Modeling an Extremely Long Delay

[Monte]

What is a good way to dealing with the Floating Point error?

My model has long delay and short delay constants. The time horizon is [0, 3.3e+170] years. The smallest delay is 100 years, and the largest is 2.772e+034 years. The model purpose is to test a religious belief of reincarnation, long held in many far eastern countries.

My dynamic hypothesis describes the dynamics of existing being (except flora) in a universe of the Three Worlds: the Earth, the Heaven, and the Hell, based on Buddha Gotama’s theory of Reincarnation (See the reply below).

PROBLEM
The maximum allowable FINAL TIME of Vensim is 1e+038 years, far less than the final time of my model. So, I change the time unit from Year to an ancient unit called “Kalpa”. One Kalpa equals 3.3e+30 years. The FINAL TIME is extended to be 5,000 Kalpa.

But we know that the rate of

Death=
Earth Life/Life Time on Earth
~ Ten Millions life/Kalpa
~ |

The value for Life Time on Earth is only 100 year, or 30.3e-028 Kalpa. Everything is O.K. except when running the model, Vensim stops the simulation and issues a warning message : Floating point overflow – saving to time 0.015625, possibly because the Death’s value got too large.

[Monte]

DYNAMIC HYPOTHESIS OF THE THREE WORLDS MODEL
People in many far eastern countries hold a common religious belief that they are in a universe of three connecting worlds: the Earth, the Heaven, and the Hell, where living things consist of human and non-human creatures who have been and will be traveling in these worlds for a long time until they are enlightened by practicing the right methods for having the right wisdom. Enlightenment makes them exist the three worlds permanently and enjoy immortality after the death in their last reincarnation.

Those who are doing bad things will go to hell after death and subjected to associated penalties. The maximum penalty lasts 1 Kalpa, or 3.3e+030 years, which applies to ghosts who had intentionally murdered their own parents when they were on the Earth. After enough punishment, they will be reborn on the earth as animals hundreds of times before becoming a poor unhappy human.

Those who are doing good things will go to hell after death too, but for spirit cleaning before going onto the celestial world, to become the residents of the Heaven. Those who have done more good things on the Earth will be able to stay on the Heaven for a longer time. The maximum heaven lifespan is 84,000 Kalpas, or 84*3.3e+033 years. After consuming all the benefit, they will be eventually reborn on the earth, to good families. While living on the earth or on the heaven, they may meet the Buddha (extremely rare event), understand his teaching, and successfully practicing, their mind will be pure and can permanently exist the three worlds after death (go to the Nirvana condition). On the contrary, if they fail to maintain doing good things, they will fall into the hell after death.

[Administrator]

I think you'll have to use some other package to do this. I cannot think of a way of doing what you want.

[Monte]

Thank you.
If Vensim cannot help, I cannot think of other package that can help. I am thinking of a new way to dealing with such an extreme delay. It is not a good way, but a necessary one if nobody can think of other good or better solutions.

I would alter the SD paradigm, in parameter estimation. We are trained to get the best estimate of a parameter value. At least it should fall in a plausible range of the parameter values being modeled. This is a barrier to problem solving.

In my case, I would not follow the conventional modeling practice. I have to simplify the parameter values too, by adjusting the values of all parameters in the model in a relative manner. This action will preserve the original invisible qualitative relationships among all parameters, i.e., delay time on the Heaven is longer than that in the Hell, which is longer than that on the Earth. For example, I would set the delay to be 1,000, 1, and 0.1 Kalpa for the Heaven, the Hell, and the Earth, respectively. The quality, or modes of model behaviors, would not be much changed by this modeling practice.

[LAUJJL]

Hi Monte

If I have correctly understood your problem, you are not testing the reincarnation belief, which will be difficult, but the compatibility of the different delays values.
You want to verify that these delays values may exist together or eventually that one at least does not make sense?

Am I right?

Regards.

JJ

[tomfid]

I think it ought to be possible to simulate portions of the dynamics in double precision Vensim DSS. The largest double is something like 2^308, so the capacity is there.

However, even if it could run, you have a problem, which is the cause of your fp error. You're running for 5000 kalpas with a time step of 3e-28 kalpa, so you're attempting about 1e30 time steps. You could hand code your model to avoid memory issues with that, but even with a petaflop of computing power, it'll take you millions of years to do one run.

I think the best you can do is:
- eliminate the Earth from the system, because its time constant is so short that it's nearly always in equilibrium with respect to Heaven and Hell, or
- solve the whole system analytically

JJ's suggestion, adopting representative delays on a more reasonable range of scales, might be a good way to start by getting some intuition.

My tentative observation is that, to generate the observed throughput on Earth, the stocks of souls in Heaven and Hell would have to be mind-bogglingly large.

