Strings and networks, Part I: In search for the dimensions of collective life
September 19, 2012 § 5 Comments
This is the most speculative text I have written. I will introduce an idea about applying string theory from physics (http://en.wikipedia.org/wiki/String_theory) to modeling what we traditionally call network behaviors. In this first part I write about these thoughts and considerations and in a later part I try to be more explicit in it – if it makes sense. But because this is hugely speculative and relies on an analogy, I will learn on the way to see what is the potential value of this approach.
A note added on 15th February 2014:
Having recently worked intensively on my ms “Behavioral Theory of the Networked Firm” and now reading Alex Pentand’s book “Social physics” I have become convinced that this blog is not at all as speculative as I originally thought. Now I see how important it is to replace the commonly used concepts of links, nodes, connections, connection strength, flow of information, ideas as they are used in current network models. Why? Well, nothing flows between people, but states of both change in interaction; no ‘connection’ between individuals of firms, for example, concerns only one property like ideas, information, material; life, in its essence is not multi-layered; links are not channels but forms of life (thank you Inma Vp for the life bridge comment); and some other insights because of which it is time to search for new representations and models of connected life. The string model is one potential candidate.
Traveling Salesman with a mind
I met my friend Antti at Espoo railway station where he arrived on a local train from Helsinki. I have taken the same trip several times, but he had his own amusing story to tell from this short, 30 min journey. Formally we both had commuted from A to B, or in a graph form, A->B, but our trips had been totally different. I had started to create a new concept for ‘injecting’ content and meaning into network representations and eagerly explained the idea to my friend who immediately started thinking aloud about the differences between our personal journeys, A->B.
Over the years, we have traveled some of the same routes and our journey maps could be easily compared in the form of a network description just like in the famous travelling salesman problem (for TS, cf. http://www.tsp.gatech.edu/ or try the game to learn about it http://www.tsp.gatech.edu/games/index.html). But how should we denote the personal meanings associated with each trip and express them in a formal representation so that we could model the essence of our travels and compare their meaning and impact?
Mathematicians solving the TS problem have not cared much for what might be going on in the travelling salesman’s mind, except of course, that the TS might be eager to find the optimal route through all the sales points on the journey. Had the mathematicians been interested in his genuine intentions, motivations or experiences, they had ended up with a different formalism to represent the problem. We can call this the Traveling Salesman with a Mind (TSM) problem. Perhaps even a better metaphor would be the Traveling Pilgrim problem because its basic premise would that the traveling person indeed has a mind and even a soul.
The TSM problem consists of the trip and its context data. But there is no generally accepted way to inject such meaningful data into its representation. This is surprising – we do not travel just to transport our bodies from one place to another. We even love specific forms of traveling like hiking on the mountains or sailing at sea. Some trips simply do not take place at all. Psychologists have not heard the mathematical siren calling.
Patterns of compassion
Rehman Ilyas and his team of Indian and Pakistani university students have created the “Romancing The Border (RTB) concept and app where people across the Indian-Pakistan border can send their positive, compassionate greetings over the border by using short web videos. The developers believe, like Mark Nelson and Margarita Quihuis from the Stanford Peace Innovation lab have described it, that this contributes measurably to peace between the two nations in conflict. As a result a network of visible positive actions is generated and can be monitored just like in the facebook app http://peace.facebook.com/. Quite recently I read about “the acts of kindness” map for a Mexican city (http://globalvoicesonline.org/2011/09/06/mexico-hero-reports-mapping-acts-of-kindness/) putting the locations of the good acts on a city map.
How should these behaviors in India/Pakistan and Mexico be formally represented? What is the real nature of the ‘kindness acts’ and their networks? How are they connected with other matters of the world? Of course we can count the good deeds or the friendly greetings over the conflict boundaries, map them and derive various statistics, but it does not help to understand what really goes on in these positive acts, what valuable human potential they carry and what other consequences they might have. We should have access to that kind of data and realistic models to deal with it. This is a huge challenge for future human and social sciences that are being transformed due to the fast technological influences.
More generally we can ask – and I’m 100% convinced that future politicians will be exited (in good and bad) about this – what really happens in the world as a result of the miniscule individual actions like in the RTB campaign, in the Mexican city and in other similar circumstances of positive behaviors? We should know, follow and analyze that and create means and tools to see farther. New approaches and methods are required, but most of all we must set the goals of analysis at a new ambition level in modeling the human and social behavior in the real world.
