From Deep Learning in imaging neuroscience to nuclear physics in Quantum Computing

UMinho2020 Nicolás F. Lori From Deep Learning in Imaging Neuroscience to Nuclear Physics in Quantum Computing Fevereiro 2020 Nicolás Francisco Lori From Deep Learning in Imaging Neuroscience to Nuclear Physics in Quantum Computing University of Aveiro University of Minho Universidade do Minho Escola de Engenharia Nicolás Francisco Lori From Deep Learning in Imaging Neuroscience to Nuclear Physics in Quantum Computing Programa de Doutoramento em Informática das Universidades do Minho, de Aveiro e do Porto Universidade do Minho Trabalho realizado sob a orientação do Professor Doutor Victor Manuel Rodrigues Alves e do Professor Doutor Nuno J. Carvalho de Sousa Fevereiro 2020 Universidade de Aveiro ii DIREITOS DE AUTOR E CONDIÇÕES DE UTILIZAÇÃO DO TRABALHO POR TERCEIROS Este é um trabalho académico que pode ser utilizado por terceiros desde que respeitadas as regras e boas práticas internacionalmente aceites, no que concerne aos direitos de autor e direitos conexos. Assim, o presente trabalho pode ser utilizado nos termos previstos na licença abaixo indicada. Caso o utilizador necessite de permissão para poder fazer um uso do trabalho em condições não previstas no licenciamento indicado, deverá contactar o autor, através do RepositóriUM da Universidade do Minho. Licença concedida aos utilizadores deste trabalho Atribuição CC BY https://creativecommons.org/licenses/by/4.0/ iii Acknowledgments Foremost, I would like to thank Eduarda Sousa for her support. I am extremely indebted to my wife, Sandra Calado Lori, for her loving presence and help, and to all the help by the other family members and friends. This thesis would have been impossible to finish without the untiring support of my two thesis advisors, Victor Alves and Nuno Sousa, thus my thankfulness to both is profound. My colleagues have been extremely generous with their time, and thoroughly patient in tolerating my mistakes, impatience, and lack of temperance. For all that, I am extremely thankful. Also, a very special word of appreciation for José Neves, which was among the first to see the value to Computer Science of my efforts in advanced mathematical Physics. The publications associated to this Thesis were supported by ERASMUS scholarship, QREN, FEDER, COMPETE: POCI-01-0145-FEDER-007043, and by FCT (Fundação para a Ciência e a Tecnologia): UID/CEC/00319/2013, Investigador FCT, Ciencia 2007, PTDC/SAU-BEB/100147/2008, MEDPERSYST - POCI-010145-FEDER-016428, REP - PTDC/SOC-SOC/29207/2017, INESC-ID multi-annual funding from the PIDDAC program (UID/CEC/50021/2019). Data collection for this work was in part from ”Human Connectome Project” (HCP; Principal Investigators: Bruce Rosen, M.D., Ph.D., Arthur W. Toga, Ph.D., Van J. Weeden, MD). HCP funding was provided by the National Institute of Dental and Craniofacial Research (NIDCR), the National Institute of Mental Health (NIMH), and the National Institute of Neurological Disorders and Stroke (NINDS). HCP data are disseminated by the Laboratory of Neuro Imaging at the University of Southern California. This data is referred to as “HCP data”. Data collection for this work was in part from SWITCHBOX Consortium project (http://www.switchboxonline.eu/) realized in the “Life and Health Sciences Research Institute” (ICVS) and acquired using a Siemens Magnetom Avanto 1.5 T MRI scanner. This data is referred to as “In-House data”. No non-human animal data was obtained or used for this thesis. The human Magnetic Resonance Imaging (MRI) used in this thesis was obtained from publicly available published data, with the published data stating that the data had been approved by the corresponding ethical committees. iv Statement of Integrity I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho. v Resumo Do Deep Learning em Neurociência de Imagem à Física Nuclear em Computação Quântica Esta tese mostra como as descobertas da Ciência da Computação e da Computação Quântica, que se desenvolveram em alguns aspectos do Deep Learning em Neurociência de Imagem à Física Nuclear em Computação Quântica, podem levar a uma drástica e inovadora fundação no campo da Ciência da Computação. De facto, abrem-se oportunidades para melhorar temas aplicados e teóricos nessas disciplinas. Em particular, descobrimos que os avanços na Tecnologia da Informação dependem mais do "Deep Learning em Neurociência de Imagem" do que da "Física Nuclear em Computação Quântica". A razão para isso é que o foco é mais nos paralelos à computação da informação em sistemas biológicos do que na miniaturização, o que se concentraria nos paralelos à Física Nuclear. Inegavelmente, uma consequência importante desta tese é que a Ciência da Computação representa uma disciplina que pode ser interpretada como base para as outras tecnologias de inferência causal, ou seja, a Ciência da Computação denota não apenas uma coleção de ferramentas para Matemática, Física, Neurociências e Economia, mas também pode ser entendida como um valor agregado de tais disciplinas à ComputaçãoQuântica. Palavras-Chave: Computação Quântica, Deep Learning, Filosofia da Informação, Neurociência de Imagem. vi Abstract From Deep Learning in Imaging Neuroscience to Nuclear Physics in Quantum Computing This thesis shows how findings from Computer Science (CS) and Quantum Computing, which developed in some aspects from Deep Learning in Imaging Neuroscience to Nuclear Physics in Quantum Computing, can lead to severe and groundbreaking foundation in the field of CS. Indeed, opportunities open up to improve both applied and theoretical topics in these disciplines. In particular, we found that advances in Information Technology depends more on "Deep Learning in Imaging Neuroscience" than on "Nuclear Physics in Quantum Computing". The reason for this is that the focus is more on the parallels to information computation in biological systems than on miniaturization, which would focus on the parallels to Nuclear Physics. Undeniably, an important consequence of this thesis is that CS stands for a discipline that can be interpreted as the basis for the other causal inference technologies, i.e., CS denotes not just a collection of tools for Mathematics, Physics, Neurosciences and Economics, but can also be understood as an added value from such disciplines to Quantum Computing. Keywords: Deep Learning, Imaging Neuroscience, Philosophy of Information, Quantum Computing. vii Contents List of Figures ix List of Tables xi Acronyms xiii 1. Introduction 1 1.1 Computer Science´s Present and Future 3 1.2 Relating the publications with Computer Science 5 2. Computer Science’s Present 10 2.1 Distributed Computing “Wormholes” approach 10 2.1.1. Wormhole approach to distributed systems 11 2.1.2. Quantum Darwinism approach to Quantum Mechanics 14 2.1.3. Relation of Wormhole approach to Computer Science’s future 20 2.2 Monte-Carlo simulations improve Diffusion MRI data-processing 23 2.2.1. White Matter tractography using Imaging Neuroscience data 25 2.2.2. Monte-Carlo approach to Imaging Neuroscience data 30 2.3 Deep Learning pipeline improves functional MRI data processing 35 2.3.1. Building a Functional Connectivity Table 37 2.3.2. Deep Learning in Functional Connectivity Table 41 2.4 Application of partial Information approaches to Management 51 3. Computer Science’s Future 59 3.1. Axiomatic formalization of human mental health 59 3.1.1. Mental state objectivity using an axiomatic system 61 3.1.2. Mental state free-will using an axiomatic system 69 3.1.3. Integrating objectivity and free-will using 3-axes approach 75 3.1.4. Experimental evidences for 3-axes approach 82 3.2. Quantum computing at sub-atomic scales and Moore’s law future 90 xiv DL - Deep Learning dMRI – Diffusion Magnetic Resonance Imaging DNN - Deep Neuronal Networks DOF - Degrees of Freedom DSIDiffusion Spectrum Imaging DTI - Diffusion Tensor Imaging E EPI - Echo-Planar Imaging ECS - Emotional-Competent-Stimulus EPR - Einstein-Podolsky-Rosen EU – European Union F FAS - Formal Axiomatic Systems FC - Functional Connectivity FDs - Failure detectors fMRI – Functional Magnetic Resonance Imaging FMRIB - fMRI of the Brain FSL - FMRIB Software Library FWP - Free-Will Perception G GM - Gray Matter GPUs - Graphical Processing Units GR - General Relativity GRA – Gratitude GUT - Grand Unified Theory xv H HARDI - High Angular Resolution Diffusion Imaging HCP - Human Connectome Project HCT - Hammersley-Clifford Theorem I ICA - Independent Component Analysis IDE - Integrated Development Environment i.i.d. - Independent Identically Distributed IPython - Interactive Console of Python ITER - International Thermonuclear Experimental Reactor K KEMs - Key-Encapsulation Mechanisms KRR - Knowledge Representation and Reasoning M MIPR - Maximum Information Processing Rate ML - Machine Learning MRI – Magnetic Resonance Imaging N NAS - Newtonian Axiomatic Systems O ODF - Orientation Distribution Function OE - Organizational Efficiency P PA - Physics-cells Approach xvi PC - Principal Components PCA - Principal Component Analysis PC-MIPR - Physics-cell Maximum Information Processing Rate PDF - Probability Distribution Function PKC - Public-Key Cryptography PQ - Prosocialness Questionnaire PQC - Post-Quantum Cryptography PRO - Prosocialness PSTHs - Postsynaptic Time Histograms Q QC - Quantum Computer QCD - Quantum Chromodynamics QD - Quantum Darwinism QE - Quantum Existentialism QM - Quantum Mechanics QF - Quantum Field R R-LWE - Ring Learning with Errors ROIs - Regions of Interest rs-fMRI - Resting-State functional Magnetic Resonance Imaging RSNs - Resting State Networks S SBA - Seed-Based Analysis SD - Spherical Decomposition SEM - Standard Error of the Mean xvii SMP - Standard Model of Physics SU(n) - Special Unitary n-dimensional W WG - Wormhole Gateways WM - White Matter 1 Chapter 1 Introduction 1.1. Computer Science’s Present and Future The term Computer Science (CS) was first defined in the 1950’s and it has always been applied and interdisciplinary in nature, but despite its name, a lot of CS does not involve the study of computers themselves, but rather its focus is mostly about software, specifically about the theory, design, development, and application of software. The CS departments can be divided in two major types, the Mathematics-based and the Engineering-based types; with the first being focused in “theory and design”, whereas the second focuses in “development and application”. Usually, each CS scientist focuses in one of these two types, but this CS Ph.D. Thesis will consider both types. The Chapter 2 is mostly about “development and application” within CS’s present, whereas Chapter 3 is also about the appropriate “theory and design” for CS’s future. The most common description of contemporary CS in comparison with other sciences is to describe it as a branch of Mathematics (Fig. 1.1.1), whereas we propose that the future CS will be itself the source of the models generating the causality approaches that are the basis of the approaches used in different Technologies (e.g. Physics, Biology, Economics) (Fig. 1.1.2), moreover CS has been affirming itself as a form of theoretical Computer Engineering and as a branch of applied statistics (e.g. Fig. 1.2.1). Key points: • Explains that the focus of the Thesis is what the future of Computer Science (CS) is likely to be given what is known in the present about the usage of CS. • The major comparison being between “Deep Learning in Imaging Neuroscience” and “Nuclear Physics in Quantum Computing”. Chapter 1 | Introduction 2 The four published works that serve as basis for the four sections of Chapter 2 are respectively in Theoretical CS, Applied Statistics, Applied CS, and in a CS application to Economics/Management: 2.1. Distributed Computing “Wormholes” approach [PUBLISHED] Lori, N. F., Alves, V. (2017). Wormhole approach to control in distributed computing has direct relation to physics. CONTROLO 2016. Proceedings of the 12th Portuguese Conference on Automatic Control. Lecture Notes in Electrical Engineering (LNEE), volume 402. SpringerVerlag. pp. 105-117. 2.2. Monte-Carlo simulations improve Diffusion MRI data-processing [PUBLISHED] Lori, N. F., Ibañez, A., Lavrador, R.; Fonseca, L., Santos, C; Travasso, R., Pereira, A., Rossetti, R., Sousa, N., Alves, V. (2016). Processing Time Reduction: an application in living human high-resolution diffusion magnetic resonance imaging data. Journal of Medical Systems. 40(11), 243. 2.3. Deep Learning pipeline improves functional MRI data processing [PUBLISHED] Lori, N. F., Ramalhosa, I., Marques, P., Alves, V. (2018). Deep Learning Based Pipeline for Fingerprinting Using Brain Functional MRI Connectivity Data. Procedia CS. Volume 141, pp. 539-544. 2.4. Application of partial information approaches to Management [PUBLISHED] Neves, J., Maia, N., Marreiros, G., Neves, M., Fernandes, A., Ribeiro, J., Araújo, I., Araújo, N., Ávidos, L., Ferraz, F., Capita, A., Lori, N., Alves, V., Vicente, H. (2019). Entropy and Organizational Performance. In: Pérez García H., Sánchez González L., Castejón Limas M., Quintián Pardo H., Corchado Rodríguez E. (eds) Hybrid Artificial Intelligent Systems. HAIS 2019. Lecture Notes in CS, vol 11734. Springer, Cham. Chapter 1 | Introduction 3 a) b) Figure 1.1.1. Contemporary Computer Science within human knowledge: a) Relation between CS and the other sciences with their corresponding scales from ref. (Wikipedia, 2019); b) Interaction between CS and the more closely related fields from ref. (UALT, 2019). The trend in Future CS described in Chapter 3 implies that CS is becoming the source of the causal inference model, rather than simply being a vehicle for causal inferences assumed by science. a) b) Figure 1.1.2. CS’s future roles: a) Development of societal improvement from ref. (Adpakkala, 2017); b) Branch of physical sciences from ref. (Eigenfactor.org, 2004). Chapter 1 | Introduction 4 The two published works that serve as basis for the two Sections of Chapter 3 are respectively in Neuroscience where it was proposed an axiomatic formalism-based description of the causal inferences associated to human mental health (Fig. 1.1.2a), and in how the different role causal inference has in quantum computers (QCs) will not be able to overcome the incapacity of classical computers (CCs) in continuing to uphold Moore’s law (Fig. 1.1.2b): 3.1. Axiomatic Formalization of Human Mental Health [PUBLISHED] Lori NF, Samit E, Picciochi G, Jesus P. (2019). Free-will Perception in Human Mental Health: an Axiomatic Formalization. IN: Automata’s inner movie: Science and Philosophy of Mind. Vernon Press. 3.2. Quantum computing at sub-atomic scales and Moore’s law future [PUBLISHED] Lori NF, Neves J, Alves, V. (2020). Some considerations on quantum computing at subatomic scales and its impact in the future of Moore’s law. Quantum Information & Computation. Vol. 20, No. 1&2. pp. 1-13. Plus, there were three published works in “Imaging Neuroscience” associated to this Thesis: 1. Ibañez, A., Zimerman, M., Sedeño, L, Lori, N., Rapacioli, M., Cardona, J., Suarez, D., Herrera, E., García, A., Manes, F. (2018). Early bilateral and massive compromise of the frontal lobes. NeuroImage: Clinical. Volume 18, pp. 543-552. 2. Sedeño, L., Piguet, O., Abrevaya, S. G., Garcia-Cordero, I., Baez, S., de la Fuente, L. A., Reyes, P., Tu, S., Mogilner, S., Lori, N., Landin-Romero, R., Matallana, D., Slachevsky, A., Torralva, T., Chialvo, D., Kumfor, F., Garcia, A. M,. Manes, F., Hodges, J., Ibañez, A. (2017). Tackling variability: A multicenter study to provide a gold-standard network approach for frontotemporal dementia. Human Brain Mapping. 38(8), Aug, pp. 3804-3822. 3. Yoris, A., Abrevaya, S., Esteves, S., Salamone, P., Lori, N., Martorell, M., Legaz, A., Alifano, F., Petroni, A., Sánchez, R., Sedeño, L., García, A. M., Ibáñez, A. (2017). Multilevel convergence of interoceptive impairments in hypertension: New evidence of disrupted body-brain interactions. Human Brain Mapping, 39(4), Apr; pp. 1563-1581. Chapter 1 | Introduction 5 1.2. Relating the publications with Computer Science The relation of CS with the works of the four Sections of Chapter 2 and the two Sections of Chapter 3 are described in Fig. 1.2.1, where it is made clear which work was done in “Applied CS” or “Theoretical CS”. Figure 1.2.1. Contemporary CS perspectives: Theoretical and Applied Computation from ref. (Connectedreams.com, 2016). To analyze contemporary CS, we focused in two aspects of science where Applied and Theoretical CS have been used, “Imaging Neuroscience” and “Quantum Computing”. The goal of this Thesis is to assess whether the future of CS will be more based in the “Deep Learning in Imaging Neuroscience” or in the “Nuclear Physics in Quantum Computing”, hence we started by analyzing 2.3 2.1 2.2 2.4 3.1 3.2 Key points: • Both Chapter 2 and Chapter 3 are based in published studies, hence the content of this Thesis is fully based in publications. • Both the relation of the publications with CS, and the relation between publications are described here. Chapter 1 | Introduction 6 distributed computing using Nuclear Physics concepts (see Section 2.1) and by analyzing how MonteCarlo processing helped reduce the processing time of “Imaging Neuroscience” data (see Section 2.2.). In Section 2.1, the topic of Wormholes in distributed computing is described as creating two different realms with different characteristics, the synchronous Wormholes and the asynchronous payload with the goal of using the Wormholes to control the synchronism of the payload processes. We describe the characteristics of Wormholes in distributed computing, and relate them to issues in Physics, specifically, Wormholes in general relativity (GR) and entanglement in quantum mechanics (QM). The entanglement in QM is about the existence of fixed relations between different physical systems as if they were still the same system. The entanglement is made evident by the occurrence of decoherence, which transform the multiple outcome possibilities of quantum systems into a single outcome “classical Physics”-like objective reality. It is here presented the similarity between the decoherence process in quantum Physics and the consensus problem in distributed computing. The approach to QM used is quantum Darwinism (QD), a Darwinian approach to decoherence where the environment controls the outcome of a measurement. It is here proposed that wormhole systems can be used to implement environment-based control of distributed computing systems. In Section 2.2., we analyze High Angular Resolution Diffusion Imaging (HARDI) which is a type of diffusion Magnetic Resonance Imaging (dMRI) “Imaging Neuroscience” data that requires a very large amount of data, and if many subjects are considered then it amounts to a big data framework, for example, the human connectome project (HCP) has 20 Terabytes bytes of data. HARDI is also becoming increasingly relevant for clinical settings, for example, in the early detection of cerebral ischemic changes in acute stroke and in pre-clinical assessments of white matter (WM) anatomy using tractography. Thus, use of very large amounts of data are becoming a routine occurrence in clinical settings. In such settings, the computation time is critical, and hence finding forms of reducing the processing time in high computation processes such as Diffusion Spectrum Imaging (DSI) which is a form of HARDI data, it is thus very useful to find forms of increasing the data-processing speed. Here, we analyze a method for reducing the computation time of the dMRI-based axonal orientation distribution function h by using Monte Carlo sampling-based methods for voxel selection. Results evidenced a robust reduction in required data sampling of about 50% without losing signal’s quality. Moreover, we show that the convergence to the correct value in this type of Monte Carlo HARDI/DSI data-processing has a linear improvement in data-processing speed of the Orientation Distribution Chapter2 | Computer Science’s Present 13 It is common in science-fiction the use of space-time Wormholes for faster than-light travel and/or the use of quantum tunneling for teleportation (e.g. Star Trek). Thus, it is fair to ask if the use of Wormholes in distributed computing accomplishes what it sets out to achieve in the real world, or if it is a sort of CS equivalent to science-fiction. This is especially relevant as QCs have recently become a reality (Arute, 2019), even though there are still some doubts about its actual impact (Lori, 2020) as we will describe in Section 3.2. Thus, this question about the Wormhole approach being practical, or just sci-fi phantasy, is a relevant question (Lori, 2017) that can be translated into two specific questions: 1. Is it feasible to construct Wormhole distributed systems? 