Spontaneous and automatic processing of magnitude and parity information of Arabic digits: A frequency-tagging EEG study

Arabic digits (1-9) are everywhere in our daily lives. These symbols convey various semantic information, and numerate adults can easily extract from them several numerical features such as magnitude and parity. Nonetheless, since most studies used active processing tasks to assess these properties, it remains unclear whether and to what degree the access to magnitude and especially to parity is automatic. Here we investigated with EEG whether spontaneous processing of magnitude or parity can be recorded in a frequency-tagging approach, in which participants are passively stimulated by fast visual sequences of Arabic digits. We assessed automatic magnitude processing by presenting a stream of frequent small digit numbers mixed with deviant large digits (and the reverse) with a sinusoidal contrast modulation at the frequency of 10 Hz. We used the same paradigm to investigate numerical parity processing, contrasting odd digits to even digits. We found significant brain responses at the frequency of the fluctuating change and its harmonics, recorded on electrodes encompassing right occipitoparietal regions, in both conditions. Our findings indicate that both magnitude and parity are spontaneously and unintentionally extracted from Arabic digits, which supports that they are salient semantic features deeply associated to digit symbols in long-term memory.

what degree the access to magnitude and especially to parity is automatic. Here we 23 investigated with EEG whether spontaneous processing of magnitude or parity can be 24 recorded in a frequency-tagging approach, in which participants are passively 25 stimulated by fast visual sequences of Arabic digits. We assessed automatic magnitude 26 processing by presenting a stream of frequent small digit numbers mixed with deviant 27 large digits (and the reverse) with a sinusoidal contrast modulation at the frequency of 28 10 Hz. We used the same paradigm to investigate numerical parity processing, 29 contrasting odd digits to even digits. We found significant brain responses at the 30 frequency of the fluctuating change and its harmonics, recorded on electrodes 31 encompassing right occipitoparietal regions, in both conditions. Our findings indicate 32 that both magnitude and parity are spontaneously and unintentionally extracted from 33 AUTOMATICITY OF MAGNITUDE AND PARITY non-symbolic comparison [92] , but also for exclusively symbolic comparison [64,91] . 149 Moreover, the same bilateral IPS region was activated during numerical magnitude 150 comparison as well as parity categorization in a PET study [63] , in which the authors 151 consequently proposed that parity and magnitude are processed in neighbouring areas. 152 It was also proposed that both the occipitoparietal network used for perceptual and 153 representational processing of Arabic digits and the frontoparietal network used for 154 semantic processing are involved in numerical processing such as magnitude 155 comparisons and arithmetical facts retrieval [64,65] . 156 The parietal cortex is also associated with automatic processing of number symbol 157 semantics. Tasks requiring the simple detection of visual numerals or number words 158 activate the IPS significantly more than the same tasks with non-numerical stimuli (e.g., 159 detection of letters or colours [69] ). To the best of our knowledge, only a few studies 160 further investigated automatic responses to number symbol magnitudes, and none 161 examined automatic parity processing. Noticeably, using fMRI, a study reported 162 stronger BOLD responses for large digits (8 or 9) than for small digits (1 or 2) within 163 two bilateral parietal regions (i.e., the inferior parietal lobule and the IPS), when 164 investigating the neural correlates of non-predictive number cues [70] . Other studies 165 reported greater ERP amplitudes across parietal electrode regions for small digits 166 compared to large digits, in a task where numbers were used as non-informative 167 attentional cues [71,72] . Nonetheless, imaging evidence in favour of unintentional 168 processing of magnitude or parity is currently lacking. 169

