Monday, August 7, 2017

Tabletop Critters and Other Examples


This is a draft of Chapter 2 in the book outline

Tabletop Critters and Other Examples


Now we will see how the Resource-Patterns Model of Life (RPM), which was outlined in Chapter 1 Section 1.4, can apply to our understanding of living systems. We start with two brief examples: a world with two continents, and a green plant. Then we will gain familiarity with tabletop critters. These examples, as you will see, provide a fruitful basis for thought-experiment agent-based modeling (TEABM), the most fruitful basis for ABM which I have employed.


 2.1 Introductory Examples


2.1.1 A world with two continents


Suppose there is a planet which has two continents. The first, a frozen polar continent, gets 99% of the planet's precipitation, but is so covered with glacier that only a few blades of grass grow during the warm week of summer. The second is a vast, warm desert, with fertile soil but no water. Notice the possibility for agriculture if fresh water can be transported from one continent to the other.

Figure 2-1: A world with two continents, promising agriculture

Suppose that this agriculture, if achieved, could support a population of one billion humans for the foreseeable future. But suppose that at present, with no agriculture, only ten thousand humans live on this planet, and they live near starvation in scattered bands.


Now obviously the task which we see, which promises vast wealth in the form of crops, cannot be achieved by any one of the humans. This task requires companies, or whole industries, of ice carvers, shippers, and farmers. But, equally obviously, the humans can achieve it if they organize and combine their efforts appropriately, each doing a small part of the whole task.


This is the kind of challenge which we consider in RPM: A small population of poor living things (LTs) could grow greatly both in numbers and wealth if they coordinate their activities appropriately. RPM gives us a workbench, so to speak, upon which we open up these questions of whether and how coordination might be achieved in circumstances resembling the challenges facing hunter-gatherer level humans on the planet with two continents.

2.1.2 A green plant, with its millions of cells in roots, leaves, and stem


The environment in which these cells live has a resource pattern: above the ground there is abundant energy in sunlight and below the ground there is abundant water; but the distance between these two necessary resources is too great for any of the cells, acting alone, to exploit. This situation is akin to the world with two continents. But we see in the plant that the needed organization has already been accomplished. The plant is an organization in which each cell plays a part. Without participating in the scheme of the plant probably few of these cells could have survived in this environment.


2.2 Tabletop critters

 

2.2.1 Initial condition


Tabletop critters provide the model of LTs which we will use most. With this model we can frame important questions about life.


Imagine a flat surface, perhaps a tabletop, upon which some tiny, perhaps one-celled, critters live. These critters need both water and sugar to live, and this tabletop upon which they find themselves is basically a desert. The wind blows and occasionally deposits a few molecules of water or sugar at random, unpredictable locations on the tabletop. Figure 2-2 shows how we will picture the three types of objects on the tabletop.

Figure 2-2: Our way of picturing critter, water, and sugar

The water and sugar provided randomly by the environment just barely enables the critters to survive and reproduce themselves — provided of course that they keep moving about so they chance to find the small deposits of water and sugar.

In Figure 2-3 we see the same three types of objects to which we were introduced in Figure 2-2, but on a smaller scale so that we can see a larger area of the tabletop. We see more considerable distances between the critters and the resources they need to survive, so it is easier to imagine the near-starvation struggle of the critters to discover resources. Figure 2-3 thus represents what we call the initial condition on the tabletop.

Figure 2-3: The initial condition on the tabletop

 

2.2.2 Opportunity


Suppose that onto this tabletop fate places a drop of water at some spot, and a crumb of sugar at another spot. See Figure 2-4. Once again we have zoomed out when compared with the previous drawing (Figure 2-3). I drew Figure 2-4 on a smaller scale to show the larger area of the tabletop affected by this large new resource pattern. Now the critters have been reduced to looking like small spots; the original wind-dropped spots of water and sugar have fallen completely out of this view because they are too small to be visible; but the new drop of water on the left and crumb of sugar on the right are huge compared to the critters.

Figure 2-4, We add a large new resource pattern. Water on left, sugar on right.

