Tag Archives: Philosophy

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 (x₀ 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 “y₀?”

Scientists and philosophers alike have examined and pondered about consciousness, one of the most central problems in our experience of the world. Both approaches may seek different methods, with science being empirical and philosophy, speculative, but they’re both relevant to any discussion on such a complicated phenomena. Understanding how neural correlates of conscious experience correspond to various parts in the brain lets scientists take “bottom-up” approaches of beginning with empirical phenomena and determining what cognitive and psychological behaviors result. On the other hand, beginning with the philosophy of mental states, including beliefs, intents, desires, emotions, knowledge, and figuring out how those can be attributed to the mind moves in the opposite direction. These mental states are whatever is the nature of the mental phenomena the mind occupies. It’s the way the brain makes sense of the world. A combination of empirical neural data from both computational and psychological models alongside a philosophical analysis would let us bridge the gap between the brain and consciousness. Either way, researchers end up with a neurobiologically accurate view of the brain in how consciousness emerges. There are many challenges to neuroscience explaining consciousness and its findings have philosophical significance to many ideas in epistemology, ethics, and metaphysics.

The difficulty of the subjective experience presents a challenge to consciousness. Any person’s experience is an external phenomena to anyone else. Philosopher Edmund Husserl’s notions of phenomenological and natural attitude show this relationship between the first- and third-person experiences. When someone perceives a car, their consciousness is directed at the car and that person is not necessarily aware of the details of the experience, such as what the steel car feels like. This is Husserl’s natural attitude. When that person focuses on the experience of perceiving the car as its own experience, it is a phenomenological attitude. A neuroscientist would generally concern themselves with the external phenomena they research and endorse the natural attitude. But the concepts of a scientific model (such as water being composed of two hydrogen atoms and one oxygen) are conscious phenomena a neuroscientist uses to understand the model. The neuroscientist can use the phenomenological attitude towards those models as experiences, and this shows we can’t escape our own point of view. Even a scientific model is a representation in one’s mind.

Consciousness as a neuroscientific phenomena requires a study of this relationship between an experience and the scientific model of it. The gap between the two can depend upon whether one endorses a realism view of science or an antirealism one. Under realism, mature scientific theories can be true and describe the world such that the gap is non-existent or narrow. Scientific realism means that all natural phenomena can be modeled using the structures and relations among them. We may model qualitative feelings, or qualia, our subjective experiences, using these structures and relations. It still leaves certain experiences difficult, such as how one may see the color red as a structural relationship given that introspection about redness doesn’t reveal its nature. Anti-realism, on the other hand, dictates we can only say whether a neuroscientific theory of consciousness is compatible with observations, not whether it captures nature. There is a large epistemic gap between any concrete phenomenon and the corresponding scientific models. The experiences are not different in this respect.

Before the 20th century difference between philosophy and science, philosophers generally studied consciousness through both philosophical and scientific means. French philosopher René Descartes performed research in mathematics, neuroscience, and philosophy. Psychologist-philosopher William James would create philosophical theories in light of empirical psychology research. With the rise of logical positivism, the idea that only statements that can be empirically verified are meaningful, in the early 20th century, philosophers focused on the semantic content of arguments instead of empirical scientific results. During this time, the three traditional perspectives of the mind-brain question, physicalism, mentalism, and dualism, emerged. Physicalism is the thesis that everything can be reduced to physical phenomena, mentalism, to mental phenomena, and dualism, that everything is either mental or physical. he rise of physicalism in the late 19th century meant to take consciousness as unscientific in some interpretations. Philosopher Galen Strawson’s realistic physicalism means the physical nature of the nervous system can manifest consciousness through mental activity. This can be illustrated with an example of philosopher Frank Jackson’s knowledge argument.

The argument uses the fictional story of a famous neuroscientist Mary who learns everything about the world through a computer but remains confined to a room that is entirely black and white. If physicalism were true, one might argue Mary knows everything about the world, but, because she has not experienced color, she does not know what it is. Upon seeing color, this argument would dictate that she would experience a subjective experience of her consciousness that she had never encountered before and, therefore, learns something new – showing she did not know everything about the world. One may conclude, from this line of reasoning, physicalism doesn’t entail everything. Possible responses to this may include the ability hypothesis – that Mary learns how to see color, but doesn’t learn what color is, therefore, what she learns doesn’t contradict that she knew everything about what the world was.

