ArticlePDF Available

Abstract and Figures

There are diverging operationalizations of insight in experimental research, especially when comparing behavioral and neuroimaging research. The question arises how comparable these types of insight are. Here, we set out (1) to evaluate the usefulness of the matchstick arithmetic task for investigating cognitive and neural processes underlying insight-based problem solving, (2) to determine whether the Aha! Experience is diminished over a multitude of trials, and (3) to compare true (correctly solved), false (incorrectly solved), and induced insights. To this end, we analysed solution rates, response times, strength of the Aha! experience, and event-related potentials (ERPs). Our results showed that the Aha! experience was not weakened over 40 trials, but showed the importance of the time for a solution attempt. True, false, and induced insights differed with regard to Aha! ratings and ERP amplitude −2000 to −1500 ms before the response. Our study underscores the importance of the operationalization of insight.
Content may be subject to copyright.
Full Terms & Conditions of access and use can be found at
https://www.tandfonline.com/action/journalInformation?journalCode=pecp21
Journal of Cognitive Psychology
ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/pecp21
Insight is not always the same: differences
between true, false, and induced insights in the
matchstick arithmetic task
Jasmin M. Kizilirmak, Nora Gallisch, Björn H. Schott & Kristian Folta-Schoofs
To cite this article: Jasmin M. Kizilirmak, Nora Gallisch, Björn H. Schott & Kristian Folta-
Schoofs (2021): Insight is not always the same: differences between true, false, and
induced insights in the matchstick arithmetic task, Journal of Cognitive Psychology, DOI:
10.1080/20445911.2021.1912049
To link to this article: https://doi.org/10.1080/20445911.2021.1912049
© 2021 The Author(s). Published by Informa
UK Limited, trading as Taylor & Francis
Group
View supplementary material
Published online: 18 Apr 2021.
Submit your article to this journal
View related articles
View Crossmark data
Insight is not always the same: dierences between true, false, and
induced insights in the matchstick arithmetic task
Jasmin M. Kizilirmak
a,b
, Nora Gallisch
a
, Björn H. Schott
b,c,d
and Kristian Folta-Schoofs
a
a
Neurodidactics and NeuroLab, Institute for Psychology, University of Hildesheim, Hildesheim, Germany;
b
German Center for
Neurodegenerative Diseases, Göttingen, Germany;
c
Department of Psychiatry and Psychotherapy, University Medicine Göttingen,
Göttingen, Germany;
d
Leibniz Institute for Neurobiology, Magdeburg, Germany
ABSTRACT
There are diverging operationalizations of insight in experimental research, especially
when comparing behavioral and neuroimaging research. The question arises how
comparable these types of insight are. Here, we set out (1) to evaluate the usefulness
of the matchstick arithmetic task for investigating cognitive and neural processes
underlying insight-based problem solving, (2) to determine whether the Aha!
Experience is diminished over a multitude of trials, and (3) to compare true (correctly
solved), false (incorrectly solved), and induced insights. To this end, we analysed
solution rates, response times, strength of the Aha! experience, and event-related
potentials (ERPs). Our results showed that the Aha! experience was not weakened over
40 trials, but showed the importance of the time for a solution attempt. True, false,
and induced insights diered with regard to Aha! ratings and ERP amplitude 2000 to
1500 ms before the response. Our study underscores the importance of the
operationalization of insight.
ARTICLE HISTORY
Received 14 January 2020
Accepted 27 March 2021
KEYWORDS
Problem-solving; matchstick
arithmetic task; insight; EEG;
ERPs
Introduction
When people stumble upon a problem that at rst
seems dicult or even impossible to solve, they
sometimes experience a sudden insight into its sol-
ution. Such insights have been of central interest to
early Gestalt psychologists such as Wolfgang Köhler,
who conducted research on the intelligence of apes
(Köhler, 1917). Problem-solving skills were at the
centre of Köhlers research. Until now, a variety of
operationalizations of insight have been developed,
such as solving problems dened as insight pro-
blems that are thought of as only solvable via
insight (e.g. Metcalfe, 1986), sudden comprehension
after a state of incomprehension (e.g. Auble et al.,
1979), experiencing a feeling of Aha!when
solving a problem correctly (e.g. Bowden &
Jung-Beeman, 2003) or incorrectly (e.g. Danek &
Wiley, 2017), or experiencing a feeling of Aha!
when comprehending the solution in general (self-
solved or revealed by the experimenter) (e.g. Kizilir-
mak, Galvao Gomes da Silva, Imamoglu, &
Richardson-Klavehn, 2016). Over the past 15 years,
most insight researchers seem to have converged
on the operationalisation of insight as a problem
correctly solved by the participant, often with the
concurrent subjective feeling of Aha! (Aziz-Zadeh
et al., 2009; Danek et al., 2013; Danek & Wiley,
2017; Salvi et al., 2016). The denition of the subjec-
tive feeling of Aha! is often based on the four
characteristics summarised by Topolinski and
Reber (2010): suddenness/surprise, a feeling of
ease or relief after the solution is comprehended,
condence regarding the correctness of the sol-
ution, and the experience of positive aect. Please
note that we did not include the subjective feeling
of Aha! as part of the current studys operationaliza-
tion of insight, but chose to assess Aha! strength as a
dependent variable.
In the present study, we were especially inter-
ested in the dierentiation between endogenous
insights (problems solved by the participant) and
induced insights (sudden comprehension of
© 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/
licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not
altered, transformed, or built upon in any way.
CONTACT Jasmin M. Kizilirmak jasmin.kizilirmak@dzne.de
Supplemental data for this article can be accessed https://doi.org/10.1080/20445911.2021.1912049.
JOURNAL OF COGNITIVE PSYCHOLOGY
https://doi.org/10.1080/20445911.2021.1912049
solutions when they were presented). This dieren-
tiation has been an ongoing topic of debate among
insight researchers. Here, we would like to illumi-
nate the neurocognitive basis of this dierentiation.
Moreover, endogenous insights can further be split
into true (correctly solved) and false insights (incor-
rectly solved). In the following, we will use these
terms as introduced here. Until now, most studies
on this topic have only compared two of the three
categories. The present study sought a comparison
between all three with the same paradigm and
participants.
Previous research on the overlaps and dier-
ences of true, false and induced insights showed
that this dierentiation seems warranted. For
example, Danek and colleagues compared true
and false insights with regard to their perceived
aective qualities, as well as their solution
1
rates
(Danek et al., 2014b; Danek & Wiley, 2017). They
found a positive relationship between the occur-
rences of Aha! experiences and the likelihood of a
solution being correct. Moreover, they reported
that the key qualitative components for both true
and false insights were the feeling of pleasure, sud-
denness, and certainty for the solution being
correct, while surprise was generally higher for
false insights, and relief was higher for true insights.
Regarding the dierentiation between endogenous
true insights and induced insights, a study from our
group found that they dier in regard to frequency
of Aha!, the strength of the positive feeling evoked,
as well as in the ability to subsequently recall the
solution later (Kizilirmak, Galvao Gomes da Silva,
et al., 2016; Kizilirmak, Wiegmann, & Richardson-
Klavehn, 2016). Rothmaler et al. found additional
electrophysiological support for a distinction
between true endogenous insights and induced
insights (Rothmaler et al., 2017). Specically, 2000
1500 ms prior to the response indicating a solution
had been found or that the presented solution was
comprehended, alpha power dierences were
observed for solutions with versus without Aha!.
Notably, there was an interaction for endogenous
and induced insights with and without Aha! with
regard to alpha power: When solved, solutions
with Aha! had a higher alpha power than those
without. On the other hand, when not solved, but
comprehended after solution presentation, sol-
utions with Aha! were associated with reduced
alpha power. The authors suggested this eect to
reect dierences related to internal versus external
foci of attention.
As became evident in the study by Rothmaler
and colleagues, neuroscientic methods can help
to gure out the extent to which operationalizations
of insight are actually comparable with regard to
their underlying cognitive and neurophysiological
processes. They are helpful uncovering temporal
dierences of neural processes that are not visible
in behaviour, e.g. electroencephalography (EEG),
as well as dierential recruitment of neuroanatomi-
cal structures, e.g. functional magnetic resonance
imaging (fMRI). Importantly, sometimes, when
behavioural responses do not dier for a certain
comparison, the cognitive and neural processes
behind them still do, and this only becomes
evident with neuroscience methods (e.g. the dier-
ence between high-functioning elderly and young
adults in episodic memory retrieval who behaviour-
ally perform at the same level; see Cabeza et al.,
2002). Such basic neural processing dierences
can even be discovered with inexpensive and
widely available methods such as event-related
potentials (ERPs). One limitation faced by the user
of these methods is the need for a suciently
high signal-to-noise ratio, which in turn means the
corresponding number of trials must be rather
large (Bowden et al., 2005; Jung-Beeman et al.,
2004). The exact number depends on the method,
the size of the true eect, and specic neurophysio-
logical correlate of interest. The most common para-
digm used in neuroscientic studies of insight
problem solving is the Compound Remote Associates
Task (CRAT), designed by Bowden and Jung-
Beeman (2003), based on Mednicks Remote
Associates Task (Mednick, 1962). The original
number of items was 144, but it has already been
translated into dierent languages and the
number of items has been expanded (German,
Chinese, Dutch; e.g. Akbari Chermahini et al., 2012;
Landmann et al., 2014; Qiu et al., 2008). The
CRAT has been used with fMRI and simple BOLD
contrasts between conditions (e.g. Jung-Beeman
et al., 2004; Kizilirmak et al., 2019; Kizilirmak,
Thuerich, Folta-Schoofs, Schott, & Richardson-
Klavehn, 2016; Tik et al., 2018), and EEG methods
including ERPs, frequency, and timefrequency;
analyses (e.g. Kounios et al., 2006; Qiu et al., 2008;
Rothmaler, Nigbur, & Ivanova, 2017; Sandkühler
et al., 2008).
1
Solution rate always refers to relative number of solutions provided. It includes correct and incorrect solutions.
2J. M. KIZILIRMAK ET AL.
While tasks with a large number of trials are
mandatory in EEG and fMRI research, they may
pose a potential problem at the cognitive and
behavioural level, namely, to what extent the
Aha! experience during tasks like the CRAT is still
comparable to the feeling of Aha! that participants
report when solving classical one-trial problems.
Our knowledge on the electrophysiological corre-
lates of insight is largely based on EEG studies
using the CRAT, which, in summary yielded the fol-
lowing key results:
.A burst of gamma activity in response to sol-
utions with Aha! relative to solutions without
Aha!, located at right temporal electrode sites,
beginning approximately 300 ms prior to the
button press indicating that the solution has
been found, and lasting roughly 1 s (Jung-
Beeman et al., 2004).
.An increase in alpha power 1750 to 500 ms
prior to button press in response to correct sol-
utions with versus without Aha! (Jung-Beeman
et al., 2004), or between 2000 and 1500 ms
respectively (Rothmaler et al., 2017).
.When further dierentiating not only between
items solved correctly with (endogenous
insight) vs. without Aha!, but also between
items whose solutions were comprehended
with (induced insight) vs. without Aha! when
shown after an unsuccessful attempt at
problem solving, there is a double dissociation.
While endogenous insights are associated with
a parietal increase in alpha power 2000 and
1500 ms before button press compared to
items solved without Aha!, induced insights are
associated with a decreased alpha power com-
pared with solutions comprehended without
Aha! within the same time range and the same
posterior topographical maximum (Rothmaler
et al., 2017).
.In the 2 s before stimulus onset, power analyses
revealed higher alpha power over temporo-parie-
tal and temporal electrode sites as well as over
central frontal electrode sites, operationalised as
above (Kounios et al., 2006).
Regarding our aim to understand the cognitive
and neural dissociation of true, false, and induced
insights, only Rothmaler et al. (2017) also compared
endogenous (true) and induced insights, whereas
no study has specically assessed the neural under-
pinnings of false compared to true insights. Hence,
our question regarding the triple-dissociation of
true, false, and induced insights has until now only
been partly answered.
Aims of the current study
The aim of the current study was to directly
compare, for the rst time, true (correctly solved),
false (incorrectly solved), and induced insights
(comprehension induced by presenting the solution
after a failed attempt at problem solving) with
regard to behavioural performance (RTs and accu-
racy), Aha! ratings, and also mean ERP amplitudes.
