Mr. Apodaca: ‘I've gotten better because of students teaching me how to be better.’
The Abstract
Mr. Apodaca—a mathematics teacher—also teaches philosophy in his major classes here at Explore.
Considering this dual expertise, we, of course, asked him about math and philosophy and even the relation between the two. Even if it was something simple—“which mathematician has contributed the most to math?”—Apodoca’s answers were very insightful yet never unclear. And in the half hour we spent with Apodaca, we were able to unpack his belief that math originates in the universe, his thoughts on philosophers new and old (especially Thomas Aquinas), and his assertion that meaning is ingrained into reality.
Of course, in addition to these philosophical dialogues, we asked Apodaca about himself. We became familiar with his love of video games, the film Captain America: The Winter Soldier, and red chile. And through his candidness, we also gained insight into how Apodaca has developed as a teacher over the years, specifically in becoming more patient and empathetic with students.
So, we are delightfully impressed not just with how much we learned about Mr. Apodaca—but how much we learned in general. To take inspiration from something Ms. Trafton said in our interview with her, if it is possible for one’s greatest skills to permeate their life such that it leads them to finding their career (which happened to Trafton), maybe the inverse is true. Maybe one’s job—and their brilliance in it—can permeate everything else.
It wouldn’t surprise us, because this interview perfectly encapsulates Apodaca’s ability as a teacher to elucidate even the most dense knowledge. It was a great interview, yes, and perhaps even a greater lecture—one we would happily sit down for time and time again.
The Interview
Leon: What are your primary hobbies outside of Explore Academy?
Apodaca: Reading—playing video games. I don't have much time for anything outside of this job.
L: Real. Neither do we.
Zephyr: Yeah, on the student end we're also quite busy.
A: That's all of us. We're all in this together.
Z: But which books?
A: Well, philosophy books—I used to be a philosophy professor. I also read some fantasy novels like The Lord of the Rings.
L: What games?
A: I used to like to play Star Wars games like Star Wars Jedi: Fallen Order—and Zelda games, stuff like that.
Z: Including Marvel and Star Wars properties, what is your favorite Disney film or TV series?
A: It would probably be Captain America: The Winter Soldier. I think all of the Captain America films are really, really good—the most recent one, maybe not. I saw it and I was like, what happened?
Z: Do you think it's one of the worst Marvel films?
A: Probably. It looks like they threw it together, DC style. You know, like how DC was constantly throwing together bad movies like Batman v. Superman, Black Adam, and stuff like that. So you can just tell it [Captain America 4] was production hell.
L: This one's a very simple question: red or green?
A: Oh, red. Because I make really good red chile. I'm a red chile snob. Most restaurants make really bad red chili because it's hard to make, but I make great red chile.
L: What do you like to put it on?
A: Everything: I'll put it on enchiladas, burritos, tacos, mashed potatoes, like pot roast. So, it's just good with everything basically.
Z: Is there any dish where green chile works better?
A: Burgers, for sure. Pizza. You can't really just put red chile on pizza or burgers.
Z: Is there anything that you prefer to put ‘christmas’ on?
A:Yeah, you know what, chile rellenos are green chilies, but sometimes I'll pour red chile on them.
Z: Which mathematician do you believe has contributed the most to math as a discipline?
A: Probably Descartes. I'm biased, though, because he was also a philosopher. But, they call it the Cartesian xy coordinate system for a reason. He's the reason. His problem is he tried to use his method of doing math—he's super mathy—for philosophy. It doesn't quite work.
L: This is sort of lifted from our interview with Mr. Robinson and a discussion that we’ve had with him. But among a lot of mathematicians, there are two main perspectives on how the laws of math are derived. Some say that they fundamentally originate within the universe and how it works. And others say it's a system of rules that's entirely made up by humans. So within that spectrum, where do you think you fall?
A: I think it's in the universe. I think that we know for sure that it's in the universe. And I think anyone who has a different opinion knows they're wrong. Because it would still function whether we were here or not.
Imagine a rock sitting on some planet that no one's ever been to, and it happens to—for some reason—fall off a cliff and split perfectly in half. That math worked whether we were there or not to know it. And the other reason is we know it works because we can send rockets to the moon.
We know it comes from reality. We can send rockets to the moon. We can calculate gravity based on math. Are the particular symbols that we use artificial? Absolutely. Could we have picked a different number system? Sure, we picked a base 10. The ancient Sumerians had a base 60, which is insane. Programming is in binary—base two.
But none of those systems would work if the fundamental underlying concepts of math were not somehow built into the universe.
