MY EDITORIAL ON YOU TUBE
I keep reviewing, upon the request of the International Journal of Energy Sector Management (ISSN1750-6220), a manuscript entitled ‘Evolutionary Analysis of a Four-dimensional Energy- Economy- Environment Dynamic System’. I have already formulated my first observations on that paper in the last update: I followed my suspects home, where I mostly focused on studying the theoretical premises of the model used in the paper under review, or rather of a model used in another article, which the paper under review heavily refers to.
As I go through that initial attempt to review this manuscript, I see I was bitching a lot, and this is not nice. I deeply believe in the power of eristic dialogue, and I think that being artful in verbal dispute is different from being destructive. I want to step into the shoes of those authors, technically anonymous to me (although I can guess who they are by their bibliographical references), who wrote ‘Evolutionary Analysis of a Four-dimensional Energy- Economy- Environment Dynamic System’. When I write a scientific paper, my conclusion is essentially what I wanted to say from the very beginning, I just didn’t know how to phrase that s**t out. All the rest, i.e. introduction, mathematical modelling, empirical research – it all serves as a set of strings (duct tape?), which help me attach my thinking to other people’s thinking.
I assume that people who wrote ‘Evolutionary Analysis of a Four-dimensional Energy- Economy- Environment Dynamic System’ are like me. Risky but sensible, as assumptions come. I start from the conclusion of their paper, and I am going to follow upstream. When I follow upstream, I mean business. It is not just about going upstream the chain of paragraphs: it is going upstream the flow of language itself. I am going to present you a technique I use frequently when I really want to extract meaning and inspiration from a piece of writing. I split that writing into short paragraphs, like no more than 10 lines each. I rewrite each such paragraph in inverted syntax, i.e. I rewrite from the last word back to the first one. It gives something like Master Yoda speaking: bullshit avoid shall you. I discovered by myself, and this is backed by the science of generative grammar, that good writing, when read backwards, uncovers something like a second layer of meaning, and that second layer is just as important as the superficial one.
I remember having applied this method to a piece of writing by Deepak Chopra. It was almost wonderful how completely meaningless that text was when read backwards. There was no second layer. Amazing.
Anyway, now I am going to demonstrate the application of that method to the conclusion of ‘Evolutionary Analysis of a Four-dimensional Energy- Economy- Environment Dynamic System’. I present paragraphs of the original text in Times New Roman Italic. I rewrite the same paragraphs in inverted syntax with Times New Roman Bold. Under each such pair ‘original paragraph + inverted syntax’ I write my second-hand observations inspired by those two layers of meaning, and those observations of mine come in plain Times New Roman.
Let’s dance.
Original text: Although increasing the investment in energy reduction can effectively improve the environmental quality; in a relatively short period of time, the improvement of environmental quality is also very obvious; but in the long run, the the influence of the system (1). In this study, the energy, economic and environmental (3E) four-dimensional system model of energy conservation constraints was first established. The Bayesian estimation method is used to correct the environmental quality variables to obtain the environmental quality data needed for the research.
Inverted syntax: Research the for needed data quality environmental the obtain to variables quality environmental the correct to used is method estimation Bayesian the established first was constraints conservation energy of model system dimensional four 3E environmental and economic energy the study this in system the of influence run long the in but obvious very also is quality environmental of improvement the time of period short relatively a in quality environmental the improve effectively can reduction energy in investment the increasing although.
Second-hand observations: The essential logic of using Bayesian methodology is to reduce uncertainty in an otherwise weakly studied field, and to set essential points for orientation. A Bayesian function essentially divides reality into parts, which correspond to, respectively, success and failure.
It is interesting that traits of reality which we see as important – energy, economy and environmental quality – can be interpreted as dimensions of said reality. It corresponds to the Interface Theory of Perception (ITP): it pays off to build a representation of reality based on what we want rather than on what we perceive as absolute truth.
Original text: In addition, based on the Chinese statistical yearbook data, the Levenberg-Marquardt BP neural network method optimized by genetic algorithm is used to energy, economy and environment under energy conservation constraints. The parameters in the four-dimensional system model are effectively identified. Finally, the system science analysis theory and environment is still deteriorating with the decline in the discount rate of energy reduction inputs.
Inverted syntax: Inputs reduction energy of rate discount the in decline the with deteriorating still is environment and theory analysis science system the finally identified effectively are model system dimensional four the in parameters the constraints conservation energy under environment and economy energy to used is algorithm genetic by optimized method network neural Levenberg-Marquardt Backpropagation the data yearbook statistical Chinese the on based addition in.