The historical trends meant changes, not only for consciousness, but for science as a whole. Scientific terms began taking new meanings. With the rise of thermodynamics around the turn of the 20th century, heat went from meaning boiling water to a specific dimension of temperature variation. Consciousness became an empirical phenomena of brain activity variation.

Consciousness presents researchers with the problem of how to explain when a mental state is conscious rather than not as well as what the content of a conscious state is given the subject experience of everyone’s consciousness. From a philosophical perspective, we rely instead on behavior and introspective testimony on the nature of consciousness in searching for common features from which we deduce knowledge about consciousness. From the neuroscientific angle, we study the central nervous system and the neural properties in the cerebral cortex. Psychologists Jussi Jylkka and Henry Railo have argued scientific models of consciousness need to explain consciousness’ constituents, contents, causes, and causal power. Though consciousness has many aspects to it, we focus on perception in this essay. Consciousness can further be differentiated into phenomenal consciousness, the properties of experience that correspond to what it’s like to have those experiences, and access consciousness, consciousness based on which states one can access.

The global neuronal workspace explains when a mental state is in consciousness such that it is accessible to systems related to memory, attention, and perception. Accessing content means it can use its content in performing computations and processing. Consciousness resides in these accessed states by the cortical structure of the brain that is involved with perceptual, mnemonic, attentional, evaluational and motoric systems. Whatever neurons are involved in someone’s current state constitute the workspace neurons. They activate such that the neural activation causes activity between workspace systems. It’s tempting to say the cortical workspace network correlates with the phenomenon of consciousness itself especially given imaging results can show which areas of the brain activate when a subject is conscious, but this correlation doesn’t tell us whether brain activity is of phenomenal or access consciousness.

Another approach, recurrent processing theory, ties perceptual to processing consciousness without a workspace and, instead, a focus on activity connecting sensory areas of the brain. It uses first-order neural representation, that we may perceptually represent the content of a mental state to mean perceiving that content, to explain consciousness. Interconnected sensory systems may use feedforward and feedback connections, such as those in the first cortical visual area, V1, which carry information to higher-level processing areas. The forward sweep of processing uses feedback connections linking visual areas. Global workspace theory and recurrent processing theory differ in the stages of visual processing they depend upon. The four stages of visual processing are superficial feedforward processing (process visual signals locally in the visual system), deep feedforward processing (the signals can influence action), superficial recurrent processing (information travels to previously visited visual areas), and widespread recurrent processing (across broad areas such as the global workspace access). Recurrent processing at the third stage, superficial recurrent processing, is necessary and sufficient for consciousness according to recurrent processing theory, and at the fourth stage, widespread recurrent processing, for the global workspace theory.

Philosopher Victor Lamme has argued that superficial recurrent processing is sufficient for consciousness because features of widespread recurrent processing are also found in superficial recurrent processing. Recurrent processing is found in both stages, and the global neuronal workspace theory allows superficial recurrent processing to correlate with widespread processing. Lamme believes that, in response to visual stimuli, there is first a fast forward sweep of processing, proceeding through the cortex. This first stage is nonconscious. Only a second stage of recurrent processing, when earlier parts of the visual cortex are activated once more by feedback from later parts, is taken to be conscious (with, again, empirical support).

Another approach to consciousness holds that one can be in a conscious state if and only if one represents oneself in that state. If one were in a conscious visual state of seeing am moving, that person must represent themselves in that visual state. The higher-order state represents the first-order state of the world and results from the consciousness of the first-order state. One must be aware of a conscious state to be in it. This lets neuroscientists correlate empirical work on higher-order representations of states with prefrontal cortex activity. For some higher-order theories, one can be in a conscious state by representing oneself even if there is no visual system activity.

Neuroscientists can use empirical tests of higher-order theory against other accounts, but neurologist Melanie Boly has argued that individuals with the prefrontal cortex removed can still have perceptual consciousness. This may prefrontal cortical activity isn’t necessary for consciousness, but one may argue the experiments didn’t remove all of the prefrontal cortex or that the prefrontal cortex is necessary, but in a more complicated system than previously suggested. Psychologist Hakwan Lau and philosopher Richard Brown have used experimental results to suggest consciousness cannot exist without the corresponding sensory processing as predicted by some higher-order accounts.

