László Pitlik,1 Marcell Pitlik,1 Mátyás Pitlik,1 László Pitlik Jr.1, Roland Dávid2,3*, László Lovass2, Krisztina Tamás2, Norbert Mórucz2
1MY-X Team, INNORIA Research and Development Ltd., 4025 Debrecen, Hungary
2Team Flow Team, INNORIA Research and Development Ltd., 4025 Debrecen, Hungary
3Service and Knowledge Economy Research and Development Institute
Kodolányi János University, 8000 Székesfehérvár, Hungary
Accepted and peer reviewed article. Content is being uploaded
*Corresponding Author: Dr. Roland Dávid, J.D., INNORIA Research and Development Ltd., 4 Simonffy St., 4025 Debrecen, Hungary, firstname.lastname@example.org
Approved (Online first): 28.05.2020
How to cite: Dávid, R., Pitlik, L., Pitlik, M., Pitlik, M., Pitlik, L. jun. (2020). Sustainability from Philosophical and Mathematical Standpoint: Butterfly-Effects in Similarity Analyses of Time Series. DRC Sustainable Future, 1 (1). DOI: 10.37281/DRCSF/1.1.10
The motivational background of this paper is to shed new light on the phenomena of butterfly effect and sustainability from a scientific-philosophical and mathematical point of view. We aim to reveal the connection between butterfly effect and sustainability by observing the observer him- or herself and exploring the most significant errors of thinking and operation of the subject, while analyzing the peculiarities of the butterfly effect. Our reasoning is based on cognitive science approach, agricultural scientific experiments, and on parallel EEG (electroencephalogram) measurements. The latter, emerged from the research area of Innoria’s Team Flow Research Team, is a completely new methodological approach in the field of cognitive science on the basis of previous comparative behavioral scientific results1, but built up on new technological opportunities and professional standpoint2,3. As a result, we can see a new contexts and define problems in measurement methodology, while researching the interactions of human minds. These EEG measurements are part of an extensive research, which focuses on the identification of the parallel perception of reality and the synchronized perception-reaction relation of human beings. In the philosophy of science approach the butterfly effect is always provided by the observer by using in his/her rationing the indicator ‘small’ or ‘seemingly insignificant’, while one finds that the effect is not linearly related to such approximate (quantitative) attributes of the cause. The consequence is unexpectedly, unpredictably large, as compared to the observer’s expectations. Therefore, the problem requires a change of perspective, namely, one needs to confer much greater importance to small causes. To discover these causes, we need to explore the mechanism of human observation much more intensively. The mathematical objective of the paper is to demonstrate an explored butterfly-effect process, based on a real, but anonymous parallel measured EEG data asset, where each step is reproducible.
The problems that need to be solved are: (i) How can we classify correctly over EEG measurements the personal time series data (raw individual EEG data series with 0.25 second sampling) within the frame of similarity analysis? (ii) How to deal with the butterfly effect? (iii) How to step forward on the theoretical path of chaotic systems4 designated by Edward N. Lorenz?
The butterfly-effect is the unexpected difference between the result of a classification based on a given data asset and the result of another classification, based on a data asset, having just one additional record as the input; in this case, we have data at about every 0.25 s, where the used length of the time series can be over 100 or 1000. Differences will be derived by means of ranked inputs – especially in case of data having the same value. Similarity analysis is a typical ranking-oriented modelling scheme, where these special effects can be detected at once, without the need for any further manipulations. Since similarity analysis produces model chains, symmetry-driven similarity analyses can have, as well, butterfly-effects in a consistence-oriented model structure. Sustainability can be regarded as a mathematical issue5, being a dynamic phenomenon. Sustainability may be redefined as a capability of forecasting system behavior. Random-like, not-planned incidents cannot be accepted as sustainable and realized plan values. The most trivial usage of the ‘here and now’ characterized sustainability approach is precision farming and its analogy, the EEG-riculture, as such.
