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In Section \ref{sec:computational-serendipity}, we applied our model to evaluate the serendipity of an evolutionary music improvisation system, a system for automatically assembling flowcharts, and a hypothetical class of next-generation recommender systems, and a system for assembling flowcharts. systems. The model has helped to highlight directions for development that would increase the a system's potential for serendipity in existing systems, serendipity, either incrementally or more transformatively. Our model outlines a path towards the development of systems that can observe events that would otherwise not be observed, take an interest in them, and transform the observations into artefacts with lasting value. %% In this section, we will show how the model allows for more precise %% thinking than other existing work touching on this area. We then

Recent work has examined the related topics of \emph{curiosity} \cite{wu2013curiosity} and \emph{surprise} \cite{grace2014using} in computing. The latter example seeks to ``adopt methods from the field of computational creativity [$\ldots$] to the generation of scientific hypotheses.'' This provides a useful example of an effort focused on computational \emph{invention}. Another related area of contemporary computing in which serendipitous events may be found is bioinformatics: ``Instead of waiting for the happy accidents in the lab, you might be able to find them in the data'' \cite[p.~70]{kennedy2016inventology}. As we indicated earlier, creativity and serendipity are often discussed in related ways. A further terminological clarification is warranted. The word \emph{creative} can be used to describe a ``creative product'', a ``creative person'', a ``creative process'' and even the broader ``creative milieu.'' Computational creativity must take acount all of these aspects \cite{jordanous2015four}. \cite{4Pjournal-version}. In contrast, the model we have presented focuses only on serendipity as an attribute of a particular kind of process. Most often, we speak of a system's \emph{potential} for serendipity. In the current work, we

in the current paper. Another issue is the widespread reliance on microdomains. However, there are other underlying factors. Existing standards for assessing computational creativity have historically focused on product evaluations. \citeA{ritchie07} uses metrics that depend on properties that a reasonably sophisticated judge can ascribe to generated artifacts: ``typicality'', i.e., the extent to which an artifact belongs to a certain genre, and ``quality'' ``quality''. These are used as atomic measures for from which more complex metrics, including ``novelty.'' ``novelty,'' can be derived. Most often, the judge is assumed to be a human. % In recent years, artefact-centred evaluations are increasingly complemented by methods that consider process

creativity. We would argue that the concept of serendipity brings autonomous creative systems into clearer focus: not as with an abstract notion of creativity \emph{sui generis}, but creativity in interaction with the world. This often requires a different mindset, and a different approach to system building and evaluation.

\paragraph{\textbf{Autonomy}.} Our case studies in Section \ref{sec:computational-serendipity} highlight the potential value of increased autonomy on the system side. The search for connections that make raw data into ``strategic data'' is an appropriate theme for research in computational intelligence and machine learning to grapple with. In the standard cybernetic model, we control computers, and we also control the computer's operating context. There is little room for serendipity if there is nothing outside of our direct control. In This mainstream model stands in contrast tothis mainstream model, von Foerster \citeyear[p. 286]{von2003cybernetics} advocated a Foerster's \citeyear{von2003cybernetics} second-order cybernetics in which ``the observer who enters the system shall be allowed cybernetics. \citeA{research-priorities} advise researchers to stipulate his own purpose.'' consider \emph{verification}, \emph{validity} and \emph{security} as well as \emph{control}. While we wouldn't advocate an uncautious approach, it must be pointed out that the dystopic scenarious surrounding loss of control may have corresponding utopic counter-scenarios; and in any event, we believe there is a more fundamental research problem. \emph{A primary challenge for the serendipitous operation of computers is developing computational agents that specify their own problems.} \paragraph{\textbf{Learning}.} Each of the case studies considered in Section \ref{sec:computational-serendipity} describes a system that

see that the creation of a new design pattern is always somewhat serendipitous (Figure \ref{fig:pattern-schematic}; compare Figure \ref{fig:1b}). %% To van Andel's assertion that ``The very moment I can plan or programme `serendipity' it cannot be called serendipity anymore,'' we reply that patterns -- and programs -- can include built-in