Finally, the Information Integration Theory of Consciousness (IIT) uses integrated information to explain whether one is in a state of consciousness. Integrated information is the effective information parts of a system carry in light of the causal profile of the system. If the information a system carries is greater than the sum of the information of each of the individual parts, then the information of that system is integrated information. IIT holds that this integrated information implies that a neural system is consciousness, and, the more integrated information there is, the more conscious the system is. Neuroscientist Giulio Tononi has argued the cerebellum has a low amount of consciousness compared to the cortex as it has far fewer connections even though it has more neurons. IIT suffers from treating many things as conscious even when they don’t seem to be. Tononi has proposed that a loop connecting the thalamus and cortex forms a dynamic core of functional neural clusters, varying over time. This core is assumed to integrate and differentiate information in such a way that consciousness results.

Neuroscientist J. H. van Hateren has presented a computational theory of consciousness in which the neurobiology of the brain allows it to compute a fitness estimate by a specific inversion mechanism that also causes the feeling of consciousness. His conjecture that consciousness is a transient and distinct cause the individual produces when he or she prepares to communicate—externally or internally. Citing the thalamocortical feedback loop, the internal variables involved in this process estimate the individual’s evolutionary fitness.

Despite how flashy it sounds to say researchers can completely understand consciousness, the challenges that neuroscientists and philosophers face mean things are far from completely figured out. There remains a lot to be discovered and examined from both scientific and philosophical angles.

While humans and computers both have the capacity to recognize faces, pattern recognition problems in computer vision seek to represent data in an appropriate way for the problem to solve. Machine learning methods approach pattern recognition as a statistical problem of searching for patterns in data. Through classifying data into different categories, reducing the data’s dimensions, approximating parts of the data, and other techniques that exploiting geometry, algebra, and other quantitative features of the data, computers can recognize faces, handwriting, images, and other visual stimuli in ways similar to humans.

Neural networks and deep learning methods have had practical applications in fingerprint analysis, disease etiology, and voice recognition, to name a few examples. Artificial intelligence continues to find success in various areas of research. But before computers can behave like humans, they need to represent the world in some way. The way computers interpret input data lets them represent the world.

These representation methods include principal component analysis (PCA), in which eigenfaces estimate variance among data. These eigenfaces, mathematical representations of key features used in human face recognition, are calculated using the the covariance matrix of the probability distribution over the high-dimensional vector space of face images. In other words, they let computers discern basic patterns among images of faces. PCA reveals eigenfaces that correspond to the least-squares solution so that the data variance is maintained while getting rid of existing correlations that don’t contribute to it. Generating eigenfaces involves extracting relevant facial information, through methods like searching for statistical variation between images, and representing them efficienctly, such as through using symmetry or other geometric features. While eigenfaces are automatic and easy to code, especially in how they can make complicated faces simple, they can become very sensitive to external features such as lighting and struggle to provide useful information about the faces themselves.

Other machine learning techniques such as classification find categories to map input data by discriminating between different features and representing those features with their distance from one another depending on their similarity. Fisherfaces, named after statistician Ronald Fisher, result from the basis vectors of a subspace representaiton of face images when performing linear discriminant analysis (LDA). Fisherfaces are less sensitive to lighting issues than eigenfaces and require data built upon continuous independent variables, such as skin tone or shape.

While eigenfaces depend upon PCA to account for data variance, fisherfaces use LDA searches for differences between classes of data. A team lead by computer science professor Peter Belhaumer at Columbia University found lower error rates among fisherfaces than among eigenfaces. In their paper, “Eigenfaces vs. Fisherfaces: recognition using class specific linear projection,” they accounted for variations in lighting and facial expressions. Regardless, researchers in computer vision can use both methods to minimize error when solving problems in recognition and representation.