Keywords: consistence, ranking, relativity, symmetry of functions, sustainability, forecasting, complexity, cognition, precision farming, and EEG-riculture
Liebig’s law or principle (linked directly to biological systems) was also identified in traffic models6. Reproducible exploration of a butterfly-effect based on a real big-data asset and in frame of a real modelling approach can quasi be regarded as a side-effect. These side-effects being relevant on system theoretical levels can, however, significantly affect the interpretations given by researchers about phenomena, like consistence and/or sustainability.
The concept of sustainability needs to be rephrased in mathematical (big data and AI) and system theoretical sense. A sustainable system can be described as follows: we know it well enough to estimate the effects (dynamic impact chain) of any change to which the system is exposed. These changes can be spontaneous, or intentionally done by someone. We should be able to forecast the effect of changes with the highest possible accuracy for the longest possible time, while including the most possible details. There is a fundamental principle for every system (even those affected by the Pygmalion effect), namely, that one can estimate the future with arbitrary high accuracy if data about the system’s past is provided. The philosophical debate on causality can be neglected yet a high level of (objective, data-based) understanding is achievable. Derived from available data of a system’s past states, the estimated future states can be compared with the actual data as the “real” future occurs. Though this comparison is mathematically complex, the accuracy of the previous estimation process can be measured. If we can improve the (previously described) accuracy of our estimations, then we can get closer to the sustainable handling of the system.
Like the KNUTH-principle7 (knowledge is what can be translated into source code), the above discussed thread leads to the following definition: sustainability is when a system reaches its previously planned states.
The concept of the butterfly effect is crucial to the definition of sustainability, as one should be able to detect it and handle its impact chain for achieving a sufficiently high level of understanding. Ultimately, sustainability is a mathematical problem, given that achieving any (subjective) human goal needs the objective understanding of the targeted systems.
In his seemingly raw approach, Robert M. Pirsig identifies the tiny moments that facilitate qualitative changes in the big whole:
„Evolution is recklessly opportunistic: it favors any variation that provides a competitive advantage over other members of an organism’s own population or over individuals of different species. For billions of years this process has automatically fueled what we call evolutionary progress. No program controlled or directed this progression. It was the result of spur of the moment decisions of natural selection.” 8
We would like to demonstrate how a seemingly marginal data point (concerning a quarter second) can massively impact the results of a chain of similarity analyses. Similarity analysis is a mathematical process able to mimic human intuitive decision-making, therefore, can be considered as an artificial intelligence service.9
Relevant literature references are hard to find with full context and datasets allowing sufficient reproducibility. Here and now, although anonymized, a full dataset will be presented to demonstrate the interpretation possibilities10.
Our dataset has two distinct levels. On one hand, there are time series (with a quarter-second resolution) of multiple measurements. On the other hand, there is a statistical descriptive data of the series mentioned above. The lengths of time series differ from one another by one single data point. It is obvious that the longer a sequence is, the more data points should fall in an extremum range, provided that the total number of data points is sufficiently large. Therefore, absolute values of these descriptive statistics should be avoided whenever the lengths of the time series differ significantly. A more beneficial way could be the use of relativized statistics (e.g., <number of data points having a specific quality> / <length of the time series>).
Our working hypothesis could be the following: when only one data point is the difference between the lengths of two time series, there is no considerable difference between using absolute or relativized descriptive statistics. This presumption would be incorrect, however, if there are recurring values in the time series.
