4
Do Algorithms Have Fun? On Completion,
Indeterminacy and Autonomy in Computation
Luciana Parisi and M. Beatrice Fazi
Algorithms, not androids
In 1968 Philip K. Dick wondered whether androids, which at the time epitomized the ultimate mechanization of mental processes, could dream of electric
sheep.1 Dick’s provocative suggestion was meant to address the prospect that
mechanized thought could develop a human unconscious, and thus become
truly autonomous. In Dick’s novel, dreaming stands as the ultimate expression
of the human capacity to think beyond logical processing, without the functions
of cognitive reflection or recognition. It could be argued that, in Dick’s story, a
mechanized being that is able to dream realizes the promise of total autonomy
from instructions and pre-programmed finalities. A dreaming android never
becomes a human subject, but is nonetheless as close to the human emotional
dimension of thinking as it could ever be.
Today, nearly 50 years after Dick’s proposition, it is similarly possible to
wonder whether algorithms – which are now the quintessence of mechanized
thought – could exhibit a dimension of autonomous thinking. While androids
had a body but were looking for a soul, in the present day mechanized thought
is instantiated in computational processes that are themselves already material
and incarnated, insofar as they are always performed and embedded in society,
culture and the economy. To be autonomous, these computational systems
do not need to simulate the more or less conscious requirements of a ‘psyche’,
insofar as they already have a ‘point of view’ (or a sort of subjective dimension,
so to speak) that is expressed through their material agency. Within the current
configuration of digital technology, it could then be claimed that the mechanization of thought carried out by algorithms has approached the ultimate goal
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of total automation by incorporating thinking as material performativity, thus
showing an immediate tendency to break free from the human master that has
nonetheless programmed them.
Following on these considerations, one could contend that, in computational science and in computational culture alike, the final goal for automated
thought is no longer to escape the pre-programmed algorithmic rule and
thus to revert into a sort of computational unconscious. Instead, automated
thought is epitomized in a new vision of the algorithmic rule itself. Now this
rule is always executed, and in this execution it can adjust itself to external
changing conditions. To sum up, most algorithms have become interactive,
and the mechanization of thought has to be accounted for vis-à-vis the now
dominant expansion of such interactive approaches to computing. It is in this
respect, one could argue, that today the quest for the autonomy of mechanized thought involves the prospect of mechanized systems changing their
own pre-programmed regulations. This interactive vision of software has
importantly questioned the self-sufficiency of axiomatics, logic and formalism,
and has tried to complement the formal rule with the environmental input.
Consequently, in the cultural analysis of these new modes of mechanization
of thought, interactive software has been seen as operating affectively; that
is, through the expansion of the field of potential activities that disrupt
and re-invent meaning.2 Here, digital technology becomes the ground for
creativity and for the production of paradoxical propositions that do not aim
to reproduce a pre-constituted intelligence, established by a representational
conception of thought. Rather, paradoxes and ambiguities strive to expose
the sensible dimension of thought against the dominance of computational
understandings of cognition.3 From this perspective, freeing the computational
unconscious becomes secondary to the possibility of producing, in computation, sense beyond formal logic.4
It is exactly within this context, we believe, that the question of fun in
software has acquired a significant momentum. Fun in computing emerges as
an affective force that exceeds the formal logic that has nonetheless generated it;
fun thus coincides with the disruption, caused by uncertainty, of the decisional
power of algorithms operating within changing data structures. We may thus
agree that the strength of this proposition is that it offers a radical account of
the exceptional condition of instability and malleability of the computational
rule – a condition that is vital to the creative drives of programming cultures. To
a certain extent, the present chapter builds upon the rich debates that have put
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forward this proposition, and at the same time it aims to push this new view of
computation in another direction.
The question that we propose – ‘Do algorithms have fun?’ – is meant to echo
the hypothesis posed by the title of Dick’s novel, Do Androids Dream of Electric
Sheep? Like Dick’s provocation, our own hypothesis may also sound absurd;
yet such an absurd proposition may nonetheless provide an opportunity to
investigate another scenario regarding the significance of fun in software. To
put it in other words, our proposition still aims to question computation, logic
and formalism as representational approaches to thought. However, in order to
do so, it is necessary for us to revisit the possibility that autonomy in computation might not be geared uniquely towards the liberation of the algorithmic
procedure from the program or the master programmer. The question, we
contend, is less whether a procedure might become free from mechanization,
but whether mechanization itself already comes with a form of autonomy,
insofar as it can be defined as a series of procedures aiming towards completion.
As will become clear further below in the chapter, the notion of completion is
used to define the process by which a final determination is achieved.
Algorithmic autonomy for us is not about a machine sharing or opposing
the human spectrum of cognition and perception in which the possibility
of having fun is traditionally inscribed. On the contrary, the question, ‘Do
algorithms have fun?’, is predicated upon a speculative move suggesting that
fun corresponds to the capacity of algorithms to enjoy themselves while processing
data. Enjoyment here is, in turn, mainly defined in terms of the final purpose
of the computational process, which is to say, by its functionalist imperative
to complete a task. In a counter-intuitive twist of the debate, we therefore take
fun not to be the subversion of a rule, or the break from the constriction of a
cold and strict procedure, rather we suggest that fun requires an end activity
on behalf of the rule itself. Rather than escaping the rule, fun thus points to a
new understanding of algorithmic order: one that complies with the question
of the fulfilment of procedures, or achievement of a result, in computation.