Second-hand observations: The strictly empirical part of the article is relatively the least meaningful. The Levenberg-Marquardt BP neural network is made for quick optimization. It is essentially the method of Ordinary Least Squares transformed into a heuristic algorithm, and it can optimize very nearly anything. When using the Levenberg-Marquardt BP neural network we risk overfitting (i.e. hasty conclusions based on a sequence of successes) rather than the inability to optimize. It is almost obvious that – when trained and optimized with a genetic algorithm – the network can set such values in the model which allow stability. It simply means that the model has a set of values that virtually eliminate the need for adjustment between particular arguments, i.e. that the model is mathematically sound. On the other hand, it would be intellectually risky to attach too much importance to the specific values generated by the network. Remark: under the concept of ‘argument’ in the model I mean mathematical expressions of the type: [coefficient]*[parameter]*[local value in variable].
The article conveys an important thesis, namely that the rate of return on investment in environmental improvement is important for sustaining long-term commitment to such improvement.
Original text: It can be better explained that effective control of the peak arrival time of pollution emissions can be used as an important decision for pollution emission control and energy intensity reduction; Therefore, how to effectively and reasonably control the peak of pollution emissions is of great significance for controlling the stability of Energy, Economy and Environment system under the constraint of energy reduction, regulating energy intensity, improving environmental quality and sustainable development.
Inverted syntax: Development sustainable and quality environmental improving intensity energy regulating reduction energy of constraint the under system environment and economy energy of stability the controlling for significance great of is emissions pollution of peak the control reasonably and effectively to how therefore reduction intensity energy and control emission pollution for decision important an as used be can emissions pollution of time arrival peak the of control effective that explained better be can.
Second-hand observations: This is an interesting logic: we can control the stability of a system by controlling the occurrence of peak states. Incidentally, it is the same logic as that used during the COVID-19 pandemic. If we can control the way that s**t unfolds up to its climax, and if we can make that climax somewhat less steep, we have an overall better control over the whole system.
Original text: As the environmental capacity decreases, over time, the evolution of environmental quality shows an upward trend of fluctuations and fluctuations around a certain central value; when the capacity of the ecosystem falls to the limit, the system collapses. In order to improve the quality of the ecological environment and promote the rapid development of the economy, we need more measures to use more means and technologies to promote stable economic growth and management of the ecological environment.
Inverted syntax: Environment ecological the of management and growth economic stable promote to technologies and means more use to measures more need we economy the of development rapid the promote and environment ecological the of quality the improve to order in collapse system the limit the to falls ecosystem the of capacity the when value central a around fluctuations and fluctuations of trend upward an shows quality environmental of evolution the time over decreases capacity environmental the as.
Second-hand observations: We can see more of the same logic: controlling a system means avoiding extreme states and staying in a zone of proximal development. As the system reaches the frontier of its capacity, fluctuations amplify and start drawing an upward drift. We don’t want such a drift. The system is the most steerable when it stays in a somewhat mean-reverted state.
I am summing up that little exercise of style. The authors of ‘Evolutionary Analysis of a Four-dimensional Energy-Economy-Environment Dynamic System’ claim that relations between economy, energy and environment are a complex, self-regulating system, yet the capacity of that system to self-regulate is relatively the most pronounced in some sort of central expected states thereof, and fades as the system moves towards peak states. According to this logic, our relations with ecosystems are always somewhere between homeostasis and critical disaster, and those relations are the most manageable when closer to homeostasis. A predictable, and economically attractive rate of return in investments that contribute to energy savings seems to be an important component of that homeostasis.
The claim in itself is interesting and very largely common-sense, although it goes against some views, that e.g. in order to take care of the ecosystem we should forego economics. Rephrased in business terms, the main thesis of ‘Evolutionary Analysis of a Four-dimensional Energy-Economy-Environment Dynamic System’ is that we can manage that dynamic system as long as it involves project management much more than crisis-management. When the latter prevails, things get out of hand. The real intellectual rabbit hole starts when one considers the method of proving the veracity of that general thesis. The authors build a model of non-linear connections between volume of pollution, real economic output, environmental quality, and constraint on energy reduction. Non-linear connections mean that output variables of the model – on the left side of each equation – are rates of change over time in each of the four variables. Output variables in the model are strongly linked, via attractor-like mathematical arguments on the input side, i.e. arguments which combine coefficients strictly speaking with standardized distance from pre-defined peak values in pollution, real economic output, environmental quality, and constraint on energy reduction. In simpler words, the theoretical model built by the authors of ‘Evolutionary Analysis of a Four-dimensional Energy-Economy-Environment Dynamic System’ resembles a spiderweb. It has distant points of attachment, i.e. the peak values, and oscillates between them.
