# To think inside the box, or to think out of the box?
Scientific discovery via the reciprocation of insights and concepts

Yu-Zhe Shi${}^{1,2\,\star{}\,\textrm{{\char 0\relax}}}$, Manjie
Xu${}^{1,2\,\star{}}$, Wenjuan Han2, Yixin Zhu${}^{1\,\textrm{{\char
0\relax}}}$
1Institute for AI, Peking University 2PersLEARN
⋆Equal contributors ✉<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

If scientific discovery is one of the main driving forces of human progress,
insight is the fuel for the engine, which has long attracted behavior-level
research to understand and model its underlying cognitive process. However,
current tasks that abstract scientific discovery mostly focus on the emergence
of insight, ignoring the special role played by domain knowledge. In this
concept paper, we view scientific discovery as an interplay between _thinking
out of the box_ that actively seeks insightful solutions and _thinking inside
the box_ that generalizes on conceptual domain knowledge to keep correct.
Accordingly, we propose Mindle, a semantic searching game that triggers
scientific-discovery-like thinking spontaneously, as infrastructure for
exploring scientific discovery on a large scale. On this basis, the meta-
strategies for insights and the usage of concepts can be investigated
reciprocally. In the pilot studies, several interesting observations inspire
elaborated hypotheses on meta-strategies, context, and individual diversity
for further investigations.

## Introduction

How do scientists come up with novel ideas that lead to significant
discoveries? Psychologists have been working long to understand the underlying
cognitive processes (Schickore, , 2022) to facilitate the progress of
scientific discovery (Campbell, , 1960). Among the diverse philosophical
theories interpreting _discovery_ , the one mostly being cited is that
discovery refers to _the eureka moment_ , a.k.a. _the Aha! moment_ , of having
a new _insight_ (Auble et al., , 1979; Kounios and Beeman, , 2009).
Originating from problem-solving, insight is the process that reconstructs the
representation of the target problem. Given the insight, the solution can be
achieved much more straightforwardly than that before the reconstruction has
been done (Ohlsson, , 1984). People tend to follow prior knowledge when
solving a problem because experience shows this may lead to success (Öllinger
et al., , 2008). But after times of trial-and-error, people can predict the
error of current problem representation (Dubey et al., , 2021), and this may
be the eve of a sudden coming of the Aha! moment. Studies have shown that
solutions discovered by insights usually be more promising than those
generated by analytical approaches (Salvi et al., , 2016), though the latter
requires much more workload than the former—this echoes how specifically
adapted representations outperform prior ones on novel problems.

Meanwhile, the prior representation is also necessary, for it provides the
relevant domain knowledge for the problem—insight is just useless without the
sense of how to deal with the problem. This contrast becomes crucial in terms
of scientific discovery—given a scientific inquiry as the target problem, the
entry is the purported paradigm of the domain that seems relevant to the
problem, which is deeply rooted in _domain knowledge_ (_i.e_., atoms,
theories, and claims) and shapes the meta-cognitive strategic knowledge
(_i.e_., methodologies). Hence, representation reconstruction is extremely
hard when the target problem becomes a scientific inquiry because that at
least means generalization from a scientific to another given few observations
(Tenenbaum and Griffiths, , 2001), and even means a paradigm shift (Kuhn, ,
1970); but without relying on domain knowledge, a scientist can go toward
nowhere because all ideas come from somewhere.

The dilemma we are facing is ubiquitous in scientific discovery. On the one
side, we must _think out of the box_ , such that to avoid missing the flashed-
by insights; but unconventional ways of thinking may also lead to ridiculous
solutions, taking a detour even compared with analytical solutions. On the
other side, we have to _think inside the box_ because domain knowledge keeps
us aware of what we are doing and where we are going; but following an
established paradigm totally restricts our mind in the prior representation of
the problem (see Fig. 1). To achieve solutions successfully and efficiently,
the two mindsets should interplay with each other. When and where should this
happen?

