Part 3 — Ways to communicate multidimensional ideas

One thing is to make ideas, yet another is to communicate them. Recently, I applied methods that I use in my own work, and it led me to building something that I called the space of ideas. But then, three questions occurred. Well actually, many questions occurred, but initially I would like to address three questions.

First, these ideas build some space, representing integrated wholes of chunks of knowledge (which I will call concepts). For example, I have learned the set of topics like {COMPLEX NETWORKS, SIMPLICIAL COMPLEXES, Q-ANALYSIS, PERSISTENT HOMOLOGY, DEGREE DISTRIBUTION, INTEGRATED CONFIGURATION OF INFORMATION, COGNITIVE BIAS, AGENT BASED MODELING, ATTITUDES AND OPINIONS, COMBINATORIAL LAPLACIAN, URBAN DYNAMICS, MONTE CARLO SIMULATIONS, INFORMATION THEORY, COGNITIVE MAP}. Groups of these concepts got integrated into ideas by imposing relations between them. Then the space of ideas builds complex structure through sharing common concepts between integrated wholes.

In the pictures below, colors are associated with different ideas, and the numbers below them represent years when ideas took some form for the purpose of communicating them. Say, relational blending between concepts {COMPLEX NETWORKS, SIMPLICIAL COMPLEXES, Q-ANALYSIS, DEGREE DISTRIBUTION} forms the idea which was treated in some form in 2009. It shares the blend of concepts {COMPLEX NETWORKS, SIMPLICIAL COMPLEXES} with the idea that was treated in some form in 2014.

But as these ideas are constructs in one’s mind their merging represents a kind of mind’s hypermap of this rather complex space. Now, in order to communicate these ideas, they are realized in a form of scientific papers, or slide shows followed by oral presentations, or informal talks. As one could guess, years that are labeling the ideas are actually the years of publishing research articles having relational blends of ideas as topics. Yet, on some occasion, such is giving an oral presentation or having informal talks, multiple ideas can be treated into a single form at the same time.

Ideas can be treated in a way to get different forms with the purpose of communicating them.

Ideas are connected by sharing blends of concepts, and taking many ideas together with their shared concepts builds a complex structure of the idea space. Suppose that this structure carries some traffic. Similarly, in the case of the physical space of urban road infrastructure, connections between streets build a complex system that carries the traffic of vehicles or citizens. To this traffic, one can associate numerals, like a certain “number of vehicles drove through the street”. On the other hand, alongside with numerical, the verbal objects can be associated with streets, like “car brand ‘….’ drove through the street”.

Following this way of reasoning, what would be analogous kinds of traffic that flow over the structure of the complex space of ideas? It surely has to depend on the form in which ideas are treated. Say, if ideas are presented in the form of published scientific articles, then numerals that can be associated with the ideas may represent the number of citations, or the number of article downloads. On the other hand, if the ideas are treated in a form conference presentation, then numerals associated with the ideas could be the number of session attendees or the number of asked questions, or the duration of the talk. Well, it seems that different numbers can be associated with the ideas, depending on the contexts and form of treatment, and on what we are interested in when considering such space. For example, from the picture below, one can see that the research paper pap(2014) received 2 citations in 2019, and 5 in 2020, whereas paper pap(2009) was cited 12 times in 2019 and 16 times in 2020.

If someone would be interested in the extraction of workable information from this kind of data, then the analysis becomes a bit complicated, yet still feasible. Say, it should be taken into consideration something like — few research papers are cited more than ones in the other paper. Or some sub-blends of concepts are attracting more citations than others, like the relational blend {COMPLEX NETWORKS, SIMPLICIAL COMPLEXES}, to which are associated numbers of citations 22 in 2019, and 34 in 2020.

