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Dehumanizing Computer Science

© Karl Fant 2006

1

Dehumanizing Computer Science

Karl Fant

Mathematics is about what mathematicians do.They devise symbol systems and algo-

rithms to manipulate the symbols of the system.They then enliven a symbol system by manipu-

lating the symbols on paper according to the rules of the algorithm. Humans have always been

integral to the works of mathematics.

1.0. The humans in computer science

Computer science with its mathematical heritage retains these humans in the works.

From the computer science point of view these humans constitute an element of arbitrarily suffi-

cient expressivity which presents a difficulty. If one is only interested in the nature of the symbol

system independent of how it might be expressed then any workable expression of a symbol

system will suffice, and appeal to arbitrarily sufficient expressivity can be conveniently effective,

but if one is seeking insight into the nature of expression itself, the presence of arbitrarily suffi-

cient expressivity fundamentally undermines the effort.

If there is an arbitrarily sufficient interstitial mortar then the conceptual pieces do not

have to fit well. Any pieces can be glued together into an apparently universal whole that is ade-

quately functional and that can even appear to be simple in some compelling sense. But such a

fudged model cannot provide insightful understanding or unifying connections.The element of

arbitrary sufficiency eliminates the necessity of the pieces fitting and precludes the possibility of

discovering the appropriate pieces and how they might fit. Appeal to arbitrary sufficiency can

reveal nothing about essential necessity. A useful conceptual view can have no arbitrarily suffi-

cient mortar.

Saying a human does it in computer science is like saying a god does it in physics.The

humans in the works both enable the computer and deny it theoretical closure.This difficulty of

humans in the works is explicitly recognized in the view of the computer as an artifact and the

acceptance that computers cannot be theorized about in the same sense that natural phenom-

ena can be theorized about [2].

“If what the computer scientist says about computers in theory does not agree with

behavior, he or she can always change the computer” to match the theory [1].

This is the essential problem.There is no way to compare conceptual models.The

human in the works assures that all models, even those with partially characterizing or mislead-

ing concepts, will appear equally successful.There is no criterion of failure. With the inability to

theorize the only approach to understanding the subject appears to be experience and experi-

ment and the only approach to managing it to be imposed rationale and convention. Imposing

mathematical rationale and convention seems reasonable and convenient.

But are computers and symbol systems as artifactual as supposed? Symbolic computing

mechanisms exist in nature, particularly in biology, that computer science aspires to encom-

pass. Can a conceptual model of symbolic expression can be conceived that encompasses the

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© Karl Fant 2006

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symbol systems both of nature and of man. A conceptual model that encompasses natures

symbol systems cannot have humans in the works.

2.0. Eliminating the Humans

It was eventually realized that a symbol system could be enlivened as a spontaneously

behaving mechanism eliminating the enlivening human from the works.The development of

computer science to date is all about substituting the enliveining human in the works with a

spontaneously behaving mechanism: the computer. But there are still humans involved in the

conception of the symbol system and in the design of the mechanism.These humans are

somewhat more difficult to remove.

2.1. The designing human

The difficulty with removing the next human is that the enlivening human provided some-

thing more than just the enlivenment of the symbolic expressions. She provided a coordination

behavior that the symbolic expressions do not express. Simply enlivening the symbolic expres-

sions in a spontaneously behaving mechanism is not sufficient.The missing coordination

behavior must be explicitly added to the spontaneously behaving mechanism.This enhancing

of the enlivening mechanism must be done by a human designer.The difficulty is illustrated with

a Boolean expression of a full adder expressed in terms of two half adders shown in Figure 1.

The Boolean logic expression is enlivened (mapped to a spontaneously behaving

expression) by enlivening the logic functions to continuously behave and by enlivening the sym-

bols to continuously flow from function to function. When a new input state is presented to the

inputs of the Boolean combinational expression, a stable wavefront of correct result values

flows from the input through the network of logic operators to the output. But since Boolean

functions are continuously responsive and since some functions and signal paths can be faster

than others, invalid and indeterminate result values may speed ahead of the stable wavefront of

valid results.This rushing wavefront of indeterminacy, may cause the output of the Boolean

expression to transition through a large number of incorrect values before the stable wavefront

of correct result values reaches the output and the expression as a whole stabilizes to the cor-

rect resolution of the presented input.The behavior of the enlivened symbolic expression is

ambiguous. It is not determined.

