#the mathematician's notion of beauty
Explore tagged Tumblr posts
geometrymatters · 1 year ago
Text
Tumblr media Tumblr media Tumblr media Tumblr media Tumblr media
The geometry of the Borromean Rings
Borromean rings are a captivating geometric structure composed of three interlinked rings. What makes them unique is their interdependency; if any one ring is removed, the entire structure collapses. This fascinating property, known as "Brunnian" linkage, means that no two rings are directly linked, yet all three are inseparable as a group. This intricate dance of unity and fragility offers a profound insight into the nature of interconnected systems, both in mathematics and beyond.
Borromean Rings and Mathematical Knots
Borromean rings also find a significant place in the study of mathematical knots, a field dedicated to understanding how loops and tangles can be organized and categorized. The intricate relationship among the rings provides a rich visual and conceptual tool for mathematicians. Knot theorists use these rings to explore properties of space, topology, and the ways in which complex systems can be both resilient and fragile. The visual representation of Borromean rings in knot theory not only aids in mathematical comprehension but also enhances our appreciation of their symmetrical beauty and profound interconnectedness.
Symbolism and Divinity in Borromean Rings
Throughout history, Borromean rings have been imbued with symbolic significance, often associated with divinity and the concept of the trinity. In Christianity, they serve as a powerful visual metaphor for the Holy Trinity – the Father, the Son, and the Holy Spirit – illustrating how three distinct entities can form a single, inseparable divine essence. This symbol is not confined to Christianity alone; many other cultures and religions see the interconnected rings as representations of unity, interdependence, and the intricate balance of the cosmos.
Borromean Rings as a Metaphor for Illusory Reality
Beyond their mathematical and symbolic significance, Borromean rings offer a profound metaphor for the nature of reality itself. They illustrate how interconnectedness can create the illusion of a solid, stable structure. This resonates with philosophical and spiritual notions that reality, as perceived, is a complex web of interdependent elements, each contributing to an overarching illusion of solidity and permanence. In this way, the Borromean rings challenge us to reconsider the nature of existence and the interconnectedness of all things.
99 notes · View notes
anocana · 8 months ago
Text
went back to read "unreasonable effectiveness of etc." now that I have real opinions on phil of math. I think it's genuinely mysterious that many parts of the world are relatively simple and consistent. but when it comes to mathematics specifically, the root of the issue is he seems to think mathematicians sit in a tower jerking off to a completely contentless notion of beauty. if we look at what makes things mathematically interesting, it's something like:
useful for studying the real world, or
useful for studying something mathematically interesting
which can be disguised by many mathematicians' preference for subjects high up the ladder of (2).
7 notes · View notes
frank-olivier · 9 months ago
Text
Tumblr media
Beyond the Numbers: The Philosophy of Mathematics and Reality
The relationship between mathematics and reality is a topic that is continually debated among philosophers and scientists. Some argue that mathematics is a human construct, while others believe it is a discovery that reveals the underlying structure of the universe. A conversation with Carl Bender, a mathematician and physicist, shed light on this topic and explored the role of mathematics in understanding the world.
Bender's work on perturbation theory and asymptotic series has contributed significantly to the solution of complex physics problems, especially those related to quantum mechanics. His research has demonstrated the importance of complex numbers for understanding the behavior of particles at the atomic and subatomic level.
The conversation touched on the history of complex numbers, from their initial development as a mathematical concept to their modern applications in physics and engineering. Bender discussed the key milestones in the development of complex numbers, including the work of the 16th century Italian mathematician Girolamo Cardano.
Bender's work also extends to the field of PT-symmetric quantum systems, a relatively new field of research that has attracted much attention in recent years. These systems have unique properties, such as non-Hermitian Hamiltonians, that have led to new insights into the behavior of particles.
During the conversation, Bender shared his thoughts on the role of beauty in mathematical discovery. He noted that the aesthetic appeal of mathematical theories and equations can guide research and lead to new discoveries. This idea is not unique to Bender, as many mathematicians and scientists have long believed that beautiful theories are more likely to be true.
Bender's perspective on the role of beauty in mathematics is interesting, especially given his interactions with Richard Feynman, a renowned physicist known for his work on quantum mechanics. Feynman's approach to problem solving, which emphasized simplicity and creativity, likely influenced Bender's own research and teaching.
The conversation with Bender raised questions about the nature of reality and the role of mathematics in understanding it. If mathematics is a discovery that reveals the underlying structure of the universe, what does that say about the nature of reality itself? Is reality a fixed, deterministic entity or a complex, ever-changing web of probabilities and possibilities?
Bender's work on PT-symmetric quantum systems suggests that reality may be more complex and nuanced than previously thought. These systems challenge our classical notions of space and time and offer a glimpse into a world where the laws of physics are different from those we are exposed to in everyday life.
Carl Bender (Escaped Sapiens, May 2024)
youtube
Tuesday, October 15, 2024
4 notes · View notes
yourdailyanticistamines · 1 year ago
Text
Tumblr media
Yves Saint Laurent: Transparencies - Part 2
Near the end of the exhibition, we got to see the working space of Yves Saint Laurent, which had mostly been preserved since his retirement and death. It was one thing to see his works, which were polished and complete, but another to see his office that was cluttered with books, sketches, and fabrics. It was like being inside his brain. As I stood inside the place where Saint Laurent made history, I felt admiration and awe.
I realized soon after that the emotions I felt there were the exact same as what I felt when I visited the graves of famous mathematicians earlier in the morning at the Cimetière du Père-Lachaise. Math is a lot like fashion, in that the specifics are highly technical, but the value of the finished work is almost entirely dependent on subjective notions of beauty, creativity, and novelty, which are heavily determined by current trends. At least, that is how it is in a short timeframe, but only the works that are truly beautiful stand the test of time. Joseph Fourier died in 1830; his name frequently appears in three different math and physics classes I’m taking this semester, and I will most likely be doing things that are heavily based on his work for the rest of my life. It’s the same with fashion - people will probably still remember Christian Dior’s New Look or Coco Chanel’s little black dress hundreds of years from now.
Looking for graves of significant people, especially mathematicians, physicists, artists, and composers, is a regular hobby of mine. I wasn’t exactly sure myself why I like grave hunting until I visited Saint Laurent’s office and Fourier’s grave - I think I have a desire to leave something beautiful and timeless in the world too.
4 notes · View notes
averycanadianfilm · 4 months ago
Text
 What Is a Quantum Field Theory? - Michel Talagrand
Okay, so I've looked at a 'preview' of this book. Those interested in quantum field theory may want to take a look for themselves.
Here's what several experts say about Talagrand's book (from Talagrand's webpage https://michel.talagrand.net/endorsements.pdf):
"This book accomplishes the following impossible task. It explains to a mathematician, in a language that a mathematician can understand, what is meant by a quantum field theory from a physicist's point of view. The author is completely and brutally honest in his goal to truly explain the physics rather than filtering out only the mathematics, but is at the same time as mathematically lucid as one can be with this topic. It is a great book by a great mathematician."
-- Sourav Chatterjee, Stanford University
"Talagrand has done an admirable job of making the difficult subject of quantum field theory as concrete and understandable as possible. The book progresses slowly and carefully but still covers an enormous amount of material, culminating in a detailed treatment of renormalization. Although no one can make the subject truly easy, Talagrand has made every effort to assist the reader on a rewarding journey though the world of quantum fields."
-- Brian Hall, University of Notre Dame
"A presentation of the fundamental ideas of QFT in a manner that is both accessible and mathematically accurate seems like an impossible dream. Well, not anymore! This book goes from basic notions to advanced topics with patience and care. It is an absolute delight to anyone looking for a friendly introduction to the beauty of QFT and its mysteries."
-- Shahar Mendelson, Australian National University
"I have been motivated to try and learn about quantum field theories for some time, but struggled to find a presentation in a language that I as a mathematician could understand. This book was perfect for me: I was able to make progress without any initial preparation, and felt very comfortable and reassured by the style of exposition."
-- Ellen Powell, Durham University
"In addition to its success as a physical theory, Quantum Field Theory (QFT) has been a continuous source of inspiration for mathematics. However, mathematicians trying to understand QFT must contend with the fact that some of the most important computations in the theory have no rigorous justification. This has been a considerable obstacle to communication between mathematicians and physicists. It is why despite many fruitful interactions, only very few people would claim to be well versed in both disciplines at the highest level.
There have been many attempts to bridge this gap, each emphasizing different aspects of QFT. Treatments aimed at a mathematical audience often deploy sophisticated mathematics. Michel Talagrand takes a decidedly elementary approach to answering the question in the title of his monograph, assuming little more than basic analysis. In addition to learning what QFT is, the reader will encounter in this book beautiful mathematics that is hard to find anywhere else in such clear pedagogical form, notably the discussion of representations of the Poincaré group and the BPHZ Theorem. The book is especially timely given the recent resurgence of ideas from QFT in probability and partial differential equations. It is sure to remain a reference for many decades."
