Contextual Emergence

What is contextual emergence?

The patterns that emerge from Conway’s Game of Life do so depending on the underlying theory.

Contextual emergence is a specific kind of relationship between different domains of scientific descriptions of particular phenomena. Although these domains are not ordered strictly hierarchically, one often speaks of lower and higher levels of description in which emergence occurs. From the lower levels (L), more fundamental in a certain sense, phenomena emerge in higher levels (H) in more complex phenomena. Strings of DNA in a genome may correspond to different transcripts on an transcriptome level for an individual. Chaotic conditions may emerge from certain differential equations subject to certain constraints. This complexity depends on the conditions of the context. Hence, contextual emergence.

Contextual emergence involves well-defined relationships between different levels of complexity. We can use a two-step procedure to create a systematic, formal way that an individual description (Li) creates a statistical description (Ls) among the lower level. This process can lead us to describe individuals at a higher level (Hi). We iterate this process (Li -> Ls -> Hi) through sets of descriptions connected with one another to reveal what emerges at higher levels.

During this method, we identify equivalence classes of individual states that are indistinguishable with respect to a certain property of the entire system. We can realize different statistical states in Ls by individual states in Li. Each state has limited knowledge, but, together, we can create probability distributions represent the statistical states Ls. This could be how spike signals from neural circuits encode for higher-level functions in the brain.

A property dualist position would also recognize three features of this emergence. The emergent property at the higher level Hi must have real instances, remain co-occurrent with some property or complex feature recognized in the lower level, and this property can’t be reduced to any property postulated by or definable within the lower level.

Then, we can assign individual states at the higher level H to coextensional statistical states at level L. We use a top-down constraint. This needs information about the higher description to choose a context setting the framework for the set of observable properties at level H created from L. We can implement stability criteria at level L such that the appropriate context emerges at level H. The stability refers to the ability for the features of the system to remain valid even under small changes. This includes equilibrium states of gas systems and homeostatic relationships between units of biological mechanisms such as glycolysis. We may also define stability as systems that have boundaries maintained under the dynamics specified for it We may choose to confine ourselves to certain electrochemical properties that emerge from membrane dynamics in synaptic networks. This allows the emergent properties to remain well-defined from the contextual topology of L. It also tells us which properties of L are relevant to the contextual emergence of H.

This interplay between upward and downward strategies lets the system remain self-consistent. Moving from a higher context to a lower one requires the stability conditions to lead to lower-level partitions of the system while moving to a higher context means the statistics of lower-level states extend to higher-level individual states we can observe.

Philosopher Aristotle argued emergent structures arise when their constituents interact in an interdependent manner, but others may argue that emergence may occur even if the parts act independently of one another or even be autonomous. In either case, to echo the theory of Gestalt, the whole is greater than the sum of its parts.

Point mechanics to statistical mechanics to thermodynamics

We can even demonstrate the relationship between different fields of science through contextual emergence. Moving from classical point mechanics, involving forces due to gravitational effects and electromagnetism, to statistical mechanics to thermodynamics illustrates this phenomena. From point mechanics to statistical mechanics particles or other individual units (Li) form ensemble distributions which can be studied using statistics. We can define many-particle systems with statistical ensemble descriptions (Ls) like momenta or energy of distributions, such as the Maxwell-Boltzmann distribution for N particles. From there, we can find mean kinetic energy, Gibbs free energy, entropy, and other statistical quantities.

We can observe expectation values of momenta distributions of particle ensembles to calculate temperature of the system as a higher-level function (Hi) on the assumption the system is in equilibrium. The zeroth law of thermodynamics does not come from statistical mechanics, but from thermodynamics. Other features such as irreversibility and adiabatic nature emerge as well. We can characterize this thermal equilibrium (Hi) using Kubo-Martin-Schwinger (KMS) states, defined by the condition that characterizes the structural stability of a KMS state against local perturbations or changes. This leads to stationarity, ergodicity, and mixing using the zeroth law of thermodynamics to define the system as stable. We can also use the second law of thermodynamics to express the stability in maximization of entropy for thermal equilibrium states.

The first step of the contextual emergence process (Li -> Ls) describes statistical states from the individual states, and the second gives individual thermal states from statistical mechanical states. Other examples may include emergence of geometric optics from electrodynamics, electrical engineering features from electrodynamics, chirality from quantum mechanics, and diffusion or friction of a quantum particle in a thermal medium. Neuroscientists have even found use in contextually emerging cognitive states from neural correlates.

Hodgkin-Huxley equations

The Hodgkin-Huxley equations that describe generation and propagation of action potential form a system of four ordinary nonlinear differential equations: an electric conductance equation for transmemberane currents and three master equations for the opening kinetics of sodium and potassium channels. These lower-level stochastic (using Markov processes as transition probabilities) phenomena lead to higher-level descriptions of ion channel function to characterize a deterministic dynamic system. We can treat ion channels as macro-molecular quantum objects with the Schrödinger equation for many particles. The Schrödinger equation describes a highly entangled state of electrons and atomic nuclei as a whole, and, on a molecular level, the structure of a closed or open pore of an ion channel through the Born-Oppenheimer approximation separates electronic and nucleonic wave functions. Then, we can use the electronic quantum dynamics in a constrained rigid nucleonic frame that has a classical spatial structure. This stochastic spatial structure gives the equations of the Hodgkin-Huxley system as a contextually emergent phenomenon.

Mental states emerging from neuroscience

To realize mental states from neural states, we specify the L level as neuron states of neural assemblies in the brain with respect to H, a class of mental states that reflects the situation under study. We may use experimental protocols that include a task for subjects to define mental states while recording brain states. We may use individual neuron properties Li to find Ls such that statistical states have equivalence classes of those individual states. The differences must be irrelevant with respect to the higher level H. Philosopher David Chalmers said a neural correlate of a conscious mental state can be multiply realized by “minimally sufficient neural subsystems correlated with states of consciousness” in “What is a neural correlate of consciousness?”

We can look at phenomenal families, sets of mutually exclusive phenomenal mental states that jointly partition a space of mental states. Creature consciousness can give us refined levels of phenomenal states of background consciousness (awake, dreaming, etc.), wake consciousness (perceptual, cognitive, affective, etc.), perceptual consciousness (visual, auditory, tactile, etc.), and visual consciousness (color, form, location, etc.). With one of these contexts, we choose stability criterion at Ls that has complicated neurodynamics to find robust, proper statistical states.

We may describe L-dynamics and H-dynamics meshing with one another if coarse graining and time evolution commute with one another. We create meshes, parts of space differentiated by complexes of cells between the two levels, that follow from higher-level stability criterion. The coarse graining means fine details of the system can be smoothed over, as entropy of the system increases, such that we can make predictions about the system as a whole.

Contextual emergence could help artificial intelligence approach its potential while accounting for the inherent, intrinsic differences between science and philosophy. We may model the mind as a contextual emergent phenomena of the neurophysiology of the brain. As we learn about the world, we can account for emergent phenomena when addressing issues in science and philosophy, and AI would benefit from these methods of understanding. AI could avoid the issues of reductionism using higher-level emergent behavior resulting from neural networks in the human brain. Backpropagation of neural networks lets us optimize the gap between reality and models they represent using feedback loops with optimal weights of individual neurons when optimized for emergent details. The same way a human can differentiate between a drawing of an lion and a photograph of a lion itself using the emergent phenomena of visual images that appear together to create a lion, intelligent machines can embrace contextual emergence to view the work with inquisitive wonder and curiosity to learn. Instead of having to show a computer hundreds of thousands of images of a lion to teach them how to identify a lion, they can realize a lion in another context, such as lines of a piece of artwork, through the emergent properties of a drawing of a lion itself.

Emergence in AI can account for emotional reactions and instincts by evolving using stochastic emergent phenomena the same way human intelligence has evolved. We may address the role emotions and biases play in decision-making and intelligence, as described by psychologists Daniel Kahneman, Amos Tversky, and Gerd Gigerenzer.

We can represent proper cells with basins of attraction and chaotic attractors with coarse-grained generating partitions. These partitions of the system lead to Markov chains with a rigorous theoretical constraint for the proper definition of stable mental states. The mathematical techniques come from ergodic theory and symbolic dynamics.

The emergence of mental states from electroencephalogram (EEG) dynamics shows that data from subjects with EEG data from sporadic epileptic seizures can correlate with mental states of the seizures themselves. Using a 20-channel EEG recording, we get a 20-dimension state space that we reduce to a lower number through principal component restrictions. We find a homogeneous grid of cells to set up a Markov transition matrix that reflects the EEG dynamics using fine-grained auxiliary partition. Then, this matrix gives eigenvalues that characterize time scales for which the dynamics can be ordered by size. The eigenvectors span an eigenvector space such that the measure principal component states form a simplex. The three leading eigenvalue give a neural state representation that has a 2-simplex with three vertices, or a triangle. We can further classify neural states by distance from the vertices of the simplex to clusters of neural data. In the principal component state space, the clusters appear as non-intersecting convex sets between mental states. We may also use recurrence structure analysis to partition the state space into recurrent clusters such that they overlap from the recurrence plot of the dynamical system. We figure out the metastable states and transitions between them using a Markov chain with one distinguished transient state and other states representing the metastable states in the dynamics.

Intentionality

Philosopher Daniel Dennett describes the intentional stance of the prediction of a system’s behavior too complex to be treated as either a physical or designed system. Intentional systems behave in predicted ways by ascribing beliefs and desires to their internal states. From thermostats to chess computers, we can make predictions of a system with necessary and sufficient conditions. The system’s dynamics have to be non-trivial, so this excludes linear systems with periodic oscillations or damped relaxations. We construct an intentional hierarchy from general case of nonlinear nonequilibrium dissipative systems to more specific intentional systems. A physical system’s physical nature is necessary for being a nonlinear dissipative nonequilibrium system while a nonlinear dissipative nonequiliibrium nature is necessary for an intentional system. An intentional system is necessary for being a true believer, according to Dennett. Sufficient conditions in the intentional hierarchy implement contextual stability conditions.

The transition from equilibrium thermodynamics to fluid dynamics represents phenomenal laws of fluid dynamics (like the Navier-Stokes equation) emerging from statistical mechanics under the assumption of local equilibrium. Sufficient boundary conditions give rise to self-organization, such as through “magnetic snakes.” We give a rationality constraint for optimal dissipation of pumped energy, and true believers emerge contextually as intentional systems under mutual adoption of the intentional stance.

The representational thought may reference aboutness, and the intentional approach concerns the contentfulness or meaningfulness of representational states. We may create a network theory of meaning that emerges from the semantics of a system. Philosopher Karl Popper argued against reductionism on the grounds there’s a world of abstract, nonphysical objects we interact with when we reason, discover proofs, speculate consequences, use language, and think about mathematics and philosophy. This autonomous reality (known as World 3, with World 1 being physical laws and World 2 as mental events and processes) we find dispositions to verbal behavior and wiring in the brain. Popper implies it’s more understandable how nonphysical states interact with intelligibilia than how neural states might.

