Noname manuscript No. (will be inserted by the editor

Wolfgang Banzhaf

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Noname manuscript No.
(will be inserted by the editor)
Response to comments on my article ”Genetic
Programming and Emergence”
Wolfgang Banzhaf
Received: date / Accepted: date
At the outset, I would like to thank all colleagues who took the time to read my
opinion piece ”Genetic Programming and Emergence”, thought about it, and ﬁnally
wrote their comments. I am very happy about these comments, as they provide clear
evidence that my contribution has been well received by the community. I shall next
take up these comments in alphabetic order of their authors, brieﬂy summarize the
gist of their argument and provide for each one what I hope is a useful response.
Lee Altenberg [1] emphasizes that emergent phenomena in Genetic Programming
are produced in a formal system. To bolster this argument, he uses the mathematical
structures of a matrix and a vector as an even simpler example of an interacting struc-
ture, whose formal manipulation leads to emergent phenomena in the mathematical
world examined by ”Linear Algebra”. As examples he mentions eigenvalues, spectral
radii, etc. Thus, he argues, that an entire ﬁeld of Mathematics occupies itself with
emergent phenomena in a formal system, and he rightly is convinced that other areas
of Mathematics do the same.
Having thus fortiﬁed the notion of emergent phenomena and their respectability
in science, he states that emergent phenomena in Genetic Programming could also be
treated in formal or mathematical terms, and possibly lead to interesting discoveries.
He concedes that such an undertaking might be more diﬃcult, due to the complexity
of interactions in Genetic Programming that give rise to emergence, but he points to
one example from the last decade where something along these lines has been achieved
[10]. In his own words: ”But this unruly space is no less formal or no less observable
than the simple matrix, and their mathematical properties are simply awaiting our
discovery”. Well spoken.
Where Altenberg notices a slight disagreement with me is in regard to the role
of selection and variation operators. I am not sure whether there really is much of a
disagreement, but his comment sheds some light on an interesting aspect of evolution,
that has been passionately discussed [6]. The argument states that ”selection and the
genetic operators are co-equal partners in the creation of these emergent phenomena”
[1]. I agree with this statement, as Figure 2 of my contribution demonstrates. The
diversity generator is of constituting importance in generating the variety of struc-
Memorial University of Newfoundland, Canada. E-mail: banzhaf@mun.ca2
ture and function from which a selection device can then select and amplify the most
appropriate.
To clearly state it again: Selection (top-down causation) can only work on varia-
tion if the latter is oﬀered, otherwise it will become powerless. But I do see a diﬀerence
between variation and causation. Variation can be said to provide ”input” to the mech-
anisms of bottom-up causation which is constituted by the mapping from genotypes
to ﬁtness.
Anika Ekart [4] agrees with the usefulness of emergence in Genetic Programming
but is not satisﬁed with the current state of aﬀairs in GP and asks what we can do to
get to what she calls ”perpetual emergence”. What she has in mind here, I believe, is
what others have called ”open-ended evolution”, i.e. a continuous process that would
allow a GP system to adapt to new and unforeseen tasks, a system that permanently
learns.
She points out that systems equipped with some sort of self-reﬂection are necessary
to arrive at more interesting and more powerful GP models and goes on to cite a few
ideas from the literature that might lead the way. Overall she is in agreement with my
observation of emergent phenomena in GP, and calls to exploit them.
In response, I would agree that some sort of internal or self-reﬂecting mechanism is
key to systems that are open-ended and continue to produce novelty. We cannot expect
perpetual emergence if we deﬁne a ﬁxed ﬁtness function. While that will allow adapta-
tion of a given structure, it does not allow the invention of higher level structures with
correspondingly more complex functions. We might be able to build a system equipped
with a number of lower levels before it comes to ﬁtness evaluation (the implementation
of genotype-phenotype maps, perhaps even involving artiﬁcial regulatory networks, is
an example), but we cannot expect the system to do anything outside its once deﬁned
ﬁtness function. The term ”open-ended evolution” can be easily misunderstood, in par-
ticular in artiﬁcial evolution because we are so accustomed to using an explicit ﬁtness
function in those approaches.
Krzysztof Krawiec [7] discusses in his contribution the role of interaction in emer-
gent phenomena and zooms in on the interaction between program code and input
of a GP system as the key to the emergence of solutions. He remarks that most of
what GPers have been doing to date was concerned with structure rather than with
semantic content/functions. ”But a GP system cannot be fully understood without
them [semantic aspects] ...”.
