Tag: programming

Cultural classes

Some of my readers asked me to explain how to get in control of one’s own emotions when starting their adventure as small investors in the stock market. The purely psychological side of self-control is something I leave to people smarter than me in that respect. What I do to have more control is the Wim Hof method (https://www.wimhofmethod.com/ ) and it works. You are welcome to try. I described my experience in that matter in the update titled ‘Something even more basic’. Still, there is another thing, namely, to start with a strategy of investment clever enough to allow emotional self-control. The strongest emotion I have been experiencing on my otherwise quite successful path of investment is the fear of loss. Yes, there are occasional bubbles of greed, but they are more like childish expectations to get the biggest toy in the neighbourhood. They are bubbles, which burst quickly and inconsequentially. The fear of loss is there to stay, on the other hand.    

This is what I advise to do. I mean this is what I didn’t do at the very beginning, and fault of doing it I made some big mistakes in my decisions. Only after some time (around 2 months), I figured out the mental framework I am going to present. Start by picking up a market. I started with a dual portfolio, like 50% in the Polish stock market, and 50% in the big foreign ones, such as US, Germany, France etc. Define the industries you want to invest in, like biotech, IT, renewable energies. Whatever: pick something. Study the stock prices in those industries. Pay particular attention to the observed losses, i.e., the observed magnitude of depreciation in those stocks. Figure out the average possible loss, and the maximum one. Now, you have an idea of how much you can lose in percentage. Quantitative techniques such as mean-reversion or extrapolation of the past changes can help. You can consult my update titled ‘What is my take on these four: Bitcoin, Ethereum, Steem, and Golem?’ to see the general drift.

The next step is to accept the occurrence of losses. You need to acknowledge very openly the following: you will lose money on some of your investment positions, inevitably. This is why you build a portfolio of many investment positions. All investors lose money on parts of their portfolio. The trick is to balance losses with even greater gains. You will be experimenting, and some of those experiments will be successful, whilst others will be failures. When you learn investment, you fail a lot. The losses you incur when learning, are the cost of your learning.

My price of learning was around €600, and then I bounced back and compensated it with a large surplus. If I take those €600 and compare it to the cost of taking an investment course online, e.g. with Coursera, I think I made a good deal.

Never invest all your money in the stock market. My method is to take some 30% of my monthly income and invest it, month after month, patiently and rhythmically, by instalments. For you, it can be 10% or 50%, which depends on what exactly your personal budget looks like. Invest just the amount you feel you can afford exposing to losses. Nail down this amount honestly. My experience is that big gains in the stock market are always the outcome of many consecutive steps, with experimentation and the cumulative learning derived therefrom.

General remark: you are much calmer when you know what you’re doing. Look at the fundamental trends and factors. Look beyond stock prices. Try to understand what is happening in the real business you are buying and selling the stock of. That gives perspective and allows more rational decisions.  

That would be it, as regards investment. You are welcome to ask questions. Now, I shift my topic radically. I return to the painful and laborious process of writing my book about collective intelligence. I feel like shaking things off a bit. I feel I need a kick in the ass. The pandemic being around and little social contacts being around, I need to be the one who kicks my own ass.

I am running myself through a series of typical questions asked by a publisher. Those questions fall in two broad categories: interest for me, as compared to interest for readers. I start with the external point of view: why should anyone bother to read what I am going to write? I guess that I will have two groups of readers: social scientists on the one hand, and plain folks on the other hand. The latter might very well have a deeper insight than the former, only the former like being addressed with reverence. I know something about it: I am a scientist.

Now comes the harsh truth: I don’t know why other people should bother about my writing. Honestly. I don’t know. I have been sort of carried away and in the stream of my own blogging and research, and that question comes as alien to the line of logic I have been developing for months. I need to look at my own writing and thinking from outside, so as to adopt something like a fake observer’s perspective. I have to ask myself what is really interesting in my writing.

I think it is going to be a case of assembling a coherent whole out of sparse pieces. I guess I can enumerate, once again, the main points of interest I find in my research on collective intelligence and investigate whether at all and under what conditions the same points are likely to be interesting for other people.

Here I go. There are two, sort of primary and foundational points. For one, I started my whole research on collective intelligence when I experienced the neophyte’s fascination with Artificial Intelligence, i.e. when I discovered that some specific sequences of equations can really figure stuff out just by experimenting with themselves. I did both some review of literature, and some empirical testing of my own, and I discovered that artificial neural networks can be and are used as more advanced counterparts to classical quantitative models. In social sciences, quantitative models are about the things that human societies do. If an artificial form of intelligence can be representative for what happens in societies, I can hypothesise that said societies are forms of intelligence, too, just collective forms.

I am trying to remember what triggered in me that ‘Aha!’ moment, when I started seriously hypothesising about collective intelligence. I think it was when I was casually listening to an online lecture on AI, streamed from the Massachusetts Institute of Technology. It was about programming AI in robots, in order to make them able to learn. I remember one ‘Aha!’ sentence: ‘With a given set of empirical data supplied for training, robots become more proficient at completing some specific tasks rather than others’. At the time, I was working on an article for the journal ‘Energy’. I was struggling. I had an empirical dataset on energy efficiency in selected countries (i.e. on the average amount of real output per unit of energy consumption), combined with some other variables. After weeks and weeks of data mining, I had a gut feeling that some important meaning is hidden in that data, only I wasn’t able to put my finger precisely on it.

That MIT-coined sentence on robots triggered that crazy question in me. What if I return to the old and apparently obsolete claim of the utilitarian school in social sciences, and assume that all those societies I have empirical data about are something like one big organism, with different variables being just different measurable manifestations of its activity?

Why was that question crazy? Utilitarianism is always contentious, as it is frequently used to claim that small local injustice can be justified by bringing a greater common good for the whole society. Many scholars have advocated for that claim, and probably even more of them have advocated against. I am essentially against. Injustice is injustice, whatever greater good you bring about to justify it. Besides, being born and raised in a communist country, I am viscerally vigilant to people who wield the argument of ‘greater good’.

Yet, the fundamental assumptions of utilitarianism can be used under a different angle. Social systems are essentially collective, and energy systems in a society are just as collective. There is any point at all in talking about the energy efficiency of a society when we are talking about the entire intricate system of using energy. About 30% of the energy that we use is used in transport, and transport is from one person to another. Stands to reason, doesn’t it?

Studying my dataset as a complex manifestation of activity in a big complex organism begs for the basic question: what do organisms do, like in their daily life? They adapt, I thought. They constantly adjust to their environment. I mean, they do if they want to survive. If I settle for studying my dataset as informative about a complex social organism, what does this organism adapt to? It could be adapting to a gazillion of factors, including some invisible cosmic radiation (the visible one is called ‘sunlight’). Still, keeping in mind that sentence about robots, adaptation can be considered as actual optimization of some specific traits. In my dataset, I have a range of variables. Each variable can be hypothetically considered as informative about a task, which the collective social robot strives to excel at.

From there, it was relatively simple. At the time (some 16 months ago), I was already familiar with the logical structure of a perceptron, i.e. a very basic form of artificial neural network. I didn’t know – and I still don’t – how to program effectively the algorithm of a perceptron, but I knew how to make a perceptron in Excel. In a perceptron, I take one variable from my dataset as output, the remaining ones are instrumental as input, and I make my perceptron minimize the error on estimating the output. With that simple strategy in mind, I can make as many alternative perceptrons out of my dataset as I have variables in the latter, and it was exactly what I did with my data on energy efficiency. Out of sheer curiosity, I wanted to check how similar were the datasets transformed by the perceptron to the source empirical data. I computed Euclidean distances between the vectors of expected mean values, in all the datasets I had. I expected something foggy and pretty random, and once again, life went against my expectations. What I found was a clear pattern. The perceptron pegged on optimizing the coefficient of fixed capital assets per one domestic patent application was much more similar to the source dataset than any other transformation.

In other words, I created an intelligent computation, and I made it optimize different variables in my dataset, and it turned out that, when optimizing that specific variable, i.e. the coefficient of fixed capital assets per one domestic patent application, that computation was the most fidel representation of the real empirical data.   

This is when I started wrapping my mind around the idea that artificial neural networks can be more than just tools for optimizing quantitative models; they can be simulators of social reality. If that intuition of mine is true, societies can be studied as forms of intelligence, and, as they are, precisely, societies, we are talking about collective intelligence.

Much to my surprise, I am discovering similar a perspective in Steven Pinker’s book ‘How The Mind Works’ (W. W. Norton & Company, New York London, Copyright 1997 by Steven Pinker, ISBN 0-393-04535-8). Professor Steven Pinker uses a perceptron as a representation of human mind, and it seems to be a bloody accurate representation.

That makes me come back to the interest that readers could have in my book about collective intelligence, and I cannot help referring to still another book of another author: Nassim Nicholas Taleb’s ‘The black swan. The impact of the highly improbable’ (2010, Penguin Books, ISBN 9780812973815). Speaking from an abundant experience of quantitative assessment of risk, Nassim Taleb criticizes most quantitative models used in finance and economics as pretty much useless in making reliable predictions. Those quantitative models are good solvers, and they are good at capturing correlations, but they suck are predicting things, based on those correlations, he says.

My experience of investment in the stock market tells me that those mid-term waves of stock prices, which I so much like riding, are the product of dissonance rather than correlation. When a specific industry or a specific company suddenly starts behaving in an unexpected way, e.g. in the context of the pandemic, investors really pay attention. Correlations are boring. In the stock market, you make good money when you spot a Black Swan, not another white one. Here comes a nuance. I think that black swans happen unexpectedly from the point of view of quantitative predictions, yet they don’t come out of nowhere. There is always a process that leads to the emergence of a Black Swan. The trick is to spot it in time.

F**k, I need to focus. The interest of my book for the readers. Right. I think I can use the concept of collective intelligence as a pretext to discuss the logic of using quantitative models in social sciences in general. More specifically, I want to study the relation between correlations and orientations. I am going to use an example in order to make my point a bit more explicit, hopefully. In my preceding update, titled ‘Cool discovery’, I did my best, using my neophytic and modest skills in programming, the method of negotiation proposed in Chris Voss’s book ‘Never Split the Difference’ into a Python algorithm. Surprisingly for myself, I found two alternative ways of doing it: as a loop, on the one hand, and as a class, on the other hand. They differ greatly.

Now, I simulate a situation when all social life is a collection of negotiations between people who try to settle, over and over again, contentious issues arising from us being human and together. I assume that we are a collective intelligence of people who learn by negotiated interactions, i.e. by civilized management of conflictual issues. We form social games, and each game involves negotiations. It can be represented as a lot of these >>

… and a lot of those >>

In other words, we collectively negotiate by creating cultural classes – logical structures connecting names to facts – and inside those classes we ritualise looping behaviours.

Cool discovery

Writing about me learning something helps me to control emotions involved into the very process of learning. It is like learning on the top of learning. I want to practice programming, in Python, the learning process of an intelligent structure on the basis of negotiation techniques presented in Chris Voss’s book ‘Never Split the Difference’. It could be hard to translate a book into an algorithm, I know. I like hard stuff, and I am having a go at something even harder: translating two different books into one algorithm. A summary, and an explanation, are due. Chris Voss develops, in the last chapter of his book, a strategy of negotiation based on the concept of Black Swan, as defined by Nassim Nicholas Taleb in his book ‘The black swan. The impact of the highly improbable’ (I am talking about the revised edition from 2010, published with Penguin Books, ISBN 9780812973815).

Generally, Chriss Voss takes a very practical drift in his method of negotiation. By ‘practical’, I mean that he presents techniques which he developed and tested in hostage negotiations with FBI, where he used to be the chief international hostage negotiator. He seems to attach particular importance to all the techniques which allow unearthing the non-obvious in negotiations: hidden emotions, ethical values, and contextual factors with strong impact on the actual negotiation. His method is an unusual mix of rigorous cognitive approach with a very emotion-targeting thread. His reference to Black Swans, thus to what we don’t know we don’t know, is an extreme version of that approach. It consists in using literally all our cognitive tools to uncover events and factors in the game which we even didn’t initially know were in the game.

Translating a book into an algorithm, especially for a newbie of programming such as I am, is hard. Still, in the case of ‘Never Split the Difference’, it is a bit easier because of the very game-theoretic nature of the method presented. Chriss Voss attaches a lot of importance to taking our time in negotiations, and to making our counterpart make a move rather than overwhelming them with our moves. All that is close to my own perspective and makes the method easier to translate into a functional sequence where each consecutive phase depends on the preceding phase.

Anyway, I assume that a negotiation is an intelligent structure, i.e. it is an otherwise coherent and relatively durable structure which learns by experimenting with many alternative versions of itself. That implies a lot. Firstly, it implies that the interaction between negotiating parties is far from being casual and accidental: it is a structure, it has coherence, and it is supposed to last by recurrence. Secondly, negotiations are supposed to be learning much more than bargaining and confrontation. Yes, it is a confrontation of interests and viewpoints, nevertheless the endgame is learning. Thirdly, an intelligent structure experiments with many alternative versions of itself and learns by assessing the fitness of those versions in coping with a vector of external stressors. Therefore, negotiating in an intelligent structure means that, consciously or unconsciously, we, mutual counterparts in negotiation, experiment together with many alternative ways of settling our differences, and we are essentially constructive in that process.

Do those assumptions hold? I guess I can somehow verify them by making first steps into programming a negotiation.  I already know two ways of representing an intelligent structure as an algorithm: in the form of a loop (primitive, tried it, does not fully work, yet has some interesting basic properties), or in the form of a class, i.e. a complex logical structure which connects names to numbers.

When represented as a loop, a negotiation is a range of recurrent steps, where the same action is performed a given number of times. Looping means that a negotiation can be divided into a finite number of essentially identical steps, and the endgame is the cumulative output of those steps. With that in mind, I can see that a loop is not truly intelligent a structure. Intelligent learning requires more than just repetition: we need consistent assessment and dissemination of new knowledge. Mind you, many negotiations can play out as ritualized loops, and this is when they are the least productive. Under the condition of unearthing Black Swans hidden in the contentious context of the negotiation, the whole thing can play out as an intelligent structure. Still, many loop-like negotiations which recurrently happen in a social structure, can together form an intelligent structure. Looks like intelligent structures are fractal: there are intelligent structures inside intelligent structures etc. Intelligent social structures can contain chains of ritualized, looped negotiations, which are intelligent structures in themselves.   

