Differences in fractal patterns and characteristic periodicities between word salads and normal sentences: Interference of meaning and sound

Fractal dimensions and characteristic periodicities were evaluated in normal sentences, computer-generated word salads, and word salads from schizophrenia patients, in both Japanese and English, using the random walk patterns of vowels.　In normal sentences, the walking curves were smooth with gentle undulations, whereas computer-generated word salads were rugged with mechanical repetitions, and word salads from patients with schizophrenia were unreasonably winding with meaningless repetitive patterns or even artistic cohesion. These tendencies were similar in both languages. Fractal dimensions between normal sentences and word salads of schizophrenia were significantly different in Japanese [1.19 ± 0.09 (n = 90) and 1.15 ± 0.08 (n = 45), respectively] and English [1.20 ± 0.08 (n = 91), and 1.16 ± 0.08 (n = 42)] (p < 0.05 for both). Differences in long-range (>10) periodicities between normal sentences and word salads from schizophrenia patients were predominantly observed at 25.6 (p < 0.01) in Japanese and 10.7 (p < 0.01) in English. The differences in fractal dimension and characteristic periodicities of relatively long-range (>10) presented here are sensitive to discriminate between schizophrenia and healthy mental state, and could be implemented in social robots to assess the mental state of people in care.


Introduction
Language is generally regarded as a one-dimensional array working in a multidimensional space where characters interact with each other, from short to long-range, resulting in the formation of particular patterns, such as words and sentences. Such patterns typically represent meaning, and include human thoughts, feelings, emotions, will, and knowledge. Words are generated by choosing an appropriate word from multiple synonyms that possess various nuances (homonymy or polysemy) [1][2][3][4][5], and during that selection, the acoustic or sound image of signs is referred to. The interference between the sound image and the meaning discriminates the natural language from programming language or mathematical language.
The present study mainly focused on vowels in texts generated by healthy individuals (normal controls), computer-generated word salads (computer salads), and word salads from patients with schizophrenia (human salads). Here we applied the meaning independent methods, i.e. fractal and Fourier analyses. To do that we initially defined the rule of random walk as shown in Fig 1 and used the fractal concept (a mathematical object that is characterized by self-similarity) to characterize the complexity at the character level in a given text. The fractal dimension shows how the detail of a fractal pattern changes with scale, and is used as an index of complexity. The positions of a vowel within the text array form a fractal pattern with a specified dimension. We calculated the differences in fractal dimensions between three categories (normal sentences, computer-generated word salads, and word salads from patients with schizophrenia) and also examined the characteristic periodicities using Fourier transformation between three groups in both Japanese and English to characterize the internal structure embedded in the texts, and discussed the interpretation of the calculated results from the view point of a classic psychiatric theory [24].