Fun in software is for us neither posthuman (there is no an alleged equivalence
between human and machine), nor inhuman (there is no opposition between
the two). Fun here deploys another level of mechanized processing altogether
– a level that is not exclusively preoccupied with human–machine relations or
the lack thereof. In this procedural order, relations are secondary to the finality
of the rule’s function. Fun, we contend, is the final achievement of autonomy in
mechanical thought.
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Forms of process
The questions raised in this chapter are directed towards the speculative
re-conceptualization of computational algorithms in terms of actualities,
expressed as forms of process. We take the latter notion from the mathematician
and philosopher Alfred N. Whitehead, who uses it to define the actual organization of data in the world.5 In our opinion, this Whiteheadian concept is key to
the possibility of re-thinking what processes (and, therefore, also computational
processes such as algorithms) are. Following the Whiteheadian view, processes
can in fact be re-thought not as a continuous movement of variation, but instead
in terms of the final achievement of a finite state.
Whitehead employs the notion of ‘form of process’ to explain the ‘final
mode of unity in virtue of which there exists stability of aim amid the multiple
forms of potentiality, and in virtue of which there exists importance beyond the
finite importance for the finite actuality’.6 In this respect, Whitehead’s ‘form of
process’ needs to be investigated vis-à-vis a key element in the Whiteheadian
philosophy: actual occasions. An actual occasion is actual not merely because
it is something that is present here in front of us and impresses us (as Hume
would have held actuality to be). In Whitehead, actuality is instead a process
of concrescence, or ‘a process in which the universe of many things acquires an
individual unity’.7 This is, for Whitehead, a process of satisfaction, or of selfenjoyment. In actual occasions, data are organized and unified; when this unity
is achieved, the actual occasion is ‘satisfied’ because it has fulfilled its scope by
becoming complete.
It is our contention that Whitehead’s philosophy of actuality can contribute
to questioning the antagonism between, on the one hand, the conception of
process (intended as the continuity of variation, forming a whole that is bigger
than its parts) and, on the other, the notion of processing (intended instead
as a self-contained procedure based on already determined and finite parts
aggregating into a whole). In Whitehead’s oeuvre, these two concepts are not
opposed; it could be said, in fact, that both process and processing contribute
to the determination of the actual occasion. We thus wish to appropriate
Whitehead’s philosophy of actuality to go beyond this opposition which seems
to pervade the critical debates about computational culture.8 To this end, we
suggest that algorithms can be conceived as discrete actual entities, whose aim
is to achieve unity. This achievement can be defined, again in Whiteheadian
terms, as satisfaction (which is, in Whitehead’s words, ‘the completion of the
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actual togetherness of the discrete components’)9 or, from the perspective of
this chapter, fun. On the one hand, an algorithm is a procedure that performs
a processing, involving the execution of a sequential number of steps that
organize data towards a result. This processing, however, does not simply lead
to the aggregation of parts into a whole, but rather corresponds to the creation
of a new unity that is added upon (and yet is not contained by) the aggregation
of parts. Enjoyment, in this respect, involves the processing of data towards a
final aim (this aim being the completion of the procedure). On the other hand,
however, we want to stress that an algorithm is also a process, inasmuch as it
involves an indeterminate capacity for variation. Yet, what should be emphasized here is that this variation is not the result of continuous change, but it is
the final product of the process of determination carried out by the algorithmic
procedure itself. This process of determination defines an algorithm that attains
its completion by realizing its function. Satisfaction, from this perspective, is the
exhaustion of the algorithmic function in the process. In computational culture,
to sum up, we find evidence that process and processing are defined less by their
differences than by a common finality, and that fun (re-worked speculatively via
the Whiteheadian notions of enjoyment and satisfaction) might be an instance
of such a finality.
To carry out such re-articulation of algorithms in terms of forms of process
– or, it is worth repeating here, in terms of discrete entities achieving satisfaction through the unification of data – we need to linger a little longer on
the proposed parallel between algorithms and actual occasions. As already
mentioned, Whitehead’s philosophy of actualities is useful for our investigation
of algorithmic computation precisely because his approach is based on an
atomistic conception of the universe that might counterintuitively help us to
revise the conceptualization of digital procedures. Moreover, it can also help
us to re-think what the unity of discrete entities might be from the standpoint
of a process of determination. Instead of describing finite entities as already
constituted unities, Whitehead argues that actual occasions are the result of
a tendency of the multiple to become united. The accomplishment of unity
marks for Whitehead the end point of an actual occasion. In this respect, actual
occasions are finite and determined, also because they are short-lived. Once
they reach unity, their process ends and they perish. One can also add here that
completion is the finality of an actual occasion, insofar as its process of unification is its ultimate goal. The atomicity of an actual occasion corresponds to
its finality: discreteness is not given, but produced from within the process. An
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actual occasion, therefore, does not come from nowhere. It inherits data from
past actualities and is characterized by the tendency to eventually terminate
just such a process of selection that ultimately constitutes it as one. Data, in
turn, do not correspond to what already exists. For Whitehead, data are transmitted from the past to the present in a manner that is not simply re-used, but
re-processed by the actual occasions under new conditions.
