme and examine robots with complete memory, i.e., a completely
detailed memory, at any time t, of all their past receptor firings. Robots
with complete memory do not resemble any actual organisms or any constructed
hardware since these latter have incomplete (in the sense of selective)
memory — they store only those parts of their past experience which are
especially significant. Some appropriate definition of "significant" can
be given in each case.
The robot with complete memory, although it is uneconomical, seems
to be conceptually simpler than the robot with selective memory. We will
examine the robot with complete memory first and the selective memory robot
can be examined later as a modification of it. Hence, "memory" here means
"complete memory" as just explained. Also we will consider only determin
istic robots since it is clear how they could be made probabilistic.
SOME UNECONOMICAL ROBOTS
These complete robots are just extensions of memoryless robots
and their circuitry is essentially the same. It is merely that the receptor
cells together with a large hank of other cells constitute the storage cells,
and this necessitates a very large increase in the number of central cells
The complete robot may be constructed as shown in Figure 6 .
C)
HZ!
Ha
HZJ
2n t
FIGURE 6 . Complete Robot. Receptor cells r 1 , rg, . . . rm .
Storage cells enclosed by rectangle. Effector cells
V V • • • V
CULBERTSON
Connections Between The Storage Cells
The storage consists of T levels, the receptor cells constituting
level i . Each level contains n cells. Each cell in levels 1 to T - 1
has an excitatory bulb on the cell immediately above it; that is, the ith
cell in the kth level has one bulb on the ith cell in the (k+1 )st level.
There are no other connections between cells in the storage. The connections
between the storage cells and the cells c ^ c2, ... c nT will be described
later. 2
If the robot is constructed, then there will be some time t *
o
which is the first time that any of its receptors have fired. Prior to t
no receptors have fired, and at t one or more receptors fire. It will be
convenient to call t the time of birth of the robot.
Prom the simple connections described above, we see that impulses
move continually upward through the storage — if the ith receptor cell
fires, then the cell immediately above that one fires, etc., until finally
the ith cell in level T fires. It is clear that, however many receptors
fire at any time, each input, however complex, is preserved intact, so to
speak, as it moves upward through the storage and that at any time after
birth and prior to tQ + T there is in the storage a record of all inputs
from birth up to that time.
The robot begins to function at birth, tQ, and ceases to func
tion at tQ + T. We can arrange this by having each cell at level T
connected directly to a charge of dynamite so that when any cell at this
last level fires, then the total clrarge goes off immediately and the robot
is destroyed. The time, tQ + T, is the time of death of the robot, and
T is called the longevity of the robot.
Since in the present discussion we care nothing about neuroeconomy,
we can make T as great as we please. Suppose we constructed a robot so
that T = 2 .2 x 1012 which gives it a life time of about seventy years.
Then it would take about seventy years for the first, or birth, input to
move upward all the way to the lethal cells at the last level. The robot
would be destroyed T time units or about seventy years after its birth.
At any time during its life there would be a completely detailed record,
in the storage, of the robot*s total past experience.
The nT storage cells we will designate s ^ s2, ... sn T - The
subscripts may be assigned to them in any convenient fixed way.
nT
There are then 2 classes or sets of these storage cells. In
the usual way, already familiar to the reader, we may label these as follows:
SOME UNECONOMICAL ROBOTS
113
1st storage set
The null set
. . .0000
2nd
S 1
. . .0001
3rd
S 2
...0 0 1 0
4 th
s1+s2
...0 0 1 1
5 th
s 3
...0 1 0 0
6 th
S1+S3
...0 1 0 1
Tth
s2+s3
...0 1 1 0
Jth
2n^th " " All the storage cells ...1 1 1 1
nT
Note that all 2 storage sets are designated, not just those
corresponding to the rows or columns or anything of that kind.
nT
Corresponding to these 2 sets of storage cells we have the
nT
2 central cells c ^ c2, . .., Cj, . .., c nT shown in Figure 6 . Now
we can connect the storage cells to these central cells as follows.
Connections From The Storage To The Central Cells
Each storage cell in the Jth set has an excitatory bulb on the
Jth central cell, while each storage cell which is not in the Jth set has
an inhibitory bulb on the Jth central cell. Also we make the threshold on
any central cell equal to the number of excitatory bulbs contacting it.
Thus the Jth storage set fires the Jth central cell.
Consider any time t (tQ < t < tQ + T) in the life of the robot.
At t some set of storage cells is firing. Which set of storage cells is
firing is uniquely determined by the particular past experience of the
robot — that is, by just which receptors fired at each instant from tQ
to t. For each possible past history of receptor firings there is a dif
ferent set of storage cells. The actual past history up to any time t
determines which storage set fires at t. Which storage set fires at t
then determines which central cell fires at t + 1, as explained in the
above paragraph. Thus, which central cell fires at time t + 1 is uniquely
determined by the entire detailed past history of experience (receptor
firings) of the robot. For a different past history a different central
cell would fire. ‘This involves an impossible number of central cells and
endbulbs at each synapse, but we will remain calm even In the presence of
such unnaturally large numbers, since certain issues become clearer when
we do so.
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