The cause of the butterfly effect is always supplied by the observer with the indicator ‘small’ or ‘seemingly insignificant’, when he or she realizes that the effect elicited is not linearly related to such approximate (quantitative) attributes of its cause. The consequence is unexpectedly, unpredictably large, relative to the observer’s expectations and thus, coincidingly large. The problem therefore requires a change of perspective; one must confer much greater importance to small causes. With the advent of AI systems and quantum computers, time has come to the philosophy of science for self-revision: the way of thinking on so called chaotic systems must step forward on the Lorenz-path. The birth story of the butterfly effect concept is, when Lorenz’s computer calculated a meteorological model with 6 decimal places instead of 3 decimal places and provided a completely different result than Lorenz expected. Then, because of the unexpected result and the insignificant title of the 4-6 decimal places, we started to call “chaotic systems” any system that we could not calculate or describe. These systems were always predictable in a general sense but are not exclusively for the observer. The time for the arbitrariness of scientific dogmatism is most likely over. Since then, we have been trying to describe such systems using statistical methods instead of linear methods. Consequence of this way of thinking are for example, the critical mass approach of economics, which is unable to provide an accurate forecast of the most important future processes. Such is also the statistical methodology of the social sciences, a discipline, which was unable to filter out Adolf Hitler’s personality and the process of his political character development in the 20th century, allowing him to unfold and inflict the deepest and most dangerous wounds ever on the body of humankind. This happens when the level of significance is arbitrarily determined by science and the ‘chaotic’ attribute is arbitrarily distributed to certain systems. The present and future of science cannot be about accepting the inevitably many factors and ignoring some of them. Chaotic systems only exist until we discover their regularities. Researching the phenomenon of intuition and the impact of the nature of human consciousness on highly complex systems by means of cognitive, AI, and quantum technologies will bring tremendous progress. The first technologies and methods in this direction are already available, one day they will reduce the ‘butterfly effect’ itself into a closed topic of our past.
Figure 1: Primary input data behind absolute and relativized OAMs (source: own calculation)
Fig. 1 shows a real but anonymized OAM (object-attribute matrix) with 28 objects and 11 attributes (Ai). It is to be seen that attributes A10 and A11 do not have distinct absolute and relativized values, but all other columns can be relativized through dividing the absolute value (e.g., number of data points in an extremum range) by the length of the corresponding time series. By this operation one obtains a time-independent OAM.
The next step with the raw-data OAM is a ranking process. In this case we have used the default (0 = the more the better) listing resulting data in Fig. 2. The left and right tables belong to the absolute and relativized primary input data, respectively.
Figure 2: Ranking based on absolute and relativized data (source: own calculation)
The two table panels in Fig. 2 can be contrasted, as shown in Fig. 3. We found considerable differences (in some unique spots regarding some attributes) between the results coming from the absolute and relativized tables, even when the lengths of the primary time series differed by only one data point.
Figure 3: Differences between the ranked tables (source: own calculation)
Results and Discussion: Description of the modeling process
As shown in Fig. 3, there are some attributes (e.g., A4 or A10 and A11), which yield the same ranked results, regardless of prior relativization. Note that this is the expected outcome in case of the latter two attributes. Attributes A3 and A7 seem to be most affected by potential butterfly effects. Yet it is impossible to tell (at this point) what role these two (or any of the attributes) will exactly have in the final optimization process of the similarity analysis.
The essence of optimization is to assign a specific exchange value to each ranked position (the greater the higher the rank is). The sum of these exchange values per every object is the estimated value. The key of optimization is to create a set of estimated values that are as homogenous as possible (cf. every object is “differently alike”) with the important restriction that the sequence of the exchange values must be strictly monotonical in case of each attribute.
Results of similarity analyses are listed in Fig. 3 (right), presenting the different outcomes of absolute and relativized OAMs.
Figure 4: Effects of model chains on the classification (source: own calculation)
Previously (seen in Fig. 3), there was executed only one optimization model to demonstrate the butterfly effect. A shown in Fig. 4, a model chain of 10 basic and +1 final optimization process can be built, which show differences between the basic estimations and the standard values and these differences represent attributes to the final modeling step. While at the end of the model chain based on absolute OAM, the objects are (almost) equally distributed along the classification scale, results of the relativized models are essentially homogenous (except for one pair of objects). Considering that the difference between the lengths of the time series (having a total length of 360 or 361 data points) is only one data point, these results (see above) show a significant impact exerted by the seemingly negligible quarter second (meaningless by the human intuition)..
Figure 5: Differences between the distribution of the ranks per attribute (source: own calculation)
Figure 5 (28×11 cells with conditional formatting) shows the distribution of ranks considering the absolute values of the primary OAM. At the top of the table (rows ‘total’, ‘max’, and ‘average’), there are some descriptive statistics of the columns. The row ‘diff(abs-vs-rel)’ is the same as the top row of the 3rd table in Fig. 3.
