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Computer code comprehension shares neural
resources with formal logical inference in the fronto-
parietal network
Liu, Y., Kim, J., Wilson, C., Bedny, M.
Johns Hopkins University
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Abstract
Despite the importance of programming to modern society, the cognitive and neural bases of
code comprehension are largely unknown. Programming languages might ‘recycle’
neurocognitive mechanisms originally used for natural languages. Alternatively, comprehension
of code could depend on fronto-parietal networks shared with other culturally derived symbol
systems, such as formal logic and math. Expert programmers (average 11 years of programming
experience) performed code comprehension and memory control tasks while undergoing fMRI.
The same participants also performed language, math, formal logic, and executive control
localizer tasks. A left-lateralized fronto-parietal network was recruited for code comprehension.
Patterns of activity within this network distinguish between “for” loops and “if” conditional code
functions. Code comprehension overlapped extensively with neural basis of formal logic and to a
lesser degree math. Overlap with simpler executive processes and language was low, but
laterality of language and code covaried across individuals. Cultural symbol systems, including
code, depend on a distinctive fronto-parietal cortical network.
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Introduction
In 1800, only twelve percent of the world’s population knew how to read, but today the world
literacy rate is over eighty-five percent (https://ourworldindata.org/literacy). The ability to
comprehend programming languages may follow a similar trajectory. Although only an
estimated .5% of the world’s population is currently proficient at computer programming, the
number of jobs that require programming continues to grow. Coding is essential in scientific fields
and in areas as diverse as artistic design, finance, and healthcare. As many industries incorporate
artificial intelligence or other information technologies, more people seek to acquire programming
literacy. Yet the cognitive and neural mechanisms supporting coding remain largely unknown.
Apart from its intrinsic and societal interest, programming is a case study of “neural recycling”
(Dehaene & Cohen, 2007). Computer programming is a very recent cultural invention and the
human brain is not evolutionarily adapted to support it. Studying the neural basis of code offers
an opportunity to investigate how the human brain enables cultural inventions.
Hypotheses about how the human brain accommodates programming range widely. One recently
popular view is that code comprehension recycles language processing mechanisms (Fedorenko,
Ivanova, Dhamala, & Bers, 2019; Fitch, Hauser, & Chomsky, 2005; Pandža, 2016; Portnoff, 2018;
Prat, Madhyastha, Mottarella, & Kuo, 2020). Computer languages borrow letters and words from
natural language. In some programming languages, like Python, the meanings of the borrowed
symbols (e.g., if, return, print) relate to the meanings of the same symbols in English. As
in natural languages, the symbols of code combine generatively according to a set of rules (i.e.,
a formal grammar). Moreover, the grammars of language and that of code share common features,
including recursive structure (Fitch et al., 2005). A recent study reported that individual differences
in learning a second language predict aptitude in learning to program among novices (Prat et al.,
2020). One possibility then is that coding recycles neurocognitive mechanisms involved in
language processing (Peitek et al., 2018; Siegmund et al., 2014).
On the other hand, other culturally derived symbol systems, such as formal logic and math do not
appear to depend on the same neural network as natural language. Like code, formal logic and
mathematics borrow symbols from natural language and are also hierarchical and recursive (e.g.
(7*(7*(3+4))). Unlike language, however, culturally derived symbol systems are explicitly taught
later in life. Computer coding, mathematics and logic, also involve manipulation of arbitrary
variables without inherent meaning (e.g. X, Y, input, ii) according to a set of learned rules
(McCoy & Burton, 1988). Each symbol system, including code, has its own conventionalized
variables and its own set of rules. In the case of code, the rules also differ somewhat across
programming languages. The deductive rules of programming also share specific features with
formal logic. For example, connectives (e.g., “if…then”, “and”, “or”, “not”) occur in both domains
and have related meanings. Consider a function containing an if conditional written in Python,
def fun(input):
result = "result: "
if input[0]=="a":
result += input[0].upper()
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return result
The value of the “result” variable depends on whether the “input” meets the specific conditions
of the if statement. Similarly, in the logical statement “If both X and Z then not Y” the value of
the result (Y) depends on the truth value of the condition “both X and Z”. One prediction, then, is
that coding depends on similar neural resources to other culturally-derived symbol systems such
as formal logic and math.
Rather than recruiting perisylvian fronto-temporal areas, mathematics and logic recruit a fronto-
parietal network, including the dorsolateral prefrontal cortex and the intraparietal sulcus (IPS) as
well as putative symbol representations (i.e. numberform area) in inferior temporal cortex (Amalric
& Dehaene, 2016; Coetzee & Monti, 2018; Goel et al., 2007; Monti, Parsons, & Osherson, 2009).
This fronto-parietal network overlaps partially with the so called central executive/working memory
system, which is implicated in a variety of cognitive tasks that involve maintaining and
manipulating information in working memory, processes that are part and parcel of understanding
and writing code (Brooks, 1977; Duncan, 2010; Letovsky, 1987; Miller & Cohen, 2001; Soloway
& Ehrlich, 1984; Weinberg, 1971; Zanto & Gazzaley, 2013)(for a review of the cognitive models
of code comprehension, see (Von Mayrhauser & Vans, 1995)). The central executive system is
usually studied using simple rule-based tasks, such as the multisource interference task (MSIT),
Stroop and executive working memory (Banich et al., 2000; Bunge, Klingberg, Jacobsen, &
Gabrieli, 2000; Bush & Shin, 2006; January, Trueswell, & Thompson-Schill, 2009; Milham et al.,
2001; Woolgar, Thompson, Bor, & Duncan, 2011; Zanto & Gazzaley, 2013; Zhang, Kriegeskorte,
Carlin, & Rowe, 2013). Logic and math activate a similar network but also have unique neural
signatures. Within the prefrontal cortex, logic recruits more anterior regions associated with more
advanced forms of reasoning and symbol manipulation (Coetzee & Monti, 2018; Ramnani & Owen,
2004).