It is important here to stress that for Whitehead this principle of inheritance cannot explain, on its own, the ‘becoming one’ of the actual occasion.
Whitehead’s metaphysical proposition instead gives a major role to what he
calls eternal objects. These are a priori yet immanent ideas, which according to
Whitehead can be described ‘only in terms of [their] potentiality for “ingression”
into the becoming of actual entities’.10 In this sense, an eternal object is pure
potentiality from the standpoint of the actualities that select them. Eternal
objects, then, cannot be described in terms of one potential plane of continual
differentiation (for instance Deleuze and Guattari’s plane of immanence and/
or the virtual) or in terms of a plurality of equivalent ideas (such as the
postmodern claim about the relativity of truth). Rather, this other element in
Whitehead’s metaphysics offers us a notion of indeterminacy. Eternal objects are
in fact non-connected among themselves, and only acquire togetherness when
selected by actual occasions. In this togetherness, they concretize indeterminacy
by allowing the actual occasion to achieve finality. Eternal objects are maximally
unknowable, but nonetheless they inform the determinate state or the atomism
of actual occasions.
At this point we should add that both eternal objects and existing actual
data are not passively received but are instead prehended by the actual occasion.
Contra the empiricist perceptual capacity to synthesize the world through
sense impressions, Whitehead argues that prehensions are modes of evaluation
and selection, measuring and dividing an infinite variety of data each time.
Instead of being just sensations, prehensions, for Whitehead, are both physical
and conceptual. This is because each actual occasion ‘is essentially bipolar’;11 in
other words it has a physical and mental pole, expressing the actual occasion’s
capacity to physically and conceptually process data. The physically prehensive
nature of an actual occasion means that actual occasions themselves are always
informed by what is no longer there, by the data of the past actual occasions
that are accumulated and crystallized in any present actuality. Moreover, as we
have just discussed, actual occasions are also informed by what is not there at
all: the unknown or indeterminate ideas or eternal objects. The prehensions of
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eternal objects are, for Whitehead, conceptual prehensions. As we saw earlier,
eternal objects define the direction towards the determinateness of the actual
occasion, its final unity and discreteness. Here again we find the processual
nature of actual occasions, in which the indeterminacy of eternal objects adds
a new level of determination to the data selected. A process becomes, however,
a processing to the extent that data are compressed and arranged in a finite
procedure, oriented by the actual occasion to drive towards its own satisfaction.
In conclusion, prehensions, we could argue, are the catalysts for the concretization of the indeterminacy of the eternal object. More interestingly, however,
they also reveal the persistent concreteness of indeterminacy itself in actuality.
Completion and indeterminacy in algorithmic processing
Having introduced these key elements and conceptual manoeuvres of
Whitehead’s philosophy, we can now return to this chapter’s initial contention:
the possibility of re-conceiving algorithms in terms of Whitehead’s actual
occasions by drawing on his notion of ‘form of process’. In our view, to claim
that an algorithm is an actual occasion implies arguing that the computational procedure is more than simply processing; i.e. more than a procedure
based on pre-established instructions. In this respect, we want to argue that
an algorithmic procedure cannot be thought of away from the indeterminacy
that it is always tending towards. This passage is complicated, and to develop
it we need first to explain what an algorithm in computation is, and what it is
supposed to do.
In formal sciences, an algorithm is described as a sequence of instructions
meant to fulfil a task. An algorithm is a procedural method for the transformation of input into output; its instructions are well defined and executed
through a finite number of inferential steps. This is the understanding of the
algorithm that entered computing via the seminal work of mathematician Alan
Turing. In his famous paper ‘On Computable Numbers, with an Application to
the Entscheidungsproblem’ (1936)249 Turing sets out to answer David Hilbert’s
question of whether, given a certain input, a universal method for taking a
yes-no decision could be ultimately found in mathematics. In that paper, Turing
rephrased the problem of decidability from the standpoint of computability. The
notion of computability, in turn, was defined by Turing in terms of an effective
procedure (i.e. an algorithm) to solve a problem in a finite number of sequential
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steps. In his attempt to answer Hilbert’s challenge, Turing developed a simple
thought experiment (the Turing Machine) that was meant to mechanize a valid
and determinate method for calculation. This hypothetical device performs
computations by moving its head left and right along an infinite tape, that is
in turn divided into discrete cells; the head moves one cell at a time, writing a
symbol from a finite alphabet for each cell according to some given instructions.
By proving that certain functions could not be computed by such a hypothetical
machine, Turing demonstrated that there is not a method of ultimate decision
of the kind that Hilbert had wished for. In addition to this, however, the
Turing Machine also offered a viable formalization of a mechanical procedure.