The individual compassionate acts in RTB may be separate and weak-appearing incidents, below any level of statistical significance. But why look at massive statistical truths only, when we can search for other impacts, like the significance of single social episodes? Often the statistical view at the world prevents us from seeing valuable single events and from imagining what would happen if we had thousands of them. Statisticians are late in jumping on the bandwagon of valuable acts. Many of the analysis methodologies suffer from this but they have still taught us that the ‘true phenomena’ in the world are always ‘big’. In physics they are assumed to be the smallest of the small.
In business and epidemiology the statistical view is a standard, but as Malcom Gladwell demonstrated in his book The Tipping Point we should have eyes for weak but relevant single behaviors and events. For example, there is no single statistically true answer to the question: how many people need to take up a certain type of sports before it becomes a trend? Sometimes one person can change the course of development and – to use a physics metaphor – open a new dimension of life. This is why the concept of “weak signals” seems very weak to me. https://gotepoem.wordpress.com/2011/03/19/weak-signals-or-weak-theory-of-observation/
A string world?
The term ‘string’ wakes up the skeptic in many a theoretical physicist. Despite that I have felt it inspiring to move in this speculative space, very much like the string theory in modern physics: many see it as a real possibility and some ignore it as a dream or confabulation.
The idea to apply string theory to the analysis of general networks owes to the charming “Little Book of String Theory” by Steven S. Gubser from Princeton, one of the many treasures I have found from Stanford bookstore, http://press.princeton.edu/titles/9133.html. It is an introduction to string theory with a friendly approach and includes lively examples that make it inspiring reading. I will use the ‘string’ concept rather loosely here without always referring to the peculiarities of the superstring or supersymmetric string theory.
I’ve had a long-time curiosity and passion for and even studied many forms of network, e.g. artificial and realistic neural nets, collaboration and communication nets, knowledge nets, social nets, internet of things, the WWW and any possible variations I have imagined myself. I even have one gloomy experience from this fascinating field when I was the main architect for the network of psychology departments (Psykonet) in Finland. Building the net environment, trying to feed the idea that ‘the net is beneficial’ to the reluctant and local-politically tuned psychologists was too much for me. But even that theme remains in the core of the present string analysis: understanding real networks. Only some time ago I wrote about the idea of internet of behaviors (https://gotepoem.wordpress.com/2012/03/16/internet-of-behaviors-ib/>) which reflects the same interest.
Lifeless network representations
Being a psychologist, I’ve been puzzled by the lack of life in most of the network models and concepts I’ve seen. For example, when dealing with human relationship descriptions or organizational sociograms they typically fail to express and preserve complex human aspects like motivation, intentions, joy, excitement, beliefs, love, engagement, reluctance, and conflict. Why?
Reading the little string book suggested a striking analogy between the unsolved problems of gravitation vs. quantum mechanics and the core problems of real-world representation of human and social behavior in modern network theory. The analogy might appear like a very distant and far-from-the-real-world idea but I see it is as a very practical one and indeed worth thinking about. Not unlike in modern physics we need to learn what are the human forces that create the major global phenomena in economics and social systems but at the same time govern the individual life, mind, and motivations. The world of human and social sciences is split in this question, just like the physics of natural forces was split in dealing with gravitation and quantum forces.
Strings of life – an idea
The web videos in RTB with their peace-promoting content are not only expressions of valuable connections over the problematic borders. They are symptoms of something more profound: the state of the local (quantum) world has changed, obtained a new state as a result of them. Furthermore, something has made this change possible to occur. It may be material or immaterial but we really don’t exactly know. It is a small wonder that this small event has specific meaning at all, why is it not only noise or a random episode of life? The world is not the same after the apparently miniscule change, but how is it different?
Using a string analogy from the String Theory (ST), a significant ‘string of life’ as I call this relationship between the two people sharing the video, has changed its state. This string of life with its specific state (and its base) is a material and real aspect of the connected world. By assigning a complex content to the string state this expression can be used as a functional description of a specific human behavior in the world. In this case it represents the nature of the relationship between the sender and the receiver who have peaceful motivations. Next we can ask what exactly is this state and what are its consequences?
