Back to blogging, trying to define what I remember

My editorial

It is really tough to get back to regular blogging, after a break of many weeks. This is interesting. Since like mid-October, I have been absorbed by teaching and by finishing formal scientific writing connected to my research grant. I have one major failure as for that last one – I haven’t finished my book on technological change and renewable energies. I have like 70% of it and it keeps being like 70%, as if I was blocked on something. Articles flow just smoothly, but I am a bit stuck with the book. Another interesting path for self-investigation. Anyway, teaching and formal writing seem to have kind of absorbed some finite amount of mental energy I have, leaving not much for other forms of expression, blogging included. Now, as I slowly resume both the teaching scheduled for the winter semester, and, temporarily, the writing of formal publications, my brain seems to switch, gently, back into the blogging mode.

When I start a new chapter, it is a good thing to phrase out my takeaways from previous chapters. I think there are two of them. Firstly, it is the concept of intelligent loop in collective learning. I am mildly obsessed with the phenomenon of collective intelligence, and, when we claim we are intelligent, it would be good to prove we can learn something as a civilisation. Secondly, it is that odd mathematical construct that we mostly know, in economics, as production function. The longer I work with that logical structure, you know, the ‘Y = K^µ*L^1-µ*A’ one (Cobb, Douglas 1928[1]), the more I am persuaded that – together with some fundamental misunderstandings, there is an enormous cognitive potential in it. The production function is a peculiar way of thinking about social structures, where one major factor – the one with the biggest exponent –  reshuffles all the cards on the table and actually makes the structure we can observe.

The loop of intelligent learning articulates into a few specific, more detailed issues. In order to learn, I have to remember what happened to me. I need to take some kind of break from experiencing reality – the capacity of abstract thinking is of great help in this respect – and I need to connect the dots, form some patterns, test them, hopefully survive the testing, and then come up with something smart, which I can label as my new skills. Collective memory is the first condition of collective learning. There is one particular issue, pertaining to both the individual memory and the collective one: what we think is our memory of past occurrences is, in fact, our present interpretation of information we collected in the past. It is bloody hard to draw a line between what we really remember, and what we think we remember. There are scientifically defined cases of mental disturbances (e.g. the Korsakoff psychosis), where the person creates its own memory on a completely free ride, without any predictable connection to what had really happened in the past. If individual people can happen to do things like that, there is absolutely no reason why whole societies shouldn’t. Yet, when it comes to learning, looping inside our own imagination simply doesn’t work: we come up with things like Holy Inquisitions or Worst Enemies, and it is not what is going to drive us into the next millennium. In order to learn truly and usefully, we have to connect the dots from our actual, past experience, as little edited as possible. The question is, how can I find out what does the society really remember? How can I distinguish it from the imaginary bullshit? Economics are very largely about numbers. The general question about memory translates into something more abstract: how can I tell that the numbers I have today somehow remember the numbers from the past? How can I tell that a particular variable remembers its own variance from the past? What about this particular variable remembering the past variance in other variables?

In order to answer those questions, I go back to my understanding of memory as a phenomenon. How do I know I have memory? I am considering a triad of distinct phenomena, which can prove I have memory: remembering, repetition, and modification of behaviour. Remembering means that I can retrieve, somehow, from the current resources of my brain, some record relative to past experience. In other words, I can find past information in the present information. My brain needs recurrent procedures for retrieving that past information. There must be some librarian-like algorithm in my brain, which can pick up bits of my past in a predictable manner. Memory in quantitative data means, thus, that I can find numbers from the past in the present ones, and I can find them in a recurrent manner, i.e. through a function. If I have a number from the past, let’s call it x(t-1), and a present number x(t), my x(t) has the memory of x(t-1) if, in a given set X = {x₁, x₂, …, x₃} of values attributed to x I can find a regularity of the type x_i(t) = f[x_i(t-1)] and the function f[x_i(t-1)] is a true one, i.e. it has some recurrent shape in it. Going from mathematics back to real life, remembering means that every time I contemplate my favourite landscape – an open prairie in the mountains, by a sunny day in summer – I somehow rehearse all the past times I saw the same landscape.

Going back to maths, there are many layers and tunes in remembering. I can remember in a constant time frame. It means that right now, my brain kind of retrieves sensory experience from the past three weeks, the whole of three weeks and just three weeks. That window in time is my constant frame of remembering. Yet, older memories happen to pop up in my head. Sometimes, I go, in my memories, like two years back. On other occasions, something from a moment twenty years ago suddenly visits my consciousness. Besides the constant window of three weeks back in time, my brain uses a flexible temporal filter, when some data from further a past seems to connect with my present experience. Thus, in the present information x_i(t), currently processed in my mind, there are two layers of remembering: the one in the constant window of three weeks, on the one hand, and that occurring in the shifting regressive reach. Mathematically, constant is constant, for example ‘b’, whilst something changing is basically a stochastic distribution, which I provisionally call ‘STOCH’, i.e. a range of possible states, with each of them occurring with a certain probability. My mathematical formula gets the following shape: x_i(t) = f₁[x_i(t – b)] + f₂[x_i(t – STOCH)].