Suppose that the distance between water and sugar, a centimeter, is much further than any one of these critters can travel in its entire lifetime, but suppose that the critters do have ability to pick up raw materials, carry them for small distances, and then drop them again. So the critters have the physical capability of establishing a line of exchange between the water and sugar. To see this capability, suppose that we give the critters some rules of behavior such as these:
  • If you sense water on the left, carry it to the right and set it down.
  • If you sense sugar on the right, carry it to the left and set it down.
  • If you get thirsty or hungry, help yourself to what you need from the materials that pass through your possession.
Following these rules, those critters who were lucky enough to start out somewhere between the water and sugar should thrive after passage of some time. These lucky critters will no longer die because of starvation, and they will reproduce more. A dense population of critters will come to live in a line of mutually cooperative exchange between the water and sugar. See Figure 2-5.
Figure 2-5, A population of critters prospering by trade between water and sugar


2.3 Reflections so far

 

2.3.1

Looking back now over our three examples (the world with two continents, the green plant, and the tabletop critters), I hope you may notice similarity. The hunter-gatherer people in the world with the two continents are in a situation like that of the critters in figure 2-4: both live impoverished in a world which promises plenty if they can cooperate. And the cells which make up a green plant already seem to have achieved a large degree of mutually beneficial cooperation toward which our critters in Figure 2-5 have taken a promising step. In all three examples a resource pattern may be exploited by the living things which succeed in discovering rules of cooperation.

2.3.2


I wrote above that rule-based behavior could lead to productive cooperation among critters. But you may wonder what exactly I mean by rule-based behavior. So, to tell more, we have designed our agent, the critter, with capability to perform a number of different acts. These acts include: move a single step in any chosen direction; take into internal storage a portion of a resource (water or sugar) to which the critter finds itself adjacent; set back onto the tabletop a portion of a resource taken from internal storage; reproduce (divide in half); do nothing (make no outward move); and perhaps other possible acts which we have empowered our critters to perform.

In each increment of time as our model runs each of our critters can perform one and only one of these acts. The critter’s “mind” has to choose one of these acts; this after all is the use of its “mind”. But how will the mind choose? This is where rules such as those we have mentioned will play a part. Rules narrow the choices among which the critter may choose in a given circumstance. Sometimes a rule may allow only one single choice. Other times a rule may prohibit a choice or set of choices. Also a rule may favor or disfavor a choice, without outright command, changing only the likelihood of that choice among the set of possible choices which may be developed by the critter’s preliminary "thought".


Thus rules, embedded in the thinking our critters, can guide the development of outcomes produced (or experienced) by groups of critters.

2.3.3

The rules are not arbitrary. The rules work because they help LTs exploit a resource pattern (or an environmental feature) which is bigger than any of the LTs, and which none of the LTs can change. So the environment in which the LTs live determines the rules more than the LTs themselves. The LTs contribute to formation of the rules only to the extent that the LTs have capabilities which – if organized into cooperative wholes – make exploitation of the RP possible. The LTs cannot make up the rules simply to serve the whims of the LTs.

It is not clear if or how the LTs can discover the rules which will lead to their flourishing:
  • In the world with two continents the humans needed to learn all the practices (rules) which could lead them to prosperity. But we cannot tell clearly and simply how they might accomplish that learning.
  • In the green plant, the cells already practice delimited (rule bound) specialties in an order of mutually beneficial cooperation. We do not know how these rules became established. But of course biologists work to elucidate this mystery.
  • On the tabletop the critters advanced from the poverty suggested by Figure 2-4 to the prosperity of Figure 2-5 because we gave them rules. But could critters have discovered such rules themselves without our help? This question expands and becomes the subject of this book.

2.3.4


We should remember that life was possible for our critters from the outset on our tabletop. It is not generally required that an opportunity for improvement of life must be exploited. Life could go on as before in most cases. And when a group of critters succeeds in advancing, by exploiting a RP, there are likely to be some critters from the initial population who are left behind by this advance. You may have noticed that I drew a few of these in Figure 2-5, still surviving in a thinly scattered population away from the thriving center of RP exploitation.


We humans who live well in cities are aware that in the hinterlands, away from our fruitfully organized lives, live many people in a style which we remember, or our parents remembered. We think, perhaps correctly, that we could always choose to return to that poorer way of living.

The availability of such a choice becomes important in our agent-based modeling, because the attempt by one critter, or a group of critters, to prosper by discovering and exploiting a previously unexploited RP, need not be a life-or-death gamble. Most attempts to advance to greater prosperity are launched from a way of living to which the attempting LT may fall back, if necessary.

2.3.5

Our modeling will generally follow the example of tabletop critters which we pictured in Figure 2-4, in that a population of agents will be modeled as living in an environment in which we modelers have posed an opportunity as a problem for the population. Some, or possibly all, agent-members of the population can advance their success in life if those members “learn” to work together.


2.4 Challenges for our critters


We have seen that organizations of critters can leap ahead in prosperity if the members in each given organization follow situation-specific rules as they choose how to act. Further, we should see that the challenge of learning what those rules need to be is the study which falls open before us as we examine life through our RPM. But before we step further into that study, here we will see a few of the difficult life-advance challenges which we modelers may present to our critters.

