Month: October 2020

Mathematical Philosophies No One Asked For (Except UChicago Admissions)

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What can actually be divided by zero?

In its simplest form, dividing a number by another is just the act of separating it into so many parts. In other words, division is sharing a group of things among an unnamed number of people. If I wanted to divide 20 by 4, my third grade self learning division would have imagined splitting my own 20 cookies into groups to share among 3 friends and myself, the answer being how many cookies we each got in the end. In this way, division becomes more than a mathematical operation – it becomes the act of sharing, a relationship between people.

Classic mathematics will tell you that no value can be divided by zero. Ask Siri, and she will tell you that there is no answer. From a third grade perspective, dividing something by zero means splitting a finite amount of things into no groups – even the original group is gone. This is puzzling under initial scrutiny. What starts as something and becomes nothing? Or, if viewed under the impression that dividing is simply the act of sharing, what can be shared and possessed by no one? In this case, most objects and concepts can be ruled out, as they can be possessed by at least one person and therefore are divisible by 1. This presents two alternative theories left as to what could possibly be divided by zero: something that is shared by everyone and therefore belongs to no one, and something that can never be possessed. 

The first option is admittedly slightly easier to explore. If something – be it a concept like ownership or a material object (or collection of objects) – can be shared by everyone and everything, then it must therefore belong to no one and nothing. In other words, something spread into such a vast, even infinite, number of groups must eventually come to the point where none of those groups truly possess that something. Some things could never fit the bill here: knowledge, while it has the potential, lacks the practical means to be distributed so widely. On the other hand, something like suffering – a universal experience that takes many forms – could be shared by an infinite, unknown number of organisms. Yet even if suffering is a shared experience, no two people or life forms experience it in the same way, and therefore it cannot be truly shared by anyone. In becoming so widely spread, it loses its ability to be uniform – the thing being divided changes and loses its essential components, which means it is scattered into nothing. When something is divided by zero, it is like trying to take something that exists (finite) and split it into nothing. When something like suffering becomes so infinitely split and spread, it loses its identity and becomes something no one shares and is possessed by no one. In this way, it can be divided by zero.

The second alternative is no less complex, albeit more restrained in its solutions. In order to be divided by zero, the original value must never be able to be shared among anyone. In other words, it is something intangible and unattainable. Such a solution under these restraints therefore exists in theory, but is not material, and can never be interacted with. For example, if something can never be found, it can never split into multiple shares – it can be divided so that no one gets a share. This is best described by knowledge. For now, these constraints apply to concepts like what existed before the Big Bang and why matter is so much more abundant than antimatter. But these mysteries may one day be solved, and will therefore eventually be divisible by much more than zero as the knowledge is shared. However, there are some things that will never be understood or attained. One example is what comes after life. This is something that, under our universe’s laws of physics, can never be known and therefore if divided by zero, can be split among no one – because there is no one to understand it. Contemplations on life after death aside, unknowable knowledge is just one example of something that can never be shared and therefore is divisible by zero. While the original value does indeed exist, it can be divided by zero because it cannot be split into any number of groups; it is not divisible into anything, and therefore cannot be shared among anyone or anything.

By all appearances, the answer to any value being divided by zero is undefined. Indeed, the great majority of values can’t be divided by zero. But if one is willing to think a little out of the box and envision division as something more than arithmetic, the answer becomes much more complicated. In the scientific world, formulas and relationships depend on division, but in its purest form, division is nothing more than splitting an original value into groups to be shared. So the question instead becomes, what can be shared by no one? In this way, the answers become clearer: something so infinite that the original value is negated, and something that is impossible to share but exists nonetheless.

The Signal-Man: Charles Dickens’ Dabble In Horror

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Everyone loves a thriller. As Halloween approaches, most of us will turn to the jumpscares and suspense of our favorite horror movies. The creeping feeling that something dreadful is about to befall the character, the shock of seeing that threat made real, is something most horror fans are familiar with. Less familiar is the unwitting, slow approach to doom – an unsuspected conclusion that leaves you feeling like you missed all the signs. 