Many scientists deal with such an interplay well—they gain insights from the
eureka moment, which are later developed into representative scientific
discoveries, such as the development of Einstein’s special relativity
(Einstein, , 1982), the discovery of Kekule structure (Gruber, , 1981). This
pattern is also found in many works throughout the life of Gauss (Dunnington
et al., , 2004). Both historical experiences and experimental results drive
the interest in understanding how insight is obtained and making computational
models (Langley and Jones, , 1988), to get close to the ultimate
goal—automated production of insights that improve scientific discovery.
Unfortunately, stories of scientists cannot lead to concrete modeling and
evaluation work at the behavior level rather than the metaphysical level, for
post-hoc simulating how scientists disentangle meta-cognitive strategies from
domain knowledge is difficult and imprecise. Hence, we are on the request of
an experimental environment that abstractly simulates the process of
scientific discovery—the domain knowledge should be crucial for solving the
problem and should be general enough to carry out large-scale behavioral
studies (Almaatouq et al., , 2021), without losing of group convergence or
individual diversity. To the best of our knowledge, we are the first to
explicitly consider the interplay between _insight-seeking_ and _domain-
knowledge-relying_. Hence, we propose Mindle111Visit mindle.cn to interact
with the web-based user interface., a semantic searching game that triggers
scientific-discovery-like thinking spontaneously, as infrastructure for
exploring scientific discovery on a large scale, filling the gap in the
literature.

Figure 1: Overview of insight in scientific discovery. In a classic Gestalt
problem, a problem solver first uses domain knowledge to analyze the problem,
then seeks for insight once she gets trapped; after reconstructing the problem
representation, she again uses domain knowledge to reach the solution. In this
case, though domain knowledge constrains the thinking, it serves as the
vehicle toward the target.

## The reciprocation of insights and concepts

Based on the dilemma over insight-seeking and domain-knowledge-relying, the
most critical feature that distinguishes scientific discovery from normal
insight problem-solving is that domain knowledge plays a crucial role in both
empowering the solution to be correct and restricting the emergence of insight
solutions efficiently. Hence, to understand scientific discovery _inside the
box_ , we should understand how the organization of concepts in domain
knowledge affects meta-cognitive strategies in advance. Conversely, to unveil
the process of scientific discovery _outside the box_ , we should look into
how insightful decisions intervene in using concepts. This bidirectional
pathway echoes the reciprocation of insights and concepts by identifying these
two questions: (1) How a problem grounded on conceptual knowledge improve the
study of insight problem-solving? (2) How does the usage of conceptual
knowledge driven by insight problem-solving improve the study of knowledge
representation? Below, we sketch Mindle by answering these questions.

### Concepts improve the study of insight problem solving

Relying on conceptual knowledge is not an obstacle to investigating scientific
discovery, but a better chance for understanding insight problem-solving.
Current insight problem-solving tasks have been long troubled by the subjects’
unawareness of the meta-cognitive strategies they have used (Metcalfe and
Wiebe, , 1987). Though this inability naturally unveils the sudden come of
insights, it is avoidable by improving experimental tasks. Some current
insight problems focus on stimulating the eureka moment, such as the nine-dot
problem (Kershaw and Ohlsson, , 2004), the matchstick arithmetic (Knoblich et
al., , 1999), and the eight-coin problem (Ormerod et al., , 2002)—these tasks
provide highly confined problem space such that subjects can solve the
problems without applying any semantics or commonsense knowledge other than
the specific background knowledge given by the problem settings. Although such
designs are motivated to disentangle representation reconstruction from
solution cleanly, it makes interpreting the solutions from the trajectories
hard, since the trajectories can only be mapped to the given problem settings.
Hence, if we expect mapping behavioral trajectories to meta-strategic
knowledge, a generally understandable semantics of problem context is
necessary, such as conceptual knowledge in human language. Other insight
problems introduce general semantics, including insight physical problem
solving (_i.e_., intuitive physics as semantics) (Allen et al., , 2020) and
remote association test (_i.e_., word association as semantics) (Mednick, ,
1963). However, these tasks come in a one-to-one input-output fashion, where
the measured behavior is directly generated from the single stimuli one-step,
thus hard to track the representation change. This is crucial in scientific
discovery because there are usually multiple steps of insights that lead to
the target (Moszkowski, , 1972). In contrast to one-shot problem solving,
scientific discovery is more like a path-finding process where the navigation
map changes every time reaching a critical point. Putting the two reasons
together, Mindle should equip with general-understandable semantics in the
context of the target problem.