We chose matchstick arithmetic problems for this
endeavour (Knoblich et al., 1999). The stimuli
consist of matchstick gures depicting equations
with Roman numerals. The equations are initially
invalid, but they can be corrected by moving a
single matchstick from one position to another.
The participants task is to nd out which single
matchstick to move where to make the equation
valid (see Figure 1A for examples). An advantage
of this task compared to the CRAT is that there are
multiple ways to solve them. We assumed that the
presence of multiple approaches to a solution
would decrease the likelihood of the Aha! experi-
ence weakening over time. There are mainly three
dierent types of problems (Knoblich et al., 2001)
for which examples are provided in Figure 1A: (1)
Items that can be solved via Serial Position
Change (SPC), that is, by shifting a single matchstick,
such as changing VI into IV, (2) items that can be
solved via Chunk Decomposition (CD), namely by
deconstructing a chunk such as V or X to create,
for example, II (or rather \\), or (3) items that can
be solved via Operator Change (OC), that is, by
changing not a numeral but rather an operator,
for example, by taking a matchstick from an =
(equal sign) to make a (minus), or by taking a
matchstick from one of the numerals to change a
(minus) into a + (plus sign). The items are highly
similar in their appearance, and the visual input
does not change during the problem-solving
stage, in contrast to magic tricks, but comparable
with CRAs. This makes the items also suitable for
EEG measures with high temporal resolution (e.g.
ERPs, timefrequency analysis). For the current
study, we therefore also chose to study ERPs. ERP
analyses are less complex than timefrequency ana-
lyses and if one could already nd a distinction
between dierent insight operationalizations in
such a simple measure, it would be very helpful to
JOURNAL OF COGNITIVE PSYCHOLOGY 3
back up the respective theoretical or cognitive pro-
cessing distinction.
The current study set out to illuminate the fol-
lowing research questions
2
and hypotheses:
(1) Is there a dierence in the mean strength of the
Aha! experiences, as measured with a rating
scale, for comprehending a particular way to
solve a problem for the rst time (rst solved
trial of each equation type), compared to the
mean Aha! experience across many trials
solved via the same method? This question
was motivated by the fact that the Aha! experi-
ence may be diminished over time, due to the
search space being more structured for a
repeated compared to the rst encounter (Der-
bentseva, 2007) and that most other studies
using matchstick equations applied only one
problem per type (e.g. Danek et al., 2016; Kno-
blich et al., 2001).
(2) We expected to replicate the following pattern
for the solution rates of dierent equation
types: SPC > CD > OC (Knoblich et al., 1999,
2001), and the reverse pattern for the corre-
sponding response times.
(3) We further expected the feeling of Aha! to be
stronger the more dicult the problem is (Der-
bentseva, 2007), with problem diculty being
associated with equation type (SPC < CD <
OC). This would also be in line with the
nding that solved items (hence, relatively
easy for the participant) were found to illicit a
lower Aha! than unsolved (relatively dicult
for the participant) presented solutions, while
solutions that were read (no automatic splitting
between subjectively easy and dicult items
Figure 1. Stimulus material and exemplary trial. Panel A depicts one example per equation type for the invalid equation (the
problem) and the valid equation (the solution). Stimuli were exactly presented as depicted. Panel B shows the trial structure.
An equation could be presented for a total of 240 s or 14 s. When no button was pressed (turquoise), a valid solution was
presented. Afterwards, participants were asked to rate the plausibility of the presented solution. When a response was made
(green), the equation remained on display and the participant was instructed to voice the corrected equation. Finally, par-
ticipants were asked to rate their Aha! experience.
2
Please note that this study is mostly exploratory in nature due to limited prior research on these issues.
4J. M. KIZILIRMAK ET AL.
based on which were solved) lay in the middle
(Kizilirmak, Wiegmann, et al., 2016).
(4) As the feeling of Aha! is partly based on the con-
dence regarding the correctness of the solution,
and because Danek and Wiley (2017) reported
that incorrect solutions with Aha! were associ-
ated with a lower condence in the correctness
of the solution, we expected the strength of
the feeling of Aha! to show the following
pattern: false insight < true insight. In this
context, we also sought to assess the strength
of Aha! experiences in the induced insight con-
dition. We expected induced insight to show a
weaker Aha! than true insight, but we could
not make strong predictions regarding whether
it would diverge from false insight in this respect.
(5) We set out to nd an ERP correlate of endogen-
ous (true and false) and induced insights. Our
ERP analyses were exploratory in nature,
because there is little ERP research on insight
problems so far, and especially none with match-
stick arithmetic tasks to base exact hypotheses
on. We explored the following questions:
a. Do endogenous true insights and induced
insights dier with respect to response-
locked ERPs?
b. Are there further dierences between true
(correctly solved) and false insights (incor-
rectly solved), as suggested by behavioural
studies (Danek et al., 2014a; Danek & Wiley,
2017)?
Material and methods
Participants
Thirty-one students of the University of Hildesheim,
mostly psychology undergraduates, participated in
the study. Twenty-eight participants were right-
handed (two were left-handed) and had normal or
corrected-to-normal vision, 28 were female and
three male. Their median age was 21 years (min =
18, max = 38; mean age = 21.6). The two left-
handers were excluded from data analysis, to
avoid any confounding eects of handedness, par-
ticularly regarding the ERP data, and one further
participant had to be excluded from data analysis,
because their behavioural response pattern (no
correct solutions) strongly suggested that they mis-
understood the task instructions. A fourth partici-
pant had to be excluded due to technical
diculties in recording the behavioural responses.
The remaining 27 participants (24 female, 3 male)
had a median age of 21 years (min = 18, max = 38;
mean = 21.9). All participated after providing
written informed consent. Additionally, they were
also informed about their rights according to Euro-
pean Union and German data protection regu-
lations. The local ethics committee of the
University of Hildesheim approved the study.
Stimuli
For the task, we created 48 matchstick equations
that used Roman numerals from 1 to 18 (I to XVIII).
The equations were created as digital drawings
made of matchsticks (see Figure 1). We intentionally
chose varying angles for laying outthe equations,
i.e. the matchsticks were not always at an orien-
tation of 0°, 45°, and 90°, but varied as if they had
been laid out by hand. This was done to make it
easier to realise that e.g. a V could be created
from a I, by just adding another matchstick (I/),
even if it did not look perfectly mirror-symmetrical
(\/). For each equation, one incorrect form and one
correct form were created. All incorrect equations
could be changed into correct ones by moving
just one matchstick to another position. The
stimuli were created using Microsoft PowerPoint
for Windows and GIMP (https://www.gimp.org/).
We created 16 items per solving option, that is, (1)
SPC, (2) CD, and (3) OC. An example item for each
equation type is depicted in Figure 1A. A subset of
the items could be solved in more than one way.
With only numerals under 20, it was impossible to
create only one-way solvable equations to that
amount. Certain combinations of Roman numerals
always allowed for several options. Of all 48 items,
28 were only solvable in one way, 16 items were sol-
vable in two ways, three items were solvable in
three ways. For one item we realised that a graphical
error rendered the item unsolvable, and this item was
therefore excluded from data analysis.A complete list
of all items, primary solutions and potential alterna-
tive solutions can be found in Appendix 1.
3
Which sol-
ution was found how often is also listed for reference.
Design
The following variables were manipulated: time for
solving an item (14, 240 s) and equation type (SPC,
3
The pictures of the items and item solutions will be provided upon request by the rst author.
JOURNAL OF COGNITIVE PSYCHOLOGY 5
CD, OC). Each type of equation comprised 16 items.
Half of all items of each equation type were ran-
domly presented with a long (240 s) and the other
with a short (14 s) duration. These durations were
chosen based on previous solution times reported
by Knoblich and colleagues (Knoblich et al., 1999,
2001), to obtain a similar amount of solved and
unsolved items. To summarise, all participants
were presented with all 48 items (16 per equation
type) and half of the items were presented with a
long and the other half with a short duration (8
per equation type long, 8 short). The following
behavioural data were collected:
.whether items were solved (solved, not solved),
.whether the solution oered was correct (correct,
incorrect),
.response time (RT) for solving an item or compre-
hending a presented solution after timeout, and
.an Aha! rating on a 7-point scale (0 = no aha, 6 =
very strong feeling of aha).
The Aha! rating was measured for both solved
and unsolved items. In case no solution was found
within the respective time limit, participants were
presented with a correct solution and were asked
to rate its plausibility on a 5-point scale, as well as
their feeling of Aha!.
Task and procedure
Before the experiment, participants were informed
about the EEG procedure and what the following
task entailed. After providing written informed
consent, participants were tested for their knowl-
edge of Roman numerals. To this end, they were
seated at a table, and Roman numerals were laid
out one after another with large matchsticks. Partici-
pants were instructed to tell the experimenter the
value as quickly as possible. After singular numerals,
they were also presented with a very simple, but
incorrect equation (II + I = I) they were instructed
to x by moving just one matchstick (solution: _I
+ I = II). This procedure served two purposes: (1) to
detect participants with insucient knowledge
about Roman numerals, and (2) to familiarise them
with the stimulus material and task. None of the
participants appeared to have any trouble recognis-
ing the numeric values of the Roman numerals.
After this brief test and familiarisation, the partici-
pant was tted with an electrode cap and the elec-
trodes were attached to the cap, which included
lowering the impedances below 10 kΩusing elec-
trolyte gel. Participants were seated in a chair
approximately 1 m in front of an LCD display with
a resolution of 1920*1080 pixel, and a refresh rate
of 60 Hz. Stimulus presentation was controlled
with Presentation 20.0 (Neurobehavioral Systems,
Inc., Berkeley, CA, USA). Behavioural data such as
button presses and response times were also
measured using this software and a standard USB
keyboard. During electrode preparation, partici-
pants received written instructions of the task,
which also informed them that sometimes, during
problem solving, they may experience an Aha!
moment. This Aha! experience was described
listing the four criteria named by (Topolinski &
Reber, 2010): suddenness, a feeling of ease, being
convinced of the correctness of the solution, and a
positive emotional response.
During the experiment, participants were pre-
sented with incorrect equations in Roman numerals
that were made of matchsticks. Their task was to
shift only one matchstick to make the equation
valid (see Figure 1B for an exemplary trial). In each
trial, a xation cross was presented for 750
1250 ms (randomly jittered to avoid cognitive prep-
aration before equation onset and to reduce the
amount of rest-related alpha EEG activity). Then an
equation was presented for either 14 s or 240 s.
4
Par-
ticipants were instructed to press the spacebar key
(four ngers of the left hand) as soon as they had
gured out which matchstick to shift where. Once
the button was pressed, the incorrect equation
was still on display with the additional instruction
to voice the corrected equation. After pressing the
spacebar key again, a 7-point colour scale was pre-
sented to rate the degree of their feeling of Aha!
from 0 (no Aha!; RGB white) to 6 (very strong
feeling of Aha!; dark red, i.e. RGB 153,0,0). The
respective part of the scale was chosen via using
the cursor keys to-the-left and to-the-right (using
the index and ring ngers of the right hand) and
by pressing space to conrm. This ended a trial,
and the next trial started.
4
Within this interval, a masking stimulus was presented for the duration of 750 ms at 12 s for the early timeout and at 60 s for the late timeout. This
procedure was included to allow for the analysis of stimulus-locked ERPs shortly before participants solved the item. However, this analysis option
was abandoned in favor of response-locked analyses that seemed more promising (see e.g., Rothmaler et al., 2017). We therefore chose to leave
out this display from the exemplary trial in Figure 1B to simplify it.
6J. M. KIZILIRMAK ET AL.
Whenever participants did not press the space-
bar key before time ran out, a correct solution was
presented. Participants were instructed to press
the spacebar key as soon as they had understood
what had been done to make the equation valid.
This was easy to see, because the shifted matchstick
was replaced by a grey bar at its original location
while it was highlighted with a red outline at its
new location (see Figure 1A). Immediately after-
wards, a 5-point rating scale, ranging from RGB
white over RGB red (5th box: 255, 0, 0) to dark red
(7th box: 153, 0, 0), was presented on which partici-
pants should rate the plausibility of the presented
solution. The same buttons were used as with the
Aha! rating scale. After the plausibility rating, a 7-
point Aha! rating scale was presented, just as with
solved equations. This was done to enable compari-
sons of endogenous (solution found by participant)
as well as induced (solution presented) Aha!
experiences.
