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Elucidations
Episode 147: Gabriella Gonzalez discusses the intersection of algebra and programming
In this episode, Matt talks to Gabriella Gonzalez about how basic concepts from the branch of math known as abstract algebra can help us simplify our
computer programs and organize our thoughts.
Algebra. That thing they make us do in school. What was that again? Oh yeah, that’s right; it’s where you get to manipulate equations containing variables. Like, if I have an equation that looks like this:
2⋅x = 16
Then I can divide both sides by two and get a new version where x stands alone, i.e. solve for x:
(2⋅x) / 2 = 16 / 2
x = 8
If you took algebra in school, you might remember learning a bunch of tricks for pushing parts of equations around to get one of the variables to appear only on one side and thus solve for it. Being able to solve for variables in equations proves useful for lots of things: like, if you can translate a word problem into one of those equations, finding the answer is often as simple as tinkering with the equation in some obvious way.
Abstract algebra is somewhat similar in that it also involves manipulating equations containing variables, except the twist is that now you aren’t necessarily manipulating numbers anymore. The variables can stand for something else, and there are more general versions of plus-like, times-like, etc. operations that you can do on these other things. You might be wondering: what on earth could a variable in an equation stand for other than a number? Well, in this episode, Gabriella Gonzalez gives a bunch of examples. You can have equations for cooking recipes, for computer programs, for transactions performed on databases, and for regular expressions. (A regular expression is a special type of computer program for identifying strings that fit a particular pattern and pulling information out of them.)
Gonzalez then goes on to argue that the point of all this is to avoid re-inventing the wheel. Often, when you write a computer program to add some numbers, though this isn’t necessariy obvious at the time of writing, you aren’t actually drawing meaningfully on the fact that they’re numbers. If that’s the case, then what you can often do is make your code that adds things abstract so you only have to write your program once, but then you can re-use it on all these different other kinds of entities other than numbers.
The overall payoff of all that, according to this month’s distinguished guest, is that by following algebra-driven design, you can keep your code simple and easy to understand, while still having it do fancy things. This is particularly important today, when our software just seems to keep getting fancier and fancier, but the usual ways of accomplishing that goal make it unreliable and well nigh impossible to keep up to date.
Join us as Gabriella Gonzalez gives us the tour through various algebraic systems that occur all over the place in computer science, philosophy, and linguistics!
Matt Teichman
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150. Episode 150: Shruti Rajagopalan discusses talent in India
46:43||Ep. 150In this episode, Matt sits down with Shruti Rajagopalan (Mercatus Center) to talk about what the future holds for India.We often have a tendency to think of the current economic and geopolitical situation as simply the way things are. Especially for people who grew up in the United States over the past 50 years, the fact that it is an economic and military superpower sorta feels set in stone. But in this episode, Shruti Rajagopalan encourages us to take the long view, regarding the current state of the US as just one phase in a decades or possibly centuries-long economic development life cycle. First, the country logs a certain number of decades as a manufacturing hub, under conditions of minimal top-down interference from regulatory bodies. This enables it to build wealth, which eventually pushes it away from being a manufacturing economy, but it’s a race against the clock. With economic growth comes a rise in average life expectancy, plus a lower birth rate, which together can lead to large aging population. Once the aging population increases, the country’s economy needs to be strong in order to accommodate all the caregiving that an aging population makes necessary.Interestingly, it’s starting to look like some other countries—particularly India—are currently poised to undergo a similar trajectory of economic development that the US did. What makes India stand out is that among the countries in the world with a large young population, they have an unusually high GDP per capita. They also have a pretty sizeable early-career, STEM-savvy middle class that is ready to move anywhere in the world, build a life wherever they end up, and culturally assimilate.Our esteemed guest argues a) that the relaxation of economic restrictions which took place in India in 1991 made this siutation possible, and that b) a few conditions still need to be met for the future to unfold in the optimal way. One is that India needs to build up its manufacturing sector that the country can get richer before the population gets too old. Another is that other countries need to take advantage of the fact that India’s young workforce is ready to emigrate. She even suggests that wealthier countries with a rising elderly population, low birthrate, or declining heritage language could perhaps address those issues by welcoming an incoming population of young workers from India.Join us as our guest outlines the (hopefully) upcoming rise of India on the world stage!149. Episode 149: Lainie Ross and Christos Lazaridis talk about defining death