The goal of the current study was to ask whether computer code comprehension has a consistent
neural signature across people and if so whether this signature is similar to other culturally derived
symbol systems (i.e., logic and math) or similar to natural language. Only a handful of studies
have looked at the neural basis of coding (Duraes, Madeira, Castelhano, Duarte, & Branco, 2016;
Floyd, Santander, & Weimer, 2017; Ikutani & Uwano, 2014; Peitek et al., 2018; Siegmund et al.,
2014). Thus far results have been largely inconsistent, possibly due to the complexity of the tasks
and absence of control conditions. Moreover, no prior study has directly compared the neural
basis of code to other cognitive domains.
A group of expert programmers (average 11 years of programming experience) performed a code
comprehension task while undergoing functional magnetic resonance imaging (fMRI). We chose
a comprehension task rather than code writing or debugging partly because it could in principle
be analogous to understanding language vignettes and because it is arguably simpler. On each
real code trial, participants saw a short function definition, followed by an input and a possible
output, and judged whether the output was valid. In fake code control trials, participants performed
a memory task with arbitrary text. A fake function was generated by scrambling a real function
per line at the level of word/symbol. Each fake function preserved the perceptual and lexical
elements of a real function, but was devoid of syntactic structure. The real code condition
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contained two subtypes or ‘control structures’, for loops and if conditionals. We used multi-
voxel-pattern analysis to decode for from if functions in order to test whether the code-
responsive cortical system encodes code-relevant information. Finally, we examined the overlap
of code comprehension with language (sentence comprehension), formal logic and mathematical
tasks. We also tested overlap of code with the MSIT to determine whether the overlap with
culturally derived symbol systems (i.e. logic and math) is more extensive than overlap with simpler
experimentally defined rule-based tasks.
Methods
Participants
Seventeen individuals participated in the study, one did not complete the tasks due to
claustrophobia, and another was excluded from analyses due to excessive movement (> 2mm).
We report data from the remaining fifteen individuals (3 women, age range 20-38, mean age =
27.4, SD = 5.0). All participants had normal or corrected to normal vision, and no known cognitive
or neurological disabilities. Participants gave informed consent according to procedures approved
by the Johns Hopkins University Institutional Review Board.
All participants had at least 5 years of programming experience (range: 5-22, mean=10.7,
SD=5.2), and at least 3 years of experience working with the programming language Python
(range: 3-9, mean=5.7, SD=1.8).
Behavioral pre-test
In addition to self-reported programming experience, Python expertise was evaluated with two
out-of-the-scanner Python exercises (one easier and one more difficult) the week prior to the fMRI
experiment. These exercises also served to familiarize participants with the particular Python
expressions that would be used during the fMRI experiment.
The easier exercise consisted of three phases: 1. test, 2. recap and 3. re-test. During the first
phase of the exercise (test), we evaluated participants’ knowledge of every built-in Python function
that would occur during the fMRI experiment. Participants were asked to type the output of a
single line of Python print() statement (e.g., for “print(”3.14”.split(“1”))” one should
type “[‘3.’, ‘4’]”). On average participants answered M=82.9% (SD=6.9%) of the questions
correctly (range: 70% - 96%). Since even expert programmers may not have used a particular
function in the recent past, the “recap” phase of the exercise explicitly reviewed the definitions
and purposes of all of the functions and expressions that would be used during the fMRI
experiment. During the final re-test phase, participants were once again asked to type the output
of a single line of Python for each function (M=92.0% (SD=7.5%), range: 72.4% - 100%).
The more difficult exercise evaluated the participants’ knowledge about when and how to use
Python functions and expressions. Each participant answered sixteen questions, each consisting
of a code snippet with a blank. A prompt was presented alongside the code snippet to explain
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what the snippet should output if executed. The participant was asked to fill in the blank in order
to complete the code (see the supplementary material for an example). The questions were
designed by the experimenter to cover some of the objectives specified in the exam syllabus of
the Certified Associate in Python Programming Certification held by the Python Institute
(https://pythoninstitute.org/certification/pcap-certification-associate/pcap-exam-syllabus/). On
average, the participants got 64.6% (SD=16.6%) of the questions correct (range: 37.5% - 93.75%).
fMRI task design and stimuli
Code Comprehension Experiment
In the real code comprehension trials, participants were presented with user-defined Python
functions. Python comprehension was compared to a fake code control trials that consisted of
incomprehensible scrambled Python functions (described in further detail below). To help
participants distinguish between real and fake code trials, real code appeared in white text and
fake code in yellow text.
Each trial consisted of three phases: function (24 seconds), input (6 seconds), and question (6
seconds) (Figure 1). First, participants viewed a Python function for 24 seconds, followed by a .5
second fixation-cross delay. During the input phase, the original code function re-appeared on
the screen with a potential input below consisting of a single line character string (6 seconds).