Whatever. I program. When I try to sift out the essential phenomenological categories out of the Chris Voss’s book ‘Never Split the Difference’, I get to the following list of techniques recommended by Chriss Voss:

>> Mirroring – I build emotional rapport by just repeating the last three words of each big claim phrased out by my counterpart.

 >> Labelling – I further build emotional rapport by carefully and impersonally naming emotions and aspirations in my counterpart.

>> Open-ended questions – I clarify claims and disarm emotional bottlenecks by asking calibrated open questions such as ‘How can we do X,Y, Z?’ or ‘What do we mean by…?’ etc.

>> Claims – I state either what I want or what I want my counterpart to think I want

Those four techniques can be used in various shades and combinations to accomplish typical partial outcomes in negotiation, namely: a) opportunities for your counterpart to say openly ‘No’ b) agreement in principle c) guarantee of implementation d) Black Swans, i.e. unexpected attributes of the situation which turn the negotiation in a completely different, favourable direction.

I practice phrasing it out as a class in Python. Here is what I came up with and which my JupyterLab compiler swallows nicely without yielding any errors:

Mind you, I don’t know how exactly it works, algorithmically. I am a complete newbie to programming classes in Python, and my first goal is to have the grammar right, and thus not to have to deal with those annoying, salmon-pink-shaded messages of error.

Before I go further into programming negotiation as a class, I feel like I need to go back to my primitive skills, i.e. to programming loops, in order to understand the mechanics of the class I have just created. Each ‘self’ in the class is a category able to have many experimental versions of itself. I try the following structure:

As you can see, I received an error of non-definition. I have not defined the dataset which I want to use for appending my lists. Such a dataset would contain linguistic strings, essentially. Thus, the type of datasets I am operating with, here, are sets of linguistic strings, thus sets of objects. An intelligent structure representative for negotiation is an algorithm for processing natural language. Cool discovery.

I got it all wrong

I like doing research on and writing about collective intelligence in human societies. I am even learning to program in Python in order to know how to code collective intelligence in the form of an artificial neural network. I decided to take on my own intelligence as an interesting diversion from the main course. I hope I can assume I am an intelligent structure. Whilst staying essentially coherent, i.e. whilst remembering who I am, I can experiment a bit with many different versions of myself. Of course, a substantial part of the existential Me works like a shuttle train, going back and forth on the rails of my habits. Still, I can learn heuristically on my own experience. Heuristic learning means that as I learn something, I gain new knowledge about how much more I can learn about and along the lines of the same something.

I want to put into a Python code the experience of heuristic, existential learning which I exemplified in the update titled ‘Something even more basic’. It starts with experience which happens through intentional action from my part. I define a vector of action, i.e. a vector of behavioural patterns, associated with the percentage of my total time they take. That percentage can be understood, alternatively, as the probability that any given minute in the day is devoted to that specific action. Some of those patterns are active, and some are dormant, with the possibility of being triggered into existence. Anyway, it is something like A = {a1, a2, …, an}. Now, in terms of coding in Python, is that vector of action a NumPy array, or is it a Pandas data frame? In terms of pure algorithmic technique, it is a trade-off between computational speed, with a NumPy array, and programmatic versatility in the case of a Pandas data frame. Here are a few points of view expressed, as regards this specific matter, by people smarter than me:

>> https://www.geeksforgeeks.org/difference-between-pandas-vs-numpy/

>> https://towardsdatascience.com/performance-of-numpy-and-pandas-comparison-7b3e0bea69bb

>> https://vitalflux.com/pandas-dataframe-vs-numpy-array-what-to-use/

In terms of algorithmic theory, these are two different, cognitive phenomena. A NumPy array is a structured collection of numbers, whilst a Pandas data frame is a structure combining many types of data, e.g. string objects with numbers. How does it translate into my own experience? I think that, essentially, my action is a data frame. I take purposeful action to learn something when I have a logical frame to put it in, i.e. when I have words to label what I do. That leads me to starting at even more elementary a level, namely that of a dictionary as regards my actions.

Anyway, I create a notebook with JupyterLab, and I start like a hamster, with stuffing my cheeks with libraries:

>> import numpy as np

>> import pandas as pd

>> import os

>> import math     

Then, I make a first dictionary:

>> Types_of_action=[‘Action 1′,’Action 2′,’Action 3′,’Action 4′,’Action 5’]

A part of my brain says, at this point: ‘Wait a minute, bro. Before you put labels on the things that you do, you need to be doing things. Humans label stuff that happens, essentially. Yes, of course, later on, me can make them metaphors and abstract concepts but, fundamentally, descriptive language comes after experience’. Well, dear part of my brain, this is a valid argument. Things unfold into a paradox, just as I like it. I need raw experience, primal to any logical structuring. How to express it in Python? I can go like:

>> Raw_experience=np.random.rand(np.random.randint(1)) #This is a NumPy array made of random decimal values, and the number of those values in the array is random as well.

I check. I type ‘Raw_experience’ and run it. Python answers:

>> array([], dtype=float64) #  I have just made a paradox: a totally empty array of numbers, i.e. with no numbers in it, and yet those inexistent numbers have a type, namely that of ‘float64’.

I try something less raw and more cooked, like:

>> Raw_experience_50=np.random.rand(50) # I assume a priori there are 50 distinct units of raw experience

>> Raw_experience_50 # yields…

>> array([0.73209089, 0.94390333, 0.44267215, 0.92111994, 0.4098961 ,

       0.22435079, 0.61447481, 0.21183481, 0.10223352, 0.04481922,

       0.01418667, 0.65747087, 0.22180559, 0.6158434 , 0.82275393,

       0.22446375, 0.31331992, 0.64459349, 0.90762324, 0.65626915,

       0.41462473, 0.35278516, 0.13978946, 0.79563848, 0.41794509,

       0.12931173, 0.37012284, 0.37117378, 0.30989358, 0.26912215,

       0.7404481 , 0.61690128, 0.41023962, 0.9405769 , 0.86930885,

       0.84279381, 0.91174751, 0.04715724, 0.35663278, 0.75116884,

       0.78188546, 0.30712707, 0.00615981, 0.93404037, 0.82483854,

       0.99342718, 0.74814767, 0.49888401, 0.93164796, 0.87413073])

This is a short lesson of empiricism. When I try to code raw, completely unstructured experience, I obtain an empty expanse. I return to that interesting conversation with a part of my brain. Dear part of my brain, you were right to point out that experience comes before language, and yet, without language, i.e. without any logical structuring of reality, I don’t know s**t about experience, and I cannot intelligibly describe it. I need to go for a compromise. I make that experience as raw as possible by making it happen at random, and, in the same time, I need to give it some frame, like the number of times those random things are supposed to happen to me.

I defined a dictionary with 5 types of action in it. Thus, I define a random path of happening as an array made of 5 categories (columns), and 50 rows of experience: Raw_experience_for_action=np.random.rand(50,5).

I acknowledge the cognitive loop I am in, made of raw experience and requiring some language to put order in all that stuff. I make a data frame:

>> Frame_of_action = pd.DataFrame (Raw_experience_for_action, columns = [Types_of_action]) # One remark is due, just in case. In the Python code, normally, there are no spaces. I put spaces, somehow in phase with interpunction, just to make some commands more readable.

I check with ‘Frame_of_action.info()’ and I get:

 
>> <class 'pandas.core.frame.DataFrame'>
RangeIndex: 50 entries, 0 to 49
Data columns (total 5 columns):
 #   Column       Non-Null Count  Dtype  
---  ------       --------------  -----  
 0   (Action 1,)  50 non-null     float64
 1   (Action 2,)  50 non-null     float64
 2   (Action 3,)  50 non-null     float64
 3   (Action 4,)  50 non-null     float64
 4   (Action 5,)  50 non-null     float64
dtypes: float64(5)
memory usage: 2.1 KB

Once I have that basic frame of action, what is my next step? I need to learn from that experience. The frame of action is supposed to give me knowledge. What is knowledge coming from action? That type of knowledge is called ‘outcomes’. My action brings an outcome, and I evaluate it. Now, in a baseline algorithm of artificial neural network, evaluation of outcomes happens by pitching them against a predefined benchmark, something like expected outcome. As I am doing my best to be an intelligent structure, there is that aspect too, of course. Yet, there is something else, which I want to deconstruct, understand, and reconstruct as Python code. There is discovery and exploration, thus something that I perceive as entirely new a piece of experience. I don’t have any benchmark I can consciously pitch that experience against.

I can perceive my fresh experiential knowledge in two different ways: as a new piece of data, or as an error, i.e. as deviation from the expected state of reality. Both mathematically, and algorithmically, it is a difference. Mathematically, any number, thus any piece of data, is the result of an operation. If I note down, in the algorithm of my heuristic learning, my new knowledge as literally new, anyway it needs to come from some kind of mathematical operation: addition, subtraction, multiplication, or division.

As I think about myself learning new stuff, there is a phase, in the beginning, when I have some outcomes, and yet I don’t have any precise idea what those outcomes are, exactly. This is something that happens in coincidence (I don’t even know, yet, if this is a functional correlation) with the actions I do.

As I think about all that stuff, I try to make a loop of learning between action and outcomes, and as I am doing it, I realize I got it all wrong. For the last few weeks, I have been assuming that an intelligent structure can and should be coded as a loop (see, for example, ‘Two loops, one inside the other’). Still, as I am trying to code the process of my own heuristic learning, I realize that an algorithmic loop has fundamental flaws in that respect. Essentially, each experimental round – where I pitch the outcomes of my actions against a pre-defined expected outcome – is a separate loop, as I have to feed forward the resulting error. With many experimental rounds, like thousands, making a separate loop for each of them is algorithmically clumsy. I know it even at my neophytic stage of advancement in Python.

When I don’t know what to do, I can ask around. I can ask people smarter than me. And so I ask:    

>> https://hackernoon.com/building-a-feedforward-neural-network-from-scratch-in-python-d3526457156b

>> https://towardsdatascience.com/how-to-build-your-own-neural-network-from-scratch-in-python-68998a08e4f6

After rummaging a bit in the content available under those links, I realize that intelligent structures can be represented algorithmically as classes (https://docs.python.org/3/tutorial/classes.html ), and it is more functional a way than representing them as loops. From the second of the above-mentioned links, I took an example of algorithm, which I allow myself to reproduce below. Discussing this algorithm will help me wrapping my own mind around it and developing new understandings.

(Source: https://towardsdatascience.com/how-to-build-your-own-neural-network-from-scratch-in-python-68998a08e4f6)

A neural network is a class, i.e. a type of object, which allows creating many different instances of itself. Inside the class, types of instances are defined, using selves: ‘self.input’, ‘self.output’ etc. Selves are composed into distinct functions, introduced with the command ‘def’. Among the three functions defined inside the class ‘NeuralNetwork’, one is particularly interesting, namely the ‘_init_’. As I rummage through online resources, it turns out that ‘_init_’ serves to create objects inside a class, and then to make selves of those objects. 

I am trying to dissect the use of ‘_init_’ in this specific algorithm. It is introduced with three attributes: self, x, and y. I don’t quite get the corresponding logic. I am trying with something simpler: an algorithm I found at https://www.tutorialspoint.com/What-is-difference-between-self-and-init-methods-in-python-Class :

I think I start to understand. Inside the ‘_init_’ function, I need to signal there are different instances – selves – of the class I create. Then, I add the variables I intend to use. In other words, each specific self of the class ‘Rectangle’ has three dimensions: length, breadth, and unit cost.

I am trying to apply this logic to my initial problem, i.e. my own heuristic learning, with the bold assumption that I am an intelligent structure. I go:

>> class MyLearning:

            def _init_(self, action, outcomes, new_knowledge = 0):

                        self.action = action

                        self.outcomes = outcomes

                        self.new_knowledge = new_knowledge

            def learning(self):

                        return action-outcomes

When I run this code, there is no error message from Python, which is encouraging for a newbie such as I am. Mind you, I have truly vague an idea of what I have just coded. I know it is grammatically correct in Python.

Boots on the ground

I continue the fundamental cleaning in my head, as the year 2020 touches to its end. What do I want? Firstly,I want to exploit and develop on my hypothesis of collective intelligence in human societies, and I want to develop my programming skills in Python. Secondly, I want to develop my skills and my position as a facilitator and manager of research projects at the frontier of the academic world and that of business.  How will I know I have what I want? If I actually program a workable (and working) intelligent structure, able to uncover and reconstruct the collective intelligence of a social structure out of available empirical data – namely to uncover and reconstruct the chief collective outcomes that structure is after, and its patterns of reaction to random exogenous disturbances – that would be an almost tangible outcome for me, telling me I have made a significant step. When I see that I have repetitive, predictable patterns of facilitating the start of joint research projects in consortiums of scientific entities and business ones, then I know I have nailed down something in terms of project management. If I can start something like an investment fund for innovative technologies, then I definitely know I am on the right track.

As I want to program an intelligent structure, it is essentially an artificial neural network, possibly instrumented with additional functions, such as data collection, data cleansing etc. I know I want to understand very specifically what my neural network does. I want to understand every step in takes. To that purpose, I need to figure out a workable algorithm of my own, where I understand every line of code. It can be sub-optimally slow and limited in its real computational power, yet I need it. On the other hand, Internet is more and more equipped with platforms and libraries in the form of digital clouds, such as IBM Watson, or Tensorflow, which provide optimized processes to build complex pieces of AI. I already know that being truly proficient in Data Science entails skills pertinent to using those cloud-based tools. My bottom line is that if I want to program an intelligent structure communicable and appealing to other people, I need to program it at two levels: as my own prototypic code, and as a procedure of using cloud-based platforms to replicate it.             