2.4.1 Challenge 1


In Figure 2-4 we have already presented our first challenge, but then we gave the critters rules to overcome the challenge. Suppose we do not give the critters rules. Can the critters somehow learn new rules themselves, rules analogous to the rules we modelers provided which enabled the critters leap to wealth shown in Figure 2-5?


In order to introduce a new symbol in our graphics we redraw Figure 2-4 in Figure 2-6. A dashed line has been drawn around the water-sugar pair of resources. It signifies that the critters have not yet learned enough to significantly exploit that RP. But of course we modelers know about it. We put it there after all. The dashed line enclosure reminds us modelers that the RP is evident, for the time being, only to us modelers and not to the critters.

Figure 2-6, A dashed line shows that a RP is unexploited.


When we see evidence of organized exploitation of an RP, as in Figure 2-5 we will usually consider that the critters have discovered that RP, although we must later on examine more carefully what mental states and processes might constitute such “discovery”.

2.4.2 Challenge 2


Figure 2-7, A world with an unexploited opportunity


In Figure 2-7 we see two resource patterns, arranged vertically this time. The RP on the left has been discovered by critters and is being exploited. These successful critters on the left must have rules which differ from the rules which helped our critters in Figure 2-5, simply because of the up-down rather than right-left orientation of the RP. But this difference does not affect our present challenge.

Instead, in this challenge we ask: Can anything which has been "learned" by the critters on the left help them to discover the similar RP on the right, and help them to discover it more quickly and with less prolonged, accidental learning (this is covered more completely in Chapter 5) than was required by the critters which first learned to exploit the RP on the left? This is a complex question which I will not pretend to answer in definite terms. But throughout the remainder of this book we will work toward answers.

You might notice that in Figure 2-7 we have once again reduced the scale of our drawing a little bit (we have zoomed out) so that we can show this challenge which involves a larger region of the tabletop.

2.4.3 Challenge 3

Figure 2-8, Different RPs require different rules.


In Figure 2-8 we see the starting point for out third challenge. The world has two resource patterns:
  • on the top the resource pattern (consisting of both water and sugar) is oriented horizontally;
  • on the bottom the resource pattern is oriented vertically.
Both RPs have been "discovered" by the critters as we can see, since in each RP a dense population of critters lives in what we can only explain as a line of trade between water and sugar.

I have tried to show a considerable distance between the top RP and the bottom RP in order to make it seem unlikely that critters would develop a line of trade between those two RPs. But let us assume that occasionally a critter might somehow make the long journey from RP to RP. Or we mischievous modelers might pluck a critter from one line of trade and drop it into the other line of trade, just to see what would happen.


What would happen? This is the challenge. But, short of all the work which we might do to bring this challenge to a computerized agent-based model, we can think and say things like:

  • If somehow a critter found its way from one community to the other and then tried to become a productive member in the new community by following the rules which it had learned in its original community, it would fail in this effort. For example, suppose a critter that has learned to carry sugar to the left (in the upper resource pattern in Figure 2-8) somehow finds itself in the other line of trade (in the lower resource pattern) where physical reality requires that sugar be moved up, not left. This critter's effort to be a good citizen by following the rules it has learned will introduce waste, not help, into the new community.
  • Where critters discover rules which enable those critters to live better, those rules are dictated by the physical realities of the critters' nearby environments. Each new resource pattern may possibly introduce a requirement for a new set of rules. So even though we might think of our critters as constituting a single biological species, our critters must be capable of conforming to various sets of behavioral rules, rules as dictated by physical circumstances beyond the control of any of the critters.

2.4.4 Challenge 4

Continuing the direction we started with Challenge 2, in Figure 2-9 we see one community of critters thriving at one RP in a world with many (albeit just six in Figure 2-9) similar and unexploited RPs. The challenge now concerns not just one neighboring RP, but a pattern in many neighboring RPs — a pattern of resource patterns.


In case it is not obvious I will say that we have zoomed out again, once again showing a larger piece of the world in which our critters live.


Figure 2-9, Can critters exploit a pattern of resource patterns?

We can start with this challenge, obviously enough, by trying to imagine how real living systems might have solved the problem. We might imagine that within that single thriving community there might be some variability among that population of critters. Let us imagine two types:
  1. The first type has only the attributes which enabled their ancestors to follow rules of cooperative exchange which resulted in this community. Members of this type do not necessarily know even that they live in a successful community. We modelers have given them no such sensual or calculational capabilities, after all.
  2. The second type have a variation, an addition to their attributes. This variation makes it more likely that they or their offspring will recognize a worthwhile gamble in sending a provisioned party of explorers off in the direction of one of their world’s unexploited RPs.