Charles Dickens is not well known for works in the horror genre. Admittedly, some might argue this and point out A Christmas Carol, but upon hearing his name, most think of the love stories of Pip and Estella in Great Expectations or Lucie and Charles in A Tale of Two Cities. Yet his work “The Signal-Man” is masterfully done. The short story follows a nameless narrator who meets a signalman for trains in Victorian era England. The signalman admits to the narrator the repeated spectres who have appeared to him in the train tunnel, warning him to clear the way for a train. Twice, days after those spectres appeared, terrible accidents had occurred. The spectre has returned, and the signalman is tormented by what it means and what he should do. At the end of the tale, the narrator returns to find the signalman dead, after he failed to hear or see the train conductor warning him of approach and using the same words and gestures the spectres had. 

The story begins with ordinary circumstances and follows this sense for the majority of the piece. As a reader, little warns of the danger the signalman faces. Surely, something terrible is going to happen, but the signs point to the signalman being the cause or prevention of such an occurrence – not the victim. Even more eerie is the detail that the conductor’s warnings are laced with the narrator’s own thoughts, combined with the spectre’s words to the signalman. Such a detail leaves a cold chill in the reader as it becomes clear that this event was, in effect, both prophesied by the signalman and influenced by the narrator. 

While this particular piece falls out of place among Dickens’ well-known works, it retains the masterful prose and attention to detail that all is evident throughout all his pieces. Dickens takes the time and words to create vivid images of his characters’ surroundings, the littlest details that reveal more to the characters than meets the eye, and relatively short dialogue in favor of more descriptive paragraphs and paraphrasing. While these choices slow the story down, it also gives the reader the opportunity to reflect more upon what is being said and realized. In novels like Great Expectations and A Tale of Two Cities, these choices are out of modern style and make reading a labor; in this short story, these choices elevate the piece from a shallow interaction between men to a deeper connection – and continue to build the mystery around the signalman’s dilemma. For example, Dickens takes great care in describing the damp and dark the narrator experiences in the train tunnel, which puts him at unease and adds to the mysterious, eerie mood the setting creates. Today, such a setting may be cliche, but in Dickens’ Victorian era such a place was not uncommon; nonetheless, it creates an atmosphere that is hospitable to believing in the specters the signalman claims to see and provides a sort of vindication when the signalman is found dead. 

Most of Dickens’ works focus on societal issues of his era: his protest against treatment of orphans, the class divide between the rich and poor that was often fatal in the Victorian era, and a constant return to morals like generosity and unconditional love. However, “The Signal-Man” takes a more unique look into the unpopular topic of mental health. Little was known in Dickens’ era about mental illnesses, yet this piece highlights the danger of prolonged isolation, especially in poor conditions. The signalman was sequestered in his train tunnel with little accessibility for long periods of time alone, with little to do except learn math or new languages. Despite these pastimes, he was evidently unused to company as shown by his strange reaction to the narrator’s company, and later when he touches the narrator’s arm during their conversation, as if to assure himself of the narrator’s presence. Dickens takes a progressive stance in this regard by having the narrator feel concern for the signalman’s wellbeing and determination to bring him to a doctor. Yet while this attention to mental health was for the most part new for Dickens, it is characteristic of his forward-thinking ideals and discontent with how society functioned in various aspects. 

One of Dickens’ unifying devices is his attention to personalization and self-actualization. Many of his characters are memorable for their strengths of character, forces of will, and unforgettable minutiae. Villains are often defined by the trait of egotism. In most of his stories, Dickens provides these characters with moments that validate their humanity and provide them with the strength to follow in the paths they desire. In “The Signal-Man,” this is less obvious to readers. The narrator is nameless and rather devoid of specific, significant opinion or personality. The signalman is the focus here, and his character is forged in the recognition and acknowledgement of the narrator, who acts more as a conduit than a real character. The force of the signalman’s sense of responsibility is what defines him, and his self-actualization comes in the form of the narrator’s shared contemplation of the spectre and the assurance of his capabilities in performing his duties as signalman.

While Dickens strayed from the road that his more famous works follow in this short story, he retained his strongest literary devices – which proved more effective in this work than others – and provided an entertaining story with complex and elusive themes that linger with the reader long after the last words.