Participants were instructed to use the input to mentally derive the output of the code function
during the input phase. After the input phase there was a .5 second fixation-cross delay followed
by a proposed output along with the prompt “TRUE?” Participants were asked to determine
whether the output was correct within 6 seconds. All trial phases had a shortening bar at the
bottom of the screen indicating the remaining time during that particular phase of the trial. Each
trial was followed by a 5-second inter-trial interval during which the text “Your response is
recorded. Please wait for the next trial” was shown on the screen.
Each real code function consisted of five lines. The first line (def fun(input):) and the last
(return result) were always the same. The second line always initialized the result variable,
and the third and fourth lines formed a control structure (either a for loop or an if conditional)
that may modify the value of the result. Real code trials were divided into two sub-conditions, for
and if, according to the control structures the functions contained. Each condition included two
variants of the for or if functions (see supplementary material for details). All functions took a
letter string as input and performed string manipulation.
Fake code trials were analogous to the real code trials in temporal structure (i.e. function, input,
question). However, no real code was presented. Instead, participants viewed scrambled text and
were asked to remember it. During the function phase of a fake code trial, participants saw a
scrambled version of a Python function. Scrambling was done within line at word and symbol level
(Figure 1, bottom row). Because fake functions were derived from real functions, the words, digits
and operators that existed in real functions were preserved but none of the lines comprised an
executable Python statement. During the input phase, an additional fake input line appeared
below the fake function. The fake input line didn’t interact with the fake function, the participants
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only had to memorize this line. During the question phase, a new character line appeared along
with the prompt “SAME?” Participants judged whether this line had been presented during the
function and input phases (including the additional input line), or it came from a different fake
function. The answer was “true” on half of the real and fake code trials.
There were 6 task runs, each consisting of 20 trials, 8 real if code, 8 real for code and 4 fake
code trials. Each participant saw a total of 48 for functions (24 per variant), 48 if functions (24
per variant), and 24 fake functions. After each run of the task, participants saw their overall percent
correct and average response time. Participants were divided into two groups such that the
variants of the functions were balanced across groups, and the same participant never saw
different variants of the same function. The order of the presentation of the functions was pseudo-
randomized and balanced across participants. In total, 192 real functions (96 per group) and 48
fake functions (24 per group) were used in the experiment. All the functions are listed in Table S1
of the supplementary material. We permuted the order of the functions systematically such that
each participant saw a unique order (see supplementary material for the algorithm of the
permutation).
Localizer Tasks
During a separate MRI session, participants took part in two localizer experiments. A single
experiment was used to localize responses to language, math and formal logic using each
condition as the control for the others: language/math/logic localizer. The task design was
adapted from Monti et al. 2009, 2012 (Kanjlia, Lane, Feigenson, & Bedny, 2016; Monti et al., 2009;
Monti, Parsons, & Osherson, 2012). On language trials, participant judged whether two visually
presented sentences, one in active and one in passive voice, had the same meaning (e.g. “The
child that the babysitter chased ate the apple” vs “The apple was eaten by the babysitter that the
child chased”). On math trials, participant judged whether the variable X had the same value
across two equations (e.g. “X minus twenty-five equals forty-one” vs “X minus fifty-four equals
twelve”). On formal logic trials, participant judged whether two logical statements were consistent,
where one statement being true implied the other also being true (e.g. “If either not Z or not Y
then X” vs “If not X then both Z and Y”).
Each trial began with a 1-second fixation cross. One pair member appeared first, the other 3
seconds later. Both statements remained on screen for 16 seconds. Participants pressed the right
or left button to indicate true/false. The experiment consisted of 6 runs, each containing 8 trials of
each type (language/math/logic) and 6 rest periods, lasting 5 seconds each. All 48 statement
pairs from each condition were unique and appeared once throughout the experiment. In half of
the trials, the correct answer was “true”. Order of trials was counterbalanced in two lists across
participants.
Note that although all of the tasks in the language/math/logic localizer contain language stimuli,
previous studies show that sentences with content words lead to larger responses in the
perisylvian fronto-temporal language network than spoken equations or logical statements with
variables (Kanjlia et al., 2016; Monti et al., 2009, 2012). The perisylvian fronto-temporal language
network shows enhanced activity for stimuli that contain meaningful lexical items and sentence
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level syntax (e.g., (Fedorenko et al., 2016)). Furthermore, previous studies found that responses
to language, logic and math when compared to each other were similar to what was observed for
each domain relative to independent control conditions (e.g. sentences relative to lists of non-
words for language, and hard vs. easy logic problems) (Kanjlia et al., 2016; Monti et al., 2009,
2012).
The multi-source interference task (MSIT) was adapted from Bush and Shin (Bush & Shin, 2006)
to engage executive control processes and localize the multiple demand network. On each trial,
a triplet of digits was shown on the screen, and two of the digits were the same. The participant
pressed buttons (1, 2, or 3) to indicate the identity of the target digit which is different from the
two distractors. For example, for “131” the correct response is “3”; for “233” it is “2”. The
participants always pressed button “1”, “2”, and “3” with their index, middle, and ring fingers,
respectively.
