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Minisode: Absolutely Nothing
3.7k Plays5 months ago
In this episode of Breaking Math, Autumn and Gabe explore the concept of nothingness and its significance in various fields. They discuss the philosophical, scientific, mathematical, and literary aspects of nothingness, highlighting its role in understanding reality and existence. They mention books like 'Incomplete Nature' by Terence Deacon and 'Zero: The Biography of a Dangerous Idea' by Charles Seife, which delve into the concept of absence and zero. The episode concludes by emphasizing the complexity and versatility of nothingness, inviting listeners to think deeper about its implications.
Keywords: nothingness, philosophy, science, mathematics, literature, reality, existence, absence, zero
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Transcript
Introduction to Nothingness in Mathematics
00:00:00
Speaker
Welcome back to Breaking Math, the podcast where we crack the code on even the most baffling mathematical concepts. I'm Autumn Feneff. And I'm Gabrielle Hesh, your host of today's mini episode. We're tackling a concept so mind bending that it might leave you speechless. We're diving into vast emptiness, the great unknown, nothing. Nothingness, believe it or not, plays a so surprisingly fascinating role in math, from sets with no members to the hunt for the ultimate zero. The absence of something can actually reveal a whole lot. So buckle up, math lovers. But before we begin, we have a few tiny announcements. Autumn, they they aren't so tiny. All right. I guess you're right.
00:00:46
Speaker
In two weeks, we have a big surprise for you, episode 101. We can't wait to tell you about it, but until then, you can support us by signing up on our Patreon at patreon dot.com forward slash Breaking Math. We also have uploaded almost all of our episodes to YouTube. A few even have videos. So if you go to youtube dot.com forward slash at Breaking Math Pod, you'll find our YouTube page. Believe it or not, Breaking Math is taken by another creator. who I'm sure has very thoughtful things to say about math. And you'll see both our audio only as well as our videos as well. There's a video on Sora. There's also a video with my interview with Levi McLean about the math of music and neuroscience. So there'll be a lot more up there soon.
00:01:32
Speaker
Um, also we have an open call. I want to let you guys all know this right now among our listeners. I'm sure we've got a lot of enthusiastic or enthusiastic mathematicians and scientists and engineers who tune in. We want to hear from you. We have an open call for all, as I said earlier, mathematicians, scientists and engineers who want to talk about their work. to email us at breakingmathpodcast at gmail dot.com or you can fill out a link in the show notes below. Now join us on this mini episode of breaking math. We're going to break down nothing, but first a message from our sponsors.
Defining Nothingness in Philosophy and Science
00:02:21
Speaker
Let's take a minute to talk about the classic Alice's Adventures in Wonderland by Lewis Carroll. As it states, take some more tea, the march here said to Alice very earnestly. I've had nothing yet, Alice replied in an offended tone. So I can't take more. You mean, you can't take any less, said the Hatter. It's very easy to take more than nothing. So, what is nothing? On the surface, it might seem simple, but as we dig deeper, we'll find that nothing has a rich tapestry of meanings across different fields. Let's start by exploring its philosophical roots.
00:03:10
Speaker
In philosophy, nothing often refers to the absence of anything. It's a state of non-existence or the void. Philosophers have pondered this concept for centuries, debating whether true nothingness can ever exist. It's a topic that touches the very core of metaphysical discussions about reality and existence. For example, when we think about the universe before the Big Bang, we might imagine or try to imagine a state of nothingness But what was it really? was Was it really empty or just beyond our comprehension? Nothingness haunts being, an awesome quote by Jean-Paul Sartre.
00:03:46
Speaker
Moving on to science, the definition shifts a bit. In physics, nothing might refer to a vacuum, a space devoid of matter. However, even in a particular vacuum, quantum physics tells us that there are still quantum fluctuations and fields at play. so Can we ever truly achieve nothing in a scientific sense? This remains a hot topic in modern physics.
Zero and Emergent Phenomena in Mathematics
00:04:18
Speaker
Now, if we look at mathematics, nothing is symbolized by zero. It represents the absence of quantity.