Symbolic grounding

The symbolic grounding problem is the problem fo assigning meaning to symbols on purely syntactic grounds. Cognitivists such as philosophers Jerry Fodor and Zenon Pylyshyn have described this problem. It can also describe how the question of how conscious mental states can be characterized by neural correlates. The relation between analog and digital systems such that syntactic digital symbols relate to the analog behavior of a system they describe symbolically needs to be further examined through dynamical automata. Piecewise linear time-discrete maps over a two-dimensional state space assume the interpretation as symbolic computers through a rectangular partition of the unit square. A single point trajectory is not fully interpretable as symbolic computation. We need higher-level macrostates from ensembles of state space points, or probability distributions of points, that evolve under the dynamics.

Writer Beim Graben showed only uniform probability distributions that have rectangular support exhibit a stable dynamics can be interpreted as computation. The huge space of possible probability distributions can be contextually restricted to a subclass of uniform probability distributions to create meaningfully grounded symbolic processes. Symbolic grounding is contextually emergent.

Mental causation

Describing the mind as causally relevant in a physical world introduces the problem of mental causation, the question of how mental phenomena can be highly significant in psychology and cognitive neuroscience. It means creating a notion of agency that includes the causal efficacy of mental states. This causal efficacy of mental phenomena seems inconsistent with vertical (interlevel, synchronic) determination of the mental state by neural correlates. Philosopher Jaegwon Kim argued supervenience (also known as exclusion) describes the problem that mental states are either causally inefficacious or have the threat of overdetermining neural states. Either mental events play nor horizontally determining causal role at all or they’re the causes of the neural bases of their relevant horizontal mental effects. Contextual emergence through different levels of complexity means the conflict between horizontal and vertical determination of mental events isn’t an issue. We can define proper mental states from dynamics of an underlying neural system through statistical neural states on proper partitions with individual mental states.

This construction implies that the mental dynamics and the neural dynamics, related to each other by a so-called intertwiner, are topologically equivalent. Instead of some mutually exclusive duality of the mental and the neural, we have a monistic idea that they are part of one and the same concept, albeit related to one another
in a significant way. We can describe it using dual-aspect monism using symmetry breakdown conceptually prior to the opposite of generalization. When symmetries between entities restore themselves, we observe the similarities brought upon by the symmetries and generate equivalence classes of increasing size that can describe contextually emergent phenomena. Given properly defined mental states, the neural dynamics gives rise to a mental dynamics that is independent of those neurodynamical details that are irrelevant for a proper construction of mental states. Mental states can be causally and horizontally related to other mental states, and they neither cause their vertical neural determiners nor cause the horizontal effects of the neural determiners. This resolve the problem of mental causation in a deflationary manner. Vertical and horizontal determination don’t compete against one another. They work cooperatively.

Mental causation is a horizontal relation between previous and future mental states with effectiveness given by the vertical relation (the downward relation of neural states from higher-level mental constraints). Psychophysical neutral elementary entities are composed to sets of such entities that depend on the composition of these sets in a way they acquire mental or physical properties. The psychophysically neutral domain does not have elementary entities waiting to be composed, but, rather, has one overarching whole to be decomposed into its parts. The mental and material from a psychophysical neural whole causes a contextual emergence that requires a new technical explanation and a metaphysical one.

The technical framework refers to the contextual emergence of multiplicity from unity. The “primordial” decomposition of an undivided whole generates different domains that gives rise to differentiations, such as the mind-matter distinction. The psychophysical neutral reality is the trivial, completely symmetric partition in which nothing is distinguished from one another. We can decompose this to give rise to more and more refined partitions in which symmetries are broke and equivalence classes become smaller and smaller. Phenomenal families of mental states emerge.

On a metaphysical level, mental and physical epistemic limits describe the undivided whole as an ontic (physical factual existence) dimension. They reminisce of philosopher Plato’s abstract perfect ideas and philosopher Immanuel Kant’s things-in-thesmelves (empirically inaccessible in principle and specifically mute). The mind-matter problem causes an emergence of mind-matter correlations as direct and immediate consequence of the ontic, undivided whole that can’t be further divided without introducing more distinctions. Many describe determinism as a feature of ontic descriptions of states and observables while stochasticity uses epistemic descriptions.

Mathematical models of classical point mechanics are most common examples of deterministic descriptions and three properties of them are important. (1) The differential dynamics mean the system’s evolution obeys a differential equation in a space of ontic states. (2) The unique evolution of the system means initial and boundary conditions give a unique trajectory. (3) The value determinateness assumes that any state can be described with arbitrarily small error. These three features define a hierarchy for the contextual emergence of deterministic descriptions assuming (1) is a necessary condition for determinism, (2) can be proven under sufficient condition that trajectories created by a vector field obeying (1) pass through points whose distance is stable under small perturbations. We assume (2) for almost every initial condition as a necessary condition of determinism that defines a phase flow with weak causality. To prove (3), we need strong causality as a sufficient condition. The deterministic dynamics of Kolmogorov flow implement microscopic chaos as a stability condition. It’s also possible a continuous stochastic process that fulfills the Markov criterion can lead to a deterministic “mean-field equation.”

Different descriptive levels can correlate with different degrees of granularity. Lower-level descriptions address systems in terms of micro-properties while more global macro-properties account for higher-level descriptions. Philosophy Bas van Fraassen noted the explanatory relativity, in which explanations are not only
relationships between theories and facts, but three-place relations between theories, facts, and contexts. Contexts determine relevance of explanation backed by relevance criteria for reproducibility in science, especially in interdisciplinary fields such as bioinformatics or computational neuroscience. This gives a framework for discussing contextual emergence alongside theories and facts as they relate to explanations. We consider the granularity of descriptions that we observe when descriptive levels transform between one another and their associated granularities by the interlevel relation of contextual emergence. This gives a formally sound and empirically applicable procedure to construct level-specific criteria for relevant observables across disciplines.

Reductionism and ontology

It may seem appealing to reduce every system down to its fundamental components and conclude that every empirical phenomena in science or other disciplines is only applied mathematics. But this misses out on the features of the whole that emerge in the contexts of the higher layers which cannot be reduced. Consciousness among neural and mental correlates of different states provide one example, but we only need to look at any example, such as the emergence of transcriptome interactions from how a genome itself structures itself, to realize that these properties come about only at the higher levels, and, therefore, involve phenomena that are not completely reducible to mathematics. Biologist Peter Corning argued in “The Re-Emergence of “Emergence”: A Venerable Concept in Search of a Theory” that whole systems produce unique combined effects that may involve the context between and the interactions with the system and its environment.

Contextual emergence has been originally conceived as a relation between levels of descriptions, not levels of nature: It addresses questions of epistemology rather than ontology. In agreement with Esfeld, who advocated that ontology needs to regain more significance in science, it would be desirable to know how ontological considerations might be added to the picture that contextual emergence provides.

Various granularity degrees raises questions of descriptions with finer grains as they relate to the fundamental nature of systems when compared to coarser grains. The majority of scientists and philosophers of science answer believe this, so there’s one fundamental ontolgoy that elementary particle physics result from reducing other descriptive levels. This reductive premise produced critical assessments and alternative proposals. Philosopher Willard Van Oramn Quine introduced the ontological relatively that, if there is one ontology that fulfills a given descriptive theory, there is more than one. Philosopher Hilary Putnam developed a related kind of ontological relativity, first called internal realism, and later referred to as pragmatic realism.

We may apply Quine’s ideas to concrete scientific descriptions, their relationships with one another, and their referents. A descriptive framework can be ontic or epistemic depending on which other framework it relates to. An engineer may consider wires of an electrical circuit to be ontic, but a solid-state physicist may consider them epistemic. We can use the relevance criteria to distinguish between context-specific descriptions and avoid pitfalls of reductionism. We create a subtle and more flexible framework while still restricting ourselves to the premises and limits of the contextually emergent model.

Strong and weak emergence

Weak emergence involves emergent properties that computer simulations can control such that the interacting cells of the system retain their independence. Other emergent properties, irreducible to the system’s constituent parts, are strong. Both are supervenient and involve novel properties as the system grows, but the distinction introduces a scale-dependency to observable phenomena.

A Computational Theory of Mind

Brains are only like computers in a specific abstract sense. We can take apart this analogy in the context of the brain-computer analogy to determine knowledge for philosophy, neuroscience, artificial intelligence, and other research areas. It’s very harmful in many ways to treat the nervous system as the hardware in such a way that we need to understand the cognitive science as software when we don’t understand the limitations of such a metaphor. Any theory of anatomical connection we demonstrate in vertebrate nervous systems may give us a basic description of what happens at each stage, but don’t tell us how a given input relates to a certain output. Instead, they obfuscate the description of the brain by using unnecessary comparisons to explain phenomena that are better off explained by describing the phenomena directly and precisely.

An output of a computer depends on its program, input, and functional stages that lead to the output. We can theorize and speculate on artificial and biological computers by using this analogy with other phenomena such as artificial neural networks in computer science and mathematics or biological computers among the brains of different organisms. These computers show connections between the disciplines underlying computation with its theory from statistical mechanics and thermodynamics. We can use ideas from information theory, entropy dynamics, and constraint problems on the resulting artificial and biological computers.

Classicalism vs connectionism

The computational theory of mind is the leading contemporary version of the representational theory of mind, in which we use mental structures to represent mental processes. The computational theory of mind tries to explain all psychological states in terms of mental representations. Philosopher Stephen Stich argued cognitive psychology doesn’t and shouldn’t taxonomize mental states by their semantic properties. Those semantic properties are determined by the extrinsic properties of a mental state. Stich proposes a Syntactic Theory of the mind, arguing the semantic properties of mental states don’t have an explanatory role in the mental states. The Syntactic Theory of Mind uses computational theories of psychological states that only concern with the formal properties of the objects the state relate to. We use semantically evaluable objects with the computations of mental processes. Computational theory of mind proponents disagree on how personal-level representations (thoughts) and process (inferences) in the brain are realized. Classical Architecture proponents (classicists) such as Turing, Fodor, Pylyshyn, Newell, and Simon, believe mental representations are symbolic structures that have semantically evaluable constituents. Mental processes are rule-governed manipulations of them that are sensitive to their constituent nature. Connectionist Architecture proponents (connectionists) like McCulloch, Pitts, Rumelhart, and McClelland believe mental representations are realized by activation patterns in simple processors (nodes). These mental processes are made of the spreading activation of these patterns. The nodes aren’t semantically evaluable typically. One may argue that localist theories are neither definitive nor representative of the connectionist program.