It is interesting how this model demonstrates the cognitive limitations of mathematics. If we are interested in controlling relations between energy, economy, and environment, our first, intuitive approach is to consider these desired outcomes as dimensions of our reality. Yet, those dimensions could be different. If I want to become a top-level basketball player, I does not necessarily mean that social reality is truly pegged on a vector of becoming-a-top-level-basketball-player. Social mechanics might be structured around completely different variables. Still, with strong commitment, this particular strategy might work. Truth is not the same as payoffs from our actions. A model of relations energy-economy-environment pegged on desired outcomes in these fields might be essentially false in ontological terms, yet workable as a tool for policy-making. This approach is validated by the Interface Theory of Perception (see, e.g. Hoffman et al. 2015[1] and Fields et al. 2018[2]).
From the formal-mathematical point of view, the model is construed as a square matrix of complex arguments, i.e. the number of arguments on the left, input side of each equation is the same as the number of equations, whence the possibility to make a Jacobian matrix thereof, and to calculate its eigenvalues. The authors preset the coefficients of the model, and the peak-values so as to test for stability. Testing the model with those preset values demonstrates an essential lack of stability in the such-represented system. Stability is further tested by studying the evolution trajectory of the system. The method of evolution trajectory, in this context, seems referring to life sciences and the concept of phenotypic trajectory (see e.g. Michael & Dean 2013[3]), and shows that the system, such as modelled, is unstable. Its evolution trajectory can change in an irregular and chaotic way.
In a next step, the authors test their model with empirical data regarding China between 2000 and 2017. They use a Levenberg–Marquardt Backpropagation Network in order to find the parameters of the system. With thus-computed parameters, and the initial state of the system set on data from 1980, evolution trajectory of the system proves stable, in a multi cycle mode.
Now, as I have passed in review the logic of ‘Evolutionary Analysis of a Four-dimensional Energy-Economy-Environment Dynamic System’, I start bitching again, i.e. I point at what I perceive as, respectively, strengths and weaknesses of the manuscript. After reading and rereading the paper, I come to the conclusion that the most valuable part thereof is precisely the use of evolution trajectory as theoretical vessel. The value added I can see here consists in representing something complex that we want – we want our ecosystem not to kill us (immediately) and we want our smartphones and our power plants working as well – in a mathematical form, which can be further processed along the lines of evolution trajectory.
That inventive, intellectually far-reaching approach is accompanied, however, by several weaknesses. Firstly, it is an elaborate path leading to common-sense conclusions, namely that managing our relations with the ecosystem is functional as long as it takes the form of economically sound project management, rather than crisis management. The manuscript seems to be more of a spectacular demonstration of method rather than discovery in substance.
Secondly, the model, such as is presented in the manuscript, is practically impossible to decipher without referring to the article Zhao, L., & Otoo, C. O. A. (2019). Stability and Complexity of a Novel Three-Dimensional Environmental Quality Dynamic Evolution System. Complexity, 2019, https://doi.org/10.1155/2019/3941920 . When I say ‘impossible’, it means that the four equations of the model under review are completely cryptic, as the authors do not explain their mathematical notation at all, and one has to look into this Zhao, L., & Otoo, C. O. A. (2019) paper in order to make any sense of it.