Both eigenfaces and fisherfaces also struggle in capturing changes in expression and emotion among faces. For researchers in computer vision to approach facial expression analysis means understanding the nuance and complexity of the face. Muscular movements originate in the nerves by the VIIth cranial nerve from the brainstem between pons and medulla. The motor root of the nerve gives somatic muscle fibers to the face that create facial expressions. With enough data and efficient routines, pattern recognition can identify emotions from expressions and determine which parts of the brain may be involved in creating them. Neuroscientists have shown face muscles in lower parts of the face are more represented in the motor cortex which are especially involved in speech. From these patterns from hundreds and thousands of faces, computers may soon be be able to discern function from the form of a face itself.

The seven universal facial expressions of emotion (happy, surprise, sadness, fear, anger, contempt, and disgust) have seven ways to regulate themselves (expression, deamplified, neutralized, qualified, masked, amplified, and simulated). Psychologist Paul Ekman determined these emotions and expressions were universal among humans across different countries and levels of industrialization or development in his manuscripts “A New Pan-Cultural Facial Expression of Emotion” and ” The repertoire of nonverbal behavior: Categories, origins, usage, and coding.” He found that humans produced these expressions in response to similar conditions even regardless of how we may judge a face as expressing a certain emotion. The extent to which the emotions are universal, however, remains up to debate. Ekman supported his work by surveying humans across different civilizations, including tribes in New Guinea, but he argued this non-cognitive component is only a part of emotion. This automatic appraisal detects stimuli almost instantly identify elicitors which then activate the seven universal expressions that further cause the physiological elements of the emotional response. This would include any bodily change such as the feeling of one’s heart dropping, skeletal muscles tightening, facial muscles loosening,  changing voice pitch, and other features of the nervous system.

As recognition and representation depend upon one another, neuroscience and artificial intelligence continue to support one another despite their different paths. As expression and emotion intertwine into one another, we create a more nuanced picture of perception that speaks to who we are as humans. While eigenfaces and fisherfaces support similar goals as well, their different methods lets computer vision researchers attend to the variety of challenges deep learning has to offer.

Once upon a time, in a small country by the sea, at the highest point of its highest castle, atop two thrones adorned with precious metals, there lived a King and a Queen. Theirs was a long and blessed reign: their people lived in good health, at peace with their neighbors, enjoying brief winters, generous summers and abundant harvests. But all fortunes must eventually change, and in time, the small country by the sea was ruled only by a King.

The bereaved King lived in mourning, sat alone and draped in dark, funerary colors. But as the years whitened his beard and tugged his jowls earthward, there came a time when the court, noting his childlessness and nervous at the prospect of an empty throne, broached with him the difficult subject of remarriage. The kingdom held lavish Balls and opulent feasts in the hopes of arranging a new match. Many noble houses competed to see one of their own crowned Queen, but in the end, the King could not bring himself to choose a new suitor, and glumly dismissed them all. The Queen’s throne remained empty, and the whole kingdom lamented. The depths of despair are often fertile soil for new ideas, and so it was that the Chief of the Royal Guild of Engineers came forward with a proposal of a very different sort.

She offered to build an heir for the King. It was to be unlike anything which had come before, a being of chrome and silicon; wise, tireless and immortal. The King accepted, and work began. A year passed, during which time the Guild’s factory worked without respite. Acrid smoke poured from its chimneys; the din of hammers and bellows rang throughout the city; and the glow of its lamps and furnaces illuminated crowds which pressed all around, hoping to glimpse the molten zygote of the new Prince. When the child was ready, it was presented in a grand ceremony to the King, who was pleased. The Guild were as skilled in the craft of flattery as they were in metallurgy, and so it was beautiful, rendered in chrome and gold, with starlight behind its eyes, and bore the mixed likeness of the King and his late wife.

But more marvelous than the look of the child, were its speech and motion. Its voice was melodic, its pronouncements sage, and its movements were as delicate as they were precise. All the kingdom looked on it with pride. But as the years drew on, and the Prince made the castle its home, the King found himself plagued by an unsettling thought. He watched as his successor played, learned and grew, and in his mind the thought grew in parallel. Just what was this creature, to which he would one day entrust his kingdom? Did a mind dwell in the maze of wires behind the chrome child’s scintillating eyes? Or was it a dead thing, eating without hunger, moving without desire, and speaking without thought.