This indeterminacy does not occur with the enlivening human with a pencil.The human

can determine when all the input symbols are available for each function and resolve each func-

tion in its proper turn.The resolution of the expression flows to completion with no ambiguity of

Figure 1: Boolean full-adder

S

CO

CI

X

Y

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© Karl Fant 2006

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behavior. It is this coordination of resolution behavior that is not expressed in the symbolic

expressions and which must be explicitly added to the enlivening mechanism.

An enlivened Boolean logic combinational expression can be relied on to eventually sta-

bilize to a correct result state but there is no way to determine, solely in terms of the behavior of

the symbolic expression itself, when this stabilization occurs. After presentation of a new

instance of input state to a Boolean expression it is necessary and sufficient to wait an appropri-

ate time interval, characterized by the slowest propagation path through the expression, to

insure that the wavefront of stable result values has propagated through the expression and that

the output of the expression has stabilized to the correct resolution of the presented input data.

During the time interval all of the erroneous output transitions due to the racing ahead values

can be ignored and at the end of the interval the correct result can be sampled. A time interval,

however, is a non-logical expression which must be associated with and coordinated with every

Boolean combinational logic expression and which is specific to each implementation of a logic

expression.

Even though the expression with its time interval behaves autonomously and correctly,

the original symbolic expression was not sufficiently expressive to map directly to a correctly

behaving enlivened expression. It required the additional expression of a time interval and the

coordination of the time interval with the logic expression. Since the time interval is implementa-

tion specific, there is no way that this mapping to an enlivened expression can be accomplished

without the participation of a designing human.

The arbitrarily expressive human in the works contrives to make the insufficiently expres-

sive Boolean expressions work. If the human is not present to facilitate functionality a criterion

of conceptual failure emerges. Since a Boolean logic expression cannot behave correctly on its

own without the assistance of a human it must be considered a conceptual failure.This circum-

stance can be viewed in two ways. One can assign theoretical primacy to Boolean logic anyway

and regard this circumstance as showing that humans are necessary and cannot be eliminated

from the works of symbolic expressions. Or one can search for a model that does work on its

own symbolic terms without human assistance.

3.0. Another Form of Symbolic Expression

The Boolean logic expression of the full-adder can be symbolically expressed in a differ-

ent way with profoundly different consequences.The Boolean logic expression uses two unique

symbols, 0 and 1, and unique places within the expression to represent different meanings

within the expression. Each unique meaning is expressed as a combination of symbol and

place.The 0 or 1 on this wire is different from the 0 or 1 on that wire.These unique meanings of

the Boolean logic expression can be mapped into a quite different form of expression.

Imagine that there are a multitude of unique symbols available such that each unique

meaning can be represented by a unique symbol. Such a mapping of unique symbols to mean-

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ings is shown in relation to the Boolean circuit in Figure 2. Two unique symbols for each wire in

the circuit represent the 0 value and the 1 value for that wire.

C means X = 0

D means X = 1

E means Y = 0

F means Y = 1 and so on for each wire in the circuit.

Next, imagine a set of rules that express how the symbols interact and transform into

other symbols such as the set of rules below. GI[S] means the combination of symbols G and I

transform into the symbol S.These rules are derived from the functionality of each gate in the

Boolean expression and the symbols associated with the gate.

“fan-out input symbols”

A[g,k,o] B[h,l,p] C[G,K,O] D[H,L,P] E[I,M,Q] F[J,N,R]

“define combinational resolution stages”

GI[S] GJ[T] HI[S] HJ[S]

KM[U] KN[U] LM[V] LN[U]

OQ[W] OR[W] PQ[W] PR[X]

“fan out input to second half-adder”

SU[a,c,e] SV[b,d,f] TU[b,d,f] TV[b,d,f]

ga[i] gb[j] ha[i] hb[i]

kc[m] kd[m] lc[n] ld[m]

oe[q] of[q] pe[q] pf[r]

im[s] in[t] jm[t] jn[t] “sum”

qW[u] qX[v] rW[v] rX[v] “carry out”

Next, imagine that the expression is directly enlivened by enlivening the symbols with

behavior that expresses their interaction rules. Symbol G knows it can interact with symbols I

and J and with no other symbols. Symbol I knows it can interact with symbols G and H and no

other symbols. G and I know when they encounter each other to spontaneously transform into S

effecting the rule GI[S]. If the symbols are in a shaking bag, all possible combinations of sym-

bols will occur and all interactable combinations will interact.The expression resolves progres-

sively and unambiguously through the spontaneous behavior of the individual symbols. Input

symbols thrown into the shaking bag will associate, transform and resolve the expression. Fig-

Figure 2: Boolean full-adder mapped to a rich symbol expression.