However, in analogy with streets and cars: What kind of words could be associated with the treatments of ideas? For example, if ideas are treated in the form of scientific papers, then the structure of idea space can provide support for the existence, and flow, of verbal objects, alongside the numerical. Well, the outcomes of research published in these articles can certainly play such a role. For example, one of the outcomes of paper pap(2008) is “insights into the structural organization of complex networks”, which is transferred and modified in pap (2009) to “complex network structure and persistent homology barcodes”. Built on that, from the outcome of pap(2008), “insights into the structural organization of complex networks” is transmitted to the outcome of pap(2014) “simplicial opinion formation model” and “consensus formation”, which is further transmitted to the pap(2018) outcome “simplicial biased opinion formation model” and “consensus formation under biased”. On the other hand, the outcome “patterns in person’s behavior” from pap(2017) is transferred to pap(2018) outcome “patterns of social behavior”.

The treatment of ideas sets forms that produce some verbal objects, which on the other hand are transmitted through shared relational blends of concepts.

There are different kinds of changes that could be related to the structure of space of ideas. For example, changes appear when building new ideas, or when transferring outcomes of research outcomes through the structure of space of ideas. So, it seems that there should be some forces that trigger such changes, and should somehow be related to the structure.

In reflections on my progress in building ideas, and treating them in a form of scientific articles, I labeled them by years in which papers are published, which is apparently a mistake. In reality, these ideas came into being before the publication date. The process of article publication takes time, whereas ideas in a form of relational blends of concepts, came into being much earlier.

For example, in 2006 I learned separately about COMPLEX NETWORKS, and that SIMPLICIAL COMPLEXES can be explored by applying the methodology of Q-ANALYSIS. It was followed by reading books and scientific articles on various topics. Then sometime in 2007 filled tringle is built when I got an insight into the possible relations between COMPLEX NETWORKS, SIMPLICIAL COMPLEXES, and Q-ANALYSIS. This filled triangle emerged as a (multidimensional) event that changed the previous structure of my knowledge and ideas, which can be interpreted as an effect of some structural force that affected it.

There are other changes that I mentioned here. The number of citations of research papers is changing from year to year. For some, they are increasing, whereas decreasing for others, hence representing a different kind of events that are happening on the structure. These objects of the structure are affected by forces of attraction and repulsion, depending on whether numbers increase or decrease. It is not just that the numbers are changing over the structure of idea space. As considered here, the outcomes of published research papers are moving along the structure, hence acting as yet another type of event, governed by another kind of force that depends on the structure.

There are events of various types which are related to changes either of the structure of idea space or of flows influenced by this structure, or both simultaneously.

Having all this above in mind, how could I set a stage for new events of the first type, if I get into collaboration with colleagues from different research fields?

Or whether publishing a scientific article with a certain combination of concepts attracts more citations hence causing the second type of events? And what kind of the third type of event it will induce?

In the above example, the most cited relational sub-blend {SIMPLICIAL COMPLEX, COMPLEX NETWORK} is taken together with concepts from other different ideas.

The application of methodology applied here is context-, and goal-dependent, and in this story, the goal is not particularly important, except to play with relations between mindset and toolset.

Why limit this kind of considerations only to the space of ideas that emerge in scientific research? There are other spaces which are having other concepts and relations between them as building blocks. The peculiarities of these worlds impose completely different contexts and environments under which wholes, flows, events, and forces are defined. For instance, the space of ideas can only expand through adding new concepts and ideas into the structure, whereas in the case of some other spaces concepts, wholes, or both, can be subtracted from the structure. Actually, that may even be beneficial for stakeholders when considering specific situations. I suppose that these kinds of actions can emerge in the case of resolving the wicked problem.

DISCLAIMER: The examples and results presented here are not scientifically rigorous, neither linguistically nor semantically, in the sense of interlacing the generality of terms, or mathematically, in the sense of strict formalism application. It represents just an informal attempt of reconstruction of conceptual maps and getting an insight into the structural relationships between them. The way of reasoning is inspired by outcomes my own works (published with collaborators), which is on the other hand notably influenced by works of Ronald Atkin, Jeffrey Johnson and other Q-analysists.