### Insight problem-solving improves the study of conceptual knowledge

The domain knowledge of sciences is believed to be organized as conceptual
knowledge (Hiebert and Lefevre, , 1986; Rittle-Johnson et al., , 2001).
Conceptual knowledge systematically combines declarative and procedural
knowledge, consisting of both facts about the concepts and active processes
about how concepts interact with each other (Abend, , 2008). Though there are
many perspectives on concept representation, we take the theory theory as a
prerequisite because it is the most accepted theory in terms of scientific
knowledge representation (Gopnik, , 1994), thus we can mimic the domain
knowledge under the form of theory theory. One implementation of theory theory
is that concepts are maintained in a fully-connected network, where each
concept is related to all other concepts in the set—many calculi on fully-
connected graphs, such as the general pattern theory (Grenander, , 2012), can
be applied to formalize the operations over concepts. Such tools help describe
scientific knowledge and meta-strategies in a computable way. Thanks to that,
the theory theory can also model how a child acquires concepts in cognitive
development (Carey, , 1985; Gopnik and Meltzoff, , 1997; Carey, , 2009);
people similarly organize normal concepts to organize scientific knowledge.
Hence, we may use such fully-connected networks statistically extracted from
natural language corpus to simulate the domain knowledge of sciences, so we
can carry out large-scale behavioral studies. Most interestingly, there is a
major feature shared by both normal and scientific knowledge—though the
semantics of concepts and relations are static and invariable viewing
knowledge in the world holistically, they may be highly overloaded according
to diverse context, task utility, and inner preference, from the view of
individuals (Wang and Bi, , 2021). In this way, the compounded concepts are
projected to simplified semantic attribute spaces (Grand et al., , 2022),
which are much more tractable to be processed due to the rational use of
limited cognitive resources (Gershman et al., , 2015; Lieder and Griffiths, ,
2020; Ho et al., , 2022). On this basis, conceptual knowledge in scientific
discovery should be studied in a dynamic way rather than a static way.
However, most current behavior-level experimental methods on semantic
understanding of concepts are confined to general and fixed contexts (Huth et
al., , 2016; Wang et al., , 2020), in a straightforward way that is given the
stimuli (input words) to obtain the descriptions or similarity judgments
(output measurements) directly; other studies on the use of concepts, such as
memory replay and human reinforcement learning (Momennejad et al., , 2017),
mostly focus on the short-term memory for skill learning without retrieving
from long-term memory that has been already formed. To capture the two
features, Mindle should test the representation of conceptual knowledge in
sequential decision-making.

In summary, we profile Mindle with two unique features to simulate the process
of scientific discovery (see Tab. 1 for details), and importantly, the two
work reciprocatively: (1) Mindle should equip with a general-understandable
conceptual knowledge as domain knowledge to help interpret the process of
insight problem solving; (2) Mindle should equip with a sequential decision-
making task to stimulate the flexible dynamic use of conceptual knowledge.

