The LBD universe (a work in progress)

"talking" at the same time

Introduction Universal Beginnings? Network Characteristics Small Groups weighted Membranes or p-branes Maximum dimensions Strings String Dimensions The Polis Gravity Record of Events Examples from Data Interaction Matrix

The truly remarkable thing about the LBD universe, is that it appears to be so many different things. A classroom. An entirely new and complicated universe. A simple chat room. A Social Network with a normal probability distribution function, P(k). A place where people gather once a week for an intensive three hour university class.

But one thing is for certain. It is a mine of data to analyze and display in so many new and interesting ways. Can one generalize about the results? Perhaps.

Over the last five years, we have been developing the LBD eClassroom and writing papers about it. We usually describe the LBD eClassroom in very classical terms: an online classroom. But, that hasn't helped much in explaining what it is and what it does. Mostly because there are so many “online classrooms” out there, that assumptions are made about what is in the LBD eClassroom.

Turns out, of course, we have an incredibly rich universe inside of our LBD eClassroom. Things happen inside, that it's hard to believe let alone comprehend.

Well, it's good to know that string theorist have just about the same problem describing their universe, which is our physical universe, to those of us who live here, as we do describing the LBD universe to those who live in the world of education.

So, what is the LBD universe? Again? What is it made of? How may it be of use? These are the questions we will try to answer. But this time we may use the words and analogies of particle physicists, string theorists, and geometers who have developed concepts, words, and visions that describe extra dimensions in ours and their physical universe, mostly because we think we have analogous issues with extra dimensions. We're not exactly sure what the physicists mean by strings in our physical universe, but we do have a good idea what they may mean in the LBD universe, mostly because we can measure the strings, calculate things about the strings, and describe the evolution of string complexity. No clue if this has anything whatever to do with the physicists world, we just like their names of things, and their concepts. The ones that we can understand, at least.

But first, what about the beginnings? How does that happen? What are the components of beginnings in the LBD universe?

Timeg
Each dot is the action of a participant in "The beginning".
[There appears to be an exponential limit to the growth in the beginning in this environment. The solid black curve represents this limit.]

(a)	(b)
Figure 1. (a) Fundamental elements in the LBD universe as a function of time and (b) the cumulative distribution function of those elements

For six months each year for the last six years, the LBD eClassroom turns on once a week. And each time it turns on, forty to sixty people gather together for three hours to take a course either in “Interpersonal Communication and Relationships”, or “Working in Task Groups”. And it appears that each time the classroom is turned on, and people populate it, there are what appear to be fundamental elements. In studying the data collected from 2001 thru 2006, it appears a “beginning” can be described for this LBD Universe by naming some of these fundamental elements. It is a beginning from which very complex and beautiful strings evolve, as well as quite simple strings, as we shall describe below.

The plots above represents about 72 of these instances of beginnings. The data from all instances are summed so the signal to noise ratio in the data increases and allows patterns to appear out of the noise. For example, in the single case of one turn-on of the LBD eClassroom, the signal to noise ratio for total energy in the system is about 10:1 and in Figure 1(a), with over 72 recordings, that ratio becomes about 1000:1.

Five different types of fundamental elements have been collected in Figure 1, each represented by a different color on the graph. These fundamental elements are:

1. Automatic computer response to the login, S{0}^- black
2. "Hi", "Hey", or "Hello" as the first word in the line,S{0} red
3. Messages sent to the polis, S{0}⁺ green
4. Messages that are part of strings S{1}⁺ yellow
5. Total Energy of the system, E white

S{0}^- a source for strings

The first piece of data plotted is an automatic computer response indicating a person has successfully logged into the LBD eClassroom. This is shown in black in the two graphs. As shown in Figure 1(a), there is a peak in this data at the beginning of class. However, in Figure 1(b), the cumulative distribution function of the data indicates that logins occur before the beginning of class. In the general case this may be described as the precursor to the appearance of a zero^th order string. This is written as S{0}^-.

S{0}^- has a near normal distribution about t₀. The tails are not symmetrical, since before t₀, the precursors to zero^th order strings is random, while after t₀, during the existence of the LBD Universe, the precursors are dense and representative of the number of players arriving to be active in the universe. The SS{0}^- over the time representing the existence of the universe represents about 4.7% of the total energy in the universe.

Since the signal of this action occurs only once during a login into the LBD eClassroom, it is the minimum action of subsequent strings. All strings must first have this action, and all other actions which may have multiple occurances are at the first, preceeded by this single string, S{0}^-; therefore, it is a source for string production.