EEG recording and preprocessing
EEG was recorded using a Brain Amp DC amplier
and 32 ActiCap active cup electrodes with Ag/
AgCl lining (Brain Products, Gilching, Germany),
arranged according to the extended 1020 system
(Jasper, 1958). The following electrode positions
were used: Fp1, Fp2, F7, F3, Fz, F4, F8, FC5, FC1,
FC2, FC6, T7, C3, Cz, C4, T8, TP9, CP5, CP1, CP2,
CP6, TP10, P7, P3, Pz, P4, P8, O1, Oz, O2. Two
additional electrodes were used to measure the
horizontal and vertical electrooculogram. One was
positioned below the right eye (later re-referenced
to Fp2) and the other at the outer right canthus.
Impedance was kept below 10 kΩfor all electrodes.
Data were recorded using BrainVision Recorder 1.21
software (Brain Products). FCz was used as reference
electrode during recording, and ground was located
at AFz.
For preprocessing, the BrainVision Analyzer
(Brain Products, Gilching, Germany), version 2.2.0,
was used. The following preprocessing steps were
applied: Re-referencing to averaged mastoids (re-
including FCz as a normal channel), applying high-
pass (0.1 Hz) and low-pass lters (35 Hz), plus a
50 Hz notch lter (to account for data being col-
lected in a non-shielded room), and applying an
Independent Component Analysis for ocular artifact
correction (Ocular Correction ICA). The ICA was used
to identify independent components (ICs) explain-
ing the variance of blinks, vertical, and horizontal
eye-movements. For each participant, at least one
IC was excluded for blinks/vertical eye-movements,
plus an additional IC for horizontal eye-movements,
in case the component was unmistakable. By visual
inspection, it was checked whether only the respect-
ive artifact was removed from the signal, and not
additional noise introduced. Then segmentation
was carried out. Based on the focus of our work,
i.e. comparing endogenous and induced insights,
and especially true and false endogenous insights,
and based on the behavioural results, items were
split into true, false, and induced insights. Segments
were chosen from time windows around the
response (button press) indicating that either the
response was found (true and false insights) or
that the presented solution had been understood
(induced insights). Segment length was 2000 ms
to 100 ms, with button press as time point 0 ms.
After segmentation, semi-automated artifact correc-
tion was performed (the following parameters were
applied that never resulted in false positives:
maximum allowed voltage step: 50 µV/ms, min/
max allowed amplitude +/200 µV, lowest allowed
activity in intervals: 0.5 µV within 100 ms). During
this step, segments including the masking stimulus
were excluded from analysis (9 segments). The last
100 ms before button press were used to perform
the baseline correction necessary for the compu-
tation of ERPs. This baseline was chosen, because
it can be assumed that motor processing is what
is happening there, as the decision making
process is already over (Roskies, 2010). Because all
participants pressed the same button under all con-
ditions (i.e. space), it can be assumed that the
process of coding and initiating the motor response
should be highly similar if not the same. Moreover,
in the most classical studies which use response-
locked ERPs, namely those on the readiness poten-
tial (Bereitschaftspotential), a 2000msor100
0 ms baseline is often used for that reason (e.g.
Jentzsch & Leuthold, 2002). Such a baseline has
also been used by other problem-solving (Paynter
et al., 2010) and insight problem-solving ERP
research (Lang et al., 2006). A pre-stimulus baseline
would be extremely inadequate as the problem-
solving process sometimes took a few seconds
and sometimes minutes, implying enormous varia-
bility in when comprehension (or insight) actually
happened. A post-response deadline would also
not make much sense, because participants may
engage in response-evaluation processing which
may dier between conditions (which is interesting
JOURNAL OF COGNITIVE PSYCHOLOGY 7
on its own, but not the current focus). For further
information, please see the Supplementary
Methods section. After baseline correction, the seg-
ments were averaged per insight condition for each
participant.
Splitting the data into more conditions would
have resulted in an insucient number of trials for
data analysis. Nevertheless, multiple participants
ended up having less than ve trials in at least
one condition. The specic conditions with low
numbers of trials varied across participants, depend-
ing on whether participants had a stronger incli-
nation towards responding when unsure or
responding only when they were completely sure
their response was correct. In this context, it
should be pointed out that all participants were
instructed to only press the button when they
were sure that they could voice the valid equation.
Statistical analysis
All statistical analyses were performed using SPSS
version 26 (IBM, Armonk, NY, USA). Considering
that participants had low numbers of trials in
dierent conditions of the experiment (see above),
not all participants contributed to each cell of a fac-
torial model and it was therefore likely that partici-
pants showed dierent patterns across conditions.
To account for this pronounced variability, all data
were analysed using Linear Mixed Models (LMM,
also known as hierarchical linear model), including
Participant as a random-eects factor to model
the interdependence of observations. Thereby, we
were able to include data from participants with
empty cells, which would not be possible in
repeated-measures ANOVAs. All parameter choices
are reported in the results section. The signicance
level was set to p< .05, and pvalues of .05 < p<
.10 were reported as trends. Regarding the assump-
tions for LMMs, these are normality of residuals, lin-
earity, and variance homogeneity. The variance
homogeneity assumption does not apply as we do
not compare groups (no between-subjects manipu-
lations). With regard to the normality of the
residuals, this was either given or if not, there was
at least no bimodal distribution or otherwise that
would have severely biased the results (Schielzeth
et al., 2020).
Response-locked ERPs were analysed using bin-
wise LMMs. We are aware that the number of seg-
ments per insight condition was quite low to dis-
cover any but relatively large amplitude
dierences. Nevertheless, we chose to include this
measure for exploratory purposes. All bins were of
250 ms length. Bins from 2000 ms to 250 ms
before the response (indication of wanting to
voice the solution for true and false insight, or
having comprehended the presented solution for
induced insight) were analysed. The bin just
before the response was assumed to mainly reect
preparation of the motor response and thus being
unspecic with respect to the cognitive processes
of interest. It was therefore not statistically analysed.
Moreover, it contained the interval used for baseline
correction, which was especially chosen for that
reason. To make the model feasible, we included
only nine electrodes with good coverage of the
head (F7, Fz, F8, T7, Cz, T8, P7, Pz, P8; located left
frontal, middle frontal, right frontal, left temporal,
middle central, right temporal, left parietal, middle
parietal, right parietal). All LMMs were computed
with xed-factors Electrode (F7, Fz, F8, T7, Cz, T8,
P7, Pz, P8) and Insight (true, false, induced), as well
as random-eects factor Participant (25 levels).
EEG data sets of two participants were unfortunately
lost due to technical problems. Covariance of
repeated measures was estimated using Compound
Symmetry, because it can be assumed that the
variability in measurements should be relatively
homogeneous.
Results
Behavioural results
Please note that item number 39 (equation: VIII-X =
III, solution template: VIII = X-III, type: OC) had to be
excluded from data analysis, because the template
solution was invalid for the item due to an error in
its graphical presentation (it should have been VII-
X = III solution: VII = X-III).
Item analysis
Of all 47 items, a mean of 42.4% was solved. The
relative number of items solved according to our
rst solution template, on which the categorisation
of equations into SPC, CD, and OC was based, was
34.3% (of all 47 items). Since this was the vast
majority (80.9% of all correctly solved items), our
categorisation appears appropriate. A minority of
7.3% (of all correctly solved items) was solved
according to the rst alternative solution, and
1.3% was solved according to a second alternative.
Mean Aha! Rating for all items was 3.8. The item
8J. M. KIZILIRMAK ET AL.
with lowest mean Aha! Rating had a rating of 3.26
(item 32, VI = IX + III VI = III + III, solution type:
CD), and the one with the highest Aha! Rating had
a mean rating of 4.42 (item 47, I = X + X I = X-IX,
solution type: OC). Note that the 7-point rating
scale was from 0 (no aha) to 6 (very intense
feeling of Aha!).
We further chose to test the potential correlation
between the solution frequency of items as an oper-
ationalisation of item diculty and mean Aha!
rating. The one-tailed Spearman correlation was sig-
nicant [r= -.298, p= .021, N= 47 items]. Please refer
to Appendix 1 for details and a complete list of all
items and solutions.
Solution rate
Solution rates were tested with an LMM with xed-
eects factors EQ_type {SPC, CD, OC} and Timeout
{14, 240 s}, and random-eects factor Participant
{27 levels}. We chose the full-factorial option,
reduced maximum likelihood estimation (REML),
and Satterthwaite approximation. Diagonal was
chosen to estimate the covariance type for xed
eects, and identity for the random-eects factor.
As can be seen in Figure 2A, the equation types
roughly showed the pattern CD (mean = .36, SE
= .04) < OC (.43, .04) < SPC (.48, .05), with long pres-
entation durations leading to higher solutions rates
for all conditions (14 s timeout: .24, SE = .04; 240 s
timeout: .61, .04). There was a signicant main
eect for EQ_type [F(2, 68.61) = 5.51, p= .006], and
a signicant main eect for Timeout [F(1, 104.65)
= 143.19, p< .001], but no interaction [F(2, 68.61) =
0.31, p= .734].
When further taking into account whether a
specic equation type appeared for the rst time
(for each of the two Timeouts), and adding First_-
time (yes, no) as an additional xed-eects factor,
this factor showed neither main eect [F(1,
190.19) = 2.21, p= .139] nor interactions with either
EQ_type, nor Timeout, nor both [all p> .55](Figure
2B). Overall, mean solution rates were slightly
lower for items of an EQ_type that appeared for
the rst time per Timeout (mean = .37, SE = .05)
compared to the 14 times afterwards (.43, .04). The
model was weaker than the previous one (more
complex without explaining considerably more var-
iance), as indicated by the Bayesian Information Cri-
terion (BIC), which rose from 20.95251.16.
Response times
Response times or rather solution times for the
dierent equation types and timeouts were com-
pared for correctly and incorrectly solved items.
Subject (28 levels) was included as a random-
eects factor, and EQ_type (SPC, CD, OC), Timeout
(14 s, 240 s), and Solution (correct, incorrect) as
xed-eects factors. All other aspects were the
same as above.
For the xed-eects factors, we found the follow-
ing: A signicant main eect for EQ_type [F(2,
54.00) = 4.37, p= .017], a signicant main eect for
Timeout [F(1, 88.12) = 156.31, p< .001], a marginal
main eect for Solution [F(1, 88.67) = 3.33, p
= .071], and a signicant interaction between
EQ_type and Timeout [F(2, 54.00) = 5.28, p= .008].
There was no interaction between Timeout and Sol-
ution [F(2, 88.13) = 2.54, p= .115]. All other potential
interactions between any two or all three factors
were tested, but remained far from signicance [p
> .93]. The pattern for mean RTs was CD (mean =
28.1 s, SE = 2.1 s) > OC (22.5 s, 1.9 s) > SPC (19.3 s,
2.1 s). Furthermore, as depicted in Figure 3B, when
given more time (240 s), CD was associated with
the longest mean RTs (48.3 s, 4.2 s) compared with
SPC (30.1 s, 4.2 s) and OC (36.0 s, 3.8 s) items,
whereas when given only 14 s (Figure 3A), OC
items showed the longest RTs (9.0 s, 0.4 s) compared
with SPC (8.5 s, 0.4 s) and CD (7.8 s, 0.5 s). Lastly, RTs
were generally somewhat longer for incorrectly
solved items (25.5 s, 2.1 s) as compared to correctly
solved ones (21.1 s, 1.2 s), a typical eect reecting
participantshigher uncertainty for incorrect sol-
utions (Kellogg, 1931; Pike, 1968). This dierence
can be seen by comparing blue (incorrect solutions)
and red (correct solutions) boxplots in Figure 3.
Aha! rating
To test our hypothesis regarding the Aha! experi-
ence associated with true, false and induced
Figure 2. Solution rate by equation type and timeout.
JOURNAL OF COGNITIVE PSYCHOLOGY 9
insights, we compared the mean Aha! ratings of cor-
rectly solved items (true insight), incorrectly solved
items (false insight), and presented solutions after
timeout (induced insight). We computed an LMM
with random-eects factor Subject and xed-
eects factor Insight (true, false, induced). Consider-
ing the potential inuence of EQ_type and Timeout,
we further added these as xed-eects factors.