Table 1: The analogy of scientific discovery to solving Mindle

| scientific discovery | solving Mindle
---|---|---
target | solve a scientific query | find out the secret word
output | the hidden answer is shaped by _the known_ | the secret word is among _the known_
problem abstraction | path searching from status quo to _the unknown_ | path searching from current guess to _the unknown_
problem context | conceptual scientific domain knowledge | conceptual knowledge from natural corpus
knowledge representation | concepts connected under logical or intuitive relations | concepts connected under intuitive relations
maintained representation | generalizing from one scientific concept to another | generalizing from one concept to another
reconstruction | changing the domain knowledge or methodology used | changing meta-strategy in action or semantics level
rationality | should be studied from specific perspectives | should be used in specific semantics subspaces
diversity | scientists with different background think differently | people with different background think differently
accessibility | captured by only a few individuals | captured by most individuals

## Mindle: an infrastructure for large-scale studies on scientific discovery

Given the specific features that Mindle should capture, we describe how to
implement Mindle. As the infrastructure for large-scale behavioral studies,
Mindle should meet three elementary satisfaction: (1) providing appropriate
tasks that abstract the target real problem to be studied; (2) providing
correct computational models to evaluate the results; (3) the abstract task
itself should be natural rather than artificial, interesting rather than
boring, to make sure that subjects are easy to get into the task; (4) the task
is easy to be propagated and is robust to unexpected user behaviors. Since the
appropriateness of task abstraction has been illustrated in detail, we
describe how Mindle meets the last three.

### The semantic searching game

Mindle requires the participants to dig out a hidden secret word. In every
single challenge, the participant is given only a starting word. In each
guess, the participant inputs a guessed word, and Mindle outputs a score (the
given starting word can be viewed as the initial guess). The score indicates
how _far_ is the current guess to the target secret word, on a 0 to 100
scale—when the score is more close to 100, the guess is more close to the
target. Once the secret word is hit, one challenge ends. The participant can
choose to quit at any time during the challenge. The guesses can be entered by
the participant through an input text bar or be selected by the participant
through some given options; the policy for proposing options will be described
later. A variant of challenge mode comes with a hint implying what topic the
secret word is related to. The topic can either be abstract or concrete, such
as _kitchen supplies_ , _classical music_ , or _freedom_ , which confines the
problem space.

### Score and vocabulary

The score is provided by the cosine similarity between the embedding vectors
of the current guess and the target word. The embedding vectors can be
generated by arbitrary embedding methods, such as Word2Vec (Mikolov et al.,
2013b, ), Skip-gram (Mikolov et al., 2013a, ), or Glove (Pennington et al., ,
2014). The score transforms the 0 to 1 scale of cosine similarity to a 0 to
100 scale. The vocabulary we used here is a subset consisting of about 40K
most frequently used concepts in the natural corpus. Here we denote the set as
$C\in\mathcal{C}$ where $\mathcal{C}$ is the space of all concepts. In bar-
entering mode, participants would be informed if the input guess is out of
$C$.

### Conceptual knowledge representation

We have mentioned that conceptual knowledge can be represented as a fully-
connected network. It can be implemented as a directed graph encoding an
adjacent matrix. The graph is obtained from natural corpus through a
Transformer model (Vaswani et al., , 2017). The connection weights in the
graph capture the co-occurrence frequency for each pair of concepts. Let graph
$G=\langle C,C\times C\rangle$ be the system of concepts, each node $c_{i}\in
C$ denotes a concept, $c_{k},k\neq i$ is a possible related concepts that
shapes $c_{i}$, and $w(c_{i},c_{k}),k\neq i$ indicates the weight $c_{i}$ is
shaped by $c_{k}$ among all related concepts. The higher $w(c_{i},c_{k})$ is,
the semantics of $c_{i}$ is more influenced by that of $c_{k}$. Note that
usually $w(c_{i},c_{k})\neq w(c_{k},c_{i})$ because the weights indicates the
conditional probability $p(c_{i}|c_{k})=w(c_{i},c_{k})/\sum_{j\neq
i}w(c_{i},c_{j})$. Intuitively, this can be viewed as the probability of
describing the concept $c_{i}$ by concept $c_{k}$ in a rational fashion (Frank
and Goodman, , 2012). $p(c_{i})$ is a vector that has $p(c_{i}|c_{k})$ as its
$k$-th dimension. And since the statistical feature is obtained from the
general natural corpus, the real conceptual knowledge distribution in
individuals’ minds is more or less different because that is highly
conditioned on diverse individual prior experiences. In this way we define all
general and individual operations over concepts as formal operations on a
graph.