Z: So, it's sort of like the principle of the tree falling in the forest. It still happens regardless of whether or not you were there to witness it.
A: What happens, though, is as we get more into more abstract math—for instance, we have a concrete individual like you. Say your name.
Z: Zephyr.
A: Now say: “I'm Zephyr, the concrete individual.”
Z: I'm Zephyr, the concrete individual.*
*He is, in fact, a concrete individual, and it just so happens that he is named Zephyr.
A: But then there's the abstract concept: humanity, right? Now that abstract concept doesn't exist anywhere in the physical world, but I derived it from reality. So, even our abstract concepts and math have some connection to the physical world. Now, the problem with math, though, is you have your concrete individuals, and then you create an abstract concept like humanity, right?*
*At this moment, Mr. Apodaca stood up from his chair and began using the white board to elucidate his point. We turned to each other—stupid, content grins on our faces—because we knew this was going to be a good one.
A: …The problem is you can have multiple abstractions; you can make another abstract concept that represents those abstract concepts. And the further we do that—up and up and up—the further we remove ourselves from physical reality, we reach a point where we have to ask ourselves: are we still talking about physical reality anymore? Or just ideas? But the fundamental concepts still come from concrete reality.
Z: We've heard that maybe in the past you've discussed this with Mr. Robinson, and I think he has the differing perspective that math is purely invented.
A: Yeah, I love Mr. Robinson. He's so great, and I get along really well with him. But, I do think he is incorrect on this. I think he's right insofar as we're not going to just meditate on concepts—like Plato meditating on the forms—and somehow realize what math is. He's right in the sense that we have to experience physical reality and try things until we find rules that work. But why do the rules that work, work? Because we derive them from our encounters with reality.
Z: So, maybe its origin is ingrained into the universe, but you still have to interact with concrete individual things to get there.
A: Yeah, so I would say I'm in a moderate position; I'm not in Plato's position where I could just meditate on the forms and know all of math, but I don’t think it's just rules that we’ve made up and they just incidentally work. Like Robinson, I think we discover the rules from encountering reality and working through them, and sometimes we make mistakes, and we have to correct them. But they wouldn't work if they weren't grounded in reality.
L: So yeah, the fundamental rules exist irrespective of humanity.
Z: Considering that you teach both math and philosophy, do you feel that the two relate and intersect?
A: It's interesting. In a couple of ways, I would say yes, they do. I think the study of math helped prepare me for the logic inherent to doing philosophy.
And in ancient times, the word philosophy had a broader use; it meant any rational study of reality. So, it wasn’t only metaphysics and ethics—there was also a philosophy of physics, there was a philosophy of mathematics.
Z: Do you think that the two should be practiced together as disciplines because, as you mentioned with Descartes, it sort of gets messy, right?
A: Yeah, so what Descartes did was he applied the qualities of math to philosophy. In math, the ideas are perfectly clear and distinct; everything is indubitable. You really can't doubt them because they’re self-evident or logically derived.
So, Descarte thought he could do philosophy in the same way where he had perfectly clear and distinct ideas, and I don't think reality is as clear as math. Like yeah, the mathematical aspect of reality is super clear, but the qualitative aspect of reality is not. You can still try to understand it in more clear terms; you can still reason logically about the qualitative aspect of reality. But because he eliminates the nuance, he loses a whole element of reality in his philosophy. And that has had horrible consequences for philosophy going forward.
Z: I feel like if reality was just crystal clear, there would be no room for philosophers.
A: Yeah, probably. Now, there are a lot of scientists and science teachers who—because science is very effective in using that mathematical model to make measurements and predictions—make the mistake of assuming that quantitative analysis captures all that is metaphysically real. Such an assumption loses the qualitative aspect of reality, like the colors that we see, and things like that. There's no logical connection between a method being useful because it ignores quality and quality simply not existing. But scientists and science teachers make that leap for some reason; most scientists don’t make good philosophers. Most of them don't know that their field depends on philosophy in the first place. They don't know how their field filters out all these aspects of our experience that science can't analyze quantitatively.
Z: I feel like some aspect of that is almost a necessary consequence of trying to do a job.
A: It's a consequence of having a specialization: I'm specialized in science. I don't know anything about philosophy, so I don't realize the logical problems in some of the assumptions that I need to make.
L: Among the various branches of philosophy like metaphysics, ethics, etc. What do you find the most fascinating, and in which branches have you invested the most time?
A: Metaphysics for sure, which inquires into the nature of reality. I particularly wrote my master's dissertation on—not proving the essence of God, but on one involved element of that question. And it's the most fundamental of all fundamental elements of metaphysics, which in turn is the most fundamental of all fundamental subjects of all subjects that exist at all; I literally was trying to address the most fundamental of fundamental questions. It was a hard Masters to write because of that.