-- Philippe Sosoe, Cornell University
0 notes
bookeysnewsletter · 1 year ago
Text
The Book Chaos: A Comprehensive Summary of Chaotic Science
Tumblr media
Chapter 1 What's The Book Chaos by James Gleick
"Chaos: Making a New Science" is a non-fiction book by James Gleick that explores the emerging field of chaos theory and its applications in various scientific disciplines. The book delves into the history of chaos theory, from its early beginnings with mathematician Edward Lorenz and his discovery of the "butterfly effect" to its widespread influence in fields such as meteorology, biology, and physics. Gleick explains complex concepts in a clear and engaging manner, making chaos theory accessible to readers of all backgrounds. Through a series of fascinating case studies and interviews with key figures in the field, Gleick shows how chaos theory has revolutionized our understanding of the natural world. Overall, "Chaos" is a captivating exploration of a groundbreaking scientific theory that has fundamentally changed the way we think about complex systems and the unpredictability of nature.
Chapter 2 The Book Chaos by James Gleick Summary
"Chaos: Making a New Science" by James Gleick explores the emerging field of chaos theory and its implications for understanding complex systems. The book delves into the history of chaos theory, from its roots in the mathematician Edward Lorenz's work on weather prediction to its applications in various fields such as biology, economics, and physics.
Gleick explains how chaos theory challenges traditional notions of predictability and order by showing how seemingly random or chaotic systems can contain underlying patterns and structures. He introduces readers to key concepts such as fractals, strange attractors, and the butterfly effect, which illustrate how small changes in initial conditions can lead to drastically different outcomes in dynamic systems.
Throughout "Chaos," Gleick uses engaging storytelling and clear explanations to make complex scientific ideas accessible to a general audience. The book showcases the innovative thinkers and experiments that have shaped chaos theory, while also discussing the philosophical and cultural implications of this new way of understanding the world.
Overall, "Chaos" is a thought-provoking and captivating exploration of a groundbreaking scientific theory that has revolutionized our understanding of complexity and unpredictability in the natural world.
Tumblr media
Chapter 3 The Book Chaos Author
James Gleick is an American author, journalist, and biographer, known for his works on the cultural impact of science and technology. He released the book "Chaos: Making a New Science" in 1987, which explores the emerging field of chaos theory and its implications for understanding complex systems.
Apart from "Chaos," Gleick has also written several other books, including "Genius: The Life and Science of Richard Feynman," "The Information: A History, a Theory, a Flood," and "Time Travel: A History."
Among these books, "The Information" is considered one of Gleick's best works in terms of editions, as it has received critical acclaim and won the Royal Society Winton Prize for Science Books in 2012. Additionally, it has been translated into multiple languages and continues to be widely read and studied in the field of information theory.
Chapter 4 The Book Chaos Meaning & Theme
The Book Chaos Meaning
The book "Chaos: Making a New Science" by James Gleick explores the field of chaos theory and how it has revolutionized our understanding of complex systems. Gleick delves into the history and development of chaos theory, introducing readers to key figures in the field and explaining the principles behind chaotic systems. He also demonstrates how chaos theory can be applied to a wide range of disciplines, from meteorology to biology to economics.
Overall, "Chaos" by James Gleick emphasizes the interconnectedness and unpredictability of the world around us, challenging traditional views of order and determinism. The book highlights the beauty and complexity of chaos theory, showing how it can help us better understand the natural world and our place within it. It encourages readers to embrace uncertainty and complexity, rather than fear it, and to appreciate the inherent chaos that shapes our lives.
The Book Chaos Theme
One of the main themes of James Gleick's book "Chaos" is the idea that seemingly random or chaotic systems can actually have underlying order and patterns. Gleick explores the concept of chaos theory and its implications for scientific fields such as mathematics, meteorology, and biology.
Another theme of the book is the interconnectedness of complex systems and how small changes or fluctuations in one part of a system can have far-reaching effects on the system as a whole. Gleick discusses how chaos theory has changed the way scientists and researchers understand and study dynamic systems, leading to new insights and discoveries in various disciplines.
Overall, "Chaos" emphasizes the beauty and complexity of chaos theory and its potential to revolutionize our understanding of the world around us. Gleick highlights the importance of embracing uncertainty and acknowledging the inherent unpredictability of complex systems, while also recognizing the hidden order and structure that can emerge from chaos.
Tumblr media
Chapter 5 Quotes of The Book Chaos
The Book Chaos quotes as follows:
1. "Chaos theory is a new way of looking at the world. It's about fractals, strange attractors, and the Butterfly Effect. It's about the way systems change and evolve over time."
2. "In chaos theory, small changes can have big effects. The tiniest perturbation can cause a system to go haywire, leading to unpredictable and chaotic behavior."
3. "Chaos is not randomness. It's a kind of order in disguise, a hidden pattern lurking beneath the surface of chaotic systems."
4. "Chaos theory challenges our assumptions about predictability and control. It tells us that the world is a complex and unpredictable place, where even the smallest actions can have far-reaching consequences."
5. "Chaos theory is a tool for understanding complex systems, from the weather to the stock market to the human brain. It helps us see patterns in the chaos, and make sense of the seemingly random events around us."
6. "Chaos theory is a revolution in science, a new way of thinking about the world. It's about embracing the unpredictable and finding beauty in the chaos."
7. "Chaos theory teaches us to embrace uncertainty and complexity. It's a way of thinking that challenges our assumptions and expands our understanding of the world."
8. "Chaos theory is about finding order in chaos, and beauty in complexity. It's a way of looking at the world that celebrates the unpredictable and the unexpected."
9. "Chaos theory is not just a scientific theory, it's a philosophy of life. It teaches us to embrace the chaos and uncertainty of the world, and find meaning in the unpredictability of everyday life."
10. "Chaos theory is a powerful tool for understanding the world around us. It's about embracing the complexity and unpredictability of nature, and finding beauty in the chaos."
Chapter 6 Similar Books Like The Book Chaos
1. "The Great Gatsby" by F. Scott Fitzgerald - This classic novel explores themes of wealth, privilege, and the American dream in the 1920s.
2. "To Kill a Mockingbird" by Harper Lee - A timeless story of racism, justice, and moral growth in the American South, this novel is a must-read for all.
3. "Pride and Prejudice" by Jane Austen - This beloved novel follows the evolving romance between Elizabeth Bennet and Mr. Darcy, set against the backdrop of early 19th century England.
4. "1984" by George Orwell - A dystopian novel that explores the dangers of totalitarianism and the power of language, this book is as relevant today as when it was first published.
5. "The Catcher in the Rye" by J.D. Salinger - This coming-of-age novel follows the adventures of Holden Caulfield as he navigates adolescence and the complexities of adulthood.
Book https://www.bookey.app/book/chaos
Author https://www.bookey.app/quote-author/james-gleick
YouTube https://www.youtube.com/watch?v=3orIIcKD8p4
Amazom https://www.amazon.com/Chaos-Making-Science-James-Gleick/dp/0143113453
Goodreads https://www.goodreads.com/book/show/64582.Chaos
0 notes
fractyll123 · 1 year ago
Text
Culture is a Fractal: The Beauty of Patterns in Human Life
Tumblr media
In the vast tapestry of human existence, culture emerges as a complex and intricate pattern, much like a fractal. Just as fractals exhibit self-similar patterns at different scales, culture too reveals itself in various aspects of life, from the grandest traditions to the smallest daily rituals. This notion of culture as a fractal offers a profound insight into the nature of human society, its diversity, and its unity.
The concept of a fractal, a geometric shape that can be split into parts, each of which is a reduced-scale copy of the whole, was popularized by mathematician Benoit Mandelbrot. He described fractals as "a way of seeing infinity." Similarly, culture can be seen as an infinite series of interconnected patterns, each reflecting the whole in its own unique way.
Fractalize
When we "fractalize" culture, we see that it is not a monolithic entity but a collection of smaller cultural elements that repeat and evolve over time. Just as a fractal pattern repeats itself at different scales, culture manifests in various forms, from the broad strokes of national identity to the intricate details of regional customs. Each layer of culture builds upon the others, creating a rich tapestry of meaning and tradition.
Fractals and art
Fractals and art share a deep connection, as both seek to capture the complexity and beauty of the world around us. Artists have long been inspired by the intricate patterns found in nature, which often exhibit fractal-like qualities. From the branching of trees to the spiral of a seashell, these natural patterns have influenced artistic expression for centuries.