String theory in physics suggests that the way our world exists in its connectivity can be described as a conglomeration of strings each with its own peculiar properties, or again, to borrow from ST, having its own state of ‘reverberation’. Furthermore, in the available space (whatever is its dimensonality), not everything is possible and the limitations are set by the properties of the space and the strings. Now, each of the peaceful acts of RTB ca be defined as ‘vibes’ that represent the specific form of good. But for this the strings have to have specific properties and be grounded in a peculiar base of life. In other words – following the superstring theory and again analogically – the strings must be attached somewhere.
The friends of the physical string theory use the concept of a brane (a spatial structure having any dimensions, e.g a membrane or a cube etc.) for this purpose and they serve this specific need of the strings to be attached to something real (if I have understood it right). Branes (or bases) are relevant aspects of the string relationship in describing the string states, just like it is relevant to the sound quality and tone of an instrument how the string is attached to its body. Without a base nothing sustainable can take place.
Vibrant string theory
The aim here is not to derive a direct ‘strings of life’ model or a theory as it is applied in modern physics. I will be working on it as a thought experiment and will blog on it later and perhaps get inspired by +/- thoughts from willing physicists. The simple motivation here is to prepare for better functional models to describe the dynamics and limitations of the content-rich, complex and interconnected world. I want to find a way to express life in nets in a way that combines global (in analogy to the gravitational forces in physics) and local (quantum mechanical) forces of life into one representational framework.
This might sound like a confabulating amateur talking but I believe – just like theoretical physicists think about their own science – that the human social sciences need to realize the value of the theoretical endeavor and to set the ambition level high. If the physicists intend to solve the problem of matter, space, and energy in the universe why should human and social scientists be less ambitious? The aim is to understand the actors, forces, and dynamics of the behavioral space on earth.
Shortly and generalizing a lot, the aim of the string theory in physics (there are numerous versions of it) is to, e.g.:
- formulate the theoretical basis for new physical space-time-other dimensions geometries, and
- to offer a ‘string interpretation’ of the nature of the elementary particles and
- to find the correspondence between string states and particle properties. In other words, string theory sees particle properties as aspects of string states.
String theory leads to a larger number than 4 of world dimensions, which is not a peculiar property in human sciences: the psychological dimensionalities of man are multi-dimensional. For some reason, however, humanists have remained rather vague on how these multi-dimensional properties like intelligence and personality are actually built on real life materials like mental structures and contents, physiological processes. They are even less theoretically oriented to how human and social behaviors are determined and constrained by these spaces. Personality and intelligence studies aside, so far I don’t know of anybody who has really tried to estimate the true dimensionality of the psycho-social-cultural man and what kind of a ‘mind and behavior universe’ it spans. An interesting question is which of these dimensions have the best explanation value when we try to model and perhaps predict what happens in the complex world of human interaction. Cf. https://gotepoem.wordpress.com/2011/10/13/entropy-of-the-human-soul/
Vibes, branes, strings and superstrings of life?
Not unknown to the hippies the ‘vibes’ but more precisely the state of a string links it to the content and meaning that it represents. In a mathematical sense it is a question of how to formally represent such states so that it would best allow description of local, collective, and global aspects of behavior and would open a new landscape to see their wider potential influences and contributions on human and social behavior and on the environment.
I cannot discuss here the number of string types that might be needed for this analogy exercise or how many of them would be required to cover relevant aspects of human connectivity. Furthermore, I’m a bit puzzled by the brane concept that refers to a space-time continuum that can have any number of dimensions. But following the analogy, I understand the branes as a necessary base of the strings of life without which strings would just float, in a haphazard manner, above or outside our reality with maximum entropy. In other words, the branes extend to all corners of life, like the basic constituents that make up any form of life, be it psychological, economical, or political in nature.
It could be argued that the number of strings required for any reasonable representation of human behavior is just infinite. But if we limit the scope to relevant aspects of behavior I don’t think it is so and by looking at simple instances, like real-like toy problems, the string concept could help us think about ways to insert content into nets, to give them life.
Here are two practical cases to explain the logic of my approach. First, as an example of far-field human and social connections, it has become commonplace in global political analyses to talk about world economy divergence and the emergence of a new ‘multi-polar world’, cf. http://www-wds.worldbank.org/servlet/WDSContentServer/WDSP/IB/2012/04/19/000158349_20120419165314/Rendered/PDF/WPS6040.pdf
Far field human forces: Multi-polar or string world?