Computational processing, as we know it today, was born.
The strength of Turing’s proposition is that, via his formalization of the
Turing Machine, the function of computation came to be defined as being
much more than just that of crunching numbers. Turing’s computing machines
– and indeed the contemporary electronic digital computing machine that has
developed from them – can solve problems, take decisions and fulfil tasks,
with the only proviso that these problems, decisions and tasks are formalized
through symbols and a set of discrete and finite sequential steps. In this respect,
Turing’s effort can be rightfully inscribed into a long series of attempts in
the history of thought geared towards the mechanization of reason. Turing’s
foundational work in the theory of computability, and his conception of a
computing machine, were meant to put the intuitive and informal operations
of a person actually computing a number into formal terms. Mechanization
implied that these formal terms could be automatically repeated because they
were inscribed as symbols and discretized as a sequence of steps.
At the technical level, we could argue that the Turing Machine epitomizes
a mechanism that works insofar as it completes an operation. Moving now to
the conceptual level, we can understand this operativity as one tending towards
unity. An algorithmic procedure can in fact be seen as an aggregation of parts;
when these parts achieve unity (that is, when the task is fulfilled), the mechanical
process shuts down and then another procedure starts over again. Here one
could object that, in light of what we have just described, the parallelism between
an algorithm and an actual occasion becomes a difficult claim to sustain. It
could in fact be argued that the Whiteheadian actual occasion does not merely
aggregate into a bigger whole; rather, its parts are realized to become another
part that is a new unity. In other words, in an actual occasion parts transform
themselves in relation to a whole. However, the actual occasion remains,
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atomic: its parts never complete the universe of possibilities of what the actual
occasion could be, or will be. An actual occasion is always a spatio-temporal
relation between elements in process; it is indeed an occasion, its own eventuality determines its own prehensions, and, consequently, its own constitution.
Continuing the objection, it could be also claimed that, in Turing’s formulation,
an algorithm, conversely, has to do with pre-established functions (indeed, with
axioms). In a Turing Machine, everything is pre-set, pre-programmed – in total
indifference to content and context. From this standpoint, a Turing Machine
merely performs processing: a linear procedure of cause and effect where one
step inferentially determines the other. The objection according to which the
parallelism between an algorithm and an actual occasion is flawed would thus
seem to be justified: while an actual occasion is dynamic, an algorithm is not.
Having identified these difficulties, might it still be possible to advance our
intended parallel between algorithms and actual occasions? Our answer is yes.
The parallel between algorithms and actual occasions is still valid by virtue of
an inherent and unavoidable character of computation itself: incomputability.
With his 1936 paper, Turing formalized the notion of computability; however,
what is most striking about that proposition is that the formal foundations
of this notion were laid on the logical discovery that some things cannot be
computed. In 1931, Kurt Gödel proved the fundamental incompleteness of
formal axiomatic systems.12 In 1936, Turing built on Gödel’s discovery to
demonstrate that computation, in its mechanized formalization, is also intrinsically limited, and that these limitations are due to the formal axiomatic nature
of computational mechanisms. Algorithms drive towards completion; this is
of course evident at the level of their execution, but it can also be suggested
that, at the formal level, completion is always entailed within the finality of the
procedure. However, in his logico-mathematical formulation of computability,
Turing foresaw that, despite the incredible versatility and efficiency of his
proposed calculating machines, there are problems that cannot be solved, tasks
that cannot be fulfilled and decisions that cannot be taken through them. These
are incomputable problems for which there is no algorithmic decision. A Turing
Machine can compute anything that can be calculated via algorithmic means.
If something cannot be computed, then nor can it be put in algorithmic terms.
For some functions, there is not a yes-no (or binary) answer. In this respect,
completion in computation cannot always be attained.
After this brief but crucial overview of the logico-mathematical origin of
computation, the significance of the proposed parallel between algorithms and
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actual occasions might perhaps become more evident, and we can thus begin
to justify our understanding of computational procedures in terms of forms
of process. We want to argue that, while the unknown dimension of the actual
occasion is the eternal object, unknowability in computation is expressed through
the notion of the incomputable. We are thus here contending that the incomputable
is to the algorithm what the eternal object is to the actual occasion. It is true to say
that the algorithmic procedure is pre-established; it is undeniably a processing of
data. However, this processing is an actuality that also has to confront the indeterminacy of the incomputable in the same way as the actual occasion is a finite
spatio-temporality whose determination results from a process of prehension of
the indeterminacy of eternal objects. In other words, eternal objects are ingredients
in the constitution of actual occasions, and thus their indeterminacy becomes one
with the finite atomistic nature of the universe. Similarly, the unknown condition
of an algorithmic occasion is an incomputable condition, which serves the
algorithmic actual occasion to speculatively become more than it was.
