# A Mathematical Analysis of Maria Valtorta’s Mystical Writings

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## Abstract

**:**

## 1. Introduction

## 2. Maria Valtorta’s Life and Literary Production

## 3. Some Mathematical Parameters of Text Analysis

## 4. Statistical Results on Maria Valtorta’s Writings

## 5. Kolmogorov−Smirnov Test for Comparing Probability Distributions

#### 5.1. Density and Probability Distribution Functions

#### 5.2. Readability Index $G$

#### 5.3. Characters per Word ${C}_{P}$

#### 5.4. Words per Sentence ${P}_{F}$

#### 5.5. Word Interval ${I}_{P}$

#### 5.6. Test Conclusions

## 6. Comparing Different Literary Texts: Euclidean Distances

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Scaling Statistics to Text Blocks of Same Length

## Appendix B. Log-Normal Probability Density and Distribution Functions

## Appendix C. Test Variable in the Kolmogorov−Smirnov Test

## References

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1 | Notice that Jesus’ crucifixion date, derived by the astronomical analyses of Maria Valtorta writings, is April 23 of the year 34. Thus, her visions seems to begin just in the anniversary of Jesus’ crucifixion (Matricciani and De Caro 2017; De Caro 2014, 2015, 2017; La Greca and De Caro 2017). |

2 | The Italian title is l’Evangelo come mi è stato rivelato, therefore E stands for Evangelo (i.e., Gospel) and MV for Maria Valtorta’s initials. |

3 | Defined by the editor Emilio Pisani. |

4 | Referred to as Azariah in the following. |

5 | Referred to as Romans in the following. |

6 | EMV chapters: 241, 245, 252, 276, 278, 281, 281, 329, 337, 338, 352, 364, 381, 385, 394, 407, 419, 425, 448, 452, 467, 484, 489, 501, 505, 513, 515, 523, 554, 558, 567, 569, 570, 572, 584, 584. |

7 | EMV chapters: 49, 50, 64, 68, 79, 92, 93, 96, 98, 108, 119, 120, 122, 123, 125, 127, 128, 129, 131, 145, 154, 157, 159, 169, 170, 171, 172, 173, 174, 176, 180, 211, 212, 277, 288, 297, 342, 344, 352, 354, 363, 371, 378, 397, 398, 399, 421, 423, 428, 447, 448, 451, 455, 457, 463, 487, 491, 493, 506, 507, 514, 518, 526, 532, 534, 540, 551, 554, 567, 577, 583, 591, 596, 596, 596, 597, 600. From 119 to 131 sermons at the Acqua Speciosa. From 169 to 176 sermons on the mount. Speech to Judas thief, 567. Last Supper, 600. |

8 | Only the texts attributed specifically to Azariah are considered. |

9 | Only the texts attributed specifically to the Holy Author are considered. |

10 | “366” indicates the chapter, “9” indicates the subdivision of the chapter. |

11 | In this case, the number refers to text blocks of about 1000 words. Notice that the reference to text blocks of a given number of words does affect the standard deviation of the random variable, but does not change its average value and standard deviation of the average value. |

12 | In this case, text blocks of about 1000 words have been analyzed. Notice that this choice has no impact on average values. |

13 | The choice of which parameter represents the component $x$ or $y$ is not important. Once the choice is made, the numerical results will depend on it, but not the relative comparisons and general conclusions. |

14 | From vector analysis, the two components of a vector are given by $x={{\displaystyle \sum}}_{k=1}^{6}{x}_{k}$, $y={{\displaystyle \sum}}_{k=1}^{6}{y}_{k}$. The magnitude is given by the Euclidean (Pythagorean) distance $R=\sqrt{{x}^{2}+{y}^{2}}$. |

15 | A compulsory reading in any Italian High School. |

16 | According to the definition of the components of the resulting vector (5), the overall standard deviation of coordinates $x$ and $y$ can be estimated, to a first approximation, as ${\delta}_{x}=\sqrt{{\sigma}_{{M}_{F}}^{2}+4{\sigma}_{{C}_{P}}^{2}+9{\sigma}_{{I}_{P}}^{2}}$ and ${\delta}_{y}=\sqrt{{\sigma}_{{C}_{P}}^{2}+4{\sigma}_{F}^{2}+9{\sigma}_{{P}_{F}}^{2}}$, where the standard deviation of the average value of each variable is given in Table 2. |

**Figure 1.**Syntactic ${G}_{C}$ (circles) and semantic ${G}_{F}$ (crosses) indices versus the readability index $G$ for single text blocks examined. Cyan and blue marks refer to the Italian literature (Matricciani 2018), corresponding red marks refer to all Maria Valtorta’s literary texts. The horizontal line is the average value of ${G}_{C}$, the slant line is the average value of ${G}_{F}$, both relative to the Italian literature.