We can ask how should we represent these far-field or ‘multi-polar’ phenomena (e.g. forces, processes, materials, values) in economics, trade and policies that are characterized by varying activities in different parts of the globe? Surely the multi-polarity must take place in a specific space as well. But we don’t have representational formalisms that could cover all relevant aspects of these relationships. For example, the concept of ‘multi-polarity’ is used to refer to strong economically dominating nodes with a new connectivity (like China, India, Brazil) that is different from its earlier state (USA, Soviet, Europe). However, using the ST approach we can consider this ‘multi-polarity’ as a dynamic and evolving string world, where the states of the hypothetical strings determine the elements of connectivity. In order to build a valid representation of this we must recognize the significant string systems to cover the relevant relationship information between the nodes. Then there is the question, what would be the base of life to which these strings are attached? I will return to this later.
If we can replace the ‘multi-polarity’ view – by recognizing and modeling the relevant strings in economy behaviors, acts, and relationships – with a string view of the complex world we can ask: do we gain something real by this change of representation? I believe we do, for example, by getting rid of a blind statistical model that overlooks ‘small acts’, by obtaining a dynamic model of the network behavior, by introducing complex contents and phenomena by the string model, by introducing space considerations, and by preserving relevant data in the representation. And there is more.
Near-field human forces: Customer service moments
The other example concerns near-field human interaction: customer experiences and behavior in a service situation. What is the string life in this simple exchange between the customer and the sales person, for example? There are a plethora of customer experience measures and typically they suffer from a lack of representing the real life context between the individuals – ‘the customer’ and ‘the service person’. What if we model this behavior by defining the relevant strings connecting the customer and the sales person (cf. the RTB example), so that it formally describes their relationship and the complex phenomena that actually exists (and interact) there?
Again someone might argue that we already have measurement scales, profiles, and inventories to measure all that. But think again: indeed such measures do reveal aspects of customer experiences but they do not connect the customer to the rest of his/her world. There is no formal methodology to do that and often various control variables are used to cover (and typically exclude) the social, economical and other relevant ‘background’ factors. In the string approach they are not ‘background’ factors but an essential part of complex human behavior. The strings of life would here be used to include the most significant aspects (meanings) of this relationship.
A difficult but vibrant topic
Interestingly, almost without exception, always when we talk about a ‘connection’ between some units, like the cities A and B in the travel example, or the peace acts over conflict boundaries, what is actually meant is the following. First, it is assumed that in such a complex situation it is possible to put aside irrelevant information (like the clothing my friend was wearing when traveling, or the personal motivations for an adventure of the just divorced traveling salesman). Second, the economy principle favors simple explanations and theories of behavior, and third, it is possible to wisely choose which phenomena are selected for independent observations. But as we all know, the world always surprises the scientists and analysts entertaining such views.
Two years ago I attended an inspiring talk by Rob Cross (http://www.robcross.org/research_books.htm) at Stanford where he described his studies on the true connectivity (sociogram data) in companies with certain type of organizational chart. It was hoped that knowing the true network among the workers could help to better understand how innovations, for example, emerge and are created socially in a company. In general, the perspective of interest in such nets can be almost anything from money and politics to knowledge sharing, entertainment and collaboration. But there is no general way to implement meaning and content into these network descriptions and that was perhaps one of the strong future guiding observations in this work as well.
It does matter how you talk and which media channel you use
Of course the persons across the border in the RTB case could have a telephone chat but that would be a different string of life with its own limited properties and impact space. In other words, it does matter how the communication is accomplished, it is not a matter of information sharing only. In a general sense, there is connecting ‘ether’ available that exists between all people, but its potential remains typically invisible or dormant unless the string state is changed properly like it happens when people talk to each other or use a specific communication channel.
The communicating parties in this example have not created the string itself but only controlled or set its state from one of ignorance or non-existence to the expression of good will in communication. More importantly, the string is not about the connection itself, but about the type of connection (positive engagement) they share.