At the juncture of those two how-will-I-know pieces of evidence, an idea emerges, a crazy one. What if I can program an intelligent structure which uncovers and reconstructs one or more alternative business models out of the available empirical data? Interesting. The empirical data I work the most with, as regards business models, is the data provided in the annual reports of publicly listed companies. Secondarily, data about financial markets sort of connects. My own experience as small investor supplies me with existential basis to back this external data, and that experience suggests me to define a business model as a portfolio of assets combined with broadly spoken behavioural patterns both in people active inside the business model, thus running it and employed with it, and in people connected to that model from outside, as customers, suppliers, investors etc.

How will other people know I have what I want? The intelligent structure I will have programmed has to work across different individual environments, which is an elegant way of saying it should work on different computers. Logically, I can say I have clearly demonstrated to other people that I achieved what I wanted with that thing of collective intelligence when said other people will be willing to and successful at trying my algorithm. Here comes the point of willingness in other people. I think it is something like an existential thing across the board. When we want other people to try and do something, and they don’t, we are pissed. When other people want us to try and do something, and we don’t, we are pissed, and they are pissed. As regards my hypothesis of collective intelligence, I have already experienced that sort of intellectual barrier, when my articles get reviewed. Reviewers write that my hypothesis is interesting, yet not articulate and not grounded enough. Honestly, I can’t blame them. My feeling is that it is even hard to say that I have that hypothesis of collective intelligence. It is rather as if that hypothesis was having me as its voice and speech. Crazy, I know, only this is how I feel about the thing, and I know by experience that good science (and good things, in general) turn up when I am honest with myself.

My point is that I feel I need to write a book about that concept of collective intelligence, in order to give a full explanation of my hypothesis. My observations about cities and their role in the human civilization make, for the moment, one of the most tangible topics I can attach the theoretical hypothesis to. Writing that book about cities, together with programming an intelligent structure, takes a different shade, now. It becomes a complex account of how we can deconstruct something – our own collective intelligence – which we know is there and yet, as we are inside that thing, we have hard times to describe it.

That book about cities, abundantly referring to my hypothesis of collective intelligence, could be one of the ways to convince other people to at least try what I propose. Thus, once again, I restate what I understand by intelligent structure. It is a structure which learns new patterns by experimenting with many alternative versions of itself, whilst staying internally coherent. I return to my ‘DU_DG’ database about cities (see ‘It is important to re-assume the meaning’) and I am re-assuming the concept of alternative versions, in an intelligent structure.

I have a dataset structured into n variables and m empirical observations. In my DU_DG database, as in many other economic datasets, distinct observations are defined as the state of a country in a given year. As I look at the dataset (metaphorically, it has content and meaning, but it does not have any physical shape save for the one my software supplies it with), and as I look at my thoughts (metaphorically, once again), I realize I have been subconsciously distinguishing two levels of defining an intelligent structure in that dataset, and, correspondingly, two ways of defining alternative versions thereof. At the first level, the entire dataset is supposed to be an intelligent structure and alternative versions thereof consist in alternative dichotomies of the type ‘one variable as output, i.e. as the desired outcome to optimize, and the remaining ones as instrumental input’. At this level of structural intelligence – by which term I understand the way of being in an intelligent structure – alternative versions are alternative orientations, and there are as many of them as there are variables.

Distinction into variables is largely, although not entirely, epistemic, and not ontological. The headcount of urban population is not fundamentally different phenomenon from the surface of agricultural land. Yes, the units of measurement are different, i.e. people vs. square kilometres, but, ontologically, it is largely the same existential stuff, possible to describe as people living somewhere in large numbers and being successful at it. Historically, social scientists and governments alike have come to the conclusion, though, that these two metrics have different a meaning, and thus it comes handy to distinguish them as semantic vessels to collect and convey information. The distinction of alternative orientations in an intelligent structure, supposedly represented in a dataset, is arbitrary and cognitive more than ontological. It depends on the number of variables we have. If I add variables to the dataset, e.g. by computing coefficients between the incumbent variables, I can create new orientations for the intelligent structure, i.e. new alternative versions to experiment with.

The point which comes to my mind is that the complexity of an intelligent structure, at that first level, depends on the complexity of my observational apparatus. The more different variables I can distinguish, and measure as regards a given society, the more complexity I can give to the allegedly existing, collectively intelligent structure of that society.

Whichever combination ‘output variable vs. input variables’ I am experimenting with, there comes the second level of defining intelligent structures, i.e. that of defining them as separate countries. They are sort of local intelligent structures, and, at the same time, they are alternative experimental versions of the overarching intelligent structure to be found in the vector of variables. Each such local intelligent structure, with a flag, a national anthem, and a government, produces many alternative versions of itself in consecutive years covered by the window of observation I have in my dataset.

I can see a subtle distinction here. A country produces alternative versions of itself, in different years of its existence, sort of objectively and without giving a f**k about my epistemological distinctions. It just exists and tries to be good at it. Experimenting comes as natural in the flow of time. This is unguided learning. On the other hand, I produce different orientations of the entire dataset. This is guided learning. Now, I understand the importance of the degree of supervision in artificial neural networks.

I can see an important lesson for me, here. If I want to program intelligent structures ‘able to uncover and reconstruct the collective intelligence of a social structure out of available empirical data – namely to uncover and reconstruct the chief collective outcomes that structure is after, and its patterns of reaction to random exogenous disturbances’, I need to distinguish those two levels of learning in the first place, namely the unguided flow of existential states from the guided structuring into variables and orientations. When I have an empirical dataset and I want to program an intelligent structure able to deconstruct the collective intelligence represented in that dataset, I need to define accurately the basic ontological units, i.e. the fundamentally existing things, then I define alternative states of those things, and finally I define alternative orientations.

Now, I am contrasting. I pass from those abstract thoughts on intelligent structures to a quick review of my so-far learning to program those structures in Python. Below, I present that review as a quick list of separate files I created in JupyterLab, together with a quick characteristic of problems I am trying to solve in each of those files, as well as of the solutions found and not found.

>> Practice Dec 11 2020.iypnb.

In this file, I work with IMF database WEOOct2020 (https://www.imf.org/en/Publications/WEO/weo-database/2020/October ).  I practiced reading complex datasets, with an artificially flattened structure. It is a table, in which index columns are used to add dimensions to an otherwise two-dimensional format. I practiced the ‘read_excel’ and ‘read_csv’ commands. On the whole, it seems that converting an Excel to CSV and then reading CSV in Python is a better method than reading excel. Problems solved: a) cleansing the dataset of not-a-number components and successful conversion of initially ‘object’ columns into the desired ‘float64’ format b) setting descriptive indexes to the data frame c) listing unique labels from a descriptive index d) inserting new columns into the data frame e) adding (compounding) the contents of two existing, descriptive index columns into a third index column. Failures: i) reading data from XML file ii) reading data from SDMX format iii) transposing my data frame so as to put index values of economic variables as column names and years as index values in a column.

>> Practice Dec 8 2020.iypnb.

In this file, I worked with a favourite dataset of mine, the Penn Tables 9.1. (https://www.rug.nl/ggdc/productivity/pwt/?lang=en ). I described my work with it in two earlier updates, namely ‘Two loops, one inside the other’, and ‘Mathematical distance’. I succeeded in creating an intelligent structure from that dataset. I failed at properly formatting the output of that structure and thus at comparing the cognitive value of different orientations I made it simulate.   

>> Practice with Mortality.iypnb.

I created this file as a first practice before working with the above-mentioned WEOOct2020 database. I took one dataset from the website of the World Bank, namely that pertinent to the coefficient of adult male mortality (https://data.worldbank.org/indicator/SP.DYN.AMRT.MA ). I practiced reading data from CSV files, and I unsuccessfully tried to stack the dataset, i.e. to transform columns corresponding to different years of observation into rows indexed with labels corresponding to years.   

>> Practice DU_DG.iypnb.

In this file, I am practicing with my own dataset pertinent to the density of urban population and its correlates. The dataset is already structured in Excel. I start practicing the coding of the same intelligent structure I made with Penn Tables, supposed to study orientation of the societies studied. Same problems and same failures as with Penn Tables 9.1.: for the moment, I cannot nail down the way to get output data in structures that allow full comparability. My columns tend to wander across the output data frames. In other words, the vectors of mean expected values produced by the code I made have slightly (just slightly, and sufficiently to be annoying) different a structure from the original dataset. I don’t know why, yet, and I don’t know how to fix it.  

On the other hand, in that same file, I have been messing around a bit with algorithms based on the ‘scikit’ library for Python. Nice graphs, and functions which I still need to understand.

>> Practice SEC Financials.iypnb.

Here, I work with data published by the US Securities and Exchange Commission, regarding the financials of individual companies listed in the US stock market (https://www.sec.gov/dera/data/financial-statement-data-sets.html ). The challenge here consists in translating data originally supplied in *.TXT files into numerical data frames in Python. The problem with I managed to solve, so far (this is the most recent piece of my programming), is the most elementary translation of TXT data into a Pandas data frame, using the ‘open()’ command, and the ‘f.readlines()’ one. Another small victory here is to read data from a sub-directory inside the working directory of JupyterLab, i.e. inside the root directory of my user profile. I used two methods of reading TXT data. Both worked sort of. First, I used the following sequence:

>> with open(‘2020q3/num.txt’) as f:

            numbers=f.readlines()

>> Numbers=pd.DataFrame(numbers)

… which, when checked with the ‘Numbers.info()’ command, yields:

<class ‘pandas.core.frame.DataFrame’>

RangeIndex: 2351641 entries, 0 to 2351640

Data columns (total 1 columns):

 #   Column  Dtype

—  ——  —–

 0   0       object

dtypes: object(1)

memory usage: 17.9+ MB

In other words, that sequence did not split the string of column names into separate columns, and the ‘Numbers’ data frame contains one column, in which every row is a long string structured with the ‘\’ separators. I tried to be smart with it. I did:

>> Numbers.to_csv(‘Num2’) # I converted the Pandas data frame into a CSV file

>> Num3=pd.DataFrame(pd.read_csv(‘Num2′,sep=’;’)) # …and I tried to read back from CSV, experimenting with different separators. None of it worked. With the ‘sep=’ argument in the command, I kept getting an error of parsing, in the lines of ‘ParserError: Error tokenizing data. C error: Expected 1 fields in line 3952, saw 10’. When I didn’t use the ‘sep=’ argument, the command did not yield error, yet it yielded the same long column of structured strings instead of many data columns.  

Thus, I gave up a bit, and I used Excel to open the TXT file, and to save a copy of it in the CSV format. Then, I just created a data frame from the CSV dataset, through the ‘NUM_from_CSV=pd.DataFrame(pd.read_csv(‘SEC_NUM.csv’, sep=’;’))’ command, which, checked with the ‘NUM_from_CSV.info()’ command, yields:

<class ‘pandas.core.frame.DataFrame’>

RangeIndex: 1048575 entries, 0 to 1048574

Data columns (total 9 columns):

 #   Column    Non-Null Count    Dtype 

—  ——    ————–    —– 

 0   adsh      1048575 non-null  object

 1   tag       1048575 non-null  object

 2   version   1048575 non-null  object

 3   coreg     30131 non-null    object

 4   ddate     1048575 non-null  int64 

 5   qtrs      1048575 non-null  int64 

 6   uom       1048575 non-null  object

 7   value     1034174 non-null  float64

 8   footnote  1564 non-null     object

dtypes: float64(1), int64(2), object(6)

memory usage: 72.0+ MB

The ‘tag’ column in this data frame contains the names of financial variables ascribed to companies identified with their ‘adsh’ codes. I experience the same challenge, and, so far, the same failure as with the WEOOct2020 database from IMF, namely translating different values in a descriptive index into a dictionary, and then, in the next step, to flip the database so as to make those different index categories into separate columns (variables).   

As I have passed in review that programming of mine, I have become aware that reading and properly structuring different formats of data is the sensory apparatus of the intelligent structure I want to program.  Operations of data cleansing and data formatting are the fundamental skills I need to develop in programming. Contrarily to what I expected a few weeks ago, when I was taking on programming in Python, elaborate mathematical constructs are simpler to code than I thought they would be. What might be harder, mind you, is to program them so as to optimize computational efficiency with large datasets. Still, the very basic, boots-on-the-ground structuring of data seems to be the name of the game for programming intelligent structures.

Once again, I don’t really know what I am doing, and I love the feeling

I am digressing a bit in my learning of programming in Python, and I come back to a task which I have kept failing at so far, namely at reading data out of the World Economic Outlook database, published by the International Monetary Fund (https://www.imf.org/en/Publications/WEO/weo-database/2020/October ). This is good training in data cleansing. When I click on that link, I can choose two different formats: TAB delimited values or SDMX. The former download as an Excel file, essentially. Frankly, I feel not up to treating the latter: it is a dynamic format, essentially based on an XML tree. Still to learn, for me. This is one of those cases when I prefer staying in the cave. Daylight can wait. I stick to Excel. I download it, I open it in Excel and I preliminarily cleanse the spreadsheet of the most salient stuff, such as e.g. title rows in the heading above the column labels.