Diagonal was chosen to estimate the covariance
type for xed eects, and identity for the random-
eects factor. The factor EQ_type, which we
expected to reect item diculty (SPC < CD < OC;
Knoblich et al., 1999,2001), however, did not
explain a sucient amount of variance (neither
main eect nor interactions with this factor
reached signicance, all p> .32). Hence, we recom-
puted the model without EQ_type, leading to an
improved BIC (396 vs. 1027). (We provide more
information on the distribution of Aha! rating cat-
egories per equation type and participant in Sup-
plementary Figure S1.)
For exploratory purposes, and because diculty
may also be operationalised via the solution rate
(the more dicult, the lower) or mean RT (the
more dicult, the higher), we also tested for poten-
tial correlations between mean Aha! ratings and sol-
ution times, and between mean Aha! ratings and
mean RT. The one-tailed Spearman correlation
between mean Aha! rating and solution rate
showed a trend towards signicance [r
S
= .307, p
= .059, N = 27], indicating that higher solution
rates went along with higher Aha! ratings (see Sup-
plementary Figure S2), while the correlation
between mean Aha! rating and mean RT (of
correct solutions) did not approach signicance [r
S
= .064, p= .376, N = 27] (see Supplementary Figure
S3).
There was no eect of Timeout [F(1, 25.18) = 2.76,
p= .109], but a main eect of Insight [F(2, 22.56) =
3.72, p= .040]. The interaction between Timeout
and Insight was not signicant [F(2, 22.35) = 2.01,
p= .158]. As can be seen in Figure 4, insights were
rated lowest for false insights (mean = 3.6, SE =
0.3), and similarly high for true (4.1, 0.2) and
induced insights (4.1, 0.3).
Notably, there was also a subgroup of partici-
pants, who did rate almost in the opposite direction,
i.e. six subjects rated their feeling of Aha! highest for
false insights on average (see Figure 5A). From the
comments in the post-experimental questionnaire
regarding the question of how Aha! experiences
felt when solutions were presented or self-gener-
ated, it seems that there were two groups of partici-
pants: those who were relieved about the revelation
of the solution (strong feeling of Aha!) and those
who were upset (lower feeling of Aha!). However,
self-reports after the experiment did not consist-
ently correspond to participantsactual aha
ratings. The most consistent eect of Timeout was
observed for induced insights: The more time
Figure 3. Boxplots of response times (s) by equation type,
correctness and timeout. Panel A shows the data for a
timeout after 14 s, panel B for a timeout after 240 s.
Figure 4. Aha! ratings according to insight type and
timeout. Data are presented as split per individual in
Figure 5A.
10 J. M. KIZILIRMAK ET AL.
participants had to think about the solution before
its presentation, the higher their Aha! ratings (with
the exception of one participant, who unfortunately
did not ll out the comment about the dierent
emotional responses regarding the Aha!
experiences).
When recomputing the aforementioned model
with Insight (true, false, induced) and First_time
(yes, no), excluding Timeout, which did not contrib-
ute signicantly to explaining the data, the model
estimate BIC was raised from 418 to 478, i.e. the
model was weaker. There was a weak trend-wise
eect of First_time [F(1, 65.42) = 2.92, p= .092],
and no interaction with Insight. Insight was again
signicant [F(2, 61.19) = 8.46, p= .001]. The mean
Aha! Rating was slightly lower for the rst time an
equation type appeared (mean = 3.5, SE = 0.2) com-
pared to afterwards (3.8, 0.1). However, when
looking at the curves of individual participants, it
becomes evident that the majority of participants
showed no change between the rst time and after-
wards. Only seven participants showed a consider-
able increase (!) of their Aha! ratings from the rst
time to afterwards (see Figure 5B). This eect is in
the opposite direction as expected, that is, no
diminishing of the feeling of Aha!, but an
enhancement.
EEG results: event-related potentials
In the following, only those eects that reached sig-
nicance (p< .05) will be described. The random-
eects parameter was signicant for all bins [Wald
Z= 3.553.56, p< .001]. For a comprehensive list of
all statistical results for the xed eects, including
also insignicant eects, please refer to Table 1.
The factor Electrode yielded signicant eects for
all bins, suggesting that overall amplitude diered
depending on electrode site.
Between 2000 ms and 1500 ms before the
response, there was a signicant main eect of
Insight. This main eect seemed to fade out
between 1500 ms and 1250 ms, where it was
still marginal. Interestingly, as can be seen in
Figure 6, true and induced insights had a lower
amplitude dierence compared to true and false
insights. Please note that, because there is no sig-
nicant interaction with Electrode in this temporal
bin, this means that the eect of Insight shows the
same direction at all electrode sites. Between
1000 to 750 ms before the response, a marginal
interaction between Insight x Electrode was
observed. For exploratory purposes, we split this
bin into two smaller bins (1000 to 875 ms,
875 to 750 ms) and computed the LMMs again.
The analysis revealed that the marginal eect origi-
nated from a signicant interaction between
1000 ms and 875 ms [Insight x Electrode: F
(16,612) = 1.68, p= .047] while it was non-signicant
for 875 ms to 750 ms [F(16,612) = 1.37, p= .153].
From visual inspection (see Figure 6), it appears that
the interaction may be due to the eect of Insight
having dierent patterns depending on location:
At left frontal electrodes (see F7) true and false
insights are mainly overlapping, diering consider-
ably from induced insight which shows a large
Figure 5. Aha! ratings according to insight type and time of occurrence. Panel A depicts the subject-wise mean Aha! rating
split by Insight (true, false, induced). Panel B shows the dierence between mean participant-wise Aha! ratings for the rst
instance of any equation type per timeout in comparison with the mean of all instances afterwards.
JOURNAL OF COGNITIVE PSYCHOLOGY 11
negative deection. In contrast, at right temporal to
posterior electrodes (see T8, P8), false insight diers
more from true and induced insights, showing a
relatively more positive deection. Please note
that FDR-corrected p-values (using the Benjamini-
Hochberg procedure) would be .094 and .153,
respectively, and thus not signicant. However,
this exploratory post-hoc analysis suggests that it
may be worth to look further into this temporal
window in follow-up studies with a higher number
of trials.
Discussion
The current study set out (1) to evaluate the useful-
ness of matchstick arithmetic items for the
Table 1. List of all results regarding the xed-eects factors.
Bin Fixed eect Numerator df Denominator df Fp
500 ms to 250 ms Insight 2 612 1.07 .343
Electrode 8 612 14.93 .000
Insight x Electrode 16 612 0.83 .652
750 ms to 500 ms Insight 2 612 1.60 .204
Electrode 8 612 21.63 .000
Insight x Electrode 16 612 0.62 .870
1000 ms to 750 ms Insight 2 612 0.91 .402
Electrode 8 612 17.90 .000
Insight x Electrode 16 612 1.52 .087
1250 ms to 1000 ms Insight 2 612 1.90 .150
Electrode 8 612 11.58 .000
Insight x Electrode 16 612 0.60 .887
1500 ms to 1250 ms Insight 2 612 2.35 .097
Electrode 8 612 7.58 .000
Insight x Electrode 16 612 0.89 .578
1750 ms to 1500 ms Insight 2 612 3.56 .029
Electrode 8 612 3.92 .000
Insight x Electrode 16 612 0.39 .986
2000 ms to 1750 ms Insight 2 612 3.56 .004
Electrode 8 612 2.15 .029
Insight x Electrode 16 612 1.08 .375
Note. Signicant eects are highlighted in italics.
Figure 6. Event-related potential data for true, false, and induced insights. Panel A depicts weighted grand averages
(according to how many segments were contributed by each participant) at the nine electrode sites included in the stat-
istical analysis. Data were 12 Hz low-pass ltered for visualisation only. Negative is up. The right panels show topographical
dierences between true and false, as well as true and induced insight for the main eect of Insight in the 1750 to
1500 ms bin (B) and 2000 to 1750ms bin (C).
12 J. M. KIZILIRMAK ET AL.
investigation of the cognitive and neural processes
underlying insight problem solving via insight, (2)
to determine whether the Aha! experience is dimin-
ished over a multitude of trials, and (3) to compare
true, false, and induced insights with regard to
potential neural and cognitive dierences.
First encounters of a problem type are only
marginally dierent to multiple encounters
Most previous studies had only employed match-
stick arithmetic items for behavioural and eye-track-
ing studies (Danek et al., 2016; Knoblich et al., 1999,
2001), using one item per equation type (i.e. SPC,
CD, and OC), or using more items, but without eval-
uating the question whether Aha! ratings changed
over time (Derbentseva, 2007). Our rst interest
was therefore, whether the processing of an item
type encountered for the rst time diered from
the processing of subsequent encounters with the
same item type. We found marginal dierences for
solution rates, which increased slightly, indicating
a small learning eect. Surprisingly, the Aha! rating
increased slightly from the rst encounter of each
equation type to the encounters afterwards. It
should be noted, though, that this eect was prob-
ably driven by seven of the 26 participants, pointing
to individual dierences in Aha! rating behaviour.
We tentatively suggest that certain personality
traits might underlie such inter-individual variability
of Aha! ratings. It would, for example, be conceiva-
ble that participants with a high need for cognition
(Furnham & Thorne, 2013) might have felt stronger
positive emotional responses when their success
rate increased. We did not assess personality traits
or other indices of individual dierences in the
present study, but our results indicate that future
investigations should be directed at the inter-indi-
vidual variability of insight experiences. Individual
dierences in insight problem solving are currently
mainly supported for cognitive abilities like spatial
or verbal working memory, uid intelligence, etc.
(see Chu & MacGregor, 2011, for a review). Our
results raise the possibility that there may be pro-
cessing dierences beyond cognitive ability. While
the increase of Aha! ratings over time in a subgroup
cannot be conclusively interpreted in the context of
the current study, our results allow us to conclude
that there seems to be little if any risk of the Aha!
experience decreasing considerably over time with
this stimulus material and multiple encounters (42,
14 encounters per equation type).
The general type of solution is not as
important as the particular way of rectifying it
Regarding the dierent equation types (or rather
solution types), we unexpectedly found a dierent
pattern than the one expected based on previous
studies employing matchstick items (Knoblich
et al., 1999,2001). Although items that could be
solved via shifting a singular matchstick (SPC)
were the easiest type as evident in their high sol-
ution rates, the most dicult type of equations
turned out to be those solved by CD (V or X), with
OC being of medium diculty. Importantly, this
pattern of diculty was independent of whether
the specic type of equation was solved for the
rst time or the many times afterwards.
For solution rates, this pattern (diculty: SPC <
OC < CD) was independent of the time participants
had for a solution attempt. Naturally, for response
times, the timeout did matter. When participants
were given more time (240 s), the pattern reported
above was found. However, when given only 14 s,
response times showed the following unexpected
pattern: CD < SPC < OC. This could potentially
have to do with the nature of the particular CD
items that drove the mean RT, i.e. the CD items
solved most often. When looking at the ve CD
items solved most often (see Appendix 1), it
becomes obvious that when taking apart the
chunk, the matchsticks that made up the chunk (X
or V) could stay next to each other, i.e. V II, IV
III, X II, and so on. In other words, when
using only very few matchstick arithmetic items,
like one item per equation type, it is extremely
important to consider the particular way(s) an
item can be solved, instead of merely considering
the equation type alone. We thus suggest that the
diverging pattern found by Knoblich and col-
leagues, who employed only one item per type,
could be due to the particular equations chosen
to represent each type. Moreover, the item cate-
gorised as OC (B: III = III + III III = III = III; Knoblich
et al., 2001) could also potentially be solved
without changing an operator by chunk compo-
sition (VI = III + III).
The strength of the aha! experience is
independent of equation type
As for our hypothesis regarding the dependence of
the Aha! rating on item diculty, there was no such
eect, at least when assuming a dependence
JOURNAL OF COGNITIVE PSYCHOLOGY 13
between the equation type and diculty, neither in
the previously expected hierarchy (SPC < CD < OC)
nor the observed one (SPC < OC < CD). There was,
however, a weak positive correlation between
mean Aha! rating and solution rate, which showed
the opposite pattern to the hypothesised relation-
ship: higher Aha! ratings for easier items, that is,
items solved more often. Thus, the strength of the
Aha! experience appears to be independent of
equation type and equation type does not reect
item diculty suciently well.