[Monte]

Thank you, JJ. Initially I was testing the belief, to see if the population of Heaven souls is depleting as stated in the scripture. The testing turns out to be very difficult, as told by the Buddha himself, because of the vast difference between the biggest and smallest values of delays, which causes an FP error. So I have to deal with this basic issue first.

Thank you very much, Tom.
1. Our experience confirms the Buddha’s conclusions: i) Time calculation for the three worlds is very difficult;
ii) The Earth is nothing [as we have to eliminate the Earth from the system when considering the Heaven and the Hell].

2. I couldn't see JJ’s suggestion in his reply. Did you mean my reply at 2.14 p.m.? If so, I would have been on the right way.

3. I reach some conclusions about spatial and dynamic models.

In spatial modeling, if a spatial model represents an infinite space (e.g., the universe area), the Earth will disappear from the model, as the SPACE STEP has to be very large. That is why we cannot find the Earth if we are observing her from another space system (e.g. another universe).

In dynamic modeling, if a dynamic model represents an infinite time (e.g., the universe time), the Earth will disappear from the model, as the TIME STEP has to be very large. That is possibly why we will not find the Earth if we are observing her from another time system (e.g. Heaven).

[Monte]

Hello JJ,

You considered my model purpose.

However, there are more to consider.
Modelers would state their model purposes (for what the model is intended) very clearly,
but rarely do they state their modeling purposes (why they build the models)

My modeling purpose is to make a history together.
I am pretty sure that we are discussing the SD model that contains
the largest constant values and represents the largest distance in the SD history.

[LAUJJL]

Hi Monte

I do not quite understand the difference between model purpose and modelling purpose which you should illustrate with an example. What I understand is that the model purpose is related to some reality and modelling purpose is more personnal and related to people? Am I wrong?

I do not understand what 'make a history together' means.

I imagine that by distance you mean horizon?

Regards.

JJ

[Monte]

Thank you for your reply and questions.

The term modeling purpose is not a jargon nor standard concept of the SD paradigm. I coined this word so that we can make a distinction between the obvious purpose (model purpose) and the subtle purpose (modeling purpose). The former is a statement of the utility for which the model is developed.
For example, model A is intended to understand the effect of a on b, to study the dynamics of B, and so on. In 2000s, I built a model called MONTE. The model purpose is to calculate the tsunami travel time along the trajectory in the Andaman Sea region, based on a 5-minute bathymetry dataset.

The later is a personal reason why the model is built. Some may want to make money, others may want to become a professor. I want to make a history. This is what I mean when using the term modeling purpose. For example, the modeling purpose of the MONTE model is to obtain an academic degree. You are right. Modeling purpose is more personal and related to self-need gratification.

The phrase “make a history together” means I would like to tell you and Vensim Forum members that we (I, you, and the Administrators) are discussing the Three World model, which is the model that represents a problem associated with the largest time delay in the system dynamics history (~Kalpa). The maximum number of years for the delay escapes Vensim’s imagination. The value of the smallest time constant is most closest to zero ever.

In terms of distance, I refer to the spatial distance aggregated in the model. Forrester’s World II model aggregates all people around the world into a single variable called Population. My model aggregates not only people but also other organisms around the world into a single variable called Earth Life. Forrester uses many stock variables to represent the world. I use only one stock to do so. Forrester’s model deals with dynamics in the biosphere. Fiddaman’s model, even bigger, deals with the dynamics in the atmosphere. The Three Worlds model deals with the universe, both physical and meta-physical systems. It connects the Heaven to the Earth and to the Hell, as well as the Hell to the Heaven, very very long distance. It is the highest aggregated SD model in modern history. That is what I mean.

[LAUJJL]

Hi Monte.

There are quite often modelers interested in problems that are to my opinion out of reach of SD capability to solve problems or describe problems.

I think that trying to describe something like Heaven that has not the slightest observable data in the real world, will force you to rely only on pure mathematics. It is eventually possible if you think like Grothendiel a Field medal in mathematics, that mathematics do not need any reality to exist and can exist even in the nought, which to my opinion does not make sense as in this case the nought would not be anymore a true nought having something existing.

You will be able to build a logical world from a mathematical point of view but with no link with the real world as are all religions which will always rely on beliefs.

This is of course my opinion, but you may or other people may be interested (a personal purpose!)
thinking about this problematic. It may even generate understanding of these metaphysic problems, why not.

The notion of model purpose and modeling purpose is a fundamental idea, that should be made clear when modeling. It is too an important reason why many modeling efforts fail as behind a common model purpose there are many modeling purposes related to all the people concerned with the modeling effort. The lack of common modeling purpose makes automatically the modeling effort prone to fail.