00:04:28
Speaker
Zero is a powerful concept that revolutionized mathematics and science. It's the cornerstone of algebra, calculus, and beyond, allowing us to represent and manipulate the idea of nothing in a tangible way. Consider the following examples. In his book, Incomplete Nature by Terrence Deakin, ah Deakin argues that the concept of absence of something can still have a very powerful effect. Deakin argues that just as the concept of zero transformed mathematics, thinking about life, mind, and other intentional phenomena in terms of constraints, that is to say, what is lacking, what is absence, can similarly help us resolve the artificial divide of the mind-body problem. A clear example of this idea is that the hole that defines the hub of a wagon a wheel.
00:05:15
Speaker
The hole itself is not a physical entity, but a source of constraints that limits the possible configurations of the wheel's components, allowing the property of rolling to emerge on a global scale. Constraints that produce emergent phenomena cannot be fully understood by examining the individual ah components of a pattern. Emergent phenomena are challenge to study are challenging to study because of their complexity it does not really easily break down into parts. When a pattern is deconstructed, the constraints are not really active. like that There is no hole, ah no absence to actually observe. ah Imagine a hub or a hole for an axle that only exists when the wheel is rolling. Breaking the wheel wouldn't really reveal how the hub emerges.
00:05:58
Speaker
you know, essentially what Deacon is saying here is that in complex systems, you have emergent property that that that really can only be meaningfully described or observed when the whole process is working together. And we're limited in in terms of our ability to take those those parts, ah you know, apart and analyze them one by one. And the central theme of this entire book here is that consciousness itself, The idea of a conscious self is something that emerges ah where there's an absence. it it There's an implied self that doesn't really exist apart from the material components, but it really only exists, at least according to Deacon here.
00:06:37
Speaker
uh in the interplay of our neurons and and our brain and all of the mapping functions that are that our brain does to make sense of reality in itself that somewhere among that ongoing process a sense of self ah emerges which is uh controversial to say the least maybe a little uncomfortable i'm not going to lie uh about that, but um that's that's his idea in his book, Incomplete Nature. Now, similarly, this parallels with the concept of zero.
Historical Journey of Zero
00:07:07
Speaker
This is where I want to talk about one of my favorite books of all time. This book was introduced to me by my little brother when he was, I want to say, in 9th or 10th grade, I believe. ah The book came out, um um oh my gosh, 20 years ago-ish, I want to say. The book is called Zero, The Biography of a Dangerous Idea, and it's by Charles Sief. Autumn, have you heard about Zero before? Yes, a little bit. okay Okay, so I'm not the first person that brought up this book to you then, am I? No. Okay, this is an exciting part ah where where you see these overlapping topics in different books. and So not only do we have the discussion of what's missing in the book, Incomplete Nature, um
00:07:45
Speaker
but But when you read Zero, the biography of a dangerous idea by Charles Sief, it it overlaps it very, very well. And it just it presents it in a unique way. So in Zero, the biography of a dangerous idea, um it's it's a ah nonfiction popular science work by American journalist Charles Sief. It was first published back in February of 2000 by Viking, which is a division of Penguin Random House, um which is not to be confused with Random Penguin House. sorry the name is and When Penguin merged with Random House, they just made it Penguin Random House. Seif, who is currently a journalism professor at the new at New York University, received great acclaim for his debut book. And this book explores the origins and the history of the concept of zero in philosophy and math and science. And major themes in the book include the perilous nature of zero,
00:08:38
Speaker
its role in unlocking the mysteries of nature as it's used in black holes, as well as its inter twly or intertwining with concepts of infinity, especially as it's used in mathematics such as calculus, which is completely integral, no pun intended. to understanding physics. Yeah, yeah. So, Saves Books is a chronological survey of zero. It covers mathematical, philosophical, and scientific aspects. It examines early numbering systems. It examines the Western rejection of zero. It's influenced by figures like ariss and Aristotle, the eventual acceptance of zero in Eastern and Islamic civilizations,
00:09:16
Speaker
And the book discusses contributions of key individuals such as Fibonacci, René Descartes, and Blaise Pascal. It also traces the evolution of mathematical concepts ah like calculus and imaginary numbers. see also explores impacts on the physical sciences from thermodynamics to quantum mechanics and the Big Bang Theory. The book concludes by highlighting zeros or the the role of zero in modern scientific inquiry and its significance in understanding the universe's expansion.