**Figure 2.**Syntactic ${G}_{C}$ (circles) and semantic ${G}_{F}$ (crosses) indices versus the readability index $G$ for single text blocks examined in Boccaccio’s Decameron (14th century), black marks, and in Cassola’s La ragazza di Bube (20th century), blue marks.

**Figure 3.**Syntactic ${G}_{C}$ (circles) and semantic ${G}_{F}$ (crosses) indices versus the word interval ${I}_{P}$ for single text blocks examined. Cyan and blue marks refer to the Italian literature (Matricciani 2018), red marks refer to Maria Valtorta’s literary texts. The time axis (seconds) refers to the time interval ${I}_{T}$ calculated by applying (4) with $v=188$ words per minute.

**Figure 4.**Syntactic ${G}_{C}$ (circles) and semantic ${G}_{F}$ (crosses) indices versus the word interval ${I}_{P}$ for single text blocks examined in Boccaccio’s Decameron (XIV century), black marks, and in Cassola’s La ragazza di Bube (XX century), blue marks. Time axis in seconds.

**Figure 5.**Probability density functions (upper panel) and probability distribution functions (lower panel) of the readability index $G$. Parables: green line; Jesus’ Sermons and Speeches: magenta; Jesus says: blue; Mary says: cyan; Azariah: black continuous line; Romans: black dashed line; Autobiography: red continuous line; Maria Valtorta’s Descriptions: red dashed line.

**Figure 6.**Probability density functions (upper panel) and probability distribution functions (lower panel) of the number of characters per word ${I}_{P}$. Parables: green line; Jesus’ Sermons and Speeches: magenta; Jesus says: blue; Mary says: cyan; Azariah: black continuous line; Romans: black dashed line; Autobiography: red continuous line; Maria Valtorta’s Descriptions: red dashed line.

**Figure 7.**Probability density functions (upper panel) and probability distribution functions (lower panel) of the number of words per sentence ${P}_{F}$. Parables: green line; Jesus’ Sermons and Speeches: magenta; Jesus says: blue; Mary says: cyan; Azariah: black continuous line; Romans: black dashed line; Autobiography: red continuous line; Maria Valtorta’s Descriptions: red dashed line.

**Figure 8.**Probability density functions (upper panel) and probability distribution functions (lower panel) of the word interval ${I}_{P}$. Parables: green line; Jesus’ Sermons and Speeches: magenta; Jesus says: blue; Mary says: cyan; Azariah: black continuous line; Romans: black dashed line; Autobiography: red continuous line; Maria Valtorta’s Descriptions: red dashed line.

**Figure 9.**(

**a**) Kolmogorov−Smirnov test probability of the test variable concerning the readability index $G$ of two literary texts. The left panel refers only to the EMV texts, the right panel refers to couples that include Maria Valtorta’s Autobiography and Descriptions. Explicitly labeled only the couples of texts for which, at the 95% confidence level (probability less than 0.95, horizontal red line) they are likely attributable to the same population. Colours are used only to better point out the position of values of Kolmogorov−Smirnov test. Their key is made explicit in the following captions. SM: Jesus’ Sermons and Speeches and Mary says; JM: Jesus says and Mary says; PS: Parables and Jesus’ Sermons and Speeches; PM: Parables and Mary says; ${\mathrm{MM}}_{\mathrm{A}}:Marysays\mathrm{and}\text{}MariaValtort{a}^{\prime}sAutobiography$. The couples not explicitly labeled should thus belong to different populations with probability larger than 0.95 and most of them with probability close to 1; (

**b**) Kolmogorov−Smirnov test probability of the test variable concerning the readability index $G$ of two literary texts. The left panel refers to couples that include Azariah, the right panel refers to couples that include Romans. Explicitly labeled only the couples of texts for which, at the 95% confidence level (probability less than 0.95, horizontal red line), they are likely attributable to the same population. A${\mathrm{M}}_{\mathrm{V}}$: Azariah and Maria Valtorta’s Descriptions. The couples not explicitly labeled should thus belong to different populations with probability larger than 0.95 and most of them with probability very close to 1.