Eventually the King could stand his uncertainty no longer, and made the long pilgrimage by winding rivers and towering cliffs to Delphi. There, he posed his question to the Oracle: how can I know, he asked, whether my heir has a mind, or is a mere machine? She sat quietly for a moment, wreathed in tendrils of pungent incense, then gave her response: “You will have the answer to your question, when you can tell me the width of a headache.” The King pondered this riddle as he made the return journey, and on arriving at his Palace summoned two of the most brilliant minds in the kingdom.

First came the head of the School of Psychologists, followed soon after by the most senior member of the Royal Society of Neuroscientists. The King relayed his conversation with the Oracle: what, he demanded to know of them, is the width of a headache? Naturally, there was some grumbling from the scholars, who pointed out that this was the 8th century and the King should really have come to his scientists first, rather than trusting drug-addled clairvoyants to provide sensible insights into the nature of minds. But they were eventually forced to concede that neither of them had an answer, either to the Oracle’s question, or the larger question of the chrome prince’s mind. The psychologist protested, not unreasonably, that though headaches may have widths, such questions had never been his remit. He was interested in headaches, to be sure, but in their subjective character, how we get them and get rid of them, and how they dispose us to think, feel and act. In his work, a headache is a thing that just *is*, a black box which exists in causal relation to other things and the world, but isn’t explained in language which would be familiar to a chemist or a microbiologist. He wasn’t in the business of studying mental life at the level of physical stuff, so the question of what a headache is in terms of physical concepts, was not one he could answer. That, surely – and at this he turned to the neuroscientist with a slight smirk – was a question for his colleague. Then it was the neuroscientist’s turn to give an unsatisfying answer. She explained that though her science was a natural science – and so dealt in the material concepts of the natural world like charge, frequency and width – headaches were not a part of that linguistic sphere. She could ask a subject questions about their mental life while scanning their brain, and in doing so sometimes identify physical goings-on which correlated with features of that inner life – the parts which light up when they are happy, and so on.

But knowing the neurons which fire when a head is in pain is not the same thing as knowing what pain is, any more than you can know what value is by studying the material qualities of paper banknotes. Neuroscience has, she explained, no real place for the word ‘headache’ in the story which begins with a bump on the head and ends with the arm reaching for an aspirin. Perhaps the head *is* hurting, but when she peers inside the brain, she sees only an electric symphony of firing neurons, not the feeling of pain. As the day drew on, more scholars were summoned to give their accounts. Each was posed the Oracle’s question, but none was able to answer it. With each sigh or shake of the head, their divisions were thrown into starker relief. To join the psychologist came the thinkers of the human sciences; economics, sociology, anthropology. They could deliver sermons in the language of the mind, and filled their books with talk of thoughts, beliefs, desires, and their sister concepts. But they could not offer a material account of these things – of what, exactly, a headache is as an arrangement of physical stuff. Then there were the natural scientists; a great swarm of physicists, chemists, biologists, geologists, and engineers, who filed in to stand behind the neuroscientist. Like her, they spoke fluently in the language of the natural world, setting out with rulers and scales to understand the universe in terms of physical concepts. But each was mute on the topic of mental life. None saw a place for headaches in their explanations of the universe, any more than they saw one for imps and fairies. At hearing all this, the King, who had until now been silent, wondered aloud (and in fouler language than mine) what good their sciences could be, if they couldn’t make sense of so simple an idea as the width of a headache. One side knew about headaches, the other about widths, but nobody could bridge the linguistic rift and pose the Oracle’s question in words which their science could make sense of. None could say what it meant for a jumble of atoms to feel pain. Dejected and impatient, the King returned to Delphi and begged for another audience with the Oracle. He marched up to where she sat, on a dais lit by sunbeams, and accused the gods of tricking him with an impossible question.

