ORIGINAL RESEARCH
JOHREI EFFECTS
ON
WATER: A PILOT STUDY 1,2
BY
COUNTING DROPS
Pedro Celso Nogueira Teixeira, PhD José Aguiar Coelho Neto, PhD Anael Viana Pinto Alberto, PhD1 and Cristina Alves Magalhães de Souza, PhD1#
Background: Water is a key ingredient in the creation and sustainment of life. Moreover, water may be a key vehicle in the processes of energy healing, such as in the preparation of homeopathic remedies and spiritual treatments. Given these properties, the purpose of this study was to investigate whether the application of Johrei to water could lead to significant changes in the hydrodynamic behaviour of the fluid. Methods: Four regular Johrei practitioners (P1, P2, P3 and P4) were selected for this study. Dripping water produced at the tip of a capillary was used as the hydrodynamic behaviour model. This behaviour was modelled mathematically, and tuning parameters φ4 and τ were used to assess significant differences in the dripping water samples that were subjected to Johrei compared with the samples that were not so treated. The tuning parameters were obtained using the LevenbergMarquardt fitting algorithm. The data sets for each Johrei
INTRODUCTION The use of alternative therapies is growing worldwide. Nevertheless, such methods, which are based in spiritual energy healing, are not fully accepted by the conventional medical and scientific communities. Johrei is one such alternative therapy that is practiced by an increasing number of people in the world. Johrei was created by Mokiti Okada in Japan (1935), and Johrei acts on its recipients through a process of spiritual purification. The practitioner believes that a spiritual energy flows through his body and that it can be directed through his hands into another person, thereby improving the recipient's health. So far, there have been few papers evaluating the efficacy of the Johrei healing technique. In the first paper to address the issue, Gomes et al.1 demonstrated the considerable influence of Johrei on the germination rate of irradiated seeds (gamma radiation, Cesium 137). Later, an article by Laidlaw et al.2
1 Laboratory of Cellular Communication, Oswaldo Cruz Institute, Oswaldo Cruz Foundation, Av. Brazil, 4365, Manguinhos, Rio de Janeiro CEP 21045-900, Brazil 2 Research Center MOA, Mokiti Okada Foundation, São Paulo, Brazil # Corresponding author. e-mail: souzacam@ioc.fiocruz.br; [email protected]
& 2015 Published by Elsevier Inc. ISSN 1550-8307/$36.00
2
practitioner and the control experiment were analysed using ANOVA and a paired t-test. Results: The mathematical model exhibited an excellent fit to our data, generating correlation coefficients (r) greater than or equal to 0.999. Significant differences were observed in both τ (P1 and P2, P o 0.05 and P o 0.01, respectively) and φ4 (P2, P o 0.01). As expected, no significant difference for the control experiment (without Johrei) was observed. Conclusions: Our results indicated a statistically significant change in the hydrodynamic behaviour of water correlated with Johrei treatment for 50% of the participating Johrei practitioners. Key words: Johrei, water cluster, energy healing, surface tension, viscosity, mathematical model (Explore 2015; ]:]]]-]]] & 2015 Published by Elsevier Inc.)
suggested that Johrei had a beneficial effect on the mood of practitioners. Following that study, Reece et al.3 demonstrated that Johrei recipients experience a significant decrease in their negative emotional states, whereas positive emotional states seem to increase in both Johrei recipients and providers. Brooks et al.4 have also concluded that after Johrei sessions, patients in treatment for substance abuse experience enhanced energy, emotional states, and well-being, as well as decreased pain and depression. Data from Gasiorowska et al.5 indicates that Johrei can serve as a good alternative method for the relief of functional chest pain. In 2010, Teixeira et al.6 investigated the growth of sucrose crystals and demonstrated that Johrei increased their crystallization with respect to the control. Additionally, Abe et al.7 have demonstrated that Johrei increases cell death and decreases cell proliferation of gastric cancer cells in vitro. Recently, Buzzetti et al.8 have studied brain markers for sleep and have verified that mice subjected to Johrei therapy exhibited improved sleep patterns compared with the control group of mice when subjected to sleep interruption. By contrast, Taft et al.9 did not detect any difference between the control and Johrei-treated cancer cells in relation to death and proliferation. Hall et al.10 have also reported that Johrei did not heal cultured cells exposed to radiation. Radin et al.11 reported that a single application of Johrei was not able to significantly alter the development of astrocytes cell cultures or
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generating random numbers produced by electronic devices; however, significant changes were observed for both systems, simultaneously, after repeated applications of Johrei. In this context, Teixeira et al.6 have proposed a hypothesis concerning the importance of water in the process of interaction between Johrei and matter, as though water may act as a mediator for the physical manifestation of Johrei. One of the mechanisms that was considered in this work to explain the observed changes in the efficiency of the crystallization of sucrose was a possible change in the state of organization of the water into clusters.12–18 Furthermore, water molecules seem to have a key role to the physical manifestation of forms of energy healing, such as homeopathy; Bach Flowers, and Johrei.6,19–24 Among the various properties of the liquid state that can be related to these organizational changes (cluster formation), we emphasize the hydrodynamic behavior of water in this work. Using a simple experimental setup to address this possibility, a study was conducted to demonstrate whether Johrei can act on water in the liquid state and change the hydrodynamic behavior of its dripping process. System Modeling The chosen experimental system was the detachment of water droplets from the tip of a capillary tube (dripping) because of its experimental simplicity and because the physical properties of this system are well studied.25–30 The experimental system that was used consisted of a vertically oriented cylindrical glass tube with an inner diameter of approximately 7 mm, whose lower portion terminated in vertical capillary tubing of a length much greater than the inner diameter. The glass tube behaved as a reservoir, and when it was filled with water and the water was allowed to flow freely (as a Newtonian fluid) through the capillary, a dripping phenomenon was produced (not chaotic) at the lower end of the capillary. The mathematical modeling of these phenomena was performed using the equations of Poiseuille and Bernoulli, and the result was a function that describes the time dependence of the accumulated droplet count from the beginning of the experiment, given as follows: Dðt Þ ¼ φ4 1eφ5 t ð1Þ where φ4 ¼ φ0 þ φ1 φ2 φ3
with 1
ð4ρghÞ3 R2 ρghR2 ρgzð0ÞR2 , φ1 ¼ , φ2 ¼ φ0 ¼ 1 , 2γ ðr ec f Þ 2γ ðr ec f Þ 3 3 3γ r 4ec f φ3 ¼
Rcosθ ρgr 4c and φ5 ¼ ðr ec f Þ 8ηh R2
The parameters in the equation are as follows (Figure 1): R ¼ internal radius of the upper reservoir tube (7.0 mm), rc ¼ internal radius of the capillary (0.25 mm), rec ¼ external radius of the capillary (0.70 mm), h ¼ length of the capillary (80 mm), z(0) ¼ initial height of the water column measured from the base of the reservoir tube (200 mm), θ ¼ contact
2
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a b c
d
e
g
f
Figure 1. Schematic diagram of the drop-counting system. (A) Reservoir glass tube—water reservoir used in the experiments; (B) solenoid valve—electromechanical control of the opening for the water droplets; (C) level sensor—trigger of the electronic system used to close the solenoid valve; (D) cylindrical glass tube—water reservoir for the droplet system, used to define the precise amount of water to be used in each assay; (E) capillary tube—water duct, used to establish the conditions for the droplet-formation process; (F) photoelectrical system—electrical pulse generator triggered by the interruption of the light beam by each droplet, allowing the system to count the droplets; and (G) electronic system—system used to control the filling of the cylindrical glass tube (D) and the recording of the number of drops per time. angle between the liquid and the inner wall of the upper reservoir tube, f ¼ Harkins correction factor,31–33 η ¼ viscosity of water, γ ¼ surface tension of water, ρ ¼ density of water, and g ¼ acceleration of gravity. Eq. (1) was used to fit the data of the droplet count versus time. From the fitting, the empirical parameters φ4 and φ5 were obtained, and these parameters were used to investigate possible differences between the Johrei-treated water and the non-treated control. In fact, τ, the inverse of φ5, was used instead of the raw φ5 value because τ is the measured time constant of variation in the water-column height in units of seconds. The primary purpose of this work could initially be evaluated simply by means of the empirical parameters φ4 and τ. Later in this article, we discuss the results of calculating the values of φ4 and τ, as predicted by the model, using values of ρ, η, and γ obtained from standard tables34 for a temperature corresponding to that of one of the control experiments (without treatment). However, a direct interpretation of the results in terms of the effects of Johrei on physical parameters such as surface strength, density, and viscosity is not performed because of the lack of a more extensive validation of
Johrei Effects on Water
the model in terms of the measured quantities for these physical parameters under the same experimental conditions as those of the experiments performed in this study.