Classicists want to find mental properties similar to language. Fodor’s Language of Thought Hypothesis (LOTH) uses mental symbols to make up the neural basis of a thought like a language. In the LOTH, the potential infinity of complex representational mental states comes from primitive representational states that form using recursive formation rules. We use a combinatorial structure to account for productivity and systematicity of the system of mental representations. We explain the properties of thought using the content of representational units and their combinability into contentful complexes. The semantics of language and thought is compositional.

Connectionists want to consider the architecture of the brain, networks of interconnected neurons. This architecture can’t carry out classical serial computations, but, instead, parallel computations lack semantic compositionality nor are semantically evaluable the way classicists argue. Representation is distributed, not local (unless it’s computationally basic). Connectionists argue information processes in these networks resembles human cognitive functioning. Connectionist networks trained by exposure to objects learn and distinguish. Some argue connectionism means there aren’t propositional attitudes. LOTH-style representation may, on the other hand, be necessary for the general features of connectionist architectures.

Stich believed mental processes are computational, but these computations aren’t sequences of mental representations. Other philosophers accept mental representation, but deny that the computational theory of mind gives the correct account of mental states and processes. Writer Tim Van Gelder doesn’t believe psychological processes are computational. Instead, dynamic cognitive systems give rise to states that are quantifiable of a complex system of the nervous system, the body, and the environment in which they are created. Cognitive processes aren’t rule-governed by discrete symbolic states. Instead, they’re continuous, evolving total states of dynamic systems by mutually determining states of the system’s components. The dynamic system leads to representation that is information-theoretic through state variables or parameters.

Philosopher Steven Horst wrote that computational models are useful in scientific psychology, but they don’t give us a philosophical understanding of intentionality of commonsense mental states. The computational theory of mind tries to reduce the intentionality of states to the intentionality of the mental symbols, but the relevant notion of symbolic content is bound by the notions of convention and intention. Horst believed the computational theory of the mind uses the very properties that it is supposed to reduce things to as a circular argument that need to be reduced themselves.

Intentionality

If we treat propositional attitudes with intentionality as a physical properties, we can build a computer with states that have genuine intentionality. But no computer model that stimulates human propositional attitudes will have genuine intentional states. Intentionality of propositional attitudes isn’t a physical property.

We may consider the network theory of meaning (or holistic theory or conceptual-role theory) such that the meaning of an expression plays a role in its internal representational economy. This way it relates to sensory input and behavioral output. Meaning is relational as an expression’s meaning is a function of its inferential and computational role in a person’s internal system. A robot that behaves like a human is still subject to the question of whether those thoughts it generates have the same meaning that represent our own meaning. Assigning meaning to the internal states of a robot would be applying a double standard arbitrarily with no useful purpose. The robot’s internal machinery doesn’t change that it believes, wants, and understands things. The robot’s intentional states depend on how complex its internal informational network of states it has.

We need altogether a better theory of representation in organisms much the same way we have theoretical definitions and ideas of what molecules, proteins, and neutrons are. We can also study the mind as it relates to the computer by differentiating between understanding its design and its function. Though we can perform actions such thinking, feeling, and arguing without knowing exactly the neuroscience of our brains, we can also use a computer for, more or less, what a computer is designed to do without knowing exactly how a computer. Albeit, we must know some computer basics such as turning on a computer by pressing a button as well taking care of our brains by taking care of our bodies, we must also account for intentionality in understanding why intentions works, rather than simply knowing that we have intentions and following in blind dogma.

Levels of organization

The brain-computer analogy presents a problem of complexity that we know we have in the brain as that relates to organization of a computer. The semantic, syntactic, and mechanistic levels introduce issues with the level of the algorithm and the structural implementation of those features. Neurobiological theory challenges the way of specifying the organizational description. The levels of membrane, cell, synapse, cell assembly, circuit, and behavior can be argued as levels, but even within them we have different partitions of the levels of themselves. We can also determine levels by the research methods such as how through learning and memory we can take a cellular approach to show modifications in presynaptic neurotransmitter releases in habituation. Which level is functional and which level is structural is difficult to determine, too.

Mental state semantics

According to the computational theory of mind, the mind operates on symbols and uses symbolic representations to represent mental states. We discuss the meaning of these symbols as the semantics and the relationships between them as the syntax. We may argue that more complicated mental states come from these basic symbolic “words” of the language of thought. The hypothesis that there’s a language of thought encoded within our brains is not obvious, nor is it agreed upon by everyone. There are many competing hypotheses and theories to how the logical form fo propositions relate to the structural form of the mental states that correspond to them. If we take an intentional stance to the mind (that we treat the object that has a behavior we want to predict as a rational agent that has beliefs, desires, and similar mental states that exhibit intentionality), we can uncover objective, real patterns of the world, and this is an empirical claim we can determine beyond the skepticism associated with it. Philosopher Daniel Dennett argued any object or system whose behavior we predict with this strategy is a believer. A true believer, Dennett argued, is an intentional system whose behavior we can reliably predict with the intentional stance. Our brains have somehow handled the statistical combinatorial explosion that accompanies its own complex nature such that we can use billions of cells in networks with one another, and the only representational system we have upon which to model is human language. We haven’t imagined any plausible alternatives in such detail as we do our own language.

Causality

A calculator’s representation and rules for manipulating representations can explain its behavior much the same way we describe how and why people do what they do. Philosopher Zenon Pylyshyn said we explain why a machine does something with certain interpretations of the symbols in a domain. Psychologcial theory would cross-classify categories of neurophysiology theory that would make neurophysiological generalizations miss important relations that are only describable at the level at which representations are referred to. The psychological maps only would map onto an indefinite mix of neurobiological categories.

Connectionism (Parallel distributed processing)

As philosopher Paul Churchland has argued, we may use connectionism or parallel distributed processing (PDP) in figuring out the computational operations in nervous systems in such a way we may use computer models of parallel distributed systems to generate the appropriate phenomena on a higher level (cognitive science, psychology, etc.) from basic processes (neuroscience, physics, etc.).

Tensor network theory

Neuroscientists began the theory began on the cerebellum because it has a limited number of neuron types that are each distinct on a physiological level and connected in a specific way that the cerebellar cortex produces the Purkinje cell with two different cell systems as input. Using wiring diagrams of cerebellar neurons to describe the connections accept input and result output in a parallel manner. We have a trade-off between detail to understand the system with how the array itself processes information. Through tensor network theory we attempt to use principles from mathematics, physics, and computer science in understanding how these systems may model the nervous system. We can create a schematic neuron to find out more about the patterns of neurons arranged in mathematical arrays. Though the model may be limited by the assumptions of casual theory and epistemic concerns of the phenomena we attempt to describe, it’s a nice heuristic to see something we wouldn’t otherwise see through single-cell data. We may use concepts from linear algebra and statistics to create output vectors in a coordinate system such that the corresponding tensor matrix governs the transformation of ensembles from input-output relationships by the corresponding reference frame. The spiking frequency defines a point on an axis of the coordinate system with the output a vector in the space of the output neurons. We may generalize a tensor mathematical to transform vectors into other vectors such that we address the basic problem of functionalist sensorimotor control as going from one different coordinate system to another.

When we figure out what the mind-brain does, then how it might implement various functions in a top-down manner among different levels of science, the theorizing is highly constrained, yet very well-informed, by the data of the level at which we implement. But, with tensor network theory, we wouldn’t label these processes as top-down, but, rather, from lower-level fundamental processes to higher-level descriptions.

We use a tensor transformer to transform in a way we still need: to transform vectors in sensory space to vectors in motor space. We may deform one phase space to get an object in the other one using representations as positions in phase space and computations as coordinate transformations between phase spaces. The Pellionisz-Llinás approach uses sensorimotor problems constrained by realistic creatures as a method of reducing at bottom the problem of making coordinate transformations between phase spaces. In tensor network theory, we look for functional relationships between connected cell assemblies and investigate them for properties relevant to phase spaces much the same way a computer or artificially intelligent machine searches for solutions among sentence-related criteria. Such AI would require this knowledge to determine what to do.

Tensor network theory still needs to unify results across the disciplines of cognitive science, psychology, and neuroscience in such a way that we can construct a universalized, common set of rules with coherent explanations that we can experimentally test and verify. Attempts to describe the vestibulu-ocular reflex, the method of determining movement from visual image stimuli, using semicircular canals of the vestibular system, we further imagine each eyeball detecting the images and communicating to those receptors. This system needs to determine how muscles contract so the eyes move in a way to reflect the head movements. The corresponding tensor approach would imagine the system converting a head position vector into a vector that describe muscle positions. The transformation from vestibular to oculomotor, according to the Pellionisz-Llinás hypothesis, takes a premotor vector intoa motor vector. The vestibulur organ, we can show, has a set of positions it prefers that we can call an eigenposition.

We further pose Churchland’s phase-space sandwich hypothesis that describes spatial organization of maps layer so that the corresponding neurons may perform any transformation from two dimensions to two dimensions. The maps representing phase spaces aren’t literally stacked upon one another. They may remain spatially distant from each other. With the topology of the cortical area, we still have to answer whether tensor network theory can account for neuroplasticity. Covariant proprioception vectors can give feedback about motor performance which can further provide information of transformations of the cerebellar matrix. The matrix would then turn into a state such that its eigenvectors are identical so that they are the “correct” coordinate transformation. Climbing fibers of the cerebellum may provide a pathway for reverbative feedback that modifies transformational properties of the cerebellar network. This is found in AI that use relaxation algorithms.

Mental states

If we determine how behavior related to cognition and complexity emerge from the basic neurophysiological theories that govern sensorimotor control, we can determine the nature and dynamics of cognition. We may construct representations at abstract levels of organization that correspond to cognitive activity as the way sentiential representations act according to logical rules. Phase spaces may recognize certain features as humans do, such as eyes of faces or shapes of animals. We may describe phase spaces in such a way that they’re occupied by these sensory stimuli. Using the cones of photoreceptors’ reflectances responsible for color, we can demonstrate a computational problem of how to represent a unique color with a triplet of reflectance values.

Parallel models

Sequential models can be powerful, but AI researchers have shown their ineffectiveness in simulation of fundamental cognitive processes in areas of pattern recognition and knowledge storage and retrieval. The differences between human brains and computer science phenomena only furthers these issues. Humans and computers use very different methods of storing memory as well as methods of connectivity among humans neurons against artificial ones.

The Hinton-Sejnowski visual recognition system uses a network of two sets of binary units: one for detecting input from external stimuli and the other for connecting detectors to nondetecting units. These networks determine the truth and validity of hypotheses by gauging which units fire and which don’t. It performs a cooperative search in which these assemblies vote for various outcomes and the one with the most votes wins. The relationships between various hypotheses depend upon synaptic weights using probability functions and distributions. They also perform relaxations that cool the system such that it may take different molecular organizations in an annealing process. During this process the crystalline structures have a global energy minimum that parallels adding noise to the system. From these fluctuations in noise, the system breaks out of superficial minimima. The Metropolis-Hastings algorithm lets us gauge locally improbably hypotheses such that they may win over other hypotheses.