As someone looks at these maths, they could ask: ‘Good, but where is the residual component on the right side? Is your current information just made of remembering? Is there nothing squarely present and current?’. Well, this is a good question. How does my intelligence work? Is there anything else being processed, besides the remembered information? I start with defining the present moment. In the case of a brain, one neuron fires in about 2 milliseconds, although there is research showing that each neuron can largely control that speed and make connections faster or slower (Armbruster & Ryan 2011[2]). Two milliseconds are not that long: they are two thousandths of what we commonly perceive as the shortest unit of time in real life. Right, one neuron doesn’t make me clever, I need more of them getting to do something useful together. How many? As I was attending my lessons at the driving school, some 27 years ago, I had been taught that the normal time of reaction, in a driver, is about 1,5 seconds. This is the time between my first glimpse of a dog crossing the tarmac, and me pushing the brake pedal. It makes 1 500 milliseconds. Divided by two milliseconds for one neuron, so if each individual neuron fired after another one, it gives 750. I have roughly 100 billion neurons in my brain (you the same), and each of them has, on average, 7000 connections with other neurons. It makes 7E+14 synaptic connections. In a sequence of 750 neurons firing one after the other, I have 750⁷⁰⁰⁰ synapses firing. In other words, something called ‘strictly current processing of information’ activates like 7,5E-09 of my brain: not much. It looks as if my present wasn’t that important, in quantitative terms, in relation to my past. Moreover, in those 750⁷⁰⁰⁰ synapses firing in an on-the-spot reaction of a driver, there is a lot of remembering, like ‘Which of those three things under my feet is the brake pedal?’.

Let’s wrap it up, partially. We are in a social system, and that social system is supposed to have collective intelligence equivalent to the individual intelligence of a human brain. If this is the case, numerical data describing the actions of that social system consists, for any practical purpose, exclusively in remembering. There is some residual of what can be considered as the strictly spoken current processing of information, but this is really negligible. Thus, I come with my first test for collective intelligence in a social system. The system in question is intelligent if, in a set of numerical time series describing its behaviour, the present data can be derived from past data, without significant residual, in a function combining a fixed window of remembering with a stochastic function of reprocessing old information, or x_i(t) = f₁[x_i(t – b)] + f₂[x_i(t – STOCH)]. If this condition is generally met, the social system remembers enough to learn on past experience. ‘Generally’ means that nuances can be introduced into that general scheme. Firstly, if my function yields a significant residual ‘Res[x_i(t)]’, thus if its empirically verified version looks like x_i(t) = f₁[x_i(t – b)] + f₂[x_i(t – STOCH)] + Res[x_i(t)], it just means that my (our?) social system produces some residual information, whose role in collective learning is unclear. It can be the manifestation of super-fast learning on the spot, or, conversely, it can indicate that the social system produces some information bound not to be used for future learning.

And so I come to the more behavioural proof of memory and learning. When we do something right now, there is a component of recurrent behaviour in it, and another one, that of modified behaviour. We essentially do things we know how to do, i.e. we repeat patterns of behaviour that we have formed in the past. Still, if we are really prone to learn, thus to have active a memory, there is another component in our present behaviour: that of current experimentation, and modification in behaviour, in the view of future repetition. We repeat the past, and we experiment for the future. The residual component Res[x_i(t)] in my function of memory – x_i(t) = f₁[x_i(t – b)] + f₂[x_i(t – STOCH)] + Res[x_i(t)] – if it exists at all, can be attributed to such experimentation. Should it be the case, my Res[x_i(t)] should reflect in future functions of memory in my data, and it should reflect in the same basic way as the one already defined. Probably, there is some recurrent cycle of learning, taking place in a more or less constant time window, and, paired with it, is a semi-random utilisation of present experience in the future, occurring in a stochastically varying time range. Following the basic logic, which I am trying to form here, both of the time ranges in that function of modification in behaviour should be pretty.

[1] Charles W. Cobb, Paul H. Douglas, 1928, A Theory of Production, The American Economic Review, Volume 18, Issue 1, Supplement, Papers and Proceedings of the Fortieth Annual Meeting of the American Economic Association (March 1928), pp. 139 – 165

[2] Armbruster, M., Ryan, T., 2011, Synaptic vesicle retrieval time is a cell-wide rather than individual-synapse property, Nature Neuroscience 14, 824–826 (2011), doi:10.1038/nn.2828