### Behavior modeling

Solving Mindle can be ideally modeled as a mdp (mdp). An mdp is a tuple
$T=(S,A,P,R,\rho)$, where $S=C$ is the set of states, $A=C$ is the set of
actions, $P:S\times A\times S\mapsto[0,1]$ is the transition probability
function $s_{t+1}\sim P(\cdot|s_{t},a_{t})$, $R:S\times A\times
S\mapsto\mathbb{R}$ is the reward function (the game score here plays the role
of reward) indicating in what condition the task is solved, and $\rho$ is the
initial guess $\rho$ where $s_{0}\sim\rho$. Under this formulation, solving
Mindle is finding the policy $\pi=(s_{0},a_{0},s_{1},a_{1},\dots)$ that
generates trajectory $\tau\sim\pi$ optimizing the objective
$\max_{\pi}\mathbb{E}_{\tau\sim\pi}[\sum_{t=0}^{\infty}\gamma^{t}R(s_{t},a_{t},s_{t+1})]$.
But this modeling is extremely ideal because the spaces of state and action
are much smaller than the whole set of concepts, due to highly limited memory
and attention slots. Hence, a mask $M$ can be applied to both $S$ and $A$ that
$S\cdot M\subset C$ and $A\cdot M\subset C$. $M$ can either be predefined by
heuristics (will be introduced next) or be extracted from trajectories
generated by subjects in pre-experiments.

### Similarity, rule, and the unrelated

Figure 2: An example of conceptual knowledge representation.

Given the current guess, where can we go? Take _worker_ as the exemplar
current guess, there are three types of candidate actions (see Fig. 2): (1)
Concepts that are highly similar to current guess, _e.g_., _labor_ , _navvy_ ,
and _staff_. (2) Concepts that are highly related to current guess by specific
rules, _e.g_., _machine_ (by rule _usage_), _salary_ (by rule _reward_), and
_supervisor_ (by rule _organization_). (3) Concepts that are hardly related to
current guess by any mean, _e.g_., _arts_ , _word_ , and _hippocampus_.
Suppose we have K proposals in each type and denote $c_{t}$ and $c_{t+1}$ as
current and next guess, respectively. The similar concepts are generated by
top-K $\max_{k}cos(\text{Vec}(c_{t}),\text{Vec}(c_{k})),k\neq t$, the related
concepts are generated by top-K $\max_{k}w(c_{t},c_{k}),k\neq t$, and the
unrelated concepts are generated by top-K $\min_{k}w(c_{t},c_{k}),k\neq t$.
Most similar concepts are synonyms to $c_{t}$, which are not highly related to
$c_{t}$; exceptions exist, thus making a filter afterward. When selecting
related concepts, we try to maximize the diversity of the candidate concepts
by filtering out duplicate concepts generated by the same rule, _e.g_., _boss_
and _supervisor_ (by rule _organization_). We implement this by applying
Agglomerative clustering to the candidate concepts and selecting from the root
(Murtagh and Legendre, , 2014). The three types are actions in the higher
level of $A$, which can be observed directly and easily identified to decision
patterns, such as _persistent searching in a local minima_ or _flexibly
jumping between locals_. Besides analyzing behavior data, the graph pruned by
the three modes is also used to control the hardness of challenges by tuning
the length of the shortest path and the number of possible paths traversing
from the initial guess to the target word.