After cross-referencing those two papers and the two models, I obtain quite a blurry picture. In this Zhao, L., & Otoo, C. O. A. (2019) we have a complex, self-regulating system made of 3 variables: volume of pollution x(t), real economic output y(t), and environmental quality z(t). The system goes through an economic cycle of k periods, and inside the cycle those three variables reach their respective local maxima and combine into complex apex states. These states are: F = maxk[x(t)], E = maxk[y(t)], H = maxk(∆z/∆y) – or the peak value of the impact of economic growth 𝑦(𝑡) on environmental quality 𝑧(𝑡) – and P stands for absolute maximum of pollution possible to absorb by the ecosystem, thus something like P = max(F). With those assumptions in mind, the original model by Zhao, L., & Otoo, C. O. A. (2019), which, for the sake of presentational convenience I will further designate as Model #1, goes like:
d(x)/d(t) = a1*x*[1 – (x/F)] + a2*y*[1 – (y/E)] – a3*z
d(y)/d(t) = -b1*x – b2*y – b3*z
d(z)/d(t) = -c1*x + c2*y*[1 – (y/H)] + c3*z*[(x/P) – 1]
The authors of ‘Evolutionary Analysis of a Four-dimensional Energy- Economy- Environment Dynamic System’ present a different model, which they introduce as an extension of that by Zhao, L., & Otoo, C. O. A. (2019). They introduce a 4th variable, namely energy reduction constraints designated as w(t). There is no single word as for what does it exactly mean. The first moments over time of, respectively, x(t), y(t), z(t), and w(t) play out as in Model #2:
d(x)/d(t)= a1*x*[(y/M) – 1] – a2*y + a3*z + a4w
d(y)/d(t) = -b1*x + b2*y*[1 – (y/F)] + b3*z*[1 – (z/E)] – b4*w
d(z)/d(t) = c1*x*[(x/N) – 1] – c2*y – c3*z – c4*w
d(w)/d(t) = d1*x – d2*y + d3*z*[1 – (z/H)] + d4*w*[(y/P) – 1]
No, I have a problem. When the authors of ‘Evolutionary Analysis of a Four-dimensional Energy- Economy- Environment Dynamic System’ present their Model #2 as a simple extension of Model #1, this is simply not true. First of all, Model #2 contains two additional parameters, namely M and N, which are not explained at all in the paper. They are supposed to be normal numbers and that’s it. If I follow bona fide the logic of Model #1, M and N should be some kind of maxima, simple or compound. It is getting interesting. I have a model with two unknown maxima and 4 known ones, and I am supposed to understand the theory behind. Cool. I like puzzles.
The parameter N is used in the expression [(x/N) – 1]. We divide the local volume of pollution x by N, thus we do x/N, and this is supposed to mean something. If we keep any logic at all, N should be a maximum of pollution, yet we already have two maxima of pollution, namely F and P. As for M, it is used in the expression [(y/M) – 1] and therefore I assume M is a maximum state of real economic output ‘y’. Once again, we already have one maximum in that category, namely ‘E’. Apparently, the authors of Model #2 assume that the volume of pollution x(t) can have three different, meaningful maxima, whilst real economic output y(t) has two of them. I will go back to those maxima further below, when I discuss the so-called ‘attractor expressions’ contained in Model #2.
Second of all, Model #2 presents a very different logic than Model #1. Arbitrary signs of coefficients ai, bi, ci and di are different, i.e. minuses replace pluses and vice versa. Attractor expressions of the type [(a/b) – 1] or [1 – (a/b)] are different, too. I am going to stop by these ones a bit longer, as it is important regarding the methodology of science in general. When I dress a hypothesis like y = a*x1 + b*x2, coefficients ‘a’ and ‘b’ are neutral in the sense that if x1 > 0, then a*x1 > 0 as well etc. In other words, positive coefficients ‘a’ and ‘b’ do not imply anything about the relation between y, x1, and x2.
On the other hand, when I say y = -a*x1 + b*x2, it is different. Instead of having a coefficient ‘a’, I have a coefficient ‘-a’, thus opposite to ‘y’. If x1 > 0, then a*x1 < 0 and vice versa. By assigning a negative coefficient to phenomenon x, I assume it works as a contrary force to phenomenon y. A negative coefficient is already a strong assumption. As I go through all the arbitrarily negative coefficients in Model #2, I can see the following strong claims:
>>> Assumption 1: the rate of change in the volume of pollution d(x)/d(t) is inversely proportional to the real economic output y.
>>> Assumption 2: the rate of change in real economic output d(y)/d(t) is inversely proportional to the volume of pollution x
>>> Assumption 3: the rate of change in real economic output d(y)/d(t) is inversely proportional to energy reduction constraints w.
>>> Assumption 4: the rate of change in environmental quality d(z)/d(t) is inversely proportional to environmental quality z.
>>> Assumption 5: the rate of change in environmental quality d(z)/d(t) is inversely proportional to real economic output y.
>>> Assumption 6: the rate of change in environmental quality d(z)/d(t) is inversely proportional to the volume of pollution x.