Current study and experimental design 170
In the present study, we aim at assessing the autonomous unintentional automaticity of 171 magnitude and parity processing, carefully avoiding any triggering of numerical information processing (such that the existence of autonomous unintentional 173 automaticity can be probed [21] ). For that purpose, we used a sensitive frequency-174 tagging approach -Fast Periodic Visual Stimulation (FPVS) -to record 175 electrophysiological responses tagged at the frequency of experimentally manipulated 176 magnitude and parity changes, in a passive viewing setting. Similar FPVS paradigms 177 relying on passive viewing have successfully been used to study high-level 178 discrimination of faces [73] , tools [74] , as well as reading (word recognition [75] , and letter 179 strings discrimination [65,76] ), and non-symbolic quantities [77] , without engaging 180 participants in any kind of explicit processing of the presented stimuli. 181 We combined the FPVS paradigm with a standard/deviant procedure (oddball method 182 [79] ). More precisely, during one-minute sequences, we displayed digits at the very fast 183 rate of 10 Hz (ten stimuli per second) following a sinusoidal contrast modulation. 184 Within the stream of standard digits, a periodic deviant was introduced every eight 185 trials such that digits from the deviant category appeared at 1.25 Hz (see Figure 1). The 186 digits used as standards or deviants varied according to the condition: In the magnitude 187 condition, digits smaller than five were presented as standard and digits larger than five 188 as deviants, or the other way around. In the parity condition, odd digits were presented 189 as standards and even digits as deviants, or the other way around. Finally, in a control 190 condition, half of the digits were arbitrary categorized as standards and the other half as 191 deviants (see Figure 1). 192 We postulate that we should record an electrophysiological response synchronized at 193 the deviation frequency (i.e., 1.25 Hz) if the brain is sensitive to the changes from one 194 category to another. In other words, if magnitude and/or parity are processed in an 195 autonomous unintentional automatic way, then the category changes should systematically elicit a specific brain response at the frequency of the changes for the 197 respective condition(s), while no such response should arise during the control 198 condition as the latter's digit categories were arbitrary and not related to any semantic 199 content. Doing so, we can objectively measure whether a given semantic number 200 information is automatically and unintentionally processed by the brain although no 201 numerical task was requested from the participant. interest and its harmonics up to the seventh (i.e., 1.25, 2.50, 3.75, 5.00, 6.25, 7.50, and 206 8.75 Hz). These maps highlight that the strongest recorded responses in each condition 207 were located over a bilateral region encompassing occipitoparietal areas. It is worth 208 noticing that there was a substantial overlap of the location of the brain responses 209 between the experimental conditions, which allows direct comparison of amplitudes 210 recorded within these regions. 211 systematically reaching values larger than five. These findings support that both 216 occipitoparietal regions specifically synchronised to the 10 Hz base rate during the 217 recording sessions. Note, however, that neural synchronisation to the base rate merely 218 reflects brain response to the periodic stimulus onsets at 10 Hz. 219 More critically for the purpose of the current study, we also observed in Figure 2b large 220 peaks in the frequency bins that are harmonics of the periodic category fluctuation (up 221 to the seventh harmonic). In the Magnitude condition, there were fewer clear peaks 222 across these frequency bins within the left electrodes, but peaks were clearly depicted in 223 the right hemisphere. For the Parity condition, we observed some clear peaks within the 224 left region of interest, and many definite peaks within the right region of interest. 225

AUTOMATICITY OF MAGNITUDE AND PARITY
Finally, more unexpectedly, we also found some responding peaks in the control 226 condition, mostly located within the right occipitoparietal regions. 227 In order to assess whether these peaks were statistically significant, we computed the 228 average signal amplitude of the frequency of interest and its harmonics up to the 229 seventh, expressed as a Z-score, as a function of the condition (see Figure 3) We additionally performed a repeated-measures ANOVA with the region of interest (two 240 levels, either left or right) and the condition (three levels) as fixed factors. There was a 241 significant main effect of the condition, F (2, 88) = 14.409, p < .001, partial η 2 = .179, and 242 a significant main effect of the region factor, F (1, 44) = 5.468, p = .024, partial η 2 = .111. 243 Although the interaction did not reach the significance level, F (2, 88) = 1.761, p = .178, 244 partial η 2 = .038, we conducted pairwise two-sided Wilcoxon tests (since assumption of 245 normality was rejected) to directly compare the amplitudes within each hemisphere. were significantly greater than the control condition, respectively Z = 35, p < .001, and Z 251 = 65, p = .025, but the experimental conditions did not differ from each other, Z = 91, p = 252 .160. 253