Preliminary cleansing done, I copy the Excel workbook to the working directory of my Anaconda, which is, by default, the root directory of my user profile. I create a new notebook in JupyterLab, and I start by importing whatever I think can be useful:

>> import numpy as np

>> import pandas as pd

>> import os

>> import math    

I check the presence of the Excel file with the ‘os.listdir()’ command, and I go:

>> WEO=pd.DataFrame(pd.read_excel(‘WEOOct2020all.xlsx’,sheet_name=’WEOOct2020all’,header=0))     

Seems cool. The kernel has swallowed the command. Just in case, I check with ‘WEO.describe()’, and I get:

 Estimates Start After
count7585.000000
mean2015.186421
std80.240679
min0.000000
25%2018.000000
50%2019.000000
75%2019.000000
max2020.000000

WTF? ‘Estimates start after’ is the last column of a two-dimensional table in Excel, and this column gives the year up to which the database provides actual empirics, and after which it is just projections. Besides this one, the database contains numerical columns corresponding to years, starting from 1980. When I go ‘WEO.columns’, I get:

Index([              ‘Country’,    ‘Subject Descriptor’,

                       ‘Units’,                 ‘Scale’,

                          1980,                    1981,

                          1982,                    1983,

                          1984,                    1985,

                          1986,                    1987,

                          1988,                    1989,

                          1990,                    1991,

                          1992,                    1993,

                          1994,                    1995,

                          1996,                    1997,

                          1998,                    1999,

                          2000,                    2001,

                          2002,                    2003,

                          2004,                    2005,

                          2006,                    2007,

                          2008,                    2009,

                          2010,                    2011,

                          2012,                    2013,

                          2014,                    2015,

                          2016,                    2017,

                          2018,                    2019,

                          2020,                    2021,

                          2022,                    2023,

                          2024,                    2025,

       ‘Estimates Start After’],

      dtype=’object’)

Aha! These columns are there, only Python sees them as non-numerical and does not compute any stats from them. As we say in Poland, I am trying to get my man from another angle. I open the source XLSX file in Excel and I save a copy thereof in the CSV format, in the working directory of my Anaconda. I remember that when saved out of an XLSX file, CSVs tend to have the semi-column as separator, instead of the coma. To everyone their ways, mind you. Thus, I go:

>> WEO2=pd.DataFrame(pd.read_csv(‘WEOOct2020all.csv’,header=0,sep=’;’))

When I check with ‘WEO2.info()’, I get:

<class ‘pandas.core.frame.DataFrame’>

RangeIndex: 8775 entries, 0 to 8774

Data columns (total 51 columns):

 #   Column                 Non-Null Count  Dtype 

—  ——                 ————–  —– 

 0   Country                8775 non-null   object

 1   Subject Descriptor     8775 non-null   object

 2   Units                  8775 non-null   object

 3   Scale                  3900 non-null   object

 4   1980                   3879 non-null   object

 5   1981                   4008 non-null   object

 6   1982                   4049 non-null   object

 7   1983                   4091 non-null   object

 8   1984                   4116 non-null   object

 9   1985                   4192 non-null   object

 10  1986                   4228 non-null   object

 11  1987                   4249 non-null   object

 12  1988                   4338 non-null   object

 13  1989                   4399 non-null   object

 14  1990                   4888 non-null   object

 15  1991                   5045 non-null   object

 16  1992                   5428 non-null   object

 17  1993                   5621 non-null   object

 18  1994                   5748 non-null   object

 19  1995                   6104 non-null   object

 20  1996                   6247 non-null   object

 21  1997                   6412 non-null   object

 22  1998                   6584 non-null   object

 23  1999                   6662 non-null   object

 24  2000                   7071 non-null   object

 25  2001                   7193 non-null   object

 26  2002                   7289 non-null   object

 27  2003                   7323 non-null   object

 28  2004                   7391 non-null   object

 29  2005                   7428 non-null   object

 30  2006                   7433 non-null   object

 31  2007                   7441 non-null   object

 32  2008                   7452 non-null   object

 33  2009                   7472 non-null   object

 34  2010                   7475 non-null   object

 35  2011                   7477 non-null   object

 36  2012                   7484 non-null   object

 37  2013                   7493 non-null   object

 38  2014                   7523 non-null   object

 39  2015                   7545 non-null   object

 40  2016                   7547 non-null   object

 41  2017                   7551 non-null   object

 42  2018                   7547 non-null   object

 43  2019                   7539 non-null   object

 44  2020                   7501 non-null   object

 45  2021                   7449 non-null   object

 46  2022                   7389 non-null   object

 47  2023                   7371 non-null   object

 48  2024                   7371 non-null   object

 49  2025                   7371 non-null   object

 50  Estimates Start After  7585 non-null   float64

dtypes: float64(1), object(50)

memory usage: 3.4+ MB

There is some progress, still it is not the entire progress I expected. I still don’t have numerical data, in ‘float64’ type, where I expect it to have. I dig a bit and I see the source of the problem. In the WEO database there is plenty of empty cells, especially before the year 2000. They correspond to missing data, quite simply. In the source XLSX file, they are either just empty, or filled with something that looks like a double hyphen: ‘- -‘. Python shows the contents of these cells as ‘NaN’, which stands for ‘Not a Number’. That double hyphen is the most annoying of the two, as Excel does not see it in the command ‘Replace’. I need to use Python. I do two phases of cleansing:

>> WEO3=WEO2.replace(np.nan,”, regex=True)

>> WEO4=WEO3.replace(‘–‘,”, regex=True)

 I check with ‘WEO4.info()’ aaaaand… Bingo! Columns from ‘1980’ to ‘2025’ are of the type ‘float64’.

The WEO database is made of several variables stacked one underneath the other in consecutive rows. You have one country, and for that country you have variables such as GDP, fiscal balance and whatnot. Essentially, it is a database presented in the two-dimensional format with multiple indexes, embedded one inside the other. The complexity of indexes replaces the multitude of dimensions in the actual data. I start intuitively, with creating lists of column labels corresponding, respectively, to numerical data, and to index descriptors:

>> Numerical_Data=[‘1980’, ‘1981’,

       ‘1982’, ‘1983’, ‘1984’, ‘1985’, ‘1986’, ‘1987’, ‘1988’, ‘1989’, ‘1990’,

       ‘1991’, ‘1992’, ‘1993’, ‘1994’, ‘1995’, ‘1996’, ‘1997’, ‘1998’, ‘1999’,

       ‘2000’, ‘2001’, ‘2002’, ‘2003’, ‘2004’, ‘2005’, ‘2006’, ‘2007’, ‘2008’,

       ‘2009’, ‘2010’, ‘2011’, ‘2012’, ‘2013’, ‘2014’, ‘2015’, ‘2016’, ‘2017’,

       ‘2018’, ‘2019’, ‘2020’, ‘2021’, ‘2022’, ‘2023’, ‘2024’, ‘2025’]

>>  Index_descriptors=[‘Country’, ‘Subject Descriptor’, ‘Units’, ‘Scale’,’Estimates Start After’]

Now, I mess around a bit with those dictionaries and with indexing that big dataset. In a moment, you will understand why I do so. I go:

>> Subject_Descriptors=pd.unique(WEO4[‘Subject Descriptor’]) # I made a data frame out of unique index labels in the column ‘Subject Descriptor’.  I get:

>> array([‘Gross domestic product, constant prices’,

       ‘Gross domestic product, current prices’,

       ‘Gross domestic product, deflator’,

       ‘Gross domestic product per capita, constant prices’,

       ‘Gross domestic product per capita, current prices’,

       ‘Output gap in percent of potential GDP’,

       ‘Gross domestic product based on purchasing-power-parity (PPP) share of world total’,

       ‘Implied PPP conversion rate’, ‘Total investment’,

       ‘Gross national savings’, ‘Inflation, average consumer prices’,

       ‘Inflation, end of period consumer prices’,

       ‘Six-month London interbank offered rate (LIBOR)’,

       ‘Volume of imports of goods and services’,

       ‘Volume of Imports of goods’,

       ‘Volume of exports of goods and services’,

       ‘Volume of exports of goods’, ‘Unemployment rate’, ‘Employment’,

       ‘Population’, ‘General government revenue’,

       ‘General government total expenditure’,

       ‘General government net lending/borrowing’,

       ‘General government structural balance’,

       ‘General government primary net lending/borrowing’,

       ‘General government net debt’, ‘General government gross debt’,

       ‘Gross domestic product corresponding to fiscal year, current prices’,

       ‘Current account balance’], dtype=object)

In other words, each country is characterized in the WEOOct2020 database with the above characteristics. I need to group and extract data so as to have those variables separated. The kind of transformation which I want to nail down is to transpose those variables with years. In the source version of WEOOct2020, years are separate columns that cut across three basic indexes: countries, for one, the above presented subject descriptors, for two, and finally the indexes of units and scale. The latter is important to the extent that most macroeconomic aggregates are presented either as absolute amounts or as percentages of the country’s GDP. Probably you remember from math classes at school, and those of physics and chemistry too, actually, that confusing units of measurement is a cardinal sin in science. What I want to do is to flip the thing on its side. I want each country to be associated with a series of index labels corresponding to years, and variables associated with proper units of measurement being the columns of the dataset.

In other words, now, years are the main quantitative categories of the WEOOct202 data frame, and categorial variables are index labels, or phenomenological units of observation. I want these two to change places, as it essentially should be: categorial variables should become phenomenological categories, and years should gracefully step down to the status of observational units.

As I don’t know what to do, I reach to what I know how to do, i.e. to creating some sort of dictionaries out of index labels. What I did for subject descriptors, I do for units,     

>> Units=pd.unique(WEO4[‘Units’])

…which yields:

array([‘National currency’, ‘Percent change’, ‘U.S. dollars’,

       ‘Purchasing power parity; international dollars’, ‘Index’,

       ‘Purchasing power parity; 2017 international dollar’,

       ‘Percent of potential GDP’, ‘Percent’,

       ‘National currency per current international dollar’,

       ‘Percent of GDP’, ‘Percent of total labor force’, ‘Persons’],

      dtype=object)

and…

>> Countries=pd.unique(WEO4[‘Country’])

…which yields:

array([‘Afghanistan’, ‘Albania’, ‘Algeria’, ‘Angola’,

       ‘Antigua and Barbuda’, ‘Argentina’, ‘Armenia’, ‘Aruba’,

       ‘Australia’, ‘Austria’, ‘Azerbaijan’, ‘The Bahamas’, ‘Bahrain’,

       ‘Bangladesh’, ‘Barbados’, ‘Belarus’, ‘Belgium’, ‘Belize’, ‘Benin’,

       ‘Bhutan’, ‘Bolivia’, ‘Bosnia and Herzegovina’, ‘Botswana’,

       ‘Brazil’, ‘Brunei Darussalam’, ‘Bulgaria’, ‘Burkina Faso’,

       ‘Burundi’, ‘Cabo Verde’, ‘Cambodia’, ‘Cameroon’, ‘Canada’,

       ‘Central African Republic’, ‘Chad’, ‘Chile’, ‘China’, ‘Colombia’,

       ‘Comoros’, ‘Democratic Republic of the Congo’, ‘Republic of Congo’,

       ‘Costa Rica’, “CÙte d’Ivoire”, ‘Croatia’, ‘Cyprus’,

       ‘Czech Republic’, ‘Denmark’, ‘Djibouti’, ‘Dominica’,

       ‘Dominican Republic’, ‘Ecuador’, ‘Egypt’, ‘El Salvador’,

       ‘Equatorial Guinea’, ‘Eritrea’, ‘Estonia’, ‘Eswatini’, ‘Ethiopia’,

       ‘Fiji’, ‘Finland’, ‘France’, ‘Gabon’, ‘The Gambia’, ‘Georgia’,

       ‘Germany’, ‘Ghana’, ‘Greece’, ‘Grenada’, ‘Guatemala’, ‘Guinea’,

       ‘Guinea-Bissau’, ‘Guyana’, ‘Haiti’, ‘Honduras’, ‘Hong Kong SAR’,

       ‘Hungary’, ‘Iceland’, ‘India’, ‘Indonesia’,

       ‘Islamic Republic of Iran’, ‘Iraq’, ‘Ireland’, ‘Israel’, ‘Italy’,

       ‘Jamaica’, ‘Japan’, ‘Jordan’, ‘Kazakhstan’, ‘Kenya’, ‘Kiribati’,

       ‘Korea’, ‘Kosovo’, ‘Kuwait’, ‘Kyrgyz Republic’, ‘Lao P.D.R.’,

       ‘Latvia’, ‘Lebanon’, ‘Lesotho’, ‘Liberia’, ‘Libya’, ‘Lithuania’,

       ‘Luxembourg’, ‘Macao SAR’, ‘Madagascar’, ‘Malawi’, ‘Malaysia’,

       ‘Maldives’, ‘Mali’, ‘Malta’, ‘Marshall Islands’, ‘Mauritania’,

       ‘Mauritius’, ‘Mexico’, ‘Micronesia’, ‘Moldova’, ‘Mongolia’,

       ‘Montenegro’, ‘Morocco’, ‘Mozambique’, ‘Myanmar’, ‘Namibia’,

       ‘Nauru’, ‘Nepal’, ‘Netherlands’, ‘New Zealand’, ‘Nicaragua’,

       ‘Niger’, ‘Nigeria’, ‘North Macedonia’, ‘Norway’, ‘Oman’,

       ‘Pakistan’, ‘Palau’, ‘Panama’, ‘Papua New Guinea’, ‘Paraguay’,

       ‘Peru’, ‘Philippines’, ‘Poland’, ‘Portugal’, ‘Puerto Rico’,

       ‘Qatar’, ‘Romania’, ‘Russia’, ‘Rwanda’, ‘Samoa’, ‘San Marino’,

       ‘S„o TomÈ and PrÌncipe’, ‘Saudi Arabia’, ‘Senegal’, ‘Serbia’,

       ‘Seychelles’, ‘Sierra Leone’, ‘Singapore’, ‘Slovak Republic’,

       ‘Slovenia’, ‘Solomon Islands’, ‘Somalia’, ‘South Africa’,

       ‘South Sudan’, ‘Spain’, ‘Sri Lanka’, ‘St. Kitts and Nevis’,

       ‘St. Lucia’, ‘St. Vincent and the Grenadines’, ‘Sudan’, ‘Suriname’,

       ‘Sweden’, ‘Switzerland’, ‘Syria’, ‘Taiwan Province of China’,

       ‘Tajikistan’, ‘Tanzania’, ‘Thailand’, ‘Timor-Leste’, ‘Togo’,

       ‘Tonga’, ‘Trinidad and Tobago’, ‘Tunisia’, ‘Turkey’,

       ‘Turkmenistan’, ‘Tuvalu’, ‘Uganda’, ‘Ukraine’,

       ‘United Arab Emirates’, ‘United Kingdom’, ‘United States’,

       ‘Uruguay’, ‘Uzbekistan’, ‘Vanuatu’, ‘Venezuela’, ‘Vietnam’,

       ‘West Bank and Gaza’, ‘Yemen’, ‘Zambia’, ‘Zimbabwe’], dtype=object)

Once again, I don’t really know what I am doing. I just intuitively look for some sort of landmarks in that landscape of data. By the way, this is what we all do when we don’t know what to do: we look for reliable ways to partition observable reality into categories.