unexpected happy outcomes more likely, by designing and developing systems that increasingly address the challenges outlined in Section \ref{sec:recommendations}. Such systems will encounter unexpected stimuli, become curious about them, sagaciously pursuing pursue enquiry within a social context, and assess the value of any outcomes. % Figure \ref{fig:va-pattern-figure} shows one example of a design pattern that can be used to \emph{plan for serendipity}, based on a the ``\emph{Successful Error}'' pattern identified by van Andel: ``\emph{Successful Error}''. Andel. In future work, we intend to build a more complete serendipity pattern language -- and put it to work within autonomous programming systems. % Is ``having a stretch goal'' an example of a serendipity pattern? I think so! \begin{figure}[!h] \vspace{.3cm} \input{pattern-schematic-tikz.tex}

detailed set of evaluation standards for serendipity. % We used this model to analyse the potential for serendipity in case studies of evolutionary computing,recommender systems, and automated programming. programming, and recommender systems. We saw that the proposed framework can be used both retrospectively, as an evaluation tool, and prospectively, as a design tool. In every case, the model surfaced themes that can help to guide implementation.

annoying, we encounter radical changes in the evaluation of what's interesting. Importantly, serendipity is not the same as luck. The notion of serendipity is increasingly seen as relevant in the arts \cite{mckay-serendipity}, arts, in the tech industry \cite{rao2015breaking}, technology sector, and elsewhere. elsewhere \cite{mckay-serendipity,rao2015breaking,kennedy2016inventology}. In the workplace, people have sought to encourage serendipity with methods drawn from architecture, data science, and cultural engineering \cite{kakko2009homo,engineering-serendipity,who-moved-cube}. Continued development of an interdisciplinary perspective on the phenomenon of serendipity promises further illumination. This paper reassesses and updates an earlier discussion of serendipity in a computational context. context \cite{pease2013discussion}. Beginning with a survey of historical definitions, perceptions, and examples of serendipity in order to surface its several facets and features, we then develop a process-based model of serendipity that can be applied

Similarly, even if we cannot plan or program serendipity, we can prepare for it. If Indeed, if serendipity was ruled out as a matter of principle, computing would be restricted to happy or unhappy \emph{unsurprises} -- preprogrammed, preunderstood behaviour -- that would be interspersed periodically, perhaps, with an \emph{unhappy} surprise.(Perhaps this latter case would ultimately reduce to ``programmer oversight''.) Venkatesh Rao \citeyearpar{rao2015breaking} uses the term \emph{zemblanity} -- after William Boyd \citeyearpar{boyd2010armadillo}: ``zemblanity, the ``the opposite of serendipity, the faculty of making unhappy, unlucky and expected discoveries by design'' -- to describe systems that are doomed to produce only \emph{only} unhappy unsurprises. According to Rao, this is the implied fate of systems that are tied inextricably to a fixed vision, from which any (inevitable) deviation constitutes a mistake. This condition stands at a sharp contrast with the ``second-order cybernetics'' introduced by \citeA{von2003cybernetics}, which envisions systems that are able to specify their own purpose, and adapt it with respect to a

what van Andel \citeyearpar[p.~639]{van1994anatomy} terms \emph{negative serendipity} -- and learn from them. These issues are particularly relevant in light of current high-profile discussions around the role of AI in society. These discussion centre on a dilemma in which the core issues described above come sharply into focus. Although we ``we cannot predict what we might achieve'' with AI, nevertheless many researchers, technologists, and policy makers subscribe to a (presumably healthy) conservatism that says that AI systems should ``do what we want them to do'' \cite{research-priorities}. A computationally robust notion of serendipity may go a considerable ways towards resolving the underlying dilemma. If we can build systems that can communicate with us about their unexpected discoveries and reason about the value of these discoveries in a socially responsible way, then we may be reasonably confident that they will behave in an ethical manner. Less controversial than ``programmed serendipity'', but no less worthy of study, is serendipity that arises in the course of user interaction. Indeed, it could be argued that everyday social media

