A Small Community Spiritual Evolution Stochastic Simulation Model

Jeffery Jonathan Joshua (ישוע) Davis; Florian Schübeler

The Embassy of Peace, Whitianga, New Zealand

joshua_888@yahoo.com, florian@theembassyofpeace.com

Stochastic Simulation has been used to model and describe the behaviour of a large diversity of systems. Here we present a simulation model intended to describe the consciousness and spiritual development of a group of people who participate in a small community that serves as a modern type of ashram-yeshiva, a learning organisation providing a place for spiritual growth and development in cultivating individual inner peace with a paradigm geared to the synthesis between modern science, ancient wisdom and personal revelation. The community is described as a system of people that can exist in one (1) of four (4) states of consciousness or spiritual development as follows: (0) survival consciousness, (1) sharing consciousness, (2) student of the Higher Spiritual Law and (3) God's Consciousness (Saint, Ambassador and Ambassadress of Peace). We simulate the system for a horizon of eighty (80) months under different conditions or scenarios in order to estimate the time at which the system (community consciousness) reaches a maximum where all members have achieved State 2, the state of a student of the Higher Spiritual Law. We then analyse the results and conclude with some future perspectives.

joms | 2019 | 1(30)
Reviewed By: Dr. Siva Shankar | Assistant Professor, Department of Computer Science and Engineering, Ahalia School of Engineering & Technology
Dates: Submission: 26-Dec-2018 | Acceptance: 02-May-2019 | Publication: 02-May-2019

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INTRODUCTION

Modern spiritual communities, which provide a place for retreat, learning and spiritual development, are emerging around the world as the need to compensate for radical materialism and secularism, religious dogma and the destructive use of science and technology. An example of that kind of community is Auroville in Tamil Nadu, India (Auroville, 2018). A significant number of people are showing interest in developing a personal relationship with The Creator or finding an impersonal way in order to achieve inner peace, and in so doing, contribute to relieve family and social tensions and aspire for a greater social harmony. These communities are very diverse in approaches depending on culture, geographical location and spiritual orientation, however most of them integrate a mixture of people with different degrees of spiritual awareness and development. In general and according to previous work (Davis & Schübeler, 2018), we can identify four (4) general states of development, spiritual awareness or consciousness ranging from reactive or survival (the lowest state) up to holiness, sainthood and enlightenment (the highest state). In our experience, both the participants and providers for such places and communities are mainly interested in maintaining a high quality of space or presence, and that, of course, depends on the capacity of each person to embody inner peace for long periods of time and quickly restore to such peace when occasional perturbations happen. Individuals in the lower state of survival and reactivity develop towards better and more desirable states by interacting with others who are more developed, and more importantly, by practicing what they learn via spiritual insights and revelations. That is usually aided by meditation (Liu et al., 2013) (Mascaro et al., 2015) (Schmidt & Walach, 2014), prayer, exercise and diverse activities, such as gardening, conducting research and doing art forms that are conducive to the growth of the soul. For many, a relationship with The Creator plays a major role, while for others the practice of unconditional love, compassion and actions of kindness (Maslow, 1970) or altruistic service suffice.

The development of each individual is unique and depends on the quality of the community as a whole, which usually necessitates one or more saints and some committed students-seekers of truth in order to assist others who still find it difficult to find inner peace by themselves, with their own inner resources, or in some cases, by the lack of trust in the process or faith in The Creator.

Based on previous experience and anecdotal evidence of members of a pilot community that acts as an Embassy of Peace in Whitianga, New Zealand, we have gathered knowledge and understanding to describe the dynamics of such a community in terms of the above mentioned states and the heuristic rules that govern the transitions from one state to another (Davis & Schübeler, 2018). We have laid a set of assumptions in order to simplify the complexity of the system and make it tractable in a way that allowed the development of a simulation model to better understand the individual and collective dynamics and the evolution of community consciousness. In the following section we describe the system with some diagrams as well as the basic aspects of the stochastic simulation model.