00:09:48
Speaker
ah There are five appendices and so many illustrations throughout the book to help clarify the kind the complex ideas for readers. The book's very accessible, unlike the book by Terrence Deacon, which has so many $50 words in it. I mean, I enjoy reading it. Don't get me wrong. I'm kind of a I'm kind of a glutton for punishment when I read. I like, you know, almost inaccessible literature and looking up all the words. But the book, you know, Zero, The Biography of a Dangerous Idea is very accessible. My brother enjoyed it as a ninth grader. And, you know, it's not even that long. I didn't
Zero in Calculus and Philosophical Challenges
00:10:22
Speaker
count how many pages. Did you by chance count how many pages? It was like 130, 150-ish.
00:10:28
Speaker
Yeah, yeah, yeah. And it gives a ah very accessible look at just the idea of zero in philosophy and math. So really, I recommend this book to anybody. It's very accessible. So phenomenal, phenomenal book. um Now, I want to tell you guys really quickly about how Charles Chief describes how it's used in calculus. What I what I appreciate about this book is that Sif really spends a lot of time emphasizing how important zero is in the discovery of calculus and what calculus allows for. Sif implies that there's this mystic art to calculus that go and he goes so far as to say that it bypasses reason and goes into the realm of faith
00:11:09
Speaker
simply because it, according to SIF, again, I'd say according to SIF, it apparently uses illogical operations such as dividing by zero, as well as summing infinite zeros to get a sum greater than zero. Now, these are not, I don't think you would find a pure mathematician today who would necessarily agree with that at a technical level. But certainly calculus was used, and it was used regularly and assumed to be true long before it was rigorishly defined with you know strict definitions. I mean, anytime you throw you throw infinity into the mix, you you get all kinds of weird things that, you know as Steve implies here, seem to bypass logic. So I certainly appreciate that. And and I still think it is
00:11:52
Speaker
You know, I think it's not insignificant that we adopted calculus before we had a real understanding of dividing, you know, of of the break in logic. I think right now we describe it as using limits, like the limit as n goes to infinity or as n goes to zero. And that that in a way, I call that a hand wavy way of technically avoiding and dividing by zero. But at the same time, um I don't know. I don't know. I kind of feel like, ah you know, Newton and others of his time kind of just swept the whole divide by zero under the rug and
Math Paradoxes and Infinity
00:12:28
Speaker
didn't think about it. You know what I mean? You just kind of just kind of they just go away. So I agree.
00:12:32
Speaker
ah Yeah, yeah. And you know even to to this day, like the the mysticism is not lost on me. Even on a computer, you can't integrate because you know you know ah with with with both machinery that uses countable elements or even pixels on a screen, I don't care you know how high definition your screen is. It could be 4K or 8K. You still have a limitation there. You're still just a bunch of really, really small pixels. You can't have an infinite K
00:13:03
Speaker
um Screen and calculus works under the assumption that you can have an infinite K. Oh, I shouldn't say for the case cream You know and and an infinite amount of something and um but that's just a working assumption that happens to be very useful as we're describing Instantaneous changes in time, you know Um, so yeah, I still feel uncomfortable with calculus, full disclosure, and it's not because I can't integrate. I can integrate and do derivatives and understand those very, very, very well. I understand the assumption here. I'm just uncomfortable at a philosophical level with like, really? Really? We were we're really just playing with infinity. Like it's, you know, one of the, uh, one of the infinity stones literally. Okay.
00:13:48
Speaker
I would be a little bit worried if you did not know how to do calculus and you were doing a math podcast. Yeah, yeah. No, no, no. All I'm saying is that I acknowledge the absurdity of dealing with infinities here. Now that I think about it, we should have an infinity gauntlet, but have it have like, you know, the six hardest math paradoxes. You know what I mean? So like Cantor's infinite series set. What would be the other, what would be all of the infinity stones in a math infinity gauntlet? I don't know. What do you think? You just made my brain just go boom. Okay. Fair enough. Fair enough.