Our result is at odds with the results reported by
Derbentseva (2007) who, also for matchstick arith-
metic tasks, reported a strong dependence
between the intensity of an insight and the
diculty to solve it, operationalised as the degree
of restructuring necessary. The dierent ndings
could, however, be solely explained by the
diering operationalizations of diculty and
insight. Insight was dichotomous, i.e. either there
was an Aha! (lightbulb ashing) experience or it
was absent, and diculty was determined by a
rating of the diculty level on a 10-point rating
scale when raters saw the solution and its problem
at the same time. A follow-up study to ours could
collect data on the diculty of items corresponding
to Derbentseva and measure Aha! strength also
with a 10-point rating scale to see whether a posi-
tive relationship between diculty and Aha! could
be replicated this way. That aside, our participants
might have been biased, as our instruction only
explicitly stated that feelings of Aha! may some-
times occur. This statement does entail that they
do not occur at other times, but that was implicit.
Therefore, participants responses may have been
biased towards Aha!.
Dierences between true, false, and induced
insights
Turning our focus on the dierentiation between
true, false, and induced insights, operationalised as
correct solutions, incorrect solutions, and solutions
presented after a failed attempt at problem
solving, our results suggest that participants did
indeed perceive a dierence between false insights
(mean = 3.6) as compared with true and induced
insights (both mean = 4.1), because their mean
Aha! ratings were lower. The higher Aha! ratings
for true as compared to false insights are in line
with ndings reported by Danek and Wiley (2017).
Our results lend further support to Daneks and
Salvis(2018) notion that insight processing diers
considerably for correct (true insight) and incorrect
(false insight) solutions, while also adding infor-
mation about the relationship between presented
solutions and Aha! ratings.
Due to the relatively low number of items per
condition, we could, unfortunately not split the
electrophysiological data as a function of Insight
(true, false, induced) and Timeout (14, 240 s) at
the same time. We therefore split the data only for
true, false, and induced insights. Here, we found
that this factor had a main eect on the overall
amplitude of the ERP between 2000 ms and
1500 ms before response button press. Interest-
ingly, overall amplitudes diered less for true and
induced insights compared to true and false
insights. In a phenomenological study of insight,
Danek and colleagues found that the main qualitat-
ive dierences between true and false insights are
that true insights are more strongly associated
with relief, while for false insights the surprise com-
ponent is more dominant (Danek et al., 2014a;
Danek & Wiley, 2017). It may be that the relief com-
ponent is similarly relevant for induced insights, as
in our study the solution was only presented after
a failed attempt at problem-solving. Moreover, par-
ticipants may be similarly convinced about the cor-
rectness of the solution for true and induced
insights, while they are less condent about their
false insights. Further qualitative studies could illu-
minate this aspect. In a very recent study, Cui and
colleagues also used response-locked ERPs in
study on learning via insight using the CRAT (Cui
et al., 2020). They incorporated a binary Aha/no
Aha decision for each item and found dierences
between ERPs 800 ms to 400 ms before the
response for items solved correctly with Aha! com-
pared to those without. Importantly, this dierence
was found in the absence of behavioural dierences
(neither in RTs nor in solution rates). Their study
adds support to our proposition that response-
locked ERPs can be especially useful for the investi-
gation of insight(-like) processing.
Until recently, there were no other ERP studies on
insight that analysed response-locked ERPs, but
instead, previous studies ERPs on insight-based
problem solving, employed stimulus-locked
approaches (Leikin et al., 2016; Qiu et al., 2008;
Shen et al., 2013). On the one hand, because the sol-
ution times diered considerably, we refrained from
this type of ERP analysis, as we could not exclude
the possibility that dierences could be solely
14 J. M. KIZILIRMAK ET AL.
explained by dierences in the timing of the cogni-
tive processes rather than the processes themselves.
On the other hand, since participants were
instructed to press the button as soon as they had
solved an equation or comprehended a presented
solution, the insight was highly likely to have
occurred within the two seconds before button
press, but earlier than 200 ms before button press,
which is the approximate time to compute and
initiate the motor response. Therefore, we are
condent that a response-locked analysis was
more appropriate in our study. However, in a
recent EEG study that employed Wavelet analysis
to analyse the timefrequency dierences
between items solved correctly with a subjective
Aha! experience (referred to as insight condition)
versus without Aha! (referred to as analysis con-
dition), Oh et al. (2020) report dierences in the
gamma range 142 ms to 79 ms before button
press, i.e., the time window of our baseline correc-
tion. Although their conditions do not correspond
to ours and we applied a 35 Hz low-pass lter, and
gamma should therefore be excluded from our
ERP measures, their study could indicate that cogni-
tive and/or aective processing dierences may still
have taken place in the 100 ms before the response.
This indicates a potential limitation of the chosen
baseline.
When looking at response-locked oscillation
data, Rothmaler and colleagues also found dier-
ences within a similar time interval as we did, only
for alpha power (as estimated via a Wavelet
decomposition). They proposed that the alpha
increase in relation to endogenous true insight
may reect an increased shift from the visually pre-
sented information on the screen to internally rep-
resented information, whereas the alpha decrease
in response to induced insight could reect a stron-
ger external focus of attention on the presented sol-
ution (Rothmaler et al., 2017). It would be
interesting to see whether the ERP dierences we
found for true endogenous, false endogenous, and
induced insights can also be attributed to the
alpha range. However, this remains to be tested in
future studies.
Conclusion
The matchstick arithmetic task seems a well-suited
task for the cognitive and neuroscientic investi-
gation of insight problem solving. No decrease of
the strength of the Aha! experience could be
observed for the rst as compared to all following
encounters of the dierent equation types. Other-
wise, our study showed the importance of taking
into account that the time a problem solver has
for a solution attempt has a considerable impact
not only on the solution rate, but also on the Aha!
rating itself. Lastly, our behavioural and electro-
physiological data show that it is important to dier-
entiate between endogenous true (correct
solutions) and false insights (incorrect solutions),
as well as induced insights (presented solutions
after failed problem-solving attempt).
Acknowledgements
This study was enabled by the local research funds
assigned to K. F.-S. by the University of Hildesheim.
Data availability statement
All data used for the above reported analyses have been
made available as SPSS.sav les at the Open Science Fra-
mework under doi:10.17605/OSF.IO/C6PX9 or https://osf.
io/c6px9/, shared under CC BY-NC-SA license. In case of
interest in the raw les (behavioural logles from Presen-
tation in.txt format, or raw.eeg,.vmrk,.hdr les from Brain-
Vision Recorder), these data will be made available upon
reasonable request by the rst author. There is sup-
plementary information available in a separate PDF le.
Disclosure statement
No potential conict of interest was reported by the
author(s).
References
Akbari Chermahini, S., Hickendor, M., & Hommel, B.
(2012). Development and validity of a Dutch version
of the remote associates task: An item-response
theory approach. Thinking Skills and Creativity,7(3),
177186. https://doi.org/10.1016/j.tsc.2012.02.003
Auble, P. M., Franks, J. J., & Soraci, S. A. (1979). Eort
toward comprehension: Elaboration or aha?Memory
& Cognition,7(6), 426434. https://doi.org/10.3758/
BF03198259
Aziz-Zadeh, L., Kaplan, J. T., & Iacoboni, M. (2009). Aha!:
The neural correlates of verbal insight solutions.
Human Brain Mapping,30(3), 908916. https://doi.org/
10.1002/hbm.20554
Bowden, E. M., & Jung-Beeman, M. (2003). Normative data
for 144 compound remote associate problems.
Behavior Research Methods, Instruments, & Computers,
35(4), 634639. https://doi.org/10.3758/BF03195543
Bowden, E. M., Jung-Beeman, M., Fleck, J., & Kounios, J.
(2005). New approaches to demystifying insight.
JOURNAL OF COGNITIVE PSYCHOLOGY 15
Trends in Cognitive Sciences,9(7), 322328. https://doi.
org/10.1016/j.tics.2005.05.012
Cabeza, R., Anderson, N. D., Locantore, J. K., & McIntosh, A.
R. (2002). Aging gracefully: Compensatory brain activity
in high-performing older adults. NeuroImage,17(3),
13941402. https://doi.org/10.1006/nimg.2002.1280
Chu, Y., & MacGregor, J. N. J. (2011). Human performance
on insight problem solving: A review. The Journal of
Problem Solving,3(2), 119150. https://doi.org/10.
7771/1932-6246.1094
Cui, C., Zhang, K., Du, X. m., Sun, X., & Luo, J. (2020). Event-
related potentials support the mnemonic eect of
spontaneous insight solution. Psychological Research,
2017.https://doi.org/10.1007/s00426-020-01421-1
Danek, A. H., Fraps, T., von Müller, A., Grothe, B., & Öllinger,
M. (2013). Aha! experiences leave a mark: Facilitated
recall of insight solutions. Psychological Research,77
(5), 659669. https://doi.org/10.1007/s00426-012-
0454-8
Danek, A. H., Fraps, T., von Müller, A., Grothe, B., & Öllinger,
M. (2014a). Its a kind of magic - what self-reports can
reveal about the phenomenology of insight problem
solving. Frontiers in Psychology,5(December), 111.
https://doi.org/10.3389/fpsyg.2014.01408
Danek, A. H., Fraps, T., von Müller, A., Grothe, B., & Öllinger,
M. (2014b). Working wonders? Investigating insight
with magic tricks. Cognition,130(2), 174185. https://
doi.org/10.1016/j.cognition.2013.11.003
Danek, A. H., & Salvi, C. (2018). Moment of truth: Why Aha!
experiences are correct. The Journal of Creative
Behavior,54, 484486. https://doi.org/10.1002/jocb.380
Danek, A. H., & Wiley, J. (2017). What about false insights?
Deconstructing the Aha! experience along Its multiple
dimensions for correct and incorrect solutions separ-
ately. Frontiers in Psychology,7(JAN), 114. https://doi.
org/10.3389/fpsyg.2016.02077
Danek, A. H., Wiley, J., & Öllinger, M. (2016). Solving classi-
cal insight problems without Aha! experience: 9 Dot, 8
coin, and matchstick arithmetic problems. Journal of
Problem Solving,9(April), 4757. https://doi.org/10.
7771/1932-6246.1183
Derbentseva, N. (2007). The intensity of the insight experi-
ence in problem solving: Structural and dynamic proper-
ties. University of Waterloo.
Furnham, A., & Thorne, J. D. (2013). Need for cognition.
Journal of Individual Dierences,34(4), 230240.
https://doi.org/10.1027/1614-0001/a000119
Jasper, H. H. (1958). The ten-twenty electrode system of
the international federation. Electroencephalography
and Clinical Neurophysiology,10(2), 370375. https://
doi.org/10.1016/0013-4694(58)90053-1
Jentzsch, I., & Leuthold, H. (2002). Advance movement
preparation of eye, foot, and hand: A comparative
study using movement-related brain potentials.
Cognitive Brain Research,14(2), 201217. https://doi.
org/10.1016/S0926-6410(02)00107-6
Jung-Beeman, M., Bowden, E. M., Haberman, J., Frymiare,
J. L., Arambel-Liu, S., Greenblatt, R., Reber, P. J., &
Kounios, J. (2004). Neural activity when people solve
verbal problems with insight. PLoS Biology,2(4), E97.
https://doi.org/10.1371/journal.pbio.0020097
Kellogg, W. N. (1931). The time of judgment in psycho-
metric measures. The American Journal of Psychology,
43(1), 65. https://doi.org/10.2307/1414239
Kizilirmak, J. M., Galvao Gomes da Silva, J., Imamoglu, F., &
Richardson-Klavehn, A. (2016). Generation and the sub-
jective feeling of aha!are independently related to
learning from insight. Psychological Research,80(6),
10591074. https://doi.org/10.1007/s00426-015-0697-2
Kizilirmak, J. M., Schott, B. H., Thürich, H., Richter, A.,
Sweeney-Reed, C. M., & Richardson-Klavehn, A. (2019).
Learning of novel semantic relationships via sudden
comprehension is associated with a hippocampus-
independent network orchestrated by the mPFC.