Now, I want to make sure that Python has the same views as me as for what index descriptors are in that dataset. I go:

>> pd.MultiIndex.from_frame(WEO4[Index_descriptors])

… and I get:

MultiIndex([(‘Afghanistan’, …),

            (‘Afghanistan’, …),

            (‘Afghanistan’, …),

            (‘Afghanistan’, …),

            (‘Afghanistan’, …),

            (‘Afghanistan’, …),

            (‘Afghanistan’, …),

            (‘Afghanistan’, …),

            (‘Afghanistan’, …),

            (‘Afghanistan’, …),

            …

            (   ‘Zimbabwe’, …),

            (   ‘Zimbabwe’, …),

            (   ‘Zimbabwe’, …),

            (   ‘Zimbabwe’, …),

            (   ‘Zimbabwe’, …),

            (   ‘Zimbabwe’, …),

            (   ‘Zimbabwe’, …),

            (   ‘Zimbabwe’, …),

            (   ‘Zimbabwe’, …),

            (   ‘Zimbabwe’, …)],

           names=[‘Country’, ‘Subject Descriptor’, ‘Units’, ‘Scale’, ‘Estimates Start After’], length=8775)

Seems OK.

Now, I need to fuse somehow the index of Subject Descriptor with the Index of Units, so as to have categories ready for flipping. I keep sort of feeling my way forward, rather than seeing it clearly. Love it, actually. I create an empty data series to contain the merged indexes of ‘Subject Descriptor’ and ‘Units’:

>> Variable=pd.Series(‘object’) # The ‘object’ part means that I want to have words in that data series

Now, I append and I check:

>> WEO4.append(Variable,ignore_index=True)

Aaaand… it doesn’t work. When I check ‘WEO4.info()’, I get the list of columns I had before, without the ‘Variable’. In other words, Python acknowledged that I want to append that columns, and it sort of appended, but just sort of. There is that thing I have already learnt with Python: there is a huge difference between having sort of expected output, on the one hand, and having it 100%, on the other hand. The one hand is bloody frustrating.  

I try another trick, the ‘df.insert’ command. I do:

>> WEO4.insert(1,’Variable’,’ ‘)

I check with ‘WEO4.info()’ aaaaand….this time, it worked sort of. I get the new column ‘Variable’, yes, and I have all my numerical columns, the one with ‘Year’ headers, turned back into the ‘object’ format. I f**king love programming. I do:

>> for i in range(0,len(WEO4.columns)):

    WEO4.iloc[:,i]=pd.to_numeric(WEO4.iloc[:,i], errors=’ignore’)

… and I check with ‘WEO4.info()’ once again. Victory: numerical is back to numerical.

Now, I am looking for a method to sort of concatenate smartly the contents of two incumbent columns, namely ‘Subject Descriptor’ and ‘Units’, into the new vessel, i.e. the column ‘Variable’. I found the simplest possible method, which is straightforward addition:

>> WEO4[“Variable”]=WEO4[“Subject Descriptor”]+WEO4[“Units”]

I typed it, I executed, and, as strange as it seems, Python seems to be OK with that. Well, after all, Python is a language, and languages have that thing: they add words to each other. It is called ‘making sentences’. Cool. I check by creating an array of unique values in the index labels of ‘Variable:

>> Variables=pd.unique(WEO4[‘Variable’])

I check by just typing:

>> Variables

… and running it as a command. I get:

array([‘Gross domestic product, constant pricesNational currency’,

       ‘Gross domestic product, constant pricesPercent change’,

       ‘Gross domestic product, current pricesNational currency’,

       ‘Gross domestic product, current pricesU.S. dollars’,

       ‘Gross domestic product, current pricesPurchasing power parity; international dollars’,

       ‘Gross domestic product, deflatorIndex’,

       ‘Gross domestic product per capita, constant pricesNational currency’,

       ‘Gross domestic product per capita, constant pricesPurchasing power parity; 2017 international dollar’,

       ‘Gross domestic product per capita, current pricesNational currency’,

       ‘Gross domestic product per capita, current pricesU.S. dollars’,

       ‘Gross domestic product per capita, current pricesPurchasing power parity; international dollars’,

       ‘Output gap in percent of potential GDPPercent of potential GDP’,

       ‘Gross domestic product based on purchasing-power-parity (PPP) share of world totalPercent’,

       ‘Implied PPP conversion rateNational currency per current international dollar’,

       ‘Total investmentPercent of GDP’,

       ‘Gross national savingsPercent of GDP’,

       ‘Inflation, average consumer pricesIndex’,

       ‘Inflation, average consumer pricesPercent change’,

       ‘Inflation, end of period consumer pricesIndex’,

       ‘Inflation, end of period consumer pricesPercent change’,

       ‘Six-month London interbank offered rate (LIBOR)Percent’,

       ‘Volume of imports of goods and servicesPercent change’,

       ‘Volume of Imports of goodsPercent change’,

       ‘Volume of exports of goods and servicesPercent change’,

       ‘Volume of exports of goodsPercent change’,

       ‘Unemployment ratePercent of total labor force’,

       ‘EmploymentPersons’, ‘PopulationPersons’,

       ‘General government revenueNational currency’,

       ‘General government revenuePercent of GDP’,

       ‘General government total expenditureNational currency’,

       ‘General government total expenditurePercent of GDP’,

       ‘General government net lending/borrowingNational currency’,

       ‘General government net lending/borrowingPercent of GDP’,

       ‘General government structural balanceNational currency’,

       ‘General government structural balancePercent of potential GDP’,

       ‘General government primary net lending/borrowingNational currency’,

       ‘General government primary net lending/borrowingPercent of GDP’,

       ‘General government net debtNational currency’,

       ‘General government net debtPercent of GDP’,

       ‘General government gross debtNational currency’,

       ‘General government gross debtPercent of GDP’,

       ‘Gross domestic product corresponding to fiscal year, current pricesNational currency’,

       ‘Current account balanceU.S. dollars’,

       ‘Current account balancePercent of GDP’], dtype=object)

Cool. It seems to have worked.

Mathematical distance

I continue learning Python as regards data analysis. I have a few thoughts on what I have already learnt, and a new challenge, namely to repeat the same thing with another source of data, namely the World Economic Outlook database, published by the International Monetary Fund (https://www.imf.org/en/Publications/WEO/weo-database/2020/October ). My purpose is to use that data in the same way as I used that from Penn Tables 9.1 (see ‘Two loops, one inside the other’, for example), namely to run it through a digital intelligent structure consisting of a double algorithmic loop.

First things first, I need to do what I promised to do in Two loops, one inside the other, that is to test the cognitive value of the algorithm I presented there. By the way, as I keep working with algorithms known as ‘artificial intelligence’, I am more and more convinced that the term ‘artificial neural networks’ is not really appropriate. I think that talking about artificial intelligent structure is much closer to reality. Giving the name of ‘neurons’ to particular fragments of the algorithm reflects the properties of some of those neurons, I get it. Yet, the neurons of a digital technology are the micro-transistors in the CPU or in the GPU. Yes, micro-transistors do what neurons do in our brain: they fire conditionally and so they produce neural signals. Algorithms of AI can be run on any computer with proper software. AI is software, not hardware.

Yes, I know I’m ranting. This is how I am gathering intellectual speed for my writing. Learning to program in Python has led me to a few realizations about the digital intelligent structures I am working with, as simulators of collective intelligence in human societies. Algorithms are different from equations in the sense that algorithms do things, whilst equations represent things. When I want an algorithm to do the things represented with equations, I need functional coherence between commands. A command needs data to work on, and it is a good thing if I can utilize the data it puts out. A chain of commands is functional, when earlier commands give accurate input to later commands, and when the final output of the last command can be properly stored and utilized. On the other hand, equations don’t need data to work, because equations don’t work. They just are.

I can say my equations are fine when they make sense logically. On the other hand, I can be sure my algorithm works the way it is supposed to work, when I can empirically prove its functionality by testing it. Hence, I need a method of testing it and I need to be sure the method in itself is robust. Now, I understand why the hell in all the tutorials which I could find as regards programming in Python there is that ‘print(output)’ command at the end of each algorithm. Whatever the output is, printing it, i.e. displaying it on the screen, is the most elementary method of checking whether that output is what I expect it to be. By the way, I have made my own little discovery about the usefulness of the ‘print()’ command. In looping algorithms, which, by nature, are prone to looping forever if the range of iterations is not properly defined, I put ‘print(‘Finished’)’ at the very end of the code. When I see ‘Finished’ printed in the line below, I can be sure the thing has done the work it was supposed to do.

Good, I was supposed to write about the testing of my algorithm. How do I test? I start by taking small pieces of the algorithm and checking the kind of output they give. By doing that, I modified the algorithm from ‘Two loops, one inside the other’, into the form you can see below:

That’s the preliminary part: importing libraries and data for analysis >>

In [1]: import numpy as np

   …: import pandas as pd

   …: import os

   …: import math

In [2]: PWT=pd.DataFrame(pd.read_csv(‘PWT 9_1 no empty cells.csv’,header=0)) # PWT 9_1 no empty cells.csv is a CSV version of the database I made with non-empty observations in the Penn Tables 9.1 database

Now, I extract the purely numerical columns, into another data frame, which I label ‘PWT_Numerical’

In [3]: Variables=[‘rgdpe’, ‘rgdpo’, ‘pop’, ’emp’, ’emp / pop’, ‘avh’,

   …:        ‘hc’, ‘ccon’, ‘cda’, ‘cgdpe’, ‘cgdpo’, ‘cn’, ‘ck’, ‘ctfp’, ‘cwtfp’,

   …:        ‘rgdpna’, ‘rconna’, ‘rdana’, ‘rnna’, ‘rkna’, ‘rtfpna’, ‘rwtfpna’,

   …:        ‘labsh’, ‘irr’, ‘delta’, ‘xr’, ‘pl_con’, ‘pl_da’, ‘pl_gdpo’, ‘csh_c’,

   …:        ‘csh_i’, ‘csh_g’, ‘csh_x’, ‘csh_m’, ‘csh_r’, ‘pl_c’, ‘pl_i’, ‘pl_g’,

   …:        ‘pl_x’, ‘pl_m’, ‘pl_n’, ‘pl_k’]

In [4]: PWT_Numerical=pd.DataFrame(PWT[Variables])

My next step is to practice with creating dictionaries out of column names in my data frame

In [5]: Names_Output_Data=[]

   …: for i in range(42):

   …:     Name_Output_Data=PWT_Numerical.iloc[:,i].name

   …:     Names_Output_Data.append(Name_Output_Data)

I start coding the intelligent structure. I start by defining empty lists, to store data which the intelligent structure produces.

In [6]: ER=[]

   …: Transformed=[]

   …: MEANS=[]

   …: EUC=[]

I define an important numerical array in NumPy: the vector of mean expected values in the variables of PWT_Numerical.

   …: Source_means=np.array(PWT_Numerical.mean())

I open the big external loop of my intelligent structure. This loop is supposed to produce as many alternative intelligent structures as there are variables in my PWT_Numerical data frame.

   …: for i in range(42):

   …:     Name_Output_Data=PWT_Numerical.iloc[:,i].name

   …:     Names_Output_Data.append(Name_Output_Data)

   …:     Output=pd.DataFrame(PWT_Numerical.iloc[:,i]) # I make an output data frame

   …:     Mean=Output.mean()

   …:     MEANS.append(Mean) # I store the expected mean of each output variable in a separate list.

   …:     Input=pd.DataFrame(PWT_Numerical.drop(Output,axis=1)) # I make an input data frame, coupled with output

   …:     Input_STD=pd.DataFrame(Input/Input.max(axis=0)) # I standardize input data over the respective maximum of each variable

   …:     Input_Means=pd.DataFrame(Input.mean()) # I prepare two data frames sort of for later: one with the vector of means…

   …:     Input_Max=pd.DataFrame(Input.max(axis=0)) #… and another one with the vector of maximums

Now, I put in motion the intelligent structure strictly speaking: a simple perceptron, which…

   …:     for j in range(10): # … is short, for testing purposes, just 10 rows in the source data

   …:         Input_STD_randomized=np.array(Input_STD.iloc[j])*np.random.rand(41) #… sprays the standardized input data with random weights

   …:         Input_STD_summed=Input_STD_randomized.sum(axis=0) # … and then sums up sort of ∑(input variable *random weight).

   …:         T=math.tanh(Input_STD_summed) # …computes the hyperbolic tangent of summed randomized input. This is neural activation.

   …:         D=1-(T**2) # …computes the local first derivative of that hyperbolic tangent

   …:         E=(Output.iloc[j]-T)*D # … computes the local error of estimating the value of output variable, with input data neural-activated with the function of hyperbolic tangent

   …:         E_vector=np.array(np.repeat(E,41)) # I spread the local error into a vector to feed forward

   …:         Next_row_with_error=Input_STD.iloc[j+1]+E_vector # I feed the error forward

   …:         Next_row_DESTD=Next_row_with_error*Input.max(axis=0) # I destandardize

   …:         ER.append(E) # I store local errors in the list ER

   …:         ERROR=pd.DataFrame(ER) # I make a data frame out of the list ER

   …:         Transformed.append(Next_row_with_error) # I store the input values transformed by the perceptron (through the forward feed of error), in the list Transformed

   …:     TR=pd.DataFrame(Transformed) # I turn the Transformed list into a data frame

   …:     MEAN_TR=pd.DataFrame(TR.mean()) # I compute the mean values of transformed input and store them in a data frame. They are still mean values of standardized data.

   …:     MEAN_TR_DESTD=pd.DataFrame(MEAN_TR*Input_Max) # I destandardise

   …: MEANS_DF=pd.DataFrame(MEANS)

   …: print(MEANS)

   …: print(‘Finished’)

The general problem which I encounter with that algorithm is essentially that of reading correctly and utilizing the output, or, at least, this is how I understand that problem. First, I remind the general hypothesis which I want to test and explore with that algorithm presented above. Here it comes: for a given set of phenomena, informative about the state of a human social structure, and observable as a dataset of empirical values in numerical variables, there is a subset of variables which inform about the ethical and functional orientation of that human social structure; orientation manifests as relatively the least significant transformation, which the original dataset needs to undergo in order to minimize error in estimating the orientation-informative variable as output, when the remaining variables are used as input.