S

CO

CI

X

Y

A,B

C,D

E,F

G,H

I,J

K,L

M,N

O,P

Q,R

S,T

U,V

W,X

g,h

a,b

k,l

c,d

o,p

e,f

i,j

m,n

q,r

s,t

u,v

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ure 3 shows the progression of resolution for input symbols B, C and F.The combinations of

symbols involved at each stage interaction are circled and the rules involved are shown above

the symbols.

Every symbol is unique and every combination of interacting symbols is unique.There is

no ambiguity of behavior at any stage of resolution of the expression.The coordination of the

symbol resolution flow is embodied in the symbolic expressions. When the expression are

directly enlivened, the behavior of the enlivened expression is completely and unambiguously

determined by the symbols and their interaction rules.There are no race ahead wavefronts of

incorrect symbols.There is only the orderly propagation of the wavefront of correct result sym-

bols. When an s or t and a u or v appear they express the correct completion of resolution.

There is no need to “engineer” the enlivened expression to make it work. It works correctly

solely in terms of the symbolic expression.

The new symbolic expression is a symbolic expression in the same sense that the Bool-

ean logic expression is a symbolic expression.There is a population of symbols with a set of

symbol interaction rules.There is a direct mapping between the Boolean symbolic expression

and the new symbolic expression.The new symbolic expression, however, works correctly on its

own symbolic merits and the Boolean symbolic expression does not

It is possible to render spontaneously behaving mechanisms purely in terms of symbolic

expressivity.The designing human is no longer needed in the works.

3.1. Humanless symbol systems

There is still the human in the works that conceived the Boolean expression. We are

used to thinking of the conception of a symbolic expression as a carefully coordinated interplay

between specifying a symbol system and specifying the symbol interaction rules, but if the

resources of expression are profligate, they are spontaneously active and they are contained in

a common place of interaction, then a large variety of symbolic expressions must spontane-

ously arise and resolve.The entire realm of the laws of physics and chemistry provide an enor-

mous domain of interaction rules for particle, atomic and molecular symbols.There are, for

instance, 10

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possible protein symbols. Spontaneous symbol interactions in the thermally agi-

tated soup contained by the gravity well of a young earth stumbled upon and ignited the expres-

sion of a sustainable chain reaction that drifting through an immense possibility space for

billions of years continues to smoulder and begins to contemplate itself. No human expressivity

was required.The conceiving human finally becomes unnecessary and the last human is

removed from the works.

Figure 3: Resolution progression for pure symbol expression of full-adder.

B

C

F

G

J

K

N

O

R

b

d

f

h

l

m

p

r

s

v

input

T

U

W

h

l

p

TU[b,d,f]

W

h

l

p

W

i

pf[r]

hb[i]

ld[m]

im[s]

rW[v]

OR[W]

GJ[T]

KN[U]

B[h,l,p]

C[G,K,O]

F[J,N,R]

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4.0. Summary

While humans can still muck around in the works as they please, they are no longer con-

ceptually integral to the works.Transcending its mathematical heritage without abandoning it,

dehumanized computer science is essential to understanding the nature of symbolic expression

and to encompassing the natural phenomena of symbolic computation as well as the expres-

sions of human computation in the same way that the science of aeronautics encompassing the

airplane’s wing and the bird’s wing.The science of symbolic computation is not as artifactual as

supposed.

References

1. Ceruzzi, Paul “Electronics Technology and Computer Science, 1940-1975: A Coevolution”, Annals

of the History of Computing, Vol. 10, No 4 1989, pp. 257-275, quote on p 267.

2. Newel,A., Perlis, A., Simon, H. Letter to the Editor of Science 157 (22 Sept.), 1967, pp.1373-1374.