**Figure 10.**(

**a**) Kolmogorov−Smirnov test probability of the test variable concerning the number of characters per word ${C}_{P}$ of two literary texts. The left panel refers only to the EMV texts; the right panel refers to couples that include Maria Valtorta’s Autobiography and Descriptions. Only the couples of texts which at the 95% confidence level (probability less than 0.95, horizontal red line) are likely attributable to the same population are explicitly labeled. Colours are used only to better point out the position of values of Kolmogorov−Smirnov test. Their key is made explicit in the following captions. PM: Parables and Mary says; SM: Jesus’ Sermons and Speeches and Mary says; PJ: Parables and Jesus says; PS: Parables and Jesus’ Sermons and Speeches; JM: Jesus says and Mary says. The couples not explicitly labeled should thus belong to different populations with probability larger than 0.95 and most of them with probability close to 1; (

**b**) Kolmogorov−Smirnov test probability of the test variable concerning the number of characters per word ${C}_{P}$ of two literary texts. The left panel refers to couples that include Azariah; the right panel refers to couples that include Romans. Explicitly labeled only the couples of texts for which, at the 95% confidence level (probability less than 0.95, horizontal red line), they are likely due to the same population. A${\mathrm{M}}_{\mathrm{A}}$: Azariah and Maria Valtorta’s Autobiography; A${\mathrm{M}}_{\mathrm{V}}$: Azariah and Maria Valtorta’s Descriptions. The couples not explicitly labeled should thus belong to different populations with probability larger than 0.95 and most of them with probability very close to 1.

**Figure 11.**(

**a**) Kolmogorov−Smirnov test probability of the test variable concerning the number of words per sentence ${P}_{F}$ of two literary texts. The left panel refers only to the EMV texts, the right panel refers to couples that include Maria Valtorta’s Autobiography and Descriptions. Only the couples of texts which at the 95% confidence level (probability less than 0.95, horizontal red line) are likely attributable to the same population are explicitly labeled. Colours are used only to better point out the position of values of Kolmogorov−Smirnov test. Their key is made explicit in the following captions. JM: Jesus says and Mary says. SM: Jesus’ Sermons and Speeches and Mary says; PS: Parables and Jesus’ Sermons and Speeches; PM: Parables and Mary says; ${\mathrm{MM}}_{\mathrm{A}}$: Mary says and Maria Valtorta’s Autobiography; ${\mathrm{JM}}_{\mathrm{A}}$: Jesus says and Maria Valtorta’s Autobiography. The couples not explicitly labeled should thus belong to different populations with probability larger than 0.95 and most of them with probability close to 1; (

**b**) Kolmogorov−Smirnov test probability of the test variable concerning the number of words per sentence ${P}_{F}$ of two literary texts. The left panel refers to couples that include Azariah, the right panel refers to couples that include Romans. No couple is found at the 95% confidence level (horizontal red line). All literary texts are due to different populations with probability larger than 095; most of them with probability very close to 1.

**Figure 12.**(

**a**) Kolmogorov−Smirnov test probability of the test variable concerning the word interval ${I}_{P}$ of two literary texts. The left panel refers only to the EMV texts, the right panel refers to couples that include Maria Valtorta’s Autobiography and Descriptions. Only the couples of texts which at the 95% confidence level (probability less than 0.95, horizontal red line) are likely attributable to the same population are explicitly labeled. Colours are used only to better point out the position of values of Kolmogorov−Smirnov test. Their key is made explicit in the following captions. JM: Jesus says and Mary says. PS: Parables and Jesus’ Sermons and Speeches; ${\mathrm{M}}_{\mathrm{A}}{\mathrm{M}}_{\mathrm{V}}$: Maria Valtorta’s Autobiography and Maria Valtorta’s Descriptions; ${\mathrm{MM}}_{\mathrm{A}}$: Mary says and Maria Valtorta’s Autobiography; ${\mathrm{MM}}_{\mathrm{V}}$: Mary says and Maria Valtorta’s Descriptions; ${\mathrm{JM}}_{\mathrm{A}}$: Jesus says and Maria Valtorta’s Autobiography. The couples not explicitly labeled should thus belong to different populations with probability larger than 0.95 and most of them with probability close to 1; (

**b**) Kolmogorov−Smirnov test probability of the test variable concerning the word interval ${I}_{P}$ of two literary texts. The left panel refers to couples that include Azariah, the right panel refers to couples that include Romans. AS: Azariah and Jesus’ sermons and Speeches; RP: Romans and Parables; RS: Romans and Jesus’ Sermons and Speeches. The couples not explicitly labeled should thus belong to different populations with probability larger than 0.95 (horizontal red line), most of them with probability very close to 1.