Text selection in six groups
For normal conversations in Japanese (NJ), 90 texts were selected from articles found in Japanese newspapers (Yomiuri-Shinbun and Kyoto-Shinbun), blogs, and E-books. The content of the newspapers and blogs included fashion, politics, culture, sports, hobbies, medicine, and everyday life. E-books were selected from various categories, including detective, mystery, history, and romance novels. Texts were selected by shuffling the texts and selecting them for further analyses using a table of random numbers.
Ninety computer-generated word salads in Japanese (CJ) were generated using a Japanese word salad generator (https://anagram.httqs.com/). For the input, we used the same condition described for NJ, including randomization. Rules of random walk. Rules of the random walk (A) Initial position of the text was always (0, 0) in the (x, y) coordinates. In Japanese, when i-th vowel was "a", then the i-th position increased by one in the y coordinate [i.e., (x i , y i ) = (x i-1 , y i-1 +1)]. When the i-th vowel was "i", then (x i , y i ) = (x i-1 +1, y i-1 ). When the i-th vowel was "e", then (x i , y i ) = (x i-1 −1, y i-1 ). When the i-th vowel was "o", then (x i , y i ) = (x i-1 , y i-1 −1). On the other hand, when the i-th vowel was "u", then it remained in the same position [i.e., (x i , y i ) = (x i-1 , y i-1 )]. (B) In English, the rule was only conventional, i.e. when i-th character was "e", then the i-th position increased by one in the y coordinate [i.e., (x i , y i ) = (x i-1 , y i-1 +1)]. When the i-th character was "o", then (x i , y i ) = (x i-1 +1, y i-1 ). When the i-th character was "a", then (x i , y i ) = (x i-1 −1, y i-1 ). When the i-th vowel was "r", then (x i , y i ) = (x i-1 , y i-1 −1). On the other hand, when the i-th vowel was "i", then it remained in the same position [i.e., (x i , y i ) = (x i-1 , y i-1 )]. https://doi.org/10.1371/journal.pone.0247133.g001 Word salads in Japanese (SJ) were obtained by searching the website of the Non-Profit Organization (NPO) Japan Medical Abstracts Society (Ichushi-Web) and 45 words salads were selected from published articles on psychological diseases. Selection criteria were as follows: 1) Diagnosis must be categorized as axis II in DSM 5 [25] (schizophrenia spectrum and other psychotic disorders) or included axis II. 2) Words or sentences of the patients must be unintelligible and long enough (> 128 characters) for the analyses. Summary of patients is listed in S1 Table, and examples in SJ are shown in S1 File. Obtained number of nouns to number of characters ratios for NJ, CJ and SJ were 0.091 ± 0.032, 0.083 ± 0.023 and 0.10 ± 0.017, respectively, and there were no statistically significant differences between them.
For normal conversations in English (NE), 91 texts were selected among the articles in English newspapers (The Asahi Shimbun and The Japan Time), blogs, and E-books. The content of the newspapers and blogs included fashion, politics, culture, sports, hobbies, medicine, and everyday life. E-books were selected from multiple categories, including detective, mystery, history, and romance novels. Texts were selected by shuffling all the texts and selecting those in Japanese.
Computer-generated word salads in English (CE) were generated using a word salad generator in English (http://cadrpear.tx0.org/wordsalad/salad.html). For the input, the same conditions as described above in NE were used, including randomization.
Word salads in English (SE) were obtained by searching PubMed (https://pubmed.ncbi. nlm.nih.gov/) using the keyword "word salad" and selected 42 words salads in published articles on psychological diseases. Selection criteria were as follows: 1) Diagnosis must be categorized as axis II in DSM 5 [25] (schizophrenia spectrum and other psychotic disorders) or include axis II. 2) Words or sentences of the patients must be unintelligible and long enough (> 128 characters) for the analyses. Summary of patients is listed in S2 Table, and examples in SE are shown in S1 File. Obtained number of nouns to number of characters ratios for NE, CE and SE were 0.044 ± 0.012, 0.057 ± 0.005 and 0.044 ± 0.010, respectively, and there were no statistically significant differences between them.
Since vowels in English are more complicated than those of Japanese, just for comparison, we selected five characters, i.e. when i-th character was "e", then the i-th position increased by one in the y coordinate [i.e., (x i , y i ) = (x i-1 , y i-1 +1)]. When the i-th character was "o", then (x i , y i ) = (x i-1 +1, y i-1 ). When the i-th charcater was "a", then (x i , y i ) = (x i-1 −1, y i-1 ). When the i-th vowel was "r", then (x i , y i ) = (x i-1 , y i-1 −1). On the other hand, when the i-th character was "i", then it remained in the same position [i.e., (x i , y i ) = (x i-1 , y i-1 )]. We ignored punctuation characters and spaces for analysis. Also the analyses were case-insensitive. Although there are many ways for selection of characters in English, and the rule described above is just conventional, but generality is not lost in view of fractal analyses and Fourier transformation.