S{0}

Once someone has logged into the LBD eClassroom, their first comment is usually a greeting. This greeting is making the rest of the people aware that the greeter is available for further discussion and interaction. This first greeting is to the polis. That is, it is to the group of people who are in the LBD eClassroom at that time. The greeting is the zero^th order string and is represented by S{0}.

In Figure 1, the S{0} strings are represented in red.

(a)

(b)

The S{0}^- strings lead the S{0} in time. The CDF of S{0} is about an order of magnitude below the CDF of S{0}^-, and this is an important observation. Before the beginning, the precursors, S{0}^- have been around, but since there is no beginning, the zero^th order strings, S{0}, have not been established, and in sufficient magnitude to creating more strings. In the LBD Universe this represents people logging in (S{0}^-), but there is no need to announce to the polis they are there. But once the class starts, at t₀ it is the group norm to announce a greeting. The ratio of precursor strings and zero^th order strings at their peak around t₀ is about 1.5:1. This growth factor represents multiple greetings as the polis forms. And may be part of a polis growth factor. The polis is the repository of all data and information in the public sphere. It does not represent all data and information, as there is another dimension beyond the public sphere we shall talk about later. The existence of the polis and it's representation will also be discussed later.

The SS{0} over the time representing the existence of the universe represents about 4.2% of the total energy in the universe. Note that SS{0} < SS{0}^-. This indicates the role of the precursor in that it announces the availablity, but not the inclination, of the zero^th order string over time.

S{0}⁺

S{1}⁺

Network Characteristics

Figure 3. Probability that a node has k edges in the facilitated LBD eClassroom compared to an unfacilitated similar environment

When each participant interacts, they send a directed message into the LBD eClassroom. The participant can direct that message to the group as a whole, or to any number of specific individuals within the group. The group entity is also considered a participant within the network and is named the polis.

The strings S{1}⁺ generated within the LBD universe have an equal probability of going anywhere. The strings are composed of stochastic properties.

The physical universe we are most familiar with is composed of four dimensions: the three dimensions for space (up-down, left-right, and backwards-forwards) and one for time. But that's not really our physical universe. Turns out, there are branes, dimensions, spacetime frames, and probably more of these things than we can count, out there in our daily lives.

With so many possibilities, it is not surprising that we have to make choices about what to talk about in the LBD universe. As it is, whenever we present a two dimensional graph about some piece of data, we have to make a choice about what goes on what axis. Or if we're clever, what three dimensions to put on the 2D drawing. What elements, what dimensions of all the things that are possible to describe in the LBD universe, do we choose to descibe? Is it the information flow? Is it how time is compressed, and we get things dones faster and more efficiently? Is it the social network diagrams? Is it about how students feel freer to express themselves? Is it the concept of anonymity? The concept of a polis? How one comment by one student can change the entire course of the lecture/discussion? A discription of Gibb's data flow and trust development?

What the string theorists have discovered is a way to describe our daily experience of the physical world while allowing for extra dimensions we do not experience. They call it a brane.

The brane is a boundary. It comes from the word membrane, but because physicists are truly a funny bunch, they chose to call their discovery, a p-brane. Nevertheless, it's a convenient way to explain our experience of the physical universe and theirs. Because inside the p-brane is the world we live in, and outside the p-brane is a world we can't even conceive of with so many possibilities and extra dimensions.

To carry this analogy further for the purposes of describing the LBD universe. It would be nice if there were a brane we could use to explain why the telling of our experience in the LBD universe is so difficult to other's in the business of educating students. Are there branes in the LBD universe?

Probably.

The maximum participating dimension of an instance of the LBD universe is N+1, where N is the number of participants, and +1 is the group, or polis. The polis is a repository of data. An instance is a time period during which the LBD universe is populated. Time is measured in hours and minutes. (Note: We don't do seconds in the LBD universe, since time is measurably compressed in the LBD universe from what we experience in the physical universe. We have measured events in the LBD universe taking half the time they would have taken in the physical universe.)

There are other dimensions of the LBD universe which are unlimited. For example, the information dimension appears to be unlimited during an instance of the LBD universe. While data flow is limited by the complexities of various functions, the posibilities of what information there is, seems to be unlimited.

Strings are created during the transfer of data into the LBD universe. 2D representations of these strings are used to study their behaviour.