They have changed the state of that (pre-existing but dormant) string into what has now made it visible to have an impact on the rest of the world, first locally, but with he help of technology like in RTB or facebook, also globally. The world state has thus permanently changed even though from mass statistical perspective the effect might look like (illusorily) miniscule. In the networks of these people this is a significant event and a change. It’s value can be understood if we imagine that there would be 10 millions of such string states. In that case the politicians in both countries would be seriously asking ‘what does that mean? Nobody could explain that with a model or a theory..
Injecting life into networks
Don Tapscott http://www.youtube.com/watch?v=rK4If-FFjW8&feature=youtu.be has a charming way to express the explosion of content in the connected world. The pivotal question remains, how could we best follow what actually happens on a large or a small scale in this connected mass of technologies, actors, and the content shared. To do that we need formal tools to help us. Had I the skills of Don Tapscott I would try to draw this same story as a string world – and perhaps learn all the problems on the way.
Future network models need to comply with the increasing demands of content production, sharing, and meaning management. We need theories that differ from the classical network analysis that is typically an idealized – and seriously biased – representation of reality. It is not an exaggeration to say that most of the computational networks models of today lack sensitivity to the complex reality and have problems in modeling significant life events like the RTB campaign and its consequences or even the simple but real traveling salesman with a mind – problems.
Content in the brain?
Take a popular example: the brain is typically described as an information processing network consisting of interconnected ‘neurons’. Forgetting the mysteries of the glial cell structures and “the other brain” http://www.scientificamerican.com/article.cfm?id=the-other-brain-cells it is generally assumed that the inner and external world has a well-defined representation in these networks. But there is a serious theoretical problem: how is the natural (inner or outer) world actually represented in our brains and how should that be done in the mathematical brain models? What material carries these representations? Even the concept of representation is problematic. Represented of what, for what, and for whom? How can we understand connected brains or millions of them? Cf. https://gotepoem.wordpress.com/2011/04/17/203/
Even the most impressive achievements using tensor analysis (cf. http://en.wikipedia.org/wiki/Diffusion_MRI) to look inside the brain and reveal its connectivity lack this content realism. The subjective reality and the inner personal space remain hidden. True, with advanced imaging and brain damage studies we can observe the activities in different brain centers in certain behaviors, see individual cell activities by direct recordings by new fluorescent methods, or to observe the scary pathologies resulting from minimal local brain lesions but the contents remain obscure. But the subjective spaces evade these methods.
When is a network representation realistic?
Garbage in, garbage out is the alarming truth for the most ingenious network analysis tools and algorithms. If the feature representations of the world elements as used in these networks fail so will also the models of the brain, world, and behavior fail. Of course the same problem concerns the string idea, but there the intention is to represent significant meanings and content and the space they cover – not their possible underlying features or other components – as string states. The aim is to improve data quality and relevance at the source.
In the brain example, we could suggest a number of alternative ways to represent the world: as a bottom-up (from sensory pathways to the many cortical projection areas), top-down (from higher brain centers towards lower neuron layers and up to the sensory pathways), or by an internally controlled mix and even a ubiquitous model of these. But we do not have an exact way to represent (and know if it is wise to use a structural representation at all) the external world with a relevant complexity. Standard models seem to assume that this is actually a problem of emergence or that we just need to use a specialized network model and analysis for each purpose.
What is real in a network?
Networks are not only used in neurophysiology but as descriptions of all sectors of human, biological, and social life where the theoretical and computational problems are similar and require an analysis of distributed activities. Surprisingly little attention has been given to the ‘reality check’ of the network models and tools. The first neural network models of learning and the brain were typically demonstrations – far from human empiria. The economical success stories by Google and facebook have not boosted this either while they rely on mass statistics, pattern recognition or classification, follow-ups, and mappings, for example.
In the very near future, with the maturation of network computations, the pattern recognition methods, fast progressing technologies in imaging, localization, and sensor apps will meet an overload of ‘dumb’ information to deal with. The Big Data (http://en.wikipedia.org/wiki/Big_data) discourse is one symptom of this crowding effect. Future networks need to deal with meaningful and massive contents, in an organized and analytical way. I believe that it is possible to avoid this crowding problem by improving the validity of the representations of reality and the quality of source data in the computations. The string approach can offer one means towards that aim.