In the realm of human culture, art serves as a mirror, reflecting the values, beliefs, and experiences of a society. Just as fractals reveal hidden symmetries in nature, art can reveal hidden truths about our own cultural landscape. Whether through painting, sculpture, music, or literature, artists have the power to illuminate the fractal nature of culture, revealing its beauty and complexity in new and unexpected ways.
Culture Fractal
One striking example of fractals in art is found in the work of African American artist, Romare Bearden. His collages, such as "The Dove" and "The Block," are composed of small, repeated elements that come together to form a larger, cohesive whole. Like a fractal, these works invite viewers to explore their intricacies, discovering new details with each viewing.
In addition to visual art, fractals have also found expression in literature. Authors like Jorge Luis Borges and Italo Calvino have explored the idea of infinite recursion in their writing, creating stories within stories that echo the fractal nature of culture itself. In Borges' famous short story, "The Garden of Forking Paths," the protagonist discovers a novel that is also a labyrinth, a metaphor for the endless possibilities of human experience.
Culture is a Fractal
Fractals can also be seen in the rituals and traditions that define a culture. Just as a fractal pattern repeats itself at different scales, cultural rituals often have both local and global significance. For example, the act of sharing a meal with family may be a small, everyday ritual, but it also reflects larger cultural values of community and hospitality.
In conclusion, the concept of culture as a fractal offers a powerful lens through which to view the complexity and beauty of human life. Just as fractals reveal hidden patterns in nature, culture reveals the interconnectedness of human experience, from the smallest gestures to the grandest traditions. By fractalizing culture, we can better appreciate its richness and diversity, recognizing that each individual is a part of a larger, infinitely complex whole.
0 notes
mybookof-you · 1 year ago
Text
The evolution of flowering plants is what made mammals possible — creatures capable of photography and poetry — and yet flowers are now evolving to bloom less. Metabolically costly since the start, producing blossoms to attract pollinators is now becoming prodigal as pollinator populations are rapidly declining. Instead of relying on pollinators, many bisexual species — the botanical term for which is perfect flowers — are evolving to fertilize their own seeds with their own pollen: a process known as selfing. Its haunting downside is that, because diversity is nature’s fulcrum of resilience, flowers pollinated by selfing replicate their own genes in the next generation of seeds, amplifying their existing vulnerabilities to disease and drought — something cross-pollination prevents by mixing the DNA of different plants into new, adaptive combinations of genes. (I am reminded of Iris Murdoch’s lovely notion that beauty and art grant us an opportunity for unselfing, disrupting the ruminative replication of our beliefs and mental states with something magnificently other — and what is psychological resilience if not the ability to see beyond our suffering, and what is compassion if not the ability to step outside the self and take in the other with a gasp of tenderness.)
0 notes
jucomx · 5 months ago
Text
I've learned about this in my mathemathical logic course, and done a bit of research about it myself. I am not an expert on this by any means (just an undergrad who really likes algebra/logic), but i think i can give a satisfying explanation. However i will take shortcuts so this post doesn't become a 20 page "why mathemathical logic absolutely FUCKS" essay.
The answer that is sufficient for category theory is the following:
Because we cannot have a set of all sets and have that set behave like a set (in particular we cannot perform comprehension on a set of all sets by Russels' paradox), we fix a set that contains enough sets to work with, in particular a set within which any set constructions (union,power set, image of a map ...) are also included, and then operate within that set. The fixed set is a universe, and proper classes are subsets of that set which are not elements of it.
Of course we could then pick another set which contains these sets and the respective constructions of those sets, so to prove anything about all sets, you have to prove it independently of the picked universe. This set theory is known as Grotendieck Universes, and technically you therefore work in U-categories, of U-sets, with object classes being U-classes. Unless you're getting really into the set theory of category theory it is safe to drop the "U-" since the entire paper is probably universe polymorphic then.
Outside of logic and set theory i will personally always assume Grotendieck Universes is a consistent set theory, because for me that is the easiest theory to visualise and it coincides well with the notion of a "set".
Now if you want i can go deeper about the nondefinability of universal truth, and in proof theory or model theory (which is essentially proof theory except we assume ZFC is true). It is really beautiful but you have to be open for it because it can really fuck with your view of Mathematics as a whole.
Once I understood Set theory is not the study of this well definable object called a set (like most of Algebra is), my mind was positively obliterated and i think it is benefucual for any mathematician to learn. It really puts things into perspective, and it is nicely humbling in terms of the "what i'm doing is science except 100% accurate" type rethoric.
I never really understood this business of classes and sets. I get that certain collections cannot be called a set (for instance, the Russell's Paradox). Ok then what exactly are classes? Do they behave like sets? Why should I care if a category is small !!
11 notes · View notes
paganimagevault · 3 years ago
Text
Tumblr media Tumblr media Tumblr media Tumblr media Tumblr media
The Pentagram of Pythagoras
"Pythagoras was the first of the great teachers of ancient Greece. Born in 580 B.C., Pythagoras became one of the most well known philosophers and mathematicians in history. Creating the Pythagorean Brotherhood, his teachings greatly influenced Socrates, Plato, and Aristotle. Pythagoras is considered as the first pure mathematician; he also founded a community/society based on religion and science. He is most widely known as the author of the Pythagorean Theorem. Some even venture to believe that the word “philosophy” was invented by Pythagoras. He claimed to be a lover of wisdom, for which the Greek word philo means love and Sophia means wisdom.
The Teachings of Pythagoras revolved around the idea that when considering the deepest level, reality is essentially mathematical in nature. Pythagoreans believed there was a system of principles that existed behind numbers. The principles form a foundation for many concepts of traditional Western thought. One of his most basic notions revolves around the symbolism and beauty associated with the Divine Proportion.
The shape of the pentad follows as the symbol of life itself. The pentad consists of all previous numerical symbols: monad’s point, the dyad’s line, the triad’s surface, and the tetrad’s three dimensional volume. The pentad also refers to the well known five point star. The pentad arises in the existence of our five fingers, five toes, the symbol that wards off evil, and a symbol for power and immunity. Because of the importance of the pentad, the construction of the symbol was first kept secret from society. The pentad was used as a secret sign among the Pythagoreans for them to distinguish themselves and recognize other members.
The pentad’s symbolism can be directly related to the Divine Proportion. And the regeneration of the pentad is related to the value of phi (Ф). The image of the pentad is found in nature in leaves and flowers. The Greeks believed each point of the pentad to represent an element: water, earth, air, fire, and idea.
At any rate all his [Pythagoras'] school in serious letters to each other began straightway with 'Health to you,' as a greeting most suitable for both body and soul, encompassing all human goods. Indeed the Pentagram, the triple intersecting triangle which they use as a symbol of their sect, they called 'Health'.
Johannes Kepler (1571-1630) wrote: "Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel."
...
"The axial structure of B-DNA is shown in Figures 2 and 4. The rotation of each base pair by 36◦, in the canonical B-DNA molecule, gives a complete 360◦ rotation every 10 base pairs and results in a decagonal structure and ten-fold rotational symmetry. These properties alone relate the axial structure of the molecule to Φ. Although a molecule with a decagonal form might be expected to show some simple relationship to Φ, and while there is always a danger in seeing patterns where there may be none, the axial form of B-DNA is neatly encompassed by 10 “golden diamonds” (refer Figure 1), the template of which is shown in Figure 4B, and overlaid on Figure 4A such that points (a) and (c) are located on the outermost hydrogens and point (b) is between the outer oxygen atoms."
...
"The ancient Greek followers of the mathematician Pythagoras kept the shape as their secret symbol, a signifier of wholeness or divine blessing. Nature.
The pentagram was a symbol, but also a window of sorts. It's not a shape so much as it is a relationship. Within it we find the Golden Ratio.
The Ratio is noted for both its seemingly fundamental aesthetic appeal and its (seemingly) persistent recurrence in natural and manmade systems, from plant biology to financial markets to human DNA.
It's a way of cutting up a line that appears to be preferred by nature, anyhow. Note that every time a line crosses another line, as in the sketch below, it results in a Golden Ratio relationship between the two resulting segments. So, follow a pentagram edge down until it hits the start of another point; that corner is a Golden joint of sorts.
It's possible to connect the points of a pentagram to come up with a new pentagon and, from the new pentagon, a new pentagram. And this can go on forever:
Presumably, the Pythagoreans spent a whole lot of time staring deeply into pentagrams. Tradition has it that a young Pythagorean, Hippasus of Metapontum, was doing just that when he happened up the first proof of the existence of irrational numbers, a startling revelation for the "all is number" crowd.
Hippasus noted what you see above, that the inner core of a pentagram is a pentagon, and inside of that could be found a new pentagram. Clearly, this went on pretty much forever. And it had to, which is what was eventually proved by the Greek.