that are taken on $T^\star$ leading to the \textbf{result} $R$, which is ultimately given a positive evaluation. %\afterpage{\clearpage} \begin{figure}[p] \begin{figure}[h] \vspace{2mm} \captionsetup[subfigure]{justification=centering} %% \begin{minipage}[b]{\textwidth}

fallible, as is the system as a whole. Thus, for example, a trigger that has been initially tagged as interesting may prove to be fruitless in the verification stage. Similarly, a system that implements all of the procedural steps in Figure \ref{fig:1c}, but that for whatever reason is never able to achieve a result of significant value cannot be said to have potential for serendipity. However, a system only produces results of high value would also be suspect, since it

%Then combining $\mathbf{a}\times\mathbf{b}\times\mathbf{c}$ gives a % likelihood score: \begin{mdframed} \vspace{.1cm} {\textbf{\emph{Likelihood score and final ruling.}} Low but nonzero A low (nonzero) likelihood score $\mathbf{a}\times\mathbf{b}\times\mathbf{c}$ and high value $\mathbf{d}$ imply that the event was ``serendipitous.'' In all other conditions, cases, the event was ``unserendipitous.''} \end{mdframed} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \item[{(\textbf{C - Factors})}] {Finally, if the criteria from Part A

\subsection{Heuristics}\label{specs-heuristics} \textbf{\emph{Choose \paragraph{Choose relevant populations to produce a useful estimate.}} estimate.} It isn't necessary to assign explicit numerical values to $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$, and $\mathbf{d}$, although that can be done if desired. More typically -- and in all of the examples that follow -- all that is required is to select a relevant population in order to make an estimate. With a population of one, there is no basis for comparison, whereas in huge large population, the chance of any particularly specific highly-specific outcome is likely to may be vanishingly small. The aim is to highlight what -- if anything -- is special about the potentially serendipitous development pathway, pathway in comparison to other possible paths. paths, and hopefully learn something relevant. Thus, we might choose to compare Fleming to other lab biologists, and or to compare Goodyear to other chemists. Even if we were to shift the analysis and look at the much smaller populations of experimental pathologists or inventors with an interest in rubber, Fleming and Goodyear would have features that stand out, particularly when it comes to their curiosity. \textbf{\emph{Find \paragraph{Find the salient features of the trigger.}} trigger.} How can we we estimate the chance of the trigger appearing, if every trigger is unique? Consider de Mestral's encounter with burrs. The chance of encountering burrs while out walking is \emph{high}: many people have

of time; in other words, it may be a pattern, rather than a fact. Noticing patterns is a key aspect of sagacity, as well. \textbf{\emph{Look \paragraph{Look at long-term behaviour.}} behaviour.} Although it is in no way required by the SPECS methodology outlined above, many systems (including all of the examples below) have an iterative aspect. This means that a result may serve as a trigger for further discovery. In

\section{Serendipity in computational systems} \label{sec:computational-serendipity} The 13 facets of serendipity from Section \ref{sec:literature-review} \ref{sec:by-example} specify the conditions and preconditions that are conducive to serendipitous discovery. Section \ref{sec:our-model} distilled these elements into a computational model, culminating in a method for evaluating computational serendipity in Section \ref{specs-overview}. model. % Along with clear criteria, it is important to clearly delineate the scope of the system being evaluated, and the position of the evaluator

flowcharts. Using our updated criteria, we discuss two new examples below, and revisit poetry flowcharts, reporting on recent work and outlining the next steps. The three case studies respectively apply the criteria to \emph{evaluate}of an existing system, \emph{design} a new experiment, and \emph{frame} a ``grand challenge.'' In the first case study, the system we evaluate turns out not to be particularly serendipitous according to our criteria. This helps to show that our