To make the model reflect empirical data in neuroscience, we must show it accounts for processing of various neurobiological pathways. Computer vision models need to account for contours of perception as well as emergent phenomena such as recognizing how a property of an image emerges from various structures working in a dynamic, systemic manner of the visual image itself. Connectionists could update their brain-computer models using evolution the same way sensorimotor mechanisms have to suit a simultaneous solution in visual recognition.

We distinguish between different levels of description of computational processes. These levels have certain reducible relationships among them in which we can make varying levels of commitment to the reductionism between them. The theory of symbolic computational functionalism of the computational theory of mind (known as computationalism) lets minds manipulate discrete, defined symbols to model discrete, defined logical structures and computer languages. A human mind may be a deterministic finite state automata under this theory, and the theory is independent of implementation. Even if different beings have different physical structures of themselves, they may have similar or the same mental states. Philosopher Patricia Churchland and neuroscientist Terrence Sejnowski have criticized that the implementation is important, especially as lower theoretical levels (such as neuroscientific phenomena) are significant to higher ones. Opponents may also argue that the representations of computationalism don’t tell us anything more than the non-representational descriptions do. Using representation may just amount to an unnecessary model or analogy that only steers us away from the precise, defined meaning of the world.

The computationalist may respond she doesn’t want to make a physiologically accurate human mind model, but wants to find intelligent features for any agent. In AI, one might want to solve a problem in computational space that doesn’t represent human features. She may also respond that representational theories note when the features of representation, such as the similarity between representations and their objects and how accurate they are, in such a way that the representational theory is more effective, valid, and justified than non-representational theories.

We may account for the intentional nature of basic emotions even if they have a physiological component to them, such as changes in facial expression or bodily mechanisms. Weak content cognitivism, the belief that emotions are or are caused by propositional attitudes, may attack this relationship of emotions to a bodily response, but the relationship of emotions to beliefs doesn’t mean all emotions are caused by propositional attitudes like beliefs. A computational theory of mind should account for emotional effects and similar affects that influence perception and judgement. But the changes in emotions don’t seem discrete as though there were differences in logical systems as we described with the Hinton-Sejnowski theory or with tensor network theory. Emotions form a continuous gradient that doesn’t seem to arise from a sort of combinatorial engine that the computationalist theory would argue. We would need a semantic activation model that adheres to principles of symbolic computational functionalism as well.

The connectionist model describes effects of some emotions, but doesn’t model emotion itself. To allow semantic activation models to use emotions in a cognitive position would mean that emotions, in some sense, are the same as similar cognitive categories such as “visual stimuli” or “beliefs.” The other features of emotion, though, semantic activation models need to describe implementation-dependent details of the model itself.

The computationalist position also has issues with how to model affects, such as those of basic emotions, independently of cognition yet still play a role in rational human behavior. The computationalist may be inclined to treat emotions as external or even unnecessary to their models. Computationalists also can’t account for the effects of basic emotions on perception and categorization using their current models. These emotions themselves may be more fundamental to those perceptions and categories that we form, given their unique nature on intellectual perception.

Neural circuitry

We may imagine the brain as a computer through neural circuitry excitation/inhibition ratios as a property for cognitive function in cortical circuits. Research in circuit function on synaptic parameters in memory and decision-making can give us parameter spaces to reduce NMDAR conductance strengths from excitatory pyramidal neurons to inhibitory interneurons or excitatory pyramidal neurons. We may apply dopamine neuronal activity using a bifurcation diagram. In math, we generally use bifurcation plots to study dynamical system behavior with respect to parameter variations or similar perturbations. We may use Ohm’s law to relate current, potential, capacitance, and resistance among membrane channel dynamics. The dopamine neuron uses ionic currents using the Hodgkin-Huxley models. We can use these fundamentals to create circuit models of neuronal activity using population firing rates to calculate dopamine efflux in the nucleus accumbens.

Functional connectivity

Functional connectivity (FC) is the statistical correlation of neural activity to two different regions. We find evidence for this at the micro-circuit level (the relationship between structure and function through anatomical and neurophysiological research techniques). We can integrate information across brain networks using large-scale brain connectivity at finer temporal and spatial resolution. If we introduce spatiotemporal models of resting-state networks, we can analyze the time frequency of these networks using wavelet analysis, sliding-windows, and similar methods of describing temporal correlations between the networks.

FC is similar to functionalism in that we’re defining our representations in terms of their functions. Functionalism holds that qualitative states (e.g., pain) are functional states of a system, interrelated to inputs, outputs, and other internal states. For this reason, cognitive models of the mind have used FC in their explanations. If we had a neuroscientific system that realizes the same set of functional states a person, it still has the problem of liberalism and chauvinism, philosopher Ned Block argued. Liberalism is the problem a mentality theory faces when it attributes mentality to systems that don’t have it, such as behaviorism, Block believed. Functional connectivity in neuroscience must address the objection against functionalism of how mentality theories attribute mentality to systems without it. A behavioral disposition may be necessary for the possession of a certain mental state, but it isn’t sufficient. Chauvinism is the problem that a theory withholds attributing mentality to systems that seem to possess it. Block argued type physicalism falls to chauvinism because it’s the view that mental state types are equivalent to physical state types.

We may talk about the mental state of pain caused by sitting on a tack that causes behaviors such as loud cries and other mental states such as anger. We define these functional definitions (of analytic functionalism) using causal roles that are analytic and a priori truths about the other mental states alongside their propositional attitude. Identities are necessary and not subject to empirical observation. Psychofunctinoalism, on the other hand, uses empirical observation (in an posteriori manner) and experimentation to determine which mental state terms and concepts are contingent to their observations.

Structural connectivity

Structural connectivity (SC) are the long-range anatomical connections among brain areas through white-matter fiber projections. We use fiber tracking using bounded diffusion of molecules in water to create non-invasive connectivity maps. In the past scientists used diffusion tensor imaging (DTI), we track neural fibers, but more recent studies have used advances in graph theory for much more research on topological features in brain connectivity.

We can characterize the relationship between FC and SC as the former relying on connections between areas and the latter the physical characteristics of the fibers. Effective connectivity (EC) characterizes the interactions between visual processing regions (a psychophysiological interaction analysis) using structural equation modeling (SEM) based on minimization of predicted and observed dependent variables. EC also refers to the broader definition of SC that captures the features that shape connectivity like synaptic strengths, neurotransmitter concentrations, and neural excitability. Through both model-driven and data-driven approaches (the former generation signals under assumptions and the latter using statistics, information theoretical measures, or phase relationships to extract EC), we can infer EC and the topology of these networks. Using binary graphs, path length measures, clustering coefficients, and other ideas from graph theory alongside results from diffusion-based tractography, we can show the resting-state networks in various regions of the brain. Scientists have introduced Network Based Statistics for comparing whole-brain connectivity between different groups of connections.

We use the covariance between populations of neural activity with the Jacobian of the system of equations describing the neural activity in each node. For an input covariance matrix, we can describe the covariance between neural populations. The Kuramoto network model uses the global graph metrics of schizophrenia patients to account for the neurophysiological impairment to describe resting-state network activity between topological properties in schizophrenia. We may use either noise-driven spontaneous dynamics and complex interactions between phase-oscillators (with coupling, delays, and noise) to introduce a dynamic nature to the model, but these two factors contradict one another. The former implies temporal correlations in spontaneous activity emerge from uncorrelated noise propagation through connections while the latter uses complex interactions of oscillatory activities in regions of the brain. We may use a supercritical Hopf bifurcation to reconcile the two using synchronized networks and their corresponding temporal variations. From this, the Kolomogorov-Smirnov distance between empirical and simulated FC dynamic distributions is optimal at this critical point and more sensitive to deviations from the critical point.

Reinforcement learning

Reinforcement learning is emerging a dominant computational paradigm for modeling psychological and neural aspects of affectively charged decision-making tasks. The Markovian assumption lets us use decision-making models that describe how nervous tissue carries out perceptual inference. The Markovian assumption lets us use Markov models such that the various states that they use to describe processes are independent of the states that came before it. Hopfield neural networks alongside the work of Hinton-Sejnowski would let computational models use rules such as the Bush-Mosteller rule (learning based on trial-based differences between predictions and outcomes) or the Sutton-Barto approach (Monte Carlo methods and temporal-difference learning in artificial neural networks). We can introduce the temporal difference error such that the agent in the system chooses an action that maximizes a temporal reward. When diffusion ascending systems of nervous systems could use temporal difference learning as a general way biological systems could learn to value states. We can used a modified form of Hebbian learning such that it depends on incorrect prediction of the future to reinforce a bidirectional synaptic change. These Hebbian synapses could then store predictions of the future in a way that accounts for the actions of dopamine neurons.

Optimizing procedures

We may use optimizing methods from mathematics, physics, and computer science in neuroscience. If we assume artificial neural networks are similar to biological ones, we may use error minimization as an optimization procedure. The way we adjust parameters and weights we may analyze the computations of a neural system in how it generate ideas from the organization of a network. We may use backpropagation in creating models that have the capacities of a biological neural network, and speculate on how networks function in a computational theory of mind. The nervous systems of the brain have too many parameters to all be entirely controlled by genetics, neurodevelopment involves a massive synaptogenesis that grow using optimization processes, some parameters are used for feedback to adapt behavior to circumstances, and natural selection optimizes nervous systems in such a way that we may regard the nervous system’s selective pressures as error-minimizing.

The neural circuit in visual tracking of moving objects uses many unknown parameters and specific weights. We can construct a network by fixing the known parameters and train it on input and output to determine the unknown parameters. The probability inference methods depend on the degree of similarity between artificial and biological networks. We may use models to generate hypotheses because the nervous system evolution may be described with a cost function and artificial models use backpropagation to search through possibilities.

Conclusion

As 18th-century German philosopher Immanuel Kant said, studying concepts of the mind without empirical science is empty and studying science without philosophy is blind. Understanding how the brain works means going from simulating in a computer to making synthetic brains. We see how models interact with the actual world (whether they simulate the world or directly use it), determine which real-world parameters are relevant to our models, and extend models to cover all levels of organization. We wrestle with reduction, causation, and other phenomena through both science and philosophy.

Don’t Read this Book if you want Solutions in Life

Cartoonist Randall Munroe shares satirical advice about the world for anyone curious. The creator of the popular webcomic xkcd has come up with solutions to life’s problems. Results may vary.