The work of mathematician Gregory Chaitin can now be introduced to
further expand on the contention that the incomputable is the eternal object
in computational processing. In his algorithmic information theory, Chaitin
combines Turing’s computability with Shannon’s information theory to
understand computational processing in terms of calculation of probabilities
– probabilities that aim to include what in this processing cannot be known
in advance. Chaitin understands the threshold of computability from the
standpoint of maximally unknowable probabilities.13 In every computational
process, he explains, the output is always bigger than the input. For Chaitin,
something happens in the computational processing of data, something that
challenges the equivalence between input and output and thus the very idea that
processing always leads to an already pre-programmed result. This something,
according to Chaitin, is algorithmic randomness. The notion of algorithmic
randomness implies that information cannot be compressed into a smaller
program, insofar as an entropic transformation of data occurs between the
input and the output of algorithmic processing, resulting in a tendency of these
data to increase in size. From this standpoint, the output of the processing does
not correspond to the input instructions; its volume tends, in fact, to become
bigger than it was at the start of the computation. Chaitin has explained the
discovery of algorithmic randomness in computational processing in terms of
the incomputable: increasing yet unknown quantities of data that characterize
information processing.
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Space constraints prevent us from expanding further on Chaitin’s work;
the brief overview above should, however, suffice to sustain the claim that his
work is indeed useful to us, inasmuch as it can contribute towards explaining
what we mean by the ‘form of process’ in computation. Chaitin’s investigation
of the incomputable reveals, in fact, that the linear order of sequential procedures (namely, what constitutes computational processing) shows an entropic
tendency to add more parts to the existing aggregation of instructions established at the input. Since now this processing inevitably includes, from the
perspective proposed by Chaitin, not only a transformation of existing data, but
also the addition of new data on top of what was already pre-established in the
computational procedure, we believe it becomes possible to argue for a form of
process in computation. In other words, here processing is also a process. From
this point of view, computational processing does not guarantee the return
to initial conditions, and does not simply correspond to the aggregation or
disaggregation of parts that can be pre-programmed. This is because Chaitin’s
conception of incomputability no longer perfectly matches with the notion of
the limit in computation (i.e. the limit to what is calculable). Chaitin’s incomputable involves, in fact, the addition of new and maximally unknowable parts
to the whole; parts, however, that might be bigger than the aggregate whole.
For us, such a reworking of the incomputable is striking and speculatively
productive, because what was conceived to be the external limit of computation (i.e. the incomputable) has now become internalized in the sequential
arrangement of algorithms (randomness works within algorithmic procedures).
One can thus even suggest that algorithmic randomness is not ‘outside’, but has
become constitutive of the actuality of the procedure. Processing then includes
a form of process, because indeterminacy is a fundamental part of information.
But if the incomputable involves parts that can be bigger than a whole, how
do we explain the completion or the achievement of a task of an algorithmic
procedure? Isn’t algorithmic randomness (i.e. the tendency of information to
increase in size) always there to threaten any achievement of a function to
complete a task? This is where, by Chaitin’s own admission, it is necessary to
see algorithmic randomness as a continuation of Turing’s attempt to account
for indeterminacy. Whereas for Turing some tasks cannot be achieved, and
thus computation stops when the incomputable begins, for Chaitin, all tasks
have a margin of incomputability. In Chaitin, incomputability does not break
from completion. A closer investigation of his theories helps to reveal that
algorithmic randomness has changed the nature of computational processing:
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completion has been expanded beyond its limits to involve the processing of
maximally unknown parts in order to accomplish a task. To put it in other
terms, completion is now demarcated by an indeterminate condition that
subtends all efforts equating computational processing with the calculation
of pre-programmed and already known outputs. In Chaitin, the finality of
completing a task importantly requires that instructions respond and resolve
unknowns each time the indeterminacy of data emerges in processing.
Interactive procedures
At this stage in our discussion, it may not be too difficult to justify the
question of indeterminacy as being a speculative problem within computational processing itself, and thus point to the existence of a ‘philosophy of the
algorithm’ that should attempt such speculations. We started our own speculative investigation by proposing a parallelism between Whitehead’s notion of
actual occasions and the computational notion of completion. Having discussed
incomputability via Turing and Chaitin, it became possible to think that the
algorithmic completion of a task cannot be achieved without the participation
of indeterminate quantities of data within processing. In particular, we have
sought to develop Chaitin’s mathematical work on algorithmic randomness
to prove that indeterminacy is always part and parcel of a determinate actual
occasion/algorithm as it strives towards completion. From this perspective, we
believe that completion in computation corresponds to unity, and unity is, in
turn, a terminal point that can be reached only if indeterminacy ingresses the
processing of data and makes the algorithmic procedure both a process and a
processing. In other words, the ‘terminus’ of an algorithm can be approached
only if the incomputable partakes in its procedure.
Recapitulating, we can think of the incomputable as the indeterminacy that
is necessary for completion, or for the unity of a form of process. However, our
revisiting of computation through the problems of completion and indeterminacy cannot be fully grasped without discussing the dominance of a new
paradigm within computing: the interactive paradigm.