42:01||Ep. 149In this episode, we are joined by Lainie Ross (University of Rochester Medical Center) and (once again!) Christos Lazaridis (UChicago Medicine), this time to talk about the different ways of defining death.In our previous episode with Christos, we talked about death and the vexed history of attempts to define it. Prior to the advent of modern life support technology in the 1950s, it was usually enough to check whether a person had a heartbeat and could breathe to determine whether they were dead. But once machines were invented that could breathe and circulate blood in patients whose lungs or hearts were failing, a new moral conundrum was born: how do you decide whether a medical patient is dead when it is now possible to keep their lungs breathing and their heart beating indefinitely?In this episode, our distinguished guests talk about the actual criteria that physicians use to determine whether a patient is dead, as well as some possible criteria that no one has tried applying but which some doctors think would be more appropriate. Furthermore, Lainie Ross argues that every person has the right to choose which criteria will be used to determine whether they are dead. These two topics interact in interesting ways.For example, I might have a strong preference for my doctor to pronounce me dead only if I have permanently lost all consciousness, even if I can still spontaneously breathe. Although we currently have no good method of objectively measuring whether a patient has permanently lost consciousness, Dr. Ross argues that I have the moral right to sign an agreement stating my preferences. Specifically: the agreement could state that if, in the future, the technology for determining whether someone has permanently lost consciousness gets invented, and, at that time, I have permanently lost consciousness, then I should be declared dead. On the flipside, some patients prefer a stricter criterion, often for religious reasons. Perhaps it is my religious belief that if I am breathing, then I should be considered to be alive. Lainie Ross argues that in that case, I have the moral right to sign an agreement stating that that is the criterion that doctors will use on me, in the event that I lose consciousness but am still able to spontaneously breathe.As of right now, people only have the legal right to sign these types of agrreements in a handful of states in the US. Join us for this episode as Christos Lazaridis and Lainie Ross argue for making this legal right more widespread!148. Episode 148: Christos Lazaridis discusses brain death
37:57||Ep. 148In this episode, Matt sits down with Christos Lazaridis (University of Chicago Medicine) to chat about what brain death is and whether brain death should count as, like, death death.Modern life support technology really hits its stride in the 1960s, allowing doctors to buy themselves more time to save their patients by connecting them to machines that can assist with breathing, blood oxygenation and/or heart pumping. But the flipside to that incredible technological breakthrough was that the medical community now needed to get more precise about the moment at which a person goes from being alive to being dead. After all, what had previously been a quick window between the two was now, due to life support technology, happening in extreme slow motion. In addition, organ transplanation was becoming more and more commonplace, meaning that it was no longer as simple as saying e.g. ‘I count someone as dead just in case their heart has stopped.’By the early 80s, the United States had settled on a standard definition for when someone counts as dead, which states that a person is dead if they have either permanently lost consciousness or permanently lost the ability to breathe and pump blood with their heart. That criterion makes certain life-saving practices possible; for example, it legally feasible for organ transplantation to begin once a patient has fallen into an irreversible coma, provided they agreed to donate their organs in advance.But should a person really count as dead just because they fell into an irreversible coma? We call that condition ‘brain death’, or sometimes the wordier ‘death by neurological criteria’, and we legally count it as a full death. Critics of the notion of brain death say that it should not count as death, because a person in this condition is still biologically alive. Their argument is that saying a person in this condition is dead is just a story we’re telling ourselves.In this episode, Christos Lazaridis—who is a practicing neurointensivist—argues that even if that is a story we’re telling ourselves, that’s fine, because this is a corner case in which it makes sense for the social/legal status of being dead to come apart from the biological status of being dead. Tune in to hear why he thinks this is the case!146. Episode 146: Gaurav Venkataraman discusses memory in DNA and RNA
39:52||Ep. 146In this episode, Matt sits down with Gaurav Vankataraman (Trisk Bio) to talk about how human memory is physically realized.Where do your memories live? In the brain, right? They’re, like, imprinted there somehow? We often think of memories as analogous with recordings, like when you do an audio recording and the air vibrations get translated into an electrical signal which reorients the magnetic particles on some tape. But is that really how it works? Is the brain some tape waiting to get recorded to, or a hard drive waiting to get data written to it? We don’t exactly have definitive answers to those questions, but in this episode, our distinguished guest discusses a line of research into whether memories could be stored outside the brain, in RNA. He then notes that there is also a lot of RNA in the human brain itself, which means that a similar mechanism for storing memories could exist there as well.This research, as it turns out, originated in some rather astonishing scientific work from the 1950s involving planarian flatworms. Planarian flatworms have the extraordinary ability to regenerate: if you cut one in half, each of the two halves can actually