Credit: Randall Munroe

Let’s say you wanted to find alternative methods to power your house. Given that the average American house uses about $1,000 per year on electricity, you turn to nature for answers. Creating an electric generator from the movement of Tectonic plates would provide a simple solution to natural electricity. If you lived on a fault line, you can figure out the force the ground exerts over a distance. Multiply this force by the distance to get energy. You decide to build a pair of giant pistons connected to the Earth’s crust. As shown above. As the pistons compress a reservoir of fluid between them, the pressure builds up to drive a turbine.

After giving this advice in his book, “How To: Absurd Scientific Advice for Common Real-World Problems,” cartoonist Randall Munroe admits the system would be “ridiculous and technically infeasible for a lot of reasons,” including cost and size. Yet these explanations make science enjoyable and entertaining no matter what your background is. Munroe’s book explores silly solutions to the most mundane problems in life such as boiling the Kansas river using teakettles so you can cross it, using butterflies to transport data or using liquid nitrogen to create snow when you want to ski. He uses scientific evidence and reasoning to back up his solutions but remains playful in explaining them, no matter how absurd they are. Setting things on fire to generate power and charge your phone can be a lifehack. Or just arson.   

A Gift to be Simple

Einstein is often paraphrased as saying, “everything should be made as simple as possible, but no simpler.” Regardless of how close this aphorism was to what Einstein actually said, simplicity is important in conveying information efficiently. Too much simplification can lead to poor representations of the universe. Munroe understands this and runs with it. His writing on simple solutions to life’s problems is friendly, lighthearted and approachable for all audiences. Much like his previous book, “Thing Explainer: Complicated Stuff in Simple Words,” he knows he can engage a broad audience through the simplicity of science. 

Though he seeks to entertain, Munroe remains cognizant about discerning seriousness from satire. He treats the reader like an intelligent being capable of understanding these tones and styles of writing. Even when he uses equations to calculate speed, force and other physical quantities, he presents them in a bite-sized, descriptive that’s easy to digest and follow. You can read the entire book in a single sitting because the explanations flow so naturally and fluidly in each chapter. Reading the book bit by bit, though, may help you become more curious about the world around you as you study Munroe’s explanations closely.

Laughing at Life

Munroe’s book is entertaining in an absurd, surreal way. He treats humans like a specimen under a microscope with enough sarcasm, wit and dry humor to keep you laughing throughout. His humor is more cultural as a satire on the rest of society – even in a self-aware sense. Making fun of the universe is how you understand it better. 

Still, some may find the humor isn’t meant for them. Munroe’s style of explaining can come across as pretentious and condescending. Readers may find that explaining simple things that they already understand only serves to show how smart Munroe is as though Munroe were some authoritative voice over all scientific knowledge. Others may find the book’s content short and thin even with thirty chapters. Some of the explanations may seem undeveloped. But the book’s personable, tongue-in-cheek nature leaves it free of presumptuous claims of the reader’s intelligence. 

The irony that an engineer would write such a treasonous attack on normalcy and established methods of scientific reasoning may put a smug, smirk on your face. But the book’s value goes beyond a few chuckles. Munroe’s humor instills curiosity and wonder of the world and how bizarre it can be. 

As Mythbusters co-host Adam Savage said he would reject reality and substitute his own, much of science and engineering come down to complicated, elaborate interpretations and explanations. You can make friends by physically running into them or jump off a mountain if you want to jump really high. Everything is up to interpretation. Munroe’s wit will let you better understand the craziness of the universe itself. Pick it up and give it a read for the sake of mad science itself. Then dispose of it by shooting it towards the sun. 

Raising the Alarm: Rhetoric on Climate Change

Shock! We realize the severe to protect the rights of individuals displaced by rising sea levels, storms, wildfires, floods and everything else brought upon by the nature of climate change.

Journalist David Wallace-Wells elucidates the assumptions, contexts, themes and other underlying features behind arguments on the future of Earth in his book “The Uninhabitable Earth: Life After Warming.” As though we were on a highway to Hell, the American journalist’s says, to avoid the doomsday scenarios of climate change spanning economic and political crises, we need a carbon tax, a method to fight against dirty energy, innovative agricultural techniques and overall funding for promoting green energy capturing waste carbon dioxide.

A Friendly Warning

As though you were meeting with him for coffee, Wallace-Wells’ writing is accessible and understandable. It lets the leader let feel at ease and understood despite the near-alarmist content of the book. Even though much of this book is content that has already been written, this book sets itself apart from others by being so frank, direct, and almost a detached objective look that Wallace-Wells takes as a journalist. As Aristotle wrote in Rhetoric, Book III, “For it is not enough to know what we ought to say; we must also say it as we ought.” Wallace-Wells provides a stunning re-contextualizing of future research, conversations and other features of existence due to climate change. The reader will feel empowered in her future ways of analyzing climate change rhetoric. It leaves the reader armed with the ability to formulate and analyze arguments on the nature of moral responsibility and power to make a difference in the world. 

The book also serves as an equalizer between contrary points of view on the issues of climate change. Wallace-wells’ writing encompasses so many perspectives to provide an accurate, multidimensional moral landscape of the issues of climate change. This makes the political message more powerful and persuasive in turning heads and changing minds. As Wallace-Wells says we have a tendency to be complacent even though we’re scared about the future of the Earth. Through comparisons and analogies, he forms predictions of how our actions affect the planet. By 2050, there will be more plastic than fish in the oceans. Even the everyday examples of our actions, such as a flight from London to New York destroying three square meters of Arctic ice, will leave you thinking twice about your role and responsibility in these global issues.

“Oh, the Humanities!”

Wallace-Wells explores many possibilities and options as he formulates his arguments. He draws comparisons from literature, history, philosophy and other disciplines in addition to science-backed conclusions. Through this, Wallace-Wells avoids pitfalls of reductionism that would come with relying on science alone. Instead of treating the issue of climate change as simply a mathematics problem with an optimal solution that we must use, it’s much more speculative. To address the crime, poverty, disease and economic collapse, he humanizes climate refugees and everyone else that shares our planet. He writes in a way we remember the fundamental ideals, values and principles we must protect. The reader may find herself in awe at how the dystopian futures found in works of “climate fiction” (or “cli-fi”) make the truth appear stranger than fiction. 

Digging deeper into the language of climate change, Wallace-Wells identifies terminology like “climactic regime,” for alleviating the effects of climate change. He uses these terms including “climate fatalism” and “ecocide” in characterizing the debates surrounding these issues. “Human futilitarianism” describes the psychoanalytic nature of climate despair, as writers Sam Kriss and Ellie Mae O’Hagan have said: 

The problem, it turns out, is not an overabundance of humans but a death of humanity. Climate change and the Anthropocene are a triumph of an undead species, a mindless shuffle towards extinction, but this is only a lopsided imitation of what we really are. This is why politics depression is important: zombies don’t feel sad, and they certainly don’t feel helpless; they just are. Political depression is, at root, the experience of a  creature that is being prevented from being itself; for all its crushing ness, for all its feebleness, it’s a cry of protest. Yes, political depressives feel as if they don’t know how to be humans buried in the despair and self-doubt is an important realization. If humanity is the capacity to act meaningfully within our surroundings, then we are really, or not yet, human.

Either way, the planet won’t grow colder or the planet won’t grow older.

What makes us special

Short answer: thinking. Why? Turning to analytic philosophy, you’ll find reasons stretching across consciousness and souls in why thinking makes us special. Evolutionary scientists explain how cognition and the ability to reflect, contemplate and ponder let humans overcome obstacles and struggle against nature. Thought transcending the surroundings of the world around us into truth, validity and other principles of reason seems nowhere in nature and, instead, only in our minds. “I think, therefore, I am human” resonates. Israeli philosopher Irad Kimhi begs to differ. That humans separate themselves from nature using thought is not only misguided but leads to false conclusions throughout philosophy, Kimhi argues in “Thinking and Being.”

Pre-Socratic philosopher Parmenides argued it’s impossible to think or say what is not. In his poem “On Nature,” he meant that what is not is nothing. To think nothing is to not think at all, and the “not”-ness of thought doesn’t differentiate it from nature and the universe itself. To think that the Earth is flat is to think from nothing in the world because there is nothing in the world that would let you think that. Though nothingness would continue in debates among thinkers including French philosopher Jean-Paul Sartre’s argument that our nothingness gives rise to consciousness, Parmenides’ reasoning that thought cannot follow from nothing doesn’t seem so appealing.

We think about what is “not” all the time. Negating anything to figure out what something isn’t is key in many lines of reasoning to figure what something is. Rejecting hypotheses and determining truth mean testing theory and detecting falsehood. But, even if we rejected Parmenides’s conclusion, we still need to figure out how to think of the “not.” Kimhi says understanding the nature of thought reveals why it doesn’t make humans so special after all.

How the sophist differs from a real philosopher, explored through Plato’s dialogue Sophist, that the Eleatic Stranger and Theaetetus discuss how discovering falsehoods let you figure out who we are. What makes thought special to the sophist is categorizing and systematizing what something is through clarifying what it is not until you figure out what it is. Thinking about what something is not is eliminates the confusion. Sophistry, then, is a productive art, the Eleatic Stranger concludes, involving imitating and copy-making to deceive and communicate with insincerity.

Philosophy in the analytic tradition means overcoming confusion similar to the way sciences do. German philosopher Gottlob Frege and British mathematician-philosopher Betrand Russell established its methods through logic. Yet the principles of logic and the appeal to science have, Kimhi believes, locked away thought’s specialness from philosophy. Frege’s belief that thought itself is fundamentally the same as nature meant thought exists independent of humans. These “propositions” stand on their own, lending credence to the idea that thought itself is part of nature just the same way “The Earth is flat” is false. Thinking, then, doesn’t set humans apart from the universe. When a philosopher debates Parmenidean’s question, her thoughts of what is “not” are false, not nothing.

Kimhi believes, however, Frege’s method of thinking about propositions is flawed. Kimhi’s argument rests on the negation of propositions. If she wanted to argue that it is raining, a philosopher could draw a picture of the sky and say “Things are as this picture shos.” To indicate that it is not raining, though, she couldn’t just draw a sky without rain. She would need the picture of rain and say “Things are not as this picture shows.” The picture, a metaphor for the proposition, needs this negation to clarify so you might conclude the picture itself, like a proposition, doesn’t say anything about how things are. Propositions mean nothing by themselves as far as stating things about the world. Kimhi attacks this idea, and believes that the picture expressing both the affirmation and the negation means a proposition says things are a certain way without having someone assert them. The same way we can’t say “Yes” or “No” to a claim without having the claim be there to begin with, Kimhi argues the propositions Frege promotes cannot be.

From a scientific perspective, if nature were an investigation of things that, by themselves have no meaning, then meaning itself is not part of nature. As Kimhi explains, thought’s place in the world doesn’t follow as separating humans from nature. Thoughts can be asserted and unasserted as a philosopher can say “It is raining, and it is not raining,” but there must be something both propositions have in common. Thinking, Kimhi believes, means representing how things are by combining elements like “the Earth” or “raining,” but the ability to put these elements together is also thinking of what these things aren’t. The difference between “It is raining” and “It is not raining” comes from our ability to think of it raining right now. Negating the claim doesn’t add any content to the thought. The two claims have a repeatable sign in common between them.