Z: How do you think you did?
A: I got an A. They passed it on and said it was great.
Z: How close do you think you got to a full answer?
A: I think I contributed to the discussion. It [my thesis] was based on—so, you know how there's you, Zephyr, and then you have a bunch of activities like running, singing, sleeping, which are called acts. Well, the most fundamental act we have is our act of existing or being, because if we didn't have that act, we'd have nothing, right? And so that was what I addressed and that eventually relates to proving the existence of God, but it was pretty complex.
Z: If you could have dinner with any philosopher, alive or dead, who would it be and why?
A: I want to say Thomas Aquinas* because I think he has the most comprehensive view of philosophy, and he integrates all the different questions and analyzes them in important ways. I always find modern philosophy very strange because they start asking questions that more brilliant philosophers have already answered. But they answer them on a much more shallow level because they buy into Descartes’ model. I want to say Aquinas, but…
*An Italian philosopher, priest, and theologian. One of the most influential thinkers of the 13th century, particularly towards ideas of human reason and natural law.
A: I think I want to talk to David Hume because he's one of the philosophers I disagree with the most.
L: How so?
A: Well, a couple of things. The first is the starting point that he works off of within his philosophy; he asserts that—whether we realize it or not—we don't know reality. We just know our sense of perceptions. So, I don't see the door; I see my seeing of the door, according to Hume. Which, to begin with, doesn't make a lot of sense. And devolves into a very broken philosophy that doesn’t get anywhere; all it contends is that we can’t really know much. But if you believe that your intellect does actually encounter reality [unlike Hume], then you can actually get somewhere philosophical.
I'd love to point out some of the inherent contradictions that he makes in his own philosophical thoughts, and I want to find out what he thinks about that because obviously he's more brilliant than me. So, it’d be more of a question of why is there this a contradiction in your philosophy? Am I missing something?
L: Is there any philosopher that you would absolutely dread having dinner with or interacting with?
A: Probably Sartre*. He’s a whiny person who's always complaining about how horrible his life is.
The famous French philosopher, playwright, and political activist.
L: So, he’d just be a depressing black hole of energy or enthusiasm.
A: It would just suck. Also, he was a Marxist, and Marxism has killed more people in all of human history than any ideology in the world.
Z: I suppose the feeling would be mutual; he probably wouldn't want to be there either*.
A: No, he'd want to be at home instead.
*For those unacquainted with his grumpiness and asociality, Sartre is known for the quote: “Hell is other people.”
A: He’d probably say: “you're not a Marxist, you're a free market guy? What's wrong with you?” And then he’d say, “wait, you have a positive view on life even though there’s suffering in the world? What’s that?”
Z: Would you say you have a greater affinity for classical philosophers versus modern philosophers?
A: There's certainly some great modern philosophers. So, I don't think you guys are like this, but you know that teenage stereotype where it's like my parents are dumb, and I'm just going to ignore everything they say? Descartes basically started that stereotype in philosophy; everyone before me was dumb; we're going to start over again.
Well, that resulted in philosophers abandoning all the brilliant insights that people like Bonaventure, Scotus, Aristotle, or Plato had. Whereas somebody like Aquinas integrates insights—old and new—into something more comprehensive. But there are modern philosophers I appreciate: Karol Wojtyła—he built upon Thomistic philosophy; Martin Buber—he merged it with something called personalism; Gabriel Marcel; and Heidegger—who was brilliant. I don't always agree with Hiedegger, and unfortunately, he was a Nazi, but I can still appreciate his philosophical insights.
L: If you had to recommend one theory or text to be studied by someone who's just starting to get into philosophy as a subject, what would it be?
A: I would say Aristotle's Nicomachean Ethics, but you would need additional commentary to understand it. Regardless, I think it's a really good way to understand how philosophy works.
L: I mean, Aristotle's all about essentialism, which I think works as a good starting point for philosophy in general.
A: It depends on what you mean by essentialism; we have to be quite careful with that word. Sociologists use the word essentialism in a completely different way—they characterize it as the idea that every aspect of social life is unchanging, without exception. Essentialism, in a philosophical sense, is the idea that we have forms, natures, and activities that we are capable of performing which result from our forms or natures.
L: So, do you think it [Essentialism] equips people with fundamental concepts that are good to use as a jumping-off point?
A: Yeah, I do. I think it's a jumping-off point. For example, Aristotle and Aquinas have a very sophisticated analysis of what we all know to be true, while providing the philosophical foundation for deeper analysis.