2. Are distributed systems with Wormholes useful? For the first question, in the Wormhole approach (Verissimo, 2006) the architectural hybridization was proposed as a new paradigm. This implies that systems may have zones (a.k.a. realms) with different nonfunctional properties, such as synchronism, faulty behavior, and quality-ofservice. This implies that the properties of each zone/realm are obtained by construction of the subsystem(s) therein, and that these subsystems have well-defined encapsulation and interface approaches through which these former properties become manifested. The Timely Computing Base (TCB) allows for the obtaining of timely actions in systems that can be asynchronous; which means that the TCB distributed Wormhole gateway provides very helpful services such as: timely execution, duration measurement, and timing failure detection. Through the TCB, it is possible (Verissimo, 2006) to make an asynchronous system perform timely (synchronous) actions or detect the failure thereof. So, the answer to the first question is yes, it is feasible to construct Wormhole distributed systems. (Lori, 2017) For the second question, it is relevant to consider that the most important implications of the use of hybrid distributed network models are: quantification of the assumptions’ substance rather than just considering what the assumptions are, difference to partial synchrony models, a new approach to the FLP impossibility (Fischer, 1985) result; and the existence of failure detectors (FDs). The substance of these assumptions is important because it is the “assumption+coverage” pair that measures the weakness or strength of the distributed network model, and because the use of architectural Chapter2 | Computer Science’s Present 14 hybridization can possibly improve the building of hybrid fault-tolerance approaches. The Wormhole approaches are different from the partial synchrony approaches in that the first are heterogeneous, whereas the second are homogeneous. Moreover, the Wormholes can circumvent the FLP impossibility result because a form of avoiding the FLP impossibility is by using synchronism (Chandra, 1996). (Lori, 2017) The avoidance of the FLP impossibility in Wormholes approaches occurs using FDs. The FDs in asynchronous systems are difficult, but the consensus in the payload systems agrees with FDs in the Wormhole realm, which implies that functionality in a Wormhole is not confined to FDs, thus opening towards other, more generic, approaches. The Wormhole approach clarifies borderline situations where homogeneous asynchronous systems fail, and when asynchronous models must be complemented with timing assumptions to address timeliness specifications; thus, there is no alternative to Wormholes for correct specification of such settings (Verissimo, 2006). So, the answer to the second question is yes, it is useful to construct Wormhole distributed systems. (Lori, 2017) The Wormholes approach allows extending partial synchrony to the space dimension, meaning that, regardless of the asynchronism of the whole system, some parts of the system exhibit a welldefined (perpetual if desired) time-domain behavior. The parallel to QM is, for example, that before a measurement in QM (Zurek, 2005)(Zurek, 2005)(Zurek, 2007) the quantum states behave as if they were the asynchronous components of the payload system, but as the quantum states interact (and thus become measured) they start behaving more as synchronous Wormholes. To better describe that parallel, we describe QM in the next section. (Lori, 2017) 2.1.2. Quantum Darwinism approach to Quantum Mechanics Contemporary Physics is based on two approaches that have not yet been reconciled, quantum fields (QFs) (Sakurai, 1994) and GR (Wald, 1984). In stable conditions, meaning when the creation and destruction of fermions (e.g. electrons, protons, and neutrons) is small, the QFs can be represented by QM (Sakurai, 1994). While GR is deterministic (implying that there are no fundamental uncertainties associated with physical variables), QM has intrinsic fundamental uncertainty which is dissipated by the interaction with the environment. It can be said that the uncertainty in QM is kept alive at long distances Chapter2 | Computer Science’s Present 15 through the occurrence of entanglement along quantum tunnels, and some recent work has indicated that the existence of quantum tunneling might be based on the occurrence of extremely tiny Wormholes (Sonner, 2013)(MIT, 2013), and following this possibility it becomes possible that although Physics’ Wormholes (a.k.a. Einstein-Rosen bridges (Einstein, 1935)) are a solution to the GR equations, they can still have strong structural similarities to a QM process called entanglement, a process by which the uncertainty associated to pairs of quantum systems can remain connected even if the systems are very far apart. Whereby for the entangled pair of quantum systems, the resolving of the uncertainty about one of the quantum systems faster-than-light resolves the uncertainty on the other quantum system, no matter how far apart each pair element is from the other pair element. It is as if there was a Wormhole joining the pair of quantum systems. Thus, Wormholes in distributed computing can be associated to both the Physics of GR’s Wormholes and/or the entanglement of QM. In both QM and GR, the physical representation of a state is always about two realms, specifically, the system and the environment (Lori, 2017). The system is what we aim to represent, and the environment is everything else that influences the system, which in extreme cases means the rest of the universe. (Lori, 2017) There are different approaches to QM, we will follow the QD (Zurek, 2005)(Zurek, 2007)(Zurek, 2009) approach, which is an approach to QM that is strongly based in the Information-transport and thus is very relevant for the analysis of QCs (Arute, 2019)(Lori, 2020) as will be described in Section 3.2. Moreover, in Section 3.1 we assess the role of distributed networks in determining objective mental health (Lori, 2019), and so it it is useful to define the axioms of QD in a format that is more general, and so applies not only to QM but also to other situations of Information-transport (e.g. in distributed networks). Thus, we move away from the QM interpretation of these postulates, but stay with their mathematical structure, which is given in terms of vector spaces. For instance, where one reads quantum system in the QD formalism, we write system, with the understanding that the characteristic property of such a system is to be individually accessible to measurements; likewise, the quantum state is replaced by a vector in a multidimensional vector space; and so on. (Lori, 2017) In Fig. 2.1.2 instead of the → used in the vector states of the rest of the article, the |> symbol will be used; and we use suits because that is a representation used in ref. (Zurek, 2005). In Fig. 2.1.2 is described how the principle of indifference, the basis of statistics, has a different meaning in quantum versus classical Physics. In Fig. 2.1.2a, the principle of indifference is described, and it states that a card Chapter2 | Computer Science’s Present 16 player who knows one of the two cards is but does not see their faces, does not care—is indifferent— when cards get swapped. So, when the probability of a favorable swap is the same before and after the swap, then the states are equivalent (≈). In Fig. 2.1.2b it is described how in classical Physics, because of its objective perspective, the states before and after the swap are equivalent but not equal. In Fig. 2.1.2c it is described how in the QD perspective of QM if the system S and the environment E interact (a.k.a. entangle), then the definition of the system S only exists in relation to the environment E , and so does not exist by itself, meaning that the states before and after the swap are equal. This means that the swapping of and ♥ in the system S is possible to compensate by the swapping of ♦ and in the environment E . (Zurek, 2005). (Lori, 2017) Figure 2.1.2. a) When the probability of a favorable swap is the same before and after the swap, then the states are equivalent (≈). b) In classical Physics, because of its objective perspective, the states before and after swap are equivalent (≈) but not equal (≠). c) In QD, the swapping of and ♥ in the system S is possible to compensate by the swapping of ♦ and in the environment E , thus obtaining a state that is equal (=) to the original state. (from (Zurek, 2005) [©2005 The American Physical Society]) The use of this new notation makes the QD axioms have the following aspect (Lori, 2017): Chapter2 | Computer Science’s Present 17 o. The universe consists of systems individually accessible to observations. i. The state of a system is represented by a vector in a multidimensional vector space, and all converging series of vectors of the vector space converge to a vector of that same vector-space. To each vector is associated a dual vector. The inner product between a dual vector and a vector is a scalar. ii. The time-evolution of a vector is such that the inner product of a vector is preserved. iii. If the outside of a system (the environment) remains unchanged, then the observation of the system remains unchanged across time. According to QD axiom iii, there must be a set of states of the system that remains unaltered by the interaction with the environment, call it vector state set Sk . So, there must be an alteration of the environment leading to the environment being now represented by the vector state set Ek . (Lori, 2017) Let’s consider that the possible states of the system S are and ♥, and that the possible states of the environment E are ♦ and . In that case, due to QD axioms o and i , the state of the system can be represented by (α and β are scalars) (Lori, 2017): 𝑆=∝ 󰇍 󰇍  +𝛽 󰇍 󰇍  (2.1.1) Consider that the environment E can make one-to-one measurements of S , such that before interacting with S the environment E is represented by the vector state (Lori, 2017): 𝐸0 󰇍 󰇍 󰇍 󰇍  =∝0 󰇍 󰇍 󰇍 󰇍 󰇍  +𝛽0 󰇍 󰇍 󰇍 󰇍 󰇍  (2.1.2) Consider that after S and E start interacting, the state vector of E is then (Lori, 2017): Chapter2 | Computer Science’s Present 18 𝐸 󰇍  =∝ 󰇍 󰇍  +𝛽 󰇍 󰇍  (2.1.3) Implying that before S and E start interacting, the state of “ S+E “ is (Lori, 2017): 𝑆𝐸 󰇍 󰇍 󰇍 󰇍 󰇍  =(∝ 󰇍 󰇍  +𝛽 󰇍 󰇍  )(0 󰇍 󰇍 󰇍 󰇍 󰇍  +0 󰇍 󰇍 󰇍 󰇍 󰇍  ) (2.1.4) After S and E start interacting, for postulate iii to be valid it is necessary that the state of “ S+E ” is (Lori, 2017): 𝑆𝐸 󰇍 󰇍 󰇍 󰇍 󰇍  =(∝ 󰇍 󰇍   󰇍 󰇍  +𝛽 󰇍 󰇍   󰇍 󰇍  ) (2.1.5) Due to QD axiom ii , the evolution of the “ S+E ” state must preserve the inner product, and thus also preserve the amplitude of the vector representing the state. Thus, the joining of QD axioms o , i , and ii implies that the evolution of the state of “ S+E ” during a measurement must be such that it is capable of going from a state of S and E being not-linked (Eq. 2.1.4), to a state of S and E being linked (Eq. 2.1.5), without altering the amplitude of the vector representing the state. If the square amplitude of the “ S+E ” vector is the same before (Eq. 2.1.4) and after S and E start interacting (Eq. 2.1.5), then (Lori, 2017): ∝𝛽( 󰇍 󰇍  • 󰇍 󰇍  )(‖0 󰇍 󰇍 󰇍 󰇍 󰇍  +0 󰇍 󰇍 󰇍 󰇍 󰇍  ‖2−  󰇍 󰇍  • 󰇍 󰇍  )=0 (2.1.6) Due to QD axiom iii , the above equation should continue being valid long after S and E start interacting. Since this result must be valid for any value of α and β, there are only two possibilities (Lori, 2017): Chapter2 | Computer Science’s Present 19 {‖0 󰇍 󰇍 󰇍 󰇍 󰇍  +0 󰇍 󰇍 󰇍 󰇍 󰇍  ‖2= 󰇍 󰇍  • 󰇍 󰇍   󰇍 󰇍  • 󰇍 󰇍  =0 (2.1.7) The upper line of the previous equation implies that the system has no influence in the environment, whereas the lower line implies that the system states are orthogonal. The joint consequence of both lines is that (Zurek, 2005)(Lori, 2010a)(Lori, 2017): “the vector states of the system capable of leaving a print in the environment, no matter how small the print, will necessarily be orthogonal vector states”. The Darwinian aspect of QD is that states of the system that fail to print themselves into the environment cease to exist (Zurek, 2005)(Zurek, 2007)(Zurek, 2009), meaning they become extinct. This aspect of QD is called Quantum Existentialism (QE) because the states only survive by their capacity for printing Information about themselves in the environment (Zurek, 2005)(Zurek, 2007)(Zurek, 2009). (Lori, 2017) The preservation in the environment, after the measurement, of the Information about the measurement in large enough quantities on the environment so as to be read by multiple observers creates the illusion of the state’s “objective reality”. The “objective reality” of the vector states of the system is given by their capacity to transmit Information into the vector states of the environment. The successful transmission of Information is the printing of the Information about the system in the environment states, such that the environment states become themselves orthogonal. When that occurs, then the system and the environment become entangled. (Lori, 2017) An entangled combination of system and environment can be described by a vector state where each component of the vector state is the product of a system output state Sk with its corresponding environment output state Ek . The coefficient associated to that product of states is called the Schmidt coefficient, which is a complex number of amplitude one (Ekert, 1995). This implies that for an entangled “system+environment” state an action on the system causes an angle shift on the Schmidt coefficient phase θ k , and that angle shift can be compensated by an action on the environment. This implies that in the presence of entanglement it is possible to describe a type of invariance where the Chapter2 | Computer Science’s Present 20 system is altered by an action on the system, but that alteration of the system can be totally compensated by an action on the environment without the occurrence of any further action on the system (see Fig. 2.1.2c). This type of invariance is called an environment-assisted invariance, which in short form is called envariance (Zurek, 2005). This analysis of the effect of Information-transport is the representation of a system is made in the Section based on ref. (Lori, 2017), in Section 3.1 based on (Lori, 2019), and in Section 3.2 based on ref. (Lori, 2020). 2.1.3. Relation of Wormhole approach to Computer Science’s future The Wormholes approach allows for different processes of the payload to communicate “immediately” through the synchronism of the Wormholes, the Wormholes thus play the same role as the entanglement in QD by assuring that there can be “immediate” connection between different components of the payload. This form of control of the payload by the Wormholes is especially useful in representing distributed quantum computing control as the Wormholes in the Wormhole model can accurately represent the role of the environment in quantum entanglement. To represent QD using the Wormholes model it should be noted that because the Wormholes are becoming synchronous within themselves, they then could be used to eliminate the time-evolution of the payload processes that are not in agreement with the Wormhole synchronization, so forcing the payload processes to become synchronous with the Wormholes or stop. So, it is possible to consider QD as a Wormhole control system occurring in quantum reality. The parallels between distributed computing, Wormholes and Physics (Lori, 2017) as described in this work might be useful a describer of QC performance within distributed quantum computing (e.g. ref. (Arute, 2019) and ref. (Lori, 2020), see Section 3.2), and for clarifying what are the computations associated to the occurrence of Consciousness in humans (Lori, 2019) which is very relevant for the issue of objective human mental health (Lori, 2019) as described in Section 3.1. For correctly understanding the relation between the Wormhole approach and QM it is relevant to describe that in the Laboratory for Attosecond Physics it was possible to generate visible flashes of light in attosecond dimensions (Hassan, 2016). At that laboratory, they dispatched light-flashes to the electrons in krypton atoms, and they were thus able to obtain that the electrons, which are stimulated by Chapter2 | Computer Science’s Present 21 the flashes, needed roughly 100 attoseconds to respond to the incident light. Until then it was assumed that particles respond to incident light without delay. These experimental results might be directly related to the Wormhole approach proposed here. The 100 attosecond of light traveling in vacuum corresponds to a travel distance of about 300 Angstroms, implying that this cannot be the size of the electron or any fundamental particle. If it is considered that electrons have a finite computation capacity, as proposed in ref. (Lori, 2017); then electrons would need to take 100 attoseconds to process the corresponding Feynman diagrams, or the physical equivalent of the mathematical object that the Feynman diagrams are, before the electron could compute the outputted light. To check if this perspective makes mathematical sense, we can check if the "lifetime of the excited state" described in ref (Hassan, 2016) can be the computation time of the Planck volumes associated to the volume of the electron. If the lifetime is T and the particle is a sphere with volume V , then if each Planck cube (a cube with sides equal to Planck length) is a processor that takes a Planck time to process the input Information into output Information, and A is the Planck area (a square with sides equal to Planck length) and c is the speed of light in vacuum, then the radius R of the electron would relate to T by the relation (Lori, 2017): 𝑅=√3 4𝜋𝑐 𝐴 𝑇 3 (2.1.8) The above equation implies that the electron has a radius of about 25*10-28 meters. It is usually assumed that "a search for a contact interaction at the LEP storage ring probes for electron structure at the 10 TeV energy scale in which case R < 2 x 10-20 m." (Bourilkov, 2001). Which is in total compatibility with the result obtained in Eq. 2.1.8. (Lori, 2017) This Section aimed at the goals of establishing a bridge between Information-transport in distributed computing and the decoherence processes in QM, which is relevant for Section 3.2; plus a bridge between Information-transport in distributed networks of biological neurons and the axioms of QD, which is relevant for Section 3.1. Thus, both goals were achieved, but before going on to Section 3.1 and Section 3.2, several intermediary steps need to be achieved. Specifically, we need to: assess if the Chapter2 | Computer Science’s Present 22 required Information-processing power necessary to high-density “Imaging Neuroscience” is too demanding for CCs, or if good-enough CS-based shortcuts can be used to achieve good-enough “Imaging Neuroscience” while still using CCs, and this is done in Section 2.2; assess if “Deep Learning in Imaging Neuroscience” can be achieved in a good enough form using contemporary CCs and this is done in Section 2.3; and assess if the qualification of the Information-transport is useful for describing human mental health by analyzing the productivity within a company, and this is done in Section 2.4. Chapter2 | Computer Science’s Present 29 . (2.2.6) The anisotropic volume is the difference between total volume and isotropic volume: The ratio between the anisotropic fraction of WM fibers, and the total amount of WM fibers is: . The ratio for the isotropic fractions (only calculated for WM voxels) is thus (Lori, 2016): (2.2.7) The Ξ iso of each voxel was correlated with the k values obtained using the approach described in the next section. The study was performed on high quality DSI dMRI data from the Human Connectome Project (HCP). Henceforth, we will refer to these data as “HCP data”. The HCP data used in the preparation of this work were obtained from the database of the MGH-UCLA section of the HCP (all the HCP data has been approved by the corresponding ethical committees and internal review boards) (UCLA, 2012), the HCP data includes an anatomical T1-weigthed volume. The anatomical data, and segmented maps were coregistered to diffusion space using “fMRI of the brain Software Library” (FSL). Furthermore, we also used anatomical labeling provided by FSL; so that WM can be distinguished from gray matter (GM), from cerebro-spinal-fluid (CSF), and from everything else that is not WM. The anatomical image had its intensity inhomogeneity corrected, contrast adjusted, voxel re-sampled, and coregistered to the dMRI data. The values of TR and TE differed depending on which gradient orientation and amplitude is considered (Lori, 2016). The HCP DSI data was acquired in Siemens 3T scanners in a cubic q-space grid format, with 514 gradient directions, 2 mm isovoxels, an image size of 104x104, and 55 transversal slices. There were available only 2 subjects with data suitable for