As an example, think about any network representation that you use: the definition of nodes and the connection strengths or weights are usually directly derived from some empirical, statistical or other quantitative measures. In other words, it is assumed that the phenomenon of ‘connection’ can be modeled by signals and the strength factor (transmittance) of each connection. In real world there are indeed phenomena that are well-behaving in this respect.
As a counter example, it is possible to express the impact of person X on person Y by counting the number of contacts X initiates with Y and by suitable scaling in the whole data set. So locally, at the person-to-person connection level it might be reasonable to assume that the contacting impact can be estimated by simply counting the number of contacting instances X->Y. But of course, the contact does not take place in a vacuum but has a source, channel, and content. The question is, how should this be represented?
I invite my (potential) readers to tune in and think about networks from the ‘string perspective’ and to judge if it could lead to interesting ways of importing real-world source data, with high meaning content, and phenomena into the computational systems that we now call ‘networks’.
What are strings and nets made of: the snet (stringnet)
Let’s push aside the idea of a classic, real-life ‘network’, the system with connected units and replace it with a string-based theoretical formulation consisting of functional strings that span over complex entities (like people, businesses, teams, real biological cells or brain centers) and that have the ability to create tangible phenomena by assuming certain states of the strings. Furthermore, we can assume that the strings are attached to a base (brane) that sustains their life. In general we could think of the branes as the layer or medium that supports the string life. Both branes and strings are then relevant entities that together have impact on the string states.
In this representation, content is a natural part of the string system. It is injected into the system as a state of reverberation of a string. The concept of reverberation remains here an open theoretical construct.
Traditionally the matching between a network representation and the real world includes emergence considerations or statistical contrasting between real processes and behavior and the corresponding network model performance. Because computational analysis of the traditional net models is so powerful this idealization is often beneficial. But the farther we go in trying to understand the complex real world the higher become the demands for realistic representation of the world. The risk of misrepresenting reaity increases abruptly. I don’t know of any computational method that would be generally accepted as a test of the level of complex realism of a network representation.
Avoiding the Ashby trap
Ashby’s excellent analysis of the isomorphic machines shows this well: we can build two systems with identical input/output functions, while their material basis can be totally different: one machine can be electronic and the other one mechanical but their transfer functions can be made identical by suitable selection of their materials and component parameters. (See Ashby: Introduction to Cybernetics, p 94). In this sense, the problem of realism is similar to that between classical Newtonian physics and quantum mechanics. When we go deeper in our understanding of the reality there is a risk that the overly idealized network representations will actually prevent the building of a theory of networks that would describe the relevant and realistic life. One way to avoid the Ashby trap is to inject content and meaning data, on purpose into the representation.
The ‘string exercise’ leaves many issues open but I still see it as a valuable one. The first thing that string theory suggested to me – by getting rid of the traditional way of representing particles – was to do the same with network nodes, and connecting links. After that it becomes possible to figure out representations that can better pay respect to the complex nature of the underlying phenomena of life. Formation of the string theory of the elementary particles and forces is based on a similar consideration of the target problem: to find an alternative way to describe the particle/wave reality and the quantum mechanical forces included.
Monkey mind networks and a bit of history
The concept of classical network has quickly achieved the position as every-man’s theory but it is not ‘holy’ by any means – it has a rather weak physical grounding. Culturally I see it as a practical concept that probably dates back to the times when people became aware of the importance of family and tribe relationships: even monkey colonies have their hierarchic and jungle-functional networks although I still doubt that monkeys see their herd structures as ‘networks’; they must entertain other concepts relevant in their wild life. There is no general formal way to represent such meaningful monkey relationships, either.
Nevertheless, the relationship conceptions of the monkeys must allow beneficial perception, collaboration, interaction and often survival in a gang fight. In other words, the monkey internal network concepts must carry significant content knowledge and meanings. We have no idea what this knowledge actually is and how it resides in their brains.
I have learned that the first influential network applications are from the late 19th century railways and road systems, and later in logistics, especially in industry and during the times of war, and finally in telecommunication. Psychologists like Jacob Moreno and Kurt Lewin, in 1930s were behind the idea of social network analysis, but mathematicians, especially Euler, had formulated topology problems already in 1730’s. The work of D.O. Hebb 1940/50’s, among many others, and the computational power of network theory led to the idea that also brains should be analyzed as network structures.