\subsubsection{Application of criteria} In our current the initial experimental design, following \citeA{pease2013discussion}, the system's potential \textbf{triggers} result from random, but constrained, trial and error with flowchart assembly. Some valid combinations of nodes will produce results, and some will not. Due to the dynamically changing environment (e.g., updates to data sources like Twitter) some flowcharts that did not produce results earlier may unexpectedly begin to produce results. % The system's \textbf{prepared mind} lies in a distributed knowledge base provided byProcessNodes themselves, describing the ProcessNodes, which provide metadata that describe constraints on their inputs and outputs; outputs -- and also in the global history of successful and unsuccessful combinations. % The system will not try combinations that it knows cannot produce results, but it will try novel combinations and may retry earlier

What made this particular combination work? Is there a pattern that could be exploited in the future? It may be that no broader pattern can be found, and the system will simply record the bare fact that the combination works. works (and this is the simple starting point from which we begin). % Successful combinations and any further inferences are stored, and referred to in future runs. The \textbf{bridge} to any a new results result is accordingly found by informed trial and error, building on previous outcomes. % The basic \textbf{result} the system is aiming to achieve is simply to generate a new combination of nodes that can fit together and that generates non-empty output. Subsequent Reviewing this design, we observed that subsequent versions of the system may have more detailed evaluation functions, setting a higher bar. bar for what counts as success. For example, a future version of the system could be tuned to search for flowcharts that generate poetry \cite{corneli2015computational}.

FloWr}, the search process is exceptionally \textbf{curious}, since it tries many combinations programmatically. However, remembering viable combinations and avoiding combinations that are known not to work offer unexceptional does not require exceptional \textbf{sagacity}. This At least, this will be so until the system learns more heuristics, heuristics for flowchart construction, which requires would require not just only pattern matching but pattern induction. At the moment, the system's criterion for attributing \textbf{value} is simply that the combination of nodes generates non-empty output; an third-party is not likely to judge such combinations as useful. \subsubsection{Ruling}

$\mathit{low}\times\mathit{low}\times\mathit{high}$, which is relatively favourable. However, until there is a more discriminating way to judge value, the attribution of serendipity to any particular run is seems premature. One route forward would be This motivates a new set of experiments that seeks to attribute meaningfully judge the value to of explanatory heuristics,rather than generated flowcharts, and texts. This would will both result in (and require) and require increased sagacity on the part of the system. %%% JAC - add citations to ICCC papers if they have been accepted. \subsubsection{Qualitative assessment} The\textbf{dynamic world} the system operates in a \textbf{dynamic world} that is dynamic in two ways: first, in the straightforward sense that some of the input sources, like Twitter, are changing; additionally, in the sense that the system's knowledge of successful and unsuccessful node combinations changes over time. time as well. The current version of the system does not seem to deal with \textbf{multiple contexts}.We have broken the search process into separate sub-populations to constrain the search, but these do not interact. In a future version of the system, interaction between different heuristically-driven search processes would be possible, and could lead to more unexpected results. Along these lines, as more goals are added, the system could more readily be

\begin{table}[p] {\centering \renewcommand{\arraystretch}{1.5} \scriptsize \begin{tabular}{p{1.5in}@{\hspace{.1in}}p{1.5in}@{\hspace{.1in}}p{1.5in}} \begin{tabular}{p{1.4in}@{\hspace{.1in}}p{1.4in}@{\hspace{.1in}}p{1.4in}} \multicolumn{1}{c}{\textbf{{\footnotesize Evolutionary music}}} & \multicolumn{1}{c}{\textbf{{\footnotesize Flowchart assembly}}} & \multicolumn{1}{c}{\hspace{-.3cm}\textbf{{\footnotesize Next-gen.~recommenders\hspace{.3cm}}}} \multicolumn{1}{c}{\textbf{{\footnotesize Next-gen.~rec.~sys.}}} \\[.05in] \multicolumn{3}{l}{\em {\textbf{Condition}}} \\ \cline{1-3}