>>> Assumption 7: the rate of change in energy reduction constraints d(w)/d(t) is inversely proportional to real economic output y.
These assumptions would greatly benefit from theoretical discussion, as some of them, e.g. Assumption 1 and 2, seem counterintuitive.
Empirical data presented in ‘Evolutionary Analysis of a Four-dimensional Energy- Economy- Environment Dynamic System’ is probably the true soft belly of the whole logical structure unfolding in the manuscript. Authors present that data in the standardized form, as constant-base indexes, where values from 1999 are equal to 1. In Table 1 below, I present those standardized values:
Table 1
| Year | X – volume of pollution | Y – real economic output | Z – environmental quality | W – energy reduction constraints |
| 2000 | 1,9626 | 1,0455 | 1,1085 | 0,9837 |
| 2001 | 3,6786 | 1,1066 | 1,2228 | 0,9595 |
| 2002 | 2,2791 | 1,2064 | 1,3482 | 0,9347 |
| 2003 | 1,2699 | 1,402 | 1,5283 | 0,8747 |
| 2004 | 2,3033 | 1,6382 | 1,8062 | 0,7741 |
| 2005 | 1,9352 | 1,8594 | 2,0813 | 0,7242 |
| 2006 | 2,0778 | 2,038 | 2,4509 | 0,6403 |
| 2007 | 3,9437 | 2,2156 | 3,0307 | 0,5455 |
| 2008 | 6,5583 | 2,2808 | 3,5976 | 0,4752 |
| 2009 | 3,283 | 2,3912 | 3,8997 | 0,4061 |
| 2010 | 3,3307 | 2,5656 | 4,602 | 0,3693 |
| 2011 | 3,6871 | 2,7534 | 5,4243 | 0,3565 |
| 2012 | 4,013 | 2,8608 | 6,0326 | 0,321 |
| 2013 | 3,9274 | 2,9659 | 6,6068 | 0,2817 |
| 2014 | 4,2167 | 3,0292 | 7,2151 | 0,2575 |
| 2015 | 4,2893 | 3,0583 | 7,6813 | 0,2322 |
| 2016 | 4,5925 | 3,1004 | 8,2872 | 0,2159 |
| 2017 | 4,6121 | 3,1942 | 9,2297 | 0,2147 |
I found several problems with that data, and they sum up to one conclusion: it is practically impossible to check its veracity. The time series of real economic output seem to correspond to some kind of constant-price measurement of aggregate GDP of China, yet it does not fit the corresponding time series published by the World Bank (https://data.worldbank.org/indicator/NY.GDP.MKTP.KD ). Metrics such as ‘environmental quality’ (x) or energy reduction constraints (w) are completely cryptic. Probably, they are some sort of compound indices, and their structure in itself requires explanation.
There seems to be a logical loop between the theoretical model presented in the beginning of the manuscript, and the way that data is presented. The model presents an important weakness as regards functional relations inside arguments based on peak values, such as ‘y/M’ or ‘y/P’. The authors very freely put metric tons of pollution in fractional relation with units of real output etc. This is theoretical freestyle, which might be justified, yet requires thorough explanation and references to literature. Given the form that data is presented under, a suspicion arises, namely that standardization, i.e. having driven all data to the same denomination, opened the door to those strange, cross-functional arguments. It is to remember that even standardized through common denomination, distinct phenomena remain distinct. A mathematical trick is not the same as ontological identity.
Validation of the model with a Levenberg–Marquardt Backpropagation Network raises doubts, as well. This specific network, prone to overfitting, is essentially a tool for quick optimization in a system which we otherwise thoroughly understand. This is the good old method of Ordinary Least Squares translated into a sequence of heuristic steps. The LM-BN network does not discover anything about the system at hand, it just optimizes it as quickly as possible.
In a larger perspective, using a neural network to validate a model implies an important assumption, namely that consecutive states of the system form a Markov chain, i.e. each consecutive state is exclusively the outcome of the preceding state. It is to remember that neural networks in general are artificial intelligence, and intelligence, in short, means that we figure out what to do when we have no clue as for what to do, and we do it without any providential, external guidelines. The model presented by the authors clearly pegs the system on hypothetical peak values. These are exogenous to all but one possible state of the system, whence a logical contradiction between the model and the method of its validation.
Good. After some praising and some bitching, I can assess the manuscript by answering standard questions asked by the editor of the International Journal of Energy Sector Management (ISSN1750-6220).
