Youtube comments of (@AWellRestedDog).
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@theaverageinternetuser6852 Hello, thank you for your comment, and I'm glad to hear that this video helped you in some way. It sounds like you have a lot on your plate... qualifying for the Math Olympiad Program (or things like it) is so impressive, and I'd imagine that it comes with a lot of pressure!
I hope you remember that whatever you're going through now is not permanent. Your worries won't ever completely go away, but they will change form. I really wish someone told me this when I was 15, so I'll just say it to you now: you're dealing with very heavy stuff, and you're doing good! You are just as much of an adult as anyone else is.
Also, I hope you can take some breaks every now and then and go for a walk, meet someone new, write down your thoughts, and maybe spend some time not thinking about math, existence, or whatever it is. If you like reading philosophical books or want to have a try reading them, I recommend reading Kierkegaard's "Lily of the Field and Bird of the Air" (this one is short, and comforting! I read it when I'm overwhelmed), and "The Sickness Unto Death" (this one is longer and so so dense. It changed how I viewed myself and my close relationships, but it's a little like reading math--it only started to make sense when I worked my way through every page very slowly, by connecting the abstract ideas to real experiences I've had).
(Also, you might like watching a cute but ominous animated youtube series called ONE, by Cheesy Hfj)
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That's one of the cons of trying to fit a millennium's worth of history into 30 minutes lol.
And that is a good question. Bressoud goes into this in more detail in chapter 2.1 of "Calculus Reordered," but I'll try to give a "quick" version of it:
I don't know what the trigonometry functions were written as, but the astronomers who used them would have wanted tables of all known approximate values of sin and cosine. To make these tables, they probably realized that
sin(30) = 1/2 is easy and known,
sin(3) = sqrt[(1-cos(6))/2] is difficult but possible to derive,
but sin(33) is really really difficult to get an exact answer for--
so using some trig manipulation rules, they approximated sin(33) by "nudging" the sin(30) by sin(3); they split sin(33) = sin(30+3) = sin(30)cos(3)+cos(30)sin(3).
Aryabhata realized that instead of "nudging" sin(θ) by sin(3), you can "nudge" it by some small sin(dθ). Thus the change between sin(θ) and sin(dθ) is:
sin(θ+dθ) - sin(θ)
= sin(θ)cos(dθ) + cos(θ)sin(dθ) - sin(θ)
= sin(θ)(cos(dθ) - 1) + cos(θ)sin(dθ)
as dθ -> 0, cos(dθ) -> 1, so sin(θ)cos(dθ) - 1) -> 0
thus sin(θ+dθ) - sin(θ) = cos(θ)sin(dθ); as sin(dθ) = dθ for small angles (you can graph y=sin(x) and y=x to see that y=x is a good approximation for sin(x)), this may as well be written as
sin(θ+dθ) - sin(θ) = cos(θ)dθ
and finally, [sin(θ+dθ) - sin(θ)] / dθ = cos(θ). Which is practically screaming the definition of the derivative at you.
Hope this partial plagiarism of Bressoud helped!
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Thank you, and I'm glad you could feel that delight for life in the morning! (I don't think my introduction is enough to trigger a genuine existential crisis, unfortunately. I guess it's there to make people try to remember what a crisis feels like)
Also, that is a compelling reading of Adam and Eve (and I am very happy that someone is interested in considering alternate arguments)! I do agree that it makes sense to think that Eve ate the fruit to become like God and gain power, wisdom and immortality like him. However, I think that if you accept that to have been her motivation, then it is difficult to accept that she and Adam felt any kind of "open and connected" love toward each other. If Eve felt open love for Adam, I don't think she would have wanted the power of wisdom that the snake promised her (why gain power and risk destroying the peace you have when you are content with your life?)--the quality of "innocence" seems to be at odds with the action of intentionally striving for power. So if you do take a desire for power/knowledge to be an explanation for Eve's decision, I think it only makes sense to say that they didn't feel love very deeply.