MSIT consisted of “control” blocks and “interference” blocks, each containing 24 trials (1.75
seconds each). On interference trials, the location of the target digit was never consistent with the
identity of the digit (e.g., trials such as “133” or “121” never existed), thus giving rise to an
interference. On control trials, the distractors were always “0”, and the target digit was always at
the same location as its identity. In other words, there were only three kinds of control trials, “100”,
“020”, and “003”.
The participant performed 2 runs of MSIT. Each run began with 15 seconds of fixation, followed
by 4 control blocks and 4 interference blocks interleaved, and ended with another 15 seconds of
fixation. Both an interference block and a control block lasted for 42 seconds. The order of the
blocks was balanced both within and between participants. The order of the trials were arranged
such that all 12 interference trials appeared exactly twice in an interference block, and all 3 control
trials appeared exactly 6 times in a control block. Two same trials never came in succession, and
the order of the trials was different across all 8 blocks of the same kind.
Data acquisition
MRI data were acquired at the F.M. Kirby Research Center of Functional Brain Imaging on a 3T
Phillips Achieva Multix X-Series scanner. T1-weighted structural images were collected in 150
axial slices with 1mm isotropic voxels using the magnetization-prepared rapid gradient-echo (MP-
RAGE) sequence. T2*-weighted functional BOLD scans were collected in 36 axial slices (2.4 x
2.4 x 3mm voxels, TR = 2s). We acquired the data in one code comprehension session (6 runs)
and one localizer session (2 runs of MSIT followed by 6 runs of language/matth/local judgment),
with the acquisition parameters being identical for both sessions.
The stimuli in both the code comprehension and localizer sessions were presented using stand-
alone PsychoPy3 software (https://www.psychopy.org/). The stimuli were projected to a rear
projection screen cut to fit the scanner bore with an Epson PowerLite 7350 projector. The
resolution of the projected image was 1600 x 1200. The participant viewed the screen via a front-
silvered, 45∘inclined mirror attached to the top of the head coil.
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fMRI data preprocessing and general linear model (GLM) analysis
Data were analyzed using Freesurfer, FSL, HCP workbench, and custom in-house software
written in Python. Functional data were motion corrected, high-pass filtered (128 s), mapped to
the cortical surface using Freesurfer, spatially smoothed on the surface (6-mm FWHM Gaussian
kernel), and prewhitened to remove temporal autocorrelation. Covariates of no interest were
included to account for confounds related to white matter, cerebral spinal fluid, and motion spikes.
The four real function code (for1, for2, if1, if2) and fake code conditions were entered as
separate predictors in a GLM after convolving with a canonical hemodynamic response function
and its first temporal derivative. Only the images acquired during the twenty-four-second function
phase were modeled.
For the localizer experiment, a separate predictor was included for each of the three conditions
(language, math, and logic) modeling the 16 seconds during which the statement pair was
presented, as well as a rest period (5 seconds) predictor. In the MSIT task, the interference
condition and the control condition were entered as separate predictors.
Each run was modeled separately, and runs were combined within each subject using a fixed-
effects model (Dale, Fischl, & Sereno, 1999; Smith et al., 2004). For the group-level analysis
across participants, random-effects models were applied, and the models were corrected for
multiple comparisons at vertex level with p < 0.05 false discovery rate (FDR) across the whole
brain. A nonparametric permutation test was further implemented to cluster-correct at p < 0.01
family-wise error rate.
ROI definition
For each participant, 4 code-responsive functional ROIs were defined to be used in the MVPA
analysis. First, random-effects whole-brain univariate analysis for the real > fake code contrast
revealed 4 major clusters in the left hemisphere: the intraparietal sulcus (IPS), the posterior middle
temporal gyrus (pMTG), the lateral prefrontal cortex (PFC), and the early visual cortex (Occ).
These clusters were used to define group search spaces. Each search space was defined by
combining parcels from Schaefer et al. that encompassed each cluster (400-parcel map,
(Schaefer et al., 2018)). Next, individual functional ROIs were defined within these clusters by
taking the top 500 active vertices for the real > fake contrast within each participant.
MVPA
MVPA was used to distinguish for and if functions based on the spatial activation pattern in
code-responsive ROIs. Specifically, we used the support vector machine (SVM) implemented in
the Python toolbox Scikit-learn (Chang & Lin, 2011; Pedregosa et al., 2011).
For each participant, the spatial activation pattern for each function was defined as the beta
parameter estimation of a GLM with each function entered as a separate predictor. Within each
ROI in each participant, the 96 spatial patterns elicited by the real functions were collected.
Normalization was carried out separately for for condition and if condition such that in either
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condition, across all vertices and all functions, the mean is set to 0 and standard deviation to 1.
The purpose of the normalization is to eliminate the difference in the baselines in both conditions
while preserving the spatial patterns.
The whole dataset was split into a training test (90%, 86 functions) and a testing set (10%, 10
functions), where in each set, half of the patterns came from for functions. A linear SVM
(regularization parameter C = 5.0) was trained on the training set and tested on the testing set.
Classification was carried out on 100 different train-test splits, and the average accuracy value
was recorded as the observed accuracy.