Kimhi further argues that, the same way negating a thought doesn’t add content to it, attributing thoughts to people doesn’t add content either. Though the judgments between “It is raining” and “It is not raining” differ, the claim is either affirmed or denied. Language doesn’t convey things in the world, but conveys the different ways we claim those things in the world. Thought itself is unique this way. The human capacity for language is part of the capacity to think. Language is the method of understanding the world and sets humans apart from everything else.

I sit and meditate on what makes us who we are. That thought runs so close to language makes intuitive sense. Language is the foundation for communication and expression. It’s role is inherent and to remove language from thought would be to lose thought itself. I worry that separating thinking from nature doesn’t do justice to the question Parmenides raised.

Though thinking isn’t something in nature, Kimhi believes, the linguistic form of human life constitutes thinking. Different from the austerity of “I” in German Idealism, philosophy is the apprehension of humans creatures of nature and thinkers not of nature. Thinking of what is not, though, remains a puzzle, but, by Kimhi’s views of thought, it doesn’t arise. Philosophy progresses through getting rid of confusion in clarifying what we already knew in some way or another.

The link between cognition and emotion

It’s easy to think of cognition and emotion as separate from one another, but research in cognitive science and neuroscience have suggested the two are more closely linked than we’d like to believe. Cognition can be defined as activities related to thought processes that let us gain knowledge about the world while emotions would be what we feel that involve physiological arousal, evaluation of what we experience, how our behavior expresses them, and the conscious experience of emotions themselves. To understand how cognition and emotion interact with one another in the brain, we may view cognitive behaviors neuroscientific phenomena as the result of both cognition and emotion, rather than simply one or the other. With research spanning philosophy, cognitive science, and neuroscience, emotions are no longer considered antagonistic to reason the way ancient Greek and Roman scholars treated them. Now, philosophers are much more inclined to view them closely linked through ideas such as reason being a slave to passion or reason giving way to passion through subjective experience.

Evidence of the mere-exposure effect, that people prefer things merely because they’re more familiar with them, in 1980 by psychologists William Raft Kunst-Wilson and R. B. Zajonc and as well as other findings in behavioral research shifted debates to focus on affect as a feature primary to yet independent of cognition. It could be related to unconscious processing and subcortical activity with cognition related to conscious processing and cortical involvement. 

Researchers generally agree on what constitutes cognition. Cognition, including memory, attention, language, problem-solving, and planning, often involve controlled neurological processes that respond to stimuli in the environment. This may include maintaining information while an external stimulus attempts to distract the mind. When cells in the dorsolateral prefrontal cortex of a monkey maintains information in the mind for brief periods of time, we can describe this link as a neural correlate for the cognitive process. With functional MRI (fMRI), we can identify which part of the brain are involved in these cognitive processes. Emotion, on the other hand, is much more subject to debate among scientists and philosophers. 

Emotions are arguably the most important part of our mental life to maintain quality and meaning of existence. We find meaning in emotions and rely on them to make sense of the world, sometimes in ways cognitive processes don’t offer. When researching emotion, some incorporate drive, motivation, and intention behind them as part of these states of mind.

Other researchers may use emotions in the conscious or unconscious assessment of events such as a feeling of disgust in the mouth. Subcortical parts of the brain such as the amygdala, ventral striatum, and hypothalamus are often linked to emotions. These brain structures are conserved through evolution and operate in a fast, sometimes automatic way. Still, how the different parts of the complex circuitry of the brain can mediate specific emotions is under research and debate. Neuropsychologists, neurologists and psychiatrists are only recently understanding the role of emotional processing in more complicated brain functions like decision-making and social behavior. 

But there’s much more to emotions than the physical phenomena in the brain. 

Imagine coming across a terrifying bear while hiking. In our most immediate reaction of fear, we can evaluate the situation (the bear is dangerous), a bodily change (increase heart rate), a phenomenological perception (feeling unpleasant), an expression of fear (eyelids raised and mouth open), a behavior component (wanting to run away), and a mental evaluation (focused attention on our surroundings). The phenomenological part involves our subjective experience as we respond to the world around us. All of these features come together in our emotions and can be debated to different degrees of necessity and sufficiency to emotions. On top of that, emotions may be directed towards objects with our intention (such as feeling angry at someone rather than just feeling anger on its own) and can shave motivation with respect to behavior (such as acting out of anger). Researchers have also debated whether emotions describe ourselves or emotions express ourselves imperatively. They’ve debated how the brain implements different types of emotions and how neural mechanisms describe emotional phenomena. 

Cognitive theories of emotions that have become popular in the latter half of the 20th century can be differentiated between constitutive and causal theories. Constitutive theories use emotions as cognitions or evaluations, while for causal theories, emotions are caused by cognitions or evaluations. For example, being frightened by a grizzly bear involves a judgement that the bear is scary. The fear may be the judgement itself or the result of the judgement. They let us differentiate between the complicated interactions of cognition emotion such as determining whether someone’s anger in response to a situation is the result of a cognitive evaluation of the situation or a reaction that’s more natural and automatic. In the mid-twentieth century, philosophers C. D. Broad and Errol Bedford emphasized constitutive approaches to emotion which would become dominant in philosopher while causal ones more popular in psychology. These philosophers argued that, if emotions had intentionality, there would be internal standards of appropriateness to which an emotion is appropriate. These cognitive evaluations, identifying emotions with judgements, have been used by philosophers such as Robert Solomn, Jerome Neu, and Martha Nussbaum since then. Identifying emotions with judgements, judgementalism, have been pivotal in cognitive theories of emotions.

Judgementalism in this way, however, doesn’t explain how emotions motivate, the subjective phenomenal experience of emotions, how one can experience an emotion with being able to identify a judgement with it, or a “recalcitrance to reason,” how we experience emotions even when they go against judgements that contradict them. Judgementalists may counter these issues by determining what judgements emotions are such as “enclosing a core desire,” as Solomon has argued, to let them motivate or “dynamic”, as Nussbaum has argued, so they may account for these issues. Through these methods, they may involve accepting how the world seems even with contradictory judgements. 

Other work in the 1960s showed how the cognitive component of emotions directly interacted with the physical bodily changes that occur alongside them. Psychologists Stanley Schachter and Jerome Singer developed a theory of emotion, known as the two-factor theory or Schachter-Singer theory, in which emotion is how we cognitively evaluate our bodily response to emotions. Injecting participants with epinephrine to arouse their subjects, the participants were told the drug would improve their eyesight with some of them additionally being told about the side effects. When witnessing other people act either happily or angrily, the participants who didn’t know about the side effects were more likely to feel either happier or angrier than the ones who were. The two theorized that, if people experienced an emotion without an explanation, they’d label their feelings using the feelings in the moment, suggesting participants without an explanation were susceptible to the emotional influences of others. The theory has faced criticism that it confuses emotions with how we label them such that we need complete knowledge of our emotions to label them as well as difficulty in explaining how we may experience emotions even before we think of them. Research in neuroscience has shown thinking about stimuli in ways to increase the emotion may boost prefrontal or amygdala activity while decreasing the emotion may reduce it. 

Integrating data and research from various parts of the brain, as they can provide the basis for cognitive phenomena, would illustrate a greater picture of emotion and cognition. There are many structures involved in functions and many functions for the individual structures of the brain. These neuron computations that underlie those phenomena also have affective and cognitive components, as described by cognitive scientists and philosophers. Viewing the relationship between emotion and cognition as a tug-of-war between the two doesn’t accurately capture the relationship between emotions and how we thinking about them. A combination of research in neuroscience, cognitive science, and philosophy would do justice. 

Time and Dreams in Political Unrest

With every tick of the clock I

awake, escape the shock as I

exit the dark of my dreams, as Jung would

remark. Yet not understood.
Now I ain’t sayin’ she’s a Heidegger, but she ain’t messin’ with no alt-right thinkers.

They say time flies. With age, the days feel shorter. Life speeds up, and it doesn’t slow down. The years start coming, and they don’t stop coming. However we look at it, we can understand how our perception has sped up in making these observations. It may be the result of memory. Every moment that passes and feels faster in our lives lets us view the present and the near-present with greater and and greater detail while losing the memories of what has gone long ago. We watch time speed up as we remember less.

Writing and other forms of immortalizing our words can fight against this. Whether its art, music, poetry or any other way of recording the tangible and conceivable into permanence, we can escape the fleeting visions of this world. As though we were waking up from a dream and recounting what had just happened, we can recognize dream states are part of our reality as Heidegger’s “Being-there” of the Dasein would describe.

The Dasein is what makes our existence more than a point in space-time that brings being from nothing. With death distinguishing existence, Dasein is the “being-toward-death” that gives our lives temporality. When Heidegger examined classical metaphysics with the hopes of creating a new ontological philosophy, he differentiated between the being and reality. All things have being while reality does not exist. Reality does not have the awareness of the world around it, and existing is what lets us determine what lies beyond ourselves. He described the technological advances of the 1930s and 1940s as threatening the world of ideas – poetry, intellectual thought, forms of art, and whatever we need to preserve who we are. Humanity becomes an object with an instrumetnal purpose through information and communication. Appreciating art and posing questions of who we are counteract these forces.

Much the same way Dennett wrote about his own dreams taking a long time, yet, in retrospect, seemed to have not taken any time at all, we may hypothesize that there is no dream experience. Instead, when we awaken, our memory banks play the dreams to us. Heidegger might respond to this claim by arguing that the times of dreams are consistent with the experience of dreams themselves.

With time moving faster, the present and the near-present become punctuated by events with less and less time between them. We find disparate events – whether its a meme about raiding Area 51 or the dispersion of fake news – coming and moving closer to one another. Our near-present perception enters a hypersensitive state that responds to the chaos and frenzy, and we can pick our poison: international turmoil, threats to the planet’s climate, the rise of fringe political groups, or whatever keeps us from falling asleep, as though we were trying to wake up from a nightmare. Even something as benign as a mock competitions between YouTube channels can turn messy when a shooter tells his audience to “subscribe to PewDiePie” before massacring a mosque.

It’s possible, though, that things had always been like this. The rise of Nazism during Heidegger’s time would lead historians to associate the philosopher and his views with the fascist movement. Heidegger watched rationalism, scientism, and market-centric forces overtake wonder, liberation, and freedom. Machines themselves reduced humans to the darkness they had created, and the fascists began attacking the mind-body dualism of Jews and liberals. The alt-right echoes Heidegger’s yearning for certainty and fixed values in modern life as well as nationalism and the interconnectedness of humans and the land. Trump’s former chief strategist Steve Bannon held up a biography of Heidegger and said “That’s my guy,” when he was interviewed by Der Spiegel.