The two 0.9 values (at the top right corner) indicate that there is a strong correlation between the maximum values of the rank-recurrence and those of the differences between the ranks based on the absolute and relativized values.
Figure 6: Effect of model chains on the consistency (source: own calculation)
It is important to highlight that detected butterfly effects need decision situation to have a chained impact. Then, we can address the probably most complex production form of humankind.
The evaluation/interpretation of a situation, where live creatures would evaluate their environment, should lead to decisions and chained impacts of these decisions (influenced the more or the less by butterfly effects). Consequently, they can cause totally different futures. In our case with EEG-signs, a decision about persons (objects) can be postponed, if the conclusion is that each object can have the same evaluation value. On the other hand, actions (building or even destroying) can be started immediately if we conclude that one or more object(s) are not norm-like (this means they are dangerous or preferable). Conclusions can only depend on one single information unit. IoT-application, where the 5G network can/will lose packages, this force field being driven by the butterfly effect, can develop problems with AI13.
After the general interpretation of the usefulness of explored butterfly effects, we found that the most trivial application of the above approach to butterfly effects is precision farming.
Precision farming and its future projection is the automation of controlling/planning of agricultural production processes in a specific way, where the more and more reduced space and/or available individuals (plants and/or animals) should be arbitrarily fine-tuned in an understandable manner.
Measurements have become inexpensive and easily available. This will lead to a scenario, where each single living creature (plant and/or animal) can be observed. In parallel, individuals-driven interpretations will not exclude the understanding about groups and their dynamical processes, or even ecological systems and their changes. Even the connections between individuals can be used as a kind of consistent frame system.
The Liebig principle14 can be measured for one single individual (cf. X = CO2 vs. Y = photosynthesis) and the result is a linearly increasing phase and a (linear) phase, where X does not have any impact on Y. Plant populations produce (seemingly as a contrast to linear phases) the so-called law of diminishing returns, where the yield (Y) and the fertilizer (e.g., a nitrogen-containing fertilizer) exhibit a parabolic relationship. We have known for decades that these two visual effects are not antagonistic. Single linear effects yield a population with parabolic views.
Big-data-systems ensure that AI-based data processing will add the less and less to the system-answer: I-do-not-know (or none). This systems-answer is a significant development within the modelling, where the models/functions have always something to say like the ‘wise rabbi’ in the known fable, where the geese are dying one after another, and the rabbi advises continuously, until each animal dies.
None-answers will always cause problems in an automation-oriented system, where human intelligence should be involved with an unplanned frequency. Nevertheless, none-answers represent the basics behind the high and higher fitting values of the model. Fitting may only be calculated within the real answers and never involved the none-cases. Involvement of human intelligence will focus on the most complex decision situations; these challenges and their solutions will be transferred/transformed/translated into source codes (following the KNUTH’s principle) for improving the already automated processes.
Based on bigdata, the frequency of observations of butterfly effects will probably be higher. It is a rational hypothesis here and now, that specific effects (like butterfly effect and Pygmalion-effect) will be recognizable behind the negative system answers. Therefore, the needed automation can hardly exclude this challenge following again and again the KNUTH’s principle.
By translating the high functions of consciousness into source code and AI technology functions, highly complex systems become transparent and their calcined essence can be explored. With technologies, we can support people to use this function of their consciousness, to use it permanently and at any time. Intuition and the butterfly effect are opposites. Intuition as a function can predict the unforeseen consequence, that is, make the unforeseen visible. As much effort as possible is needed in the direction of researching this field. This way, the direction of our current technological development can be better parameterized.
What is the current trend of our technological sustainable development? We are generally increasing storage capacities and the amount of unanalyzed information. What do we want to sustain? How do we improve this process? These data sets need real precognitive AI systems and the users need brain-computer technologies that can condition any of our fellow human beings to make good decisions, filter bigdata by putting their own (yet unrecognized) cognitive abilities in order15.