Z: Which philosophical theories do you think offer the most practical application in our everyday lives?
A: Again, Nicomachean Ethics by Aristotle. It's the healthiest, sanest view of life that I've ever read. It's so universal in scope that it can be practiced by Atheists, Christians, Buddhists, Muslims, Jews—basically by anybody, because it's so grounded in our human nature. Additionally, Martin Buber's I, Thou, particularly due to its context in the 20th century; he founded personalism in stark contrast to ideologies like Fascism and Marxism, which killed all of his people.*
*Buber, an honorary professor at the University of Frankfurt am Main, was forbidden from lecturing by the Nazi Party shortly after it came to power, causing him to resign in protest. He was eventually forced to flee Germany, settling in Jerusalem. Jewish himself, the untold atrocities inflicted upon his fellow man moved him further towards Zionism and anti-fascist beliefs.
Z: I think it's good to absorb texts that encourage you to interact with others and be a kind person.
L: Instead of, “hell is other people.”
A: So, many of us philosophers just want to slap Sartre and tell him to stop whining.
L: So, what is most crucial for students to know about transitioning into the adult world?
A: I don't want to be pessimistic about this, but it's kind of hard not to be. Being an adult—and I can say this because I’ve been both—is about 100 times harder than being a minor. Even when you're a teenager and you start to have more responsibilities, those don’t pale in comparison to the responsibilities of adulthood. So, my advice to students as they're transitioning into adulthood is do just as Aristotle says: practice virtues over and over until they become a habit; practice responsibility over and over until it becomes the most ingrained habit you’ve ever possessed, because it is the main virtue that's gonna control whether you have a successful adult life or not. I wish I had done that in my 20s, and I know it sounds boring and silly, but it's the truth.
A lot of people will say the best advice is to simply “follow your dreams.” Truthfully, sometimes people's dreams are ridiculous. I'm gonna turn 44 in a few weeks here; I'm not in shape. If I had the dream of becoming a male basketball star, it's not happening. That isn’t to say you shouldn’t follow your dreams, though, so long as they are feasible and good dreams. But more importantly, you have to be responsible every moment, every day that you can. Carry your burdens.
Z: Yeah, and I think the only way whatever dreams you have can manifest is through discipline.
A: I think most people can develop reasonable dreams to maintain, but make sure you have the discipline and responsibility to get there. And temper dreams with responsibility. Because responsibility comes first, especially with family.
L: Are there any particularly special moments where you feel students have taught you something at Explore—or a previous school?
A: I'm gonna give you one from before I was at explore, if that's okay. So, there was one year where I was teaching this remedial math class at this school, and I had a student who was really, really disruptive and he would often fall asleep in class. And one day I scolded him; I was pretty angry. And he told me that day, “I'm so sorry Mr. Apodaca. I had to work at the restaurant till two in the morning last night.” So, I asked him, “why were you working at the restaurant till two in the morning?” He's helping his parents pay the rent. And what that taught me was, when students have a behavior that's negative, I shouldn't jump to the conclusion of getting mad at them. I should stop and think that maybe there's a good reason, and we should address that first.
Z: So, instead, you try to approach it from a place of gentleness and understanding.
A: Yeah, when I talk to people outside of class, who have low grades or missing assignments, I ask: “Why are the assignments not being turned in? Why is this happening?” Because they might have a very good reason—we may just need to come up with a plan that can work around it.
Z: If you were a student here, in which other teacher's class would you like to enroll, even for just a day?
A: Mr. Robinson, or Ms. Sanchez. Mr. Robinson for sure, because I know he's very crazy—like, funny crazy. I also know he's a very good teacher. I also would love Ms. Sanchez’s classes, because I know she's an excellent teacher, and I want to see what happens in her classroom.
Z: Do you know this from talking to other students, or did you find out personally?
A: I acquired Mr. Robinson’s reputation from talking to other students, who all said that he's a very good teacher. I also just know that he's zany and funny in his own way from interacting with him on a regular basis. With Ms. Sanchez, I know she's a good teacher because students love her. Although I haven’t interacted with her a ton, her distinction amongst the student body, plus having seen her selected as a speaker for the senior class more than once, signifies to me that she’s an amazing teacher.
L: If you have to say, what are some of your favorite memories as a teacher at Explore Academy?
A: So, I had a student who was failing math class after math class last year. This year I had that same student a couple times; now, they’re acing math classes. And this is gonna sound a little self-serving, but I asked her what changed, and she gave two reasons. One, she said, “last year you pulled me on the hallway and told me how smart it was and there was no reason for me to be getting these low grades and if I would just try I would pass.” Two, she said, “I took it to heart.”