Arguably, interaction has become an all-encompassing principle of explanation in contemporary technoscience. Fields of enquiry such as biology,
social theory, neuroscience and robotics have all pushed forward an alternative
understanding of thought – understandings that see the latter as always already
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environmentally ‘situated’. Interaction is, in this respect, the interactive behaviour
of multiple distributed agents. In computing, prediction and simulation now
have to account for situations that are outside the confines of the black box and
are instead always embedded into and dependent upon the environment. This
interactive approach has clashed with the algorithmic constraints of the Turing
Machine. Turing’s model of computation has been considered insufficient or
unable to cope with the complexity of the empirical world – a complexity that,
one could say, philosophically speaking, has its own non-representational logic.
In this respect, efforts have been advanced in computer science to revisit Turing’s
algorithmic modelling.14 While Turing’s conceptualization of mechanism based
on a priori instructions can arguably be said to correspond to first-order cybernetics (due to its closed system of feedback), the combination of environmental
inputs and a posteriori instructions proposed by the interactive paradigm more
clearly embraces second-order cybernetics and its open-feedback mechanisms.
Returning to our investigation of computational completion, we can claim
that what we defined earlier as the algorithmic drive towards completion has
perhaps changed now. In particular, we want to stress that if interaction is
more powerful than algorithms,15 it is because indeterminacy, from the point
of view of interaction, might now imply and represent something else. The
volatility and malleability of lived situations are no longer obstacles for mechanisms of prediction. The goal of interaction is indeed to account for variation
and novelty, and to enlarge the horizon of calculation to include qualitative
factors as external variables of the mechanism. We want, thus, to suggest that,
according to an ‘interactivist’ approach, the problem of the incomputable might
be partly eluded. This is because completeness is no longer a solipsistic affair;
rather, completeness becomes a prospect that is achievable only by virtue of
the contribution of the outside world. In this sense, the algorithmic procedure
might be incomplete per se. However, it reaches completeness by virtue of its
interactive execution. From the standpoint of interaction, then, the successful
running of an algorithm is a performance in the environment (i.e. computation
is embedded in the world) and of the environment (i.e. computation needs the
world and the data extracted from it to fulfil the algorithmic task).
In our opinion, various approaches to interactive computing share a common
goal of pointing towards a new mode of mechanization of a procedure, in which
the starting condition of the program does not dictate the procedure’s final
output. We can see this mode everywhere, from the imperative of participation
in artworks, to social media strategies for user input geared to data-mining via
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neuro-cognitive mappings that now involve actions and perceptions. Taking
into account such ubiquity and pervasiveness of computational interaction,
it should be commented here that interactive computing is the result of the
challenges that computation has to confront today: a quick and efficient responsiveness to vast data spaces, the quantification of desires, beliefs, inclination and
knowledges that underpins the statistical calculation of trades and prices. We
are keen to stress that, in this contemporary scenario of computational interactivity, completion is attained by adding new levels of quantification of variation.
These new levels afford completeness insofar as the function of the algorithm
is extended by external inputs, and is, thus, able to bypass its internal limits by
simply posing the limit of computation elsewhere. The interactive paradigm,
then, concerns the capacity of algorithms to respond and adapt to its external
inputs. However, we want to suggest that this interactive form of adaptation
does not serve to overcome, but only to postpone the threat of computational
indeterminacy.
In order to understand further how these new dynamic attributes of the
interactive algorithm work, we can ask whether the interactive algorithm could
be seen as being conceptually closer to Whitehead’s actual occasion. Is this
discussion of interaction in computation a way to prove our parallel between
the two notions? The answer is no: we believe that there is an inherent problem
with the interactive paradigm’s reworking of indeterminacy aiming to calculate
the variations of lived situations. Indeterminacy, we argue, is only approximated
by the interactive algorithm; the problem of the incomputable is not solved
but merely optimized through the addition of an external input. In this sense,
the interactive algorithm harnesses the speculative power of the incomputable
for computational processing. Going back to Chaitin, we can argue that the
incomputable is not simply a limit that must be resolved by the addition of
environmental variations, but that – as a problem – it remains an active ingredient or element of every computation, however many variables and data may
be involved in it. Incomputability, like an eternal object, conditions the finality of
the algorithmic occasion.
We are thus saying the interactive paradigm is not so different from the
Turing one: both are geared towards the fulfilment of a task. From both perspectives the pre-established procedure clashes with the unknown quantities of
the incomputable. While in Turing computation stops, with the interactive
algorithm the problem is bypassed by the addition of more and more data so as
to enrich, diversify and vary the goal of the function. It could then be argued
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that the interactive paradigm interprets the incomputable from a human (or
humanist) standpoint: it tries to solve the limit from the viewpoint of the human
capacity to comprehend or compress data, or as how a human would cognitively
cope with the unknown. Instead, our contention is that in fulfilling a task the
algorithmic procedure inevitably confronts information indeterminacy, and
by this encounter it fully realizes itself. This is completion from the standpoint
of a computational process that cannot ‘not’ be incomplete. In other words,
the limit of computation cannot be eluded, as it is intrinsic to computation
itself. Computation may account for variations from the environment and thus
become more powerful because of this inclusion. Yet the internal limit remains
as the mark of the radical indeterminacy that constitutes computation.