This, as it turned out, was a slight severe enough to earn their indignation. The Oracle’s lips moved, and the voice of Apollo emerged: “That is a serious accusation.” The King relayed the testimonies of his scientists, that for all they could tell, the question was nonsense. If, he reasoned, we cannot ask sensical material questions about minds, like how wide or heavy or pink they are, then they must be immaterial things. Pain, like the number four or the concept of liberty, has no width, no physical presence in the world, and so the question was a trick. Apollo’s answer came in the form of another riddle: “Do atoms have a physical presence in the world?” The King feared yet more travel and fruitless exchanges with academics, but much to his relief, this time the god did not wait for an answer. “Nobody has ever seen an atom,” Apollo continued. “They are too small. All we see is a footprint, a beep on a measuring machine here, the buffeting of a pollen grain there, a set of causes and effects which somebody one day pointed to and said “let’s call that an ‘atom’. This is all it really means to *be* a physical thing, to sit as a node in the causal web of other physical things, influenced by them and influencing them in return. For what would be the difference between a world made of physical atoms, and a world made of non-physical entities which did all the same things? If water really boils thanks to angels hiding in the kettle, after all, then angels hiding in the kettle are really just heat.” The King pondered for a moment. “But surely not everything with causal powers is a physical thing? What of abstract things, like businesses or governments? You can’t touch or feel a government, and they certainly don’t have widths, and yet they can affect and be affected by goings on in the natural world. When I need taxes, I tell the government, and when the government shows up at your door, you pay it taxes. Cause and Effect.” “Ah,” replied Apollo, “but there is no mystery there. A government can influence the world and be influenced in return because the word ‘government’ is just a label we apply to a great assemblage of physical entities – politicians, bureaucrats, police officers – who act together in concert. The government may collect taxes, but it is the tax man, not the abstract concept of the State, who rings the doorbell. The parts may exist in constant flux, but without any parts, the government would, like that of ancient Babylon, be only an idea or a memory. So as far as cause and effect go, a government just is the sum of those parts, just as an ocean wave just is a rhythmic disturbance of water molecules. “ With this, the King was forced to agree, but confessed he didn’t see the point.

Apollo went on: “To be a material thing is to nudge the world, and be nudged back in return. If the mind, then, is an immaterial thing, how do we make sense of its connection to the world? When you believe there is a fly on your nose and desire its absence, your arm moves to swat it. When you consume food, hunger is sated. Mind and material. Cause and effect. Now, you might be tempted to wonder whether the mind, like a government or a water wave, is just a convenient linguistic stand-in for some underlying system of moving parts. If you want to make a wave machine, after all, you don’t cast about for something which can generate the abstract concept of a wave, you find a way to make water move rhythmically, which is really the same thing. But what, in the case of the mind, is that underlying system? This is the question your scientists struggled to comprehend, let alone answer, which is what makes minds very different to governments and water waves, whose physical reality is easy to understand. The science of brains has no thoughts on minds, and the science of minds has little to say about brains. If we could answer this question, and say with confidence what moving parts were sufficient to create a mind, then this whole discussion would be moot, and the task of building one would be much simpler. But we do not, and so the mind resists efforts to sweep it under the carpet in this way. “So you want me to believe the mind is a material thing,” mused the King, a note of despair creeping into his voice, “an object in the material world, but one which doesn’t appear anywhere in scientific accounts of it. So where do we find it? What is the width of a headache?” The Oracle shrugged: “It needn’t have been the width of a headache; it could just as easily be the charge density of a belief, or the volume of a desire. The point is, that if your goal is to arrange matter so as to create these things, you must have some idea of how these things result from arrangements of matter; how nerves become nervous. Only then will you be able to look at the chrome child, and know whether it is everything it purports to be. You were right to suspect that this question matters. A competent zombie may not make for a bad king, but the chrome prince will not be the last of its kind, and when they are subjects as well as administrators, then you will have to know how to treat them. As ever, philosophy must keep apace with technology.

But where you went wrong, was to imagine that this is a question which science alone can answer. If you want to make a machine pump water or fly to the moon, for that you need only science. But to make a machine appreciate beauty, or understand ideas, or feel a headache, for all this you need something additional: you need to understand what all these words mean. You need to understand what minds are.” The King paused for a moment, lost in thought. “I don’t suppose there’s an answer to my question hidden in this thicket of riddles?” The Oracle chuckled dryly. “There are some wrong answers. But no right ones, as yet. Not a very satisfying response, perhaps, but the best I can do under the circumstances. In any case, this is really a question for you humans to answer. We made you guys, this next lot is all on you.”