Induction by Baigali Nyamdulam

    When I first crossed paths with induction, I was a high school freshman. The word
intrigued me; maybe because of the way it sounded; maybe because it was a widely used term for upperclassmen in math settings; maybe because it was too powerful - powerful enough to accurately foretell the future for eternity.

    In simple terms, induction refers to a technique used in math to prove a certain statement through its first case or base case and the one immediately succeeding the first case - if you can prove the first and second dominoes will fall consecutively then it implies that all of the dominoes in line will fall regardless of the number of dominoes. Simple yet powerful. It might be quite obvious why mathematicians like this technique a lot. You just have to find the most basic case where the statement holds true, and the induction allows you to prove the truth of the statement regardless of the number of dominoes. Meaning, you’ll be able to prove its truthfulness in infinitely many cases.

    People like to say that there’s no equation in life. Perhaps life has too many variables;
perhaps it is too unpredictable; perhaps a math equation is too simple for something as vast but I’d argue the opposite. I want to prove that there is an equation in life.

Proof:
1°. Base case:

    It’s 8 pm at night. After another practice with soon to be athletes, I drowsily move my
legs to the locker room. A missed call from an unknown number. Out of habit, I ignore it like I’ve done hundreds of times before. Another call from the same number. Despite the irritation, I answer.

- “Hello, who is this?”.
- “We’re contacting you from the police department regarding your brother.”

I’m an only child but I have 5 uncles from my mom’s side. I still wanted to disregard the call and go on with my day but, somehow, it couldn’t be ignored. An uncomfortable feeling settled deep beneath my gut. I forwarded the call to my mom, and my intuition was correct. My uncle was found dead somewhere in the city, and they wanted a family member to identify the body.

    If there’s anything I remember of him, it would be his alcohol stench in his clothes,
bloodshot eyes, slurry speeches, and fear. He was aggressive and violent when he was drunk;
shattered glasses, broken fine china, and animalistic screams often followed him like a shadow. One time, my grandma and I pretended we weren’t at home when he visited us late at night. We hid like preys hiding from a predator. He knew we were there and continued to shout and bang on the door. Of course a steel door can’t be opened with bare hands but a small irrational part of me still feared that he might somehow manage to open it. Fortunately, he couldn’t and left.

    The news of his death didn’t surprise me. He was an alcoholic. From the moment I
started forming my own opinion and judge for myself, I rarely saw him sober, and it was obvious where his life headed. There was more than enough evidence to suggest that he would eventually die from a complication related to alcohol - alcohol poisoning in particular.

Thus, the base case is proven to be true.

2°. Induction Hypothesis:

    Assume the statement, induction works in real life, is true for any arbitrary instance
named k.

3°. We’ll prove the truth of the statement for an instance k+1:

    For k+1, we’ll look at k’s brother who was born right after him.

    On the surface, he’s a good father, hard working employee, and hopefully a good son and
husband. He’s one of the thousands of miners working at a coal mining company. His schedule is quite simple - 2 weeks of work and another 2 weeks of rest. You can be sure he’s completely sober in the 2 weeks he has to work but as soon as the flight from the mining site to his home touches down, it’s a different story. Day and night, he is drunk. He might not be as aggressive as his brother when drunk but the bloodshot eyes, slurry speeches, and alcohol stench in his clothes remain the same.

    The only difference in this case is that he drinks beer, at least so he tells. In my eyes and
our family’s eyes, however, he’s just another alcoholic who hasn’t lost his life. Not yet. My
verdict is that he’ll eventually lose his life to something related to alcohol as his life is already half-consumed. I just hope he will outlast my grandma so that she doesn’t have to see another son's death.

Thus, the case, k+1, is proven to be true.

∴ The hypothesis is proven to be true.

If we end the induction at this point, the rest of the siblings, including my mom, and the
entire lineage should have some kind of problem related to alcohol, like a domino effect that tips over each other until the last one standing. From a purely mathematical point of view, induction above is logically sound and will hold true for any instances above k (including k), and even from a non-mathematical point of view it looks completely reasonable to conclude that the same fate awaits me and my cousins as research suggests that alcohol use disorder genetically runs in the family - from sibling to another sibling, from father to son, from mother to daughter, and so
on and so forth.

4°. We’ll CHECK the truth of the statement for an instance k+2:

    It’s not common and frankly unnecessary to continue the induction when it’s already
proven for k+1, and if we do end up continuing the logic, we should eventually come to the same conclusion no matter the n in k+n if we let n go to infinity.

    If my uncle whose blood is replaced by beer is k+1, then my mother who was born right
after him would be k+2. My mom is a tax consultant and has worked in foreign invested
companies the majority of her career. According to the hypothesis, we should come to the
conclusion that she also has some sort of problem related to alcohol. Except, she doesn’t. Sure, she drinks wine here and there but even those times have changed after the death of her brother. She has stopped consuming alcohol altogether.

    On the day of my uncle’s funeral, I noticed my mom rubbed her eyes ever so frequently -
a sign of crying. Insensitively, I dared to ask why. My mom looked at me as if I had gone crazy but managed to tell me that her brother was gone.

5°. We’ll CHECK the truth of the statement for an instance k+8:

    Continuing the lineage, I’m at somewhere around k+8. Logically speaking, even if the
induction was disrupted along the way, there’s still a good chance that I might end up abusing alcohol. After all, there’s the base case and evidence that are in support of it. On the day of the burial, my uncle - k+1 - and I didn’t go to the burial site due to tradition but we still saw him in the morgue. All we had to do was to circle around the body three times. It only took one glance at his blue lips, closed eyes, and pale face to churn my insides and make me feel nauseous.

    A few years later when we ran out of disinfectant solution during the Covid-19 pandemic,
I decided to use a bottle of spirit to clean the house. Not long after, my hand was itchy and red, and I concluded I was allergic to alcohol. It was convenient. Convenient because I don’t have to tell the real reason I decided to abstain from alcohol. Convenient because it's a completely valid reason that no one will question me for. Convenient because I don’t have to be reminded of the cold lifeless body that I once used to call uncle.

Conclusion:

    So, what do instances, k+2 and k+8, do to our hypothesis and our “domino effect”?
These two instances disrupted my induction, and the hypothesis basically can’t be proven to be true, at least from a mathematical point of view. The mathematician in me is frustrated that the induction didn’t hold for an infinite number of cases but I’m more than happy that k+2 was the one that shattered the statement. I couldn’t prove that induction works in real life in a mathematically sound way. After all, it was true that life had too many variables to be contained in an equation, at least in this case. The difference is each individual n in k+n as n goes to infinity is given a choice to divert from the future they are foretold - whether it be our genes or issues that run in the family. The dominoes before us might seem to be falling without a choice but when our turn comes we do have the freedom to choose which is why k+2 -my mom- didn’t fall. Which is also why it was easier for k+8 -me- to stay upright.

∴ The induction does NOT work in real life.

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