When the empirical dataset in question is being used as training set for an artificial neural network of the perceptron type, i.e. a network which tests for the optimal values in the input variables, for minimizing the error in estimating the output variable, such neural testing transforms the original dataset into a specific version thereof. I want to know how far away  from the original empirical dataset  does the specific transformation, oriented on a specific output, go. I measure that mathematical distance as the Euclidean distance between the vector of mean expected values in the transformed dataset, and the original one.

Therefore, I need two data frames in Pandas, or two arrays in NumPy, one containing the mean expected values of the original input data, the other storing mean expected values of the transformed dataset. Here is where my problems start, with the algorithm presented above. The ‘TR’ data frame has a different shape and structure than the ‘Input’ data frame, from which, technically, it is derived.  The Input data frame has 41 columns, and the TR has 42 columns. Besides, one column from ‘Input’, the ‘rgdpe’, AKA real GDP on the final consumption side, moves from being the first column in ‘Input’ to being the last ‘column’ in ‘TR’. For the moment, I have no clue what’s going on at that level. I even checked the algorithm with a debugger, available with the integrated development environment called Spyder (https://www.spyder-ide.org ). Technically, as far as the grammar of Python is concerned, the algorithm is OK. Still, it produces different than expected vectors of mean expected values in transformed data. I don’t even know where to start looking for a solution.    

There is one more thing I want to include in this algorithm, which I have already been doing in Excel. At each row of transformed data, thus at each ‘Next_row_with_error’, I want to add a mirroring row of mean Euclidean distance from each individual variable to all the remaining ones. It is a measure of internal coherence in the process of learning through trial and error, and I already know, having learnt it by trial and error, that including that specific metric, and feeding it forward together with the error, changes a lot in the way a perceptron learns.    

Two loops, one inside the other

I am developing my skills in programming by attacking the general construct of Markov chains and state space. My theory on the bridging between collective intelligence in human societies and artificial neural networks as simulators thereof is that both are intelligent structures. I assume that they learn by producing many alternative versions of themselves whilst staying structurally coherent, and they pitch each such version against a desired output, just to see how fit that particular take on existence is, regarding the requirements in place.  

Mathematically, that learning-by-doing is a Markov chain of states, i.e. a sequence of complex states, described by a handful of variables, such that each consecutive state in the sequence is a modification of the preceding state, through a logically coherent σ-algebra. My so-far findings suggest that orienting the intelligent structure on specific outcomes, out of all those available, is crucial for the path of learning that structure takes. In other words, the general hypothesis I am sniffing around and digging into is that the way an intelligent structure learns is principally determined by the desired outcomes which the structure is after, more than by the exact basket of inputs it uses. Stands to reason, for a neural network: the thing optimises inputs so as to make it fit to the outcome it seeks to get as close to as possible.  

As I am taking real taste in stepping out of my cavern, I have installed Anaconda on my computer, from https://www.anaconda.com/products/individual/download-success . When I use Anaconda, I use the same JupyterLab online functionality which I have been using so far, with one difference. Anaconda allows me to create a user account with JupyterLab, and to have all my work stored on that account. Probably, there are some storage limits, yet the thing is practical. 

Anyway, I want to program in Python, just as I do it in Excel, intelligent structures able to emulate the collective intelligence of human societies. A basic finding of mine, in the so-far research, is that intelligent structures alter their behaviour significantly depending on the outcome they pursue. The initial landscape I start operating in is akin a junkyard of information. I go to the website of World Bank, for example, I mean the one with freely available data, AKA https://data.worldbank.org , and I start rummaging. Quality of life, size of economies, headcount of populations… What else? Oh, yes, there are things about education, energy consumption and whatnot. All that stuff just piled up nicely, each item easy to retrieve, and yet, how does it all make sense together? My take on the thing is that there is stuff going on, like all the time and everywhere. We are part of that ongoing stuff, actually. Out of that stream of happening, we perceptually single out phenomenological cuts , and we isolate those specific cuts because we are able to measure them with some kind of gauge. Data-driven observation of ourselves in the world is closely connected to our science of measuring and counting stuff. Have you noticed that a basic metric, i.e. how many of us is there around, can take a denominator of one – when we count the population of a city – or a denominator of 10 000, when we are interested in the incidence of criminality. 

Each quantitative variable I can observe and download the dataset of from https://data.worldbank.org  comes out of that complex process of collective cognition, resembling a huge bunch of psychos walking around with rulers and abacuses, trying to measure everything they perceive. I use data as phenomenological description of both the reality those psychos (me included) live in, and the way they measure that reality. I want to check which among those quantitative variables are particularly suitable to represent the things we are really after, our collectively desired outcomes. The method I use to do it consists in producing as many variations of the original dataset as I have variables. Each variation of the original dataset has one variable singled out as output, and the remaining ones are input. I run such variation through a simple neural network – the simpler, the better – where standardised, randomly weighed and neurally activated input gets compared with the pre-set output. I measure the mean expected values of all the variables in such a transformation, i.e. when I run it through 3000 experimental rounds, I measure those means over the same 3000 rounds. I compute the Euclidean distance between each such vector of means and its cousin computed for the original dataset. I assume that, with rigorously the same logical structure of the neural network, those variations differ from each other just by the output variable they are pegged on. When I say ‘pegged’, by the way, I mean that the output variable is not subject to random weighing, i.e. it is not being experimented with. It comes exogenously, and is taken as it is. 

I noticed that each time I do that procedure, with whatever set of variables I take, one or two among them, when taken as output ones, produce variations much closer to the original dataset that other, in terms of Euclidean distance. It looks as if the neural network, when pegged on those particular variables, emulated a process of adaptation particularly similar to what is represented by the original empirical data. 

Now, I want to learn how to program, in Python, the production of alternative ‘input <> output’  couplings out of a source dataset. I already know the general drill for producing just one such coupling. Once I have my dataset read out of a CSV file into a Data Frame in Python Pandas, I start with creating a dictionary of all the numerical columns:

>> dict_numerical = [‘numerical_column1’, ‘numerical_column2’, …, ‘numerical column_n’]

A simple way of doing that, with large data frames, is to type in Python:

>> df.columns

… and it yields a string of labels in quotation marks ‘’, separated with commas. I just copy that lot , without the non-numerical columns, into the square brackets of dict_numerical = […], and Bob’s my uncle. 

Then I make a strictly numerical version of my database, by:

>> df_numerical = pd.DataFrame(df[dict_numerical])

By the way, each time I produce a new data frame, I check its structure with commands ‘df.info()‘ and ‘df.describe()’. At my neophytic level of programming, I want to make sure that what I have in a strictly numerical database is strictly numerical data, i.e. the ‘float64’ type. Here, one hint: when you convert your data from an original Excel file, pay attention to having your decimal point as a point, i.e. as ‘0.0’, not as a comma. With a comma, the Pandas reader tends to interpret such data by default as ‘object’. Annoying. 

Once I have that numerical data frame in place, I make another dictionary of the type:

>> dict_for_Input_pegged_on_X_as_output = [‘numerical_input_column1’, ‘numerical_input_column2’, …, ‘numerical_input_column_k’]

… where k = n -1, of course, and the 1 corresponds to the variable X, supposed to be the output one. 

I use that dictionary to split df_numerical:

>> df_output_X = df_numerical[‘numerical_column_X’]

>> df_input_for_X = df_numerical[dict_for_Input_pegged_on_X_as_output]     

I would like to automatise the process. It means I need a loop. I am looping over a range of numerical columns df_numerical. Let’s dance. I start routinely, in my Anaconda-Jupyter Lab-powered notebook. By the way, I noticed an interesting practical feature of Jupyter Lab. When you start it directly from its website https://jupyter.org , the notebook you can use has somehow limited functionality as compared to the notebook you can create when accessing Jupyter Lab from the Anaconda app on your computer. In the latter case you can create an account with Jupyter Lab, with a very useful functionality of mirroring the content of your cloud account on your hard drive. I know, I know: we use the cloud so as not to collect rubbish on our own disk. Still, Python files are small, they take little space, and I discovered that this mirroring stuff is really useful. 

I open up with importing the libraries I think I will need:

>> import numpy as np

>> import pandas as pd

>> import math

>> import os

As I am learning new stuff, I prefer taking known stuff as my data. Once again, I use a dataset which I made out of Penn Tables 9.1., by kicking out all the rows with empty cells [see: Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), “The Next Generation of the Penn World Table” American Economic Review, 105(10), 3150-3182, www.ggdc.net/pwt ].

I already have that dataset in my working directory. By the way, when you install Anaconda on a MacBook, its working directory is by default the root directory of the user’s profile. For the moment, I keep ip that way. Anyway, I have that dataset and I read it into a Pandas dataframe:

>> PWT=pd.DataFrame(pd.read_csv(‘PWT 9_1 no empty cells.csv’,header=0))

I create my first dictionaries. I type:

>> PWT.columns

… which yields:

Index([‘country’, ‘year’, ‘rgdpe’, ‘rgdpo’, ‘pop’, ’emp’, ’emp / pop’, ‘avh’,

       ‘hc’, ‘ccon’, ‘cda’, ‘cgdpe’, ‘cgdpo’, ‘cn’, ‘ck’, ‘ctfp’, ‘cwtfp’,

       ‘rgdpna’, ‘rconna’, ‘rdana’, ‘rnna’, ‘rkna’, ‘rtfpna’, ‘rwtfpna’,

       ‘labsh’, ‘irr’, ‘delta’, ‘xr’, ‘pl_con’, ‘pl_da’, ‘pl_gdpo’, ‘csh_c’,

       ‘csh_i’, ‘csh_g’, ‘csh_x’, ‘csh_m’, ‘csh_r’, ‘pl_c’, ‘pl_i’, ‘pl_g’,

       ‘pl_x’, ‘pl_m’, ‘pl_n’, ‘pl_k’],

      dtype=’object’)

…and I create the dictionary of quantitative variables:

>> Variables=[‘rgdpe’, ‘rgdpo’, ‘pop’, ’emp’, ’emp / pop’, ‘avh’,

       ‘hc’, ‘ccon’, ‘cda’, ‘cgdpe’, ‘cgdpo’, ‘cn’, ‘ck’, ‘ctfp’, ‘cwtfp’,

       ‘rgdpna’, ‘rconna’, ‘rdana’, ‘rnna’, ‘rkna’, ‘rtfpna’, ‘rwtfpna’,

       ‘labsh’, ‘irr’, ‘delta’, ‘xr’, ‘pl_con’, ‘pl_da’, ‘pl_gdpo’, ‘csh_c’,

       ‘csh_i’, ‘csh_g’, ‘csh_x’, ‘csh_m’, ‘csh_r’, ‘pl_c’, ‘pl_i’, ‘pl_g’,

       ‘pl_x’, ‘pl_m’, ‘pl_n’, ‘pl_k’]

The ‘Variables’ dictionary serves me to mutate the ‘PWT’ dataframe into its close cousin, obsessed with numbers, namely into ‘PWT_Numerical’:

>> PWT_Numerical = pd.DataFrame(PWT[Variables])

I quickly check the PWT_Numerical’s driving licence, by typing ‘PWT_Numerical.info()’ and  ‘PWT_Numerical.shape’. All is well, data is in the ‘float64’ format, there are 42 columns and 3006 rows, the guy is cleared to go.

Once I have that nailed down, I mess around a bit with creating names for my cloned datasets. I practice with the following loop:

>> for i in range(42):

    print(“Input_for_”+PWT_Numerical.iloc[:,i].name) 

It yields a list of names for input databases in various ‘input <> output’ configurations of my experiment with the PWT 9.1 dataset. The ‘print’ command gives a string of 42 names: Input_for_rgdpe, Input_for_rgdpo, Input_for_pop etc. 

In my next step, I want to make that outcome durable. The ‘print’ command just prints the output of the loop, it does not store it in any logical structure. The output is gone as soon as it is printed. I create a loop that makes a dictionary, this time with names of output data frames:

>> Names_Output_Data=[] # Here, I create an empty dictionary

>> for i in range(42): # I design the loop

    >> Name_Output_Data=PWT_Numerical.iloc[:,i].name # I create a mechanism for generating strings to fill the dictionary up. 

    >> Names_Output_Data.append(Name_Output_Data) # This is the mechanism of appending   the dictionary with names generated in the previous command 

I check the result by typing the name of the dictionary – ‘Names_Output_Data’ – and executing (Shift + Enter in Jupyter Lab). It yields a full dictionary, filled with column names from PWT_Numerical. 

Now,  pass to designing my Markov chain of states, i.e. into making an intelligent structure, which produces many alternative versions of itself and tests them for fitness to meet a pre-defined desired outcome. In my neophyte’s logic, I see it as two loops, one inside the other. 

The big, external loop is the one which clones the initial ‘PWT_Numerical’ into pairs of data frames of the style: ’Input variables’ plus ‘Output variable’. I make as many such cloned pairs as there are numerical variables in PWT_Numerical, i.e. 42. Thus, my loop opens up as ‘for i in range(42):’. Inside each iteration of that loop, there is an internal loop of passing the input variables  through a very simple perceptron, assessing the error in estimating the output variable, and then feeding the error forward. Now, I will present below the entire code for those two loops, and then discuss what works, what doesn’t, and what I have no idea how to check whether it works or not. The code is grammatically correct in Python, i.e. it does not yield any error message when put to execution (Shift + Enter in JupyterLab, by the way).  After I present the entire code, I will discuss, further below, its particular parts. Anyway, here it is:

>> List_of_Output_DB=[]

>>Names_Output_Data=[]

>>MEANS=[]

>> Source_means=np.array(PWT_Numerical.mean())

>> EUC=[]

>>for i in range(42):

    >> Name_Output_Data=PWT_Numerical.iloc[:,i].name

    >> Names_Output_Data.append(Name_Output_Data)

    >> Output=pd.DataFrame(PWT_Numerical.iloc[:,i])    

    >> Mean=Output.mean()

   >> MEANS.append(Mean)

    >> Input=pd.DataFrame(PWT_Numerical.drop(Output,axis=1)) 

   >> Input_STD=pd.DataFrame(Input/Input.max(axis=0))

    >> ER=[]

    >> Transformed=[]

      >> for j in range(30):        

>> Input_STD_randomized=Input.iloc[j]*np.random.rand(41)

        >> Input_STD_summed=Input_STD_randomized.sum(axis=0)

        >> T=math.tanh(Input_STD_summed)

        >> D=1-(T**2)

        >> E=(Output.iloc[j]-T)*D

        >> E_vector=np.array(np.repeat(E,41))        

>> Next_row_with_error=Input_STD.iloc[j+1]+E_vector

>> Next_row_DESTD=Next_row_with_error*Input.max(axis=0)

        >> ER.append(E)

        >> ERROR=pd.DataFrame(ER)

        >> Transformed.append(Next_row_DESTD)

        >> CLONE=pd.DataFrame(Transformed).mean()

>> frames=[CLONE,MEANS[i]]

>> CLONE_Means=np.array(pd.concat(frames))

>> Euclidean=np.linalg.norm(Source_means-CLONE_Means)

>> EUC.append(Euclidean)

>> print(‘Finished’)   

Here is a shareable link to my Python file with that code inside: http://localhost:8880/lab/tree/Practice%20Dec%208%202020.ipynb  . I hope it works. 