Imagine Hippasus gazing into the trippy arrangement of nested pentagrams above. Each one lives within a pentagon, with its dimensions limited by that pentagon. All of these shapes clearly live within some hard and fast relationship; they define each other. That relationship is what we'd normally think of as a ratio. One shape is to the other as some quantity a is to some quantity b."
-taken from jwilson.coe.uga.edu, MDPI, freemasonrymatters, and vice
Sources and more detailed descriptions on my blog post: https://paganimagevault.blogspot.com/2022/05/the-pentagram-of-pythagoras.html
65 notes · View notes
Text
An old friend
My memory of our first conversation is not entirely clear -- in some places I remember it clearly, and in others I find it very vague, but not necessarily less so for that reason. I remember the first thing about her that struck me, but I've forgotten since.
I have a strong memory of a short, thin, dark-haired girl who was dressed like a scientist. She wore some sort of a lab coat, or lab gown, or lab coverall, maybe, and was always looking up into a microscope or something. (I don't actually remember the details of her clothes or hair, at least not clearly.) This struck me as strange, given that her face was visible on most occasions. If I had met her and then seen her for the first time some time later, there would be no memory of her outfit, which had disappeared in my mind to make way for her face.
I had read the account of this first meeting as part of one of my mandatory reading assignments in an upper-level college course. The topic was an early work of John von Neumann, who had apparently had a sort of rivalry with Kurt Gödel, which I didn't understand -- the textbook had a long section about them, and at one point the text said that they were "neurotic" and that "they had a deep antipathy, which in the end led to a violent feud." At the time I assumed this was something similar to, and yet somehow incompatible with, what I knew of mathematicians.
Now, though, when I look up the history of that feud, I find that their rivalry may have actually been more like what I imagined it, and my textbook more of a garbled version of what they actually said about each other. It is not at all clear from the text itself that von Neumann and Gödel ever got involved in a feud. What the textbook describes seems instead to be a very professional and cordial rivalry. The textbook quotes a letter from von Neumann that began, "Dear Dr. Gödel," and the textbook does not say that this letter ended in violence.
Nonetheless, the memory of that first conversation has the atmosphere of a violent feud. I remember not just the thin scientist who wore a lab coat, but an entire culture, entire social class, with its history and its customs and its values. And I remember this only because I remembered the moment when that culture, that class, was disrupted. Something happened that destroyed them and remade them all into... something else. What was the word that got used in the letters? Something that was more like an identity than an outfit.
It was all of a sudden so vivid to me that the idea of this old friend (I don't know if I would have called her old, but let it pass) was that the thing I had known her as was gone. Was gone. Gone, and replaced by a new thing she would never be able to understand.
I did not immediately make any attempts to contact her at all, since my first reaction was just, "Why would I do that?" I was just struck by the very notion of any effort. But then the culture she lived in vanished and was replaced with some foreign thing she wouldn't be able to understand either. And so I decided to find out whether that was indeed true.
The culture she lived in was not quite gone, exactly -- but it was on the road to disappearance. It was a culture that existed in one location, on a campus, that existed in a specific age of human history, that existed as part of a subculture. It was not just that it was gone, but that it was no longer a single thing. It had grown. It had grown, like a plant, or like a culture, so that it was no longer just about that one location, just in the area of that one location, but it had grown and spread far away.
Her campus was not much different from any other campus on any other planet in any other age. If there were "genders" in this planet, they weren't nearly so different from the ones I've seen in my travels. There was one part of it, which was not just the campus but a particular quadrant, which was particularly beautiful and strange, which was in many ways a very special place. And there were other parts of it, which were much less pretty and special, which were not even part of the quadrant but just somewhere on that campus. And then there was another campus, which was the rest of it. So many quadrants, with parts of them not being part of any quadrant at all.
It was a kind of life that one might have, it turns out -- the life of one who lives in a campus which is also a quadrant, which is really part of a much bigger quadrant, but is not in any quadrant, not just of a quadrant, and which does not live there -- but is a kind of quadrant-of-a-quadrant-of-a-quadrant (the quadrants that one gets are not as nice as the ones I've seen). When one lives in a campus that is just a campus that is just a campus that is just a campus, and not some kind of quadrant-of-a-quadrant-of-a-quadrant or a quadrant-of-a-quadrant-of-a-campus, then there is not much one can do, because there is no culture outside of one's campus.
It was not a life that I would have wanted to live myself, and this fact seemed to me very strange, and to demand explanation -- what would such a culture look like? A culture of people who wore lab coats and had long hair and were studying mathematical objects called "sets"? And it turned out that was the explanation, at least the beginning of the explanation. There was not only no culture of this type, but it was hard to imagine a way for such a culture to exist. These people, these people wearing lab coats studied sets.
I knew about sets from my college course. They were special, I had learned -- they were the objects of mathematical study, the very basic objects of all of mathematics. You could build up all sorts of things out of them -- other sets, other things that were defined in terms of sets, different ways of defining those things, sets that would be useful for studying other kinds of things. But there was no actual universe out there, in the physical world, that was any sort of set. If you tried to imagine one, you would quickly run into problems, like the fact that there was nothing but sets, and no one to study them.
That did not seem strange to me, because of my familiarity with this one particular subculture that I had known from one of my college courses. But now there were two subcultures in place on this campus. There were people who wore lab coats, who studied sets. There were other people, who wore clothes and studied some other kind of sets. But there weren't any sets, out there, to be studied. There weren't any universes out there which were sets, but no one knew what it would mean for them to exist. There weren't any people living in universes, but no one knew how to live in them. They weren't just, and it wasn't as if they weren't more than, and I didn't really understand what it meant to understand "more than" and "more than" and "more than" and "more than."
There was something there, in the campus quadrants, in those lab-coat people, in that sense of "more than," and there was something else there, farther away, something which no one even could understand.
We could never meet again, as people living in quadrants in a campus
4 notes · View notes
rhetoricandlogic · 4 years ago
Text
Tumblr media
Stories of Your Life and Others - Ted Chiang
A book review by Danny Yee
© 2011 https://dannyreviews.com/
The stories in Stories of Your Life and Others tackle big ideas intelligently, in the grand tradition of science fiction. They postulate some fundamental change in how the world works and explore its implications through the experiences or challenges faced by their protagonists.
"Tower of Babylon" is set in a Mesopotamia where there really is a vault of heaven for a tower to reach. In "Understand" an experimental drug makes the protagonist really, really intelligent, capable of understanding not only the world but his own mind. And "Division by Zero" is about a mathematician who discovers that arithmetic is inconsistent.
In "Story of Your Life" a linguist is drafted to help decipher the language of heptapod aliens. Interspersed with the narrative of her linguistic discoveries are vignettes of her lifetime relationship with her daughter. At first these two strands appear to have no connection at all — and their link turns out to be indirect, involving variational approaches to physics and a different kind of consciousness, challenging our notions of memory and free will.
"Seventy-Two Letters" is set in a 19th century England where industrialisation is kabbalah-inspired, with automata (golems) manufactured by applying names to sculptures. And reproduction works in accordance with preformationist theory, with tiny homunculi recursively nested inside sperm. This is mixed up with some politics, involving eugenics and class tensions, and some action. "The Evolution of Human Science", originally published in Nature, is less a story than an abstract speculation about how human science might react to a "metahuman" population with a superior but incommunicable knowledge system.
In "Hell is the Absence of God" angels regularly visit the earth, dealing out miracles (and incidental damage); statistics are kept on the results, and on the fraction of people who are taken to Heaven or condemned to life in Hell, without God. The lead character is desperate to learn how to love God so he can rejoin his dead wife in Heaven; two other characters face rather different challenges.
Presented in a documentary format, with short perspectives from different people, "Liking What You See" is set in a near future where it's possible to reversibly modify people's brains so that they don't perceive beauty or ugliness in faces. A progressive university is debating whether this, known as calliagnosia, should be a requirement for students.The significant novelties involved in Chiang's stories require some serious suspension of disbelief, but he manages this well. He doesn't dwell on the presuppositions or back-story, attempting to justify the impossible, but rapidly introduces the setting and elaborates on it only as much as is necessary for the plot and the exploration of ideas. (The occasional exceptions are jarring, for example in "Story of Your Life" when some nonsensical argument is presented to explain why the aliens haven't learned anything from human television broadcasts.)
None of the characters have much depth. They are driven by intellect rather than emotion and their personalities presented from the outside, fairly clinically. A focus on their understanding of the world is arguably necessary for the elaboration of the story ideas, however, and there's only so much that can be fitted into a short story. (I am not convinced that Chiang could produce a decent novel using the same approach.)The plots work effectively, both in unfolding the implications of the central ideas and in holding the reader's attention. This is true both in the stories with straightforward chronological narratives and in the more unusually structured ones, with resolutions provided by a mix of goal seeking, problem solution, and structural cadence.Stories of Your Life and Others is the most entertaining and thought-provoking collection of science fiction stories I've read for a long time.