Consciousness and Cognition,69(January), 113132.
https://doi.org/10.1016/j.concog.2019.01.005
Kizilirmak, J. M., Thuerich, H., Folta-Schoofs, K., Schott, B.
H., & Richardson-Klavehn, A. (2016). Neural correlates
of learning from induced insight: A case for reward-
based episodic encoding. Frontiers in Psychology,7
(NOV), 116. https://doi.org/10.3389/fpsyg.2016.01693
Kizilirmak, J. M., Wiegmann, B., & Richardson-Klavehn, A.
(2016). Problem solving as an encoding task: A special
case of the generation eect. The Journal of Problem
Solving,9(1), 5976. https://doi.org/10.7771/1932-
6246.1182
Knoblich,G.,Ohlsson,S.,Haider,H.,&Rhenius,D.(1999).
Constraint relaxation and chunk decomposition in
insight problem solving. Journal of Experimental
Psychology: Learning, Memory, and Cognition,25(6),
15341555. https://doi.org/10.1037/0278-7393.25.6.1534
Knoblich, G., Ohlsson, S., & Raney, G. E. (2001). An eye
movement study of insight problem solving. Memory
& Cognition,29(7), 10001009. https://doi.org/10.
3758/BF03195762
Köhler, W. (1917). Intelligenzprüfungen an anthropoiden.
Royal Prussian Society of Sciences.
Kounios, J., Frymiare, J. L., Bowden, E. M., Fleck, J. I.,
Subramaniam, K., Parrish, T. B., & Jung-Beeman, M.
(2006). The prepared mind: Neural activity prior to
problem presentation predicts subsequent solution
by sudden insight. Psychological Science,17(10), 882
890. https://doi.org/10.1111/j.1467-9280.2006.01798.x
Landmann, N., Kuhn, M., Piosczyk, H., Feige, B., Riemann,
D., & Nissen, C. (2014). Entwicklung von 130 deutsch-
sprachigen Compound Remote Associate (CRA)-
worträtseln zur untersuchung kreativer prozesse im
deutschen sprachraum. Psychologische Rundschau,65(4),
200211. https://doi.org/10.1026/0033-3042/a000223
Lang, S., Kanngieser, N., Jaśkowski, P., Haider, H., Rose, M.,
& Verleger, R. (2006). Precursors of insight in event-
related brain potentials. Journal of Cognitive
Neuroscience,18(12), 21522166. https://doi.org/10.
1162/jocn.2006.18.12.2152
Leikin, R., Waisman, I., & Leikin, M. (2016). Does solving
insight-based problems dier from solving learning-
based problems? Some evidence from an ERP study.
ZDM - Mathematics Education,48(3), 305319. https://
doi.org/10.1007/s11858-016-0767-y
Mednick, S. A. (1962). The associative basis of the creative
process. Psychological Review,69(3), 220232. https://
doi.org/10.1037/h0048850
16 J. M. KIZILIRMAK ET AL.
Metcalfe, J. (1986). Feeling of knowing in memory and
problem solving. Journal of Experimental Psychology:
Learning, Memory, and Cognition,12(2), 288294.
https://doi.org/10.1037/0278-7393.12.2.288
Oh, Y., Chesebrough, C., Erickson, B., Zhang, F., & Kounios,
J. (2020). An insight-related neural reward signal.
NeuroImage,214(March), 116757. https://doi.org/10.
1016/j.neuroimage.2020.116757
Paynter, C. A., Kotovsky, K., & Reder, L. M. (2010). Problem-
solving without awareness: An ERP investigation.
Neuropsychologia,48(10), 31373144. https://doi.org/
10.1016/j.neuropsychologia.2010.06.029
Pike, A. R. (1968). Latency and relative frequency of
response in psychophysical discrimination. British
Journal of Mathematical and Statistical Psychology,21
(2), 161182. https://doi.org/10.1111/j.2044-8317.
1968.tb00407.x
Qiu, J., Li, H., Yang, D., Luo, Y., Li, Y., Wu, Z., & Zhang, Q.
(2008). The neural basis of insight problem solving: An
event-related potential study. Brain and Cognition,68
(1), 100106. https://doi.org/10.1016/j.bandc.2008.03.004
Roskies, A. L. (2010). How does neuroscience aect our
conception of volition? Annual Review of
Neuroscience,33(1), 109130. https://doi.org/10.1146/
annurev-neuro-060909-153151
Rothmaler, K., Nigbur, R., & Ivanova, G. (2017). New
insights into insight: Neurophysiological correlates of
the dierence between the intrinsic ahaand the
extrinsic oh yesmoment. Neuropsychologia,95
(December 2015), 204214. https://doi.org/10.1016/j.
neuropsychologia.2016.12.017
Salvi, C., Bricolo, E., Kounios, J., Bowden, E., & Beeman, M.
(2016). Insight solutions are correct more often
than analytic solutions. Thinking & Reasoning,22-
(4), 443460. https://doi.org/10.1080/13546783.2016.
1141798
Sandkühler, S., Bhattacharya, J., & Zak P. (2008).
Deconstructing insight: EEG correlates of insightful
problem solving. PLoS ONE,3(1), e1459. https://doi.
org/10.1371/journal.pone.0001459
Schielzeth, H., Dingemanse, N. J., Nakagawa, S., Westneat,
D. F., Allegue, H., Teplitsky, C., Réale, D., Dochtermann,
N. A., Garamszegi, L. Z., & Araya-Ajoy, Y. G. (2020).
Robustness of linear mixed-eects models to violations
of distributional assumptions. Methods in Ecology and
Evolution,11(9), 11411152. https://doi.org/10.1111/
2041-210X.13434
Shen, W., Liu, C., Zhang, X., Zhao, X., Zhang, J., Yuan, Y., &
Chen, Y. (2013). Right hemispheric dominance of crea-
tive insight: An event-related potential study. Creativity
Research Journal,25(1), 4858. https://doi.org/10.1080/
10400419.2013.752195
Tik, M., Sladky, R., Luft, C. D. B., Willinger, D., Homann, A.,
Banissy, M. J., Bhattacharya, J., & Windischberger, C.
(2018). Ultra-high-eld fMRI insights on insight:
Neural correlates of the Aha!-moment. Human Brain
Mapping,39(June 2015), 32413252. https://doi.org/
10.1002/hbm.24073
Topolinski, S., & Reber, R. (2010). Gaining insight into the
Ahaexperience. Current Directions in Psychological
Science,19(6), 402405. https://doi.org/10.1177/
0963721410388803
JOURNAL OF COGNITIVE PSYCHOLOGY 17
Appendix 1
Item
Roman
equation Type
Template
solution 1
Template
solution 2
Template
solution 3
Aha!
mean
Match
template
solution
1
Match
template
solution
2
Match
template
solution
3
Match
any
template
solution
Number of
alternative
solutions
1I+V=
VIII
SPC I + VI = VII V + II = VII 3,43 0,21 0,39 0,61 1
2III + III =
IV
SPC III + III = VI 3,54 0,89 0,89 0
3IV-I = V SPC V-I = IV VI-I = V 4,11 0,21 0,46 0,68 1
4VI + II =
VI
SPC VI + I = VII IV + II = VI V + II = VII 3,43 0,32 0,07 0,04 0,43 2
5VI-V = III SPC VI-IV = II VII-V = II 3,62 0,23 0,19 0,42 1
6IX + XI =
XVIII
SPC IX + IX =
XIII
4,11 0,59 0,59 0
7VI + V =
XIII
SPC VI + VI =
XII
VII + V =
XII
3,61 0,43 0,07 0,50 1
8IV + VI =
VIII
SPC IV + IV =
VIII
3,96 0,25 0,25 0
9VIII = II +
IV
SPC VIII = II +
VI
VIII = III +
V
VII = III +
IV
4,00 0,29 0,07 0,14 0,50 2
10 VII = III +
II
SPC VI = III + III 3,64 0,14 0,14 0
11 I = VII-VIII SPC I = VIII-VII 3,43 0,50 0,54 0
12 VI = VIII-
IV
SPC IV = VIII-IV 3,59 0,33 0,33 0
13 I = II + I SPC II = I + I 4,04 0,46 0,50 0
14 IX + I =
XII
SPC X + II = XII XI + I = XII IX + II = XI 3,70 0,11 0,22 0,15 0,48 2
15 X + III =
XI
SPC X + II = XII IX + II = XI 3,46 0,43 0,07 0,50 1
16 V-IV = III SPC VI-IV = II 3,89 0,33 0,33 0
17 III-II = II CD IV-II = II 3,75 0,43 0,43 0
18 V-I = III CD V-I = IV 3,71 0,36 0,36 0
19 VII = IV +
IV
CD VII = III +
IV
3,68 0,04 0,07 0
20 VII-I = III CD VII-I = VI VII-V = II 3,43 0,39 0,04 0,46 1
21 III-III = I CD IV-III = I 3,89 0,36 0,36 0
22 VI-IV = X CD VI-IV = II 4,00 0,54 0,57 0
23 V-V = X CD VI-V = I V-IV = I 3,64 0,14 0,07 0,21 1
24 XI-IX = X CD XI-IX = II 3,93 0,37 0,37 0
25 VI = III +
IV
CD VI = III + III 4,00 0,48 0,48 0
26 III = V-X CD III = V-II 4,00 0,56 0,56 0
27 X = I + I CD II = I + I 4,18 0,46 0,46 0
28 VII = I +
III
CD VII = I + VI VII = V + II 4,14 0,32 0,07 0,00 0,39 1
29 VI = XI +
III
CD VI = III + III 3,43 0,25 0,00 0,00 0,25 0
30 VI = VI +
V
CD XI = VI + V VII = VI + I 3,93 0,29 0,00 0,00 0,29 1
31 III = XV-IV CD XI = XV-IV 3,85 0,30 0,00 0,00 0,30 0
32 VI = IX +
III
CD VI = III + III 3,26 0,26 0,00 0,00 0,26 0
33 II-VI = VII OC II + V = VII I + VI = VII 3,93 0,04 0,32 0,00 0,36 1
34 IV-II = V OC IV + I = V IV-II = II 4,07 0,30 0,33 0,00 0,63 1
35 V + I = V OC V-I = IV VI-I = V 3,39 0,43 0,21 0,00 0,64 1
36 III-III = VII OC III + III = VI 3,89 0,50 0,07 0,07 0,57 0
37 X + I = X OC X-I = IX XI-I = X 4,18 0,46 0,11 0,00 0,57 1
38 XV = III-
XII
OC XV-III = XII 3,86 0,32 0,00 0,00 0,32 0
40 I-X = IX OC I = X-IX X-I = IX 4,00 0,11 0,25 0,00 0,36 1
41 VII = I-VI OC VII-I = VII 3,54 0,29 0,00 0,00 0,29 0
42 VI = IV-II OC VI-IV = II 3,93 0,54 0,04 0,04 0,57 0
43 VI = V-I OC VI-V = I IV = V-I 4,04 0,43 0,11 0,00 0,54 1
44 IV = III-I OC IV-III = I 3,67 0,26 0,00 0,00 0,26 0
45 XI = IX-II OC XI-IX = II 3,54 0,32 0,00 0,00 0,32 0
46 X = II-VIII OC X-II = VIII 3,86 0,32 0,00 0,00 0,32 0
47 I = X + X OC I = X-IX I = XI-X 4,44 0,26 0,15 0,00 0,41 1
48 XIII = III-X OC XIII-III = X 3,75 0,36 0,00 0,00 0,36 0
18 J. M. KIZILIRMAK ET AL.
... For example, Gruber & colleagues find that high states of curiosity to know the answer to a trivia question improves memory both for the answer and for incidentally presented visual stimuli (i.e., faces) presented during an anticipation phase before receiving the answer. The state of curiosity generated by a trivia question and the state of insight generated by realizing the solution to a puzzle share common elements both psychologically and neurobiologically (e.g., activation throughout the dopaminergic midbrain and striatum) (Danek & Wiley, 2017Kizilirmak et al., 2016Kizilirmak et al., , 2019Kizilirmak et al., , 2021Gruber et al., 2014;Oh et al., 2020;Tik et al., 2018). However, there are important distinctions in the temporal dynamics between states of curiosity generated by trivia questions and insight-based problem-solving that may affect memory for incidental information presented in temporal proximity. ...