differentiate individual threads or system runs. Some elements of this population might be deemed more serendipitous than others. \item The flowchart assembly process would need more stringent, and more meaningful, criteria for value before third-party observers would be likely to attribute serendipity to the system. In addition to raising challenges for autonomous evaluation (as in the evolutionary music system case), this requirement would impose more sophisticated constaints on processing in earlier steps, which would require the system to be more sagacious. \item The next-generation recommender systems we've envisioned need to be able to make inferences from aggregate user behaviour. This points to long-term considerations that go beyond the unique serendipitous event. How ``curious'' should these systems be? One

step towards building an artificially-intelligent recommender system, users might be explicitly given tasks that are designed to trigger serendipity on the system-side. \item The flowchart assembly process would need more stringent, and more meaningful, criteria for value before third-party observers would be likely to attribute serendipity to the system. In addition to raising challenges for autonomous evaluation (as in the evolutionary music system case), this requirement would impose more sophisticated constaints on processing in earlier steps, which would require the system to be more sagacious. \end{enumerate}

\begin{abstract} Most There is relatively little prior work that deals dealing with serendipity in a computing context context, and the majority of it focuses on computational ``discovery''. support for human discovery via recommender systems. We argue that serendipity also includes an important ``invention'' invention aspect. Building on a survey that describes of serendipitous discovery and invention in science and technology, we advance a definition of serendipity and an accompanying model that can be used evaluate the potential for serendipity in serendipitous discovery and invention of autonomous or interactive computational systems. The Practitioners can use this model adapts existing recommendations to evaluate a system's potential for evaluating computational creativity. It unexpected online behaviour that may have a beneficial outcome. In addition to a quantitative rating of serendipity potential -- computed in terms of population-based estimates of chance and curiosity (in the discovery phase) and sagacity and value (in the invention phase) -- the model also suggests qualitative features that can guide development work. We show how the model is applied used in three case studiesthat evaluate the serendipity of existing and hypothetical systems systems, in the context of evolutionary computing,recommender systems, and automated programming. programming, and (next-generation) recommender systems. From this analysis, we extract recommendations for practitioners working with computational serendipity, and outline future directions for research. \\[.3cm] \keywords{serendipity, evaluation, computational creativity, autonomous systems}

%% Saved with string encoding Unicode (UTF-8) @article{4Pjournal-version, author = {Anna Jordanous}, title = {Four {PPPP}erspectives on computational creativity in theory and in practice}, journal = {Connection Science}, volume = {0}, number = {0}, pages = {1-23}, year = {0}, doi = {10.1080/09540091.2016.1151860}, URL = { http://dx.doi.org/10.1080/09540091.2016.1151860 }, eprint = { http://dx.doi.org/10.1080/09540091.2016.1151860 } } @article{research-priorities, author = {Stuart J. Russell and Daniel Dewey and Max Tegmark}, title = {{R}esearch {P}riorities for {R}obust and {B}eneficial {A}rtificial {I}ntelligence}, journal = {{AI} {M}agazine}, volume = {36}, number = {4}, year = {2015}, } @book{russo2010companies, title={Companies on a mission: Entrepreneurial strategies for growing sustainably, responsibly, and profitably}, author={Russo, Michael},

@book{austin2003chase, title={Chase, chance, and creativity: The lucky art of novelty}, author={Austin, James H}, year={2003 [1978]}, year={[1978] 2003}, publisher={MIT Press} }

Author = {Bergson, Henri}, Publisher = {Henry Holt and Company}, Title = {Creative {E}volution}, Year = {1911 [1907]}} {[1907] 1911}} @article{milan2013kiki, Author = {Mil{\'a}n, E and Iborra, O and de Cordoba, MJ and Ju{\'a}rez-Ramos, V and Artacho, MA Rodr{\'\i}guez and Rubio, JL},