This challenge can be reformulated if we are searching for models, where the Liebig Minimum Law can be identified, and compared to the nowadays used regressions and/or artificial neural networks, where most kinds of average impacts can be aggregated/cumulated. Similarity analyses can produce Liebig-bubbles and describe a phenomenon (a consequence variable) as interaction of the independent variables – however, only object by object in different ways! These Liebig-bubbles demonstrate what kind of limitations can be assumed behind certain consequences16.
Such kind of bubbles can be explored if we are capable to estimate data, unit by data unit, what status seems to be norm-like, or even what is too high or too low, compared to one another. These norm-oriented views support the detection of static and/or dynamic unsustainability.
A theoretical conclusion
The butterfly effect suggests that changes thought to be tiny may produce effects that appear to be significant, but which must be distinguishable from random effects and/or irrational model behaviors. Existence of the butterfly effect and irrational model behavior (or their conceptual generation by the observer) calls for approaching and rethinking from the standpoint. If a phenomenon lies within the limits of the observer, then it is only a phenomenon existing for him/her. Changing the way of perception, increasing the capacity to perception information reveals all the causes, eliminates random or unpredictable phenomena. Logically, there is no accidental event, only unconceived or underestimated information related to it; the butterfly effect is accordingly a recognized, perceived, and analyzed “random” phenomenon. Human intervention (in our case, decoupling), even if done according to the rules of mathematics and statistics, produces an observational intervention that obscures one or more elements present that concern the final results. By using the example above, the intervention unacceptably distorts the ranking relations of real data and processed data of the measured subjects. (This also distorts the ranking of subjects if we associate data with such consequences.)
Besides, it does not associate or assign an adequate weight to the obscured element found only in the deep data layers. Thus, it makes it impossible to conclude on the cause or analyze the causal chain it evokes.
Human thinking is inherently preoccupied with the question of what the limits of perception are. Over the past centuries, man has chosen a horizontal and quantitative solution to broaden the boundaries of perception. We sought to process more data and then to organize the information on a new qualitative basis, to attempt an independent and non-conceptual evaluation of all elements.
Regarding sustainability, it is imperative to state that, while creating massive storage and data analytics intelligence, we must place at least as much weight on expanding the boundaries of our minds and developing them qualitatively, not quantitatively. We need to realize that the level of sophisticated intelligence or cognitive complexity of the AI systems we bring to life also depends on our ability of understanding and analyzing events. The high prevalence and technological integration of the cognitive sciences (tools to increase the competitiveness of our minds) will show in the coming decades that the quality of our AI solutions is evolving with us or interacting with us for joint development. The value-organizing ability of human mind dictates the foundations of value judgment in AI systems. Human IQ value is being exceeded by artificial systems. Nevertheless, we create these systems ourselves. This shows that the potential inherent to human complexity and to human mind (and especially in the ability to recognize and organize value) are still untapped. We can exploit it in old or new ways. In old ways, as it was known in every culture how to approach higher qualities and how to implement the acquired knowledge into community life. These qualities were available through mind/consciousness. Human qualities and abilities, as they are today, can be placed in a horizontal and vertical value matrix. In present, technology greatly supports us in accelerating the exploration and achievement of ultimate values and reaching many subjects via new avenues. Our answer to the question ‘What is worth sustaining?’ is to keep moving toward a higher level of individual and community quality matrix.
The problem of ‘divide one into infinite parts’ and the problem of the ‘small detail, which also includes infinity’ is still the subject of philosophy (abstract mathematics), or art. Although we recognize art as the highest manifestation of human quality, we have not sought enough to understand it, but have separated it from science. Today, technologies are available to detect, isolate, and teach (neurofeedback) the highest levels of the human mind’s most useful functions.
Improvements in the monitoring process, along with accuracy and qualitative development, can be guaranteed. So far, we have developed a predominantly finite computational capacity. At the same time, the paradigm shift shows that all information can become available to us at any time, if we start monitoring the process of our observation with our computational capacities. Reasons for the butterfly effects lie in the deep layers of data that is only noticeable from the higher layers of our thinking. A higher level of understanding of high-profile social matters (health, environment, and social coexistence rules) depends on making ‘random events’ predictable. That is why cognitive sciences today are core technologies; the quality of the future depends on us.