METHODS In this study, the measurement of the number of drops over time was performed using semi-automated equipment designed and constructed especially for this purpose. In this apparatus (Figure 1), a thermally insulated stock bottle containing 250 mL of test water was placed above the upper opening of the vertical glass tube reservoir. The control of the water flow into the reservoir tube was accomplished using a solenoid valve and an upper level sensor in the reservoir tube, the signal from which was used to shut off the solenoid valve, thereby stopping the filling process. As the capillary attached to the lower part of the glass tubing was always open, droplets began to fall even during the filling process, but counting was begun only after the solenoid had been shut off. An electronic counter was setup to report the droplet counts in successive intervals, the duration of which could be adjusted to be one, two, or five minutes, using a time basis derived from divisions of 60 Hz. The counts were stored by a RAM chip inside the counter and, at the end of each reporting period, transferred to a computer by means of a serial interface. The electric signal for the counting of the droplets was generated through the detection of each droplet just as it began to fall by a photoelectric gate placed near the capillary tip. The temperature of the water was measured throughout the experiment using a mercury thermometer placed in the stock bottle and another in a thermally insulated container that collected the droplets below the apparatus. In each experiment, the first four runs were performed using non-treated water. After these runs, the Johrei practitioner applied Johrei treatment to the remaining water inside the stock bottle for a duration of 30 minutes, and then another set of four runs was performed. The Johrei treatment was performed with the stock bottle in its measurement position. Experiments were performed with four volunteer Johrei practitioners (P1, P2, P3, and P4), yielding a total of four sets of runs. Before the experiments with the Johrei treatment, two control experiments were performed, in which all eight runs (of each control experiment) were performed without Johrei treatment. The results for each set of six runs are labeled as follows: control group I—first run (CWJ1) and second run (CWJ2) of the first control experiment without Johrei treatment; control group II—first run (CWJ1') and second run (CWJ2') of the second control experiments without Johrei treatment; group 1—first run without Johrei treatment (WJP1) and second run with Johrei treatment (JP1) performed by practitioner 1; group 2—first run without Johrei treatment (WJP2) and second run with Johrei treatment (JP2) performed by practitioner 2; group 3—first run without Johrei treatment (WJP3) and second run with Johrei treatment (JP3) performed by practitioner 3; and group 4—first run without Johrei treatment (WJP4) and second run with Johrei treatment (JP4) performed by practitioner 4. After each set of
Johrei Effects on Water
Figure 2. Results of a droplet experiment showing the number of drops per time () and the fit to the data (r ¼ 1). runs, all glass equipment was washed with the neutral detergent Extrans, rinsed with distilled water and left submerged for two hours in a bi-distilled water bath. Afterward, the glass equipment was dried in a stove at 501C for 24 hours. Eq. (1) was used as a fitting function to fit the data of the accumulated droplet counts versus time. The fits were performed using the software package Microcal Origin 8.0s, using the Levenberg–Marquardt fitting method.35 The statistical analysis of the experiment was performed using the Biostat 5.0s software package.36
RESULTS For all experimental data, the fit function was in very good agreement with the data. A typical fit is presented in Figure 2. The correlation coefficient values were 0.9999–1, indicating a high degree of correlation between the experimental data and the proposed model (Eq. (1)). The fitting parameters φ4 and τ, grouped by experiment and by whether they corresponded to a control group or a treatment group, as presented in Table 1, were analyzed to assess their normality using the Lilliefors test.37 This analysis revealed statistical behavior consistent with normal distributions for the sets of φ4 and τ values for all experiments, indicating that the use of parametric statistical tests (ANOVA and Student's non-paired t-test) would be appropriate. For each of the four experiments in which Johrei treatment was performed and the control experiment, the mean values and standard deviations of the parameters φ4 and τ are presented in Figures 3 and 4. Among the sets of results found for each of the four Johrei practitioners, it was found that in groups 1 and 2, there were statistically significant differences between the average values of parameter τ that corresponded to the treated and nontreated sets of runs. The P values for these groups were P o .05 and P o .01, respectively. There were also statistically significant differences for parameter φ4 in group 2.
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Table 1. Adjust Parameters of φ4 and τ Grouped by Control Group (CWJ1, CWJ2, and CWJ1', CWJ2') and Johrei-Treated Group (P1, P2, P3, and P4) Control Without Johrei φ
Control Without Johrei
τ
φ
τ
CWJ1 1880.50 1836.93 1833.05 1850.16
CWJ2 849.34 810.68 811.01 823.68
1848.84 1854.55 1883.93 1862.44
CWJ1' 1845.69 1848.55 1843.24 1853.47
CWJ2' 824.57 825.85 823.88 827.25
1844.72 1840.29 1849.71 1853.16
Without Johrei (WJ) φ
812.31 821.08 851.35 828.25
825.82 816.18 831.56 827.51
With Johrei (J)
τ
φ
τ
1804.66 1797.23 1789.73 1814.67
759.90 756.03 746.90 758.26
P1 1826.98 1848.82 1766.32 1838.70
802.69 816.55 750.07 794.92 P2
1861.78 1849.69 1872.74 1861.40
Figure 3. Bar-graph data for parameter φ4 (mean ⫾ SD) for the control group (CWJ1 and CWJ2, CWJ1', and CWJ2') and the Johreitreated groups (WJP1 and JP1, WJP2 and JP2, WJP3 and JP3, WJP4 and JP4). **P o .01. The temperatures above each pair of bars represent the mean value of the temperature and its standard deviation for the corresponding experiment.