SYSTEM DIAGRAMS AND MODELS

There are many ways of modelling complex stochastic systems (Allen, 1978) (Ross, 1983) (Ross, 1985), where the system makes transitions from one state to another. Our approach includes a collection of probabilistic and mathematical models derived from a Semi-Markovian framework (Howard, 1971) translated into a stochastic simulation model (Law & Kelton, 1991). The system describes each of the N members of the community by four (4) states of consciousness or degrees of spiritual evolution, namely: (0) survival consciousness, (1) sharing consciousness, (2) student of the Higher Spiritual Law and (3) God's Consciousness, Ambassador and Ambassadress of Peace (righteous-saintly-holy-enlightened human being).

$$ S(t)_k~:~ \{0,~1,~2,~3\}~~for ~k = 1 ~~~~~~~~~~~~~~~~~~ (1) $$

The system evolves dynamically by allowing individuals to make transitions between states T_ij for i, j = 0, 1, 2 & 3 (see Table I). The rules that govern the transitions are stochastic in nature and depend on different variables, parameters, probability distributions and other functions as depicted in Figure 1.

The number of meaningful insights derived from encounters contributes to generate a transition depending on the type of encounter. There are ten (10) types of encounters between individuals in different states of consciousness as described in the following Table I. Note that an encounter T₀₁ is equivalent to an encounter T₁₀ and that applies to different types of encounters like, for example, T₁₃ is equivalent to T₃₁. However, in this example, only the individual in State 1 can make a transition to State 2 by a contribution from the individual in State 3.

Some types of encounters, like individuals with themselves are meaningless and never generate transitions, namely T₀₀, T₁₁, T₂₂, T₃₃ in Table I, which simply means that the individual stays in the same state.

In general, when two (2) individuals meet, the one (1) in a higher state may cause the one (1) in the lower state of consciousness to score a meaningful insight according to a certain probability distribution. Generally speaking, a transition from state i to state j, T_ij, will happen only after a certain number of meaningful insights (MI) exceeds a prescribed threshold (T_tresh).

$$ T_{ij} = 1 ~when ~\sum_{\forall l} MI_l \geq T_{tresh} ~\forall~ MI_l = 1 ~~~~~~~~~~~~~~~~~~ (2) $$

Otherwise T_ij = 0

The time in our simulations moves by month as well as every actualization of the state variables for each individual k:

$$ S(t+1)_k = S(t)_k + T_{ij}^k ~\forall~ S(t)_k <~2 ~~~~~~~~~~~~~~~~~~ (3) $$

Note that after the individual has reached State 2, our simulation generates no more transitions according to this rule (see equation 3) and individuals will reach State 3 after a time generated according to a certain probability distribution, which is omitted from this seminal model. For simplicity it is assumed that the number of encounters N_e, per person with every other person in the community responds to a stationary Poisson process (Ross, 1985) (Ross, 1983). However, different processes could apply to different types of communities, where sometimes encounters may be random, some other times cyclical or pre-scheduled. It is also possible to model a community with population growth, however we assume a stationary population for our simulations. We have also simplified the model to limit any spontaneous transitions from one state to another, whether it be to higher or lower states of consciousness. It is important to note that retrogressive behaviour could also be modelled via a probability distribution conditional to certain parameters like level of commitment (Davis & Schübeler, 2018).

In the following section we describe the different parameters, probability distributions and other functions relevant to the simulation model.

SIMULATION MODEL, PROBABILITY DISTRIBUTIONS, PARAMETERS AND OTHER RELEVANT FUNCTIONS

In order to model the transitions, we have prescribed the probability distributions, parameters and other functions that allow for such events. The first random variable to keep in mind, as mentioned before, is the number of encounters per person Ne(t)_ij, with each member of the community, where here both i & j take values from 1 to N, where N is the number of members in the community. As mentioned before, this is generated with a stationary Poisson distribution. After that we need to determine the types of encounters (E_ij) based on the states i and j of each person in the encounter, namely:

• Encounters between individuals in State 0 & State 1 (E₀₁)
• Encounters between individuals in State 0 & State 2 (E₀₂)
• Encounters between individuals in State 0 & State 3 (E₀₃)
• Encounters between individuals in State 1 & State 2 (E₁₂)
• Encounters between individuals in State 1 & State 3 (E₁₃)

Note that here i & j are states of consciousness that take values from 0 to 3.

This list is summarised in Table II and describes the types of encounters, which are able to potentially and probabilistically generate meaningful insights (MI), always for the person embodying the lower state of consciousness. Note that E_ij = E_ji and therefore we only need to specify the upper diagonal in Table II.

E_ii as mentioned before is meaningless or null and therefore there is no need to specify it. Based on the type of encounter and the number of encounters per month per person, we compute the probability of occurrence of a meaningful insight. Also as mentioned before, when a person has reached a certain prescribed number of meaningful insights (T_tresh), then a transition from state i into state j, T_ij, occurs.