We tested the classifier performance against chance (50%) using a combined permutation and
bootstrapping approach (Schreiber & Krekelberg, 2013; Stelzer, Chen, & Turner, 2013). We
derived the t-statistic of the Fisher-z transformed accuracy values against chance (also Fisher-z
transformed). The null distribution for each participant was generated by first shuffling the
condition labels 1,000 times, then computing the mean accuracy derived from the 100 train-test
split of each shuffled dataset. Then, a bootstrapping method was used to generate an empirical
distribution of the t-statistics. In each of the 106 iterations of the bootstrapping phase, one Fisher-
z transformed null accuracy value (out of 1,000) per participant was randomly selected, and a one
sample t-test was applied to the null sample. The empirical p-value of the real t-statistic was
defined as the proportion of the null t-statistics greater than the real value.
Overlap analysis
For each participant, in each hemisphere, we used cosine similarity to quantify the overlap of the
activated vertices between code comprehension and each of the four localizer contrasts:
language (language > math), math (math > language), logic (logic > language), and multi-source
interference (hard > easy). First, we generated the binary activation map for each contrast. A
vertex was assigned the value 1 if the significance of its activation is above the 0.05 (FDR
corrected) threshold, and 0 otherwise. Each binary map was regarded as a vector, and the cosine
similarity between two vectors (e.g., code comprehension and logic) was defined as the inner
product of the vectors divided by the product of their respective lengths (norms). The cosine
similarities of code to each of the localizer tasks was then compared using repeated-measure
ANOVA and post-hoc pairwise comparisons with false discovery rate (FDR) correction.
The empirical lower bound was calculated separately for each localizer task to account for
differences in the number of activated vertices across tasks. For each participant, for each
localizer task, we computed the cosine similarity between the binary map for code comprehension
and a shuffled binary map for each localizer task. This step was repeated 100 times to generate
the null distribution of the similarity values.
We used a bootstrapping approach to test whether each observed cosine similarity value was
significantly above the empirical lower bound. For each localizer task, we randomly selected one
similarity value from the null distribution of one participant and computed a null group mean
similarity. This step was repeated 106 times to derive the null distribution of the null group mean
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similarity. The empirical p-value of the real group mean similarity was defined as the proportion
of the null values greater than the real value.
We operationalized the empirical upper bound as the cosine similarity of code comprehension
and itself. For each participant, we split the data for code comprehension in half, ran a GLM for
each half, and derived two binary maps whose cosine similarity was computed. We averaged all
the similarity values resulting from the 10 possible splits of the 6 runs and across all participants.
Results
Behavioral results
Accuracy was similar across real and fake code trials (real M=92%, SD=0.045; fake M=0.90,
SD=0.069; binary logistic mixed regression, real to fake odds ratio β = 1.27; Wald’s z statistic, z
= 1.21; p = 0.23). Accuracy was also similar across if and for trials (if M=0.92, SD=0.076;
for M=0.92, SD=0.056; if to for odds ratio β = 0.95; Wald’s z statistic, z = -0.28; p = 0.77).
Participants were slower to respond to fake as compared to real code trials (real M=1.73 sec,
SD=0.416; fake M=2.03 sec, SD=0.37; t(73) = 2.329, p = 0.023) and slower to respond to for as
compared to if trials (for M=1.85 sec, SD=0.46; if M=1.60 sec, SD=0.44; t(58) = 2.127, p =
0.038) (Figure S1).
In the language/math/logic localizer task, participants performed least accurately on logic trials,
followed by math and language (logic M=0.82, SD=0.13; math M=0.94, SD=0.028; language
M=0.98, SD=0.023; one-way-ANOVA, F(2, 42) = 18.29, p < 0.001). Participants were slowest to
respond to logic trials, followed by math trials, and fastest on the language trials (logic M=6.47
sec, SD=2.42; math M=4.93 sec, SD=1.32; language M=4.03, SD=1.27; one-way-ANOVA F(2,
42) = 7.42, p = 0.0017) (Figure S1).
In the MSIT experiment, hard and easy conditions did not differ in terms of accuracy (hard M=0.97,
SD=0.038; easy M=0.98, SD=0.034; t(28) = -1.363, p = 0.18), but the hard trials took significantly
longer to respond to than the easy trials (hard M=0.792 sec, SD=0.092; easy M=0.506 sec,
SD=0.090; t(28)=8.59, p < 0.001) (Figure S1).
fMRI results
Code comprehension experiment
As compared to fake code, real code elicited activation in a left-lateralized network of regions,
including the lateral PFC (middle/inferior frontal gyri, inferior frontal sulcus; mainly BA 44 & 46,
with partial activation in BA 6, 8, 9, 10, 47), the parietal cortex (the IPS, angular and supramarginal
gyri; BA 7) and the pMTG and superior temporal sulcus (BA 22 & 37). Activity was also observed
in early visual cortices (Occ) (p < 0.01 FWER, Figure 2) (Table S2 in the supplementary material).
MVPA analysis revealed that for and if functions could be distinguished based on patterns of
activity within PFC (accuracy = 64.7%, p < 0.001), IPS (accuracy = 67.4%, p < 0.001) and pMTG
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(accuracy = 68.4%, p < 0.001). for and if functions could also be distinguished within the early
visual cortex (accuracy = 55.7%, p = 0.015), however, decoding accuracy was lower than in the
other regions (F(3, 56) = 4.78, p = 0.0048) (Figure 3).