He then argues that the semantics of a program cannot be seen only on the level
of the program as a whole, but must be assigned at least partially, to parts of the
program, for instance, to modules or larger building blocks gradually emerging from
randomness. He states: ”Nevertheless - and this is the pivot of my argument - there
is room for emergence during program execution.” Thus, Krawiec wants to (re-)use
intermediate results. I agree that this approach is fruitful. However, the premise that
semantics cannot emerge on the level of the program as a whole seems to be a mis-
understanding of what I said. While in Section 4 of my contribution I indeed refer
to various phenomena of emergence I did never state that the entire solution did not
emerge. The presence of selection that selects for high ﬁtness does not rule out to state
that highly ﬁt solutions emerge. The point is that ﬁtness selection does not prescribe
(”instruct”) what a program has to look like. There is considerable freedom to realize
high ﬁtness with diﬀerent program code. Agreed, the ﬁtness itself does not emerge, but
the programmatic solution that is able to produce this ﬁtness can be said to emerge.3
I fully agree that it is no surprise that selection for high ﬁtness results in highly ﬁt
individuals. Yet, the actual way these individuals realize their high ﬁtness is emergent,
and often surprising, especially when, upon running a GP system we realize that it
has found a way to wiggle out of our tight descriptions and found a shortcut to high
ﬁtness we deem ”illegal”. In fact, emergence is the explanation for this tendency of
evolutionary systems.
Andre Leier [8] comments that it is the multi-scale nature of evolution in time and
space that makes evolution such a powerful paradigm: ”From genes to proteins, to
organelles, to cells, to tissue, to organs, and complete organisms: Between genome and
phoneme there are many spatial and temporal scales, and functional levels and emer-
gent phenomena can be observed at each of these.” He then asks whether additional
levels in living organisms are a means to increase adaptability and success of survival.
I fully agree with this point of view, but think that multi-level systems in GP have so
far not garnered the attention they deserve.
How can we allow GP systems to foster emergent levels of organization, both at
higher levels from where we currently have deﬁned ”ﬁtness” and at lower levels where
we need to learn to compose solutions in diﬀerent ways? How can we open up the
scales of time and space for evolution? As Bonner points out [3], a key discovery of
natural evolution was that greater size of an organism would allow it to occupy empty
ecological niches. This, in the end, brought about the success of multicellularity. Clearly,
a change in spatial scale of evolution is involved. But it is interesting to note that
multi-cellularity also involves an increase in the range of control over temporal scales:
Development requires epigenetic interactions which control dynamic, time-dependent
switches to provide for structural control [5].
Leier also asks whether we need to start studying what he calls evolutionary risk
management, perhaps in the form of repair mechanisms that are itself under the control
of the artiﬁcial evolutionary process. This is an interesting idea, however, one might
argue that what is studied in general under the heading of ”parameter self-adaptation”
in evolutionary algorithms is an abstraction of this idea.
David Montana’s comment [9] is one of the most critical. He is skeptical about
the claim that we ﬁnd emergence in artiﬁcial systems such as a GP system. Montana
speaks of ”top-down emergence”, a term that I did not use nor understand. Rather
than interpreting what Montana means, I would respond to the strongest statement
he makes:” ...the emergent system must be self-contained. When an external driver
causes emergence in a system, this should not be considered an example of top-down
emergence.”
Thus, Montana starts his argument by making a distinction between the system in
which emergence occurs, and the ”driver” of that system. My response would be that
every system must have a boundary, otherwise it would not be a system, separated
from its environment. So we can agree that there will always be insides and outsides
to a system. I am, however, unclear what Montana means by the driver. He alludes
to it with the example of the development of ﬂocking behaviour, but I am afraid this
confuses me even more.
I guess that if we accepted Montana’s argument, we would have to deny that breed-
ing foxes for tamability [12], i.e. the artiﬁcial evolution of mammals for a particular
trait, an experiment which produced a number of emergent side-eﬀects, would also not
count as emergent. Yet in this particular example we clearly see that both intended and
unintended features are emergent. This happens despite of the fact that ”the driver”4
is outside the system. A case in point is that Darwin based a substantial portion of his
writing about evolution by natural selection on the knowledge of breeders.