our analysis, for our analysis required data which was acquired using the maximum gradient strength and that could be processed using DSI approach. = Chapter2 | Computer Science’s Present 30 The subject 1, was acquired using a maximum gradient of 300 mT/m, b maximum of 15000 s/mm2; whereas subject 2 was acquired at a maximum gradient of 90 mT/m and b-value maximum of 10000 s/mm2. The segmentation of the WM was performed in HCP data using FSL (Zhang, 2001). The anatomical data, and segmented maps were coregistered to diffusion space using FSL. (Lori, 2016) 2.2.2. Monte-Carlo approach to Imaging Neuroscience data The Diffusion Toolkit/TrackVis software (Wedeen, 2008) was used to obtain a 181 points ODF surface (not the axonal ODF). The obtained ODF data contains ODF peaks, which are the orientations for which the ODF is higher. The ODF peaks data binary data takes the value of 1 if the value of the ODF is a local maximum, and zero otherwise. For each peak, there is a peak pointing in the opposite direction with almost equal amplitude. If the ODF contains more than 3 pairs of opposing peaks, only the 3 highest ODF pairs of opposing peaks will be used. In this Section, we call the orientation of a pair of ODF opposing peaks, an axis. In an axis, a connection to a neighboring voxel can be made by either advancing or retreating along that axis. We developed an automatic approach method based on previous works (Wedeen, 2012), which is a WM axis extension approach where for each WM point it is determined the number of axes parallel to the axis of another WM point. The obtained topological structure is a 3-plane crossing grid, such as occurs in Fig. 2.2.2 (Lori, 2016). The number of coincident axes between two neighboring points is denoted by a non-negative integer k , implying that in the same voxel there can be different k values depending on which neighboring WM points are considered. The value of k between two neighboring points defines the number of parallel fiber axes between the two sets of 3 axes, one set per point. The axes extension and parallelism detection are only performed for WM voxels, Fig. 2.2.4. The isotropic fractions are higher near the vicinity of GM, as it is expected, since the fibers theoretically become less organized and with a less defined main direction. The regions with lower Ξ iso are mostly located in the corpus callosum, superior longitudinal fasciculus, and corticospinal tracts (Fig. 2.2.4). The regions with lower isotropic fraction are in agreement with bigger k values from the tractography method. It is apparent that high k values correspond to low values of Ξ iso . This was confirmed by calculating the mean values of the Ξ iso for each group of voxels with a given k value, Table Chapter2 | Computer Science’s Present 31 2.2.2. To assess the required amount of data needed to get the correct results without needing to deal with the multiple comparison problems, we used the Monte Carlo permutation test. The data were randomly sampled without replacement, so as to guarantee that the same data point is not sampled twice, This also limited the number of possible samples to the maximum number of data points existing with the feature of the population being sampled (e.g. k=1). One of the advantages of the Monte-Carlo method is that the sampling ordering is random, which reduces the systematic errors caused by sequential sampling. (Lori, 2016) The relation between the percentage of voxels used (x-axis) and the value of Ξ iso represented as a fraction of the Ξ iso obtained when all voxels are used (y-axis) appears in Fig. 2.2.5. We obtain the relations between the percentage of voxels used (x-axis) and the percentage of sub-partitions whose averages are within ±1 standard error of the mean (SEM) of the true average (y-axis) (Fig. 2.2.6), the needed percentage of used voxels being defined when the percentage of means within ±1 SEM is 68%, as it should be. These results were obtained for each of the three axis connections possibilities, specifically, k=1 , k=2 , and k=3 . For both Fig. 2.2.5 and Fig. 2.2.6 the voxels are randomly sampled without replacement using a Monte Carlo method. (Lori, 2016) Figure 2.2.4. Example of results using HCP DSI human data overlaid on HCP anatomical MRI. (Lori, 2016) Chapter2 | Computer Science’s Present 32 Table 2.2.2. Isotropic fractions’ Ξ iso relation to k values for two subjects. Only k values with more than 5 voxels were considered statistically significant. (Lori, 2016) a) b) c) Figure 2.2.5. Comparison of Ξ iso calculated with all the voxels (straight line ± 1 SEM) versus Ξ iso calculated with a Monte Carlo fraction of the voxels (y-axis) as a function of the fraction of the Monte Carlo-selected voxels (x-axis): a) k=1 , b) k=2 , c) k=3 . (Lori, 2016) a) b) c) Figure 2.2.6. Calculation using Monte Carlo method of the fraction of voxels with Ξ iso within ±1 SEM of the Ξ iso calculated with all the voxels (y-axis) as a function of the fraction of the Monte Carlo-selected voxels (x-axis): a) k=1 , b) k=2 , c) k=3 . (Lori, 2016) Chapter2 | Computer Science’s Present 33 We show that the use of Monte Carlo voxel sampling obtained the correct result within ±1 standard (SEM) 68% of the times using only about 50% of the data, which is what allows us to say that the Monte Carlo method is capable of reducing the computation time by about 50% without loss in result quality. Plus, we found that the regions with higher k values correspond to regions with lower Ξ iso . An arrangement k=3 between voxels suggests a lower isotropic fraction, which means that the 3-axis arrangement of the axons is a good representation of the majority of the axons’ distribution, in agreement with the results of ref. (Wedeen, 2012) used in Section 3.1. The simpler the arrangement, respectively k=2 and k=1 , the higher the isotropic component of axonal distribution. (Lori, 2016) The neuroscience of big data has challenged the processing speed requirements, especially in the field of connectomics (Lichtman, 2014)(Marder, 2015). Recent developments of new brain network technologies will soon allow for scalable data analysis. In dMRI data, high image resolutions are needed to accurately reconstruct connections, making the size of the input set very large (Lichtman, 2014); and we describe in Section 3.1 how these types of “Imaging Neuroscience” data will allow for the clarification of what objectively is human mental health. To make assessment like those proposed in Section 3.1 using contemporary CCs, it is likely that an improvement in “Imaging Neuroscience” data-processing speed will have an exponential effect in big data platforms (Lichtman, 2014)(Craddock, 2015)(Marder, 2015)(Boubela, 2015), especially in the context of current collaborative multicenter studies (Sedeño, 2017) and also in clinical settings (Ibañez, 2018). Hence, the brain structural connections among regions and their mapping to clinical and individual differences in healthy, psychiatric and neurological domains will have a critical growing with future big data connectome, open science resources, and massive clinical assessment (Craddock, 2015). (Lori, 2016) As will be described in Section 3.1, the alteration of brain connectivity is observed across a large range of psychiatric and neurological disorders. In fact, most of them have some degree of aberrant connectivity (Barkhof, 2014)(Worbe, 2015)(Zhou, 2014)(Sharp, 2014). This knowledge will soon have direct applications for both clarification of the biology of these diseases as well as in drug discovery process. In the future, it is very likely that connectomics will become part of the routine clinical assessment. In these settings, short time windows between recordings and evaluation became crucial. Hence, although the approach provided here needs to be replicated in larger samples, in different Chapter2 | Computer Science’s Present 34 recordings, with dissimilar scan qualities, and in diverse neuropsychiatric conditions, approaches such as those proposed here will likely be useful in application to “Neuroscience Imaging” big data. Chapter2 | Computer Science’s Present 35 2.3 Deep Learning pipeline improves functional MRI data processing A major goal of this thesis is the use of “Deep Learning in Imaging Neuroscience” and in this Section we will directly assess this topic. Neuroimaging has a major clinical application of serving as medical support in the field of Neurology, and even more so for the case of diagnosis. Nevertheless, the use of “Imaging Neuroscience” has been growing in other fields, e.g. in Psychiatry as a mean of a better understanding psychiatric disorders (Lori, 2019) (see Section 3.1). Moreover, a new dimension called brain-body medicine focuses in the study and understanding of the interactions between the brain, peripheral pathways and bodily organs (e.g. (Yoris, 2017)). These new advances give three new approaches to “Imaging Neuroscience” research (Lori, 2018): mind-body connections, psychosomatic behavior, and integrative medicine (Lane, 2009)(Horowitz, 2009). These three new approaches are used in Section 3.1 to objectively define what is human mental health (Lori, 2019), but in this Section we will focus in how to use DL in this type of “Imaging Neuroscience” data. In “Imaging Neuroscience”, the study of brain structure (e.g. by dMRI) is not enough, as it doesn’t give relevant Information for the diagnosis of pathologies when structural alterations are not anatomically detected. Thus, it was necessary to find an appropriate method to assess brain function, which led to the development of fMRI, a technique that monitors hemodynamic events related to changes in neuronal activation in the brain, relying on the Blood Oxygenation Level-Dependent (BOLD) contrast (FMRI, 2009)(Ogawa, 1990). This use of fMRI has countless advantages such as non-invasiveness, relative easiness of implementation, and high spatial resolution. Moreover, the resulting signal is robust, it is easily reproducible and highly consistent. (Horowitz, 2009). The fMRI is typically used in the context of a Key points: • To reach the goal of analyzing the future of CS in using “Deep Learning in Imaging Neuroscience” as described in Section 3.1, we start here by assessing its use in the present of CS. • The results obtained here increase the applicability of the new forms of using CS described in Section 3.1, and it is the joining of Section 2.2, Section 2.3, Section 2.4, and Section 3.1 that allow for some of the perspectives proposed in Section 3.2. Chapter2 | Computer Science’s Present 36 given task, performed within the magnetic resonance equipment (a.k.a. scanner), so as to identify brain regions associated with the neuronal processes involved in the performance of that task. However, this precludes the analysis of the default interactions between different brain regions (i.e. default brain connectivity). Nowadays the neuroimaging community is changing emphasis from functional specialization towards functional integration (Smith, 2012). Functional Connectivity (FC) is based on the temporal correlation between spatially remote neurophysiological events in the brain (Friston, 1994)(Biswal, 1995). The FC can be measured using a variety of different techniques, but the most used is the resting-state fMRI (rs-fMRI) (Gusnard, 2001). The use of fMRI together with the dMRI technology described in Section 2.2. has been used for a long time (e.g. (Conturo, 1999)(Ibañez, 2018)) and is the basis for the HCP which was already describe in Section 2.2; and the perspective described in Section 3.1 which is partially based (Lori, 2019) in the results of the HCP. There are three main methods used by the “Imaging Neuroscience” community to analyze and evaluate FC: Seed-Based Analysis (SBA), Independent Component Analysis (ICA), and Connectomic Analysis (CA). All these methods have the same final goal which is the attainment of brain connectivity networks. In this section, we will use the CA method. The CA analyzes the interactions between every possible pair of brain regions. The CA method uses the fMRI time-series extracted for each region belonging to a given atlas, or for every voxel in the dataset. Then, the correlations between the time-series of all pair of regions are calculated. Thus, this results in a correlation for each pair, quantifying the FC between pairs of regions. The CA data is typically represented as a connectivity matrix (see an example in Fig. 2.3.1). The connectivity matrix is the schematization in matrix form of the values of the correlation between all pairs of regions. So, its size is N x N, where N is the number of regions or nodes resulting from the brain parcellation. The Information obtained in the connectivity matrices has shown a lot of applications (e.g. (Sedeño, 2017)), such as the study of changes in brain functionality due to Alzheimer’s Disease (AD) (Dennis, 2009) or Autism (Maximo, 2014). Another application is the study of the main networks in the connectome responsible for a specific psychological trait (Jung, 2016) or some mental capacity (Yoris, 2017)(Lori, 2019). Moreover, these matrices are used for classification recurring to Machine Learning (ML) or statistical methods (Lori, 2018). In some publications (Ball, 2016), those FC matrices have been able to discriminate preterm infants at term - equivalent age and healthy term – with born controls with 80% accuracy using a ML method. Plus, their approach was used to distinguish between healthy controls and depressed patients Chapter2 | Computer Science’s Present 37 with accuracy values of 85.85% and 70.75%, respectively for patients with treatment resistant depression and patients with non-treatment resistant depression (Byun, 2014). Furthermore, this connectivity matrices have shown to be reliable fingerprints, making possible to identify accurately a specific subject from a large group. The research made in Functional Connectome Fingerprinting which identified individuals using FC patterns (Finn, 2015) demonstrated that when applied to resting-states, these methods can predict and identify an individual, respectively, with 92.5% and 94.4% accuracy. For fMRI acquisition in task conditions, they also obtained results that presented a great accuracy, with rates of about 87.3%. Relatively to classifications using train and test data with different fMRI conditions (resting or task), for each one, the final accuracy values achieved were lower, with maximum rates of 50.4%. (Lori, 2018) The approach to FC used here is based in techniques of ML, and hence there is always a learning process in order to obtain accurate representation of data and prior knowledge (Suzuki, 2012). In “Imaging Neuroscience”, ML can be used as both a supporting tool to studies of FC and as a form for solving the need for classification models. A novelty of the approach used here (Lori, 2018) being the use of Deep Neuronal Networks (DNN) to make the analysis of the rs-fMRI-based FC data so as to achieve a classification model for each person. The DL allows for the modelling of higher-level data-structure abstraction using Artificial Neural Networks (ANN), and thus improves the predictions by providing a better classification (LeCun, 2015). The DL is a technique that has seen its usage expand quickly and has allowed for the creation of a lot of applications such as new approaches to object recognition. Since the FC values are saved in large dimension connectivity matrices completed with a lot of features, they allow these features’ granularity to be diversified, where the unit in study can be a voxel, or a brain region obtained from brain parcellation (Wang, 2016)(Greenspan, 2016). (Lori, 2018) 2.3.1. Building a Functional Connectivity Table Using the FC technique, several spatially distributed patterns were observed across subjects and presented a strong similarity between them (Friston, 1994)(Biswal, 1995). These patterns were denominated as the Resting State Networks (RSNs) (Biswal, 1995)(Gusnard, 2001) because they use rsfMRI data. The fMRI is also used to determine the effective connectivity (Friston, 1994). The effective Chapter2 | Computer Science’s Present 38 connectivity establishes which brain regions are mainly active during action, perception and cognition, plus the causal relations between those regions. (Lori, 2018) The data used as features for the models in this Section were the FC matrices extracted from rsfMRI data obtained from different subjects. The learning process of the models is based in the supervised learning, hence we used some Information of the subjects, such as: identity, gender or age. There was also the necessity to use atlases so that FC data can be associated to specific brain regions. Part of the work developed in this Section is related to the results and work performed by ref. (Shen, 2013), wherein the FC provided from rs-fMRI is used as the subjects’ fingerprint. Therefore, the approach followed in this work aims at a comparison with ref. (Shen, 2013) in order to find a better approach. The ref. (Shen, 2013) work used two different sessions of rs-fMRI acquired in different days as the subjects’ set. Plus, each correlation matrix with FC data for each session was correlated by Pearson’s correlation with all the other FC matrices in the other session. (Lori, 2018) The different atlases have different number of Regions of Interest (ROIs), and different creation processes by use of different MRI data types (Table 2.3.1). The name of the atlas in ref. (Shen, 2013) don’t coincide with the total number of anatomical regions because the name is associated to the number of “seeds” used in each cerebral hemisphere during the atlas application process. The rs-fMRI data used in this Section was obtained from the SWITCHBOX Consortium project (http://www.switchbox-online.eu/) realized in the “Life and Health Sciences Research Institute” (ICVS) and we call it the “In-House data” (Magalhães, 2015), and moreover we chose to use this In-House data as it is a 1.5T clinical scanner similar to the clinical scanners more commonly used worldwide (Rentz, 2012). The In-House data used in this work are volumes with the temporal data saved from rs-fMRI. Initially, the data is a set of "Digital Imaging and Communications in Medicine" (DICOM) brain images of different temporal points of the acquisition which are converted into a single volume file. Then they undergo a pre-processing pipeline to obtain a file with the values of the correlation of intensities between each pair of brain regions, for each of the 76 subjects (39 male and 37 female). The scanner used was a Siemens Magnetom Avanto 1.5 T MRI scanner with a 12-channel receive-only head-coil. The rs-fMRI was obtained using BOLD sensitive EchoPlanar Imaging (EPI) sequence with these parameters: 30 axial slices; TR/TE = 2000 ms/30 ms; flip angle = 90º; slice thickness = 3.5 mm; slice gap = 0.48 mm; voxel size = 3.5 x 3 x 3.5 mm2; FoV = 1.344 mm. The final outcome of the standard FSL data processing of the rs-fMRI data is a file with 355 Chapter2 | Computer Science’s Present 45 House data, with static FC for the set of atlases used in this Section, and the obtained values are presented in Table 2.3.3. These values in Table 2.3.3 are the objective values to be outperformed by the DL approach described in this Section (Lori, 2018). Analyzing the average correlations values for correct and incorrect classifications, it was verified that the correlation value affects positively the classification result. Implying that the difference between the two situations was significant, thus, the amount of correlation value is also correlated with the average accuracy over the dataset (see Table 2.3.) (Lori, 2018). Table 2.3.3. Resume of the values obtained by the approach from ref. (Finn, 2015) using the In-House dataset for “Predict session 1” and “Predict session 2”, for the different brain parcellations. (Lori, 2018) Predict session 1 Predict session 2 Parcellation Value Difference Parcellation Value Difference 150 nodes 0.342 0.000 150 nodes 0.342 0.0000 100 nodes 0.316 0.026 268 nodes 0.303 0.0395 268 nodes 0.316 0.026 100 nodes 0.289 0.0526 Freesurfer 0.263 0.079 AAL 0.276 0.0658 AAL 0.250 0.092 Freesurfer 0.250 0.0921 50 nodes 0.237 0.105 50 nodes 0.237 0.1053 Table 2.3.4. Mean, Standard Deviation, Max and Min of the correlation values in the correct and incorrect classifications, and respective difference for the In-House data. (Lori, 2018) Correct classification Incorrect classification Difference Average value 0.464 0.394 0.070 Standard Deviation 0.082 0.089 -0.006 Maximum 0.650 0.625 0.025 Minimum 0.271 0.190 0.081 Chapter2 | Computer Science’s Present 46 The search for the best set of hyperparameters started with a simple model, followed by the adding of both depth and convolutional networks. Using the best set of hyperparameters, the models can be extended for other parcellations having new features and values