Determination of fractal dimensions
Text is a specific arrangement of characters in a one-dimensional array that carries meaning. Random rearrangement of the characters across the text significantly reduces its meaning; hence, the ordering of the characters is important to the meaning. In other words, the meaning shows regularity in a text, which may manifest itself in a pattern of occurrence of each character in the text array. If we consider the text array as a one-dimensional space, the spatial pattern of occurrence of any character will form a fractal set or simply a fractal. We can assign a fractal dimension to any character in a given text using the practical method of box counting using software, such as the box count routine in MatLab (Mathworks) or Fractal Analysis System by Hiroyuki Sasaki at National Agriculture and Food Research Organization. Using this method, the obtained fractal dimension of random walk was between 1 and 2. IBM SPSS Statistics Base (version 26) was used for statistical analysis (one-way ANOVA).

Fourier analyses
Microsoft Excel 2016 functions were used to perform Fast Fourier transform analyses and power spectra were obtained as a function of periodicity. Baseline biases were removed by calculating the difference in periodicities between each pair of groups and statistically evaluating the significance of each periodicity. IBM SPSS Statistical Base (version 26) was used for statistical analysis (one-way ANOVA).

Universal properties of texts
All random walk patterns for the utilized texts are shown in S1 Fig. In Japanese texts, the use of "i" was dominant compared with the use of "e," and the use of "a" was slightly dominant compared with that of "o". Similar tendencies were also observed in English, in that the use of "e" or "o" was predominant compared with that of "r" or "a", respectively. Several representative curves were plotted to show the details of the random walks (Figs 2 and 3). Random walk patterns were markedly different between the three groups NJ and NE, CJ and CE, and SJ and SE). In normal conversations (NJ and NE), the curves were smooth with gentle undulations, whereas in computer-generated word salads (CJ and CE), they were rugged with mechanical repetitions. Word salads generated from patients with schizophrenia (SJ and SE) were unreasonably winding with a meaningless repetitive pattern or even artistic cohesion. These tendencies were similar in both languages.

Determination of fractal dimensions
In box counting, the space is divided into boxes and each box that contains a component of the fractal set is called a filled box. The fractal law is a power law relationship between the number of filled boxes and the box size. To calculate the fractal dimension of a character using boxcounting method, the text array is divided into boxes of size s, and each s consecutive character is placed in a box. The number of such boxes is N s = N/s, where N is the length of the text. If the considered character appears in one of the boxes, that box is a filled box, and N b (s) stands for the number of filled boxes. A power law relationship exists between the number of filled boxes and the box size, s, as follows: N b (s) / s -D , where D is the fractal dimension of the character. The fractal dimension is obtained by measuring the slope of log-log plot of N b (s) versus s.

Characteristic periodicities
The characteristic periodicities were calculated for the six groups. The results of the whole Fourier analysis are shown in S2-S4 Figs. Characteristic periodicities with statistical significance (p < 0.01) are shown in Table 1, and the representative plots of the p-value as a function of periodicities are shown in Fig 5. Relatively long-range periodicities (>9) were observed between NJ and SJ, NE and SE, and CJ and SJ (Fig 5A and 5B and Table 1). On the other hand, relatively short-range periodicities (<4) were frequently observed when computer-generated word salads were included, such as NJ and CJ, and NE and CE (Fig 5C and 5D and Table 1). These results suggest that short-range periodicities were mainly embedded in the computergenerated word salads, whereas long-range periodicities were observed in the differences between normal sentences and word salads, suggesting that the interference between meaning and sound may occur in the long-range periodicity regions.