762.28 756.91 766.72 761.97
1813.78 1838.92 1838.63 1830.44
734.23 749.52 750.12 744.62
1890.24 1899.98 1857.54 1866.62
772.63 774.35 747.50 743.45
1830.98 1829.54 1856.20 1885.38
797.58 797.73 808.50 838.27
Statistically significant differences were also found between the value of parameter τ that corresponded to the two combined control groups and the values obtained for the non-treated results for groups 1–3 (WJP1, WJP2, and WJP3), with P o .05. No statistically significant difference was found between the combined control groups and WJP4.
DISCUSSION The proposed mathematical model (Eq. (1)) is in excellent agreement with the experimental data for droplet count over time. This agreement implies that our method offers a high
P3 1893.39 1864.73 1862.54 1873.55
764.05 748.62 748.67 753.78 P4
1838.53 1835.36 1850.51 1855.33
820.10 817.60 829.72 838.02
As expected, there were no statistically significant differences between CWJ1 and CWJ2 (the control group I) and CWJ1' and CWJ2'for either φ4 or τ.
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Figure 4. Bar-graph data for parameter τ (mean ⫾ SD) for the control group (CWJ1 and CWJ2, CWJ1' and CWJ2') and the Johreitreated groups (WJP1 and JP1, WJP2 and JP2, WJP3 and JP3, WJP4 and JP4). *P o .05 and **P o .01. The temperatures above each pair of bars represent the mean value of the temperature and its standard deviation for the corresponding experiment.
Johrei Effects on Water
sensitivity for the identification of possible variations in the empirical parameters as a consequence of the treatment under test, lending credence to our observation of the first evidence of variations produced by Johrei in the time constant τ in the involving groups 1 and 2 and in the parameter φ4 for group 2. In addition, the future prospects are very good for using this model to establish a correlation between the investigated parameters and variations in the viscosity and surface tension. Using Eq. (1), we calculated the expected values of φ4 and τ using tabulated values for η, γ, and ρ for water at a temperature of 26.91C (η ¼ 8.54 104 Pa s, γ ¼ 7.169 102 N m1, and ρ ¼ 996.5 kg m3). The value of f used in this calculation was estimated based on the drop volume determined in accordance with the equilibrium stalagmometric conditions. The drop volume (Vd) was used to calculate the ratio recV1/3 and to obtain the correspond ding f value of 0.766.31,33 For θ, a value of θ ¼ 0 (perfect wetting) was used as an approximation38 of the glass–water interface. The following values were found: φ4calc ¼ 1855 drops and τcalc ¼ 829 seconds. These values are in excellent agreement with the values obtained for the control experiment (the control group I) when the CWJ1 and CWJ2 values are averaged: φ4exp ¼ (1856 ⫾ 19) drops and τexp ¼ (826 ⫾ 16) s. This agreement suggests a high degree of accuracy for the model. However, as noted above, a more extensive validation of parameters φ4 and τ in terms of the measured values of η, γ, ρ, and θ must be performed to achieve a reliable interpretation of the effects of Johrei treatment with respect to variations in these parameters. The statistically significant differences found for the parameter τ when comparing the control group with the non-treated results for groups 1–3 are in good agreement with the observed variations in temperature. For a temperature range between 251C and 301C, the variations in η, γ, and ρ (as estimated using Eq. (1)) yield calculated thermal sensitivities of approximately 4.6 drops 1C1 for φ4 and 24 s 1C1 for τ. Considering the absolute values of φ4 and τ in this range, these thermal sensitivities correspond to relative variations of 0.29% 1C1 for φ4 and 2.8% 1C1 for τ. Therefore, φ4 is expected to exhibit a much smaller temperature dependence than τ. Linear regressions of the values of φ4 and τ (Supplementary material S1 and S2) with respect to temperature for the nontreated groups (CWJ2, CWJ2', WJP1, WJP2, WJP3, and WJP4) yielded a slope of (8 ⫾ 3) drops 1C1 for φ4 with a determination coefficient of 0.22, indicating a very small correlation, and a slope of (32 ⫾ 4) s 1C1 for τ with a determination coefficient of 0.74, indicating a reasonably good correlation. Therefore, the thermal sensitivities observed for φ4 and τ were also in good agreement with the predictions of the model. The thermal behavior of φ4 and τ described above may be considered to be a good explanation for why no statistically significant differences in φ4 were found for the control groups of the treatment experiments, WJP1 to WJP4, with respect to the control experiments, control group I and control group II and why significant differences in τ were found only for
Johrei Effects on Water
WJP1, WJP2, and WJP3 with respect to control group I and control group II and not for WJP4; the temperature difference between WJP4 and the control–experiment groups, control group I and control group II was only 0.21C and 0.41C, respectively. CONCLUSION The differences in τ observed between WJP1 and JP1 and between WJP2 and JP2 as well as the difference in φ4 observed between WJP2 and JP2 were found to be above the level of random variation with a statistical confidence of 95% or higher. Therefore, it may be concluded that there was a true change in the hydrodynamic behavior of the water that was significantly correlated with the Johrei treatment with Johrei for 50% of the practitioners who were evaluated. Moreover, because the temperature dependence of the investigated parameters is known, it could be established that a variation in temperature of 11C or more would be required to explain the observed variation in τ for groups 1 and 2 and that a variation of more than 61C would be required to explain the observed variation in φ4 for group 2. The potential temperature uncertainty within the same experiment is considered, in the worst case, to be less than 0.41C. Therefore, the observed variations cannot be explained in terms of temperature variations throughout the experiment. The conclusion is that the observed differences may be considered to be at least an initial indication of a possible effect of Johrei treatment. Improvements in the method and in the quantity and reproducibility of the results are necessary to confirm these results. Therefore, a future study is planned with a greater number of repetitions per experiment, blind analysis, and more stringent temperature control throughout each experiment. Acknowledgments
We would like to express our gratitude to Dr. Luiz Anastacio Alves for his noticeable good will and spirit of collaboration, who help make this work possible. This work was supported by Mokiti Okada Foundation, Centro de Pesquisa MOA-Rio de Janeiro. The authors that do not belong to the Mokiti Foundation have no commercial association that might create a conflict of interest in connection with this article. APPENDIX A. SUPPLEMENTARY INFORMATION Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.explore. 2015.08.001. REFERENCES 1. Gomes A, Teixeira PCN, Coelho JA, Rocha H, Furtado KG, Souza HVC. Influence of the laying on of hands technique (Johrei) on the germination of gamma rays irradiated canary seeds. J Conscientiol. 2001;3(11):169–181. 2. Naito A, Laidlawa TM, Henderson DC, Farahani L, Dwivedi P, Gruzelier JH. The impact of self-hypnosis and Johrei on lymphocyte subpopulations at exam time: a controlled study. Brain Res Bull. 2003;62:241–253.