I feel good about that memory, because it made me feel like what I did accomplished something. And because I saw in the student that she had the ability to make a change, and she chose to.
Z: I think that exemplifies what you talked about before, trying to approach with understanding and some faith.
A: Admittedly, I don't always do it; I can be grumpy and cynical. I think that's my biggest weakness is that, when stuff is not getting done the way it's supposed to, I get a little edgy. But I try, and I've gotten better because of students teaching me how to be better.
Z: Alright, simple question. Why is nihilism stupid and dumb?
L: We have a lot of bias; we dislike nihilism.
A: Nihilism is shallow, because it never engages with what a human being is or what it means to be human. And there's this principle in metaphysics called final causality, which means that things are limited to certain goals or ends by their nature. That's obvious. Human beings can only do human things; I can't fly in the way a bird flies. And when you have final causality and things, you can already figure out what we mean by what is good and bad, what is desirable and undesirable. Something is good if it fulfills its nature. The nature of a doctor is a professional who produces health, right? So, a good doctor is one that is effective at producing health. I know what a good or healthy heart is, because it's nature is to be an organ that pumps blood. To the degree that it’s effective at that, it's a good heart. It’s the same thing with human beings. I know that a human being is a rational animal, so I know that I am good insofar as I live my animal life in a rational way. That means just by existing, by having a nature, meaning is already built into reality, whether we want it to be there or not.
Z: That actually ties really well into our next question because we were going to ask you if you think meaning is inherent to the world and reality.
A: You can't avoid it. The reason why people have started to doubt that now is the imperialism of the scientific community; the scientific community studies everything through the lens of quantity. And you can't talk about things’ natures or purposes or causes or ends when you're analyzing quantity. It’d be fine if scientists said that's all we're doing—we're just analyzing quantity.
But the problem is many of them have gotten drunk on their technological success; because they’ve gotten so good at quantitative analysis and measurement prediction, they assume that all that exists in the world is quantitatively measurable and predictable. If so, there’s no meaning, there’s no ends or goals. But it’s a philosophical mistake.
Z: As a follow up question, we wanted to ask, what degree of objectivity is there to that meaning? Or, how much can we determine that meaning for ourselves?
A: That's a good question. I think some of it can be determined by us. But I think we know that human beings need to live their animal life in a rational way, which means reason is more in control, and our passions and desires and emotions follow the lead. And we can empirically demonstrate that if one does whatever they feel like doing at every moment, they’re gonna have a disaster of a life. And some of those things we know from our nature too, like we're social animals, so I know if I'm a dishonest person, I'm not gonna have good social bonds, which means I'm not gonna flourish.
I think there's a lot of objectivity. I think when people believe stuff is subjective it’s more about the difficulty of applying objective rules to reality because of the variability of circumstances. Let me give you an example. I would say stealing from people is always wrong. So, I have a moral obligation to return an axe that I borrowed from somebody. But what if the circumstances are such that I know that they're going to use that axe to murder somebody? Now, I have a moral obligation to not let them have it. You see the rule there.
So, what people miss is that circumstances can sometimes take something that would normally be a good act and make it evil. And those circumstances are often difficult to navigate, which is why people think that it's not objective. But there's still an objective answer; it just might be really hard to figure out.
Z: In terms of purpose or how we discover a sense of meaning and worth for ourselves, is there choice in that? Is it more so that we have choice, so long as it exists within the constraints of our nature?
A: Yeah, it’s not like we all have to live our lives exactly the same way, like we all have to be an engineer, or we all have to be a philosopher, or we all have to be a scientist. No. There's a lot of variability in human life. But there are certain boundaries built into our nature which tell us what constitutes a good human life or a good rational animal life.
All that variability has to fit in those boundaries; otherwise, you go outside those boundaries, and you're probably doing something evil. And by evil, I don't mean the worst, most deplorable thing ever. It could just be telling a white lie—a very small evil, right?
L: Yeah, just tying back into complaining about nihilism, I feel like nihilism negates that in a way that's very frustrating to me. Nihilism poorly answers every question with this dismissive nope, that means nothing, shut up.
A: Yeah, I can see somebody who's had difficulties in their life falling into nihilism, but even then it’s a cheap cop-out. No matter how bad your life is, you can always improve it to some degree. And as bad as the context of the things around you are, you can always improve that for the people around you too. There's improvement to be had. Even if you're living in a really bad situation, don't turn it into hell. And nihilism will turn it into hell.
Leon Atweh & Zephyr Mack
