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In order to participate in a group improvisation, the Live Algorithm has to con-
vince the other participants that it is listening to and engaging with their contri-
butions. As with conversation, this is achieved by the assimilation of inputs into
outputs. Participation can therefore be measured by the degree of reference and re-
action.
A novel contribution has to be surprising in some way to those engaged in the
musical conversation. Novelty can be measured by the extent to which an output is
independent (of inputs) and is self-exploratory.
The concept of leadership is very subtle: what can the system do so that the en-
vironment is persuaded into participation? In order to lead, a player has to embark
on a musical direction that is picked up by the other participants. Copy cat scenar-
ios such as
Ψ
out
={
should not be considered to
involve a leader. Leadership therefore requires both pre-emption and novelty.
We would naturally regard any musical human partner as autonomous. A central
problem of Live Algorithm research is to persuade human musicians that a machine
partner is making valid contributions, contributions that should be respected, and
not ignored or regarded as a malfunction. This is a problem of perceived autonomy.
Operationally we suppose that a non-heteronomous and non-automatic system is
autonomous
, where a system with no referential or reactive elements is defined as
automatic
and a system that is fully determined by its environment, i.e. has no in-
dependent elements, is
heteronomous
(i.e. subject to external control). Autonomy
is a relative term, with degrees of autonomy ranging in extent form marginal to
very tight coupling with the environment. In this definition of autonomy,
Ψ
out
is
not entirely determined by either the history
A,B,A...
}
;
Ψ
in
={
B,A,B ...
}
or
the internal state
x
alone. An
autonomous system sits between heteronomy and automation.
Bertschinger et al. (
2008
) point out that in order to avoid heteronomy, different
actions must be possible given the same environment. In our formulation, future
actions are contingent on both histories,
{
Ψ
in
}
, so that a specific
Ψ
in
occurring at
t
1
and again at
t
2
>t
1
would, in general, be followed by a different
response
Ψ
out
since the histories
{
Ψ
in
}
and
{
Ψ
out
}
{
Ψ
in
}
t
1
,
{
Ψ
out
}
t
1
and
{
Ψ
in
}
t
2
,
{
Ψ
out
}
t
2
will generally
differ.
A Live Algorithm that deploys stochastic methods (or at least some degree of sta-
tistical uncertainty) could also supply different actions given the same environment:
completely random behaviour should not be considered autonomous (Bertschinger
et al.
2008
). Randomness is avoided if the Live Algorithm provides structured out-
put, which may or may not incorporate past inputs or outputs. Although a Live
Algorithm might produce randomness over one epoch
, an exploratory sys-
tem would eventually produce structured output in order to avoid repeating epochs
of randomness.
3
Exploratory behaviour, as noted above, prohibits prolonged repeti-
tions of periods of randomness that might otherwise be counted as trivially novel.
Improvisation is not just about acting spontaneously, although this plays an im-
portant part. Output that lacks coherence and darts from idea to idea is a feature of
[
t
1
,t
2
]
3
We sidestep issues concerning the randomness, or not, of sequences of finite length.