Discussion 254
Magnitude and parity are very salient features of number symbols [5,30] . While there are 255 several studies demonstrating the existence of automatic number symbols processing in 256 educated adults, only a few studies could unequivocally demonstrate the existence of 257 autonomous and unintentional number magnitude processing. Therefore, it is still 258 necessary to provide further evidence by triggering magnitude as little as possible in 259 order to disentangle autonomous from intentional automatic processing [21] . Moreover, 260 data concerning an automatic processing of parity are currently lacking. 261 The current FPVS paradigm allows investigating the spontaneous and autonomous 262 nature of specific cognitive processes during passive viewing of rapid sequence [87] . This 263 technique has not yet been used to investigate number symbol processing, though it is 264 very relevant for our objective since it is an objective measure of the brain response at a 265 frequency defined a priori by the experimenter, which allows direct and straightforward 266 analysis of the neural synchronisation. Moreover, the recorded responses quantify the 267 processing of digits' magnitude and parity without an active task and thus, without the 268 implication of decision-making processes [78] . Taken together, the current design 269 avoided any conscious triggering of magnitude or parity during the recording session 270 and thus probe the autonomous nature of these numerical processes. 271 We observed a significant neural synchronisation to changes in numerical magnitude 272 and parity within right occipitoparietal areas, whereas no such synchronisation was 273 found during the control condition. It is noteworthy that visual inspection of SNRs 274 suggests that some brain responses peaked at some harmonics of interest in the control 275 condition, where category was based on temporarily constructed rules, but these peaks 276 did not reach the statistical significance. In contrast, the strong responses within the 277 AUTOMATICITY OF MAGNITUDE AND PARITY right occipitoparietal electrodes indicate that participants implicitly processed the 278 category to which numerical stimuli belong and reacted to changes with respect to the 279 category. Additionally, parity yielded significantly larger brain responses than the other 280 conditions in the left hemisphere. 281 We thus measured substantial implicit responses to the two manipulated semantic 282 features, but not to short-term arbitrary associations. This means that we can exclude 283 that the brain synchronisations recorded in both experimental tasks were only due to 284 the rare nature of the deviant stimulus. These evidences support the view that both 285 numerical magnitude and parity were automatically accessed and processed during 286 passive viewing sessions. In other words, both semantic features are spontaneously and 287 unintentionally extracted from Arabic digits, which corroborates previous observations 288 that several deliberate tasks on Arabic digits (such as naming) are necessarily 289 semantically mediated [14] . It is noteworthy that the automaticity of parity that we 290 observed here does not support the hypothesis arguing that parity is computed by 291 dividing the number by two [56] , but our findings are rather in line with the idea of a 292 direct retrieval from semantic memory [35,57] . 293 The topography of the frequency-tagged responses corresponds with seminal models of 294 numerical cognition, such as the triple-code model [66,80] , since we found significant 295 responses over right occipitoparietal electrodes specifically related to both magnitude 296 and parity changes. This is in line with the hypothesis that the semantic of number 297 representations are housed in parietal regions [98] . The occipitoparietal responses that 298 we obtained during Magnitude and Parity conditions are typical in ERP studies 299 investigating the neural distance effect with Arabic numbers [64,67,68] . These studies 300 highlighted a neural distance effect illustrated by a modulation of the positivity of P2p 301 AUTOMATICITY OF MAGNITUDE AND PARITY recorded over occipitoparietal electrodes as a function of the numerical distance during 302 numerical comparison. These studies, except [68] , also found a dominance of the right 303 hemisphere for numerical magnitude comparison. In the absence of an active task, we 304 similarly found significant right-sided dominance for numerical symbols' processing. 305 We did not, however, observe any significant differences between right hemisphere 306 electrodes responding to parity and magnitude, which is partly in line with a PET study 307 indicating that parity and magnitude information are processed in neighbouring area 308 inside the IPS [81] . 309 Finally, it is noteworthy that each digit presentation only lasted 100ms in the current 310 experimental design (since our base rate was 10Hz, see Figure 1). Previous ERP studies 311 showed that number processing actually follows a time course that involves distinct 312 stages of neural processes [99] . Critically, numerical magnitude was already reported to 313 be early extracted (within 200ms) from digit symbols [99] . Due to the fast display period 314 in the current FPVS paradigm, fewer than 100ms, we can assume that our method 315 mostly captured early cognitive processes. Because we observed significant brain 316 synchronization to magnitude and to parity, our results consequently support that not 317 only magnitude, but also parity information, can be extracted and processed very early 318 in the brain. The time course of the autonomous processing of numerical features could 319 be investigated in future studies by, for instance, varying the base rate of similar FPVS 320 paradigms. More generally, the current paradigm provides strong evidence of 321 unintentional and autonomous processing of semantic information from digits, and it 322 could be easily implemented to follow how symbols' semantic processing becomes 323 automatic across typical and atypical development. 324