So if we accept that Eve wanted power, I think it makes more sense to read Eve as a calculating actor, weighing the benefit of power against the threat of death. I do admit this rational approach does not reflect actual human decision making (for example, Eve could have just been clueless and merely acted because she was told to, which would be a convincing way of understanding what it means for her to be "innocent"), but I chose this approach toward analysis because I think this way of thinking is what led to the adoption of an "existentialist" perspective in the first place. Existentialism as I understand it tries to react against the hyper-rationalizing tendency of the culture from which it arose out of. Thus, I tried to adopt a hyper-rational analysis of Adam and Eve to see where and how the existentialism could have arisen (in other words, where the idea of wisdom and faith came from).
If you somehow had the patience to read this comment, I think you may find my extra commentary (go to the link in the description) interesting. I'd love to talk more if you have any other ideas (and you can email me if you'd rather communicate there instead of through this video's comments section). Thank you for your curiosity!
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@sourish.biswas The books I talked about in this video are ones I'd recommend! I'll also add Nietzsche's On The Geneology of Morality, which you will probably read if you major in philosophy.
If you are interested in metaphysics and natural philosophy, you may enjoy reading Descartes' Meditations on First Philosophy, Correspondence between Descartes and Princess Elisabeth (these are kind of classics of the beginnings of metaphysics!), Selected Philosophical and Scientific Writings of Emilie du Chatelet (this is a collection of works by an elite woman, who was friends/lovers with Voltaire. I think she wrote the "first" physics textbook), and Kant's Prolegomena to Any Future Metaphysics (this is a much more accessible version of Critique of Pure Reason). Also, one comment: these writers will talk about forming the foundations of science and society in many strange ways. You may notice a lot of metaphors alikening metaphysics to the infrastructure of a city. I find these kinds of more "literary" aspects of philosophical texts to be just as informative and interesting as the theoretical parts--I encourage you to pay attention to them, if you like!
I hope you have fun in college, and meet lots of cool people to talk with! As for myself, I don't think I'll make videos any time in the next few years about metaphysics/natural philosophy. If I do, it will probably be centered around how the enlightenment changed societal roles.
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I do think this is from a secular view, but like all of Western philosophy in general, heavily inspired by Christianity. The pattern that this series is about, which is often called "existentialism", originated in one form as a response to the dominating culture of Christianity (through Kierkegaard, whose view I emphasized in this video) and in another form as a response to mass culture (through Nietzsche, who I will talk about in the next video). I think both origins are crucial to understanding what this pattern is actually about (actually, both origins highlight the two sides of the same coin of existential crisis), and in order to do that, I have paid particular attention to some of the ideas that became popular in Christianity in this video.
The other parts are unfortunately far from being finished (hopefully part 2 can be released over the summer, but I can't guarantee). But if you are curious to know where this pattern is going, in a nutshell, existentialist writers seem to agree that our self-understanding has been polluted by our desire for control, and something like Kierkegaard's idea of faith (which can be understood as a willing giving up of control, which I don't think necessarily has to be understood religiously) needs to be taken seriously. This is what I mean by "wisdom" and "faith" must come together. If you are curious, I would recommend reading the sections of the books that I outlined in the commentary, and then to pick up and read Notes from Underground (Dostoevsky) and Beyond Good and Evil (Nietzsche).
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@user-ll4cu5dh3b Thanks for the comments. I'll admit that my characterization of faith, especially around 43:23-43:38, splits from Kierkegaard's faith, and that my presentation was a bit deceptive--in hindsight I should have saved those comments for the conclusion section. My goal in that part was to try to identify some element of Kierkegaardian faith that makes faith so important to him (as opposed to making no movement in the first place, or of just infinite resignation). Like I said in the video, I personally found it difficult to understand what Kierkegaard was saying, but I had some idea of a secular version of faith that I could characterize with "hope". That being said, I don't think that your description is all that far from how I characterized faith in my video: I don't think I confused infinite resignation with faith on the basis of relying on reason to derive faith (of course, I may be misremembering what I said).
Even if I secularized Kierkegaard, the thing I cared about in the video was to evoke some intuitive sense of the incredible hope and active fight against reason that the knight went through. I feel like identifying that part of Kierkegaardian faith--that feeling of "hope" or intense "passion"--is what really matters for my conclusion about "gaining strength to live through death". Of course, I'm not sure how useful my characterization of faith, which was inspired by Kierkegaard, is for my weird theory of wisdom and faith.
And yes, I'll also admit that my example about Eve being "faithful" was flawed. I'll continue to think about if it interfered with my goal of trying to understand what the feeling of "existential crisis" is.