Nothingness in Culture and Literature
00:14:27
Speaker
ah Maybe, maybe imaginary numbers. I mean, you know, those are pretty cool. Yes. Gosh. Non euclidean geometry. Well, I don't know. I wouldn't, I wouldn't put non euclidean geometry quite at infinity stone level epicness here. You know what I mean? I think e to the i pi.
00:14:44
Speaker
That proof, yeah, e to the i pi equals negative one or e to the i pi plus one equals zero would certainly be one of the infinity stones here on your math gauntlet where you could snap and make new realities or something. so Okay, help us get creative here. what are What are the biggest math paradoxes that could go onto our math infinity gauntlet? And I'm trying not to use the word infinity too much here. Obviously, Cantor's infinite set series, you know what I mean? But just like maybe n or maybe ah p equals np, you know, that that whole conjecture. Yes. Something about, you know, with the collapse conjecture, that would be our, our you know, mathematics gauntlet here.
00:15:26
Speaker
so Okay. Hey, we warned you this would be an episode about nothing. So if you're listening to this thing, where's the substance? Well, well, there you go. There you go. That's exactly what we set out to do. Precisely. So, so, okay. Okay. Here. Uh, let me, let me, uh, pass, pass the baton on, on, on, on. Okay. I actually know there's, there's actually a lot more, a lot more to say here. Sorry here. I have this awesome script here. Give me a second.
00:15:58
Speaker
Okay. um Now, let's bring this whole discussion back to everyday language. When we say there's nothing in the box, we simply mean the box is empty. It's a straightforward practical use of the word that we all understand. ah Sometimes nothing is the best we can do, which is an unknown is you know unknown said that I think unknown and nothing You know, there's the political party that know nothings, but yeah, it's unknown who said that. In logic and computing, nothing can represent a null value, an absence of data. um This is crucial in programming and database management where null values indicate missing or undefined information. I'm going to pass the baton on to you here. Nellis Inferba, which is the Royal Society's motto, meaning take nobody's word for it.
00:16:44
Speaker
That summarizes that completely. Now. Oh, sorry. Nothing more to s say on that. Right.
00:16:54
Speaker
You're like the king of dad jokes right now. and Now, literature often uses nothing as a theme to explore deeper human experiences. Think about existential works where and nothing symbolizes nihilism, emptiness, or the void of human life. It's a powerful literary tool that evokes strong emotions and reflections. It also reflects a storm known as The Nothing, which is the main antagonist in the never-ending story. It's a power which destroys Fantastica, one of the worlds in the story, bit by bit absorbing it.
00:17:38
Speaker
But the truth is the result of humans, which no longer believe in the world of fantasy. And without their beliefs, fantasies disappearing, leaving nothing behind. This also kind of reminds me of ah believing in Tinkerbell in Neverland. Okay. So you you must believe in fairies. Yeah. Fair enough. So this is almost the same concept of nothing. We're kind of like ah in the Polar Express, you know the belief in Santa Claus and all that. um It brings you to the North Pole. Yeah, exactly. You find the Polar Express.
Conclusion and Gratitude
00:18:20
Speaker
But with these big concepts, where does it really leave us? Nothing is far from simple. It's a versatile concept that stretches across philosophy, science, mathematics, literature,
00:18:35
Speaker
religion and everyday conversation. It challenges our understanding and invites us to think deeper about existence and the nature of reality. Yeah, we help this exploit odious sorry we hope this exploration of nothing has sparked your curiosity and made you think about this seemingly simple concept in new ways. Don't forget to subscribe and leave a review if you enjoyed the show. Join us next time as we we dive deeper into another fantastic episode. Until then, I'm Gabrielle Hesh. And I'm Autumn Fenev, and we can take this mini-sode as a perception of reality or an illusion until the next time on Breaking Math.
00:19:15
Speaker
you