### Evaluation metrics

One significant indicator to be evaluated is the emergence of the eureka
moment. We use both absolute and relevant measurements. First, we identify the
Aha! moments in a single trajectory
$\tau=(s_{0},a_{0},a_{1},s_{1},\dots,a_{-1},s_{-1})$. First, we calculate the
first-order reward difference between adjacent trials $\Delta
r(t)=r_{t+1}-r_{t}$. For action $a_{t}$, if there exists $i<t$ that $\Delta
r(i)\geq\Delta r(t)$, let $r(i:t)=\sum_{k=i+1}^{t}r_{k}/(t-i)$, if not then
let $i=0$; if there exists $j>t$ that $\Delta r(j)\geq\Delta r(t)$, let
$r(t:j)=\sum_{k=t+1}^{j}r_{k}/(j-t)$, if not then let $j=-1$. We have $\Delta
a(t)=r(t:j)-r(i:t)$ as the cumulative difference between the critical points.
Those critical points with high $a(t)$ tend to be eureka moments from the view
of a single trajectory. Also, we observe the trajectories in a counterfactual
fashion, and we ask what would happen if other actions have been taken. The
action space can be either the concept space $C$ or masked $C\cdot M$ in the
low level, or the space of the three high-level action types (similarity,
rule, and unrelated). Then, we define the updating rate as
$\min\\{0,1-\min_{a\in A}R(s_{t},a,s_{t+1})/R(s_{t},a_{t},s_{t+1})\\}$. Thus,
the current guess can be viewed as an intervention to the status quo following
the semantics gradient, supporting investigations on semantics overload. The
evaluation metrics can be flexibly modified to meet the need of specific
experiments.

### Playability as a game

In the post-interview of our pilot study (25 subjects, 11 are female), after 3
challenges per subject, 24 in 25 subjects think that _playing Mindle is
interesting_ and 18 in 24 subjects think that _I want to play Mindle everyday_
; 15 in 25 have succeeded at least one challenge and 8 in 15 have experienced
at least one eureka moment in at least one challenge. All solved challenges
are finished in about 80 steps of guessing on average, and the number of
insightful solutions is about 50. These results imply that Mindle is
attracting enough with an appropriate success rate, having the potential to
propagate with ease. Also, Mindle is unique for its sense of infinite answer
space and harmless trial (Hamari, , 2007). Thus, Mindle can be played through
a long term, even though a challenge is disrupted in the middle—instead, a
long period of discontinuous thinking may even stimulate the Aha! moment.

## Case Studies

In this section, we discuss three interesting observations from the pilot
study. These phenomena may inspire elaborated hypotheses that lead to further
investigations. This shows how Mindle empowers large-scale experiments.

### Thinking out of the box: action level

Some challenges succeed due to action-level insights. The trajectories have a
common point—participants switch smoothly between _searching in a local
minima_ or _making traversals between locals globally_. Once they have been
optimizing a local minima for a time without gaining a significant score
increase, they changed to jump randomly between concepts that seem unrelated
to each other, until they hit a local with a much higher score. Then they
settle down again to optimize the guess locally with synonyms or similar
concepts. The eureka moments usually come when hitting a _hot solution_ in the
global random jump. Interestingly, the concepts in the trajectories are highly
different from each other, indicating that such behavior pattern is not
constrained by semantics, but be driven by the inner preference of
participants. That is, no matter what concepts I am guessing, I just switch
between local search and global jump flexibly. This lead to a hypothesis: Do
people apply meta-strategies ignoring the problem context?

### Thinking out of the box: semantic level

Some challenges succeed due to semantic-level insights. This happens when
participants hit a local with a relatively high score, which is easy to
believe that target lies in this local. Affected by prior experience,
participants tend to search in a subspace of the semantics space, where the
selected concepts are projected onto a plate of reduced semantics space. For
example, a participant has guessed _school_ , _class_ , and _grade_ , where
she projects the concept to the semantics subspace of school-related concepts.
However, these words cannot help go further. The participant decides to
project the anchor concept, say _class_ , to another semantics space, say
_computer-related terminologies_. Then, she guessed _type_ and unexpectedly
takes a large step toward the target. Hence, she understands that she has been
trapped in a semantics subspace. This case shows that representation
reconstruction can also change the semantics subspace. Hence, we come up with
another hypothesis: Do people apply meta-strategies according to the problem
context? This hypothesis seems to be in contrast to the one in the last
paragraph, but combining these two together, we have a comparative hypothesis,
which is more related to our big picture on scientific discovery: Do people
use meta-strategy as policy regardless of context, or subject to the
subjective understanding of context semantics?