It remembers me an experience some years ago, when I contacted an Sd consultant who concentrated on the model purpose, but never tried to consider my modeling purposes. At that time the modeling effort was bound to fail, and this is what happened.

Regards.

JJ

[Monte]

Hi JJ,

Thank you for sharing your ideas.

SD CAPABILITY
At this moment, I tend to believe that SD can describe
any dynamic problem conceptually, and cannot describe some problems
numerically. By conceptually, I mean we can build a conceptual model
(e.g., stock-flow diagram) of any dynamic problem.

As you know, there are some weak points of SD. A major one is of
policy implementation. SD can give a good or the best policy,
but cannot garuntee it will be successfully implemented.
Most SDers are more concerned about building model confidence,
publishing models, getting them adopted by the cliants.
That cannot meet the ultimate goal of model building
(to solve a dynamic problem). SD allows us know what the
right things to do are, but dose not teach us how to get them
done as intended. This is the gap of knowledge in SD paradigm.
but some experts percieve this weak point as an advantage of SD.
They usually assert that in SD models we can implement all
the policies which cannot be implemented in the real world.
So, I think, some of their recommended best policy options
will never be implemented. We need to learn from other
paradigms too. SD has limited capability as you pointed out.

META-PHYSICAL RESEARCH
A rational manager or an empirical scientist may study a meta-physical
dynamic problem like this one if the model purpose is to test
a religious belief, not against the absolute truth which cannot be
observed empirically, but against the verbal description in
a considered scripture, to see if there are any self-contradictory
descriptions therein. No effort can be successfully made
to assert that the model represents the meta-physical world.
We can assert that it represents a mental model of the
meta-physical world. Religious teachers may use the model
for teaching their students to better and more quickly understand
the belief being lectured, not for making them beleive the belief.
We cannot teach wise persons anything. That is impossible and
beyond the SD capability (or, in fact, all scientific methods capability).

Actually, other professional modelers and the general public
may not believe in even a well-tested physical or social SD model
created by a famous system dynamicist,
not to mention a meta-physical one.


Best regards,
MonTe

[LAUJJL]

Hi Monte


You write :

<As you know, there are some weak points of SD. A major one is of
<policy implementation. SD can give a good or the best policy,
<but cannot garuntee it will be successfully implemented.

I do not share this opinion.

If lots of models policies are not implemented, the cause is not the SD paradigm, but eventually the model itself, or the client, or something else.

There are lots of such models at the SD conference. These models are published but often not even read. The purpose of publishing these models is not implementation, but nourishing the CV of the authors. Their models are generally not credible and are built out of the sight of eventual policy makers.

Nothing can guarantee an implementation. The purpose of the model is to help decision makers better understand their problematic and take therefore better decisions. But the implementation is the responsability of the decision makers.

SD has then to my opinion no limited capacities. The limit exists with the complexity of the problem, the motivation and the capability of the decision makers and modelers and time allocated to buid and especially study, learn to use the model.

The way every one works with SD, probably varies considerably, depending on the type of problem, his own situation (teacher, researcher,consultant etc.) and books cannot propose methods adapted to these multiple different people.

I studied with books and attended courses that were totally unadapted to my case. I build models for myself and will have to implement them myself too.

I complained about that fact for years, but finally found out that complaining is counterproductive.

I try now to find myself how to work, not expecting much help from elsewhere. Now if there is only say 10 % of what is written, said in the SD community that is worth being considered, I am glad. It is better than nothing. I accept things are they are, and make the best out of them, and forget the 90 % not interesting (for me but maybe not for someone else).

Life is far from perfect and the SD world is the same. But SD is mathematics and the only problem is to use it correctly.

Regards.

JJ

[Monte]

Hi JJ,

Last year I took a course on Kepner and Tregoe's systematic problem solving and decision making, which makes me know an approach that guarantees implementation, e.g., Potential Problem Analysis, which leads to preventive actions and contingent actions. "No matter what might happen, the show would go on." "NASA, in its space programs, has been a heavy user of Potential Problem Analysis."

Their book, The New Rational Manager, is worth reading:
One of my favorites. Very practical approach.

Regards,
Monte

[LAUJJL]

Hi Monte.

It is possible to include implementation problems in the model to ease the implementation phase.

I think too that using SD, adds sufficient rationality in my decision processes, in fact it covers to my opinion all the possible useful rationality. If there is an optimal amount of rationality to include in management, I think that I am probably more above than underneath it. Business uses too intuition, experience and there will always be a part of unpredictable. Wanting to be fully rational, will generate a fear to move on or take any risk.
Anyhow, thank you for your recommendation.

Best

JJ

[Monte]

Thank you.