**Figure 13.**Coordinates $x$ and $y$ of the resulting vector (5) of a literary work, referred (normalized) to the coordinates of the Boccaccio and Cassola, by assuming Cassola’s La Ragazza di Bube as the origin, coordinates (0,0), and Boccaccio’s Decameron located at (1,1). Colours are used only to better point out the position of values. Their key is made explicit in the following captions. P: Parables; S: Jesus’ Sermons and Speeches; J: Jesus says; M: Mary says. A: Azariah; R: Romans; JJ: letter of John of Endor to Jesus; SJ: letters of Sintica to Jesus; MJ: letter of Mary to Jesus; ${\mathrm{M}}_{\mathrm{A}}$: Maria Valtorta’s Autobiography; ${\mathrm{M}}_{\mathrm{V}}$: Maria Valtorta’s Descriptions; C: Cassola; D: De Amicis’ Cuore; ${\mathrm{M}}_{\mathrm{PS}}$: Manzoni’s I Promessi 200; ${\mathrm{M}}_{\mathrm{FL}}$: Manzoni’s Fermo e Lucia; ${\mathrm{F}}_{\mathrm{S}}$: Fogazzaro’s Il Santo; ${\mathrm{F}}_{\mathrm{P}}$: Fogazzaro’s Piccolo Mondo Antico; ${\mathrm{C}}_{\mathrm{M}}$: Calvino’s Marcovaldo; ${\mathrm{C}}_{\mathrm{B}}$: Calvino’s Il Barone Rampante; IT: barycenter of the Italian literature. The blue box gives $\mp \mathsf{\delta}$ overall standard deviation of the vector’s coordinates of Jesus says; the red box gives the $\mp \mathsf{\delta}$ overall standard deviation of the vector’s coordinates of Maria Valtorta’s Autobiography.

**Table 1.**Characters, words and sentences in Maria Valtorta’s writings, and average values of the corresponding readability index $G$, the semantic index ${G}_{C},$ and the syntactic index ${G}_{F}$, the standard deviation of averages (in parentheses) and the standard deviation estimated for text blocks of 1000 words (see Appendix A for more details). The characters are those contained in the words. All parameters have been computed by weighting the text blocks according to the number of the words contained in them (Appendix A) For instance, in Parables the average value of $G$ can be estimated in $64.71\pm 0.72$ and its standard deviation for text blocks of 1000 words is 4.17.

Maria Valtorta’s Writing | Characters | Words | Sentences | $\mathit{G}$ | ${\mathit{G}}_{\mathit{C}}$ | ${\mathit{G}}_{\mathit{F}}$ |
---|---|---|---|---|---|---|

Parables6 (EMV) | 150,764 | 33,808 | 2289 | 64.71 | 44.59 | 20.31 |

(0.72) | (0.18) | (0.69) | ||||

4.17 | 1.06 | 3.89 | ||||

Jesus’ sermons and speeches7 (EMV) | 489,162 | 111,033 | 6831 | 63.33 | 44.06 | 18.46 |

(0.53) | (0.14) | (0.48) | ||||

5.63 | 1.43 | 5.03 | ||||

Jesus says (Valtorta 2001, 2006a) | 1,179,975 | 262,450 | 15,078 | 61.28 | 44.96 | 17.24 |

(0.25) | (0.07) | (0.23) | ||||

3.98 | 1.10 | 3.68 | ||||

Mary says (Valtorta 2001, 2006a, 2006b, 2006c) | 138,850 | 31,234 | 1862 | 62.39 | 44.45 | 17.88 |

(1.07) | (0.21) | (0.96) | ||||

5.99 | 1.19 | 5.35 | ||||

Azariah8 | 502,182 | 110,261 | 5494 | 58.42 | 45.55 | 14.95 |

(0.37) | (0.13) | (0.30) | ||||

3.91 | 1.37 | 3.19 | ||||

Romans9 | 375,047 | 80,756 | 3014 | 53.78 | 46.44 | 11.20 |

(0.41) | (0.15) | (0.35) | ||||

3.71 | 1.33 | 3.19 | ||||

Letters of Sintica to Jesus (EMV 366.910; EMV 461.13) | 14,151 | 3184 | 205 | 63.87 | 44.44 | 19.32 |