### Thinking inside the box: semantic level

Some challenges succeed through analytical solutions, especially when the
participant, fortunately, reaches the right track at the start. The
participant optimizes a gradient of the semantics landscape in mind. The
gradient can be extremely flexible—for example, hierarchy, _arts_ to
_painting_ to _gallery_ ; extent, _large_ to _larger_ to _largest_ ; or the
distance with human, _human_ to _chimpanzee_ to _monkey_. The hypothesis space
for such a gradient is almost infinite because the semantics space is in very
high dimensionality (Grand et al., , 2022). Since the choice of the gradient
is subjected to personal cognitive bias, the trajectories for the same
challenge can be highly diverse. This echoes the diverse _mindsets_ of
different genres of science. And compared with previous work on testing
personal diversity in knowledge representation (Wang and Bi, , 2021), Mindle
(1) stimulates the spontaneous use of the commonsense knowledge, in contrast
to other experimental paradigms that probe human knowledge representation
explicitly; (2) empowers the scaling-up of pilot studies, both in the
broadness of semantics and the diversity of subjects, to obtain more
elaborated results on the landscape that where people converge or diverge on
concept representation. By recovering all trajectories generated by the same
group of participants, we can build a computational model that captures their
semantics landscape, _i.e_., a function that outputs the sense of _which
concepts are more similar or more related to each other than to others_. The
function can be approximated through inverse reinforcement learning (Abbeel
and Ng, , 2004), thus we can analyze group diversities of concept
representation quantitatively. In this way, we may reverse-engineer the
organization of conceptual knowledge in peoples’ minds.

### Combining the three hypotheses

Testing the three hypotheses helps us understand the interplay between
insight-seeking and domain-knowledge-relying. First, on a confined problem
space, we test the existence of these thinking patterns, by stimulating the
spontaneous use of action-level metastrategies, semantic-level metastrategies,
and semantic-level landscape optimization. After this, we study given
different constrained topics, are people tend to emerge and converge to a set
of similar parameters that controls the interplay. Assuming that insight-
seeking and domain-knowledge-relying are on the two ends of a continuum, one
possible hypothesis is that people rationally control the interplay according
to their uncertainty on the use of domain knowledge—high uncertainty on
_knowing what_ may lead to reconstruction at action level; high uncertainty on
_deciding which_ may lead to reconstruction at semantic level; and low
uncertainty may lead to maintaining the current representation. Such intuition
defines the _balance point_ between the two ends, thus irrational behaviors,
_e.g_., more close to insight-seeking, can be identified comparing with the
rational case. On this basis, we scale up the behavioral studies to generalize
the results to larger groups of individuals, and also collect a large dataset
of trajectories and reverse-engineer the semantic landscapes in the open
domain.

(a)

(b)

(c)

Figure 3: (a) Concepts that have high and low associations to concept _dog_ ;
(b) Concepts that have high similarity to concept _cat_ ; (c) Concepts that
have high similarity to concept _class_ , with the potential for the from the
semantic subspace of _education-related-concepts_ (_e.g_., _school_ and
_grade_) to _computer-related-concepts_ (_e.g_., _subclass_ and _type_).

### Acknowledgement

The authors thank Mr. David Turner for inspiring and helpful discussions on
designing Mindle.

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##  Appendix A User interface of Mindle

Given a starting word, the users are expected to navigate toward a secret
target word. Users travel in the semantic world by guessing words. For each
time jumping to a word, the users will get a similarity score indicating the
distance between their current position and the target. For the sake of
Mindle’s pilot study, we designed two versions of our Mindle game. Especially,
the Web-based Mindle is designed for both lab-based and online experiments
(see Fig. 4(a)), and the Mobile-based Mindle can be accessed from mobile
terminals, making it suitable for larger-scale online experiments (see Fig.
4(b)).