... Given the conceptual and potential mechanistic overlap between the insight memory advantage and emotional memory enhancements, we predicted an enhancement in memory for incidental facts presented at the moment accompanying a sense of insight versus a problem solution reached without insight. Given research indicating the insight memory advantage also occurs for induced insights (Kizilirmak et al., 2015(Kizilirmak et al., , 2021, we did not predict a difference in memory for incidental facts presented after puzzles solved via insight (Aha! moments) versus incidental facts delivered after the solution for puzzles subjects could not answer (an induced insight, what we refer to as D'oh! moments). ...
Article
Full-text available
Research on creative problem-solving finds that solutions achieved via spontaneous insight (i.e., Aha! moment) are better remembered than solutions reached without this sense of epiphany, referred to as an “insight memory advantage.” We hypothesized that the insight memory advantage can spread to incidental information encoded in the moments surrounding insight as well. Participants (N = 291) were first given Rebus puzzles. After they indicated that they had found a solution, but before they could submit this solution, they were presented with scholastic facts that were incidental and unrelated to the problem at hand. Participants indicated whether they reached the solution via either insight or a step-by-step analysis. Memory results showed better performance for incidental scholastic facts presented when problem solving was accompanied by a spontaneous (Aha! experience) and induced (D’oh! experience) insight compared with solutions reached with analysis. This finding suggests that the memory advantage for problems solved via insight spreads to other unrelated information encoded in close temporal proximity and has implications for novel techniques to enhance learning in educational settings.
... For all their physical affordancing-touching, lifting, moving-matchstick problems are typically not presented in a manner that actualises these affordances: that is, they are presented on a monitor as a static image and participants stare at them until they can articulate a solution to a researcher (e.g. Kizilirmak et al., 2021;Knoblich et al., 1999;Ö llinger et al., 2008; but see Danek et al., 2016, where a matchstick arithmetic problem is presented with movable artefacts although the nature of the interaction is not recorded by these researchers). Methodologies are performative, and here what they perform is a type of explanation, a mental one, that draws exhaustively on mental skills -visual imagery, working memory -and if insight is experienced, subconscious processes are thrown into the mix. ...
Article
Full-text available
A laboratory procedure employing insight problems allows researcher to capture how new ideas are discovered or constructed. Insight problems are relatively simple riddles designed to encourage an initially incorrect interpretation of the problem that leads to an impasse: Researchers are then poised to capture the moment the impasse is overcome , that is when a new productive interpretation of the problem is developed resulting in the solution. Researchers call this process 'restructuring': while the term describes the phenomenon, it is not clear how it explains it nor how restructuring comes about. The case study we describe here reveals the micro-processes involved in restructuring by using an interactive problem-solving procedure involving matchstick arithmetic problems. Originally developed by Knoblich et al., these problems present a simple but false arithmetic expression using Roman numerals: Participant must discover which matchstick can be moved and where to turn it into a true expression. The participant can manipulate matchsticks, and in doing so creates a dynamic object, the behaviour of which triggers new actions and cues new hypotheses about the solution. We present the case-study data in the form of a video of a participant instructed to narrate hunches and hypotheses as she interacts with a physical model of the solution, over three separate problems. On the basis of a granular coding of the participant's verbal protocol along with an equally granular coding of the changes to the object (using ELAN; https://archive.mpi.nl/tla/elan), the case study is the first to clearly reveal the restructuring process that results in the phenomenon of 'outsight', that is when the behaviour and poly-morphic changes to the object qua model of the solution guides the participant to the solution.
... This assumption is close to the idea expressed by Dubey et al. (2021). However, our idea explains not only the process of solution generation (endogenous insights) but also cases of sudden understanding of the presented solution (induced insights), when participants report an Aha! experience after being introduced to the correct answer (see, e.g., Kizilirmak et al., 2016Kizilirmak et al., , 2021Moroshkina et al., 2022). ...
Article
Full-text available
The study investigated the correlation between the intensity of the Aha! experience and participants’ subjective difficulty ratings of problems before and after finding their solutions. We assumed that the Aha! experience arises from a shift in processing fluency triggered by changing from an initially incoherent problem representation to a coherent one, which ultimately leads to the retrieval of a solution with unexpected ease and speed. First, we hypothesized that higher Aha! experience ratings would indicate more sudden solutions, manifesting in a reduced correlation between the initial difficulty ratings and solution times. Second, we hypothesized that higher Aha! experience ratings would correspond to a greater shift in the subjective difficulty ratings between the initial and retrospective assessments. To test our hypotheses, we developed a novel set of rebus puzzles. A total of 160 participants solved rebuses and provided initial (within 5 s of problem presentation) and retrospective difficulty ratings (following the generation or presentation of a correct solution). They also rated their Aha! experience (after solution generation or presentation), confidence in solutions, and the likability of each rebus. Our findings revealed that the initial ratings of the problem’s subjective difficulty were positively correlated with the solution time and that this correlation decreased in the case of a stronger Aha! experience. Aha! experience ratings were positively correlated with the differences between initial and retrospective difficulty ratings, confidence, solution accuracy, and rebus likability. We interpreted our results to be in line with the processing fluency and metacognitive prediction error accounts.
... For all their physical affordancing-touching, lifting, moving-matchstick problems are typically not presented in a manner that actualises these affordances: that is, they are presented on a monitor as a static image and participants stare at them until they can articulate a solution to a researcher (e.g. Kizilirmak et al., 2021;Knoblich et al., 1999;Ö llinger et al., 2008; but see Danek et al., 2016, where a matchstick arithmetic problem is presented with movable artefacts although the nature of the interaction is not recorded by these researchers). Methodologies are performative, and here what they perform is a type of explanation, a mental one, that draws exhaustively on mental skills -visual imagery, working memory -and if insight is experienced, subconscious processes are thrown into the mix. ...
Preprint
Insight problems offer an interesting laboratory procedure to capture the origin of a new idea. These problems are relatively simple riddles designed to encourage an initially incorrect interpretation of the problem that leads to an impasse: Researchers are then poised to capture the moment the impasse is overcome, that is when a new productive interpretation of the problem is developed resulting in the solution. Researchers call this process ‘restructuring’: while the term describes the phenomenon, it is not clear how it explains it nor how restructuring comes about. The case study we describe here reveals the micro-processes involved in restructuring by using an interactive problem-solving procedure involving matchstick arithmetic problems. Originally developed by Knoblich et al. (1999), these problems present a simple but false arithmetic expression using Roman numerals: Participant must discover which matchstick can be moved and where to turn it into a true expression. The participant can manipulate matchsticks, and in doing so creates a dynamic object, the behaviour of which cues new actions and triggers new hypotheses about the solution. We present the case-study data in the form of a video of a participant instructed to narrate hunches and hypotheses as she interacts with a physical model of the solution, over three separate problems. On the basis of a granular coding of the participant’s verbal protocol along with an equally granular coding of the changes to the object (using ELAN; https://archive.mpi.nl/tla/elan), the case study is the first to clearly reveal the restructuring process that results in the phenomenon of ‘outsight’ (Vallée-Tourangeau & March, 2020), that is when the behaviour and polymorphic changes to the object qua model of the solution guides the participant to the solution.
... Overall, the insight literature provides robust evidence that processing fluency is an effective predictor of solution accuracy in this specific domain of creative problem solving. That said, even in the context of insight problem solving there are occasions when processing fluency is seen to be a misleading cue that can lead to "false insights", whereby an answer that comes to mind quickly is, in fact, erroneous (e.g., Danek & Wiley, 2017;Kizilirmak et al., 2021). More generally in the 12 reasoning and problem-solving literature there are many situations where a default, intuitive Type 1 response arises with high fluency, but where this response is incorrect. ...
Chapter
Full-text available
Meta-reasoning refers to the metacognitive processes that monitor and control ongoing thinking, reasoning and problem-solving. These monitoring processes are usually experienced as feelings of “certainty” or “uncertainty” regarding how well a process is unfolding. The “meta-reasoning framework” advanced by Ackerman and Thompson (2017) captures many existing findings relating to meta-reasoning at an individual level, which raises questions about how the framework can be expanded to reflect collaborative meta-reasoning. This development is important given the multitude of real-world domains that involve collaborative thinking and reasoning, including those involving team-based creativity (e.g., design, innovation, entrepreneurship, advertising and scientific discovery). In such collaborative situations, monitoring processes need to be attuned to shifting uncertainty in team activities and communications, whereas control processes need to ensure coordinated and negotiated strategy selection. In this chapter we aim to progress the development of a collaborative meta-reasoning framework of relevance to creative contexts by drawing upon the limited existing research, which is primarily focused on meta-reasoning in design teams. We conclude our discussion by delineating a series of key questions to motivate future research.
... of a problem, which was generated by the problem solver and accompanied by a subjective feeling of 139 example been addressed by Kizilirmak et al. (2021). The results suggest that at least up to 48 problems do not diminish the strength of the feeling of Aha!. "Aha!" (Bowden & Jung-Beeman, 2003b;Danek et al., 2013). ...
... Whether solving the problem or merely presenting the solution induces the same Aha! experiences is an ongoing discussion. (Kizilirmak et al., 2021;Rothmaler et al., 2017). However, this discussion is not relevant to the processing-fluency account, because different cognitive processes can cause high processing fluency. ...
Preprint
Full-text available
People sometimes experience Aha! moments when solving problems, but the nature of these experiences and their sources have not been extensively explored. According to the processing fluency framework, an Aha! experience may be considered a result of a sudden increase in processing fluency. Based on this, we suggested that Aha judgements could be affected by the misattribution of processing fluency. In two experiments, we tested this hypothesis using remote associate problems with mirrored letters. The first experiment demonstrated that problems with mirrored letters are less likely to be judged as solvable compared to normally written problems, suggesting that mirroring letters reduces processing fluency. In the second experiment, participants judged Aha! experiences in response to solutions' presentation. Our findings indicate that participants were more likely to report an Aha!-like comprehension when the mirrored writing changed to normal at the moment of the correct solution presentation. That is, a sudden increase in perceptual fluency led to higher chances of experiencing Aha! moments. These results indicate that Aha! experiences can be affected by fluency misattribution.
... The N400 for insight problem solving was suggested to reflect breaking the prior problem representation and establishing new connections Qiu et al. 2006;Zhou et al. 2018). In recent years, researchers began to explore the differences between insight and noninsight by response-locked ERPs (Cui et al. 2021;Kizilirmak et al. 2021). They paid attention to the electrophysiological differences within about 1000 ms before the response of the solution that was generated with an Aha experience or not. ...
Article
Full-text available
The insight memory advantage refers to the situation in which memory performance could be improved by solving a problem with an Aha experience. In re-solution tests and recognition tests, studies demonstrate an insight memory advantage by spontaneous insight or induced insight. For the re-solution test, the neural mechanisms of the effect of induced insight were studied by the fMRI technique. However, the neural mechanisms of the effect of insight on re-solution in the temporal dimension were not known. The neural mechanisms of the effect of spontaneous insight on re-solution were not known. In the present study, we use the compound remote-associated (CRA) task to reveal the neural mechanisms of the effect of spontaneous insight on re-solution by the event-related potentials (ERPs) technique. The 25 participants were asked to solve a series of Chinese verbal CRA tasks and then perform a re-solution test 1 day later. Our results indicated that the solution with the Aha experience evoked a larger N400 in the early solution phase and a more negative wave in the late solution phase than the solution with no Aha experience. In the re-solution phase, items with an Aha during the solution phase were re-solved better with higher Aha rates than items with no Aha. In the re-solution phase, compared with items with no Aha, items with an Aha during the solution phase evoked a larger positive ERP in the 250 to 350 ms time window in the early phase, and a more negative deflection before the response (−900 to −800 ms) in the later phase. In one word, spontaneous insight during the solution phase could promote re-solution and elicit ERP deflection in the re-solution phase.