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3. Reece K, Schwartz GE, Brooks AJ, Nangle G. Positive well-being changes associated with giving and receiving Johrei healing. J Altern Complement Med. 2005;11(3):455–457. 4. Brooks AJ, Schwartz GE, Reece K, Rev. Nangle G. The effect of Johrei healing on substance abuse recovery: a pilot study. J Altern Complement Med. 2006;12(7):625–631. 5. Gasiorowska A, Navarro-Rodriguez T, Dickman R, et al. Clinical trial: the effect of Johrei on symptoms of patients with functional chest pain. Aliment Pharmacol Ther. 2008;29:126–134. 6. Teixeira PCN, Rocha H, Neto JAC. Johrei, a Japanese healing technique, enhances the growth of sucrose crystals. Explore. 2010;6:313–323. 7. Abe K, Ichinomiya R, Kanai T, Yamamoto K. Effect of a Japanese energy healing method known as Johrei on viability and proliferation of cultured cancer cells in vitro. J Altern Complement Med. 2012;18(3):221–228. 8. Buzzetti RA, Hinojosa-Kurtzberg M, Shea TJ, Ibuki Y, Sirakis G, Parthasarathy S. Effect of Johrei therapy on sleep in a murine model. Explore. 2013;9:100–105. 9. Taft R, Moore D, Yount G. Time-lapse analysis of potential cellular responsiveness to Johrei, a Japanese healing technique. BMC Complement Altern Med. 2005;5(2):1–7. 10. Hall Z, Luu T, Moore D, Yount G. Radiation response of cultured human cells is unaffected by Johrei. Evid Based Complement Alternat Med. 2006;4(2):191–194. 11. Radin DI, Taft R, Yount G. Possible effects of healing intention on cell cultures and truly random events. J Altern Complement Med. 2004;10:103–112. 12. Tanaka H. A simple physical model of liquid water. J Chem Phys. 2002;112:799–809. 13. Chaplin F. A proposal for the structure of water. Biophys Chem. 2000;83:211–221. 14. Stanley HE, Buldyrev SV, Campolat M, et al. The puzzle of liquid water, a very complex fluid. Physica D. 1999;133:453–462. 15. Cho CH, Singh S, Robinson GW. Liquid water and biological systems. The most important problem in science that hardly anyone wants to see solved. Faraday Discuss. 1996;103:19–27. 16. Stanley HE, Kumar P, Xu L, et al. The puzzling unsolved mysteries of liquid water. Some recent progress. Phys A Stat Mech Appl. 2007;386:729–743. 17. Lo SY, Li WC, Huang SH. Water clusters in life. Med Hypotheses. 2000;54(6):948–953. 18. Loftsson T, Brewster M. Physicochemical properties of water and its effect on drug delivery. A commentary. Int J Pharm. 2008;354: 248–254. 19. Schwartz SA, DeMattei RJ. Infrared spectra alteration in water proximate to the palms of therapeutic practitioner. Subtle Energies. 1991;1:43–54. 20. Shishki GG, Ageev IM, Rybin YM, Shishki AG. Research of water response under the action of the infrared human body radiation by water conductometric sensors. Open J Appl Sci. 2013;3:278–284. 21. Bellavite P, Marzotto M, Olioso D, Moratti E, Conforti A. Highdilution effects revisited. 1. Physicochemical aspects. Homeopathy. 2014;103(1):4–21.
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22. Elia V, Ausanio G, Gentile F, Germano R, Napoli E, Niccoli M. Experimental evidence of stable water nanostructures in extremely dilute solutions, at standard pressure and temperature. Homeopathy. 2014;103(1):44–50. 23. Radin D, Hayssen G, Emoto M, Kizu T. Double-blind test of the effects of intention on water crystal formation. Explore. 2006;2 (5):408–411. 24. Thaler K, Kaminski A, Chapman A, Langley T, Gartlehner G. Bach flower remedies for psychological problems and pain: a systematic review. BMC Complement Altern Med. 2009;9(16):1–12. 25. Lee B-B, Pogaku R, Chan E-S. New drop weight analysis for surface tension determination of liquids. Colloids Surf A Physicochem Eng Aspects. 2009;332:112–120. 26. Dreyer K, Hickey FR. The route to chaos in a dripping water faucet. Am J Phys. 1991;59(7):619–627. 27. H Matsumoto T, Ueda T, Nogi K. A new method for simultaneous measurement of surface tension and viscosity. J Mater Sci Mater Med. 2005;4(9–10):2161–2166. 28. Franses EI, Basaran OA, Chang C-H. Techniques to measure dynamic surface tension. Curr Opin Colloid Interface Sci. 1996;1(2): 296–303. 29. Molki M, Abbasi B. Effect of temperature on the vorticity field of an evolving water droplet. Int J Heat Mass Transfer. 2010;53: 18–28. 30. D'Innocenzo A, Paladini F, Renna L. Experimental study of dripping dynamics. Phys Rev E. 2002;65:056208-1–056208-8. 31. Wilkinson MC, Kidwell RL. A mathematical description of the Harkins and Brown correction curve for the determination of surface and interfacial tensions. J Colloid Interface Sci. 1971;35 (1):114–119. 32. Hartland S, Srinivasan PS. The basis of theoretical correction factors for use with the drop weight method of surface tension measurement. J Colloid Interface Sci. 1974;49(2): 318–320. 33. Harkins WD, Brown FE. The determination of surface tension (free surface energy), and the weight of falling drops: the surface tension of water and benzene by the capillary height method. J Am Chem Soc. 1919;41(4):499–524. 34. Haynes WM. CRC Handbook of Chemistry and Physics. 94th ed. CRC Press; 2013. 35. Marquardt DW. An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math. 1963;11:431–441. 36. Ayres M, Ayres MJ, Ayres D, Santos AS. BioStat 4.0: aplicações estatísticas nas áreas de ciências biológicas e médicas. Sociedade Civil Mamuirá MCT. 4a Edição. Pará, Brasil: Imprensa Oficial do Estado do; 2005. 37. Lilliefors HW. On the Kolmogorov–Smirnov test for normality with mean and variance unknown. J Am Stat Assoc. 1967;62: 399–462. 38. Vargaftik NB, Volkov BN, Voljak LD. International tables of the surface tension of water. J Phys Chem Ref Data. 1983;12(3): 817–820.