Heidegger soon denounced Nazism. After he saw Hitler’s worship of efficiency and mythologized machines as though they were part of nature itself – part of who we are and how things should be – he condemned the anti-intellectualism running rampant. The racism and anti-Semitism followed an “I do not think, therefore I am,” inversion of Descartes’s famous proclamation.

When Horace wrote Caelum non animum mutant qui trans mare currunt (“those who rush across the sea change the sky above them, not their soul”), our souls still desire a connection to something permanent and fixed. Even Aristotle’s observation that we can only benefit from studying ethics when we already have “noble habits,” the philosopher must already have an idea of what she wants to learn. Heidegger believed that the philosopher with a main idea that she is a rooted being, tied to time and place and living within and through a land and language, her only interest is that she was born, worked, and died.

If only modern political discourse could heed the guidance of Aristotle. The philosopher’s first treatise on politics described a middle class that would lead to liberalist ideals by later intellectuals like Locke. The free rule because of their virtue and responsibility to rule. The commitment to philosophical thought, at the very least, eases the burden of time.

“Not in our nature,” a poem

(This poem is about the parable “The Scorpion and the Frog” https://en.wikipedia.org/wiki/The_Scorpion_and_the_Frog)

Nature embraces with all her ill,
The creatures being by her will,
Seduced by the scorpion’s cunning skill,
The frog and him were killed.

The scorpion’s sting was in his nature,
The ultimate cause of the dictator.
How humans fight like gladiators
For fear of our behavior.

The scorpion stung, the frog was fraught,
A lesson of nature’s punishment brought.
Yet men, endowed with rational thought,
Can act as they ought.

But reason with instinct become a hindrance,
The guilt and shame for our existence,
As we may keep these sins at distance.
Then man and nature, different.

The Weil Conjectures: A tale of mathematics, philosophy, and art

riemannhypo
The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.

For some, mathematics much more than a matter of solving problems. It transcends abstraction and intellectual pursuit into a way of determining meaning from life. For a brother and sister, it can mean a relentless search for truth that reads like a Romantic fable. A history that consists of settings across time and space punctuated by individual actions and events, the novelist creates a narrative that sheds light on a new meaning of truth. Truth may be elusive, especially in a post-truth society, but, in a metamodernist manner, it’s closer to reality – an authentic, original reality – than it seems.

In Karen Olsson’s The Weil Conjectures: On Math and the Pursuit of the Unknown, she intertwines the stories of French brother and sister André and Simone Weil during a Europe in the midst of World War II. The former, a mathematician known for his contributions to number theory and algebraic geometry, and the latter, a philosopher and Christian mystic whose writing would go on to influence intellectuals like T.S. Eliot, Albert Camus, Irish Murdoch, and Susan Sontag. Hearkening back to the childhood of the siblings, we follow their stories studying poetry, mathematics, tragedies, and other artists and scientists. Between these glimpses of their lives, Olsson throws in her personal anecdotes studying mathematics as an undergraduate at Harvard. She describes a “euphoria” from thinking hard about mathematics such that, while knowledge itself is the goal, it’s a disappointment to reach it. You lose your pleasure and sensation in seeking truth once you find it. André characterizes his own search for happiness through this search for truth. Drawing parallels between herself and the siblings, their stories depend less on the context that surrounds them and more on the similarities in their narratives. 

With multiple stories happening at once, the reader feels a sense of timelessness in the writing. The plot has less to do with one event happening after another, but more with a grand narrative carrying each part of the story with one another. A mix of elements of modernism and postmodernism together, Olsson’s book serves as a sign of the next step: metamodernism. In separate directions, mathematics and philosophy, the two venture for truth that seems to lie just outside their reach. Olsson tells the narratives through letters between the siblings, the notebooks upon which Simone scribbled her thoughts – philosophic, mathematical, and religious. On the purposes of mathematics and philosophy, Olsson questions how mathematics had become disconnected from the world around them. So focused on attacking problems in an abstract, self-referential setting, the field’s myopic focus on truth had strayed from meaning, she believed. Simone’s story through working in factories and a Resistance network with a wish to free herself from the biases of her own self would lead to her death by starvation in solidarity towards war victims. 

If the labor of machinery is so oppressive, Simone wondered how to create a successful revolution technological, economic, and political. The pain she sought through suffering made her who she was. It humanized her as she wrote about the German army defeating France. The evil in the world was God revealing, not creating, the misery inside us. Simone sought to achieve a state of mind that liberated herself from the material pursuits of the world through philosophy and Christian theology. She wanted an asceticism to provide she could a morally principled life on her self-imposed rules. This included donating money during her career as a teacher so that she would earn the same amount as the lowest-paid teachers. 

D. McClay, senior editor of The Hedgehog Review, wrote that Simone’s own struggle with Catholicism partly had to do with her anti-Semitism in his essay “Tell Me I’m OK.” “Though Weil was herself Jewish, she did not identify as Jewish in any significant sense, and her sense of solidarity with the oppressed did not extend to other Jews,” McClay said. Feminist philosopher Simone de Beauvoir who, according to her memoir, didn’t get along with Weil when they met, offers a contrast to Weil in how to live a good life. 

In Beauvoir’s The Ethics of Ambiguity, she argued existentialist ethics are rooted in recognition of freedom and contingency, McClay said. Beauvoir wrote, “Any man who has known real loves, real revolts, real desires, and real will knows quite well that he has no need of any outside guarantee to be sure of his goals; their certitude comes from his own drive…. If it came to be that each man did what he must, existence would be saved in each one without there being any need of dreaming of a paradise where all would be reconciled in death.” Beauvoir’s atheism created friction with Weil, McClay said. They also define a reality of what we do in the world that defines their own “drive,” which seems like a response to the threats of existential nothingness. 

McClay continued to compare the two Simones to provide an account for how to live a moral life, involving abandoning the idea of a “good person” in favor of goodness without regard to how others judge us. “It might mean living more like Weil—taking what you need, and giving away the surplus—”, McClay said, “with the caveat that one takes what one actually needs.” Beauvoir and Weil, moral philosophers that describe how “we are always, simultaneously, together and alone,” may even be guides for the crises of our age. Living together and alone, through the community of one another and the isolation of intellectual work, we can live like Weil intended. McClay’s writing also shows this mix of modernity’s unified, centralized identity withothers with postmodernism’s decentered self. 

Interspersed in Olsson’s book are stories about Archimedes’ having “eureka” moments, René Descartes’ search for the “unknown” (x in algebra), L. E. J. Brouwer’s work in topology, and even the mathematician Sophie Germain who studied mathematics in secrecy and corresponded with male mathematicians under a pseudonym. Tracing the foundations of mathematics, language, and other tenets of society to the Babylonians, she carefully compares the methods of problem solving and invention using language to reveal deeper nature of the phenomena (“Negative numbers infiltrated Europe during the Middle Ages” making mathematics seem deceptive or insidious) or method in discovery (“Are numbers real or not? Were they discovered or invented? We pursue this question for a couple of minutes.”). The figures comment on their own judgements on the deeper meaning and purpose in their work such as George Cantor saying “I see it, but I do not believe it.” Olsson drops these quotes and glimpses of history in between moments of trials of other characters.

When the early 20th-century Jewish-born mathematician Felix Hausdorff set the grounds for modern topology, an anti-semitic mob claiming they would send him to Madgascar where he could”teach mathematics to the apes” gathered around his house. Olsson then switches to her perception that she always read André and Simone Weil’s last name as “wail,” despite it actually pronounced as “vay.” Then, Olsson returns to Hausdorff’s story of taking a lethal dose of poison after failing to find a way to escape to America. In a farewell letter to his friend Hans Wollstein, who would later die in Auschwitz, Hausdorff wrote “Forgive us our desertion! We wish to you and all our friends to experience better times.” Olsson’s juxtaposition of the “wail” last name alongside the Kristallnacht, a systematic attack on Jews, compares the personal struggles of André and Simone as inseparable from the Nazi’s persecution of Jews – as though the siblings were “wailing” in response to their persecution. It also emphasizes Olsson’s own perception of the siblings that, no matter how hard she tries, she still has her own take on the story. Even when she shares the rise of Nazis in Europe, Olsson’s limited perspective preserves the postmodern disunity of culture alongside a modern master narrative. The art of narration is both a process of Olsson’s own struggles to share and an authenticated, objective authority of knowledge that can forgive Hausdorff’s suicide and provide a better future for everyone. 

With Descartes’ discovery of the “unknown,” he also introduced methods of standard notation of mathematics that would let researchers use superscripts (x² as “x squared”) and subscripts (x as “x naught”). Olsson demonstrates the similarities between the methods of reasoning that let mathematical invention become the same engine underneath the creation of science, art, and literature, as French mathematician Jacques Hadamard explained. Hadamard’s interest of what goes on in a mathematician’s mind as they do what they do was also in response to the crisis of modernity having witnessed the horrors of both world wars. The mathematician frequently seek new ways of looking at problems in mathematics as researchers came and visited during seminars twice a week. The pieces of each story come together in a flow that uses a variation in style, length, and meaning to create a multidimensional work of art that is the book. Each passage flows seamlessly in the interplay between exposition and narrative, description and action, showing and telling.

At one point, Simone and André’s reading habits are interrupted by the narrator of Clarice Lispector’s Agua Viva proclaiming mathematics as the “madness of reason.” The rational, coherent, commonsense nature of mathematics would seem to contradict the foolish wildness of madness. But, as an interruption to Simone’s love of Kant and Chardin as a child and André’s interest in the Bhagavad Gita in college, this “madness of reason” becomes more apparent. In Why This World: A Biography of Clarice Lispector, Benjamin Moser wrote: 

My passion for the essence of numbers, wherein I foretell the core of their own rigid and fatal destiny,” was, like her meditations on the neutral pronoun “it,” a desire for the pure truth, neutral, unclassifiable and beyond language, that was the ultimate mystical reality. In her late works, bare numbers themselves are conflated with God, now without the mathematics that binds them, one to another, to lend them a syntactical meaning. On their own, numbers like the paintings she created at the end of her life, were pure abstractions, and as such connected to the random mystery of life itself. In her late abstract masterpiece Água Viva she rejects “the meaning that her father’s mathematics provide and elects instead the sheer “it” of the unadorned number: “I still have the power of reason-I studied mathematics which is the madness of reason-but now I want the plasma-I want to feed directly from the placenta.

The Renaissance depiction of madness as an intrinsic part of man’s nature is found in the literature and philosophy of the time period. An imbalance, or excess, of reason could lead to the madness that seeks this mysterious, “pure truth” that transcends language itself. Much the same way Simone and André seek the essence through different forms of this “madness.” Simone’s personal battles with health and existential issues seem more alike a mathematician’s search for reason. Olsson later mentions the “madness of reason” as she narrates her own lonely experience “trying to demonstrate small truths” an undergraduate in her lonely dorm room on a cold, wintery day. It’s a localized truth that Olsson finds in her work, but still remains part of a grander narrative that connects their stories. The interjecting quote from Lispector’s text highlights this search for truth in the stories of Simone, André, and Olsson herself. 