Discussion
Various meaning models, such as the latent semantic analyses [8,17,26] was applied to schizophrenia to analyze the incoherence of speech. They used 37,651 text samples with 92,408   Table 1). (D) In Japanese 'e', significant difference between were observed at short-range periodicities (See Table 1 unique words and matrices of 300 dimensions to perform SVD analyses. The basic question is whether it is possible to differentiate the coherence and the incoherence of speech in terms of meaning by the usage count. Rare usage or rare combination of words do not necessarily mean the incoherence in terms of meaning. We should remember that the novel scientific findings were explained only by the novel combinations of ever-existing words. Coherence of meaning in words is independent of the usage count, and is connected to cognitive function of the brain. Computational linguistic analysis on verbal fluency has been conducted using an automated tool, CoVec [27] to detect the speech disorganization, such as derailment and tangentiality in schizophrenia. In this analysis, coherence was defined as the average similarity (norm) of each word to other words. Statistical tests (such as ANOVA) on the calculated norm was performed for pairwise comparison between control subjects and patients. However, the low similarity defined above does not necessarily mean any disorganization or abnormality in speech. Rare combinations of words with clear logical connection does not mean derailment nor tangentiality. Logical connections of words may not allow such usage count analyses, because completely new word connections, novel concepts or creative works must originate from a zero matrix element. Furthermore, more important linguistic aspects, such as acoustic characteristics [28] are still missing, and it is essentially questionable whether they could be further characterized using natural language processing (NLP) and machine learning (ML) techniques [29].
Here we employed fractal analysis and Fourier transformation methods for analyzing word salads, which are essentially independent of above meaning models. Differences in fractal dimension and characteristic periodicities between normal sentences and word salads may represent interference between meaning and sound in languages. We predominantly observed high power at relatively long-range periodicity around 6 and 9 in normal sentences in Japanese (S2A, S2K, and S2P Fig). These differences suggest that the vowel sound around the periodicity of 6 and 9 may affect the meaning. Although the working mechanism remains unclear, these characteristic periodicities are essential for understanding sentences or transmitting the exact meaning.
Several approaches have been reported regarding brain rhythmicity [30] or category fluency [31] and genes, network connectivity using a computational model [32], symptomatology and white matter tracts [33], and relationship with antipsychotic medication [34]. Although the reading mechanism of DNA sequence is well-understood biologically, the cognitive mechanism of language remains unclear. Thus, we propose a hypothetical theory based on the classic theory of psychiatry, which may explain our findings.
In 1960, the psychiatrist, Jacques Lacan, described the notion of "le point de capiton" [24], at which in individual sews two pieces of cloth together. One cloth is referred to the "signifier", represented by curve S in Fig 6, which denotes the desire that leads the individual to express the sign, and the other is referred to as the "signified", represented by curve S', which results in the signification during speech or writing [35]. Sassure proposed that the signified predominates over the signifier because the language is used to transfer the exact meaning [35], whereas Lacan argued that the signifier predominates at the level of unconsciousness and determines the logic by which symptoms are organized [24]. This indicates that the signifier and signified do not necessarily coincide. In fact, incoherence in speech has been reported in schizophrenia and quantified compared with that of healthy controls [17], and normative associations in the speech of individuals at familial high-risk of schizophrenia were reportedly decreased [18].
The present study found that the fractal dimension for normal sentences was significantly higher than that of word salads in both Japanese and English (Fig 4). A fractal dimension of 1.0 indicates a simple repetition of short segments, suggesting meaningless sentences. Hence, a fractal dimension >1.0 may correlate with the complexity of sentences i.e., the higher density of meaning. Thus density of the meaning in normal sentences are higher than those in word salads of schizophrenia both in Japanese and English. We also found that the characteristic periodicities in vowels in words salads were longer range than those of normal sentences (S2 and S3 Figs, Fig 5).
These findings suggest that the "le point de capiton" of words salads are sparser than those of normal sentences (Fig 6). If "le point de capiton" becomes sparse enough, it would lead to loosening of the association between S and S', which corresponds to the typical symptoms of schizophrenia generating word salads. In other words, at "le point de capiton," deeply impressive words with an emotional sound would appear to have imperturbable meaning, and the meaning of words between the "le point de capiton" would emerge spontaneously with clear meaning. "Le point de capiton" would be repeated at a long-range periodicity and the meaning of whole sentences would become deterministic.
Regardless of the detailed mechanism, the analyses used in the present study could be used to elucidate mental state, such as schizophrenia, and could also be implemented in future in social robots to assess the mental state of a person in care.

Conclusion
The fractal dimension and Fourier analyses of human languages focusing on vowels presented in the present study useful for elucidating differences in normal sentences and various word salads. These methods are essentially independent of the meaning of the written or spoken word, and thus the relevant algorithms presented in the present study could be easily implemented in social robots to assess the mental state of a person in care. In future, we aim to construct a social robot that can communicate with people to determine their cognitive state and offer appropriate advice.