As time goes by, each month we need to check for such an accumulation of meaningful insights per person k, in the model, which is codified as:

$$ T_{ij}^k = 1 ~\forall~ CMI(t)_k~ \geq T_{tresh} ~for~k= 1,~N ~~~~~~~~~~~~~~ (4) $$

$${where~~CMI(t)_k = \sum_{\forall l} MI_{l}^{k} ~~ \forall ~MI_l=1 }$$

It is important to note that when a transition happens, CMI(t)_k is reset to zero (0). The probability of occurrence of a meaningful insight for a particular person based on the number of encounters per type in a particular month is of the general form shown in Figure 2.

However, the particular values and shapes are conditional to the type of encounters, where the function associated to the person with the highest state of consciousness, is chosen to compute the probability of occurrence for a meaningful insight. Basically if a person in State 0 meets with a person in State 1, E₀₁, we use function-1 (Pm₁) to compute the occurrence of a meaningful encounter for person in State 0. If the encounter happens to be of the type E₀₂ or E₁₂, then we use function-2 (Pm₂), otherwise if the encounter happens to be E₀₃ or E₁₃, then we use function-3 (Pm₃).

All of them, Pm₁, Pm₂ and Pm₃ are probability functions describing the occurrences of a meaningful insight, each associated with people in different states of consciousness. Figure 3 shows the three (3) different probability functions Pm₁, Pm₂ and Pm₃.

SCENARIOS AND SIMULATION RESULTS

A. Scenario Descriptions

In this section we describe the different scenarios explored based on: (1) the average rate of encounters per month per person with all other members of the community, λ , assuming a Poisson process, (2) the minimum number of meaningful insights per person, T_tresh, required to make a transition, T_ij, from state i to state j, (3) the initial configuration of the community based on number of people, N and (4) the time horizon or simulation length.

Table III displays the values for the different parameters associated with each scenario. All scenarios were run for a community number, N = 20 & 40 people, where 65%, 15%, 15% and 5% of the members were in State 0, State 1, State 2 and State 3 respectively. The Time horizon, T_horiz, was eighty (80) months for all simulations and we ran 1000 simulations per scenario.

This configuration of scenarios allows the comparison between: (a) different population sizes, (b) different frequency of encounters between the members of the community and (c) different delays for transitions between states of consciousness for each community member.

Following in Figure 4 we present a flow chart of the simulation model with the main parameters, vectors and matrices that represent the system with its computations.

A basic list of definitions for the parameters, vectors and matrices is provided as follows:

• λ is the mean rate of encounters per person per month.
• N is the number of people in the community.
• T_tresh is the minimum number of meaningful insights required to make a transition from state i to state j.
• T_horiz is the number of months simulated.
• S(t)_k is the state of consciousness for person k at time t.
• MS(t) is the mean of all persons' states of consciousness, mean of {S(t)_k}. It represents the average consciousness of the community at time t.
• Ne(t)_ki is the number of encounters that person k has with person i and it responds to a stationary Poisson process with parameter λ.
• MEPM(t)_ij is a probability matrix of a meaningful insight conditional to both Ne(t)_ij and type of encounter E_ij.
• NME(t)_k number of meaningful insights for person k.
• Clock is the time of the system.

B. Simulation Results and Analysis

In this section we present a set of simulation results for each scenario based on Table III together with a comparative analysis. In Figure 5 (top) we present an example of what we observe as the evolution of the mean consciousness state (MCS) of the community together with the Standard Deviation (SD) around MCS of the community along time (Figure 5, bottom).

The MCS shows a typical, s-shape, learning curve while the standard deviation around the MCS shows a growth followed by a decay. This means that for the middle of the growth process, around the maximum, we observe more variability. In Figure 6 (top) we can observe a comparison between three (3) different scenarios where the average rate of encounters per person per month (λ) is fixed to the value of 1, while the minimum number of meaningful insights (T_tresh) required to make a transition from state i to state j, is set to 1, 2 and 3 for Scenario 1, 4 and 7 respectively as shown in Table III.

Generally speaking, the greater the value for T_tresh, the slower the growth process where:

• for T_tresh = 1, the average community consciousness reaches a maximum of 2 in about 12 months on average.
• for T_tresh = 2, the average community consciousness reaches a maximum of 2 in about 60 months on average.
• for T_tresh = 3, the average community consciousness will take a very long period of time far exceeding any meaningful horizon for this analysis.