We expect then, after the clock of life has run for a time, that the other five RPs will come to be inhabited by thriving communities of critters descended almost entirely from Type 2, not Type 1. Type 2 will dominate in this world because of what we can see as natural selection.

Such a conclusion to our thought experiment draws much from Darwin as I understand that theory:  variation followed by natural selection. But it also adds an explanation for the selection mechanism. It suggests how nature selects: by affording much greater reproductive opportunity to variants able to exploit the available RPs.

As you must have guessed, I intend this modeling with critters to suggest explanations for some of our human experiences, as we will be seeing.


2.5 A more detailed look at the critters


Now that we have had our first introduction to the critters and to a few situational challenges which we can pose in the model of critters, we will back up a bit to take a more detailed look at what these critters are and can do.

The additional details which we will review here in Chapter 2 were developed by me as I wrote a computer program to implement a CABM of tabletop critters. As I said in Section 1.5, the labor of creating computer models forces a modeler to make many model-specifying decisions which the modeler had not dreamed necessary beforehand. While the challenge of programming agents to achieve a desired society-wide observable can be insurmountable, the effort is always educational.


One critter property, which I promptly discovered required my judgment, was the distance a critter could travel in any time increment. I decided this maximum step-size of a critter should be roughly equal to the diameter of its body (the yellow oval), as show in Figure 2-10.

Figure 2-10, definition of critter step size

Also I decided a critter may move in any direction in the plane provided its body does not collide with anything (with a resource or another critter’s body). In order to preserve the visual clarity of the model, objects are not allowed to pile on top of each other in the plane.

Next, while in thought-experiment mode I had assumed critters could sense, by some sort of feel, other objects on the tabletop nearby or adjacent to the critter’s location. But in computer mode this must be defined specifically, so I decided the seven rays extending outward from the critter's body suggest the sense area. See Figure 2-11 in which the dotted oval shows this area. My CABM critter can sense the presence of another object which lies at least partially inside its sense area but not anything outside that area. So in this picture it can sense the spot of sugar but not the drop of water.

Figure 2-11, definition of critter sense area


A critter can attempt to consume a resource which it can sense in its sense area. For this purpose of consumption it is not necessary that the critter move any closer (to the point where its body is touching the resource). A critter cannot consume a resource outside its sense area. In Figure 2-11 the critter can attempt to consume the sugar but not the water.

A critter does not always accomplish what it decides to do, as we saw first in the assumptions outlined in Section 1.4.2 under “ability to act”. In each increment of time it decides upon an action to undertake, then it attempts that action. But larger fate determines whether and how much the critter's attempt succeeds. For example two critters may move in one time increment to where both can sense a single water drop. Both may decide to consume the whole drop with their next act. See Figure 2-12.

Figure 2-12, Showing why a critter does not always succeed in its chosen act.

In the picture above, both critters attempt to imbibe the water drop at time n+1. But obviously both cannot succeed. So the program running the model plays the role of Fate and somehow decides how to allot the water in the drop.


2.6 Clarifying the Initial Condition


Shifting back now to thought-experiment mode, we have asserted that we start with an initial condition in which a small population of critters just barely survives by foraging for water and sugar. For each individual critter, there is no steady and certain source of water or sugar. Instead a small portion of water or sugar appears now and then, randomly dropped into the world. These resources come as gifts from fate perhaps, or are carried in by the wind as we said. In any case the critters' only hope of survival comes from moving about almost continuously in hope of encountering water or sugar. The critters are hunter-gatherers. Death because of starvation for either water or sugar is their most common fate. But fate can also be good sometimes. Sometimes a critter finds enough water and sugar to enable it to reproduce. So the population hangs on — barely. In our initial condition the population of critters is probably near the maximum that the environment can sustain, given the rate of influx of resources.

But in my effort of computerized agent-based modeling (CABM) I found this idea, of a stable population just barely hanging onto life, difficult to achieve. Truth be told, the best I got was a population which cycled in number between small, approaching and sometimes reaching extinction, and large, with many more foraging critters than could be sustained with the program's set rate of sprinkling new resources onto the tabletop at random locations.

I suppose that I could approach closer to achieving the initial condition, as we described it for our thought-experiment ABM, in computerized ABM — given time and impetus. But, at this still early stage of use of the resource-patterns model of life, the promise of more thought experiments outweighs, in my thinking, the promise of CABM. We carry on in thought-experiment mode, for the most part.