Also, I hope I made it clear that I am not trying to pretend to be an expert on anything I talked about. At the time of the video, these ideas were only a few months into being developed, and thinking back now I feel like my ideas were confused (and still are confused). I don't agree with (or honestly remember) everything I said in the video, but I hope that I was able to get some intuitive impression across that there is this really interesting pattern of reacting to death by finding some way to reason our way into being immortal, and that while it is easy to get sucked into those abstract, reason-led ideas of immortality or meaning, at the same time we seem to all care about this completely irrational thing like faith, and maybe those two blurry concepts--reason/wisdom and faith, interact together to make up our human experience. I don't know.
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That's a very valuable perspective as well, but I think that's a different (but related) conversation than the one this video is about. More than just reacting to death, the thing I'm interested in is reacting to an overwhelming "crisis" in general (with death as one clear example of it). Even if someone is immortal (for example, the greek gods), they still experience the crisis of losing power (which to them, is just as terrifying as dying). The way they might react to that crisis, and the way they can live a good life in the face of that crisis, is what this video is about.
The idea that we can overcome death by becoming immortal addresses the particular "problem" of death but sidesteps the actual crisis. We still need to deal with what to do when we come across some crisis that is completely out of our control (for example, say we do become literally immortal, but the society we live in is unjust. How do we deal with the infinitely meaningful problem of living an immortal life in horrible conditions?) In that case, we will need not just the wisdom to overcome death, but the faith to experience happiness despite the uncontrollable situation we find ourselves in. I think existentialist literature/philosophy is more interested in this kind of thing than in the pragmatic question of how to (and if we even should) become immortal.
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@sourish.biswas Disclaimer: I'm not an expert, I'm just sharing what I learned from a college course I took. The ones I recommended are all great for if you want to learn about the foundations of physics and metaphysics. My understanding is that the philosophy of physics was called "natural philosophy" in the 1500-1700s, and "began" as an attempt to explain things like movement, fire, and with Newton, gravity. Metaphysics developed because while doing physics, people disagreed on what counted as a good explanation versus a bad explanation, and they disagreed with what humans are able to understand in the first place. People like Galileo, Descartes, Locke, and so on tried to establish what humans can understand and what counts as a good explanation. The books I recommended earlier on some in this tradition that stand out to me, but you can find more if you dig. I think some people like to start with Descartes, which you can find in English or pretty much any language.
On another note, it seems that you may also enjoy watching Sabine Hossenfelder on youtube, who is a physicist who dabbles in everything, including metaphysics-y stuff! She has two books, one called "Existential Physics: A Scientist's Guide to Life's Biggest Questions," and another called "Lost in Math: How Beauty Leads Physics Astray." I haven't read either of them, but I'd imagine that they are good places to start, if the 300+ year old books are a bit daunting to you!
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@@KarminsLynn That's a valid concern. My short response to this is, "Sure, I agree."
But since I find this concern interesting, here's a longer response: I do think there is a difference between "tarot reading"-like interpretations and interpretations that use an existentialist perspective to reexamine an ancient story. The former seems to make conclusions about life by free association (I don't know how tarot readings work, but this is generally what I think a "bad" literary interpretation is); the latter tries to "test" a perspective and structure of analysis against a legendary story, to see what parts of ancient thought are still influencing the modern perspective. For example, Adam and Eve could remind me of some friends I have, Alex and Emily, who I think lives a life that balances between wisdom and faith; thus I might conclude that this is a fundamental trait of all humans. This is a bad interpretation, as opposed to what I did in this video, where I tried to see if the pursuit of wisdom and faith can convincingly explain what Adam and Eve did. Because I was convinced, I concluded that there is great potential in understanding wisdom and faith as a fundamental trait in humans. Although this is the same conclusion, I think this is a valid interpretation whereas the other one is not. The key difference is that this interpretation tests my version of existentialism against that story, to see if the story that has been understood by many cultures to capture some truth about the human condition is consistent with an existentialist perspective. It seems to me that it is, and that is why I made the conclusion that wisdom and faith are "fundamental".
However, I do admit that the line gets blurred, and I think that the question of "what is a valid interpretation and use of a story?" is a real debate in literary theory.