Johrei Effects on Water
JOHREI EFFECTS
ON
WATER: A PILOT STUDY 1,2
BY
COUNTING DROPS
Pedro Celso Nogueira Teixeira, PhD José Aguiar Coelho Neto, PhD Anael Viana Pinto Alberto, PhD1 and Cristina Alves Magalhães de Souza, PhD1#
Background: Water is a key ingredient in the creation and sustainment of life. Moreover, water may be a key vehicle in the processes of energy healing, such as in the preparation of homeopathic remedies and spiritual treatments. Given these properties, the purpose of this study was to investigate whether the application of Johrei to water could lead to significant changes in the hydrodynamic behaviour of the fluid. Methods: Four regular Johrei practitioners (P1, P2, P3 and P4) were selected for this study. Dripping water produced at the tip of a capillary was used as the hydrodynamic behaviour model. This behaviour was modelled mathematically, and tuning parameters φ4 and τ were used to assess significant differences in the dripping water samples that were subjected to Johrei compared with the samples that were not so treated. The tuning parameters were obtained using the LevenbergMarquardt fitting algorithm. The data sets for each Johrei
INTRODUCTION The use of alternative therapies is growing worldwide. Nevertheless, such methods, which are based in spiritual energy healing, are not fully accepted by the conventional medical and scientific communities. Johrei is one such alternative therapy that is practiced by an increasing number of people in the world. Johrei was created by Mokiti Okada in Japan (1935), and Johrei acts on its recipients through a process of spiritual purification. The practitioner believes that a spiritual energy flows through his body and that it can be directed through his hands into another person, thereby improving the recipient's health. So far, there have been few papers evaluating the efficacy of the Johrei healing technique. In the first paper to address the issue, Gomes et al.1 demonstrated the considerable influence of Johrei on the germination rate of irradiated seeds (gamma radiation, Cesium 137). Later, an article by Laidlaw et al.2
1 Laboratory of Cellular Communication, Oswaldo Cruz Institute, Oswaldo Cruz Foundation, Av. Brazil, 4365, Manguinhos, Rio de Janeiro CEP 21045-900, Brazil 2 Research Center MOA, Mokiti Okada Foundation, São Paulo, Brazil # Corresponding author. e-mail: souzacam@ioc.fiocruz.br; [email protected]
& 2015 Published by Elsevier Inc. ISSN 1550-8307/$36.00
2
practitioner and the control experiment were analysed using ANOVA and a paired t-test. Results: The mathematical model exhibited an excellent fit to our data, generating correlation coefficients (r) greater than or equal to 0.999. Significant differences were observed in both τ (P1 and P2, P o 0.05 and P o 0.01, respectively) and φ4 (P2, P o 0.01). As expected, no significant difference for the control experiment (without Johrei) was observed. Conclusions: Our results indicated a statistically significant change in the hydrodynamic behaviour of water correlated with Johrei treatment for 50% of the participating Johrei practitioners. Key words: Johrei, water cluster, energy healing, surface tension, viscosity, mathematical model (Explore 2015; ]:]]]-]]] & 2015 Published by Elsevier Inc.)
suggested that Johrei had a beneficial effect on the mood of practitioners. Following that study, Reece et al.3 demonstrated that Johrei recipients experience a significant decrease in their negative emotional states, whereas positive emotional states seem to increase in both Johrei recipients and providers. Brooks et al.4 have also concluded that after Johrei sessions, patients in treatment for substance abuse experience enhanced energy, emotional states, and well-being, as well as decreased pain and depression. Data from Gasiorowska et al.5 indicates that Johrei can serve as a good alternative method for the relief of functional chest pain. In 2010, Teixeira et al.6 investigated the growth of sucrose crystals and demonstrated that Johrei increased their crystallization with respect to the control. Additionally, Abe et al.7 have demonstrated that Johrei increases cell death and decreases cell proliferation of gastric cancer cells in vitro. Recently, Buzzetti et al.8 have studied brain markers for sleep and have verified that mice subjected to Johrei therapy exhibited improved sleep patterns compared with the control group of mice when subjected to sleep interruption. By contrast, Taft et al.9 did not detect any difference between the control and Johrei-treated cancer cells in relation to death and proliferation. Hall et al.10 have also reported that Johrei did not heal cultured cells exposed to radiation. Radin et al.11 reported that a single application of Johrei was not able to significantly alter the development of astrocytes cell cultures or
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generating random numbers produced by electronic devices; however, significant changes were observed for both systems, simultaneously, after repeated applications of Johrei. In this context, Teixeira et al.6 have proposed a hypothesis concerning the importance of water in the process of interaction between Johrei and matter, as though water may act as a mediator for the physical manifestation of Johrei. One of the mechanisms that was considered in this work to explain the observed changes in the efficiency of the crystallization of sucrose was a possible change in the state of organization of the water into clusters.12–18 Furthermore, water molecules seem to have a key role to the physical manifestation of forms of energy healing, such as homeopathy; Bach Flowers, and Johrei.6,19–24 Among the various properties of the liquid state that can be related to these organizational changes (cluster formation), we emphasize the hydrodynamic behavior of water in this work. Using a simple experimental setup to address this possibility, a study was conducted to demonstrate whether Johrei can act on water in the liquid state and change the hydrodynamic behavior of its dripping process. System Modeling The chosen experimental system was the detachment of water droplets from the tip of a capillary tube (dripping) because of its experimental simplicity and because the physical properties of this system are well studied.25–30 The experimental system that was used consisted of a vertically oriented cylindrical glass tube with an inner diameter of approximately 7 mm, whose lower portion terminated in vertical capillary tubing of a length much greater than the inner diameter. The glass tube behaved as a reservoir, and when it was filled with water and the water was allowed to flow freely (as a Newtonian fluid) through the capillary, a dripping phenomenon was produced (not chaotic) at the lower end of the capillary. The mathematical modeling of these phenomena was performed using the equations of Poiseuille and Bernoulli, and the result was a function that describes the time dependence of the accumulated droplet count from the beginning of the experiment, given as follows: Dðt Þ ¼ φ4 1eφ5 t ð1Þ where φ4 ¼ φ0 þ φ1 φ2 φ3
with 1
ð4ρghÞ3 R2 ρghR2 ρgzð0ÞR2 , φ1 ¼ , φ2 ¼ φ0 ¼ 1 , 2γ ðr ec f Þ 2γ ðr ec f Þ 3 3 3γ r 4ec f φ3 ¼
Rcosθ ρgr 4c and φ5 ¼ ðr ec f Þ 8ηh R2
The parameters in the equation are as follows (Figure 1): R ¼ internal radius of the upper reservoir tube (7.0 mm), rc ¼ internal radius of the capillary (0.25 mm), rec ¼ external radius of the capillary (0.70 mm), h ¼ length of the capillary (80 mm), z(0) ¼ initial height of the water column measured from the base of the reservoir tube (200 mm), θ ¼ contact
2
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a b c
d
e
g
f
Figure 1. Schematic diagram of the drop-counting system. (A) Reservoir glass tube—water reservoir used in the experiments; (B) solenoid valve—electromechanical control of the opening for the water droplets; (C) level sensor—trigger of the electronic system used to close the solenoid valve; (D) cylindrical glass tube—water reservoir for the droplet system, used to define the precise amount of water to be used in each assay; (E) capillary tube—water duct, used to establish the conditions for the droplet-formation process; (F) photoelectrical system—electrical pulse generator triggered by the interruption of the light beam by each droplet, allowing the system to count the droplets; and (G) electronic system—system used to control the filling of the cylindrical glass tube (D) and the recording of the number of drops per time. angle between the liquid and the inner wall of the upper reservoir tube, f ¼ Harkins correction factor,31–33 η ¼ viscosity of water, γ ¼ surface tension of water, ρ ¼ density of water, and g ¼ acceleration of gravity. Eq. (1) was used to fit the data of the droplet count versus time. From the fitting, the empirical parameters φ4 and φ5 were obtained, and these parameters were used to investigate possible differences between the Johrei-treated water and the non-treated control. In fact, τ, the inverse of φ5, was used instead of the raw φ5 value because τ is the measured time constant of variation in the water-column height in units of seconds. The primary purpose of this work could initially be evaluated simply by means of the empirical parameters φ4 and τ. Later in this article, we discuss the results of calculating the values of φ4 and τ, as predicted by the model, using values of ρ, η, and γ obtained from standard tables34 for a temperature corresponding to that of one of the control experiments (without treatment). However, a direct interpretation of the results in terms of the effects of Johrei on physical parameters such as surface strength, density, and viscosity is not performed because of the lack of a more extensive validation of
Johrei Effects on Water
the model in terms of the measured quantities for these physical parameters under the same experimental conditions as those of the experiments performed in this study.