One set of dimensions exhibited by strings in this universe is dependent on the number of people participating in the string. Another dimension is the content of the string. Another dimension is the information in the string. The information dimension is not only related to the content of the string, but the background of the universe at the time a string exists. This is the relative information of the string. All the background in the universe is composed of strings of various dimensions. A participating dimension zero string is data that is computer generated due to an action by a participant in an instance of the LBD universe. See event-00  for examples of computer generated data which defines a participating dimension zero string.

A participating dimension 1 string is undirected data presented by a participant in the form of a post that is not responded to by other participants. An example of these events, elements of greeting data, can be seen in a record of event-09. Participating dimension 1 strings, as do all participating dimension strings, have the potential to become strings of higher participating dimension. As strings come into existence they may or may not attract other participants which will increase the participating dimension.

Participating dimension 1 strings are the foundation of the polis. These strings of data are not necessarily information dimension 1 strings. In fact, they may have been created based upon the background of information already in the instance of the LBD universe of which they are participants.

The polis appears to be an entity which has the potential of collecting unlimited informational dimensions. What this means is participants observe the polis, and decide which strings to attach themselves to, making, at minimum, a participating dimension 2 string. What are the elements of the attraction? (Doesn't this sound a lot like gravity?) What drives a participant to select one string over another in the polis? Is it possible that gravity, both in the physical universe and the LBD universe is nothing more than unlimited possibility? And how we "gravitate" towards one possibility over another, is our contribution to gravity? So is it possible that gravity has two parts: the polis and the observer?

These are questions we will be asking and attempting to answer as we document the extra dimensions in the LBD universe.

A 3D example of a polis is found here. In this figure, the size of nodes representing individual participants are proportional to their in-degree. In-degree is the count of directed messages sent to a participant during the elapsed time of the instance of the LBD universe depicted.

The notion that the polis has unlimited potentials in information with participating dimension 1 strings, suggests that higher participating dimension strings may be limited in number. As shown in Table I, this is indeed the case. The number of participating strings are inversely proportional to their dimension in an instance of the LBD-universe. And appear to correlate strongly to a power law relationship as shown in the graph.

Table I  Dimension  Number of Strings 1 2489 2 167 3 36 4 19 5 10 6 8 7 6 8 4

Gravity is composed of two elements and a process. The first element is the polis. In physical universe terms, the polis is a quantum field of all possiblities. In the LBD universe, it appears that the lowest order strings of all dimensions are what makes up the polis.

In the example of an instance in the LBD universe described above, the brane of the polis is represented by the blue sphere. Data in the form of lowest order strings are deposited in the polis. Data is the constant in all universes and is known as words. In the LBD universe the polis is the beginning of all higher order strings. The second part of gravity is the process of reading the data in the polis and responding. The response in a post is the second element making a string of higher dimension.

Interaction Matrices

These directed adjacency matrices are generated from the interactions during a class session. Usually, the students meet in the larger classroom at the beginning of class, and then break up into their smaller groups to participate in exercises. The students are assigned to these groupings on a random basis at the beginning of the semester. They maintain their colored group identity throughout the rest of the semester. In the main room, this identity is maintained by using text the color of their group. Each group is assigned a facilitator.

The polis is the bottom node. And unlike networks used in studying small worlds. The polis is available to all participants to both enter data as well as extract data. The polis, by itself, is passive. The polis provides all it's data to all participants.

Likewise, the messages that form the edges of the network diagrams are available to all participants to read. The reason why a participant reaches out and makes a connection to another participant in the group session is not generally known; however, in some class sessions, the exercise dominates the formation of edges. For example in the last class on 11-17-05, the exercise was the process of "gives and gets", and the instructions are to give to each other their observations. Since the instructions to the participants were to speak with all others in the group, this network diagram represents the greatest degree of interaction. All other meetings of the groups can then be measured relative to it.

Weighted Network Diagrams with vertices marked to identify the small group facilitator (white circle) and the professor (black circle) and facilitator helpers (gray circles). The small group polis is located in the center of the display. The distance between vertices is generated by the MDS option in Ucinet. The feature that seems to be important in this display is how little or how much the participants are speaking to one another, as opposed to the group or the facilitator. When participants are seen to speak mostly to the group the diagram is more star-like. The more the participants speak to each other, the greater they become a large cluster.

Date	Group (all participants equally weighted)
	blue	green	orange	purple	red
9-8-05
9-15-05
9-22-05
9-29-05
10-6-05
10-20-05
11-3-05
11-10-05
11-17-05