According to Olsson, Descartes used “x” to refer to the unknown because the printer was running out of letters, but there may have been an aesthetic choice in addition to the pragmatic use. “x “ would come to mean that which we don’t know in other contexts such as sex shops and invisible rays. Olsson continues her personal story asking the question “What is my unknown? My x?” She narrates her venture back to mathematics after writing novels in her time since she graduated from Harvard University. 

Olsson emphasizes Simone’s inferiority complex to her brother as one of the primary causes for this perspective on the world. Simone’s own desire to be a boy, use the name “Simon,” and absence of any lover while André proposed the Weil Conjectures, married, and had children show these contexts. She found truth in this suffering and disregard for material pleasures – even chasing states of mind in which she could perceive the world in a state of purity and without any biases of her own self. The conjectures would become the foundation for modern algebra, geometry, and number theory. 

When Olsson took a course under Harvard mathematician Barry Mazur, she didn’t dare speak to him. The conjecture, Mazur explained, would lay down the basis of a theory, expectations believed to be true, driven by analogy. Olsson still recalls her feeling of awe when she first learned and geometry and the power of understanding the world without memorizing it. After André was arrested while on vacation in Finland in 1939 on suspicion of spying, he barely missed execution when a Finnish mathematician suggested to the chief of police during a dinner before the day of the execution to deport him instead. While André is forced by train to Sweden and England, Olsson returns to her childhood excitement in middle school learning about “math involving letters.” She then recalls moments teaching her two-year-old daughter how to count as the child asks “Where are numbers?” When Olsson returns to André’s story, now as he’s transferred to a prison in France and requires unidle intellectual activity, she comments that escaping France was a more pressing problem than anything in mathematics. 

As André longs for an ability to engage in research even in the cloistered sepulchre of a prison cell, he writes to Simone comparisons of mathematics to art. Simone is allowed to visit him for a few days a week, and the two rassure each other that they’re okay. André tells Simone he told an editor to send page proofs of his article to her so she can copyedit them. The writing between the two goes into stories of Babylonians and Pythagoreans reminiscent of the dialogue the two siblings had as children. Olsson’s own story intertwined with the communication between Simone and André serves as a parallel to demonstrate that she, too, can make mathematics accessible to the common person the same way Simome did with André’s work. André’s colleagues would even start to envy the quiet solitude of prison in which he could produce work undisturbed.  Comparing mathematics to art, though, André described the material essence of a sculpture that limit a mathematician’s objectivity while remaining an explanation in and of itself. In this sense, it has both objective and subjective value the same way a mix of modern and postmodern story would. Simone doubted this, though. Works of art that relied on a physical material didn’t directly translate to a material for the art of mathematics. Though the Greeks spoke of the material of geometry as space, André’s work, Simone argued, was an inaccessible system of previous mathematical work, not a connection between man and the universe. 

The brother responded with the role of analogy in mathematics far beyond a mental activity. It was something you felt, a version of eros, “a glimpse that sparks desire,” Olsson wrote. Going through the history of mathematics from the nineteenth-century watershed time in which questions of numbers were solved using equations, the mathematician feels “a shiver of intuition” in connecting different theories. Simone would imagine societies built upon mathematics, mysticism, and existential loneliness. Through this, all of Olsson’s jumping between stories becomes clear. She had set the reader up to view mathematics as an art the way André did and, through the world Simone created, something the general audience could understand. Olsson continues with her personal experience as an undergraduate being recommended by a professor to write about mathematics for a general audience as a career alongside dream sequences of André and Simone. 

In 1938, Simone attended a Bourbaki conference, a group of French mathematicians that André had initiated with the purpose of reformulating mathematics on an abstract and formal, yet self-contained basis. The mathematicians would sign their names collectively as “Bourbaki” on papers as they attempted to unify contemporary mathematics with a common language just as Euclid did centuries ago. While the group members would yell at one another with hard-hitting questions, even threatening at times, Simone began to believe that mathematics should be made more accessible to a mass audience. The Bourbaki group’s vision lead them to describe hundreds of pages of set theory before defining the number 1. They sought to create an idea of mathematics as a system of maps and relationships that were more important than the intrinsic qualities of numbers and other mathematical objects themselves. Scientific American would call André “the last universal mathematician.” This method of universalizing while still emphasizing relationships among objects shows a modernist tendency, the former, interacting with a postmodernist one, the latter.

Olsson’s own stories through studying mathematics as a student and teaching her children She explains the highlight of her mathematics career was finding the answer to a course problem before one of her classmates did. Her humility and sense of humor make her writing all the more approachable and relatable.

The book’s weakness is that the individual stories feel abbreviated at times. Olsson switches back and forth between many narratives that may leave the reader feeling confused or even frustrated that desires and beliefs of the characters are unexpanded. It can make it difficult to get committed to the story events or feel connected to characters when their moments are so brief and spread out across the book. The short snippets of stories across time and space alongside Olsson’s juxtaposition of them with one another make the reading easy to understand for anyone without a strong background in either mathematics or philosophy. Still, much the same way Olsson describes the search for truth, it leaves the reader in a perpetual search. We get a feeling of excitement that we are bound to get to the correct answer to a problem or find meaning in research while still never quite achieving it. 

Olsson’s book serves as a beacon of the power of evidence and justification in a post-truth world. Olsson addresses the constant searches for truth and meaning in our current society by capturing opposites and extremes in her writing. The empirical, hypothesis-driven mathematics and speculative, argument-driven philosophy contrast one another on the meandering search for truth. The isolation of intelligence for both André and Simone in their work contrast the warmth of community and social engagement the two find in their respective environments. Truth becomes less of something that we must obtain by being on one side or the other and more of finding appropriate methods of addressing problems. It’s objective in that it lies in the techniques of various disciplines, but constructed because it comes from the individual’s choice. In a typical mix of modernism and postmodernism, Olsson’s personal story to find the answers to her personal curiosities by turning back to mathematics demonstrates this mix of the personal with the impersonal. 

Like postmodern stories, Olson’s book is non-linear and reveals truth as a series of localized, fragmented pieces. Like modernism, we find greater purposes and narratives between the different stories as a testament to the power of science and technology. It switches between the progressive, exalted story of André with the melancholic, tragedy of Simone with parallels between the stories together. The grand themes of the power and style of mathematics and philosophy dictate the rules and principles that set the foundation for the stories. André’s story and Simone’s may even be treated with the former as a modernist tale of the triumph of science and the latter, a postmodern warning of society’s so-called “progress.” In regular metamodernist fashion, Olsson uses elements of both modernism and postmodernism in her book. In metamodernist fashion, the two searches for truth become one and the same. Philosophy may ask “Why?” but, for mathematics, the question is “y?”

Neuralink: the allure of brain-computer interfaces

Screen Shot 2019-07-18 at 4.02.10 PM
“You better be careful telling him something’s impossible. It better be limited by a law of physics or you’re going to end up looking stupid.” – Max Hodak, Neuralink president

As the gap between humans and computers becomes smaller every day, the startup Neuralink, backed by figures including Elon Musk, Vanessa Tolosa, and other individuals, recently hosted a public conference in which they revealed their efforts create neural interfaces between brains and computers. The futuristic dream of a brain-computer interface for mutual exchange of information between humans and works of artificial intelligence may sound like something out of a science fiction dream, but the neural interface, a device to enable communication between the human nervous systems and computers, would include invasive brain implants and noninvasive sensors on the body.

During the livestream on July 16, 2019, Neuralink revealed their work to the public for the first time with the pressing goal of treating neurophysiological disorders and a long-term vision of merging humans with artificial intelligence. With $158 million in funding and nearly 100 employees, the team has made advances in flexible electrodes that bundle into threads smaller in width than human hair inserted into the human brain. As the computer chip processes brain signals, the first product “N1” is meant to help quadriplegic individuals using brain implants, a bluetooth device, and a phone app.

In their paper “An Integrated Brain-Machine Interface Platform with thousands of channels,” Musk and other team members noted that electrode impedances after coating were really low allowing for efficient information transmission. Each electrode uses pixels at 3 Hz bandwidth to measure spikes, a neuron’s responding to stimuli that are generally about 200 Hz but can reach up to 10 kHz at times. The dense web that the team creates would let them feed the entirety of a brain’s activity to a deep learning program for creating artificial intelligence at a great degree of accuracy, study the neuroscientific basis for phenomena, or even decode the basics of other features such as language. For the Human Connectome project, an initiative to create a complete map of the human brain, Neuralink’s scale would give more precision than the project has done before.

This precision could address the ethical issues raised when the cognitive response of a brain-computer interface doesn’t appropriately match what a patient communicates. Neuralink’s work should take into account the risks associated with such a fine level of precision. Most strikingly, brain-computer interfaces so intimate to who we are raise the ethical issues of whether neurologically compromised patients can make informed decisions about their own care. Philosopher Walter Glannon said in his paper “Ethical issues with brain-computer interfaces,” the capacity to make decisions is a spectrum of cognitive and emotional abilities without a specific threshold that would indicate how much constitutes the ability to make an informed decision. Just as philosophers and ethicists have studied the basis for ethical frameworks in the decision-making process among physicians, patients, and other roles in health care, the complex semantic processing of brain-computer interfaces may not constitute enough to show a patient has the cognitive and emotional capacity to make an informed and autonomous decision about life-sustaining treatment. It would need some a behavioral interaction between the patient and the health care professional so that the brain-computer interface’s response reflects only what it’s capable of communicating.

Tim Urban of “Wait But Why” described Neuralink as Musk’s effort to reach the “Wizard Era” – in which everyone could have an AI extension of themselves – “A world where AI could be of the people, by the people, for the people.” The promise of cyborg superpowers as humans step into the digital world calls back to science fiction stories such as 2001: A Space Odyssey and Jason and the Argonauts. From the electrode array that joins the limbic system and cortex of the human brain gives Nerualink the information for those regions of the brain. It creates a reality in which information and the metaphysical nature of what we are depend less on the physical structures of the brain itself, but, rather the information of the human body. Prior to artificial intelligence, the brain evolved to develop communication, language, emotions, and consciousness through the slow, steady, aimless walk of natural selection, and a collective intelligence that can contribute to machine learning algorithms like Keras and IBM Watson. The Neuralink interface would let us communicate effortlessly with anyone else in the collective intelligence. The AI extension of who are means that the machines that are built upon this information are part of us as much as they are machines. With machines connecting all humans, we achieve a collective intelligence that goes against how human and animal minds have evolved over the past hundred million years.