by simply making some adjustments to the model’s architecture. The In-House dataset has 76 subjects (Lori, 2018), hence the probability of correct classification by a random process is 1/760.01316. The selection process of the best set of hyperparameters is started by using the 50 nodes atlas, which has the fewer number of features and the worst results, and so it will have a greater interval for improvement with a lesser number of parameters and thus less features to learn (Lori, 2018). The first set of hyperparameters wasn’t selected randomly but by use of refs. (Ball, 2016)(Finn, 2015)(Fischl, 2004)(Byun, 2014), and tests were made before testing the models. The Tested i-iii and Fixed iv-vii model parameters were (Lori, 2018): i. Learning rate: {0.5; 0.3; 0.1; 0.05; 0.01; 0.005; 0.001; 0.0005; 0.0001}, ii. Loss function set: {Categorical cross-entropy, hinge and squared hinge}, iii. Activation functions set: {Relu, Leaky Relu, Sigmoid, Prelu and tanh function}; iv. Epochs: 2000, v. Optimizer: SGD, vi. Bias initializer: Truncated Normal class with standard deviation equal to 1, vii. Weights initializer: Variance Scalling class, with the average of the inputs and outputs. The models described above amount to a total of 135 models, and for each model we made 10 tests, with each test having a different set of alpha rates used for the activation function Leaky relu (Table 2.3.5), where: alpha rates= {0.1; 0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8; 0.9}. The values obtained (Lori, 2018) demonstrated that the best alpha is 0.8 which implies that the models give some importance (near to 1.0) to the negatives values in the dataset so as to obtain better classifications results (see Figure 2.3.4)(Lori, 2018). The probability of the improvement with the increase of epochs is very likely as the training accuracy continually increases as the epochs increase, and so does the learning process. Plus, for these tests, we only intended to get a comparison between the results for different tests, and hence we were not yet aiming for the best model. (Lori, 2018) Chapter2 | Computer Science’s Present 47 Table 2.3.5. Average validation accuracy and cost values of 3 tests for different alpha rates in the Leaky Relu activation function for 50 nodes parcellation. (Lori, 2018) Alpha Validation accuracy average Validation cost mean 0.1 0.08553 ± 0.02648 0.99918 ± 0.00015 0.2 0.08421 ± 0.01785 0.99926 ± 0.00014 0.3 0.08289 ± 0.02568 0.99919 ± 0.00015 0.4 0.08816 ± 0.02825 0.99914 ± 0.00016 0.5 0.08947 ± 0.02186 0.99917 ± 0.00016 0.6 0.08684 ± 0.03540 0.99913 ± 0.00032 0.7 0.06711 ± 0.02528 0.99931 ± 0.00014 0.8 0.09737 ± 0.02510 0.99912 ± 0.00020 0.9 0.07763 ± 0.02387 0.99918 ± 0.00019 Figure 2.3.4. The best result of one of 3 tests for Leaky Relu with alpha equal to 0.8. (Lori, 2018) As the number of combinations in analysis for the i-viii Tested and Fix model parameters are 135, wherein 15 models with different loss and activation function were tested for 9 learning rates; thus, after Chapter2 | Computer Science’s Present 48 analyzing the 15 different models for different parameters, it was obtained that the best model for a 50 Nodes parcellation, for both accuracy and cost, was the model with the following parameters (Lori, 2018): Loss function = Categorical cross-entropy Activation function = Tanh Learning rate = 0.01 Batch Size: 1 Kernel Initializer: Glorot Uniform Bias Initializer: Random Uniform # Hidden Layers: 1 Nodes per hidden layer:200 Learning Rate: adjustable Initial Learning Rate: 0.001 Best Learning Rate: 0.0001 fMRI Data Temporal Filtering: none This best model (Lori, 2018) obtained an average accuracy of 0.3132 ± 0.0129 and an average validation cost of 3.1422 ± 0.0668, which clearly outperformed the published Pearson correlation approach performance with a 50 Nodes parcellation (Finn, 2015), which had a validation accuracy of 0.237. The parameters of the best model were (Lori, 2018): Loss function = Categorical cross-entropy Chapter2 | Computer Science’s Present 49 Activation function = Tanh Initial Learning rate = 0.01 (the number of epochs recommended are 1000 or more) Batch Size = 1 Kernel Initializer = Glorot uniform Bias Initializer = Random uniform Optimizer = RMSprop For the comparison between the different models; we used a set of metrics to assess the behavior of the model in both training and validation, such as, accuracy and loss. In addition, during the training we also calculated other values, such as, the maximum accuracy in validation with corresponding epoch occurrence, and the differences between the different data (e.g. training vs. validation). The crossvalidation approach is the most correct form of validation; however, it was not possible to use that approach for this Section, as for the static FC there were too few cases for each label. Thus, we chose instead to divide the FC data of each acquisition session into two equal parts, one part being used as the validation data and the other as the test data. Hence, by joining all the different aspects of this Section, it was possible to create an architecture framework which uses rs-fMRI in raw format (e.g., DICOM images) combined with DL models to improve FC-based classifications tasks. (Lori, 2018) In this Section, we describe a complete “Deep Learning in Imaging Neuroscience” approach that comprehends the pre-processing of the raw data, the creation of datasets with different FC Information, and the creation of a DL module which helps fine-tune the different DL models before getting the best model which is then used to make the final analysis. This description is a good description of what “Deep Learning in Imaging Neuroscience” can be done using CS’s present capacities by use of CCs, but to obtain a hint of what CS’s future entails for “Deep Learning in Imaging Neuroscience” it is necessary to go through the descriptions presented in Section 3.1., whereas to fully understand the potential economic impact of Section 3.1 it is first necessary to go through Section 2.4, where an analysis is made of how a Chapter2 | Computer Science’s Present 50 perspective of CS based in Information-transport (Neves, 2019) can help improve the economic performance of a company. Chapter2 | Computer Science’s Present 51 2.4 Application of partial Information approaches to Management The use of partial Information in CS to improve management performance is relevant (Neves, 2019), but for this thesis its applicability lies in certain aspects of the present approach, in particular the use of either Information-transport in CS or the use of partial Information as a key aspect in the attribution of economic value to a management act. The former is most important for section 3.2, while the latter is chief for section 3.1. Section 3.1 is critical because it shows how neuronal dynamics have strong parallels with economic systems (Montague, 2002), and by what means social interactions (including the attribution of economic value to a management act) play a role in the described model of mental health (Lori , 2019) (in Section 3.1.) In this Section, efficiency refers to understanding the phenomenon of improving organizational sustainability, in view of the inputs used and the achievable results. When the focus is on the process of improving work effectiveness, one of the dimensions that influence the process depends on the interaction between people and their behavior in the organizational environment, as well as their impact on the process of achieving improved results. It is often assumed that people act as the engine for Key points: • To show how findings from Computer Science (CS) and Quantum Computing, which developed in some aspects from Deep Learning in Imaging Neuroscience to Nuclear Physics in Quantum Computing, can lead to severe and groundbreaking foundation in the field of CS; in particular, it was developed a partial Information system to healthcare management that coincides well with the partial Information perspective of objective human mental health as described in Sections 2.1, 3.1 and 3.2. • Undeniably, an important consequence of this thesis is that CS stands for a discipline that can be interpreted as the basis for the other causal inference technologies, i.e., CS denotes not just a collection of tools for Mathematics, Physics, Neurosciences and Economics, but can also be understood as an added value from such disciplines to Quantum Computing. Chapter2 | Computer Science’s Present 52 increasing efficiency at the organizational level to support the sustainability of the corporation. While in 1973 David McClelland questioned this assumption in his article "Testing for Competence Instead of Intelligence" (McClelland, 1973), pleading that individual academic aptitude and literacy are not compatible with a person's good performance in a corporation. He argued that there were a number of skills that played an important role in the organizational environment, and focused on a number of skills that supported professional performance for success, such as empathy, self-discipline, and initiative (Neves, 2019). These factors, empathy, self-discipline and initiative were good predictors of leader performance in leading their teams. A characteristic of these people was the ability to read, interpret and influence other people's feelings and emotions. The analysis of this attitude was the goal of ref. (Neves, 2019), being the objective of this Section to provide a brief overview of how much of it has been achieved through the use of Logic Programming for Knowledge Representation and Reasoning (KRR), and how the evolution of their induced scenarios can be understood as a process of energy devaluation (Wenterodt, 2014) (Neves, 1984). In addition, a case study on organizational efficiency was presented and as in ref. (Neves, 2019), considering the emotions and feelings of the workforce. A diverse mix of features was used that indicate the level of collective confidence, gratitude, and pro-sociality, i.e. how employees respond to certain questionnaires that, when translated into logical programs and viewed in isolation, form the organization's knowledge base (Neves 2019). All KRR practices can be understood as a process of energy devaluation (Wenterodt, 2014). A data element is understood to be at a certain point in time, at a given entropic state as untainted energy, ranging in the interval from 0 to 1, that, according to the First Law of Thermodynamics is a quantity wellpreserved that cannot be consumed in the sense of destruction, but may be consumed in the sense of devaluation. It can be introduced by dividing a certain amount of energy by the following three parameters (Neves, 2019), viz. • Exergy, sometimes called available energy or more precisely available work, is the part of the energy which can be arbitrarily used after a transfer operation or, in other words, its entropic counterpart; Chapter2 | Computer Science’s Present 53 • Vagueness, the corresponding energy values that may or may not have been transferred and consumed; and • Anergy, that stands for an energetic potential that was not yet transferred and consumed, being therefore available, i.e., all of energy that is not Exergy. These three terms refer to all possible energy operations as pure energy transmission and consumption practices. In order to make the process traceable, it is shown graphically. An example of the types of questions that are asked is the group of 6 (six) questions that make up the Collective SelfEsteem Questionnaire-Six-Item (CSEQ – 6) (Luhtanen, 1992)(Neves, 2019), viz. Q1 – I am a worthy member of the social groups I belong to; Q2 – Overall, my social groups are considered good by others; Q3 – The social groups I belong to are an important reflection of who I am; Q4 – I am a cooperative participant in the social groups I belong to; Q5 – In general, others respect the social groups that I am a member of; Q6 – In general, belonging to social groups is an important part of my self-image. This questionnaire is designed to assess the workers’ general feelings about their corporation, on the assumption that high collective self-esteem will cause positive outcomes and benefits. The scale used was made based upon these terms (Rosenberg, 1965)(Baumeister, 2003), viz. strongly agree (4), agree (3), disagree (2), strongly disagree (1), disagree (2), agree (3), strongly agree (4) Chapter2 | Computer Science’s Present 54 Moreover, it is included a neutral term, neither agree nor disagree , which stands for uncertain or vague . The reason for the individual’s answers is in relation to the query (Neves, 2019), viz. On the other hand, as an individual, how much would you agree with each one of CSEQ – 6 referred to above? Once the questions have been answered, the results can be summarized in structures like Table 2.4.1 and Figure 2.4.1. After multiple calculations we get results like those in Table 2.4.2. The input for Q1 means that he/she strongly agrees (4) but does not rule out that he/she will agree (3) in certain situations. The inputs are to be read from left to right, from strongly agree (4) to strongly disagree (1) (with increasing entropy), or from strongly disagree (1) to strongly agree (4) (with decreasing entropy), i.e., the markers on the axis correspond to any of the possible scale options, which may be used from bottom → top (from strongly agree (4) to strongly disagree (1) ), indicating that the performance of the system decreases as entropy increases, or is used from top → bottom (from strongly disagree (1) to strongly agree (4) ), indicating that the performance of the system increases as entropy decreases (Neves, 2019). Table 2.4.1. CSEQ – 6 single worker answer. (Neves, 2019) Questions Scale (4) (3) (2) (1) (2) (3) (4) vagueness Q1 × × Q2 × × Q3 × × Q4 × Q5 × Q6 × Fig. 2.4.1 Leading to Leading to Chapter 3 | Computer Science’s Future 61 3.1.1. Mental state objectivity using an axiomatic system There has been a lot of work questioning the existence or non-existence of free-will (Stanford, 2010b) 4 , and such work can be extended to fields in the border of what constitutes Philosophy (Dennett, 2003)(Lori, 2009)(Lori, 2010a)(Damasio, 2010), but the goal of this Section is not related to that specific search. The goal here is to analyze the role of Free-Will Perception (FWP) in the possibility of mental health. FWP is a term, defined elsewhere (Lori, 2019) and used here, as the perception of agency and self-ownership, in the sense that one perceives consciously the influence of one’s own decisionmaking guiding one’s conduct. The basis for the FWP definition is the definition of free-will used in Damasio’s analysis of the relation between Spinoza and contemporary Neuroscience (Damasio, 2003). (Lori, 2019) Some authors claim that FWP is a false perception, or delusional belief, because its conscious aspect turns out to be objectively false (Wegner, 2002)(Dennett, 2003); whereas others contend that FWP can be considered factually true-enough (Lori, 2009)(Lori, 2010a) as it only requires that conscious elaborations have an effect in decision-making, not necessarily an immediate or all-controlling effect in decision-making (Damasio, 2010). In short, Physics, Chemistry, and Neuroscience seem to indicate that FWP is a valid-enough perception of objective reality to not be dismissed as a fairy-tale. Thus, FWP can play a role in structuring mental health without the risk of its collapsing when confronted with objective reality (Lori, 2019). An issue we plan to address in this Section is if the FWP plays any role in structuring human mental health, and how important or significant that role might be in the possibility of objectively identifying mental health. Moreover, by using an axiomatic approach to represent mental processes, we are helping CS in its ability to represent mental processes, which would increase its capacity for achieving the goals outlined in Section 2.4. The origin, structure, and function of the claustrum, a small bilateral structure of the brain, has been unclear since its discovery in the 17th century (Crick, 2005). With the contemporary use of dMRI it has been shown that the claustrum has the greatest connectivity per volume in the human brain (Torgerson, 2015), and a possible reason is that the claustrum is in the human Central Nervous System 4 “philosophers have debated this question for over two millennia, and just about every major philosopher has had something to say about it”. Chapter 3 | Computer Science’s Future 62 (CNS) to serve as the gate-keeper for the Information flow necessary for self-consciousness or metacognitive processes. Recently (Reardon, 2017), it has been discovered an extremely large neuronal connection emanating from the claustrum. This is very important because the claustrum is a region of the brain which is very connected to brain areas that are associated to advanced integration of sensory patterns, for example in language. This very large neuron might thus play an important role in the existence of conscious thoughts (Crick, 2005). (Lori, 2019) Before events occur, before reality reaches our senses, the brain is already generating a virtual environment allowing it to anticipate what is about to happen (Baars, 2002). The prediction of the future is a statistical guess, and it can at times make mistakes, a lot of magic is based on the predictable occurrence of such mistakes. The capacity to accurately predict the future favors environmental adaptation, because having to wait for the Information to arrive and be processed might sometimes take too long to avoid danger, and so “living in the future” is a very relevant survival-skill. This virtual scenery is coherent with the situational environment the person is in, but this process is not conscious (Dehaene, 2004), as in this case there is no access to the working-memory which is essential for conscious futureplanning (Bennett, 2007). Associated to this anticipatory visualization there might be an anticipatory perception if the perceivable phenomenon is strong-enough to become conscious. (Lori, 2019) Initially, the concept of social perception referred to the influence of cultural and social factors in perception, but more recently that term is starting to include the perception about other people, the recognition of emotions in others, and the perception the individual has about its physical and social environment, which includes the mechanisms of causal attribution (Arias, 2006). There have also been suggestions by Salazar (Salazar, 1986), and others, that the concept of social perception is not appropriate for describing all these social aspects of the interaction, but rather, that such concept is an incomplete and ambiguous description often referred to as social cognition. Thus, because of the difficulty in defining what social cognition entails, in this Section we will assess objective human mental health only at an individual level. (Lori, 2019) In Mathematics, the structure of a mathematical language is obtained from an axiomatic system also used in CS (Chaitin, 2006), and which is constituted by these components: alphabet, grammar, axioms, rules of inference, and proof-checking algorithms. The CS approach (Neves, 2019) described in Section 2.4 is a formal approach, and so it has direct connections to the approach proposed here (Lori, Chapter 3 | Computer Science’s Future 63 2019), but the approach of this section has the advantage of detailing all the different components of the axiomatic system; and this detailing will be very relevant for the description at the end of this Section of what constitutes objective human mental health. The axioms of an axiomatic system are complete if all the phrases expressed in the axiomatic system can be logically evaluated given the logical value of the axiomatic system’s axioms; and the axioms of an axiomatic system are consistent if for no phrase can both the phrase and its negation be proved from the axioms. For non-trivial axiomatic systems, the Information-based approach to Gödel’s incompleteness theorems obtains that an axiomatic system having a finite amount of Information cannot be both complete and consistent. (Chaitin, 2006) We consider here that the proof-checking in the input is the proof-checking from the output of a preceding axiomatic system inference process. (Lori, 2019) In Psychology, there are multiple definitions of what feelings are, but in general feelings are understood as being in part a result of negotiating with our historical and cultural community (Gonçalves, 2000). This negotiating process puts feelings into a narrative order, of which our memory is a subjective selection that is strongly influenced by which narratives we consider to be more realistic. The narrative grammar structure used in Psychology is defined as being constituted by: setting, initiating event, internal response, goal, actions, outcome, and ending. (Gonçalves, 