AUTOMATICITY OF MAGNITUDE AND PARITY
In summary, we observed significant brain responses tagged at the frequency of 325 magnitude and parity periodic changes over occipitoparietal electrodes during passive 326 viewing of a rapid stream of Arabic digits. We demonstrate that numerical magnitude is 327 spontaneously processed, and we also provide evidence that parity is a semantic feature 328 that is unintentionally activated by Arabic digits in numerate adults. The current study 329 thus provides evidence that culturally learned number symbols become automatically 330 processed by the human mind. 331

Method 332
Participants 333 Twenty-nine undergraduate students from the University of Luxembourg participated in 334 the study. Any history of neurological or neuropsychological disease or any uncorrected 335 visual impairment constituted exclusion criteria. To ensure participants had no major 336 mathematical difficulties, participants' arithmetic fluency was evaluated with the 337 Tempo-Test Rekenen [82] , which is a timed pen-and-paper test (five minutes) consisting 338 in arithmetic problems of increasing difficulty. All participants reached the inclusion 339 criterion, which was 100 correct items out of 200, and were included into the present 340 study. Six participants were excluded from the final sample due to substantial noise in 341 their EEG signal (mostly due to transpiration). The final sample thus consisted in 23 342 adults, with a mean age of 24 years (SD = 3.5). Participants received 30 euros for their 343 participation. 344

Experimental setup 345
We used MATLAB (The MathWorks) with the Psychophysics Toolbox extensions [83:85] to 346 display the stimuli and record behavioural data. The EEG recording took place in a 347 shielded Faraday cage (288 cm × 229 cm × 222 cm). Participants were seated at 1 meter 348 from the screen, with their eyes perpendicular to the centre of the screen (24'' LED 349 monitor, 100 Hz refresh rate, 1 ms response time). Screen resolution was 1024 × 768 350 px, with a light grey background colour. The order of the conditions during the EEG 351 recording session was counterbalanced across participants. 352

Material and Procedure 353 AUTOMATICITY OF MAGNITUDE AND PARITY
Although FPVS paradigm theoretically only involves passive viewing of the stimuli, we 354 introduced a basic orthogonal active task during the recording sessions in order to 355 ascertain that participants were looking at the computer screen. Participants were thus 356 instructed to fixate the centre of the screen where a small blue diamond (12px size) was 357 displayed, and they were asked to press a button with their right forefinger when they 358 detected that the diamond changed its colour from blue to red. This colour change was 359 not periodic and could randomly occur six to eight times in a given sequence. 360 Participants were also informed that black digits ranging from 1 to 9 -excluding 5 -361 would quickly appear on the screen. They were explicitly instructed not to actively look 362 at the digits but to keep their gaze on the central diamond. On average, participants 363 took 640 ms (SD = 121 ms) to respond to the colour change that affected the fixation 364 diamond. Misses were very rare, occurring only in 1.5% of the trials. Such high 365 detection rate indicates that participants followed the instruction and kept their gaze on 366 the centre of the screen during EEG acquisition. 367 Digits were sequentially presented at the fast base frequency of 10 Hz (i.e., ten stimuli 368 per second) following a sinusoidal contrast modulation from 0 to 100 % [73, 77, 86] (see 369 fade-out, which we did not analyse. 373 We used the FPVS variation of the oddball design [79] in which we introduced a periodic 374 fluctuation within the standard sequence: the stimulus category changed every eight 375 items (i.e., at 1.25 Hz). Our design included three different experimental conditions, 376 each consisting in a different category change. In the magnitude condition, periodical 377