Interestingly, still today, I don’t know of a brain theory that would, at neuron-level detail, explain any significant component of our normal everyday behavior, like having at a lunch, riding a bike, making love, following and enjoying a theatre play. Neurologists know the roles of various sensory and motor pathways and brain areas, and some have even studied the brain activities related to reading Jane Austen novels (http://news.stanford.edu/news/2012/september/austen-reading-fmri-090712.html) but that is about it, it is dead map data. The resolution in these studies is far-far from a single neuron or distributed neurons together function. I know that serious brain scientists have no problems in admitting this and that there is much to learn from the life of neurons as we see them today. Honest neuroscience works on these problems.
The roll-out of network theory during the last 30 years or so became possible due to the fast technological and mathematical development in network analysis but the real drivers were the social applications of networking. Not so long ago – when I studied mathematics, at the end of 1960’s, network theory did not have too many real-world applications. This may well be one reason why there is still no general theory that integrates networks with real world phenomena in a way that would describe the nature of this connection.
The evolution of www and mobile communication was driven by the human and social power, but another alternative development pattern can be easily imagined. What if the networks had remained solely for the machine and automated industrial systems to communicate with each other, and not with humans. Had this been the case then the network theory, net apps and their UIs had become quite different. Indeed, it is possible to think about a totally different cause of actions even today when ‘the net’ is something that we all take as a granted ground truth – which it is not. It has become a dominating paradigm.
In summary and as I see it, the main forces underlying the evolution of the present type of network analysis and thinking have been the introduction of topological problem formulation in mathematics, the cultural basis of the social network concepts, the apparent similarity between artificial (e.g. McCoullgh & Pitts -neuron) and natural neurons (Ramon y Cajal), and later the learning, pattern recognition, and general mathematical properties of artificial neural nets. The next step is open.
I was lucky to closely, albeit at different University, but as one of the founding members of the Pattern Recognition Society of Finland, to follow the pioneering work of prof. Teuvo Kohonen first with diode networks and then, together with his teams and students, the models of associative memory in the early 1970s that later led to self-organizing maps (SOM) and other truly innovative distributed learning concepts. These developments have proved – and are still doing it – the amazing power of network mathematics, but even they are constrained by the theory that maps reality to these networks. I believe that all network scientists applying SOM to real-life problems are painstakingly aware of the reality and interpretation problem when they analyze the learned maps and try to figure out what they tell about the reality.
As a brutal example, the road maps of New York and Moscow both represent their realities but something else is needed if the aim is to understand life in New York and in Moscow: the contents and meanings. The popular technological question today is what else do we need besides the road maps in order to uncover the life of these magnificent cities. An implicit answer – considering what is happening in the field – is that we need more content and location specific network models and integration between them. An alternative solution can be imagined: less networks but more and richer content in them, in other words, something along idea and the concepts offered by the string theory.
The situation reminds me of the Heisenberg’s uncertainty principle: true understanding of the real world requires high-level concepts but computational economy and accuracy demands focused measurements. The string approach is one way to at least move towards the higher-level representations without loosing the computational potential.
A friend and colleague of mine, prof. Timo Järvilehto sometimes reminded, referring to neural Darwinism and related theories: neurons do not communicate, humans do it, neurons just ‘try’ to stay alive by acting and adapting biologically in their bio-environment, in a reasonable way. Their signaling activity is a sign of this – their life is not information processing, it is cell life, the life of cell communities, or part of the states of the complex biological control systems. It is beneficial to build a theory that describes that life; communication or pattern recognition theories alone do not suffice, content and meaning must find their rightful places in these models.
Modern network maps have become popular and their colorful visual architecture diagrams are fascinating. Often such maps assume the relevance of the basic net elements and connections and they carry fuzzy content information and don’t have a way to express the actors’ (units’) intentions, interpretations, or other relevant processes or states, energy considerations can be missing, network dynamics is difficult to depict, they do not represent complex episodic processes or needs, they have numerous invisible momentums, and the context of the units and their real activities remain often obscure. To put it shortly: the present-day network maps and models lack signs of life.
Hence, a general theory of networks in the brain, and of an economical system for that matter, must be – in its essence – grounded in a general theory of life, not in a theory of communication. This is true for any other networks that aim to describe living, human, and/or social systems.