2000) The setting is a set of probability distributions for words constructed using symbols of a certain set of symbols. For the grammar to exist there must be a stored knowledge of the symbols and the frequencies of those symbols, the frequencies then being used as estimators of the probabilities. An axiomatic system therefore needs a storage device to work properly. In the somatic marker hypothesis (Damasio, 2000)(Damasio, 2003)(Damasio, 2010), the initiating event of a feeling is either an emotion occurring in the body, or a re-enacted memory of a past emotion. (Lori, 2019) As described in previous paragraphs, the approach chosen here for mathematically representing narratives is by use of axiomatic systems. Let S be the set of symbols of the alphabet, and w represent a symbol-cluster/word, then a grammar, in a practical sense, is the joint set of: probability distribution of words P[w] ; plus the probability distribution of words for each structure j , P[wj] ; plus the probability distribution of words for structure location j given that certain word l are occurring for other structure locations that are not j , P[<lj|wj>] , which would be the probability a phrase makes sense; plus the joint probabilities of consecutive phrases P[<lj|wj>] & P[<lf|wf>] & ··· , which would amount to the probability Chapter 3 | Computer Science’s Future 64 of a paragraph making sense; and so on. The components of the axiomatic system, and the hereproposed relation to the Psychology’s narrative structure is described in Table 3.1.1. (Lori, 2019) In Mathematics, the axioms are typically considered to be consistent rather than complete. Previously, it has been proposed (Lori, 2010b) that when the axioms are complete, rather than consistent, then the axiomatic system should be a Darwinian Axiomatic System (DAS). The axiomatic system where the axioms are consistent will be called Newtonian Axiomatic Systems (NAS) to distinguish them from DAS. In short, Formal Axiomatic Systems (FAS) can be either based on consistent or complete sets of axioms, in the first case they will be NAS and in the second they will be DAS. In the NAS, the rules of inference generate only one statement from the axioms, and the proof-checking algorithm verifies the compatibility of that statement with the axioms. In the DAS, the rules of inference generate multiple statements from the axioms, and the proof-checking algorithm verifies the validity of the statements by making those statements compete with other statements (both internal and external), with the consequent extinction of the loosing statements. In most of Mathematics, the axiomatic system used is the Zermelo–Fraenkel set theory with the axiom of Choice (Ciesielski, 1997), usually shortened to the ZFC set theory, the axioms of ZFC are consistent, and the nomenclature FAS is used for what we call here the NAS. (Lori, 2019) To describe the difference between NAS and DAS in a form that directly relates to Information transmission in CS, and in a more general sense to Information transmission in other fields of science such as Neuroscience and Physics, it is best to first describe the ubiquitousness of central limit theorem conclusions. The outcome of the collective effect of random independent forces acting in fluid-state molecules is Brownian motion in which deterministic behavior is obtained by the constraining effects of the environment where the molecules move (Bar, 2013), and the creation of Brownian motion from random independent forces is valid even if we consider quantum effects (Zurek, 2007). Plus, Darwinian evolution displays a pattern that can be very similar to Brownian motion (Hallotschek, 2011), the major difference between Darwinian and Brownian dynamics being that for Brownian dynamics the molecules/species cannot be destroyed, whereas in Darwinian dynamics they can (Fischer, 2011)(Smerlak, 2016). Chapter 3 | Computer Science’s Future 65 Table 3.1.1. Structure of Information-based axiomatic system, and its relation to Psychology. (Lori, 2019) Axiomatic System Psychology’s Narrative Alphabet( S ) + Grammar( P[w],P[wj],P[<lj|wj>],… ) Setting Proof-checking algorithm input (internal vs. external) Initiating event Axioms (consistent vs. complete) Internal response Rules of inference (single-alternative vs. multi-alternatives) Goal + Actions Inferred statements Outcome Proof-checking algorithm output (internal vs. external) Ending Hence, Darwinian evolution is like Brownian motion because of all the “random” effects occurring to the species as it moves throughout its life, but while the friction aspect of Brownian motion simply makes molecules tend to have the velocity typical for gases/liquids at that temperature, the friction in Darwinian evolution makes species only continue existing up to what the environment around them can support. This implies that Brownian motion is an egalitarian stochastic process as all molecules have the same infinite survival capacity and eventually all molecules pass through the same situations, whereas Darwinian evolution is a non-egalitarian stochastic process where all species have finite and non-equal survival capacities. The Brownian motion is deterministic for the characteristics of the system for which the central limit theorem makes it so (Bar, 2013), but that is not the case for Darwinian evolution because species extinction and sexual procreation destroy the independent identically distributed (i.i.d.) characteristic that is required for the central limit theorem to be valid (Rouzine, 2003). The link between Brownian motion and Darwinian dynamics has also been described in both Economics (Beinhocker, 2006) and Neuroscience (Montague, 2002), which allows for a link between this Section and both Section 2.4 and Section 2.3, respectively. (Lori, 2019) The Darwinian dynamics are only partially predictable, being the predictable part the shape of the fitness Probability Distribution Function (PDF) as defined by the fitness of the most recent species (Smerlak, 2016). Looking at the fitness PDF as an index of validity, it is possible to relate NAS and DAS respectively with Brownian and Darwinian processes. The NAS is related to a stochastic process where Chapter 3 | Computer Science’s Future 66 fitness is identical for all elements, as it occurs in isotropic random walks; whereas DAS is like a Darwinian evolution, since validity is not identical for all axioms. The Brownian motion with unequal and molecule-destroying boundary conditions is the intermediary stage between Physics and Biology (Nowak, 2008)(Lori, 2010c). If isotropic random walks are considered, then there is no specialization, but for anisotropic random walks there can be specialization based on boundary conditions; so much so, that in extreme conditions the boundary conditions can allow for objective randomness to occur in axiomatic systems. (Lori, 2010a)(Lori, 2019) Moreover, the axiom-driven CS is similar to Physics whereas the environment-driven CS, e.g. DL, is similar to Biology, hence allowing CS to play an important role in integrating Physics, Biology, and Economics; as is described in Section 4.2. The independence from the past as perceived by a system of representations is associated to the characteristics of that system, and this quality is what allows that system to be considered as having free-will (Lori, 2009). As we are searching for an axiomatic approach compatible with free-will (Lori, 2010a), the approach followed here is to use the same axioms as those used to prove the existence of objective randomness in QD, and which we then extend so as to be applicable to other situations. (Lori, 2010a). By doing so, we will start from an axiomatic system that is compatible with objective randomness, hence it is compatible with independence from the past, and thus by the same token it is compatible with free-will as its independence from the past allows for the most free-will (Lori, 2011) that can coexist with the known laws of nature. Those random-causality axioms are equivalent to the QD axioms in P. 18 of Section 2.1 and are as follows (Lori, 2019): o. The considered universe consists of systems individually accessible to measurements. i. The state of a system is represented by a vector in a multidimensional vector space with inner product, and in that vector space any vector infinitesimally close to a vector of that vector space will also belong to that vector space. ii. The alteration of state vectors is such that the inner product between state vectors is preserved. iii. If the environment remains unchanged, then the outcome obtained by the axioms remains unchanged. Chapter 3 | Computer Science’s Future 67 The relation of the o-iii random-causality axioms above to the Darwinian evolution of species can be established using the relations (Lori, 2019): o. Means that for any species, their fitness to the environment can be known by interacting the species with a large enough range of environments. i. Means that for any two species with different fitness it is possible to conceive of a species with intermediate fitness. ii. Means that evolution in time preserves the fitness amplitude norm. iii. Means that if the environment is unchanged, then the fitness remains the same. The relation of the o-iii random-causality axioms above with the structure of axiomatic systems described in Table 3.1.1 can be done using the relations (Lori, 2019): o . Is like an alphabet definition for an axiomatic system. i. Is like a grammar definition. ii. Is like the rules of inference. iii. Is like a proof-checking device. It is widely accepted that neurons (or at least small ensembles of about 200 neurons) represent negative-minimum PDFs (Knill, 2004)(Anderson, 1994); it is thus not a problem for neuronal ensembles to represent grammars, axioms, and the other aspects of axiomatic systems. Using the Weyl-Wigner transforms (Weyl, 1927), it is possible to transform any PDF into a density matrix, which can then always be represented by a vector state with complex numbers as elements. So, mathematically, a PDF is a complex vector state. Thus, any negative-minimum PDF can be represented as a complex vector state. A vector state is different from a vector in the sense that a system’s vector state is the full describer of that Chapter 3 | Computer Science’s Future 68 system. The velocity of a car is a vector associated to a car but is not the vector state of the car, as the velocity does not fully describe the car. For example, the velocity does not provide the color of the car. It is thus possible to consider that the state of a Topological Representation zone (a.k.a. association areas (Damasio, 2003)) is described by a complex vector state, with each component of that vector state associated to a certain element of a basis state. A Topological Representation consists in a representation that is invariant over an object’s continuous deformations, by continuous transformations meaning in our case not only mathematical transformations such as translation, rotation, stretching, crumpling and bending, but also sensory transformations such as changes of color, sound, and smell (each to a certain extent). (Lori, 2019) The random-causality axiom o establishes the existence of systems. Let us consider system S surrounded by a set of systems that surrounds S and that we call E . Henceforth, S will be called “system” and E will be called “environment”. As an example, it is possible to consider that a Topological Representation zone is the system S and that the other Topological Representation zones are the environment E . Any considered universe can therefore be represented as “ S coexisting-with E ”, meaning the combined occurrence of the system S and the environment E . The random-causality axiom i establishes that both the system and the environment are represented by vectors in a multi-dimensional vector space and that such vector space has an inner product and contains all (finite and infinite) linear combinations of its vectors. Due to random-causality axioms o and i , the state of the system can be represented by a vector state 𝑆 defined as the linear superposition of vectors of the system S, where the scalars in the linear superposition that multiply the vectors are complex numbers; whereas the state of the environment can be represented by a vector state 𝐸 󰇍  defined as the linear superposition of vectors of the environment E . The complex numbers, such as 𝑧=|𝑧|𝑒𝑗𝜃, are a combination of an amplitude |𝑧| (a positive real number) with a phase 𝜃 (a real number), with j the imaginary unit and e=2.718281… being the Euler number. (Lori, 2019) Let’s assume that a time evolution satisfying random-causality axiom ii can be defined. Then, for the time evolution of system S and environment E , a sharp and deterministic evolution obeying randomcausality axioms o-iii is almost impossible to find, except for situations where the force between the system S components is either independent or linearly dependent on the “distance” separating the states of the system S components (Klein, 2012), for when the force fails to obey these very sharp Chapter 3 | Computer Science’s Future 69 conditions, then the sharp deterministic evolutions only occur for durations shorter than a knowable amount (Lori, 2009). When not in these extraordinary circumstances, what is obtained, instead of sharp deterministic evolutions, are classical statistical dynamics which can often be approximated by a Brownian motion description (Lori, 2011). Thus, what are almost never obtained are the sharp deterministic evolutions assumed by Newton Physics. The form of the Hodgkin-Huxley equations (Hodgkin, 1952), describing the membrane potential in a neuron, has forces that are either independent or linearly dependent on the “distance” separating the states of the system, with time being proportional to the imaginary unit j . Thus, it is not surprising that this equation can represent a sharp action potential at the neuronal membrane moving deterministically along an axon. Whereas, in other models, such as the Galves-Löcherbach (Galves, 2013) model which takes the dendritic trees into account, the forces are neither independent nor linearly dependent on the “distance” separating the states of the system, and so sharp determinism is no longer to be expected, which agrees with the Galves-Löcherbach model being a stochastic model and not a sharp deterministic model (Galves, 2013). (Lori, 2019) The successful transmission of Information is the printing of the Information about the system in the environment states. The vector states, prior to the choice of a system state occurring by the interaction with the environment, have a certain ontic aspect to them, as the vector states are all that the system is before the measurement (meaning that they are all that can be said about the system); and the vector states of the system after the measurement have a certain epistemic aspect to them, as the system does not completely adopt an objective existence, but only does so in as much as it is capable of leaving imprints about itself in the environment. These vector states can therefore be called epiontic (Zurek, 2007). (Lori, 2019) 3.1.2. Mental state free-will using an axiomatic system In Table 3.1.1, the grammars are described by PDFs, and the axioms are subsets of the set of all possibly valid grammar statements. As noted in previous paragraphs, it is possible for neuronal ensembles to represent PDFs, and thus it is also possible for neuronal ensembles to represent grammars, axioms, and the other aspects of axiomatic systems. To relate Consciousness Types 0-1-2 (Shea, 2016)(Kahneman, 2011) with vector states, it is helpful to search for an axiomatic and thus Chapter 3 | Computer Science’s Future 70 computational, yet simple, representation of what the different Consciousness Types relate to. We propose that conscious narratives are correctly described using Psychology’s narrative structure, and that the relation of such structure to the axiomatic systems is as presented in Table 3.1.1. (Lori, 2019) In Fig. 3.1.1, it is proposed that Darwinian extinction can be associated to Consciousness Type 2 processes, and that Darwinian extinctions can be associated to DAS. The relation between Consciousness Types and axiomatic processes is for us, the structure represented in Fig. 3.1.1. There is a major difference between Fig. 3.1.1 and Table 3.1.1, in that a new Translation aspect in introduced. The reason for its non-inclusion in Table 3.1.1 is that in there it is assumed that the Translation is unique and universal, whereas in this Thesis we propose that a key characteristic of the different Types of Consciousness is that they use different types of Translations. In Fig. 3.1.1, the Translation location is represented by a filled-circle. The Translation is different for each of the Types of Consciousness. For the Type 0 the Translation is one-to-one, meaning that for each of the group of Axioms there corresponds a unique Rule of Inference. For the Type 1, the Translation filters the group of Axioms into a single Rule of Inference, thus the Translation is multiple-to-one. For the Type 2, the Translation filters multiple Grammars into multiple groups of Axioms, thus the Translation is multiple-to-multiple. (Lori, 2019) For a decision to be felt as free, meaning a FWP is associated to that decision, there must be at least two different ways a neuronal system could be perceived as being able to go from the immediate past to the present, and those two different ways must be swappable in the sense that they can be interchanged without needing to change anything in the infinite past (as much as can be perceived by the neuronal ensemble). It has been obtained by neuron modeling (Montague, 2002) that a successful outcome prediction in a neuron (or small ensemble of neurons) improves the access to nutrients of the neuron, therefore increasing the “state of pleasure of the neuron” (Damasio, 2000)(Damasio, 2003)(Damasio, 2010). Thus, the continuing survival of the neuron requires the successful broadcasting of the validity of the neuron’s predictions. The ontic/existence of the neuron thus requires the success obtained by its epistemic/broadcasting aspect, meaning that the requirements for the neuron’s survival are epiontic. (Lori, 2019) There are also strong indications that neuronal dynamics are themselves Darwinian (Edelman, 1987). For example, the motor nerve cells’ neurons struggle to control the muscle occurs by sending out multiple-branched fingers called axons; these branches contact many muscle fibers, which are also in Chapter 3 | Computer Science’s Future 77 The brain function locations and hemispheric preferences described above should not be considered as absolute, but rather as an assistant to the axiomatic structure representation of human decision-making. As can be seen in Fig. 3.1.1, the sum of the three axes above also provides an association that is mostly in agreement with the Neuroscience-known relation between brain function and brain area (see Fig. 3.1.3). We also use the evolution of the body and brain axes to relate the body axes, the brain axes, the axiomatic axes, the animal action-types, and the axiomatic aspects (see Fig. 3.1.2). (Lori, 2019) Figure 3.1.3. Simplified relation between brain 3-axes approach and brain function. On the left is a view from above ( Sandra Lori), and on the right a view from the left side ( Sandra Lori). The first animals (meaning here structured multi-cellular organism) are believed to have been either a sponge (635 million years ago) or a comb jelly, but in any case, something sphere-like with a topology of simply "inside vs. outside" [1st animal evolution]. About 600 million years ago, before the Cambrian period, the arthropods started appearing and thus defined a medial-lateral axis of movement (with eyes eventually developing on each of the sides), thus assuming a flat disk-like shape with a “leftright” choosing axis [2nd animal evolution]. Around 550 million years ago the first predators appear as indicated by their predation marks, likely the flat worms. The need for hunting requires not only a choosing orientation but also a matching of the space and time concepts into the concept of trajectories. Chapter 3 | Computer Science’s Future 78 Thus, animals developed the concept of time and adopted an arrow-like anterior-posterior axis marking its desired trajectory [3rd animal evolution]. The first gut that appeared remained mostly unchanged since the appearance of the Eukaryotes about 1700 million years ago [1st neuronal evolution], until when, about 800 million years ago a part of the gut started evolving, to then become a heart about 542 million years ago [2nd neuronal evolution]. The appearance of the brain occurred about 500 million years ago [3rd neuronal evolution]. The brain itself had three stages of evolution; the original hindbrain [1st brain