AUTOMATICITY OF MAGNITUDE AND PARITY
variations were based on the magnitude of the Arabic digit (i.e., smaller than 5 or larger 378 than 5). For half of the sequences, the standard stimuli displayed at the base rate were 379 randomly drawn among the smallest numbers (1, 2, 3, 4) whereas the deviant item was 380 randomly drawn among the largest numbers (6, 7, 8, 9). For the other half, it was the 381 opposite, the greatest numbers were standards and the smallest ones were deviant. In 382 the parity condition, periodical variation was based on the parity of the Arabic digit (i.e., 383 odd vs. even). For half of the sequences, the odd category (1, 3, 7, 9) was standard and

EEG acquisition 400
We used a 128-channel BioSemi ActiveTwo system (BioSemi B. V., Amsterdam, The 401 Netherlands) tuned at 1024 Hz to acquire EEG data, as in [77] . We positioned the 402 electrodes on the cap according to the standard 10-20 system locations (for exact 403 position coordinates, see http://www.biosemi.com). We used two supplementary 404 electrodes, the Common Mode Sense (CMS) active electrode and the Driven Right Leg 405 (DRL) passive electrode, as reference and ground electrodes, respectively. We held 406 electrodes offsets (referenced to the CMS) below 40 mV. We also monitored eye 407 movements with four flat-type electrodes; two were positioned lateral to the external 408 canthi, the other two placed above and below participant's right eye; but we did not 409 further analyse these electrodes. 410

EEG analysis 411
Analyses were conducted with the help of Letswave 6 412 (http://nocions.webnode.com/letswave). Before starting the analyses, we down-413 sampled our data file resolution from 1024 Hz to 512 Hz for faster computer processing. 414 We used a 4-order band-pass Butterworth filter (0.1 to 100 Hz) and we then re-415 referenced the data to the common average. We did not interpolate any electrode nor 416 correct the EEG signal for the presence of ocular artefacts. The fade-in and the fade-out 417 periods were excluded from the analyses leading to the segmentation of an EEG signal of 418 60 seconds (corresponding to the display of 600 stimuli). We averaged the signal from 419 all repetitions 3 of each condition for each participant. We then performed a Fast Fourier 420 3 We did not expect that brain responses to deviant odd digits within a sequence of standard even digits would be different than brain responses to deviant even digits within a sequence of values [73, 77, 88:90] ). We used SNRs to depict the frequency spectra and illustrate the 431 topographies of our results (see Figure 2). 432 We also computed a Z-score to assess the statistical significance of the brain responses 433 to the category change. To do so, for each condition and for each participant, we 434 cropped the FFT spectra around the frequency of interest (1.25 Hz) and its subsequent 435 harmonics up to the seventh (i.e., 1.25, 2.5, 3.75, 5, 6.25, 7.5, and 8.75 Hz) surrounded by 436 their twenty respective neighbouring bins (ten on each side [77] ). We summed all 437 cropped spectra and then applied a Z-transformation to the amplitudes. We finally 438 extracted from this Z-transformation the value across the frequency bins of interest. 439 This value represents the brain response specific to the experimental manipulation at 440 1.25Hz, which can be interpreted as the neural detection of the change of the stimulus 441 category. As a Z-score, a value larger than the threshold of 1.64 (p < .05, one-tailed, 442 standard odd digits in the Parity condition (and similarly for small and large numbers in the Magnitude condition). We thus aggregated all repetitions for these conditions. AUTOMATICITY OF MAGNITUDE AND PARITY testing signal level > noise level) indicates a significant response to our experimental 443 manipulation. 444

Ethical considerations 445
All procedures performed in this study were in accordance with the ethical standards of 446 the APA, and with the 1964 Helsinki Declaration and its later amendments or com-447 parable ethical standards. The Ethic Review Panel from the University of Luxembourg 448 approved the methodology and the implementation of the experiment before the start of 449 data collection. Informed consent was obtained from all individual participants included 450 in the study. 451

Authors' contribution 452
All authors contributed to designing the study; CS and AVR directed the project; MG 453 created the acquisition software; MG and AP collected the data; AP analyzed the data; AP 454 and MG wrote the paper with input from AVR and CS. 455

Acknowledgements 456
The authors would like to thank Aliette Lochy for her advises in data analysis. 457

Conflicts of interest 458
The author(s) declared no potential conflicts of interest with respect to the research, 459 authorship, and/or publication of this article.