Satisfaction and the autonomy of rules
The question of confronting indeterminacy and fully realizing oneself in relation
to it needs to be explained by returning yet again to Whitehead. Whitehead, we
said, calls the capacity of an actual occasion to constitute itself through the
prehensions of data coming from other actual occasions and eternal objects
‘satisfaction’. An actual occasion reaches satisfaction as it reaches completion.
For Whitehead, this condition of ‘exhaustion’ corresponds to the constitutive
function of every actual occasion, and is not simply an option. Satisfaction
should thus be interpreted not as emotional gratification, but as the final
fulfilment of an appetite. In this sense, the actual occasion’s tendency to reach
completion corresponds to its final determinations, which, however, as we have
seen, can only be achieved through the ingression of indeterminacy in actuality.
It is exactly at this point in our discussion that we would like to go back to
the debate about fun in software. The long treatment of algorithms as actual
occasions was in our opinion necessary to add an ulterior challenge to the
conceptualization of fun in computational culture. Here, we return to our
initial question: ‘Do algorithms have fun?’ So far we have proposed that we
can articulate this question in the Whiteheadian terms of satisfaction and
enjoyment, and, thus, in relation to the question of completion in computation.
An algorithm that has fun is an algorithm that ‘enjoys’ its own process of determination. As anticipated earlier, in computation this process of determination
is explicated in the processing of data on behalf of sequences of instructions. Drawing on Chaitin, we have said above that this processing involves a
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tendency of information to increase in size (i.e. algorithmic randomness). Via
Chaitin, it is also possible to argue that the introduction of randomness, entropy
or indeterminacy within computational processing describes algorithms that
select a multiplicity of data which gets unified into an output. This output is a
unity that is still a part, but that, however, can be bigger than the whole set of
instructions from which the computation started. From this standpoint, and yet
again following Whitehead, we can add that satisfaction can only correspond to
the final expression of such constitutive indeterminacy within computational
processing. Here, one can see that satisfaction, understood as algorithmic
completion, might bring a further level of speculation to the debate about fun in
software. From this perspective, there is fun in software because the algorithmic
procedure entails a dimension of enjoyment that derives not from the breaking
down of the mechanization, but instead from the fulfilment of the internal
dynamic of completion via indeterminacy in computation. We do not deny
that there is fun in going outside of the grains of formal logic, as the epitome of
representational thought in computing. We maintain, however, that computational processing already implies a dimension of enjoyment or satisfaction – one
that is being understood here as a process of completion determined by the
ingression of indeterminacy within algorithmic procedures.
Despite the fact that the process by which an algorithm enjoys itself might
still remain obscure, we believe that this proposition offers an opportunity to
address one of the main challenges that software poses. Crucial to the history
of computation is the quest for an ultimate procedure for the mechanization
of thought, and thus the possibility of finding a new form of conceptual
function. To propose that algorithms are actual occasions means to confront
both this quest and this possibility, and to reformulate what the mechanization
of thought could be from the standpoint of the Whiteheadian notion of ‘form
of process’. We want to argue that, in a Whiteheadian sense, the algorithmic
mechanization of thought does not aim to establish an equivalence between
emotional intelligence and the execution of a rule. By taking algorithms and
not androids as our object of investigation, we can say that we are ultimately
interested in re-directing the question of the autonomy of thought from
emotion to reason. As mentioned earlier, we suggest that algorithms, taken as
the contemporary epitome of automated thinking, reveal that the execution of
rules (indeed, the mechanical) might have another order of autonomy – one
that can be found not without or against but within reason. This is because
algorithmic reason is already mechanical, insofar as it is the processing of rules.
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This last sentence should, however, be introduced with a disclaimer: we are not
suggesting that algorithms exhaust all forms of thinking, nor are we asserting
that all thought is determined by reason or by the processing of rules. We are
rather making the case for a mechanization of thought that is already a form of
reason. Algorithms might have an autonomy that is not to be understood as
mere replication of what makes us autonomous (this is instead what Dick’s
androids were aiming to do). Algorithms, we believe, have their own form of
autonomy: one that pertains, we are keen to stress, to the final aim of executing
rules (i.e. completion).
The question of whether algorithms have fun becomes, from this broader
reading of the mechanization of thought, an enquiry into instructions that
operate by means of decision. It could be argued that our vision of fun in
software shares, to a certain extent, some of the assumptions that motivated
Dick’s critique of mechanical thought. His dreaming androids were meant to
think beyond the rule, so as to deviate from what the traditional idea of mechanized thought was based on (i.e. the repetition of a rule and the constant return
to initial conditions). Dick was thus exposing the limits of representation to
contain the reality of thought. For Dick, a computational unconscious was a way
to argue for non-representational thought, or for drives that cannot be reduced
to symbols and steps, and which, thus, cannot be mechanized. In this respect,
our contention that algorithmic fun needs to be understood in terms of computational completion similarly opposes the idea that rules represent thought.