evolution] gained a limbic system about 250 million years ago [2nd brain evolution], and then the cerebrum appeared about 200 million years ago [3rd brain evolution]. The relation between axiomatic system aspects, and body/brain development axes is proposed in Table 3.1.2 and Fig. 3.1.3. The three different types of evolution and representation presented in Fig. 3.1.2 are justified using different types of arguments (e.g. mathematical, computational, neuroscientific, evolutionary), but for a more rigorous basis for the 3-aspects it is necessary to define an axiomatic representation general enough to account for all the phenomena described in Fig. 3.1.2., but with axiomatic expressions simpleenough to be able to be included in common speech. A major function of the brain is to execute Economics-like (Beinhocker, 2006) forecasts of costs and benefits using Bayesian inference rules (Anderson, 1994)(Montague, 2002)(Knill, 2004). For example, if a single form of neurotransmitter is postulated, then the corresponding economical system can reach a state of economical equilibrium (Montague, 2002). Moreover, it has been described how economical systems behave like Informationdriven Darwinian systems (Beinhocker, 2006). In Section 4.2, a brief description is made about the importance of value attribution in the development of CS’s future, and in that description Kant’s perspective will again be relevant, and it will play the same role as in Fig. 3.1.3, which thus creates further evidence of this Thesis’ self-consistency. (Lori, 2019) Historically, in Psychology, there are only two major axes, the Eros and the Thanatos axes. The Eros is associated to the desire for pleasure, which can also be described as a “will to Pleasure” (Freud, 1990); and the Thanatos with the desire for conquest, which can also be described as a “will to Power” (Adler, 1927). Whereas, there were actually three Psychotherapy schools of Vienna, which left one of those schools, corresponding to a “will to Meaning” (Frankl, 2006), without an axis. We propose in Fig. 3.1.3. (Lori, 2019) and elsewhere in this Section, a 3-axes system, hence, to define a better connection between the approach proposed (Lori, 2019) in this Section and Psychology, it is preferable to propose a Choosing/free-will axis for Psychology. We proposed for that axis (Lori, 2019) the name of the Greek Chapter 3 | Computer Science’s Future 79 goddess of prosperity and randomness: Tyche. The 3-axes of Psychology thus becoming: Eros-TycheThanatos. This 3-axes proposal is relevant, as since the proposal of the “will to Meaning”, the mental health in Psychotherapy has been defined as a balance between these three axes of will, and this Section agrees with that. Moreover, as it will be described in Section 4.2.2, the use of the word “will” in defining the 3-axes of Psychology is not an accident, as the will is a key aspect of Schiller’s attribution of objectiveness to Beauty (Moland, 2017), which in Section 4.2.2. is used to analyze the possibility of attributing an objectiveness to value, a key necessity for the validity of the CS approach (Neves, 2019) described in Section 2.4. Table 3.1.2. Comparison of the axiomatic axes system with other axes systems. (Lori, 2019) Animal Step Evolution Novelty Brain Axes Body Axes Action Type Axiomatic Aspects Psychiatry Disorder Psychology Axes Will Type 1st Space ventral-dorsal inner vs. outer Eating Internal-External Eat/Sleep Eros Pleasure 2nd Alternative middle-lateral left vs. right Choosin g Complete-Consistent Mood Tyche Meaning 3rd Time anterior-posterior soon vs. late Hunting Input-Output Anxiety Thanatos Power For the Tyche feelings to be associated to an objective reality, it is needed that free-will in a certain objective sense exists. Thus, for Tyche feelings to be associable to objective reality, it must be possible to represent objective arbitrariness by using axiomatic systems. That is not an easy task, as axiomatic systems have been built to avoid arbitrariness through maintaining the logic validity of the axioms assumed to be valid. It has been proposed that independence of the present state of a system from the past located outside the system is necessary (Lori, 2009) and sufficient in realistic neuronal systems (Lori, 2010a) for the existence of free-will in those systems in a form that is compatible with the existent knowledge of the laws of nature. Thus, the Tyche feelings based on a FWP (see Table 3.1.3) do not contradict Reality. (Lori, 2019) The number of different feelings considered in Damasio’s model of feelings (Damasio, 2003) is quite thorough, thus, we will use both the grouping of feelings (Damasio, 2010) and Damasio’s self- Chapter 3 | Computer Science’s Future 80 model perspective (Damasio, 2003), with some minor alterations. The feelings are the mind representations of present and past emotions, but in this work, the feeling and emotion terms will be used interchangeably. The feelings are divided by Damasio into three types (Damasio, 2003) and into four groups (Damasio, 2003). The three Damasio types of feelings are: Background emotions, Primary emotions and Social emotions. The four Damasio groups of feelings are constituted by four parts: Definer Emotion, Emotional-Competent-Stimulus (ECS), Consequences and Basis Emotions. Using the four Damasio groups (Damasio, 2003), we obtain the division below (Lori, 2019). Group 1: Definer→ embarrassment, shame, guilt; ECS→ violations in personal space/purity; Consequences→ prevent continued aggression by others; Basis→ fear, submission. Group 2: Definer→ contempt, indignation; ECS→ violation of cooperation/purity; Consequences→ enforcement of social norms by violation punishment; Basis→ disgust, anger. Group 3: Definer→ sympathy, compassion; ECS→ another person in suffering/need; Consequences→ restoration of harmony in group; Basis→ attachment, sadness. Group 4: Definer→ awe/wonder; elevation, gratitude, pride; ECS→ recognition in self/others of contribution to cooperation; Consequences→ reinforcement of cooperation; Basis→ happiness. Using both the three types and the four groups, it is possible to use the success vs. frustration of the Eros-Tyche-Thanatos desires for the construction of Table 3.1.3, which includes all Background, Primary, and Social emotions. The two forms of separating the emotions, by types and/or by groups, has many coincident emotions. Nevertheless, there are four emotions (surprise, jealousy, envy, admiration) in the types, which are not mentioned in the groups; and four emotions (embarrassment, attachment, compassion, submissive) in the groups, which do not occur in the types. The surprise and embarrassment emotions can be considered to represent the same emotion, as can jealousy and attachment, and also sympathy and compassion, plus also envy and jealousy. Moreover, the feeling of admiration towards someone is very connected to feeling submissive towards that person. Thus, there is Chapter 3 | Computer Science’s Future 81 an agreement between the two forms of separating the emotions, that is, between separating by types and separating by groups. (Lori, 2019) We will use the Groups 1-2-3 as representing emotions associated to, respectively, difficulties in: Eating, Hunting and Choosing, respectively. Whereas the fourth group is associated to the non-existence of those difficulties/frustrations, and thus a sense of balance for which we propose the use of the Greek word for Reason: Logos. The sadness emotion appears as a Basis emotion in both Groups 1 and 3, hence we consider that the association to the Group 1 is the most appropriate as sadness typically causes feelings of shame and guilt. We propose that although there is an Eating-Choosing-Hunting succession in Darwinian evolution, the satisfying occurrence of the positive feelings requires all three simultaneously. (Lori, 2009) Damasio’s levels of Consciousness (Damasio, 2003) are only explicitly differentiated up to the Extended Consciousness level (Damasio, 2003), and no further. In a previous work, some of us proposed (Lori, 2010a) that it is useful to divide the Extended Consciousness between three components: Personal-Consciousness based on one’s memory about one’s life, Historical-Consciousness about one’s perceived interaction with the culture one feels to be a part of, and Universal-Consciousness about one’s perceived interaction with the whole universe. Although a person is typically feeling as an “individual”, what that individual-ness means depends on the level of Consciousness. At the Proto-self level are the Background emotions, at the Core Consciousness level are the Primary emotions, at the Personal Consciousness level are both the Primary and Social emotions, whereas at all upper Consciousness levels there are only Social emotions. The neuronal correlates of the highest Consciousness level (the Universal-Consciousness) are proposed here to be the sub-sections of the anatomical regions attributed to Extended Consciousness by Damasio, the more anterior portion of the temporal cortex (Grabowski, 2003), and the more anterior portions of the pre-frontal cortex (Bechara, 2005)(D’Argembeau, 2008). Whereas, Historical-Consciousness level areas are located between the Personal-Consciousness, and the Universal-Consciousness areas (see Table 3.1.3). (Lori, 2019) Chapter 3 | Computer Science’s Future 82 Table 3.1.3. Relationship between the Eating-Choosing-Hunting axes, and feelings. (Lori, 2019) Consciousness level Frustration → Axis → Disorder → Eating [1st Step] EROS [Group 2] Eat/Sleep Choosing [2nd Step] TYCHE [Group 1] Mood Hunting [3rd Step] THANATOS [Group 3] Anxiety No Frustration LOGOS [Group 4] None Universal Consciousness Guilt Jealousy Indignation Wonder Historical Consciousness Shame Envy Contempt Elevation Personal Consciousness Embarrassment Bipolarity Dispersiveness Pride Core Consciousness Fear Sadness Anger Happiness Proto-Self Submission Attachment Disgust Enthusiasm 3.1.4. Experimental evidences for 3-axes approach In Mathematics and CS, an axiomatic system is considered complete if it is applicable in all circumstances and consistent if it has no internal self-contradictions (Chaitin, 2006). Both consistence and completeness are forms of Kantian ethics reversibility, by reversibility meaning indifference to a change/swap of roles. In Kantian ethics, the universality of a rule implies that all deciding-agents necessarily acted according to that rule in all circumstances; and the failing of such universality can occur because of two types of reversibility failure: a) reversibility is not viable for the considered physical universe, b) reversibility contradicts the deciding-agent’s intention. (Kant, 1993) The first type of Kantian reversibility failure in the axiom-based decision-process indicates a failure of axiomatic completeness, and is thus a failure in contextual-reversibility, which Kant called “perfect duties” (Kant, 1993); whereas the second type indicates a failure of axiomatic consistence, and it is thus a failure in formal-reversibility, which Kant called “imperfect duties”. We thus recover Gilligan’s concepts (Gilligan, 1985) in Psychology of “post-conventional formalism” and “post-conventional contextualism” by replacing “post-conventional” with “Kantian reversibility”. Kant considers that “imperfect duties”, as opposed to universal rules, can ethically be overcome by one’s inclinations, e.g., by prefering pleasure rather than pain, satiety rather than hunger, health rather than sickness, happiness rather than misery, and so should not be included in civil legislation; whereas “perfect duties” cannot be ethically overturned by one’s inclinations, and so can and should be included in civil legislation. (Lori, 2019) Chapter 3 | Computer Science’s Future 83 Mythical hero stories are often focused in growing through increasing Consciousness levels. Moreover, although Campbell’s study of the hero stories in multiple cultures (Campbell, 1972) is widely known (e.g. its use in George Lucas’ Star Wars movies), a more recent work (Vogel, 2007) was able to found a more succinct structure for the Hero Story, which is composed by: A) Departure, B) Initiation, C) Return. These three parts, have the following components (Lori, 2019): A) Departure: 1. Ordinary World, 2. Call to Adventure, 3. Refusal of the Call, 4. Meeting with Mentor; 5. Crossing threshold into Special World. B) Initiation: 1. Tests with Allies and Enemies, 2. Approach to innermost Cave, 3. Going through Ordeal, 4. Receiving the Reward. C) Return: 1. Traveling the Road back, 2. Hero’s Resurrection, 3. Bringing back the Elixir. We relate Consciousness Levels with the Hero Story by making the association (Lori, 2019): A) Departure is a departure from Personal Consciousness. B) Initiation is an initiation into a communal life and establishes the hero’s Historical Consciousness. C) Return is a return by the hero so as to bring a gift of Universal Consciousness which must be shared to be preserved. The universal appeal of Shakespeare identifies him as someone that has deeply understood what is universal in human behavior. In his writings, it is possible to identify a “tragic equation” (Hughes, 1993) used throughout his plays. That “tragic equation” consists of an alteration of the Greek legend of Venus and Adonis by use of the writings of Seneca to replace Venus by Lucrece, and by the creation of a new type of Adonis. This new Adonis freely chooses a path of female-distancing and contemplation. In Shakespeare’s “tragic equation”, when the archetypical male encounters an actual female, he compares her to the extreme forms of female behavior; with the female doing likewise about the male. We have proposed (Lori, 2019), the joining of the two extreme forms of behavior in Shakespearean drama with Chapter 3 | Computer Science’s Future 84 the actual person, and so create the three-component archetypes for both the male and the female. The male archetype triplet is Collatine-Tarquin-Adonis, and the female archetype triplet is Venus-PersephoneLucrece. (Lori, 2019) In the history of human religion there are two major archetypes, that of the female Mother Earth, and that of the male Father Thunder. (Robbin, 1990)(Hughes, 1993) We hence propose that in Shakespeare’s “tragic equation”, we have “Mother Earth = Venus-Persephone-Lucrece” and “Father Thunder = Collatine-Tarquin-Adonis”. Thus, for Shakespeare, any romantic relationship between a female and a male is projected into their minds, as being a relationship between Mother Earth and Father Thunder. Hence, all romantic relationships are always both transcendental and earthly, constituting a three-part structure for both the female and the male archetypes. The three parts being: Heavenly MaleFather Thunder, Earthly Female-Mother Earth, and their male or female human offspring connecting with both the Father Thunder and the Mother Earth. It is possible to see this structure as the result of the conflict in Shakespeare’s time between Catholics and Puritans, with Adonis representing the Puritan Male-ideal and with Lucrece representing the Catholic Female-ideal (Hughes, 1993). Using Shakespeare’s “tragic equation” (Hughes, 1993), it can be considered that for Shakespeare the mental health is the balance between the 3 archetypes, and that it is the difficulty of implementing this balance which constitutes the source of the difficulties in achieving and maintaining the state of mental health. (Lori, 2019) The vision of contemporary Psychology goes beyond the prospect of a Manichean conflict between good and evil, towards the Shakespearean perspective where the evil is the stingy irrational search for the absolute power of either Nature or Reason. The mental health to Shakespeare is a balance between Catholicism\Nature\Female and Puritanism\Reason\Male, with a slight preference for the former (Hughes, 1993). We also propose here that a reason for the success of Shakespeare is in his discovery of the three Freudian identity types, Id-Ego-Superego, three centuries before they were proposed by Freud as the three parts of the Psyche (Freud, 1949). It should also be noted that such a discovery by Shakespeare might have been based on the approach to theatre developed by the Jesuits of that period (Wilson, 1997), and the Jesuit approach to spirituality has been known since Jung to have strong parallels to Psychotherapy (Becker, 2001). Those relations between Shakespeare, Freud, and Damasio Consciousness levels are expressed in Table 3.1.4. (Lori, 2019) Chapter 3 | Computer Science’s Future 85 Table 3.1.4. Relation between Shakespeare, Freud, and Damasio Consciousness levels. (Lori, 2019) 5 Consciousness Level Shakespearean Female Archetype Shakespearean Male Archetype Freud’s Identity Types Universal Venus Adonis Superego Historical Lucrece Collatine Ego Personal Persephone Tarquim Id The entry of blood in the brain is regulated by the amount of neuronal activity, but there is both a seconds-long delay between neuronal activity and blood flow, and an excess of blood supply to the regions where the neuronal activity increases (Leopold, 2009). The magnetic field alterations caused by that excessive blood flow is what constitutes the fMRI signal. The fMRI data of ref. (Huth, 2016) obtained a cortical word-map presented in Fig. 3.1.4, for which the 3 principal components (PC) obtained using Principal Component Analysis (PCA) are (Lori, 2019): PC1} locational/visual/tactile emotional/communal (dorsal-ventral brain axis) PC2} locational/visual/tactile social/professional (medial-lateral brain axis) PC3} locational/visual/tactile mental/abstract (anterior-posterior brain axis) There are several different approaches to Psychiatry based in different authors, such as Freud or Jung just to mention two classical examples. We chose to use the definitions used in what we consider to be a standard book in Psychiatry (Gerder, 2007). The Psychiatric pathologies can be divided between state (based in Table 3.1.2) and process (based in Table 3.1.1) pathologies, respectively. The 3 types of state pathologies are: a) mood disorders, which we consider to be social-role assessment issues; b) 5 Structural causal modeling has been often used in Psychology, and the approach proposed here could be wrongly interpreted as a specific form of structural causal modeling, but it is a different approach, as it proposes specific archetypes as the source of the causal models. Chapter 3 | Computer Science’s Future 86 anxiety, which we consider to be future-prediction issues, and c) eating/sleeping disorders which we consider to be body-awareness issues. (Lori, 2019) The proposed relation above agrees in general with Fig. 3.1.3, and also obtain the results that Eating is about emotional satisfaction, that Choosing is about social rank, and that Hunting is about mental abstraction. This relation is obtained from the experimental data of ref. (Huth, 2016) and is represented in Fig. 3.1.4, thus being a further validation of the proposed 3-axes approach. (Lori, 2019) Figure 3.1.4. Cortical Word Map obtained by fMRI correlations. (Huth, 2016) The mood disorders vary between depression and mania, with depression being associated to a lack of the appropriate amount of thinking needed to resolve the person’s issues, whereas mania is associated to an excessive amount of thinking. Thus, mood disorders are mostly a problem in defining Chapter 3 | Computer Science’s Future 93 pointing up is represented as e and we can assign it the bit state |1>. Likewise, for a neutron QF, the spin can be down, represented as n, or up, represented as n, which would then correspond to the bit states |0> and |1>, respectively. (Lori, 2020) The establishment of a direct connection between spin states and bit states can be done because the existence of spin follows directly from the linear relation between energy and momentum with both being proportional to the derivative of the QF over spacetime coordinates, and hence is not at its core a relativistic phenomenon (Lévy-Leblond, 1967)(Hamdan, 2008), which implies that spin is a well-defined fundamental property of particles, and as such can be used as a bit representation for fermionic QFs. It is important that the QFs representing the bit are fermionic QFs, rather than bosonic QFs, so that to each spatial location there can be a single bit assigned to it. (Lori, 2020) The range of a gauge force caused by a gauge-invariant SU( n ) is inversely proportional to the mass of the force carrier, and so depending on the scale-range of the stored bits, different SU( n ) gauge invariance forces will need to be considered. The range of the U(1)SU(1) electromagnetic force is infinite as its carrier, the photon, is massless, which implies that the electromagnetic force is relevant for all ranges; whereas the range of the SU(2) weak nuclear force is inversely proportional to the mass of the Z0 particle, m𝑍0, and so it is about 10−18 m; and