4 notes · View notes
transgenderer · 9 months ago
Text
hmm, i think this argument holds if you grant total relativism/subjectivism of knowledge/experience/beauty/etc but i dont think you should grant that! this is an argument towards valuing societies only by the material comforts they provide. and dont get me wrong, those material comforts are great and significant! but i think its a mistake to reject the notions of beauty or knowledge? to only value our subjective experience of those things, and not those things themselves. its a wireheading argument, or stronger, an argument towards willful simulationism, everyone existing in simulated fantasy worlds that they think are real.
knowledge is good because it feels good, but its not JUST good because it feels good, it's also good because...its true! its good to believe true things instead of false things! beauty is good because it feels good, but its not just good because it feels good, its good because its beautiful! its good for things to be beautiful.
what i want to express is an...adulthood. we're adults! we're full people! we dont need to be in a coddled world where we think we're expanding the frontier of human knowledge when we're actually just reinventing the wheel for the millionth time, to pass this knowledge on to no one because then they wouldnt get to discover it for the first time themselves. like...discovering something yourself is FUN, and sometimes worthwhile because it helps you understand it more intimately. but the feeling of discovering something yourself is not the point, at least not the full point. its like...life is not pretend! it's a real thing! we're playing for real, when we look at a painting we're ACTUALLY experiencing the painting, the painting is ACTUALLY beautiful or not, it actually has specific aesthetic traits that are or are not achieved by specific other works of art
maybe i expressed myself wrong in the first post, by focusing on aesthetic and intellectual satisfaction. i dont mean the experience of being deluded that you are cultivated, i mean the experience of actually being cultivated!
and EVEN from the subjectivist perspective, while we can acknowledge different works affect different people differently, this does not force us to grant that all SETS of works are equally good at inducing aesthetic pleasure to any population. i dont know why we would grant that! surely a larger, more diverse set of works is better at inducing aesthetic pleasure in a given population, precisely because the people are different from each other! and similarly with the experience of knowledge, EVEN if we grant that we only want to be deluded into believing we are discovering, a culture that provides more "hooks" to pull you towards a more diverse boundary of knowledge provides intellectual pleasure to a larger variety of preferences! where is the place for the archeologist, the microbiologist, the mathematicians, the author, the director, in a hunter gatherer society! would we be no worse if we outlawed 95% of art forms?
i mean. okay. from one perspective, this idea of "taking values seriously" is a bit silly. we're post-existentialist, we know all values are made up, and its only about pleasure or whatever. but like, man, idk. SHOULD we grant that? i dont know that we should! its true that the idea of "real" values is difficult to ground. but i think to the extent we are using our common sense to reason philosophically, we should listen to that common sense when it tells us something! and like, that common sense tells us to care about what is true, and what is beautiful. and we can ignore it, but the thing that tells us to ignore it isnt really in stronger epistemological ground than the thing that tells us to believe it!
So the standard argument against primitivism is about food and medicine. I'm not talking about that argument. Grant for a moment hunter gatherer life, minus famines and infectious disease. I think this life is still much less valuable than life in modern society, and I think this gets at a broader question I struggle with, of "calibrating" our idea of what makes life worth living by history
OK, so what is valuable in life? In my subjective experience, it's mostly beauty and knowledge. Or maybe, as experiences, aesthetic satisfaction and intellectual satisfaction. Learning new things, reading good books, making art, listening to music, going to museums, taking classes, all that stuff.
And Hunter gatherer life is just..worse for this? I mean sure, they genuinely had a lot of free time. But their options were so paltry, for what to do with that time! They lived...not "in nature" in a literal sense, because they influenced their environment so much. But in an unconstructed environment, say. And that's beautiful! The unconstructed environment is beautiful. But like. I can go to that too! And sure, they had an encyclopedic knowledge of their local area. But like. If they wanted to learn other stuff, they were out of luck! That sucks! And they could make art, listen to stories, but surely beauty is so much more than this! Their options were so limited. They could only make with the circumscribed supplies available. And they can see beautiful things, but only those made by their culture, or some nearby ones. Some HGs had long trade routes, but surely almost all of them were only seeing local art. Spending your whole life, only knowing one culture! No reading, just storytelling. Nothing wrong with storytelling, but surely the form of the book allows other things, it's better to have both!
But the point of this post is not anti-primitivism, it's trying to calibrate what I hold valuable. Because it troubles me, to know that the vast majority of human lives were so relatively impoverished in valuable experience. Most people were illiterate, couldn't learn on their own by getting a book. Most people never saw a great painting. They saw sculpture, but only the best in their village. Surely such a life is missing the most valuable parts? But that seems wrong. It seems silly to conclude that most human lives were so much less lived than ours. Surely it was possible to live a good life, as a hunter gatherrer, or a peasant. I mean, obviously it probably wasn't possible to live a good life as like...a slave. I'm not saying ALL lives should have been possible to live well. But surely *most*!
I think the issue here is that actually, most people find human relationships the most valuable part of life. And ofc those were always available. But I'm not sure I get this perspective. I like my human relationships, but I like them for beauty and knowledge reasons. They say interesting and funny things, they teach me things they've read about, they expound new perspectives, they find holes in my logic. But if it was just us, if we weren't all bringing new interesting things from outside some closed community, that would suck! I wouldn't find that nearly as valuable. So that wouldn't be sufficient, for me. But maybe it would be, for most people?
132 notes · View notes
perkwunos · 4 years ago
Text
Aristotle, I have been told, has said, that Poetry is the most philosophic of all writing: it is so: its object is truth, not individual and local, but general, and operative; not standing upon external  testimony, but carried alive into the heart by passion; truth which is its own testimony, which gives strength and divinity to the tribunal to which it appeals, and receives them from the same tribunal. Poetry is the image of man and nature. The obstacles which stand in the way of the fidelity of the Biographer and Historian, and of their consequent utility, are incalculably greater than those which are to be encountered by the Poet, who has an adequate notion of the dignity of his art. The Poet writes under one restriction only, namely, that of the necessity of giving immediate pleasure to a human Being possessed of that information which may be expected from him, not as a lawyer, a physician, a mariner, an astronomer or a natural philosopher, but as a Man. Except this one restriction, there is no object standing between the Poet and the image of things; between this, and the Biographer and Historian there are a thousand.
Nor let this necessity of producing immediate pleasure be considered as a degradation of the Poet's art. It is far otherwise. It is an acknowledgment of the beauty of  the universe, an acknowledgment the more sincere because it is not formal, but indirect; it is a task light and easy to him who looks at the world in the spirit of love: further, it is a homage paid to the native and naked dignity of man, to the grand elementary principle of pleasure, by which he knows, and feels, and lives, and moves. We have no sympathy but what is propagated by pleasure: I would not be misunderstood; but wherever we sympathize with pain it will be found that the sympathy is  produced and carried on by subtle combinations with pleasure. We have no knowledge, that is, no general principles drawn from the contemplation of particular facts, but what has been built up by pleasure, and exists in us by pleasure alone. The Man of Science, the Chemist and Mathematician, whatever difficulties and disgusts they may have had to struggle with, know and feel this. However painful may be the objects with which the Anatomist's knowledge is connected, he feels that his knowledge is pleasure; and where he has no pleasure he has no knowledge. What then does the Poet? He considers man and the objects that surround him  as acting and re-acting upon each other, so as to produce an infinite complexity of pain and pleasure; he considers man in his own nature and in his ordinary life as contemplating this with a certain quantity of immediate knowledge, with certain convictions, intuitions, and deductions which by habit become of the nature of intuitions; he considers him as looking upon this complex scene of ideas and sensations, and finding every where objects that immediately excite in him sympathies which, from the necessities of his nature, are accompanied by an overbalance of enjoyment.
William Wordsworth, Preface to Lyrical Ballads
9 notes · View notes
blue-lions-baby · 5 years ago
Text
Operation Confession (Dimitri x F!Reader) [Ch. 3] [FINALE]
hi!! well, this is it. the final chapter of operation confession. to be very honest, with everything going on it was quite difficult to write this, but i hope the quality is still relatively the same as my previous chapters! i had so much fun writing this series, and i hope reading it was just as entertaining! thank you so much for sticking with it-- it means the absolute world to me :)
this will prob be my last post for a bit before i head off to college; please rest assured i do not plan to leave this blog or this wonderful community anytime soon! thank you for being patient with me as i adjust to this very new chapter of my life!!
without further ado, please enjoy ch. 3!