1Konrad Lorenz, Russian Manuscript (1944-48) (Hungarian edition: Az orosz kézirat) Cartaphilus Kiadó, Budapest, 1998. pp.1-496
2 Josef Faller, Jennifer Cummings, Sameer Saproo, Paul Sajda (2019). Regulation of arousal via online neurofeedback improves human performance in a demanding sensory-motor task. Proc. National Acad. Sci.(PNAS), 116 (13), 6482-6490 DOI: 10.1073/pnas.1817207116
3Albert V. Carron, Michelle M. Colman, Jennifer Wheeler (2002). University of Western Ontario, Cohesion and Performance in Sport: A Meta-Analysis, J. of Sport & Exercise Psychology, 24, 168-188 (Human Kinetics Publishers, Inc.)
4 Edward N. Lorenz, The Essence of Chaos, University of Washington Press, Seattle, 1994.
5 László Pitlik, Zoltán Varga (2015). The operationalism of sustainability is a mathematical issue Medium on Internet for Applied/Agricultural Informatics HU ISSN 14191652 MIAU-Nr-206 http://miau.my-x.hu/miau/206/Full_text_template_synergy2015_pl.doc – https://miau.my-x.hu/miau2009/adatlap.php3?where[azonosito]=23855&mod=l2003
6László Pitlik László, Marcell Pitlik Marcell, Mátyás Pitlik, László Pitlik, Jr. (2018). Szimulált közlekedési szcenáriók összehasonlító elemzése (Benchmarking of simulated traffic scenarios) – 2018 – Medium on Internet for Applied/Agricultural Informatics HU ISSN 14191652 MIAU-Nr-241 – https://miau.my-x.hu/miau/253/traffic-simulations.docx / https://miau.my-x.hu/miau2009/adatlap.php3?where[azonosito]=24204&mod=l2003
7 Knuth D.E. (1998). The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, 3rdedn. Reading, MA Addison-Wesley.
8 Robert M. Pirsig Lila (1991). An Inquiry into Morals, Bantam Books, pp. 1-409 – https://terebess.hu/zen/mesterek/Robert_Pirsig-Lila.rtf
10 The primary input data and partial results are available here: https://miau.my-x.hu/miau/257/butterfly
11 Pitlik L. (1993). Automatisierte Generierung problemspezifischer Prognosefunktionen zur Entscheidungsunterstützung, , Diessertation, JLU-Giessen, 1993, Wissenschaftlicher Fachverlag, ISBN 3-928563-60-2, O.1-194.
14 van der Ploeg, R.R., W. Böhm, M.B. Kirkham (1999). “On the origin of the theory of mineral nutrition of plants and the Law of the Minimum.” Soil Sci. Soc. Am. J. 63-1055-1062.
15 Christopher Ring, Andrew Cook, Maria Kavussanu, David McIntyre, Rich Masters, Investigating the efficacy of neurofeedback training for expediting expertise and excellence in sport, School of Sport, Exercise & Rehabilitation Sciences, University of Birmingham, Birmingham B15 2TT, UK School of Sport, Health & Exercise Sciences, Bangor University, LL57 2PZ, UK, Institute of Human Performance, University of Hong Kong, 111-113 Pokfulam Road, Hong Kong (http://innoriatech.com/#studies)
16 László Pitlik (2018). Derivation of the next critical attribute in a complex risk management system, https://miau.my-x.hu/miau/238/exploring_critical_attributes_for_risk_management_v1.pdf
17 Andor Dobó (1992).–A hasonlóságelmélet alkalmazása a Joker rendszerben (Application of similarity theory in the Joker system), Prodinform, pp. 1-62
Background files for the figures: https://miau.my-x.hu/miau/257/butterfly
Online test environment: http://moralmachine.mit.edu/
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