Place = {London}, Publisher = {John Brindley}, Title = {Zadig, or the Book of Fate}, Year = {1749 [1748]}} {[1748] 1749}} @article{chumaceiro1995serendipity, Author = {D{\'{\i}}az de Chumaceiro, Cora L.},

Pages = {283--286}, Publisher = {Springer}, Title = {Cybernetics of cybernetics}, Year = {2003 [1979]}} {[1979] 2003}} @book{von2003essays, Author = {von Foerster, Heinz},

Author = {Dewey, John}, Publisher = {Courier Dover Publications}, Title = {How we think}, Year = {1997 [1910]}} {[1910] 1997}} @article{delanda1993virtual, Author = {Delanda, Manuel},

Place = {Westport, Connecticut}, Publisher = {Greenwood Press}, Title = {{T}he {C}reative {M}ind}, Year = {1946 [1941]}} {[1941] 1946}} @book{deleuze1991bergsonism, Annote = {Trans. Hugh Tomlinson and Barbara Habberjam.},

Place = {New York}, Publisher = {Zone}, Title = {Bergsonism}, Year = {1988 [1966]}} {[1966] 1988}} @article{moukas1997amalthaea, Author = {Moukas, Alexandros},

Author = {Jevons, W. S.}, Publisher = {Macmillan}, Title = {{P}rinciples of {S}cience: {A} treatise on logic and scientific method}, Year = {{1913 [1874]}}} {[1874] 1913}} @incollection{dunbar:05, Address = {Mahwah, NJ},

Place = {London}, Publisher = {Bloomsbury Academic}, Title = {Difference and repetition}, Year = {2004 [1968]}} {[1968] 2004}} @inproceedings{colton-flowcharting, Author = {Simon Colton and John Charnley},

Author = {Poincar{\'e}, Henri}, Publisher = {Courier Dover Publications}, Title = {Science and method}, Year = {2013 [1914]}} {[1914] 2013}} @incollection{stakeholder-groups-bookchapter, Author = {Simon Colton and Alison Pease and Joseph Corneli and Michael Cook and Rose Hepworth and Dan Ventura},

year={2015}} @incollection{keller2014ubimus, title={Ubimus Through title={{U}bimus {T}hrough the Lens {L}ens of Creativity Theories}, {C}reativity {T}heories}, author={Keller, Dami{\'a}n and Lazzarini, Victor and Pimenta, Marcelo S}, booktitle={Ubiquitous Music}, booktitle={{U}biquitous {M}usic}, pages={3--23}, year={2014}, publisher={Springer} } @book{slack2003noble, title={Noble Obsession: Charles Goodyear, Thomas Hancock, title={{N}oble {O}bsession: {C}harles {G}oodyear, {T}homas {H}ancock, and the Race {R}ace to Unlock {U}nlock the Greatest Industrial Secret {G}reatest {I}ndustrial {S}ecret of the 19th Century}, {C}entury}, author={Slack, Charles}, year={2003}, publisher={Hyperion} } @book{kennedy2016inventology, title={{I}nventology: {H}ow {W}e {D}ream {U}p {T}hings {T}hat {C}hange the {W}orld}, author={Kennedy, Pagan}, year={2016}, publisher={Houghton Mifflin Harcourt} } @book{antifragile-software, title={{A}ntifragile {S}oftware: {B}uilding {A}daptable {S}oftware with {M}icroservices}, author={Miles, Russ}, year={2015}, publisher={Leanpub} }

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\usepackage{dialogue} \usepackage{placeins} \usepackage{tikz} \usepackage{onimage} \usetikzlibrary{positioning,backgrounds,fit,arrows,arrows.meta,shapes,shadows} %\usepackage{onimage} \usetikzlibrary{positioning,backgrounds,fit,arrows,shapes,shadows} \usetikzlibrary{shapes.multipart} \usepackage{wrapfig} \usepackage{enumitem}