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@robertwallace5498 This is a good question! I understand your question as being, "Why can we cut a circle into as many slices as we want? If we have a circle in real life, say, we have a pizza, then we can't cut the pizza into a googleplex number of slices, because there is no pizza big enough or pizza cutter thin enough to make that many slices in real life. So why can we assume that we can do that to a circle?"
If this is your question, my response is that the circle we are thinking about does not exist in any kind of physical space, but in an imagined "perfect" space. In this imaginary space, we assume that if you have any 2D shape A, you can make a shape B that is smaller than A. In other words, you can cut any shape into as many pieces as you want.
This assumption is actually a version of Archimedes' Principle: if you have a quantity a, there exists a quantity b such that 0<b<a. Here's the connection between Archimedes' Principle and cutting up shapes. Imagine that a shape A has area a. Then there exists a shape B with area b, such that 0<b<a. So, basically, the reason why we can keep cutting a circle into a googleplex slices and beyond is because we assume that the circle lives in an imaginary space that satisfies the Archimedes Principle.
One last thing: you say, "Doesn't this already assume infinity?" In short, yes. The Archimedes Principle is "assuming infinity" in this one really specific way (for any given quantity a, there is a smaller quantity b). But it "assumes infinity" in an imaginary space where a perfect circle lives--it doesn't assume infinity in "real life." In "real life" there is no such thing as a perfect circle and the Archimedes Principle may not hold (I mean, there's probably nothing smaller than a quark, right?). But we still think about imaginary spaces where there are perfect circles and where Archimedes' Principle holds because it lets us understand what are the consequences of thinking in a certain way. Say that it was possible to cut a shape into as many slices as we want; what happens then? That's one of the things that makes math different from physics; as I understand it, physics tries to explore how the "real world" works, while math tries to explore how the basic ideas that we can have work!
I hope this long comment helps. You can ask more questions if you have them!
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Thinking back on the video, I agree with you that the way I used the story of Adam and Eve didn't make much sense. The point I was trying to make was that in the moment of eating the fruit, Adam and Eve's lives were fundamentally changed, so the decision to make that change must have been incredibly difficult for them. But, to make that point, I assumed that Adam and Eve were aware of their lives and were in active rebellion against their old ways of living. This assumption is not trivial because if Adam and Eve were "innocent" before eating the fruit of knowledge, they shouldn't have been aware that they were in active rebellion. The meaning of eating from the tree of knowledge is also not specified, allowing for my kind of messy analysis of the story.
I don't think I agree with the specific point I was trying to make anymore; Adam and Eve, for instance, could easily have made the decision to eat without feeling the weight of it, so it doesn't necessarily mean that they were in the anguish that I described in the ~39:30 part.
That aside, I still think, maybe a bit stubbornly, that the overall idea I was trying to highlight is interesting. Namely, the idea that changes in life (for instance, Adam and Eve eating from the tree of knowledge) can be considered "fundamental" when they make what it means to live unrecognizable from before, and that existential crises are when humans relate in some way to the fundamental changes in their lives. I think my understanding of this point was fuzzier when I wrote the script for this video, and I started to go down a path that won't work out.
Thank you for your keen comments!
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Those are some fair points, and I'm glad that you felt dissatisfied by my video. Now, by your second sentence, are you saying that not all humans care about being immortal? For example, not all humans want their name (or their children, or their philosophical impact on the world) to represent their long-lasting influence on the world, so using Achilleus, Abraham and Diotima as representations of the human condition is flawed? If something like this is what you are saying, I agree with you that this is a sad way of understanding humans. (If it is not, then please correct me and clarify what you mean).
You said that "Death gives value to living[...]If you recognize the value of living then you would live, if not you would die." It seems that you are saying that humans only live when they realize that they are going to die (because living is to value living, and you value living because you will die). I think this is similar to what I tried to say in chapter 4, and which I summarized with "Through death you can get faith, and through faith you can live more" (43:42-43:46).
What I meant when I said that I liked when I was dying was something like what you said: there is something about death that gives life value, and maybe the reason is because death forces you to experience faith. This nagging feeling that maybe something about death gives value to life is actually what is at the core of this whole investigation, and I'm glad that you seem to agree that this is worthy to think about.
Thank you for the challenging comment. I am surprised that someone who says that they would rather watch a TikTok short than my video seems to have actually sat through a good chunk of my 50 minute long video.
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