I start explaining this code casually, from its end. This is a little trick I discovered as regards looping on datasets. Looping takes time and energy. In my struggles to learn Python, I have already managed to make a loop which kept looping forever. All I did was to call the loop as ‘for i in range PWT.index:’, without putting any ‘break’ command at the end. Yes, the index of a data frame is a finite number, yet it is also a sequence. When you don’t break explicitly the looping over that sequence, it will loop over and over again. 

Anyway, the trick. I put the command ‘print(‘Finished’)’ at the very end of the code, after all the loops. When the thing is done with being an intelligent structure at work, it simply prints ‘Finished’ in the next line. Among other things, it allows me to count the time it needs to deal with a given amount of data. As you might have already noticed, whilst I have a dataset with index = 3005 rows, I made the internal loop of the code to go just over 30 rows: ‘for j in range (30)’. The code took some 4 seconds in total to create 42 big loops (‘for i in range (42)’) , and then to loop over 30 rows of data inside each of them. It gives like 42*30 = 1260 experimental rounds in 10 seconds, thus something like 0,0079 seconds per one round. If I took the full dataset of 3005 rows, it would be like 42*3000*0,0079 = 1000 seconds, i.e. 16,6666 minutes. Satanic. I like it. 

Before opening each level of looping, I create empty lists. You can see:

>> List_of_Output_DB=[]

>>Names_Output_Data=[]

>>MEANS=[]

>> Source_means=np.array(PWT_Numerical.mean())

>> EUC=[]

… before I open the external loop, and…

  >> ER=[]

>> Transformed=[]

… before the internal loop.

I noticed that I create those empty lists in a loop, essentially. This is more than just a play on words. When I code a loop, I have output of the loop. The loop does something, and as it does, I discover I want to store that particular outcome in some kind of repository vessel, and I go back to the lines of code before the loop opens and I add an empty list, just in case. I come up with a smart name for the   list, e.g. MEANS, which stands for the mean values of numerical variables, such as they are after being transformed by the perceptron. Mathematically, it is the most basic representation of expected state in a particular transformation of the source dataset “PWT’. 

I code it as ‘MEANS=[]’, and, once I have done that, I add a mechanism of updating a list, inside the loop. This, in turn, goes in two steps. First, I code the variable which should be stored in that list. In the case of ‘MEANS’, as this list is created before I open the big loop of 42 ‘input <> output’ mutations, I append it in that loop. Logically, is must be appended with the mean expected values of output variables in each instance of the big loop. I code it in the big loop, and before opening the internal loop, as:

>> Output=pd.DataFrame(PWT_Numerical.iloc[:,i])  # Here, I define the data frame for the output variable in this specific instance of the big loop   

>> Mean=Output.mean() # Now, I define the function to generate values, which later append the ‘MEANS’ list

    >> MEANS.append(Mean) # Finally, I append the ‘MEANS’ list with values generated in the previous line of the code. 

It is a good thing for me to write about the things I do. I have just noticed that I use two different methods of storing partial outcomes of my loops. The first one is the one I have just presented. The second one is visible in the part of code presented below, included in the internal loop ‘for j in range(number of rows experimented with)’, range(30) in the occurrence tested. 

In this situation, I need to store in some kind of repository the values of input variables transformed by the neural network, i.e. with local error from each experimental round fed forward to the next experimental round. I need to store the way my data looks under each possible orientation of the intelligent structure I assume it represents. I denote that data under the general name ‘Transformed’, and, before opening the internal loop, just at the end of the big external loop, I define an empty list: ‘Transformed=[]’, which is supposed to contain those values I want.

In other words, when I structure the big external loop, I go like: 

# Step 1: for each variables in the dataset, i.e. ‘for i in range(number of variables)’, split the overall dataset into into this variable as the output, in a separate data frame, and all the other variables grouped separately as input. These are the lines of code:

>> Output=pd.DataFrame(PWT_Numerical.iloc[:,i])  # I define the output variable 

[…]    

>> Input=pd.DataFrame(PWT_Numerical.drop(Output,axis=1)) # I drop the output from the entire dataset and I group the remaining columns as ‘Input’

# Step 2: I standardise the input data by denominating it over the respective maximums for each variable:    

>> Input_STD=pd.DataFrame(Input/Input.max(axis=0))

# Step 3: I define, at the end of the big external loop, containers for data which I want to store from each round of the big loop:

>> ER=[] # This is the list of local errors generated by the perceptron when working with each ‘Input <> Output’ configuration

    >> Transformed=[] # That’s the container for input data transformed by the perceptron 

# Step 4: I open the internal loop, with ‘for j in range(number of rows to experiment with)’, and I start by coding the computational procedure of the perceptron:

>> Input_STD_randomized=Input.iloc[j]*np.random.rand(41) # I weigh each empirical, standardised value in this specific row with a random weight

        >> Input_STD_summed=Input_STD_randomized.sum(axis=0) # I sum the randomised values from that specific row of input. This line of code together with the preceding one are equivalent to the mathematical structure ‘∑x*random’.

        >> T=math.tanh(Input_STD_summed) # I compute the hyperbolic tangent of summed, randomised input data

        >> D=1-(T**2) # I compute the local first derivative of the hyperbolic tangent

        >> E=(Output.iloc[j]-T)*D # I compute the error, as: (Expected Output minus Hyperbolic Tangent of Randomised Input) times local derivative of the Hyperbolic Tangent

        >> E_vector=np.array(np.repeat(E,41)) # I create a NumPy array, with the error repeated as many times as there are input variables.

>> Next_row_with_error=Input_STD.iloc[j+1]+E_vector # I feed the error forward. In the next experimental row ‘j+1’, error from row ‘j’ is added to the value of each standardised input variable. This is probably the most elementary representation of learning: I include into my input for the next go the knowledge about what I f**ked up in the previous go. This line creates the transformed input data I want to store later on. 

# Step 5: I collect and store information about the things my perceptron did to input data in the given j-th round of the internal loop:

>> Next_row_DESTD=Next_row_with_error*Input.max(axis=0) # I destandardise the data transformed by the perceptron. It is like translating the work of the perceptron, which operates on standardised values, back into the measurement scale proper to each variable. In a sense, I deneuralise that data. 

        >> ER.append(E) # I collect and store error in the ER list

        >> ERROR=pd.DataFrame(ER) #I transform the ER list into a data frame, which I name ‘ERROR’. I do it a few times with different data, and, quite honestly, I do it intuitively. I already know that data frames defines in Pandas are somehow handier to do statistics with than lists defined in the basic code of Python. Just as honestly: I know too little yet about programming to know whether this turn of code makes sense at all.   

        >> Transformed.append(Next_row_DESTD) # I collect and store the destandardized, transformed input data in the ‘Transformed’ list.

# Step 6: I step out of both loops, and I start putting some order in the data I generated and collected. Stepping out of both loops means that in my code, the lines presented below have no indent. They all start at the left margin, just as the definition of the big external loop.

       >> CLONE=pd.DataFrame(Transformed).mean() # I transform the ‘Transformed’ list into a data frame. Same procedure as two lines of code earlier, only now, I know why I do it. I intend to put together the mean values of destandardised input with the mean value of output, and I am going to do it by concatenation of data frames. 

    >> frames=[CLONE,MEANS[i]] # I define the data frames for concatenation. I put together mean values in the input variables, generated in this specific, i-th round of the big external loop, with the mean value of the output variable corresponding to the same i-th round. You can notice that in the full code, such as I presented it earlier in this update, at this verse of code I move back by one indent. In other words, this definition is already outside of the internal loop, and still inside the big external loop. 

    >> CLONE_Means=np.array(pd.concat(frames)) # I concatenate the data I defined in the previous line. 

    >> Euclidean=np.linalg.norm(Source_means-CLONE_Means) # Something I need for my science. I estimate the mathematical similarity between the source data set ‘PWT_Numerical’, and the data set created by the perceptron, in the given i-th round of the big external loop. I do it by computing the Euclidean distance between the respective vectors of mean expected values in this specific pair of datasets, i.e. the pair ‘source vs i-th clone’.

    >> EUC.append(Euclidean) # I collect and store information generated in the ‘Euclidean’ line. I store it in the EUC list, which I opened as empty before starting the big external loop. 

One step out of the cavern

I have made one step further in my learning of programming. I finally have learn’t at least one method of standardising numerical values in a dataset. In a moment, I will show what exact method did I nail down. First, I want to share a thought of more general nature. I learn programming in order to enrich my research on the application of artificial intelligence for simulating collective intelligence in human societies. I have already discovered the importance of libraries, i.e. ready-made pieces of code, possible to call with a simple command, and short-cutting across many verses of code which I would have to write laboriously. I mean libraries such as NumPy, Pandas, Math etc. It is very similar to human consciousness. Using pre-constructed cognitive structures, i.e. using language and culture is a turbo boost for whatever we do of things that humans are supposed to do when being a civilisation.  

Anyway, I kept working with the dataset which I had already mentioned in my earlier updates, namely a version of Penn Tables 9.1., cleaned of all the rows with empty cells [see: Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), “The Next Generation of the Penn World Table” American Economic Review, 105(10), 3150-3182, www.ggdc.net/pwt ]. Thus I started by creating an online notebook at JupyterLab (https://jupyter.org/try), with Python 3 as its kernel. Then I imported what I needed from Python in terms of ready-cooked culture, i.e. I went:

>> import numpy as np

>> import pandas as pd

>> import os

I uploaded the ‘PWT 9_1 no empty cells.csv’ file from my computer, and, just in case, I checked its presence in the working directory, with >> os.listdir(). I read the contents of the file into a Pandas Data Frame, which spells: PWT = pd.DataFrame(pd.read_csv(‘PWT 9_1 no empty cells.csv’)). Worked.  

In my next step, as I planned to mess up a bit with the columns of that dataset, I typed: PWT.columns. The thing nicely gave me back a list of columns, i.e. literally a list of labels in quotation marks [‘’]. I used that list to create a dictionary of columns with numerical values, and therefore the most interesting to me. I went:

>> Variables=[‘rgdpe’, ‘rgdpo’, ‘pop’, ’emp’, ’emp / pop’, ‘avh’,

       ‘hc’, ‘ccon’, ‘cda’, ‘cgdpe’, ‘cgdpo’, ‘cn’, ‘ck’, ‘ctfp’, ‘cwtfp’,

       ‘rgdpna’, ‘rconna’, ‘rdana’, ‘rnna’, ‘rkna’, ‘rtfpna’, ‘rwtfpna’,

       ‘labsh’, ‘irr’, ‘delta’, ‘xr’, ‘pl_con’, ‘pl_da’, ‘pl_gdpo’, ‘csh_c’,

       ‘csh_i’, ‘csh_g’, ‘csh_x’, ‘csh_m’, ‘csh_r’, ‘pl_c’, ‘pl_i’, ‘pl_g’,

       ‘pl_x’, ‘pl_m’, ‘pl_n’, ‘pl_k’]

The ‘Variables’ dictionary served me to make a purely numerical mutation of my dataset, namely: PWTVar=pd.DataFrame(PWT[Variables]).  

I generated the fixed components of standardisation in my data, i.e. maximums, means, and standard deviations across columns in PWTVar. It looked like this: 

>> Maximums=PWTVar.max(axis=0)

>> Means=PWTVar.mean(axis=0)

>> Deviations=PWTVar.std(axis=0)

The ‘axis=0’ part means that I want to generate those values across columns, not rows. Once that done, I made my two standardisations of data from PWTVar, namely: a) standardisation over maximums, like s(x) = x/max(x) and b) standardisation by mean-reversion, where s(x) = [x – avg(x)]/std(x)]. I did it as:

>> Standardized=pd.DataFrame(PWTVar/Maximums)

>> MR=pd.DataFrame((PWTVar-Means)/Deviations)

I used here the in-built function of Python Pandas, i.e. the fact that they automatically operate data frames as matrices. When, for example, I subtract ‘Means’ from ‘PWTVar’, the one-row matrix of ‘Means’ gets subtracted from each among the 3005 rows of ‘PWTVar’ etc. I checked those two data frames with commands such as ‘df.describe()’, ’df.shape’, and df.info(), just to make sure they are what I think they are. They are, indeed. 