} \makeatother \setlength{\parskip}{0pt} \setlength{\parsep}{0pt} %\setlength{\headsep}{0pt} \setlength{\topskip}{0pt} \setlength{\topmargin}{0pt} \setlength{\topsep}{0pt} \setlength{\partopsep}{0pt} \raggedbottom \begin{document} % TITLE INFORMATION

% ``poet generates poem'' \node[single, right=8mm of discovery.east,text width=1.5cm] (poet) {\emph{generative\\ process}}; \node[single, right=6mm of poet.east] (poem) {$T$}; \draw [-latex] [->] (poet.east) -- (poem.west); % ``critic listens to poem and offers feedback'' \node[ellipse, draw, right=9mm of poem.east,text width=1.3cm] (critic) {\emph{feedback}}; \draw [-latex] [->] (poem.east) -- (critic.west); \node[single, above=8mm of critic.north,text width=1.4cm] (experience) {\emph{reflective\\ process}}; \node[draw,diamond,inner sep =.3mm, above right=4mm and 3mm of critic] (comment) {\raisebox{2mm}{$p\vphantom{^{\prime}}_1$}} ; \node[draw,diamond,inner sep =.3mm, above left=4mm and 3mm of critic] (reflection) {\raisebox{2mm}{$p\vphantom{^{\prime}}_2$}} ; \draw[-latex,thick] \draw[->,thick] ([yshift=1mm]critic.east) to [out=0,in=270] (comment.south) ; \draw[-latex,thick] \draw[->,thick] (comment.north) to [out=90,in=0] (experience.east) ; \draw[-latex,thick] \draw[->,thick] (experience.west) to [out=180,in=90] (reflection.north) ; \draw[-latex,thick] \draw[->,thick] (reflection.south) to [out=270,in=140] ([yshift=1.5mm]critic.west) ; % nonprinting point to use to bend curve \coordinate[below right=3mm and 7mm of critic] (mid1);

\node[below=.65cm of discovery] (focusshift) {{\small \textbf{\emph{[Focus shift]}}}}; % draw the first curve into focus shift \draw [-latex] [->] ([yshift=-1mm]critic.east) to[out=0,in=90] (mid1) to[out=270,in=0] (feedback.east); %%% Next phase \node[below=2cm of discovery] (invention) {\textbf{\emph{Invention:}}};

\coordinate[above left=2mm and 9mm of integrator] (mid2); % draw the second curve out from focus shift \draw [-latex] [->] (feedback.west) to[out=180,in=90] (mid2) to[out=270,in=160] (integrator.west); % ``poet asks questions about the feedback''

\node[draw,diamond,inner sep =.3mm, below right=4mm and 5mm of integrator] (question) {\raisebox{2mm}{$p^{\prime}_1$}}; \node[draw,diamond, inner sep =.3mm, below left=4mm and 5mm of integrator] (answer) {\raisebox{2mm}{$p^{\prime}_2$}}; \draw[-latex,thick] \draw[->,thick] ([yshift=-1mm]integrator.east) to [out=0,in=90] (question.north) ; \draw[-latex,thick] \draw[->,thick] (question.south) to [out=270,in=0] (explainer.east) ; \draw[-latex,thick] \draw[->,thick] (explainer.west) to [out=180,in=270] (answer.south) ; \draw[-latex,thick] \draw[->,thick] (answer.north) to [out=90,in=200] ([xshift=1mm,yshift=-1.8mm]integrator.west) ; \node[yshift=1mm,single, right=10mm of integrator.east] (problem) {$R$}; \draw [-latex] [->] ([yshift=1mm]integrator.east) -- (problem.west); % ``poet reflects on feedback and updates codebase'' \node[single, right=6mm of problem.east,text width=1.6cm] (pgrammer) {\emph{evaluation}\\ \emph{process}}; \draw [-latex] [->] (problem.east) -- (pgrammer.west); \node[single, right=4mm of pgrammer.east,text width=.3cm] (etc) {...}; \draw [-latex] [->] (pgrammer.east) -- (etc.west); \end{tikzpicture}