METHODS In this study, the measurement of the number of drops over time was performed using semi-automated equipment designed and constructed especially for this purpose. In this apparatus (Figure 1), a thermally insulated stock bottle containing 250 mL of test water was placed above the upper opening of the vertical glass tube reservoir. The control of the water flow into the reservoir tube was accomplished using a solenoid valve and an upper level sensor in the reservoir tube, the signal from which was used to shut off the solenoid valve, thereby stopping the filling process. As the capillary attached to the lower part of the glass tubing was always open, droplets began to fall even during the filling process, but counting was begun only after the solenoid had been shut off. An electronic counter was setup to report the droplet counts in successive intervals, the duration of which could be adjusted to be one, two, or five minutes, using a time basis derived from divisions of 60 Hz. The counts were stored by a RAM chip inside the counter and, at the end of each reporting period, transferred to a computer by means of a serial interface. The electric signal for the counting of the droplets was generated through the detection of each droplet just as it began to fall by a photoelectric gate placed near the capillary tip. The temperature of the water was measured throughout the experiment using a mercury thermometer placed in the stock bottle and another in a thermally insulated container that collected the droplets below the apparatus. In each experiment, the first four runs were performed using non-treated water. After these runs, the Johrei practitioner applied Johrei treatment to the remaining water inside the stock bottle for a duration of 30 minutes, and then another set of four runs was performed. The Johrei treatment was performed with the stock bottle in its measurement position. Experiments were performed with four volunteer Johrei practitioners (P1, P2, P3, and P4), yielding a total of four sets of runs. Before the experiments with the Johrei treatment, two control experiments were performed, in which all eight runs (of each control experiment) were performed without Johrei treatment. The results for each set of six runs are labeled as follows: control group I—first run (CWJ1) and second run (CWJ2) of the first control experiment without Johrei treatment; control group II—first run (CWJ1') and second run (CWJ2') of the second control experiments without Johrei treatment; group 1—first run without Johrei treatment (WJP1) and second run with Johrei treatment (JP1) performed by practitioner 1; group 2—first run without Johrei treatment (WJP2) and second run with Johrei treatment (JP2) performed by practitioner 2; group 3—first run without Johrei treatment (WJP3) and second run with Johrei treatment (JP3) performed by practitioner 3; and group 4—first run without Johrei treatment (WJP4) and second run with Johrei treatment (JP4) performed by practitioner 4. After each set of
Johrei Effects on Water
Figure 2. Results of a droplet experiment showing the number of drops per time () and the fit to the data (r ¼ 1). runs, all glass equipment was washed with the neutral detergent Extrans, rinsed with distilled water and left submerged for two hours in a bi-distilled water bath. Afterward, the glass equipment was dried in a stove at 501C for 24 hours. Eq. (1) was used as a fitting function to fit the data of the accumulated droplet counts versus time. The fits were performed using the software package Microcal Origin 8.0s, using the Levenberg–Marquardt fitting method.35 The statistical analysis of the experiment was performed using the Biostat 5.0s software package.36
RESULTS For all experimental data, the fit function was in very good agreement with the data. A typical fit is presented in Figure 2. The correlation coefficient values were 0.9999–1, indicating a high degree of correlation between the experimental data and the proposed model (Eq. (1)). The fitting parameters φ4 and τ, grouped by experiment and by whether they corresponded to a control group or a treatment group, as presented in Table 1, were analyzed to assess their normality using the Lilliefors test.37 This analysis revealed statistical behavior consistent with normal distributions for the sets of φ4 and τ values for all experiments, indicating that the use of parametric statistical tests (ANOVA and Student's non-paired t-test) would be appropriate. For each of the four experiments in which Johrei treatment was performed and the control experiment, the mean values and standard deviations of the parameters φ4 and τ are presented in Figures 3 and 4. Among the sets of results found for each of the four Johrei practitioners, it was found that in groups 1 and 2, there were statistically significant differences between the average values of parameter τ that corresponded to the treated and nontreated sets of runs. The P values for these groups were P o .05 and P o .01, respectively. There were also statistically significant differences for parameter φ4 in group 2.
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Table 1. Adjust Parameters of φ4 and τ Grouped by Control Group (CWJ1, CWJ2, and CWJ1', CWJ2') and Johrei-Treated Group (P1, P2, P3, and P4) Control Without Johrei φ
Control Without Johrei
τ
φ
τ
CWJ1 1880.50 1836.93 1833.05 1850.16
CWJ2 849.34 810.68 811.01 823.68
1848.84 1854.55 1883.93 1862.44
CWJ1' 1845.69 1848.55 1843.24 1853.47
CWJ2' 824.57 825.85 823.88 827.25
1844.72 1840.29 1849.71 1853.16
Without Johrei (WJ) φ
812.31 821.08 851.35 828.25
825.82 816.18 831.56 827.51
With Johrei (J)
τ
φ
τ
1804.66 1797.23 1789.73 1814.67
759.90 756.03 746.90 758.26
P1 1826.98 1848.82 1766.32 1838.70
802.69 816.55 750.07 794.92 P2
1861.78 1849.69 1872.74 1861.40
Figure 3. Bar-graph data for parameter φ4 (mean ⫾ SD) for the control group (CWJ1 and CWJ2, CWJ1', and CWJ2') and the Johreitreated groups (WJP1 and JP1, WJP2 and JP2, WJP3 and JP3, WJP4 and JP4). **P o .01. The temperatures above each pair of bars represent the mean value of the temperature and its standard deviation for the corresponding experiment.