Letter of Mary to Jesus (EMV,133.4) | 3799 | 917 | 54 | 65.24 | 41.43 | 17.67 |

Letter of John of Endor to Jesus (EMV, 366.6) | 4136 | 938 | 69 | 63.78 | 44.09 | 22.07 |

Maria Valtorta’s descriptions (EMV) | 491,612 | 107,183 | 5030 | 57.20 | 45.87 | 14.08 |

(0.36) | (0.10) | (0.31) | ||||

3.69 | 1.01 | 3.22 | ||||

Autobiography11 | 688,003 | 151,334 | 8325 | 60.04 | 45.46 | 16.50 |

(0.35) | (0.11) | (0.32) | ||||

4.24 | 1.35 | 3.88 |

**Table 2.**Average values of number of characters per word ${C}_{P}$, words per sentence ${P}_{F}$, punctuation marks per sentence ${M}_{F}$ and word interval ${I}_{P}$. Standard deviations are calculated as in Table 1.

Maria Valtorta’s Writing | Characters per Word ${\mathit{C}}_{\mathit{P}}$ | Words per Sentence ${\mathit{P}}_{\mathit{F}}$ | Punctuation Marks (and Word Intervals) per Sentence ${\mathit{M}}_{\mathit{F}}$ | Word Interval (Words per Punctuation Marks) ${\mathit{I}}_{\mathit{P}}$ |
---|---|---|---|---|

Parables | 4.459 | 15.71 | 2.36 | 6.63 |

(0.018) | (0.66) | (0.08) | (0.11) | |

0.106 | 3.83 | 0.47 | 0.61 | |

Jesus’ Sermons and Speeches | 4.406 | 17.13 | 2.47 | 6.91 |

(0.136) | (0.46) | (0.06) | (0.08) | |

0.143 | 4.85 | 0.62 | (0.82) | |

Jesus says | 4.496 | 18.37 | 2.42 | 7.59 |

(0.068) | (0.26) | (0.03) | (0.06) | |

0.110 | 4.16 | 0.46 | 0.94 | |

Mary says | 4.445 | 18.71 | 2.42 | 7.64 |

(0.021) | (1.05) | (0.11) | (0.22) | |

0.119 | 5.90 | 0.57 | 1.20 | |

Azariah | 4.555 | 20.96 | 2.97 | 7.0781 |

(0.013) | (0.43) | (0.06) | (0.07) | |

0.137 | 4.46 | 0.60 | 0.74 | |

Romans | 4.644 | 28.68 | 4.23 | 6.76 |

(0.015) | (1.02) | (0.14) | (0.07) | |

0.133 | 9.20 | 1.23 | 0.66 | |

Letters of Sintica to Jesus | 4.444 | 15.53 | 2.33 | 6.68 |

Letter of Mary to Jesus | 4.143 | 16.98 | 2.33 | 7.28 |

Letter of John of Endor to Jesus | 4.409 | 13.59 | 2.28 | 5.98 |

Maria Valtorta’s Descriptions | 4.587 | 24.22 | 3.18 | 7.60 |

(0.10) | (0.57) | (0.07) | (0.07) | |

0.101 | 5.86 | 0.70 | 0.69 | |

Autobiography12 | 4.546 | 19.29 | 2.50 | 7.71 |

(0.011) | (0.41) | (0.05) | (0.07) | |

0.135 | 5.026 | 0.58 | 0.83 |

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**MDPI and ACS Style**

Matricciani, E.; De Caro, L.
A Mathematical Analysis of Maria Valtorta’s Mystical Writings. *Religions* **2018**, *9*, 373.
https://doi.org/10.3390/rel9110373

**AMA Style**

Matricciani E, De Caro L.
A Mathematical Analysis of Maria Valtorta’s Mystical Writings. *Religions*. 2018; 9(11):373.
https://doi.org/10.3390/rel9110373

**Chicago/Turabian Style**

Matricciani, Emilio, and Liberato De Caro.
2018. "A Mathematical Analysis of Maria Valtorta’s Mystical Writings" *Religions* 9, no. 11: 373.
https://doi.org/10.3390/rel9110373