Overlap between code comprehension and other cognitive domains
The language/math/logic localizer task activated previously identified networks involved in these
respective domains. Responses to language were observed in a left perisylvian fronto-temporal
language network, to math in parietal and anterior prefrontal areas as well as posterior aspect of
the inferior temporal gyrus, and finally to logic, like math, in parietal and anterior prefrontal areas
as well as posterior aspect of the inferior temporal gyrus. Logic activated more anterior and more
extensive regions in prefrontal cortex than math. The MSIT hard > easy contrast also activated a
fronto-parietal network including the IPS, however, the activation in the lateral frontal cortex was
posterior and close to the precentral gyrus. (Figure 4, see Table S2 in Supplemental Materials for
full description of activation patterns associated with language, logic, math and MSIT). Note that
although in the current experiment logic, math and language were compared to each other, the
networks observed for each domain are similar to those previously identified with other control
conditions (e.g. lists of non-words for language and hard vs. easy contrast in a logic task)
(e.g.(Coetzee & Monti, 2018; Fedorenko, Behr, & Kanwisher, 2011)).
Because code comprehension was highly left lateralized, overlap analyses focused on the left
hemisphere. Right hemisphere results are reported in supplementary materials. Code
comprehension (real > fake) overlapped significantly above chance with all localizer tasks: logic,
math, language and MSIT (each task compared to chance p’s < 0.001 compared to code split-
half overlap p’s < 0.001) (Figure 4). The degree of overlap differed significantly across tasks
(repeated-measures ANOVA: F(3,42) = 5.04, p = 0.0045). Code comprehension overlapped most
with logic (logic > language), followed by math and least with MSIT and language (Figure 4).
Overlap with logic was significantly higher than with all other tasks, while the overlaps with the
other three tasks (language, math, MSIT) were statistically indistinguishable from each other
(post-hoc paired t-tests, FDR-corrected p’s < 0.05) (Table S3 in the supplementary material).
The overlap of code with logic and math was observed in the IPS, PFC and a posterior portion of
the inferior temporal gyrus (IT). PFC overlap was localized to the anterior middle frontal gyrus
(aMFG, BA 46) and posteriorly in the precentral gyrus (BA 6). Overlap of code and the MSIT (hard
> easy) was also observed in the IPS, precental gyrus and a small portion of the inferior temporal
sulcus. Although MSIT and code overlapped in frontal and parietal areas, like code with logic/math,
the precise regions of overlap within these general locations differed.
Finally, code overlapped with language (language > math) in portions of the inferior frontal gyrus
and the posterior aspect of the superior temporal sulcus/middle temporal gyrus. The overlap
between language and code was on average low, and the degree of overlap varied considerably
across participants (cosine sim range: [0.105, 0.480]), with only half of the participants showing
above chance overlap. Notably there was no relationship between overlap of code and language
and level of expertise, as measured either by years of experience coding (regression against
code-language overlap: R2 = 0, p = 0.99; regression against code-math overlap: R2 = 0.033, p =
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0.52) or performance on coding assessments (regression against code-language overlap: R2 =
0.033, p = 0.52; regression against code-math overlap: R2 = 0.064, p = 0.36).
Lateralization
The group activation map suggested that code comprehension is left-lateralized. Analyses of
individual lateralization indices showed that indeed, code comprehension was as left-lateralized
as language (Code lateralization index mean = 0.451, one-sample t-test against 0: t(14) = 5.501,
p < 0.001; Language mean = 0.393, t(14) = 5.523, p < 0.001; paired t-test between code and
language: t(14) = 1.203, p = 0.25). Moreover, lateralization indices of code and language were
highly correlated across individuals (R2 = 0.658, p < 0.001) (Figure 5).
Discussion
A consistent network of left-lateralized regions was activated across individuals during Python
code comprehension. This network included the intraparietal sulcus (IPS), several regions within
the lateral prefrontal cortex (PFC) and the posterior-inferior aspect of the middle temporal gyrus
(pMTG). This code responsive network was more active during real than fake code trials, even
though for expert Python coders, the fake code task was more difficult (as measured by reaction
time) than the real code task. Within this code-responsive neural network, spatial patterns of
activation distinguished between for vs. if code functions, suggesting that this network
represents code-relevant information and is not merely activated during the coding task due to
general difficulty demands. In overlap analyses, the code comprehension network was most
similar to the fronto-parietal system involved in formal logical reasoning and to a lesser degree
math. By contrast overlap with the perisylvian fronto-temporal language network is low.
Code overlaps with logic
Code, logical reasoning, math and the MSIT task all activated aspects of the so-called fronto-
parietal executive control system. However, overlap of code with logic was most extensive,
followed by math and finally the MSIT. The difference between the MSIT task on the one hand
and code comprehension, logic and math on the other, was particularly pronounced in the frontal
lobe. There only code, logic and math activated more anterior regions of prefrontal cortex,
including BA 46 and BA 9, although logic-associated activation extended even more anteriorly
than code. These findings suggest that neural overlap between logic and code is specific, and not
fully accounted for by the general involvement of the central executive system.