- Originality: Does the paper contain new and significant information adequate to justify publication?
The paper presents a methodological novelty, i.e. the use of evolution trajectory as a method to study complex social-environmental systems, and this novelty deserves being put in the spotlight even more than it is in the present version of the paper. Still, substantive conclusions of the paper do not seem original at all.
- Relationship to Literature: Does the paper demonstrate an adequate understanding of the relevant literature in the field and cite an appropriate range of literature sources? Is any significant work ignored?
The paper presents important weaknesses as for bibliographical referencing. First of all, there are clear theoretical gaps as regards the macroeconomic aspect of the model presented, and as regards the nature and proper interpretation of the empirical data used for validating the model. More abundant references in these two fields would be welcome, if not necessary.
Second of all, the model presented by the authors is practically impossible to understand formally without reading another paper, referenced is a case of exaggerate referencing. The paper should present its theory in a complete way.
- Methodology: Is the paper’s argument built on an appropriate base of theory, concepts, or other ideas? Has the research or equivalent intellectual work on which the paper is based been well designed? Are the methods employed appropriate?
The paper combines a very interesting methodological approach, i.e. the formulation of complex systems in a way that makes them treatable with the method of evolution trajectory, with clear methodological weaknesses. As for the latter, three main questions emerge. Firstly, it seems to be methodologically incorrect to construe the cross-functional attractor arguments, where distinct phenomena are denominated one over the other. Secondly, the use of LM-BN network as a tool for validating the model is highly dubious. This specific network is made for quick optimization of something we understand and not for discovery inside something we barely understand.
Thirdly, the use of a neural network of any kind implies assuming that consecutive states of the system form a Markov chain, which is logically impossible with exogenous peak-values preset in the model.
- Results: Are results presented clearly and analysed appropriately? Do the conclusions adequately tie together the other elements of the paper?
The results are clear, yet their meaning seems not to be fully understood. Coefficients calculated via a neural network represent a plausibly possible state of the system. When the authors conclude that the results so-obtained, combined with the state of the system from the year 1980, it seems really stretched in terms of empirical inference.
- Implications for research, practice and/or society: Does the paper identify clearly any implications for research, practice and/or society? Does the paper bridge the gap between theory and practice? How can the research be used in practice (economic and commercial impact), in teaching, to influence public policy, in research (contributing to the body of knowledge)? What is the impact upon society (influencing public attitudes, affecting quality of life)? Are these implications consistent with the findings and conclusions of the paper?
The paper presents more implications for research than for society. As stated before, substantive conclusions of the paper boil down to common-sense claims, i.e. that it is better to keep the system stable rather than unstable. On the other hand, some aspects of the method used, i.e. the application of evolutionary trajectory, seem being very promising for the future. The paper seems to create abundant, interesting openings for future research rather than practical applications for now.
- Quality of Communication: Does the paper clearly express its case, measured against the technical language of the field and the expected knowledge of the journal’s readership? Has attention been paid to the clarity of expression and readability, such as sentence structure, jargon use, acronyms, etc.
The quality of communication is a serious weakness in this case. The above-mentioned exaggerate reference to Zhao, L., & Otoo, C. O. A. (2019). Stability and Complexity of a Novel Three-Dimensional Environmental Quality Dynamic Evolution System. Complexity, 2019, https://doi.org/10.1155/2019/3941920 is one point. The flow of logic is another. When, for example, the authors suddenly claim (page 8, top): ‘In this study we set …’, there is no explanation why and on what theoretical grounds they do so.
Clarity and correct phrasing clearly lack as regards all the macroeconomic aspect of the paper. It is truly hard to understand what the authors mean by ‘economic growth’.
Finally, some sentences are clearly ungrammatical, e.g. (page 6, bottom): ‘By the system (1) can be launched energy intensity […].
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[1] Hoffman, D. D., Singh, M., & Prakash, C. (2015). The interface theory of perception. Psychonomic bulletin & review, 22(6), 1480-1506.
[2] Fields, C., Hoffman, D. D., Prakash, C., & Singh, M. (2018). Conscious agent networks: Formal analysis and application to cognition. Cognitive Systems Research, 47, 186-213. https://doi.org/10.1016/j.cogsys.2017.10.003
[3] Michael, L. C., & Dean, C. A. (2013). Phenotypic trajectory analysis: comparison of shape change patterns in evolution and ecology. https://doi.org/10.4404/hystrix-24.1-6298