Impressive network work
Lazlo Barabasi’s http://www.barabasi.com/ has published beautiful work on mathematical network analysis that shows a number of ways to analyze e.g. network structure, strength, stability, growth, adaptation and ‘gravitation’ between the nodes. While these mathematical methods help to classify network types, to understand how networks evolve, and gain specific properties like connectivity, strength, and competitive fitness, they still do not explain why (from content, motivation, intent, meaning –perspective) this happens and what reallyunderlies the behavior ofthe nodes and links, what is their life and what is their exact nature. There is no general theoretical framework that would describe how content and context are related to each net considered.
The burning questions remain: how are ‘network nodes and links’ related to the real life that they are supposed to represent and how are ‘connections’ related to the real-life phenomena that form them? How do these nodes and connections grow, originally? Someone might argue that this is trivial, but I believe it is the most essential theoretical problem in trying to understand the complex systems and processes that we have learned to call network phenomenon. It is a no less ambitious problem than the study of matter and its elementary particles.
A general network theory of biological, social and human life forms should cover the elements of life in complex nets. Think about the following few questions, for example: how are nets grounded in real-life material and immaterial phenomena and how should we formalize this? What underlies network life and energy, how are meanings generated in the nets? How is network synchronization accomplished at different scales?
Twitter messages do carry content information and their maps (cf. http://www.dailymail.co.uk/news/article-2191250/Twitter-heat-map-tracks-polite-rudest-cities.html) have become attractive social information sources because they indeed follow the spread of real and relevant communication and influences in various domains from politics, to sports and activism. In order to tell more about what is going on in the underlying life they include content information, like the name of the commenting or commented political candidate or other names, key words, locations, or other relevant data. http://www.guardian.co.uk/news/datablog/2012/jul/04/us-fourth-july-twitter-beer-church#zoomed-picture
But even then, the life events don’t have a place in these maps and they have to be inferred somehow from the map data. However, the twitter maps do seem to me like the closest candidates for string theoretical modeling but as far as I know there is no general theory that combines the content, processes and data representations, and the network properties. Perhaps it already hides somewhere in mathematics that I’m not familiar with?
String view to a simple example case
Take a simple example, the Romancing The Borders web videos. We can apply the following scheme:
1. Let’s assume that there is a dormant string (link) available to actors In (from India) Pm(from Pakistan) to activate, that is, to tune the specific state of the string – something that they have not done before. Positive action between two people is nothing new, it has been exercised and practiced over the history of mankind. As such it has its peculiar cultural nature and consequences. Hence we can assume that there is a specific class of strings that can represent this behavior. When either of the actors prepares a friendly web-video, nothing has yet happened, but when the video is sent or it is made available for someone over the border to receive it, something significant takes place and the state of the string between In and Pm changes. It is now in the state of a ‘shared friendly connection’. A mathematical representation for this state is needed but I will not try to do it here.
2. There are a large number of ways to accomplish this friendly connection in the real world and one may argue that this kind of an approach requires an infinite number of strings and states and that there is no sense in it. But if we are interested in this specific form of significant and intentional engagement the theoretical number of strings and their states needed can be assumed as limited as the number of behavior classes in the human positive engagement culture.
What is here relevant to the network considerations? First, the state of the string of life has changed and there is a new element in the world that now is real, tangible and that has impact on other world activities, perceptions or acts. We need a way to represent these consequences and a system to formalize them.
Let’s imagine that we have a very large mass of such string state changes, in other words, a large number of friendly connections between In (from India) and Pm(from Pakistan). The string states have specific ‘energy’, a form of ‘kindness energy’ that was not available (although it existed in people’s minds) before these connections were made. In this case the personal kindness energies drove the use of web videos and was expressed as the specific string state change. However, the personal kindness energies could drive other activity forms (strings) as well if the space where they take place allows it. In other words, the state change of a string is a way to make tangible something that resides in people’s minds and remains dormant there unless there is a way to channel that energy to become a part of the world state.
The other side of the coin is that the string classes cover all behaviors that we as humans are capable of. In that sense there are limitations as well since not any kind of behavior is possible. Hence, the strings – if we can define them – are bound to the realities of life and that takes place through the branes.
Is there theoretical or intelligent potential in this view? I will continue the development of the concept further in part II of this blog and try to be more specific about the theoretical formulations – while I study more of the string theory basics.