Previous studies also find that the fronto-parietal network, including anterior prefrontal areas, are
involved in logical reasoning (Prado, Chadha, & Booth, 2011; Tsujii, Sakatani, Masuda, Akiyama,
& Watanabe, 2011). For example, anterior PFC is active when participants solve formal logical
problems with quantifiers (e.g. all X are Y; Z is a X; therefore Z is Y) and connectives (e.g. if X
then Y; not Y; therefore not X) and plays a key role in deductive reasoning with variables (Coetzee
& Monti, 2018; Goel, 2007; Goel & Dolan, 2004; Monti et al., 2009; Reverberi et al., 2010;
Reverberi et al., 2007; Rodriguez-Moreno & Hirsch, 2009)
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A fronto-parietal network has also been consistently implicated in math (Friedrich & Friederici,
2013; Maruyama, Pallier, Jobert, Sigman, & Dehaene, 2012; Piazza, Pinel, Le Bihan, & Dehaene,
2007; Wendelken, 2015). Some of the parietal responses to math have been linked to the
processing of quantity information (Eger et al., 2009; Nieder, 2016; Nieder & Miller, 2004; Piazza
& Eger, 2016; Roitman, Brannon, & Platt, 2007; Tudusciuc & Nieder, 2009). For example, neurons
in the IPS of monkeys code numerosity of dots (Nieder, 2016). However, much of the same fronto-
parietal network is also active during the processing of mathematical statements free of digits and
arithmetic operations (Amalric & Dehaene, 2016, 2018; Wendelken, 2015). In the current study,
both the anterior prefrontal areas and parietal areas involved in math also overlapped with code
and logical reasoning. Some of this activation could therefore reflect common operations, such
as the manipulation of rules and symbols in working memory. On the other hand, the lower overlap
between coding and math as compared to overlap with coding and logic could be because only
math involves quantitative processing.
The present evidence suggests that culturally derived symbol systems (i.e., code comprehension,
formal logic and math) depend on a common fronto-parietal network, including the executive
system. As noted in the introduction, although each of these symbol systems has its unique
cognitive properties, they also have much in common. All involve the manipulation of abstract
arbitrary symbols without inherent semantic content (e.g. X, Y, input, result) according to
explicit rules. In the current logical inference and code experimental tasks, mental representations
of several unknown variables are constructed (for logic “X”, “Y”, and “Z”, for code “input” and
“result”) and the relationships between them deduced according to rules of formal logic or code.
There are also important differences between the rules of logical inference and programming.
Take “if” conditional judgement for example again. In formal logic, the statement “if P then Q”
doesn’t imply anything about what happens when P is false. On the contrary, in Python and most
other programming languages, the statement
if condition==True:
do_something()
automatically implies that when the condition is false, the function “do_something()” isn’t
executed, unless otherwise specified. Learning to program involves acquiring the particular set of
conventionalized rules used within programming languages and a syntax that specifies how the
programming language in question expresses logical operations (Dalbey & Linn, 1985; Pea &
Kurland, 1984; Pennington, 1987; Robins, Rountree, & Rountree, 2003). We speculate that such
knowledge is encoded within the fronto-parietal network identified in the current study. Future
studies comparing coders with different levels of expertise should test whether learning to code
modifies circuits within the code-responsive neural network identified in the current study.
The involvement of the multiple-demand executive control system in code
comprehension
Code comprehension showed partial overlap with the MSIT task, particularly in the parietal cortex
and in posterior frontal areas. Previous work has noted cognitive and neural similarity between
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arbitrary small-scale working memory tasks, such as the MSIT, and formal symbol systems
(Anderson, 2005; Qin et al., 2004). As noted in the introduction, the MSIT task is a classic localizer
for the executive function system (e.g., Stroop, n-back and MSIT) (Duncan, 2010; Fedorenko,
Duncan, & Kanwisher, 2013; Miller & Cohen, 2001; Woolgar et al., 2011; Zanto & Gazzaley, 2013;
Zhang et al., 2013). Like code comprehension, most experimental tasks that activate the central
executive system involve the maintenance, manipulation and selection of arbitrary stimulus
response mappings according to a set of predetermined rules (Woolgar et al., 2011; Zhang et al.,
2013). For example, in the MSIT task among the many possible ways to map a visually presented
digit triplet to a button press, the participants had to maintain in their working memory the rule to
press the button whose index corresponds to the value of the unique digit in the triplet. In the
difficult condition, participants use a less natural rule to make a response.
Previous studies also showed that the fronto-parietal executive system was involved in rule
maintenance and switching, as well as variable representation. In one task-switching study the
fronto-parietal executive system was active when participants maintained a cued rule in working
memory and the level of activity increased with the complexity of the rule maintained (Bunge,
Kahn, Wallis, Miller, & Wagner, 2003). Patterns of neural activity within the executive system
encoded which rule is currently being applied and activity is modulated by rule switching
(Buschman, Denovellis, Diogo, Bullock, & Miller, 2012; Crittenden & Duncan, 2014; Xu et al.,
2017). Finally, studies with non-human primates found that neurons in the frontal lobe encode
task-based variables (Duncan, 2010; Kennerley, Dahmubed, Lara, & Wallis, 2009; Nieder, 2013).
Such processes, studied in the context of simple experimental tasks, may also play a role in code
comprehension.
Although formal symbol systems and simple rule-based tasks share cognitive elements, tasks
such as the MSIT involve simple rules that specify stimulus response mappings, rather than
mental manipulations of variables. An intriguing possibility is that the neural machinery supporting
code comprehension, as well as other culturally derived symbol systems, is a subset of a system
that originally evolved for the maintenance and manipulation of simpler variables and rules
(Anderson, 2005; Qin et al., 2004).
Code comprehension and language
We find that the perisylvian fronto-temporal network that is selectively responsive to language,
relative to math, does not overlap with the neural network involved in code comprehension.