Standardisation allowed me to step out of my cavern, in terms of programming artificial neural networks. The next step I took was to split my numerical dataset PWTVar into one output variable, on the one hand, and all the other variables grouped as input. As output, I took a variable which, as I have already found out in my research, is extremely important in social change seen through the lens of Penn Tables 9.1. This is ‘avh’ AKA the average number of hours worked per person per year. I did:  

>> Output_AVH=pd.DataFrame(PWTVar[‘avh’])

>> Input_dict=[‘rgdpe’, ‘rgdpo’, ‘pop’, ’emp’, ’emp / pop’, ‘hc’, ‘ccon’, ‘cda’,

        ‘cgdpe’, ‘cgdpo’, ‘cn’, ‘ck’, ‘ctfp’, ‘cwtfp’, ‘rgdpna’, ‘rconna’,

        ‘rdana’, ‘rnna’, ‘rkna’, ‘rtfpna’, ‘rwtfpna’, ‘labsh’, ‘irr’, ‘delta’,

        ‘xr’, ‘pl_con’, ‘pl_da’, ‘pl_gdpo’, ‘csh_c’, ‘csh_i’, ‘csh_g’, ‘csh_x’,

        ‘csh_m’, ‘csh_r’, ‘pl_c’, ‘pl_i’, ‘pl_g’, ‘pl_x’, ‘pl_m’, ‘pl_n’,

        ‘pl_k’] 

#As you can see, ‘avh’ is absent from the ‘Input-dict’ dictionary 

>> Input = pd.DataFrame(PWT[Input_dict])

The last thing that worked, in this episode of my learning, was to multiply the ‘Input’ dataset by a matrix of random float values generated with NumPy:

>> Randomized_input=pd.DataFrame(Input*np.random.rand(3006,41)) 

## Gives an entire Data Frame of randomized values

It works again

I intend to work on iterations. My general purpose with learning to program in Python is to create my own algorithms of artificial neural networks, in line with what I have already done in that respect using just Excel. Iteration is the essence of artificial intelligence, to the extent that the latter manifests as an intelligent structure producing many alternative versions of itself. Many means one at a time over many repetitions. 

When I run my neural networks in Excel, they do a finite number of iterations. That would be a Definite Iteration in Python, thus the structure based on the ‘for’ expression. I am helping myself  with the tutorial available at https://realpython.com/python-for-loop/ . Still, as programming is supposed to enlarge my Excel-forged intellectual horizons, I want to understand and practice the ‘while’ loop in Python, thus Indefinite Iteration (https://realpython.com/python-while-loop/ ).

Anyway, programming a loop is very different from looping over multiple rows of an Excel sheet. The latter simply makes a formula repeat over many rows, whilst the former requires defining the exact operation to iterate, the input domain which the iteration takes as data, and the output dataset to store the outcome of iteration.

It is time, therefore, to describe exactly the iteration I want to program in Python. As a matter of fact, we are talking about a few different iterations. The first one is the standardisation of my source data. I can use two different ways of standardising it, depending on the neural activation function I use. The baseline method is to standardise each variable over its maximum, and then it fits every activation function I use. It is standardised value of x, AKA s(x), being calculated as s(x) = x/max(x). 

If I focus just on the hyperbolic tangent as activation function, I can use the first method, or I can standardise by mean-reversion, where s(x) = [x – avg(x)]/std(x). In a first step, I subtract from x the average expected value of x – this is the the [x – avg(x)] expression – and then I divide the resulting difference by the standard deviation of x, or std(x). 

The essential difference between those two modes of standardisation is the range of standardised values. When denominated in units of the max(x), standardised values range in 0 ≥ std(x) ≥ 1. When I standardise by mean-reversion, I have -1 ≥ std(x) ≥ 1.

The piece of programming I start that specific learning of mine with consists in transforming my source Data Frame ‘df’ into its standardised version ’s_df’ by dividing values in each column of df by their maximums. As I think of all that, it comes to my mind what I have recently learnt, namely that operations on Numpy arrays, in Python, are much faster than the same operations on data frames built with Python Pandas. I check if I can make a Data Frame out of an imported CSV file, and then turn it into a Numpy array. 

Let’s walse. I start by opening JupyterLab at https://hub.gke2.mybinder.org/user/jupyterlab-jupyterlab-demo-nocqldur/lab and creating a notebook with Python 3 as its kernel. Then, I import the libraries which I expect to use one way or another: NumPy, Pandas, Matplot, OS, and Math. In other words, I do:

>> import numpy as np

>> import pandas as pd

>> import matplotlib.pyplot as plt

>> import math

>> import os

Then, I upload a CSV file and I import it into a Data Frame. It is a database I used in my research on cities and urbanization, its name is ‘DU_DG database.csv’, and, as it is transformed from an Excel file, I take care to specify that separators are semi-columns.

>> DU_DG=pd.DataFrame(pd.read_csv(‘DU_DG database.csv’,sep=’;’)) 

The resulting Data Frame is structured as:

Index([‘Index’, ‘Country’, ‘Year’, ‘DU/DG’, ‘Population’,

       ‘GDP (constant 2010 US$)’, ‘Broad money (% of GDP)’,

       ‘urban population absolute’,

       ‘Energy use (kg of oil equivalent per capita)’, ‘agricultural land km2’,

       ‘Cereal yield (kg per hectare)’],

      dtype=’object’)

Import being successful (I just check with commands ‘DU_DG.shape’ and ‘DU_DG.head()’), I am trying to create a NumPy array. Of course, there is not much sense in translating names of countries and labels of years into a NumPy array. I try to select numerical columns ‘DU/DG’, ‘Population’, ‘GDP (constant 2010 US$)’, ‘Broad money (% of GDP)’, ‘urban population absolute’, ‘Energy use (kg of oil equivalent per capita)’, ‘agricultural land km2’, and ‘Cereal yield (kg per hectare)’, by commanding:

>> DU_DGnumeric=np.array(DU_DG[‘DU/DG’,’Population’,’GDP (constant 2010 US$)’,’Broad money (% of GDP)’,’urban population absolute’,’Energy use (kg of oil equivalent per capita)’,’agricultural land km2′,’Cereal yield (kg per hectare)’]) 

The answer I get from Python 3 is a gentle ‘f**k you!’, i.e. an elaborate error message. 

KeyError                                  Traceback (most recent call last)

/srv/conda/envs/notebook/lib/python3.7/site-packages/pandas/core/indexes/base.py in get_loc(self, key, method, tolerance)

   2656             try:

-> 2657                 return self._engine.get_loc(key)

   2658             except KeyError:

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc()

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item()

KeyError: (‘DU/DG’, ‘Population’, ‘GDP (constant 2010 US$)’, ‘Broad money (% of GDP)’, ‘urban population absolute’, ‘Energy use (kg of oil equivalent per capita)’, ‘agricultural land km2’, ‘Cereal yield (kg per hectare)’)

During handling of the above exception, another exception occurred:

KeyError                                  Traceback (most recent call last)

<ipython-input-18-e438a5ba1aa2> in <module>

—-> 1 DU_DGnumeric=np.array(DU_DG[‘DU/DG’,’Population’,’GDP (constant 2010 US$)’,’Broad money (% of GDP)’,’urban population absolute’,’Energy use (kg of oil equivalent per capita)’,’agricultural land km2′,’Cereal yield (kg per hectare)’])

/srv/conda/envs/notebook/lib/python3.7/site-packages/pandas/core/frame.py in __getitem__(self, key)

   2925             if self.columns.nlevels > 1:

   2926                 return self._getitem_multilevel(key)

-> 2927             indexer = self.columns.get_loc(key)

   2928             if is_integer(indexer):

   2929                 indexer = [indexer]

/srv/conda/envs/notebook/lib/python3.7/site-packages/pandas/core/indexes/base.py in get_loc(self, key, method, tolerance)

   2657                 return self._engine.get_loc(key)

   2658             except KeyError:

-> 2659                 return self._engine.get_loc(self._maybe_cast_indexer(key))

   2660         indexer = self.get_indexer([key], method=method, tolerance=tolerance)

   2661         if indexer.ndim > 1 or indexer.size > 1:

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc()

pandas/_libs/index.pyx in pandas._libs.index.IndexEngine.get_loc()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item()

pandas/_libs/hashtable_class_helper.pxi in pandas._libs.hashtable.PyObjectHashTable.get_item()

KeyError: (‘DU/DG’, ‘Population’, ‘GDP (constant 2010 US$)’, ‘Broad money (% of GDP)’, ‘urban population absolute’, ‘Energy use (kg of oil equivalent per capita)’, ‘agricultural land km2’, ‘Cereal yield (kg per hectare)’)

Didn’t work, obviously. I try something else. I proceed in two steps. First, I create a second Data Frame out of the numerical columns of DU_DG. I go:

>> DU_DGNumCol=pd.DataFrame(DU_DG.columns[‘DU/DG’, ‘Population’,’GDP (constant 2010 US$)’, ‘Broad money (% of GDP)’,’urban population absolute’,’Energy use (kg of oil equivalent per capita)’, ‘agricultural land km2’,’Cereal yield (kg per hectare)’])

Python seems to have accepted the command without reserves, and yet something strange happens. Informative commands about that second Data Frame, i.e. DU_DGNumCol, such as ‘DU_DGNumCol.head()’, ‘DU_DGNumCol.shape’ or ‘DU_DGNumCol.info‘ don’t work, as if DU_DGNumCol had no structure at all.

Cool. I investigate. I want to check how does Python see data in my DU_DG data frame. I do ‘DU_DG.describe()’ first, and, to my surprise, I can see descriptive statistics just for columns ‘Index’ and ‘Year’. The legitimate WTF? question pushes me to type ‘DU_DG.info()’ and here is what I get:

<class ‘pandas.core.frame.DataFrame’>

RangeIndex: 896 entries, 0 to 895

Data columns (total 11 columns):

Index                                           896 non-null int64

Country                                         896 non-null object

Year                                            896 non-null int64

DU/DG                                           896 non-null object

Population                                      896 non-null object

GDP (constant 2010 US$)                         896 non-null object

Broad money (% of GDP)                          896 non-null object

urban population absolute                       896 non-null object

Energy use (kg of oil equivalent per capita)    896 non-null object

agricultural land km2                           896 non-null object

Cereal yield (kg per hectare)                   896 non-null object

dtypes: int64(2), object(9)

memory usage: 77.1+ KB

I think I understand. My numerical data has been imported as object, and I want it to be float values.  Once again, I have the same valuable lesson: before I do anything with my data, in Python, I need to  check and curate it. It is strangely connected to my theory of collective intelligence. Our human perception accepts empirical experience for further processing, especially for collective processing at the level of culture, only if said experience has the right form. We tend to ignore phenomena, which manifest in a form we are not used to process cognitively.

Just by sheer curiosity, I take another dataset and I repeat the whole sequence of import from CSV, and definition of data type. This time, I take a reduced version of Penn Tables 9.1. The full citation due in this case is: Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), “The Next Generation of the Penn World Table” American Economic Review, 105(10), 3150-3182, available for download at www.ggdc.net/pwt. The ‘reduced’ part means that I took out of the database all the rows (i.e. country <> year observations) with at least one empty cell. I go:

>> PWT=pd.DataFrame(pd.read_csv(‘PWT 9_1 no empty cells.csv’)) 

…aaaaand it lands. Import successful. I test the properties of PWT data frame:

>> PWT.info()

yields:

<class ‘pandas.core.frame.DataFrame’>

RangeIndex: 3006 entries, 0 to 3005

Data columns (total 44 columns):

country      3006 non-null object

year         3006 non-null int64

rgdpe        3006 non-null float64

rgdpo        3006 non-null float64

pop          3006 non-null float64

emp          3006 non-null float64

emp / pop    3006 non-null float64

avh          3006 non-null float64

hc           3006 non-null float64

ccon         3006 non-null float64

cda          3006 non-null float64

cgdpe        3006 non-null float64

cgdpo        3006 non-null float64

cn           3006 non-null float64

ck           3006 non-null float64

ctfp         3006 non-null float64

cwtfp        3006 non-null float64

rgdpna       3006 non-null float64

rconna       3006 non-null float64

rdana        3006 non-null float64

rnna         3006 non-null float64

rkna         3006 non-null float64

rtfpna       3006 non-null float64

rwtfpna      3006 non-null float64

labsh        3006 non-null float64

irr          3006 non-null float64

delta        3006 non-null float64

xr           3006 non-null float64

pl_con       3006 non-null float64

pl_da        3006 non-null float64

pl_gdpo      3006 non-null float64

csh_c        3006 non-null float64

csh_i        3006 non-null float64

csh_g        3006 non-null float64

csh_x        3006 non-null float64

csh_m        3006 non-null float64

csh_r        3006 non-null float64

pl_c         3006 non-null float64

pl_i         3006 non-null float64

pl_g         3006 non-null float64

pl_x         3006 non-null float64

pl_m         3006 non-null float64

pl_n         3006 non-null float64

pl_k         3006 non-null float64

dtypes: float64(42), int64(1), object(1)

memory usage: 1.0+ MB

>> PWT.describe()

gives nice descriptive statistics. This dataset has been imported in the format I want. I do the same thing I attempted with the DU_DG dataset: I try to convert it into a NumPy array and to check the shape obtained. I do:

>> PWTNumeric=np.array(PWT)

>> PWTNumeric.shape

I get (3006,44), i.e. 3006 rows over 44 columns. 

I try to wrap my mind around standardising values in PWT. I start gently. I slice one column out of PWT, namely the AVH variable, which stands for the average number of hours worked per person per year. I do:

>> AVH=pd.DataFrame(PWT[‘avh’])

>> stdAVH=pd.DataFrame(AVH/AVH.max())

Apparently, it worked. I check with ‘stdAVH.describe()’ and I get a nice distribution of values between 0 and 1. 

I do the same thing with mean-reversion. I create the ‘mrAVH’ data frame according to the s(x) = [x – avg(x)]/std(x) drill. I do:

 >> mrAVH=pd.DataFrame((AVH-AVH.mean())/AVH.std())

…and I get a nice distribution of mean reverted values. 

Cool. Now, it is time to try and iterate the same standardisation over many columns in the same Data Frame. I have already rummaged a bit and apparently it is not going to as simple as in Excel. It usually isn’t.

That would be all in that update. A short summary is due. It works again. I mean, learning something and keeping a journal of how exactly I learn, that thing works. I feel that special vibe, like ‘What the hell, even if it sucks, it is interesting’. Besides the technical details of programming, I have already learnt two big things about data analysis in Python. Firstly, however comfortable it is to use libraries such as NumPy or Pandas, being really efficient requires the understanding of small details at the very basic level, e.g. conversion of data types, and, as a matter of fact, the practical workability of different data types, selection of values in a data set, by row and by column, iteration over rows and columns etc. Secondly, once again, data works well in Python when it has been properly curated prior to analysis. Learning quick algorithmic ways to curate that data, without having to do is manually in Excel, is certainly an asset, which I need to learn.