In summary, let me refute David Montana’s argument by stating:
1. There is no such process as ”top-down emergence”. There is only emergence, a
process by which ”global” phenomena appear, produced by the interplay of bottom-
up and top-down causation.
2. In a variation - selection mechanism, top-down causation is realized by selection,
regardless of what or who is doing the selection.
3. The actual material of what is under emergence is not relevant, as long as that
material has the potential to provide a rich set of variations.
The only point I am willing to concede is that emergence might be richer in systems
with access to the level structure of itself, something Ekart calls ”internal emergence”.
I have spoken of this in the context of multi-level systems and consider it empowering,
so it is not really a concession. The diﬀerence is a matter of degree but not of principle.
Moshe Sipper [11] points out his work on a test for emergence which involves a
scientist in a simulation-based experiment who would (i) design the system, (ii) ob-
serve the system’s behaviour and (iii) compare the observations with his expectations.
Emergence in this view can be tied to the fact that ”there is a cognitive dissonance
between the observer’s mental image of the system’s design stated in [a language] L1
and his contemporaneous observation of the system’s behaviour in [a language] L2.”
Sipper states that this approach to emergence could be considered complementary
to my approach.
Let’s for a moment delve into the inner workings of his idea. A gut reaction to trying
to deﬁne a ”mental image” is that it might be diﬃcult to come up with something
objectively measurable in such a context. However, we are assured by the existence of
languages that at least something formal can be stated about this mental image. The
key, however, to Sipper’s emergence test is the existence of a second language, with the
second one - sic! - describing global behaviour, most likely over a longer time-scale than
individual events which are the subject of the ﬁrst. By changing scope (both in space
and time), this second language is able to capture other patterns than the former. So
a diﬀerence (”cognitive dissonance”, in Sipper’s words) between these descriptions is
plausible to exist.
Sipper’s test raises a number of questions:
1. If the languages are constructed as described, isn’t there always a diﬀerence (”cog-
nitive dissonance”) in the description of some phenomenon, by the deﬁnition of
these languages?
2. If there are bound to be diﬀerences anyway, the test hinges on ”results are not
obvious”. But that is in the eye of the beholder, and isn’t it therefore subjective?
So are we not back to where we started without the formal description in L1 and
L2?
3. Suppose, the test can be done. Is it only valid for simulation environments? We
hear claims that emergence only happens in Nature (I dispute such a claim) [2],
but shouldn’t the test work in natural systems in particular? What about the
”formalizability” of these natural systems, is it reasonable to expect that at all?
Peter Whigham [13] was inspired to demonstrate by simulation experiment that
the notions in my opinion piece are only part of the story. The gist of his argument is
that selection is not fundamental to the process of emergence. He states: ”Therefore5
selection is just an ampliﬁer of patterns and that the emergence of such patterns is
a fundamental and inevitable consequence of recombination acting on variable-length
representations.” He goes on to demonstrate this by studying the development of the
number of repeated patterns, an emergent phenomenon claimed by my essay to be the
result of its mechanisms.
In particular, he studies the emergence of repeated patterns under drift and recom-
bination, but in the absence of selection. He uses a variable length representation, and
corrects for the expected number of repeated sequences that might appear randomly.
The result of his study is that repeated patterns emerge even without selection. As a
proxy for a selection process, he uses a system with a smaller population. His conclu-
sion is that (i) either repeated patterns are not emergent, or (ii) the mechanism by
which they appear has nothing to do with selection.
My response is that (a) a smaller population is only an approximation for selection.
The experiment would better be repeated using a population of the same size as the
original population. Most likely, the distribution will look diﬀerent under those condi-
tions; (b) I am happy to concede that even under drift and recombination only (without
selection) an eﬀect might be visible. Perhaps this can be termed ”weak emergence”.
This eﬀect, however, is usually orders of magnitude smaller than an eﬀect under selec-
tion. In addition, repeated patterns are only under weak selection pressure in Genetic
Programming. Finally, there are more mechanisms that lead to emergent phenomena.
I have not stated that selection is the only way to produce emergence.
Acknowledgements
I am indebted to Lee Spector, the Editor-in-Chief of Genetic Programming and Evolv-
able Machines, for proposing this contribution format and for handling the process of
submission so diligently.
References
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Programming and Emergence”

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