762.28 756.91 766.72 761.97
1813.78 1838.92 1838.63 1830.44
734.23 749.52 750.12 744.62
1890.24 1899.98 1857.54 1866.62
772.63 774.35 747.50 743.45
1830.98 1829.54 1856.20 1885.38
797.58 797.73 808.50 838.27
Statistically significant differences were also found between the value of parameter τ that corresponded to the two combined control groups and the values obtained for the non-treated results for groups 1–3 (WJP1, WJP2, and WJP3), with P o .05. No statistically significant difference was found between the combined control groups and WJP4.
DISCUSSION The proposed mathematical model (Eq. (1)) is in excellent agreement with the experimental data for droplet count over time. This agreement implies that our method offers a high
P3 1893.39 1864.73 1862.54 1873.55
764.05 748.62 748.67 753.78 P4
1838.53 1835.36 1850.51 1855.33
820.10 817.60 829.72 838.02
As expected, there were no statistically significant differences between CWJ1 and CWJ2 (the control group I) and CWJ1' and CWJ2'for either φ4 or τ.
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Figure 4. Bar-graph data for parameter τ (mean ⫾ SD) for the control group (CWJ1 and CWJ2, CWJ1' and CWJ2') and the Johreitreated groups (WJP1 and JP1, WJP2 and JP2, WJP3 and JP3, WJP4 and JP4). *P o .05 and **P o .01. The temperatures above each pair of bars represent the mean value of the temperature and its standard deviation for the corresponding experiment.
Johrei Effects on Water
sensitivity for the identification of possible variations in the empirical parameters as a consequence of the treatment under test, lending credence to our observation of the first evidence of variations produced by Johrei in the time constant τ in the involving groups 1 and 2 and in the parameter φ4 for group 2. In addition, the future prospects are very good for using this model to establish a correlation between the investigated parameters and variations in the viscosity and surface tension. Using Eq. (1), we calculated the expected values of φ4 and τ using tabulated values for η, γ, and ρ for water at a temperature of 26.91C (η ¼ 8.54 104 Pa s, γ ¼ 7.169 102 N m1, and ρ ¼ 996.5 kg m3). The value of f used in this calculation was estimated based on the drop volume determined in accordance with the equilibrium stalagmometric conditions. The drop volume (Vd) was used to calculate the ratio recV1/3 and to obtain the correspond ding f value of 0.766.31,33 For θ, a value of θ ¼ 0 (perfect wetting) was used as an approximation38 of the glass–water interface. The following values were found: φ4calc ¼ 1855 drops and τcalc ¼ 829 seconds. These values are in excellent agreement with the values obtained for the control experiment (the control group I) when the CWJ1 and CWJ2 values are averaged: φ4exp ¼ (1856 ⫾ 19) drops and τexp ¼ (826 ⫾ 16) s. This agreement suggests a high degree of accuracy for the model. However, as noted above, a more extensive validation of parameters φ4 and τ in terms of the measured values of η, γ, ρ, and θ must be performed to achieve a reliable interpretation of the effects of Johrei treatment with respect to variations in these parameters. The statistically significant differences found for the parameter τ when comparing the control group with the non-treated results for groups 1–3 are in good agreement with the observed variations in temperature. For a temperature range between 251C and 301C, the variations in η, γ, and ρ (as estimated using Eq. (1)) yield calculated thermal sensitivities of approximately 4.6 drops 1C1 for φ4 and 24 s 1C1 for τ. Considering the absolute values of φ4 and τ in this range, these thermal sensitivities correspond to relative variations of 0.29% 1C1 for φ4 and 2.8% 1C1 for τ. Therefore, φ4 is expected to exhibit a much smaller temperature dependence than τ. Linear regressions of the values of φ4 and τ (Supplementary material S1 and S2) with respect to temperature for the nontreated groups (CWJ2, CWJ2', WJP1, WJP2, WJP3, and WJP4) yielded a slope of (8 ⫾ 3) drops 1C1 for φ4 with a determination coefficient of 0.22, indicating a very small correlation, and a slope of (32 ⫾ 4) s 1C1 for τ with a determination coefficient of 0.74, indicating a reasonably good correlation. Therefore, the thermal sensitivities observed for φ4 and τ were also in good agreement with the predictions of the model. The thermal behavior of φ4 and τ described above may be considered to be a good explanation for why no statistically significant differences in φ4 were found for the control groups of the treatment experiments, WJP1 to WJP4, with respect to the control experiments, control group I and control group II and why significant differences in τ were found only for
Johrei Effects on Water
WJP1, WJP2, and WJP3 with respect to control group I and control group II and not for WJP4; the temperature difference between WJP4 and the control–experiment groups, control group I and control group II was only 0.21C and 0.41C, respectively. CONCLUSION The differences in τ observed between WJP1 and JP1 and between WJP2 and JP2 as well as the difference in φ4 observed between WJP2 and JP2 were found to be above the level of random variation with a statistical confidence of 95% or higher. Therefore, it may be concluded that there was a true change in the hydrodynamic behavior of the water that was significantly correlated with the Johrei treatment with Johrei for 50% of the practitioners who were evaluated. Moreover, because the temperature dependence of the investigated parameters is known, it could be established that a variation in temperature of 11C or more would be required to explain the observed variation in τ for groups 1 and 2 and that a variation of more than 61C would be required to explain the observed variation in φ4 for group 2. The potential temperature uncertainty within the same experiment is considered, in the worst case, to be less than 0.41C. Therefore, the observed variations cannot be explained in terms of temperature variations throughout the experiment. The conclusion is that the observed differences may be considered to be at least an initial indication of a possible effect of Johrei treatment. Improvements in the method and in the quantity and reproducibility of the results are necessary to confirm these results. Therefore, a future study is planned with a greater number of repetitions per experiment, blind analysis, and more stringent temperature control throughout each experiment. Acknowledgments
We would like to express our gratitude to Dr. Luiz Anastacio Alves for his noticeable good will and spirit of collaboration, who help make this work possible. This work was supported by Mokiti Okada Foundation, Centro de Pesquisa MOA-Rio de Janeiro. The authors that do not belong to the Mokiti Foundation have no commercial association that might create a conflict of interest in connection with this article. APPENDIX A. SUPPLEMENTARY INFORMATION Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.explore. 2015.08.001. REFERENCES 1. Gomes A, Teixeira PCN, Coelho JA, Rocha H, Furtado KG, Souza HVC. Influence of the laying on of hands technique (Johrei) on the germination of gamma rays irradiated canary seeds. J Conscientiol. 2001;3(11):169–181. 2. Naito A, Laidlawa TM, Henderson DC, Farahani L, Dwivedi P, Gruzelier JH. The impact of self-hypnosis and Johrei on lymphocyte subpopulations at exam time: a controlled study. Brain Res Bull. 2003;62:241–253.