~*~
“Hey, false alarm!” Sylvain traipsed back in, hands behind his head. “(F/N) and Felix are actually gonna freshen up a bit before heading to dinner.”
Groans and angry huffs spilled out of the frazzled Lions; the menacing stares that the redhead bore made him squeak, and he cleared his throat.
“Hey, look, I’m sorry! They ran into us while His Highness was changing--”
“While he was changing?” Dedue and Ingrid looked like they were about to have a stroke.
“I-It’s a long and,” Sylvain looked at The Hand, “painful story, but what’s important is that they didn’t see him! All thanks to Yours Truly.”
“You were a blubbering idiot. The only reason why (F/N) didn’t bother questioning you further was because she was too tired to care.” Felix joined in, the permanent scowl on his features deepening.
“Felix!” Sylvain’s countenance lit up joyfully before hazing into confusion. “Wait, I thought you were gonna freshen up before heading to dinner.”
“I don’t need to. Hardly broke a sweat during training.”
“W-What?! How?!”
“I guess you wouldn’t understand, seeing as how your only form of exercise is chasing after anything that wears a skirt.”
Sylvain’s eyes took on a glossy, hollow quality as the Lions hollered in laughter.
“Uh... So Sylvain, where’s His Highness?” Asked Annette, having expected him to walk in.
“Oh, he ran back to his quarters to put his clothes away. He should be coming back any minute now.”
♠ ♥ ♣ ----------------------------------------------------------- ♣ ♥ ♠
After neatly hanging his uniform in his closet and giving himself a quick once-over in the mirror, he gave himself one last pep talk before swinging the door open and--
Seeing the side of your head as you idly engaged in conversation with a fellow student.
Oh Sothis, help him.
As quickly (and loudly) as he opened the door, he closed it and promptly went back inside to scream into his pillow. Where in the world did you even come from? Weren’t you supposed to be ‘freshening up?’ Your quarters weren’t even down this hallway; what in the Goddess’s name were you even doing here?
He pressed his ear further into the door, straining to pick up bits and pieces of your conversation in hopes to inform himself on your sudden visitation. Nothing. All he could hear was muffled banter bouncing between either of you-- muffled banter that didn’t sound like it was going to end any time soon. He screamed curses in his head and awkwardly slid down onto the floor, lightly banging his cranium against the solid wooden door.
He desperately wished for someone, anyone to save him.
He sighed while rubbing his temples-- a desperate attempt to quell the arising headache. Dimitri combed through his options, each less viable than the last. After eliminating any and all half-baked ideas of escape, he was face-to-face with the one option he didn’t want to consider.
Sit here and wait until you left.
So Dimitri sat (more like paced) in his room, occasionally pressing his ear against the door in hopes that he didn’t hear your lighthearted banter outside. Why was it the one time he didn’t want to run into you, there you were! Right outside his door. You might as well have come with a giant bow on your head!
The floor beneath him rumbled slightly, pulling him from his thoughts; the even pacing grew stronger and stronger until it stopped just a little ways past his door.
“(F/N).”
Wait... That’s... It’s unmistakable! That has to be--!
“Dedue! Hello!”
“I apologize for the interruption, but I have come to remind you that it is your turn to tend to the greenhouse today.”
A short pause ensued, followed by an audible gasp.
“Wait, yes! You’re right! I’ve completely forgotten, thank you so much for reminding me!”
Dimitri heard muffled apologies and goodbyes sputter out of your lips, followed by light footsteps scurrying away. Your former companion proceeded to engage in very light talk with the Duscur man before quickly excusing themselves from the scene; Dedue, glancing down the hall to ensure that no one else was nearby, approached and gently rapped his lord’s door with calloused knuckles.
“Your Highness, you may come out now.”
The inner mechanisms of the door clicked softly, the hesitancy of the room’s occupant translating directly through the brass knob.
“Oh, thank the Goddess you came, Dedue. Frankly, I had given up any hope of escape.” Dimitri rubbed the back of his neck tiredly.
“I knew something was wrong when you did not return. I am glad that I came.” Dedue gave a curt bow.
“Thank you Dedue. Come. Let us head to the dining hall, shall we?”
“Of course, Your Highness. (F/N) should be preoccupied with her greenhouse duties for a time.”
“Yes... Actually, Dedue, how did you know it was (F/N)’s turn to tend to the greenhouse today?”
“Truthfully, Your Highness, I didn’t. It was pure luck she was scheduled today.”
“You mean--” Dimitri’s eyes widened.
“Yes. That was just a fluke. I have no knowledge of the schedule, other than the times either you or I are assigned.”
“Hah!” Dimitri’s hand landed on his retainer’s shoulder. “What luck! After hearing that, I can not help but feel a bit more confident about tonight.”
“And why is that, Your Highness?”
“If fate is as real as the ground beneath us, I would say that, perhaps, (F/N) and I are truly meant to be together.”
“That is quite a romantic notion, Your Highness.”
“It is, isn’t it?” Dimitri sighed as they crossed the threshold to the outside. The sun was just starting its descent past the hills; the slowly extinguishing rays of light brushed the sky with vibrant hues of vermilion and marigold.
“Despite that, I can not help but feel... hopeful. And... happy.”
“I am glad that this whole experience has collectively been a pleasant one, Your Highness.” Dedue responded as they neared the dining hall. “You deserve to be happy.”
Dedue’s words echoed in Dimitri’s head, ringing alongside Sylvain’s previous sentiment. Guilt wrung his heart until the familiar pangs of remorse pounded in his chest.
“Do I... Do I really deserve such a thing?”
“Without a doubt, Your Highness.”
“Even after everything that I’ve done... Even after... everything... I still... deserve it?”
“Of course, Your Highness. You deserve to be happy, just like everybody else.”
As the duo ascended the stairs and approached the Lions that were all congregated together for Dimitri’s cause, the prince’s features relaxed and-- just for a moment-- the voices that incessantly plagued his thoughts ceased.
“Thank you, Dedue.”
“I am always happy to help, Your Highness.” Like his prince, Dedue’s rough exterior melted away to reveal a warm, genuine smile.
“Hey, there you are!” Sylvain bounded up to them, meeting them halfway across the platform. “We were gettin’ worried about you! What happened?”
After Dimitri and Dedue explained what transpired, Sylvain couldn’t help but laugh at the terrible wonderful luck that Dimitri possessed.
"Dedue really got you out of a tough spot, huh?”
“As he always does.” Dimitri cast a grateful look at his retainer.
“I was shocked when I learned that (F/N) was actually scheduled today.”
“What were you gonna do if she wasn’t?” Sylvain queried.
Dedue paused thoughtfully.
“Perhaps I could have asked her to help me weed the courtyard, or to tend the horses.”
“Fair enough.” Sylvain nodded. “Well, it’s getting late so people are starting to leave the dining hall. Hopefully by the time (F/N) is done tending the plants, you two will be all alone.”
Sylvain wriggled his eyebrows and peered cheekily at the reddening face of the prince.
“Please do not be so nervous, Your Highness. (F/N) will surely appreciate all the effort you had put in.”
“Yeah!” Sylvain propped an arm on Dimitri’s shoulder. “Remember what I told you, Your Highness? You’re the leader of the Blue Lions! Start actin’ like your namesake! You gotta be bold!”
“R-Right. Bold.” Truthfully, Dimitri looked anything but; however, this only prompted a deluge of much-needed encouragement and hype that the two happily supplied-- Sylvain taking a more... fiery approach to his psyching while Dedue slightly doused the ecstatic flames set by the redhead with more grounded assurances.
“Now remember, Your Highness. Look her in the eyes, smile, and tell her that she’s beautiful. Like this!” Sylvain turned to Dedue, who suddenly became an unwilling participant in the playboy’s example.
“Hey, babe. You look gorgeous tonight. I gotta admit, I’m no mathematician, but I can still see you’re a ten outta ten.”
“Please get away from me ... Thank you, Sylvain.”
Dimitri stared at the duo with a confused fixed smile plastered on his face. The gears in his head took their sweet, sweet time to churn and process the cursed pick-up line, but it eventually clicked.
“Hah! I get it now! That’s a great one, Sylvain. I’ll definitely remember that.”
A flush of pride stained Sylvain’s cheeks and he rubbed the back of his neck.
“Thanks! Oh, here’s another one. This one’s also super popular with the ladies.”
Sylvain cleared his throat and turned to Dedue, who was quietly trying to shuffle away.
“Hey, hun. Do you have a map? I keep getting lost in your eyes.”
“If that is the case, perhaps it would be in your best interest to stop looking at me.” Dedue lightly glared. Dimitri’s eyes crinkled gleefully.
“Ah, these are all wonderful! I look forward to using them on (F/N).”
“Great! But remember Your Highness-- too much of a good thing is a bad thing. You can’t just spout a couple lines like that and expect her to fall for you instantly. You gotta do it tastefully.”
“Tastefully... Got it.”
Dimitri nodded his head, soaking and digesting this newfound knowledge. His eyes suddenly shot up, excitement bubbling out of its watery depths.
“Oh! It appears that I have come up with something!”
“Go for it, Your Highness!”
“I’ve got no taste, but I’d still like a bite of you.”
. . .
. . .
. . .
“Sylvain?”
. . .
. . .
“Dedue?”
. . .
“... Perhaps the map one wasn’t so terrible after all.”
“You said it, Dedue.”
“Wha--! Surely it wasn’t that atrocious, was it?”
“I believe it would serve His Highness well if you taught him more pick-up lines, Sylvain.”
“Sure. Whatever it takes to keep him from saying stuff like that.”
“H-Hey!!!”
♠ ♥ ♣ ----------------------------------------------------------- ♣ ♥ ♠
After sprinkling the few remaining drops of water onto a patch of slightly wilting plants, you dropped the empty watering can with a clatter and threw your arms high above your head, stretching all the bundles and ties that knotted in your shoulders. Your stomach gurgled and a pulse of hunger radiated throughout your core. Perhaps it wasn’t the brightest idea to completely skip your meals.
You placed the watering can in the shed and, making sure everything was as orderly as it could be, stalked out of the greenhouse while still massaging the few stubborn knots that remained tied in your muscles. The sun had long disappeared below the horizon; whatever light remained served only as a prelude to the beginnings of a starry night.
A nippy breeze nibbled your exposed skin, contrasting the slightly humid atmosphere that you’ve grown accustomed to in the greenhouse. Teeth chattering and tummy churning, you hastened your feet to move faster to the brightly lit dining hall.
As you approached the door, you were pleasantly surprised to see that the hall was practically empty, save for some guards and faculty sneaking in a nightly snack-- but even they didn’t linger for long. As you were racking your brain for ideas on what to eat, you walked into the warm building; the ambrosial aroma of succulent, roasted duck caught your attention immediately.
To say that you didn’t shed a small tear from the experience would be a lie.
You scouted and scoured the kitchen for the fowl of your dreams, but it eluded you. Where in the world could this duck--
“A-Ahem.”
You had come dangerously close to collapsing from shock.
Your body jumped and slowly turned around to face the owner of the voice.
“Good evening, (F/N). You look as radiant as ever.”
A young man wearing a white suit decorated with small pins and medals stood before you. Gloved, quivering fingers delicately brushed the lone strands of hair that slipped onto his forehead to the side.
“D-Dimitri...? Is that you?”
“Ah y-yes, it is I. Please forgive me if I had surprised you.”
“N-Not at all!” You replied, your cognitive processes hiccuping at the sight of this magnificent angel. The light from the torch gently surrounded the prince with an almost ethereal quality, rendering him simply divine. The corner of his lips turned up slightly, pulling his handsome features into a half-smirk.
“Please, allow me to escort you to our table.”
“O-Okay...”
He took a step towards you and his eyes flickered down; you followed his gaze and saw his slightly shaking hand slowly reaching for yours.
“May I...?”
Whether it was a simple case of the jitters or the excitement bubbling from within, it didn’t matter much as you enthusiastically clasped your hand in his. Dimitri froze in place, every muscle in his being stiffening at that small point of contact. However, he managed to get his racing pulse (somewhat) under control-- just enough to pull you into a stiff walk at least.
“Please follow me, (F/N).”
The pounding in Dimitri’s heart found its way into his ears, drumming and thundering an aggressive beat. He never knew that fear and glee could intertwine so readily with one another-- until he felt your hand gently press into his palm. Worries and questions and warmth spurred his thoughts into a hazy flurry of emotion. Was he squeezing too hard? Was he holding your hand correctly? Were you at all uncomfortable? Oh Goddess, you look so beautiful when you smile like that--
“Ah! Dimitri, what is all this?”
“W-Well,” Dimitri swallowed what felt like a boulder, “it is our dinner.”
“Our... Dinner...?”
“Yes. Um...” His locked fingers reluctantly separated from yours. “We have prepared a roasted duck, a fine, savory pastry called ‘garlic bread,’ a simple salad, and baked sweets made by Mercedes. I pray this is enough to whet your appetite.”
“You whet my appetite Everything looks so good...” You swallowed thickly, eyes resting heavily on the succulent fowl. “Heh, well... I actually didn’t eat at all today, so--”
“I beg your pardon?!” You blinked and immediately found yourself sitting in front of the palatable entrees. Dimitri’s countenance-- full of concern and tinged with anger-- stared at you from across the sea of food.
“You mustn’t skip meals. That is terribly unhealthy for you.”
“You’re one to talk, Dimitri!” You laughed. “You skip meals all the time!”
Dimitri’s visage fell and his entire face took on all shades of red.
“I... admit, I am not one to berate you on this matter, but regardless, I ask that you still heed my warnings... You should never skip meals.”
Giggling to yourself, you rested your chin on folded hands and your head tilted slightly. That, combined with your killer smile and rosy cheeks, introduced Dimitri’s palpitating heart to a livelier pace.
“Okay, okay. I’m sorry. I promise I’ll do my best not to skip meals.”
“Urgh-- Yes! Please... don’t.”
Your lips curved into a smile and your eyes lustily darted to the food in front of you.
“Well, let’s dig in, shall we?”
You, of course, immediately reached for the duck-- as did Dimitri.
Your hands collided en route to the silver cutlery by the fowl, and a fountain of apologies spewed out of either of you. Dimitri, somehow managing to awkwardly bounce back from the innocent error, cleared his throat and took this opportunity to impress you with his... gentlemanly charms.
“Please excuse me, (F/N). Allow me to cut a slice for you.”
“Oh! Well, um... sure?”
Dimitri’s fingers rounded the shiny handles of the knife and fork before cutting into the tender meat. Delectable smells spilled forth from the bird, eliciting a growl from your stomach-- a... very, very loud growl. A growl that was loud enough for Dimitri to stop and look up.
“Uh... I’d like to apologize...” You mumbled ashamedly, your cheeks growing hot to the touch.
Dimitri chuckled, slipping a thick slice of duck onto your plate along with a small bushel of salad, a few pieces of garlic bread, and some sweets.
“Do not worry, my Beloved. I know you haven’t eaten all day.”
You smiled, graciously accepting your plate filled to the brim with food. You cut the slice of meat into more manageab--
Wait...
‘Beloved?’
It seemed that Dimitri realized his mistake around the same time you did.
“Dimitri--”
“Er, (F/N)! Aside from this morning, how was your day?”
“Huh? I-I mean it was fine, but Dimitri--”
“Ah, splendid! I am glad your day had gotten better. I was really worried when you suddenly left class like that.”
“Dimitri,” you cut in, “did you just call me... your... ‘Beloved?’“
Dimitri simply sat there as his brain was fried and shriveled into a crisp.
“W-Well, uh, I-- You see-- I deeply apologize for-- That was, very inappropriate of me--”
“Oh! No, no, it’s okay... Um, I was just a bit surprised is all.” You brought your cup to your lips in a pathetic attempt to cover the bashful grin that threatened to escape.
“Ah... Of course...” Dimitri stabbed a small tomato with the prongs of his fork and shoveled it into his mouth, his cheeks seeming to absorb the color of the little red berry.
You cleared your throat and thumbed the surface of a macaron with light fingers, a heavy silence blanketing the table. The quietly screaming royal took a bite of some garlic bread, his brain hardly processing the soft, fluffy texture of the dish.
Dimitri’s eyes widened inconspicuously, his mind flashing to the one thing that could save this dumpster fire of a date from certain demise--
His pick-up lines.
He could only pray that you were a fan of such things.
He cleared his throat and borderline slammed his fists onto the table, rocking a handful of mini cupcakes from their tiered seats. You quite literally jumped in your seat and got caught in the fierce stare of your house leader.
He can do this.
Come on, Dimitri! Remember your training with Sylvain!
He can do this.
Be a lion! Be bold!
He can do this!
“A-Are you ten? Because y-you look lost and I’d like to bite you.”
. . .
. . .
. . .
If-- in that moment-- Dimitri were to suddenly be thrown onto the path of a charging chariot, he would make no effort to move.
Simultaneously, you were well on your way to combusting into open flames-- if your swiftly coloring cheeks were any indication of that.
Neither of you spoke for a long time, gawking at the other in a silent, unconscious contest to see who could reach strawberry red first.
And Dimitri was the unwilling winner.
“I--”
“You--”
“I am so--”
“What did you--?”
“I am so, so sorry--”
“You want to bite me--?”
“Oh Goddess, I am so sorry (F/N)-- I can explain--”
“U-Um, perhaps it would be best for me to go...”
“Wait!” Dimitri shot out of his seat with a clatter. “I-- um--”
“Goodnight, Dimitri.”
You made a mad dash for the door, leaving the flustering royal a metaphoric fish out of water.
“(F/N)!”
He tailed after you, the delicious food that he and all the other Lions labored to prepare becoming a distant memory.
The sun and any trace of it had all but vanished from sight, replaced by its nightly counterpart. You were speed walking to the stairs when your wrist was snagged by a firm grip.
"(F/N)...!”
“Dimitri, listen, I really appreciate the food and everything, but I really should get going now--”
“Wait, please! I...” He gulped, finally throwing caution to the wind. “I love you.”
Your heart had stopped beating altogether and your lungs ceased operations. Your clenched jaw prohibited you from speaking, and you simply stared at him as those three simple words resonated in your mind.
“Er, that is to say...” He sighed, resignation taking hold of his features. “Can we... talk about this please?”
He loosely pointed to a nearby bench shaded under a tall tree. His hard grip softened, moving to interlace his fingers with yours as he led the two of you to the secluded spot. He sat with a deep exhale and pulled you beside him.
“(F/N).” He gazed at you steadily, his fingers rubbing shallow circles into your hands. “It is no exaggeration on my end to say that you mean everything to me. I-- along with the other Lions-- labored to make tonight the best it could be. Though truthfully, I never imagined my confession would turn out like this. But alas...”
Dimitri chuckled tiredly then sighed.
“I’m afraid I can’t hide my feelings for you a moment longer. I love you, (F/N). With all of my being. You motivate me to work harder, train harder-- to be a better man. You are so kind, and smart, and... absolutely mesmerizing. I can not keep my eyes off you, really.”
He laughed at your sheepish response then continued.
“You mean the world to me. So... I humbly ask that you... Um...” He cleared his throat and lowered his voice to a husky whisper. “Be mine.”
A gentle breeze swept through, carrying his small plea along with it. He stared at you, intensely and unblinkingly, with bated breath.
“Although,” he added, pain thinly veiled in his eyes, “if you do not feel the same way, I understand. I promise I will not hold anything against you. If it’s not too much trouble, I... I hope we can still be friends after all this--”
You dove straight into Dimitri’s arms, effectively knocking his words and the air right out of him. You felt his muscles tighten and the thumping in his chest blared loudly in your ears. You nuzzled your face into him and looked up, smiling.
“I love you too, Dima!”
D-Dima...?!
Poor Dimitri looked like he was about to choke. The little streams of moonlight that slipped through the holes in the trees reflected off of the prince’s reddening face; for a long time, all he could do was stare at you-- cheeks darkening and eyes widening.
Finally, the Goddess re-granted him the ability to speak.
“R-Really...?”
“Yes! Yes, I do!” Your arms moved from his torso to snake around his neck, pulling him a bit more to your level. “I love you, Dimitri. I’ve loved you for so long...”
You drew him into a hug again, burying your face in the crook of his neck. The crisp, sharp scent of his cologne flooded your senses, sending pleasant tingles and goosebumps throughout your body. You felt the prince’s arms wound around your frame, pulling you closer to his racing heart.
“If this is a dream, I wish to never wake.” He muttered into your hair, thankful that he could appreciate the light apple notes that came from it to the fullest.
“This isn’t a dream, Dimitri.” You whispered against his skin, causing a sweet shiver to run down his spine. “I love you, Dimitri. I love you so, so much...”
“My (F/N)... My Beloved...” He pulled away from you slightly, cupping your cheeks in his hands and brushing it gently. He could hardly contain all the love and pure adoration he held towards you; the way that you and only you reflected in his beautiful eyes showed that. With a gentle smile he pressed his forehead against yours, relishing the moment.
“May I... May I have the honor of kissing you, my love?”
His hot breath tickled your sensitive skin and you couldn’t help but laugh at the sensation, in addition to his endearingly adorable politeness.
“Yes, you may.”
Dimitri’s eyes flickered to your slightly parted, wet lips and leaned closer, his eyes fluttering shut. You followed suit, guided only by the synchronous beating of your hearts. A warmth like no other blossomed upon your lips, melting any and all tension into nothingness. Your lips engaged in a clumsy yet heartfelt dance, eliciting an airy chortle out of you.
Dimitri’s chest rumbled with a chuckle of his own and he parted to catch his breath. Not a moment later, his lips found yours again and again, more ravenous than the last. Each kiss left your head spinning faster and your heart wanting more, more, more. His teeth nibbled your bottom lip, drawing out a gasp from you; his fingers found residence in your hair as he slipped his hot tongue into your mouth. He explored your wet cavern excitedly, every one of his senses wracked with newfound pleasure. Your moans and sharp breaths intertwined heatedly, sending your thoughts into a frenzy and numbing oblivion all at once.
The chatter of guards and metal boots clanking against cobble spurred warning bells in your head, and a painful reminder of how exposed you were for any curious passerby. Dimitri reluctantly leaned away, still pressing his lips to yours until the last possible moment.
“Ahem... M-My apologies... I got a little too excited just now...” Dimitri panted, a dazed yet elated expression on his face. You, panting as hard as he, shook your head in response and pressed a chaste kiss on his forehead, down to his nose, his cheek, and finally stopping at his flushed, pink lips.
“Not a problem, Dimitri. I know you mentioned you wanted to bite me.” You gazed at him teasingly.
“T-That’s...” Dimitri sighed, burying his face in your neck to hide his blush (though how hot his skin felt against yours was all the confirmation you needed). “Please don’t tell anyone what I said...”
You snickered and patted his head, smiling when you felt him relax into your touch.
“Okaaay, I promise.”
“Good. Thank you, (F/N).”
He pulled away from your neck and adjusted himself into a more comfortable seating position. He securely placed his arm around your shoulder and you both sat in comfortable silence for a long time.
“It’s getting quite late, no?” Dimitri mumbled out of the blue. “Allow me to walk you back to your room.”
“Actually, Dima... Do you think we can go back and finish dinner? I’m still really hungry...”
“O-Oh! I have completely forgotten about that! Yes, of course we can. Although... Regrettably, our food would have gotten cold by now.”
“That’s okay. Being with you warms my heart anyways.”
“Ah-- Um--” Dimitri coughed, looking away. “I confess that your teasing will take some getting used to... But it is a pleasant thing nonetheless.”
You giggled as he stood up and helped you to your feet.
”Hey, Dimitri?”
“Yes, my Beloved?”
“I love you.”
Dimitri planted a soft kiss on your forehead and stared fondly into your eyes.
”I love you too, (F/N).”
bonus: despite swearing to himself that he would *never* use pick-up lines ever again (its powers being too great for any mortal to fully wield), dimitri would still indulge a line or two for you if you asked him hard enough (and swore on your life you would never divulge what he shared with you to anyone else). and yes, when you two eventually got more comfortable with each other, he did get a bite of you from time-to-time but that’s a story for another day.
51 notes · View notes
luxe-pauvre · 4 years ago
Quote
Pacioli's books focused on the golden ratio, or divine proportion, an irrational number that expresses a ratio that pops up often in number series, geometry, and art. It is approximately 1.61803398, but (being irrational) has decimals that stretch on randomly forever. The golden ratio occurs when you divide a line into two parts in such a way that the ratio between the whole length and the longer part is equal to the ratio between the longer part and the shorter part. For example, take a line that's 100 inches long and divide it into two parts of 61.8 inches and 38.2 inches. That comes close to the golden ratio, because 100 divided by 61.8 is about the same as 61.8 divided by 38.2; in both cases, it's approximately 1.618. Euclid wrote about this ratio is around 300 BC, and it has fascinated mathematicians ever since. Pacioli was the first to popularise the name divine proportion for it. In his book by that title, he described the way it turns up in studies of geometric solids such as cubes and prisms and polyhedrons. In popular lore, including in Dan Brown's The Da Vinci Code, the golden ratio is found throughout Leonardo's art. If so, it is doubtful it was intentional. Although it is possible to draw diagrams of the Mona Lisa and Saint Jerome asserting this notion, the evidence that Leonardo consciously made use of the precise mathematical ratio is not convincing. Nevertheless, Leonardo's interest in harmonic ratios was reflected in his intense studies of the ways that ratios and proportions are manifest in anatomy, science, and art. It led him to search for analogies between the proportions of the body, the notes of musical harmonies, and other ratios that underpin the beauty manifest in the works of nature.
Walter Isaacson, Leonardo da Vinci
2 notes · View notes