Previous studies also found that math and formal logic did not depend on classic language
networks (Amalric & Dehaene, 2016; Monti et al., 2009). Lack of overlap between code and
language is intriguing given the cognitive similarities between these domains (Fedorenko et al.,
2019; Pandža, 2016; Peitek et al., 2018; Portnoff, 2018; Prat et al., 2020; Siegmund et al., 2014).
As noted in the introduction, programming languages borrow letters and words from natural
language, and both natural language and code have hierarchical, recursive grammars (Fitch et
al., 2005) .
One possible explanation for low overlap between the perisylvian fronto-temporal language
network and code is that the language system is evolutionarily predisposed to support natural
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language processing and not generalizable even to similar domains, like computer code and
formal logic (Dehaene-Lambertz, Hertz-Pannier, & Dubois, 2006; Fedorenko et al., 2011). Timing
could also play a role. The perisylvian fronto-temporal language network may have a sensitive
period of development during which it is most capable of learning (Cheng, Roth, Halgren, &
Mayberry, 2019; Mayberry, Davenport, Roth, & Halgren, 2018; Ramirez et al., 2016). By the time
people learn to code, the network may be incapable of taking on new cognitive functions. Indeed,
even acquiring a second language late in life leads to lower levels of proficiency and responses
outside the perisylvian fronto-temporal system (Hartshorne, Tenenbaum, & Pinker, 2018;
Johnson & Newport, 1989). These observations suggest that domain-specific systems, like the
perisylvian fronto-temporal language network, are not always amenable for “recycling” by cultural
inventions. The fronto-parietal system might be inherently more flexible throughout the lifespan
and thus more capable of taking on new cultural skills (Riley, Qi, Zhou, & Constantinidis, 2018).
Despite lack of direct overlap, lateralization patterns of language and coding were highly
correlated across individuals i.e. those individuals with highly left-lateralized responses to
sentences also showed highly left lateralized responses to code. This intriguing observation
suggests that the relationship between code and language may be ontogenetic as well as
phylogenetic. It is hard to imagine how code in its current form could have been invented in the
absence of language (Fitch et al., 2005). Ontogenetically, code-relevant neural representations
might be enabled by the language system, even though they are distinct from it.
An analogous example comes from the domain of reading (Dehaene et al., 2010; McCandliss,
Cohen, & Dehaene, 2003). Reading-relevant regions, such as the visual word form area (VWFA),
are strongly co-lateralized with the perisylvian fronto-temporal language network across people
(Cai, Paulignan, Brysbaert, Ibarrola, & Nazir, 2010). The VWFA has strong anatomical
connectivity with the fronto-temporal language network even prior to literacy (Bouhali et al., 2014;
Saygin et al., 2016). Analogously, code comprehension may colonize a left-lateralized portion of
the central executive system due to its stronger (i.e., within hemisphere) connectivity with the
perisylvian fronto-temporal language network.
Conclusions
A fronto-parietal cortical network is consistently engaged in expert programmers during code
comprehension. Patterns of activity within this network distinguish between for and if functions.
This network overlaps with other culturally derived symbol systems, in particular formal logic and
to a lesser degree math. By contrast, the neural basis of code is distinct from the perisylvian
fronto-temporal language network. Rather than recycling domain specific cortical mechanisms for
language, code, like formal logic and math, depends on a subset of the domain general executive
system, including anterior prefrontal areas. The executive system may be uniquely suited as a
flexible learning mechanism capable of supporting an array of cultural symbol systems acquired
in adulthood.
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Figures
Figure 1. The experiment design. The FAKE function (bottom row) in this figure is created by
scrambling the words and symbols in each line of the REAL function (top row). Note that for the
purpose of illustration, the relative font size of the text in each screen shown in this figure is
larger than what the participants saw during the actual MRI scan.
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Figure 2. Whole brain contrasts. Areas shown are p<0.05 cluster-corrected p-values, with
intensity (both warm and cold colors) representing uncorrected vertex-wise probability. In the
maps for each localizer contrast, both warm and cold colors indicate activated vertices in the
contrast, with the cold color labelling the overlap with the code contrast.
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Figure 3. (a) The four search spaces (IPS, pMTG, PFC, OCC in the left hemisphere) within
which functional ROIs were defined for the MVPA. (b) The MVPA decoding accuracy in the four
ROIs. Error bars are mean ± SEM. *P<0.05. ***P<0.001.
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Figure 4. (a) Brain map with the activated regions in the five contrasts reported in Figure 2
overlain. The language network is shown in transparent blue, math in transparent red, and logic
in transparent green. The regions activated in the MSIT contrast are enclosed in black outlines,
and the code-responsive regions are enclosed in yellow outlines. (b) Cosine similarity between
code contrast and each localizer contrast, in each hemisphere. Each dot represents the data
from one participant. The dotted line on each bar indicates the null similarity between code
contrast and the given localizer contrast. The yellow dashed line in each hemisphere indicates
the empirical upper bound of the cosine similarity, the similarity between code comprehension
and itself, averaged across participants. Error bars are mean ± SEM. *P<0.05. **P<0.01.
***P<0.001
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Figure 5. (a) The lateralization index of the code contrast and the localizer contrasts. Each white
dot stands for one participant, and the enlarged dots represent the mean values. (b) The
lateralization indices of code contrast and language contrast are highly correlated.
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