grow back into a new worm. At that time, there was some preliminary evidence to suggest that if a planarian flatworm learned something, and you cut it in half, when the half that didn’t have a brain grew back, it still retained what the original worm had learned. What the what? It could remember something even though it had a brand new brain? Those initial studies went through a period of being discredited, but in recent years a number of researchers have been exploring new, more rigorous evidence that something of this nature could be going on. Perhaps the flatworms could actually be storing some of their memories in their RNA or DNA, and perhaps RNA has the ability to preserve some of that information both in and outside of the brain.In this episode, Gaurav Venkataraman argues that the RNA in the brain not responsible for making proteins (called non-coding RNA) has a specific type of mathematical structure that is particularly well-suited for transmitting information both fast and accurately. Not only that, but entities with that kind of structure transmit information more accurately the faster they transmit it. So the fact that RNA in the brain is structurally arranged in the way it is actually makes it a viable candidate for being sort of like the brain’s “software” for storing and manipulating memories.145. Episode 145: Andrew Sepielli discusses quietism and metaethics
39:46||Ep. 145This episode, Matt and Joseph sit down with Andrew Sepielli (University of Toronto) to talk about metaethical quietism. His new book on the topic, Pragmatist Quietism, is out now from Oxford University Press. Click here to listen to episode 145 of Elucidations.Metaethical quietism is the view that ethical statements—or anyway, a large portion of the ethical statements we’re usually interested in—can’t be justified or disproved by statements from outside of ethics. There’s something autonomous about the topic of ethics (or rather, about a lot of ethics). Consider the question: in the scenario where a trolley is barreling down the track, on its way to clobber five people, and you have the ability to divert it to the other track where it will only clobber one, should you do so? According to quietists such as our guest, you can’t answer this question by asking metaphysicians or logicians for help. It won’t do to investigate whether moral facts are part of the furniture of the universe, or to study the grammar of words like ought. The only way you can answer a question like that is, well, whatever we usually do to answer ethical questions.Why are philosophers often tempted to think we can turn to metaphysics, logic, or the philosophy of language to help answer ethical questions? Andrew Sepielli thinks it’s because we conflate two different kinds of ethical statements: the statements he calls deep and the statements he calls superficial. A deep statement is one such that, if you believe it, that belief can impact your mental picture of how things are laid out in the world and guide your action. The fancy word for this mental picture of how the world is laid out is non-conceptual representation. A superficial statement is one belief in which does not influence your non-conpceptual representation of the world. The questions that moral philosophers often write about—such as whether one should divert the trolley, or whether utilitarianism is true—are superficial, which is part of why you can only answer them from within ethics. But there are also deep moral questions, such as: will the party we’re thinking of going to be attended by a bunch of jackasses? When you ask that question, you’re deploying moral language—jackass, specifically, so it is definitely a moral question—but you’re also trying to find out which individuals are going to be at the party. And which individuals happen to be at the party is part of the information in your non-conceptual mental map.In this episode, Sepielli argues that keeping track of when we’re having a superficial debate vs. when we’re having a deep debate can make it seem less mysterious how ethics could be its own autonomous area of inquiry. Tune in to see why he thinks this is the case!144. Episode 144: Christopher Beem discusses democratic virtues
37:39||Ep. 144This episode, Matt talks to Christopher Beem (Penn State University) about how we can cultivate those skills that conduce to having a functioning democracy. His book on the topic, The Seven Democratic Virtues, is out now from Penn State University Press.The storming of the US Capitol Building in 2021 was an eyebrow-raising event, to say the least. It prompted historians, political scientists, and political philosophers to ask whether deep down, everything was going okay with our democratic system. Was this event some kind of sign that the voting process was under unusual strain? Was it time to start thinking about measures we can take to try to support and maintain it?Our guest says yes: that time is upon us. In light of evidence from evolutionary psychology that natural selection imbued us all with an instinct for tribalism, he argues that there are pretty strong causal forces working to congeal us into increasingly disjoint political camps. If we don’t do anything about it, members of these communities may one day no longer be willing to vote in the same elections. But what are we supposed to do about it? Although no one simple trick is likely to work, Beem argues that there are personal moral virtues that we can all work on developing. Democracy doesn’t just function by default; we have to actively work on ourselves in order to make it function. It’s not like we wave a magic wand, follow a couple simple steps and then we’re “done”. Rather, it’s always going to be an ongoing process to keep this crazy thing afloat.Tune in to hear Christopher Beem’s thoughts about what these virtues are and how exemplifying them can get our democracy back into whack!143. Episode 143: Mark Linsenmayer discusses alternative models of education