finally the longer range of the SU(3) strong nuclear force is at most inversely proportional to 𝑚𝜋 which is the mass of the lightest quark doublet, the pion, and so it has a range of about 10−15 m. The SU(3) gauge force in the short range is carried by the massless gluons, but the existence of the quark confinement (Peskin & Schroeder, 1995) prevents the gluons from existing outside of either quark doublets (such as the pion) or quark triplets (such as the neutron). (Lori, 2020) The scale of the CCs is in the hundred atoms scale, meaning about 10−8 m, and a temperature of about 70 ºC. The highest Contemporary Maximum Information Processing Rate (CMIPR) is from about 1011 bit s for an Ethernet network (Jain, 2016) or a Central Processing Unit (CPU) (Connatser, 2018), to about 1019 bit s at a Temperature of 70 ºC for a Summit super-computer (Oak, 2018). The Information contained in current QCs is at most a few bits in a volume of a few atoms, corresponding to a processing power for the IBM Q System One of about 0.7∙1013 bit s (Devoret, 2013)(Cross, 2018)(Loeffler, 2019)(Nersisyan, 2019), which is not yet competitive with the Summit Chapter 3 | Computer Science’s Future 94 Super Computer in processing power, but with the caveat that the QC is a lot smaller than it. For Moore’s law to continue being valid, it will be very useful for the miniaturization improvements to continue, but for such miniaturization to continue it is necessary to go beyond the 1 bit/atom Information content limit that is currently being reached. Even if Information is stored in the nucleus’ spins rather than in the electron’s spin, the difference is not very large as in both cases the spins of fermions tend to cancel each other at each nucleon energy-level because of the Pauli exclusion principle which prevents fermions from occupying the same quantum state. Hence, the Pauli exclusion principle implies that pairs of identical nucleons cancel each other’s spin at each nuclear energy-level, and thus, at best, the total spin of the nucleus is equal to the number of nuclear-energy levels having a single nucleon. Hence, although there can be as much as 10 bit/atom in some especially prepared nuclei, that is not a large difference to the 1 bit/atom atomic Information storage that the electron’s spin can already achieve. (Lori, 2020) For the amount of bit/atom to increase, a possibility would be the use of neutronium (a.k.a. neutrium or neutrite) (Inglis-Arkell, 2012), which is basically a cluster of neutrons which would allow to put about 1015 neutrons in the volume of an atom, but neutronium is for now impossibly hard to keep stable, e.g. the best result yet for a stable neutronium was a 4-neutron state lasting about 10−21 s (Bertulani & Zelevinsky, 2016). Moreover, although neutronium at near absolute zero is likely to form a degenerate gaseous Bose–Einstein condensate, that condensate would be composed of neutron pairs called dineutrons, which would have zero spin because of the Pauli exclusion principle. But, for high pressure and temperature, the Pauli exclusion principle makes the energy levels occupied by the neutrons become degenerate, which would allow for stable large particle number neutronium states. Unfortunately, the pressure and temperature required for a stable neutronium state are in the neutron star range, meaning temperatures of about 106 K (Lattimer, 2015) and pressures of about 1031 to 1034 Kg m−1 s−2 (Ozel, 2016), whereas the highest pressure contemporary science has managed to create is about 1012 Kg m−1 s−2 (Dubrovinsky, 2015) and hence we disregard the use of neutronium in the foreseeable future. The limit of 1 bit/atom was experimentally reached in 2017 using Holmium atoms with the possibility of reaching working temperatures as high as -243 ºC (Natterer, 2017). The DNA/RNA have about 0.7 bit/atom at 40 ºC if the Holmium of ref. (Natterer, 2017) is used as an atom-size definer, Chapter 3 | Computer Science’s Future 95 which is quite close to 1 bit/atom. Thus, Biology has apparently not been able to go beyond the limit of about 1 bit/atom, either. (Lori, 2020) The Pauli exclusion principle imposes limitations in the maximum Information storage and/or processing rate of Information transport by the spin of fermionic QFs, a more general limitation concerning Information transport (not just the spin-based Information transport) is the Bekenstein bound (Bekenstein 1981)(Bekenstein 2005) which requires that the Information contained in a spherical region of radius R cannot exceed that of a black hole of the same size which, in turn, is proportional to the surface area of the black hole, not to its volume. More specifically, if D is the diameter of the black hole, I is the total Information in the black hole, and 𝑙𝑃=1.62∙10−35 m/s is Planck’s length, then: 𝑰≤ 𝜋 ln16 [𝑫 𝑙𝑃]2≃1.1[𝑫 𝑙𝑃]2. This Information limit signifies that a black hole can store a tremendous amount of Information in a small volume, but there are a few important caveats. First, the smallest known black hole is called XTE J1650-500 and has about 5 times the mass of the sun occupying a sphere with a diameter of 24 Km. This is too heavy for a workable computer placed anywhere in our solar system, as for it to be safe to Earth’s trajectory it would need to be located further away than Alpha Centauri. (Lori, 2020) A different possibility are micro black holes (Hawking, 1971), which are theoretically possible but have not been experimentally detected yet, moreover the micro black holes have problems of their own as viable computers. Even if a micro black hole has a mass as large as the largest machine humanity has ever built, specifically the Large Hadron Collider which weighs about 2.8∙108 𝐾𝑔, the corresponding Hawking Temperature is about 4.4∙1014 K , which is considerably higher than what contemporary technology can handle. If the temperature of the micro black hole is made low enough to be manageable by today’s technology, such as that of the International Thermonuclear Experimental Reactor (ITER) project (ITER, 2006) which aims at fusion reaction temperatures of about 108 K , then the mass would need to be about 1.2∙1015 Kg , which is about five thousands larger that the Three Gorges Dam (Three, 2010), and over a million times larger than the largest QC-like machine that contemporary technology can build, the ITER (ITER, 2006). Thus, micro black holes are not viable computers in the foreseeable future. (Lori, 2020) Chapter 3 | Computer Science’s Future 96 Moreover, although there has already been a lot of work concerning Information transport in relativistic thermodynamics (e.g., (Nakamura, 2006)), unfortunately there has been little attention paid to the Information transport’s difference between zero spin (Nakamura, 2006) and non-zero spin particles. The relativistic QF theory of a zero spin Lagrangian density is the Klein-Gordon Lagrangian, whereas for the semi-integer spin particles (e.g. electrons and quarks) it is the Dirac Lagrangian, finally for integer non-zero spin particles it is the Yang-Mills Lagrangian (Peskin & Schroeder, 1995). The low velocity-limit of the Klein-Gordon Lagrangian is the well-known Schrödinger equation, but the low velocity limit of the Dirac equation is not the Schrödinger equation, but rather the Schrödinger equation with the extra Pauli matrices associated to the spin (Hamdan, 2008). Thus, the reason for existing spin is that particles can be represented by a wavefunction with phase terms having a covariant structure in accordance with Einstein’s special relativity, and hence it is not valid to assume that spin is associated to the occurrence of relativistic speeds (Hamdan, 2008). (Lori, 2020) We obtain here that the relativistic relation between the Information amount variation, 𝑑𝐼, and the variation of energy density in the comoving frame, 𝑑𝜖, is identical to that of the spin zero case except for the adding of an extra term which is dependent on the 4x4 Dirac gamma matrices 𝛾𝜇, the flat spacetime metric 𝜂𝜇𝜐, the ensemble´s 4 velocity 𝑢𝜐, the Boltzmann constant 𝐾, the temperature 𝑇, and the speed of light in vacuum c , through the expression: ∑𝛾0𝛾𝜇𝜂𝜇𝜐[𝑢𝜐 𝑐] 3 𝜇,𝜐=0 , which for velocities much lower than c becomes in average equal to 1. Thus, the relation between the variation of Information 𝑑𝐼 for a fixed rest-frame volume 𝑉0 is: 𝑑𝐼=[∑𝛾0𝛾𝜇𝜂𝜇𝜐[𝑢𝜐 𝑐] 3 𝜇,𝜐=0 ]∙[𝑉0 𝐾 𝑇]𝑑𝜖, which is dependent on the chosen reference frame through the [𝑢𝜇 𝑐] term. Moreover, if the spacetime is not flat (a very likely occurrence in the presence of micro black holes), then the flat spacetime metric tensor 𝜂𝜇𝜐 must be replaced by an energy/momentum/stress-dependent general metric tensor 𝑔𝜇𝜐 obtained from Einstein’s GR (Wald, 1984), and thus (Lori, 2020): 𝑑𝐼=|∑𝛾0𝛾𝜇𝑔𝜇𝜐[𝑢𝜐 𝑐] 3 𝜇,𝜐=0 |[𝑉0 𝐾 𝑇]𝑑𝜖 (3.2.1) Chapter 3 | Computer Science’s Future 97 Hence, if micro black holes are used as computers, then the amount of Information being transmitted and/or received by the micro black holes is strongly affected by the presence and movement of the micro black holes, which is another reason why micro black holes are impractical as computation devices. In a 1959 lecture at Caltech, Feynman said that “there is plenty of room at the bottom”. Whereas, in our opinion, we are reaching the end of the Information-workable room, long before we reach the room’s bottom. But as miniaturization is reaching its limits, it is our opinion that lateralization is the direction from which the new source of Moore’s law will come, and we discuss this in the next paragraphs below. For the more mathematically inclined, the calculation of Eq. 3.2.1 is deduced in the Mathematical Appendix at the end of this Section. (Lori, 2020) 3.2.2. From miniaturization to lateralization If one cannot go down in the miniaturization scale, then the only possibility is to go side-ways, and in this sub-Section, we will describe what we mean by lateralization. By looking at a contemporary motherboard, there are computer chips which have an extremely fast rate of data processing, which are then connected through high conductance connections; with all these connected computer chips being cooled by fans and other heat dissipation devices. Nevertheless, when we look at the table where the computer is, often the only connection the computer has is through a wireless router to external devices (e.g. a printer). This is not how Biology works, as in Biology there are mechanisms at multiple scales interacting with each other, hence what we propose by lateralization is that computer systems become more and more integrated at multiple scales. This has been proposed before (e.g. the “Brain scan: Bruno Michel” in ref. (Technology, 2016)), but the novelty in our approach is the suggestion that a lower-strength of miniaturization is capable of being a good improvement if a higher multi-path relational dynamic between data-processing units is achieved. The key points for achieving this higher multi-path relational dynamic between data-processing units requires thorough knowledge about two components of Information transport: a) how Information is being transmitted from the DNA/RNA to the cells as the genetic code appears to be able to have a strong influence in cell behavior (e.g. (Lorna, 2019)), and Chapter 3 | Computer Science’s Future 98 from the cells towards the external and internal behavior; b) how the general rules of Information representation differ between QM, Biology, and CS. (Lori, 2020) The component a) is a major topic of Neuroscience, and advancements in that area are being done at multiple scales, but it is an area that is outside the scope of this Section. For the component b), a commonly used theory for Information representation in neuronal ensembles uses the negative minimum probability distribution functions (PDFs) approach (Anderson, 1994)(Knill, 2004), which by using the Weyl-Wigner transform (Wejl, 1927) implies that such a PDF can be transformed into a density matrix (as described in Section 3.1). In QM, a fermion that has been measured so as to be in a position eigenstate (meaning it is localized in a certain position as much as it is allowed by the Heisenberg uncertainty (Heisenberg, 1927)) has a density matrix that is diagonal when represented in the locationbasis, moreover the elements in the diagonal are positive numbers that add up to one (implying that they can be understood as probabilities). In the wave-particle duality present in QM, the electron has in this case totally opted for particle-like characteristics. If the wave-like aspect of the electron becomes relevant, then off-diagonal elements of the density matrix in the location-basis start growing above zero, which implies that the Information amount associated to that location-basis is becoming reduced; likewise the density matrix in the momentum-basis would start to become more diagonal, and hence having a higher Information amount. The existence of off-diagonal elements in the location-basis density matrix for fermions is equivalent to the fermion’s PDF no longer being a sharp gaussian-like PDF centered in its location, but rather becoming a PDF with negative minimum (Zurek, 2007). (Lori, 2020) Thus, the density matrix corresponding to the negative minimum PDFs represented in the neurons is non-diagonal. This would imply that the classical CMP being implemented in the neurons has similarities to semi-classical approximations of QM, as they both obtain negative minimum PDFs, but it does not imply that neuronal dynamics are quantum, and we will see in the next paragraphs why they are not. (Lori, 2020) There have been several efforts in CS for the inclusion of quantum algorithms in non-quantum environments: by generalizing the concept of Markov random walk to that of a quantum walk and then apply it to the modeling of judgments measured by rate scales (Wang, 2015); by applying the concept of “Information Vagueness” to the role of social hierarchy in organizational management improvement (Maia, 2019) in Section 2.4 (Neves, 2019); and by using the QD-based random-causality o-iii axioms to Chapter 3 | Computer Science’s Future 99 represent objective human mental health in Section 3.1 (Lori, 2019). Nevertheless, the goal of this Section is not to find interesting applications of quantum-like algorithms, but rather to find new forms of doing CS that allow for the keeping of Moore’s law validity. We obtain here that the only path remaining for major CS improvements is lateralization, and so the use of quantum-like or Biology-like algorithms is only useful to us in as much as they can improve the capacity for lateralization. (Lori, 2020) The process of building lateralized computer infrastructures is favored by the existence of desirable representation characteristics, and we will now compare the general representation characteristics of QC vs. CC-based representations. In classical Physics, the events can be typically separated between two types: the clearly discrete events where there are large regions of nonoccurrence, and the clearly continuous events where the likelihood of occurrence is never zero. The clearly discrete events are typically represented by binomial random processes, whereas the clearly continuous events are typically represented by a Brownian motion random process. The binomial and Brownian processes can then typically be approximated by the Poisson and Wiener continuous processes, respectively. The Poisson and the Wiener process constitute the two major examples of classical CMPs, hence classical Physics’ perspective of reality can always be approximated by CMP processes. Moreover, both Poisson and Wiener processes have always positive probabilities. Before getting into the quantum perspective, we find useful to notice that the mutual Information and the conditional mutual Information are defined in the same way for classical and quantum systems, which implies that the Markov property is also defined in the same way for both classical and quantum systems, as the Markov property is simply an affirmation of a constraint in the conditional mutual Information (Baez, 2012)(Poulin, 2012). (Lori, 2020) In what concerns Information representation, the major difference between quantum and classical CMP is the difference between the classical and quantum versions of the Hammersley-Clifford Theorem (HCT). The classical version of the HCT (Hammersley & Clifford, 1971)(Clifford, 1990) being applicable to classical CMPs, and the quantum version of the HCT (Baez, 2012)(Poulin. 2012) being applicable to quantum CMPs. The classical HCT obtains that an always positive probability distribution satisfying the Markov property can always be represented by a random field satisfying a Gibbs measure (a.k.a. Gibbs random field) and vice-versa, hence implying that any positive probability distribution of a Chapter 3 | Computer Science’s Future 100 finite system can always be represented by the maximum entropy realization of a graph (meaning the Gibbs measure) and such realization is factorizable as a product of clique potentials. (Lori, 2020) In short form, the classical HCT obtains that “locality is equivalent to factorization” (Ganchev, 2018). For the quantum HCT, the equivalence is valid in the Markov→Gibbs direction, but is not valid in the Gibbs→Markov direction unless the sub-Hamiltonians for each of the cliques of the graph commute with each other (Baez, 2012)(Poulin. 2012). This general commutative-ness between sub-Hamiltonians is a level of clique-independence that in general is physically unattainable. Hence, in the quantum HCT the Gibbs random fields can represent quantum probability fields that are not quantum CMPs, meaning that they are not physically realizable above the femtosecond/nanometer scale, as all the quantum Physics above the femtosecond/nanometer scale are quantum CMPs. Thus, the classical Gibbs random field has a space of possible arrangements which coincides with the space of possible arrangements of the classical CMPs, implying that if a biological entity uses a classical Gibbs random field to map the external reality, then that map would work for any type of classical CMP, meaning it always works in all classical Physics situations. Whereas, if a biological entity uses instead a quantum Gibbs random field to map external reality it would have a very large (possibly infinite) number of different possible representations for each physically occurring quantum CMP. (Lori, 2020) The quantum approach is thus equivalent to having thousands of words representing the same object, meaning it would make the energetic cost of constructing a grammar with such words unbearable, unless the range of possible objects is very limited. Based in our analysis of the classical and quantum versions of the HCT, we obtain that Biology’s Darwinian evolution would favor the use of the classical Gibbs random field as a form of representing classical reality (both internal and external), and that the use of quantum Gibbs random fields to represent quantum reality is too energetically expensive to be evolutionarily advantageous for biological systems. (Lori, 2020) Recent works in Neuroscience have confirmed that the best fit to the in-vivo postsynaptic time histograms (PSTHs) obtained in non-human animals’ cortex are cliques of neurons that represent the basic units of Information in the cortex (Reimann, 2017), and also that the neurons implement a classical diffusion event (describable by a classical CMP) that is capable of explaining in detail the experimental results for rats undergoing decision-making tasks (Pardo-Vazquez, 2019). Using the classical CMP perspective of the HCT, we propose here that what the rat’s neurons are doing is to use Chapter 3 | Computer Science’s Future 101 the classical HCT to establish a one-to-one relation between the edge-interconnected cliques of neurons (where the edges are synaptic connections between neurons, and the nodes are neurons’ cell bodies) with the physiological 3D areas constituting the vicinity of the neurons’ cell bodies (which is where the classical diffusion/CPM occurs). Moreover, the experimentally found highest dimensionality of cliques obtained in statistically relevant quantities is a clique having 3-simplices (see Figure 2D (left) and Section 4.1.5 of ref. (Reimann, 2017)), meaning it is composed by 4 neurons, and hence the highest dimensionality of the diffusion process it can represent is 3D. (Lori, 2020) Also, very high mean activity correlation was attained for connections belonging to 3-simpleces (Reimann, 2017), which using our HCT-based perspective implies that most of the brain’s “thinking” occurs in 3D, including the “thinking about feelings”. This is in strong agreement with Neuroscience work which indicates that: feelings have a strong parallelism to 3D space (Damasio, 2003)(Damasio, 2010); the brain’s WM (meaning the brain’s long-range neuronal connections) determined using dMRI has a 3-axes structure (Wedeen, 2012); the fMRI data of word-listening obtained a cortical word-map with the 3-axes structure determined using PCA (Huth, 2016); and several of these 3D-axes experimental data were integrated into a 3-axes approach for describing all mental processes, which helped describe the characteristics occurring in schizophrenia, from normal to pathological levels as described in Section 3.1 (Lori, 2019). (Lori, 2020) We obtain in this Section that the future validity of Moore’s law is unlikely to be based in further miniaturization, mostly because of Pauli’s Exclusion Principle. Hence, it follows that lateralization is the most likely path for the maintaining of Moore’s law validity; and moreover, the difference between the classical HCT and the quantum HCT implies that quantum-based representation of natural phenomena is largely over-representative in complex situations, which explains why Darwinian evolution in Biology “chose” the classical rather than the quantum approach to “reality representation”. Our analysis and the “choice” made by biological evolution are, for us, strong indicators that the future CS developments will be made by lateralization-inducing architectures that almost exclusively use CCs. (Lori, 2020) Contemporarily, there is already a strong tendency towards accepting that although QCs might be better at certain tasks than CCs, the capacity for clever algorithms to overcome the capacities of QCs is likely to remain (Bleicher, 2018). This tendency agrees well with the perspective we propose in this Section, with the slight caveat that we are of the opinion that QCs are likely to out-perform CCs when the Chapter 3 | Computer Science’s Future 102 physical system being represented is made of a small number of objects that can assume a very large number of possible states/values (e.g. the specification of a password). Also, rather than encryption, the focus of QCs has been in the modeling of quantum phenomena that cannot be modeled using classical CMPs, e.g. “modeling the interior of Black holes; calculate reaction rates, combustion and other effects” (Chhabra, 2019). Moreover, “There are lots of areas where quantum algorithms that show any improvement over classical areas do not exist” (Chhabra, 2019), which will imply that “the end user experience for an average user will not change” (Chhabra, 2019). (Lori, 2020) Finally, although future high-level QCs might in the future be able to break public-key cryptography (PKC) systems, such as RSA and Diffie-Hellman (Martin, 2018), those QCs are unlikely to be able to break PKC systems developed in the NIST Post-Quantum Project (NIST, 2019)(Martin,2018). Some of the major Post-Quantum Cryptography (PQC) approaches that are candidates to winning the NIST Post-Quantum Project competition are (Microsoft, 2019) these: FrodoKEM uses a family of keyencapsulation mechanisms (KEMs) that are designed to be a conservative but practical PQC approach; SIKE uses arithmetic operations over finite fields; PICNIC uses a zero-knowledge proof approach; and qTESLA uses an improved decisional Ring Learning With Errors (R-LWE) approach. Thus, the lateralization computation proposed here can be correctly protected against hacking, even against hacking made by QCs, without needing to use QCs. (Lori, 2020) Mathematical Appendix (Lori, 2020): The deduction of Eq. 3.2.1 describing the variation of Information amount in an ensemble of particles expressed in bits, 𝑑𝐼, is described here. The 𝑑𝐼 is directly proportional to the entropy change 𝑑𝑆 through the relation 𝑑𝐼= 1 𝐾ln2𝑑𝑆, where 𝐾 is the Boltzmann constant. The relativistic equation for the Information amount change when Information is transported by spin 0 particles was obtained (Nakamura, 2006) to be: 𝑑𝐼=[ 𝑉0 𝐾ln2 𝑇]𝑑𝜖− [𝑷 𝐾ln2 𝑇]𝑑𝑉0, where 𝑉0 is the rest-frame volume, 𝑇 is the temperature, 𝑑𝜖 is the variation of energy density in the comoving frame, and 𝑷 is the pressure. This relativistic Information variation expression was obtained by generalizing the non relativistically-invariant thermal energy equation, 𝑈=𝐸−|𝑝|2 2∙𝑀 where 𝐸 is the energy and 𝑝 is the 3D linear momentum of the Information-carrying spin 0 particle of Chapter 4 | Conclusion and Discussion 109 Work in progress #2; by Nicolás F. Lori, José Neves, and colleagues It is focused in Physics and aims at complementing the work of Section 3.2 by attempting to determine the role CS can have in explaining certain features of the SMP and GR. Both works in-progress will allow the relation between CS and Reality to go both ways, that is, they will both allow the establishment of a direct relation between CS and Reality where both the actualReality (meaning the Physical Universe) and our mental perception of a perceived-Reality (meaning the human Mind) can be put in a one-to-one relation with CS. This possibility elevates the theoretical aspects of CS to the status of a Philosophy. In Plato`s Philosophy there are three Transcendental aspects of reality (a.k.a. Platonic Triad), viz. • Truth • Beauty • Good Contemporary Science fields, such as, Neuroscience, Psychology, and Psychiatry have clarified the relationship between the Actual Reality (i.e., the Physical Universe) and our mental perception of a Perceived Reality (i.e., the human mind). On the other hand, the role that computation can play in these areas may increase the need and / or capacity for the existence of computing tools that are able to deal with issues that have been in the past associated with Philosophy and its main branches, viz. • Aesthetics • Epistemology • Ethics • Logic • Metaphysics Chapter 4 | Conclusion and Discussion 110 which deal with the questions, viz. • What is Beauty? • What is Truth? • What is Good? • Which axioms and conclusions are valid? • What is one`s origin and end? Although branches such as Logic and Metaphysics seem to be a very natural adaptation to contemporary computer tools, the other branches are not normally included in such devices; but in areas like healthcare, the relationship between Actual Reality and Perceived Reality breaks down when it comes to health, namely in Actual Health (the lack of physical harm) or Perceived Health (the lack of a feeling of discomfort). Therefore, when computer tools are used for health care, their applicability can be improved by including some taxonomies from the field of Philosophy, in which Beauty, Good and Truth are the most common. Undeniably, the two branches of Logic and Metaphysics fit well with the usual methods of today's computer tools once they implement a kind of axiomatic system that is in direct correspondence to Newtonian Axiomatic Systems (NAS) and Darwinian Axiomatic Systems (DAS), with a match into the system`s area of Deterministic Physics and Darwinian Biology (Lori, 2010a)(Lori, 2010b)(Lori, 2019) (see Section 3.1 and Table 4.1.1). The Philosophy branches Aesthetics, Epistemology and Ethics look at different areas of human knowledge and depend, undoubtedly, on how these words are interpreted. For example, Truth may symbolize Experimental, Economic, and / or Personal truth. Depending on what the words Truth , Beauty and Good are thought to mean, the relationship to actual computer implementations may diverge. One`s perception is that the word Truth should only refer to the experimental value allocate to a strategy; and that Good should only relate to what improves patient health, while Beauty denotes the economic values corresponding to the staff`s salary. This last relationship between Beauty and value is possible above all because Beauty and Economic value are both physiologically (Montague, 2002) and culturally (Beinhocker, Chapter 4 | Conclusion and Discussion 111 2006) linked. Thus, the analysis in these final paragraphs also provides an assessment of the validity of the approach (Neves, 2009) described in Section 2.4. In Kant's perspective there could be no objective definition, in principle, for Beauty , since the aesthetic experience of Beauty relates only to the subjective pleasure of the subject and not to a property of the object (Moland, 2017). In Schiller's viewpoint, Beauty can be defined objectively (Moland, 2017). Schiller's work uses the term Beauty and not value , but in our approach, they are inter-linked, and therefore the Beauty-value notation is used. The reason for keeping the Beauty-value notation is that it is possible to argue that the basis of all beauty feelings is the market value of neurotransmitters in the brain (Montague, 2002), and that the basis of all market values is the Beauty appreciation that people assign to the objects (Beinhocker, 2006), i.e., Beauty is the basis for value and vice versa. Therefore, and in accordance with Kant and Schiller, no finite Beauty-value can be assigned to a person, since each person is an archetypal of their freedom and is, consequently, a matter of their own (Moland, 2017). Thus, only countless Beauty-value can be assigned to people as people are both capable and entitled to freedom. As a result, Schiller ascribes the utmost Beauty-value to the objects that present the uppermost freedom, i.e., the objects that have the least usefulness and are therefore closer to a thing that exists for itself. While this definition of Beauty seems to be in direct contradiction with the definition of value in contemporary economy, which assigns value to knowledge, meaning "useful Information" (Beinhocker, 2006), and that we designed as Truth . Therefore, contemporary economics seems to place more value on Truth than Beauty , and people are prepared to spend large amounts of their wealth to improve their health, suggesting that Good is also worthwhile. In fact, there are three types of values, viz., • Truth-value ; • Good-value • Beauty-value . The infinite value that Kant and Schiller ascribe to man relates only to Beauty , and it is an ascription that characterizes Kant and Schiller's philosophical period, the romantic, which is a preDarwinian one. The development of Darwinism as a Biological (Smerlak, 2016), Mathematical (Chaitin, Chapter 4 | Conclusion and Discussion 112 2006), Economic (Beinhocker, 2006) and Physical (Zurek, 2009) concept raises new questions that may be assessed with the help of computing tools. In order to be able to judge these three types of values, we must be able to work with an "axiom-driven value calculation" for the Truth-value , e.g. NAS; and with an "environmentally-driven value calculation" for the Good-value , e.g. DAS; while a new form of calculation is required for the Beauty-value . This new form of adding up, which is suitable for calculating the Beautyvalue of an object, is the partial Information-driven calculation given in (Neves, 2019) (see Section 2.4) and further developed in (Lori, 2019) (see Section 3.1), that presents the 3 axes of Psychology , viz. • Thanatos • Eros • Tyche. The relation between the 3-axes of Section 3.1 (Lori, 2019), the three factors of Section 2.4 (Neves, 2019), and the Plato’s Transcendentals (a.k.a. Platonic Triad) of Philosophy are represented in Table 4.2.1 by integrating Fig. 3.1.3, Table 3.1.2, Table 3.1.3, and Fig. 3.1.4. Table 4. 2.1. The relation between value and Beauty is described: Plato Neves Lori Truth Initiative Hunting/Power/Thanatos Good Empathy Eating/Pleasure/Eros Beauty Self-Discipline Choosing/Meaning/Tyche This new form of calculation, appropriate for the calculation of the Beauty/value of an object, is the partial Information driven calculation (Neves, 2019) described in Section 2.4, and further developed (Lori, 2019) in Section 3.1, to allow for the conclusion of Section 3.2 that lateralization, not miniaturization, is the future of CS (Lori, 2020). The Information concept used here is that of Shannon Information , i.e., the logarithm of the inverse of the probability of occurrence of a symbol in an alphabet; Chapter 4 | Conclusion and Discussion 113 which is thus based on probability theory. This new form of calculation, the partial Information calculation, is a probabilistic one, without necessarily assuming that these probabilities are the result of a lack of discipline of the observer, but that the Information available is not sufficient to provide more than the probabilities. A key question for this new form of partial Information-driven calculation named Statistical Philosophy , a here-proposed branch of the Philosophy of Information , is the importance of the role causality plays in the observed system. This is a central issue for Statistical Philosophy , since causality plays a direct role in the appropriate control of variables, which enables an appropriate statistical estimation of the probability of events. The correct way to use variable control depends on whether the variable ◊ acts as a mediator , confounder or collider . The role of the variable ◊ is defined by whether it is causality that will, viz., (Pearl, 2018) • go through ; → ◊ →; indicating a mediator • diverge ;  ◊ →; indicating a confounder • converge ; → ◊ ; indicating a collider In order to use causality correctly in statistical analysis, it is necessary to carry out causal interventions in probabilistic inference using the MAKE operator, which corresponds to the occurrence of a causal effect (Pearl, 2018). The use of the MAKE enables the creation of a counterfactual statistical analysis, which enables the creation of the two upper levels of the causal inference above the correlation level, i.e., the interventional and counterfactual levels. The correlative causality resembles an act of seeing , meaning it identifies the likelihood of the simultaneous occurrence of events; the intervention an act of doing , meaning it identifies the likelihood that an effect resulted from a certain cause; and the counterfactual an act of imagining , meaning it identifies the likelihood that an effect that did not occur resulted from a certain cause not occurring (Pearl, 2018). Moreover, because of the conclusions in Section 3.2, the classical causality rules used in ref. (Pearl, 2018) will continue to be used in CS despite the recent appearance of QC (Arute, 2019), as according to Section 3.2, CC will continue to be the most Chapter 4 | Conclusion and Discussion 114 relevant contributor to CS, and so the causality characteristics of quantum causality, such as the timereversibility of the U(1) gauge invariance force, need not be considered. This new form of calculation enables a Statistical Philosophy based on computational tools (Pearl, 2018). The counterfactual definition of causality was already available in the biblical dialogues of Abraham (Pearl, 2018), but was not used by Aristotle (Pearl, 2018); and it was not used by Hume in his work from 1739, but only appeared in Hume's work from 1748 (Pearl, 2018). In addition, it was Hume's analysis of ethics and causality that prompted Kant to develop his own thorough approach to ethics and causality (Wilson, 2018). This is relevant to the approach proposed here, since it is directly related to the distinction between Hume and Kant morals (Greene, 2004) (see Fig. 3.1.3); since Kant's ethics are based on duty (therefore associated with language), and Hume’s are based in emotion (hence associated with tone of sound); moreover, “Kantian reversibility” (Kant, 1993) was described in Section 3.1 as being equivalent to Gilligan’s concept of “post-conventional” (Gilligan, 1985), again centered in the issue of duty. Thus, it is a key issue the difference between Kant's view that Beauty is not objective and Schiller's view that Beauty can be objective (Moland, 2017). The Kantian preference for a NAS approach implied that the causality rules can be axiomatically accepted but not empirically proven. Hume's 1739 approach opted for empirically based correlationdriven DAS validation of the causality rules, although such approach cannot resolve the induction problem (Henderson, 2019). It is Bayes' causal probability that enables the causality to be obviously derived from data. In fact, Bayes' causal probability can only infer correlative causality (Pearl, 2018), the first level of causal reasoning, as suggested by Hume's 1748 approach. However, the counterfactual algorithms currently implemented in today's computers use Bayesian networks (Pearl, 2018). In fact, the selection of the best possible counterfactual causality rules is already carried out in the big data analysis (Forney, 2017). The goal of maximizing the Truth , Beauty , and the Good values seems to be the obvious answer to the health management problem raised here; but, just like in health management it seems impossible to have staff wages, equipment costs, and patient improvement maximized without going bankrupt. It will be shown here that when one tries to maximize Truth-value , Beauty-value and Good-value often leads to a kind of trilemma restriction that occurs in many forms (e.g. Fries’ Trilemma (Fries, 2011)(Popper, 1959)). In this work the focus will be on the economic perspective, specifically in the "political trilemma" that Chapter 4 | Conclusion and Discussion 115 confirms the paradox "Democracy vs. national sovereignty vs. global economic integration" (Rodrik, 2007)(Rodrik, 2011), and the impossible trinity that confirms the paradox "independent monetary policy vs. fixed exchange rate vs. free movement of capital ", which has been confirmed by empirical studies (Boughton, 2003)(Obstfeld, 2005). The relationship between the three aspects of the "political trilemma" (Rodrik, 2007)(Rodrik, 2011), and the "impossible trinity" (Boughton, 2003)(Obstfeld, 2005) is straightforward; however, it is proposed here a form by which computational tools can be used in clarifying the balancing-characteristics of the “Impossible Trinity”. Specifically, the attempt at an “independent monetary policy” is an attempt at establishing a NAS Truth-value using locally-defined consistent axioms, whereas a “free capital movement” is an attempt at establishing a DAS Good-value using globally-defined complete axioms. Yet, as it is known by the Gödel Incompleteness theorems, the axioms with a finite-amount of Shannon Information cannot simultaneously be Complete and Consistent (Chaitin, 2006), which can have implications in both Brain Behavior (Lori, 2010a)(Lori, 2019) and Fundamental Physics (Lori, 2010b). The time evolution dynamics of Darwinian advancement is only partially predictable, not only because it is probabilistic, but also because the form of the aptitudeProbability Distribution Function ( PDF ) is only partially predictable, as the predictable part of the time evolution is only the aptitude of the newest types (Smerlak, 2016). The Darwinian evolutionary processes of DAS , i.e., the "free movement of capital" in the sense of Good value, are fundamentally unpredictable (Smerlak, 2016), whereas the Newtonian evolutionary processes of NAS, i.e., the "independent monetary policy" that means the Truth value, are fundamentally predictable (Chaitin, 2006); The balance between the NAS and the DAS, which represents the "fixed exchange rate" for the Beauty value, is therefore a weak balance between Predictability vs. Unpredictability, local influence vs. global influence, consistent axioms vs. complete axioms, between NAS vs. DAS. The calculation of this balance takes place in our brain when we evaluate the value of an action (Montague, 2002) and also the value of an object in the world economy (Beinhocker, 2006). The choice of the clinical action that is more worthy, as it often occurs in health management, inevitably requires the projection of a three-dimensional value vector, i.e., [ Truth value, Beauty value, Good value] into a one-dimensional worthiness-scalar. This projection is necessary, as the concept of best is necessarily one-dimensional. The various forms of projecting the value 3-vector to the one-dimensional Chapter 4 | Conclusion and Discussion 116 worthiness-scalar form the political / ethical / religious decision that every person and every society makes. The Statistical Philosophy computational tools are unlikely to provide an unique answer to what is the best political, ethical or religious choice, but the Statistical Philosophy computational tools offer new and more thorough perspectives for the best possible assessment of what is the cause and what are the consequences of the political / ethical / religious decisions that occur. The future developments in the fields of Biomedicine , Neuro-informatics or Health Management pose special requirements, which have led to the development of different approaches for calculating the associated value. We have found that the simple use of computing tools makes it difficult to estimate the value associated with a clinical act. However, these arithmetic tools are best used if they are integrated with philosophical perceptions, which have become clearer through recent developments in the fields of Neuroscience , Economics , Physics or Mathematics . 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