Article
Full-text available
p>This work is devoted to situational factors of experimental research influence on the insight assessment of problem solving. We considered such factors as the solution strategy (insightful, step-by-step), the form of problem presentation (visual, verbal), the solution independence (solution found by the participant or presented by the experimenter) and the solution speed (fast, slow). Understanding the impact of these factors on the insight assessment can contribute to both improving research practice and developing a unified theoretical model of insight and insightful solution. The studies included in this paper were carried out in various research approaches, with different materials, by different experimenters and under different experimental conditions. Danek and Wiley’s questionnaire was used for the insight assessment in all studies. According to the results, all the above situational factors have a significant impact on the differentiated subjective assessment of insightful solutions.</p
Article
Full-text available
The mnemonic effect of insight refers to the situation in which experiencing an "aha" moment when solving problems could improve memory performance for both the question and its solution. The aha experience can be triggered either by external stimuli or by internal solution attempts, namely "induced" or "spontaneous" insight, respectively. Tests of the neural correlates of the insightful memory effect are typically conducted in induced insight paradigms. The neural mechanism of the mnemonic effect of spontaneous insight is unclear. In the present study, the mnemonic effect for spontaneous insight was examined by the event-related potentials (ERPs) technique and behavioral measures. Subjects were required to solve a set of Chinese verbal compound remote-associated tasks (CRA), and performed a recognition test 10 min later. The results showed that the spontaneous insight solution elicited a more negative deflection than did the non-insight solution before the button reaction (− 800 to − 400 ms) in the study phase. In the recognition test phase, items which elicited insight during study were recognized faster, compared with non-insight study items. And spontaneous insight solution elicited a more positive deflection than did non-insight solution in the time window from 400 to 700 ms after onset of the answer. Moreover, brain–behavior correlations revealed a relationship between N400 amplitude during study and later memory performance which revealed a double-dissociation between items solved with and without insight during study. The different predictions for recognition indicate that the encoding of spontaneous insight may differ from that of non-insight, suggesting that different encoding mechanisms may mediate the encoding of items and solutions found by insight versus non-insight
Article
Full-text available
Linear mixed‐effects models are powerful tools for analysing complex datasets with repeated or clustered observations, a common data structure in ecology and evolution. Mixed‐effects models involve complex fitting procedures and make several assumptions, in particular about the distribution of residual and random effects. Violations of these assumptions are common in real datasets, yet it is not always clear how much these violations matter to accurate and unbiased estimation. Here we address the consequences of violations in distributional assumptions and the impact of missing random effect components on model estimates. In particular, we evaluate the effects of skewed, bimodal and heteroscedastic random effect and residual variances, of missing random effect terms and of correlated fixed effect predictors. We focus on bias and prediction error on estimates of fixed and random effects. Model estimates were usually robust to violations of assumptions, with the exception of slight upward biases in estimates of random effect variance if the generating distribution was bimodal but was modelled by Gaussian error distributions. Further, estimates for (random effect) components that violated distributional assumptions became less precise but remained unbiased. However, this particular problem did not affect other parameters of the model. The same pattern was found for strongly correlated fixed effects, which led to imprecise, but unbiased estimates, with uncertainty estimates reflecting imprecision. Unmodelled sources of random effect variance had predictable effects on variance component estimates. The pattern is best viewed as a cascade of hierarchical grouping factors. Variances trickle down the hierarchy such that missing higher‐level random effect variances pool at lower levels and missing lower‐level and crossed random effect variances manifest as residual variance. Overall, our results show remarkable robustness of mixed‐effects models that should allow researchers to use mixed‐effects models even if the distributional assumptions are objectively violated. However, this does not free researchers from careful evaluation of the model. Estimates that are based on data that show clear violations of key assumptions should be treated with caution because individual datasets might give highly imprecise estimates, even if they will be unbiased on average across datasets.
Article
Full-text available
Moments of insight, a phenomenon of creative cognition in which an idea suddenly emerges into awareness as an “Aha!” are often reported to be affectively positive experiences. We tested the hypothesis that problem-solving by insight is accompanied by neural reward processing. We recorded high-density EEGs while participants solved a series of anagrams. For each solution, they reported whether the answer had occurred to them as a sudden insight or whether they had derived it deliberately and incrementally (i.e., “analytically’). Afterwards, they filled out a questionnaire that measures general dispositional reward sensitivity. We computed the time-frequency representations of the EEGs for trials with insight (I) solutions and trials with analytic (A) solutions and subtracted them to obtain an I-A time-frequency representation for each electrode. Statistical Parametric Mapping (SPM) analyses tested for significant I-A and reward-sensitivity effects. SPM revealed the time, frequency, and scalp locations of several I > A effects. No A > I effect was observed. The primary neural correlate of insight was a burst of (I > A) gamma-band oscillatory activity over prefrontal cortex approximately 500 ms before participants pressed a button to indicate that they had solved the problem. We correlated the I-A time-frequency representation with reward sensitivity to discover insight-related effects that were modulated by reward sensitivity. This revealed a separate anterior prefrontal burst of gamma-band activity, approximately 100 ms after the primary I-A insight effect, which we interpreted to be an insight-related reward signal. This interpretation was supported by source reconstruction showing that this signal was generated in part by orbitofrontal cortex, a region associated with reward learning and hedonically pleasurable experiences such as food, positive social experiences, addictive drugs, and orgasm. These findings support the notion that for many people insight is rewarding. Additionally, these results may explain why many people choose to engage in insight-generating recreational and vocational activities such as solving puzzles, reading murder mysteries, creating inventions, or doing research. This insight-related reward signal may be a manifestation of an evolutionarily adaptive mechanism for the reinforcement of exploration, problem solving, and creative cognition.
Article
Full-text available
Sudden comprehension—or insight—during problem-solving can enhance learning, but the underlying neural processes are largely unknown. We investigated neural correlates of learning from sudden comprehension using functional magnetic resonance imaging and a verbal problem-solving task. Solutions and “solutions” to solvable and unsolvable verbal problems, respectively, were presented to induce sudden comprehension or continued incomprehension. We found activations of the hippocampus, medial prefrontal cortex (mPFC), amygdala, and striatum during sudden comprehension. Notably, however, mPFC and temporo-parietal neocortical structures rather than the hippocampus were associated with later learning of suddenly comprehended solutions. Moreover, di!cult compared to easy sudden comprehension elicited midbrain activations and was associated with successful learning, pointing to learning via intrinsic reward. Sudden comprehension of novel semantic associations may constitute a special case of long-term memory formation primarily mediated by the mPFC, expanding our knowledge of its role in prior-knowledge-dependent memory.
Article
Full-text available
Having a sudden insight is often associated with inherent confidence, enough for Archimedes to run nakedthrough the streets shouting “Eureka!”. Recent evidence demonstrates that public displays of enthusiasm, suchas the ancient polymath’s, are actually supported by a higher likelihood of being correct.
Article
Full-text available
Finding creative solutions to difficult problems is a fundamental aspect of human culture and a skill highly needed. However, the exact neural processes underlying creative problem solving remain unclear. Insightful problem solving tasks were shown to be a valid method for investigating one subcomponent of creativity: the Aha!‐moment. Finding insightful solutions during a remote associates task (RAT) was found to elicit specific cortical activity changes. Considering the strong affective components of Aha!‐moments, as manifested in the subjectively experienced feeling of relief following the sudden emergence of the solution of the problem without any conscious forewarning, we hypothesized the subcortical dopaminergic reward network to be critically engaged during Aha. To investigate those subcortical contributions to insight, we employed ultra‐high‐field 7 T fMRI during a German Version of the RAT. During this task, subjects were exposed to word triplets and instructed to find a solution word being associated with all the three given words. They were supposed to press a button as soon as they felt confident about their solution without further revision, allowing us to capture the exact event of Aha!‐moment. Besides the finding on cortical involvement of the left anterior middle temporal gyrus (aMTG), here we showed for the first time robust subcortical activity changes related to insightful problem solving in the bilateral thalamus, hippocampus, and the dopaminergic midbrain comprising ventral tegmental area (VTA), nucleus accumbens (NAcc), and caudate nucleus. These results shed new light on the affective neural mechanisms underlying insightful problem solving.
Article
Full-text available
The subjective Aha! experience that problem solvers often report when they find a solution has been taken as a marker for insight. If Aha! is closely linked to insightful solution processes, then theoretically, an Aha! should only be experienced when the correct solution is found. However, little work has explored whether the Aha! experience can also accompany incorrect solutions (“false insights”). Similarly, although the Aha! experience is not a unitary construct, little work has explored the different dimensions that have been proposed as its constituents. To address these gaps in the literature, 70 participants were presented with a set of difficult problems (37 magic tricks), and rated each of their solutions for Aha! as well as with regard to Suddenness in the emergence of the solution, Certainty of being correct, Surprise, Pleasure, Relief, and Drive. Solution times were also used as predictors for the Aha! experience. This study reports three main findings: First, false insights exist. Second, the Aha! experience is multidimensional and consists of the key components Pleasure, Suddenness and Certainty. Third, although Aha! experiences for correct and incorrect solutions share these three common dimensions, they are also experienced differently with regard to magnitude and quality, with correct solutions emerging faster, leading to stronger Aha! experiences, and higher ratings of Pleasure, Suddenness, and Certainty. Solution correctness proffered a slightly different emotional coloring to the Aha! experience, with the additional perception of Relief for correct solutions, and Surprise for incorrect ones. These results cast some doubt on the assumption that the occurrence of an Aha! experience can serve as a definitive signal that a true insight has taken place. On the other hand, the quantitative and qualitative differences in the experience of correct and incorrect solutions demonstrate that the Aha! experience is not a mere epiphenomenon. Strong Aha! experiences are clearly, but not exclusively linked to correct solutions.
Article
Full-text available
Insight refers to a situation in which a problem solver immediately changes his understanding of a problem situation. This representational change can either be triggered by external stimuli, like a hint or the solution itself, or by internal solution attempts. In the present paper, the differences and similarities between these two phenomena, namely “extrinsic” and “intrinsic” insight, are examined. To this end, electroencephalogram (EEG) is recorded while subjects either recognize or generate solutions to German verbal compound remote associate problems (CRA). Based on previous studies, we compare the alpha power prior to insightful solution recognition with the alpha power prior to insightful solution generation. Results show that intrinsic insights are preceded by an increase in alpha power at right parietal electrodes, while extrinsic insights are preceded by a respective decrease. These results can be interpreted in two ways. In consistency with other studies, the increase in alpha power before intrinsic insights can be interpreted as an increased internal focus of attention. Accordingly, the decrease in alpha power before extrinsic insights may be associated with a more externally oriented focus of attention. Alternatively, the increase in alpha power prior to intrinsic insights can be interpreted as an active inhibition of solution-related information, while the alpha power decrease prior to extrinsic insights may reflect its activation. Regardless of the interpretation, the results provide strong evidence that extrinsic and intrinsic insight differ on the behavioral as well as the neurophysiological level.
Article
Full-text available
Experiencing insight when solving problems can improve memory formation for both the problem and its solution. The underlying neural processes involved in this kind of learning are, however, thus far insufficiently understood. Here, we conceptualized insight as the sudden understanding of a novel relationship between known stimuli that fits into existing knowledge and is accompanied by a positive emotional response. Hence, insight is thought to comprise associative novelty, schema congruency, and intrinsic reward, all of which are separately known to enhance memory performance. We examined the neural correlates of learning from induced insight with functional magnetic resonance imaging (fMRI) using our own version of the compound-remote-associates-task (CRAT) in which each item consists of three clue words and a solution word. (Pseudo-)Solution words were presented after a brief period of problem-solving attempts to induce either sudden comprehension (CRA items) or continued incomprehension (control items) at a specific time point. By comparing processing of the solution words of CRA with control items, we found induced insight to elicit activation of the rostral anterior cingulate cortex/medial prefrontal cortex (rACC/mPFC) and left hippocampus. This pattern of results lends support to the role of schema congruency (rACC/mPFC) and associative novelty (hippocampus) in the processing of induced insight. We propose that (1) the mPFC not only responds to schema-congruent information, but also to the detection of novel schemata, and (2) that the hippocampus responds to a form of associative novelty that is not just a novel constellation of familiar items, but rather comprises a novel meaningful relationship between the items—which was the only difference between our insight and no insight conditions. To investigate episodic long-term memory encoding, we compared CRA items whose solution word was recognized 24 h after encoding to those with forgotten solutions. We found activation in the left striatum and parts of the left amygdala, pointing to a potential role of brain reward circuitry in the encoding of the solution words. We propose that learning from induced insight mainly relies on the amygdala evaluating the internal value (as an affective evaluation) of the suddenly comprehended information, and striatum-dependent reward-based learning.