This means that our system of community consciousness development is very sensitive to the minimum amount of meaningful encounters (T_tresh) per person per month required to make a transition to a higher state of consciousness.

In Figure 6 (middle) we can also observe that the initial configuration of the community can impact the speed of the development of the community consciousness (see Table IV) where the three (3) scenarios P1, P2 and P3 show different values for the initial mixture of people in terms of states of consciousness (S) where as mentioned before State 0, 1, 2 and 3 refer to survival consciousness, sharing consciousness, student of the Higher Spiritual Law and God's Consciousness respectively.

Finally, also in Figure 6 (bottom) we can observe a comparison of three (3) scenarios (4, 5 and 6 as shown in Table III), where in this case, λ varies between 1 and 3 while T_tresh is fixed to the value of 2.

It is evident from the graphs that the greater the average number of encounters per month per person (λ), the faster the development time where for λ = 1, 2, 3, the times to reach a collective maximum average state of consciousness are about 10, 18 and 57 months, for Scenarios 4, 5 and 6 respectively. This shows that λ is also a very sensitive parameter.

Apart from the scenarios we have already presented, we consider relevant to mention that the population size could also be a mitigating factor in the speed of the evolution of community consciousness as shown in Figure 7.

For all scenarios, the larger the population, the faster the process, moreover for Scenarios 4 and 7, for λ = 1 and T_tresh = 2, 3 the population size becomes a very sensitive parameter. This could mean that for slow learners, the population size, as well as having more people to interact with, makes a difference in aiding and speeding up the growth process.

CONCLUSIONS AND FUTURE PERSPECTIVE

We have developed a seminal simulation model to investigate the dynamics of small community groups aiming at growing spiritually. We have proposed that the process can be described as a set of transitions from State 0 to State 1 and then to State 2. State 3 is the highest possible achievable state in our model and can only be accessed after a certain random time while in State 2. We have left out of the simulation model transitions from State 2 to State 3, since the nature of these transitions is more connected to inner work, altruistic service and meditation rather than to the number of encounters per person per month. However, it would be appropriate to include these kinds of transitions since they would have the tendency to speed up the process since encounters with a holy person (State 3) has higher probabilities associated to them to produce a meaningful insight when compared to encounters with people in State 1 or State 2. In general, we can conclude that both λ and T_tresh show high sensitivity to a different set of values. For a linear increase in the values of λ the system accelerates non-linearly in the development of consciousness, while for a linear increase of the values of T_tresh the system slows down significantly also non-linearly. We therefore propose to inquire more deeply of how to determine those two (2) variables and understand better their dependencies on community conditions, such as availability of people and shared vision amongst other factors.

We also conclude that the initial conditions of the system both in population size and mixture or diversity, significantly affects the development of the system. When the mixture favours initial higher states of consciousness, the development speeds up and the opposite is also observed. With population size the results can initially be counterintuitive since the process will speed up its development for an increase in population size. When we reflect on that we easily realise that this is so because the more people make transitions to higher states, the more likely it is that people will experience meaningful insights in larger numbers of encounters per person per month.

Our model has laid some assumptions that could be lifted in future research by including, for example, backward transitions based on level (lack) of commitment or at random, such as, transitions from State 2 to State 1 or State 1 to State 0. These transitions are observed in community development and learning processes where people, even when advancing, sometimes also devolve for short or long periods of time. However, we conjecture that these types of transitions will slow down the development of consciousness in the system similarly for all scenarios studied. Also, another assumption that could be lifted would be the one of a static population for the horizon studied, where we could introduce population growth, decline or oscillatory patterns due to people entering or leaving the community. Other types of events could also be thought of and simulated, however we leave that for future research.

It seems to us that this model has supported the members of The Embassy of Peace in Whitianga, New Zealand, both as a learning tool while building the model as well as when immersed in an exploratory scenario analysis. Further, we are convinced that the model produces results in consonance with our observation of the development of our own pilot community, however this requires a different kind of report that is outside the scope of this work.

ACKNOWLEDGEMENTS

We would like to acknowledge the team at The Embassy of Peace, in Whitianga, New Zealand for its invaluable participation. Particularly, we acknowledge Colin and his contribution in designing the simulation scenarios and tables. We further want to acknowledge the contributions of Kali, Enya, Carey, Sarah, Shiloh, Matthew and Keryn.

REFERENCES

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