44:24||Ep. 143This episode, Matt Teichman talks to Mark Linsenmayer about alternative models of education. Mark is creator and host of the Partially Examined Life, Nakedly Examined Music, Pretty Much Pop, and Philosophy vs. Improv podcasts. He is also the author of the recent book, Philosophy For Teens.There’s going to college and there’s listening to podcasts. Both can give you a way to learn new things, so in that general sense, both can count as forms of education. Going to college has advantages over listening to podcasts when it comes to learning—a college class can kick off a feedback loop where you’re given work to do, then you’re given one-on-one feedback on that work, then you do more work, and so on. In the best college classes, there’s a dynamic interplay between the state of your understanding and what happens next in the lesson. That means that at least for people who end up connecting with the college experience—not necessarily everyone, but some significant number of people—being in college has a certain intensity to it. It feels like you’re gaining understanding at a more concentrated dose.That said, though, in addition to these upsides, there is a downside to college, which is that it ends! The learning is nice and concentrated, but it’s also relatively short compared to listening to podcasts, which you can do for way more than just four years—theoretically, it’ll be possible for as long as the technology exists. (And it’s showing no signs of ever going away.) Sure, people can’t just go to college forever. If literally every single person went to college for their entire lives and no one ever did any of the work that makes society function, it wouldn’t be clear how we’d keep the lights on, run hospitals, create enough food for everyone to eat, build houses for everyone to live in, etc. At the same time, a lot of college students have the joyous experience of having their intellectual horizon expanded for four years, only to get suddenly thrust into a demanding work environment upon graduation that may not afford time for all that. Wouldn’t it be nice if there was a way to embark upon your career while not giving up on exploratory learning? At least not entirely?This is where podcasts come in, according to our guest. They let you continue to explore new topics with a more free-form, lower-stakes structure. Maybe you don’t know whether you want to know more about something yet, but you suspect you might, and that’s enough. The fact that listening to a podcast doesn’t have to end means you can do it at your own pace, and more fundamentally, that you won’t suddenly go from having it to not having it anymore—the way it always seems to happen with formal education.Tune in to hear Mark Linsenmayer explain the kind of experience he seeks to foster in his listeners by way of four (!!) different podcasts!142. Episode 142: Emily Dupree discusses the rationality of revenge
36:07||Ep. 142In this episode of Elucidations, Matt sits down with Emily Dupree to learn about whether it’s rational or irrational to try to seek revenge.As a culture, we kind can’t decide what we think about revenge. Out of one side of our mouths, we talk a big game about letting bygones be bygones, about how revenge and retaliation lead to cycles of violence, and about how nothing good can really come of getting back at people. But acts of revenge, where clearly warranted, also have a visceral moral appeal that it would be absurd to deny. If we didn’t think there were at least some situations in which a person ought to get their comeuppance, then there wouldn’t be so many heroic adventure movies centered around the protagonist’s quest for revenge. When the hero gets back at the villain, it just feels right, like the movie needs to end here and we can all go home; and no amount of pedantic, post-hoc reasoning can ever make that feeling go away.Solving that dilemma is hard, but as a way of working up to it, our distinguished guest decides to tackle a slightly different question. Not: can seeking revenge ever be the right thing to do—but: can seeking revenge ever be a rational thing to do. Traditionally, most philosophers have answered that question in the negative. Calling it irrational means that it’s senseless and unintelligible, like anyone who does it is undergoing a (possibly temporary) lapse in their basic mental faculties. The reason most philosophers think that it’s irrational to take revenge is that there’s no way to undo the wrong that was done to you in the past. If Person A did something truly horrible to Person B, that thing doesn’t get undone when Person B does a new horrible thing to Person A. And if that’s the case, why do it? Doing it is all cost and no benefit.In this episode, Emily Dupree argues that in fact, it can be rational to take revenge. How come? It isn’t all cost and no benefit, because in some cases, successfully taking revenge can lead to a unique benefit: namely, the restoration of the vengeance seeker’s moral personhood. For the unique benefit to come, certain background conditions have to hold: the original harm has to have been genuinely morally wrong, it has to have been as egregious as it can be (so it can’t be minor/inconsequential), it has to have taken place under conditions of the political state failing, and it has to have undermined the vengeance seeker’s moral personhood. In that case, it is possible for an act of vengeance to be intelligible as an attempt on the part of the vengeance seeker to get their moral personhood back. Note that our guest isn’t saying the vengeance seeker is right to seek vengeance in these circumstances. The view is just that seeking vengeance under these circumstances can be comprehensible, rather than just bonkers.Tune in to hear our guest discuss some historical examples of revenge that we can comprehend!Matt Teichman