Ultimately, representation is for us, just as it is for Dick, insufficient to explain
the reality of a process. The difference between our proposition and Dick’s,
however, is that while his androids oppose rules to imagination by emphasizing
the indeterminacy of dreaming and/or affective thought, our algorithms/actual
occasions reveal that procedural and mechanical thought already contains
much more indeterminacy than one could imagine. This indeterminacy is not
simply readable via representational means, but remains nonetheless logical,
formal and computational.
This is the sense in which we understand the mechanization of thought as a
rule-based mechanism that does not simply exclude or optimize indeterminacy,
but instead cannot avoid expressing it. This is also to say that the incomputable,
far from being the ultimate indeterminacy that eludes computation, is instead
the indeterminate condition of every information system and, as such, it is
constantly realized in algorithmic procedures. Our emphasis on the incomputable vis-à-vis Whitehead’s eternal objects therefore aims to put forward the
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idea that something has changed in the nature of the rule itself. We suggest that
the computational rule is dynamic, but this dynamism is not uniquely derived
from the interaction that the rule entertains with its outside when executed.
In our view, the rule is instead dynamic by virtue of its processual function.
Computational processing is thus also a process, even though it cannot be
reduced to it.
In conclusion, we suggest that computational processing can correspond to a
non-human intelligibility of indeterminacy. From this perspective, algorithmic
rules are what they are: instructions. As such, they are meant to fulfil a task. Yet,
we believe that this instrumentality is not a symptom of an undefeatable power
that programs our very human capacity of thought. Instead this instrumentality
can be understood as defining an irreducible, and fundamentally algorithmic,
form of process. In this respect, the fact that the rule accomplishes a function is
what for us justifies the autonomy of such a function. To ask whether algorithms
have fun is then a speculative exercise to test the hypothesis of the autonomy of
algorithms as a new form of mechanical thought. Perhaps the question remains
absurd, nevertheless it must be posed.
Notes
1
2
3
4
Dick, Philip K. Do Androids Dream of Electric Sheep? (New York: Ballantine
Books, 1996).
See, among others, Munster, Anna Materializing New Media. Embodiment in
Information Aesthetics (Hannover: Dartmouth College Press, 2006); Hansen, Mark
B. N., New Philosophy for New Media (Cambridge, MA: MIT Press, 2004).
Such understandings would instead take thought to be a mere aggregation of
fixed rules. This occurs, for instance, in Putnam’s computational theory of mind:
Putnam, Hilary Mathematics, Matter and Method (Cambridge: Cambridge
University Press, 1979).
The notion of ‘sense’ here is derived from Deleuze’s project to challenge the
logic of representation from within. Deleuze, Gilles, The Logic of Sense (London:
Continuum, 2004). Against the legacy of representational thought and theories of
signification, Deleuze addresses and overcomes the linguistic turn in philosophy
by proposing a ‘logic of sense’, according to which the genesis of value and
significance is more important than truth and meaning conditions. For Deleuze,
sense is neither original nor final, but an ontological event that is expressed in its
effects – effects that are intensive, affective, material.
Do Algorithms Have Fun?
5
6
7
8
9
10
11
12
13
14
15
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See Whitehead, Alfred N. Modes of Thought (New York: The Free Press, 1968), in
particular, refer to ‘Lecture Five’.
Whitehead, Modes of Thought, 86.
Whitehead, Alfred N., Process and Reality (New York: The Free Press, 1978), 211.
Massumi’s elaboration of process and processing in terms of an opposition
between the analog and the digital (both conceived as modes of articulating
the real) has arguably influenced many juxtapositions of these notions in
computational culture. For Massumi, analog processes are ontologically ‘superior’
to digital processing. The latter, for him, can never fully account for the virtual
potential of thought and experience, a potential that is continuous (therefore,
analog) and not discrete (or digital). See Massumi, Brian Parables for the Virtual.
Movement, Affect, Sensation (Durham, NC and London: Duke University Press,
2002). See, specifically, ‘On the Superiority of the Analog’.
Whitehead, Process and Reality, 85.
Whitehead, Process and Reality, 23.
Whitehead, Process and Reality, 108.
Gödel, Kurt ‘On Formally Undecidable Propositions of the Principia Mathematica
and Related Systems I’, in The Undecidable: Basic Papers on Undecidable
Propositions, Unsolvable Problems and Computable Functions, ed. Martin Davis,
trans. E. Mendelson (Mineola, NY: Dover Publications, 2004), 4–38.
See Chaitin, Gregory, Meta Maths. The Quest for Omega (London: Atlantic Books,
2005); Chaitin, Gregory, Exploring Randomness (London: Springer-Verlag, 2001).
For an overview of some of the key issues in interactive computing, refer to
Goldin, Dina, Smolka, Scott A. and Wegner, Peter (eds) Interactive Computation:
The New Paradigm (New York: Springer, 2006).
This hypothesis has been advanced, for instance, in Wegner, Peter, ‘Why
Interaction is More Powerful than Algorithms’, Communications of the ACM, 40(5)
(1997): 80–91.