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3. Reece K, Schwartz GE, Brooks AJ, Nangle G. Positive well-being changes associated with giving and receiving Johrei healing. J Altern Complement Med. 2005;11(3):455–457. 4. Brooks AJ, Schwartz GE, Reece K, Rev. Nangle G. The effect of Johrei healing on substance abuse recovery: a pilot study. J Altern Complement Med. 2006;12(7):625–631. 5. Gasiorowska A, Navarro-Rodriguez T, Dickman R, et al. Clinical trial: the effect of Johrei on symptoms of patients with functional chest pain. Aliment Pharmacol Ther. 2008;29:126–134. 6. Teixeira PCN, Rocha H, Neto JAC. Johrei, a Japanese healing technique, enhances the growth of sucrose crystals. Explore. 2010;6:313–323. 7. Abe K, Ichinomiya R, Kanai T, Yamamoto K. Effect of a Japanese energy healing method known as Johrei on viability and proliferation of cultured cancer cells in vitro. J Altern Complement Med. 2012;18(3):221–228. 8. Buzzetti RA, Hinojosa-Kurtzberg M, Shea TJ, Ibuki Y, Sirakis G, Parthasarathy S. Effect of Johrei therapy on sleep in a murine model. Explore. 2013;9:100–105. 9. Taft R, Moore D, Yount G. Time-lapse analysis of potential cellular responsiveness to Johrei, a Japanese healing technique. BMC Complement Altern Med. 2005;5(2):1–7. 10. Hall Z, Luu T, Moore D, Yount G. Radiation response of cultured human cells is unaffected by Johrei. Evid Based Complement Alternat Med. 2006;4(2):191–194. 11. Radin DI, Taft R, Yount G. Possible effects of healing intention on cell cultures and truly random events. J Altern Complement Med. 2004;10:103–112. 12. Tanaka H. A simple physical model of liquid water. J Chem Phys. 2002;112:799–809. 13. Chaplin F. A proposal for the structure of water. Biophys Chem. 2000;83:211–221. 14. Stanley HE, Buldyrev SV, Campolat M, et al. The puzzle of liquid water, a very complex fluid. Physica D. 1999;133:453–462. 15. Cho CH, Singh S, Robinson GW. Liquid water and biological systems. The most important problem in science that hardly anyone wants to see solved. Faraday Discuss. 1996;103:19–27. 16. Stanley HE, Kumar P, Xu L, et al. The puzzling unsolved mysteries of liquid water. Some recent progress. Phys A Stat Mech Appl. 2007;386:729–743. 17. Lo SY, Li WC, Huang SH. Water clusters in life. Med Hypotheses. 2000;54(6):948–953. 18. Loftsson T, Brewster M. Physicochemical properties of water and its effect on drug delivery. A commentary. Int J Pharm. 2008;354: 248–254. 19. Schwartz SA, DeMattei RJ. Infrared spectra alteration in water proximate to the palms of therapeutic practitioner. Subtle Energies. 1991;1:43–54. 20. Shishki GG, Ageev IM, Rybin YM, Shishki AG. Research of water response under the action of the infrared human body radiation by water conductometric sensors. Open J Appl Sci. 2013;3:278–284. 21. Bellavite P, Marzotto M, Olioso D, Moratti E, Conforti A. Highdilution effects revisited. 1. Physicochemical aspects. Homeopathy. 2014;103(1):4–21.
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22. Elia V, Ausanio G, Gentile F, Germano R, Napoli E, Niccoli M. Experimental evidence of stable water nanostructures in extremely dilute solutions, at standard pressure and temperature. Homeopathy. 2014;103(1):44–50. 23. Radin D, Hayssen G, Emoto M, Kizu T. Double-blind test of the effects of intention on water crystal formation. Explore. 2006;2 (5):408–411. 24. Thaler K, Kaminski A, Chapman A, Langley T, Gartlehner G. Bach flower remedies for psychological problems and pain: a systematic review. BMC Complement Altern Med. 2009;9(16):1–12. 25. Lee B-B, Pogaku R, Chan E-S. New drop weight analysis for surface tension determination of liquids. Colloids Surf A Physicochem Eng Aspects. 2009;332:112–120. 26. Dreyer K, Hickey FR. The route to chaos in a dripping water faucet. Am J Phys. 1991;59(7):619–627. 27. H Matsumoto T, Ueda T, Nogi K. A new method for simultaneous measurement of surface tension and viscosity. J Mater Sci Mater Med. 2005;4(9–10):2161–2166. 28. Franses EI, Basaran OA, Chang C-H. Techniques to measure dynamic surface tension. Curr Opin Colloid Interface Sci. 1996;1(2): 296–303. 29. Molki M, Abbasi B. Effect of temperature on the vorticity field of an evolving water droplet. Int J Heat Mass Transfer. 2010;53: 18–28. 30. D'Innocenzo A, Paladini F, Renna L. Experimental study of dripping dynamics. Phys Rev E. 2002;65:056208-1–056208-8. 31. Wilkinson MC, Kidwell RL. A mathematical description of the Harkins and Brown correction curve for the determination of surface and interfacial tensions. J Colloid Interface Sci. 1971;35 (1):114–119. 32. Hartland S, Srinivasan PS. The basis of theoretical correction factors for use with the drop weight method of surface tension measurement. J Colloid Interface Sci. 1974;49(2): 318–320. 33. Harkins WD, Brown FE. The determination of surface tension (free surface energy), and the weight of falling drops: the surface tension of water and benzene by the capillary height method. J Am Chem Soc. 1919;41(4):499–524. 34. Haynes WM. CRC Handbook of Chemistry and Physics. 94th ed. CRC Press; 2013. 35. Marquardt DW. An algorithm for least-squares estimation of nonlinear parameters. J Soc Ind Appl Math. 1963;11:431–441. 36. Ayres M, Ayres MJ, Ayres D, Santos AS. BioStat 4.0: aplicações estatísticas nas áreas de ciências biológicas e médicas. Sociedade Civil Mamuirá MCT. 4a Edição. Pará, Brasil: Imprensa Oficial do Estado do; 2005. 37. Lilliefors HW. On the Kolmogorov–Smirnov test for normality with mean and variance unknown. J Am Stat Assoc. 1967;62: 399–462. 38. Vargaftik NB, Volkov BN, Voljak LD. International tables of the surface tension of water. J Phys Chem Ref Data. 1983;12(3): 817–820.
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