(a)

(b)

Figure 4: User interface of Mindle. (a) Web-based Mindle; (b) Mobile-based
Mindle

##  Appendix B Examples of conceptual knowledge representation

Tab. 2 shows some canonical examples of conceptual knowledge representation.
Each example shows the highly associated concepts to the centered concept. A
set of stop words have been removed to make the results more representative.

Table 2: Examples of top-associated conceptual knowledge representation Word | Top associated concept
---|---
school | building, county, education, national, community, family, government, city, house, university
cat | life, name, family, medal, known, me, house, into, your, time
work | press,have,government,community, title, zone, action, field, works, working, more, time
apple | park, famous, story, award, album, music, different, out, title
train | tour, population, district, project, zone,
gift | what, new, different, ’something, house, special, story, inside

##  Appendix C Examples of score contour line

Table 3: The score contour line based on the cos similarity.
Top 1 Top 10 Top 100 Top 500

(a) cat Target | Word | Cos Similarity
---|---|---
| cat | 1
| cats | 0.809938
| dog | 0.760946
| kitten | 0.746498
| feline | 0.732624
| beagle | 0.715058
| puppy | 0.707545
| pup | 0.693429
| pet | 0.689153
| felines | 0.675593
| chihuahua | 0.670976
| bassets | 0.520498
| rooster | 0.51893
| owl | 0.518349
| pinscher | 0.517772
| tiger | 0.517296
| piglet | 0.516684
| kelpie | 0.515803
| dachshunds | 0.515763
| schnauzers | 0.514645
| bird | 0.514626
| earless | 0.392231
| hoarder | 0.392067
| lynx | 0.392044
| shrike | 0.392036
| panleukopenia | 0.391696
| iguanas | 0.391474
| doglike | 0.391446
| yelping | 0.391318
| crow | 0.391283
cat | rabbity | 0.391252

(b) green Target | Word | Cos Similarity
---|---|---
| green | 1
| greener | 0.809938
| red | 0.760946
| greening | 0.746498
| yellow | 0.732624
| blue | 0.715058
| brown | 0.707545
| florescent | 0.693429
| greenest | 0.689153
| nongreen | 0.675593
| purple | 0.670976
| pistache | 0.520498
| echeveria | 0.51893
| paspalum | 0.518349
| greened | 0.517772
| bicolored | 0.517296
| multicolored | 0.516684
| brittlebush | 0.515803
| arborvitaes | 0.515763
| stripes | 0.514645
| sienna | 0.514626
| conserve | 0.392231
| photovoltaic | 0.392067
| leafier | 0.392044
| euonymous | 0.392036
| alpenglow | 0.391696
| coppery | 0.391474
| tomatillo | 0.391446
| beautifying | 0.391318
| marram | 0.391283
green | tangelo | 0.391252

Tab. 3(b) shows some canonical examples of the similarity-based semantic
landscape. A contour line is shaped by different concepts with the same-level
score to the target concept. Each example shows a series of contour lines by
different scores. Concept _cat_ has a single major semantic meaning, while
_green_ has two major semantic meanings. Hence, the similar concepts to _cat_
lie in a single semantic subspace, while those to green lie in two semantic
subspaces (color and plant).

##  Appendix D Player trajectories

Figure 5 shows some exemplar trajectories generated by players. Thinking
patterns mentioned in the paper, such as _insight-seeking_ and _domain-
knowledge-relying_ can be clearly observed in these trajectories. Besides,
several a.k.a. _Aha! moment_ can be observed in the test process.

(a) Target Word: Finish

(b) Target Word: Northest

(c) Target Word: Friend

Figure 5: Examples of player trajectories in Mindle.

  *[mdp]: