Prompt: A sea-turtle rises from oceanic depths in golden hour, breaking the surface with its head at the very center of an elliptical wooden yoke floating upon the vast open sea. From a neuronally-mediated probabilistic spatio-temporal past the echo of the original words being spoken in Pali, long-unheard by mortal beings:
“Monks, suppose that this great earth were totally covered with water, and a man were to toss a yoke with a single hole there. A wind from the east would push it west; a wind from the west would push it east. A wind from the north would push it south; a wind from the south would push it north. And suppose a blind sea turtle were there. It would come to the surface once every one hundred years. Now what do you think? Would that blind sea turtle, coming to the surface once every one hundred years, stick his neck into the yoke with a single hole?” “It would be a sheer coincidence, lord, that the blind sea turtle, coming to the surface once every one hundred years, would stick his neck into the yoke with a single hole.” “It’s likewise a sheer coincidence that one obtains the human state. It’s likewise a sheer coincidence that a Tathāgata, worthy & rightly self-awakened, arises in the world. It’s likewise a sheer coincidence that a Dhamma & Vinaya expounded by a Tathāgata appears in the world. Now, this human state has been obtained. A Tathāgata, worthy & rightly self-awakened, has arisen in the world. A Dhamma & Vinaya expounded by a Tathāgata appears in the world. “Therefore your duty is the contemplation, ‘This is stress … This is the origination of stress … This is the cessation of stress.’ Your duty is the contemplation, ‘This is the path of practice leading to the cessation of stress.’”
Prompt: The Littlewood-Richardson coefficients are combinatorial numbers that arise in the study of the representation theory of symmetric groups and general linear groups. The visual representations of the Littlewood-Richardson coefficients are often depicted using tableaux, which are graphical devices for keeping track of various combinatorial objects. Such coefficients can be computed by counting skew tableaux of a certain type, and arise in the decomposition of the tensor product of irreducible representations of the general linear group or in Schubert varieties. These tableaux provide a way to understand and compute the coefficients, making intricate undergirding algebraic relationships more accessible and easier to visualize.
Prompt: Imagine you have a list of natural numbers (1, 2, 3, 4, ...). Riemann's zeta function takes a number 's' and sums the reciprocals of all the numbers in that list raised to the power of 's'.
For example, zeta(2) = 1/1^2 + 1/2^2 + 1/3^2 + ... (sum of reciprocals of squares of natural numbers).
This function is interesting because it helps solve many problems related to prime numbers, which are the building blocks of all natural numbers. However, the zeta function is not defined for all values of 's'. It gets a bit tricky at 's' = 1.
The trickiness at s = 1 in the Riemann zeta function can be visualized by imagining a teeter-totter:
Think about the sum for zeta(2) again: 1/1^2 + 1/2^2 + 1/3^2 + .... Each term gets smaller and smaller as you go further down the list. This makes the sum well-behaved and eventually converges to a specific value.
But now, imagine s = 1. The sum becomes 1/1 + 1/2 + 1/3 + .... Here, each term is either 1 or bigger than 1. It's like putting only heavy weights on one side of the teeter-totter. The sum keeps getting bigger and bigger, never settling on a specific value. Mathematicians call this situation "divergence."
There are ways to define the zeta function for other values of 's' even though the simple sum diverges at 1. It's like using advanced techniques to balance the teeter-totter so it makes sense even with those heavy weights. But understanding that initial imbalance at s = 1 is the first hurdle.
Prompt: Linguistics (Latin lingua 'tongue' + Greek -ikos 'of, relating to') is the broad study of human language. It delves into grammar, pronunciation, history, and how languages function across cultures.
Semantics (Greek σημαίνει (semainei) 'to signify' + -ics) zooms in on meaning within language. It analyzes how words, phrases, and sentences convey ideas and how context influences interpretation.
Semiotics (Greek σημεῖον (semeion) 'sign' + -ics) takes the biggest umbrella. It's the general theory of signs and symbols, encompassing everything from traffic signs and emojis to fashion trends and body language. Semantics becomes a branch within semiotics, focusing specifically on signs within human language.
So, linguistics is the foundation, exploring the structure of languages. Semantics builds on that, examining how meaning is built within those structures. And semiotics is the overarching field, investigating all forms of signs and symbols humans use to communicate.
Prompt: The young mathematician stared intently at the chalkboard, the equations and diagrams seeming to swirl before her eyes. She was trying to wrap her mind around one of the most enigmatic ideas in modern mathematics - the Grothendieck-Teichmüller tower. It began with moduli spaces, those abstract realms where all the curves and shapes of a certain kind could be catalogued and studied. The Teichmüller tower was a staggering edifice made up of moduli space after moduli space, each level corresponding to curves of increasing complexity and intricacy. At first glance, it seemed like a bizarre piece of mathematical architecture with no greater purpose. But the brilliant mind of Alexander Grothendieck had seen its deeper significance. He realized this geometric tower could unlock the mysteries of the absolute Galois group - that most fundamental object in arithmetic's secret laws. Grothendieck didn't just glimpse this connection, he formally conjectured that the two were inexorably linked. The absolute Galois group, which had vexed mathematicians for centuries, could be understood through the geometric symmetries of the Teichmüller tower itself. To bridge this arithmetic and geometric realms, Grothendieck's disciples had defined a new mathematical group - the Grothendieck-Teichmüller group. A group whose elements encoded the hidden shapes and transformations preserving the structure of the enigmatic tower. As she stared at the chalkboard, the young mathematician felt like she could almost see the Teichmüller tower stretching up into higher dimensions. If Grothendieck's bold conjecture could be proven, it would reveal a profound truth about numbers and their most elusive mysteries. (In Grothendieck's time Abstract Expressionism, Pop Art, and Minimalism were in vogue.)
Prompt: In a vast expanse of mathematical wonder, there exists a captivating machine—a Storytelling Machine. Picture it as a device weaving tales from the essence of numbers and symbols, its gears both forming and traversing intricate mathematical patterns. Within this machine reside characters, each governed by its unique set of rules dictating their interactions. Imagine figures, each with its own distinct shape and color, representing these characters, gathering around the machine, ready to contribute to the unfolding narrative.
Now, envision a special version of this machine—the Monster Storyteller. Its structure is adorned with intricate mathematical symbols and diagrams, reminiscent of ancient runes etched onto its surface. This extraordinary creation delves into the realm of mathematical marvels known as vertex algebras. Here, instead of characters, it hosts mathematical entities called "vertex operators," depicted as dynamic shapes pulsating with energy, each with its own distinct behavior. These operators too - much like characters in a story - follow precise rules governing their interactions within the mathematical narrative.
At the core of the Monster Storyteller lies a connection to an enigmatic group—the Monster group. Visualize this group as a vast, intricate tapestry, stretching across the mathematical landscape, its threads weaving together in mesmerizing patterns. Just as the Monster Storyteller weaves its tales, the Monster group reveals symmetries and patterns beyond comprehension, depicted as interlocking shapes and symbols, forming an elaborate web of mathematical beauty.
Prompt: The concept of a simplicial symmetric sphere spectrum into simple terms:
Spheres of differing dimensions. A 0-sphere is just two points, a 1-sphere is a circle, a 2-sphere is the surface of a ball, and so on.
A “spectrum” is like a sequence of these spheres, where each sphere is connected to the next one in a way that helps us study shapes and spaces in a stable manner.
The “sphere spectrum” is a particular sequence that starts with the 0-sphere, and includes all higher-dimensional spheres.
The "symmetric" part means we're keeping track of how these spheres can be rearranged or swapped around; important because it allows us to do more operations with our spectrum.
“Simplicial” refers to a way of building complex shapes from simple pieces, like Legos. Meaning that we're using a particular mathematical structure to describe how our spheres connect.
Thus a “simplicial symmetric sphere spectrum” is a sequence of spheres of increasing dimensions, built such that we can swap them around and perform various operations on them; this structure is useful for studying shapes and spaces in a way that's more flexible and powerful than just looking at individual spheres.
Thus the “simplicial symmetric sphere spectrum” is a powerful mathematical concept that bridges the gap between geometry and abstract algebra. It's a sequence of spheres of increasing dimensions, connected in a way that allows mathematicians to perform complex operations across dimensions. This is crucial in topology, the study of shapes and spaces. The "symmetric" aspect allows for rearrangements of spheres, enabling operations like addition and multiplication of entire spaces. The "simplicial" component allows building complex shapes from simple elements – the “Lego block” approach, making the concept computationally manageable, and also connecting it to fields like computer graphics and data science. Thus mathematicians gain insights into the very fabric of reality as we u
I shall conquer untruth by truth. And in resisting untruth, I shall put up with all suffering.
Model:
AIVision
Size:
1792 X 1008
(1.81 MP)
Used settings:
Prompt: Let the first act of every morning be to make the following resolve for the day:
- I shall not fear anyone on Earth.
- I shall fear only God.
- I shall not bear ill will toward anyone.
- I shall not submit to injustice from anyone.
- I shall conquer untruth by truth. And in resisting untruth, I shall put up with all suffering.
Prompt: A majestic tabby hairy Norwegian Forest Cat, lying on an old antique Victorian crimson couch in an steampunk style dark library room, in background many bookshelves with a lot of old books and brass steampunk artifacts like clocks, steampunk mechanical devices, clockwork instruments, steampunk weapons, whisky bottles, an old antique globe, some cobwebs, illuminated by candles, orange candlelight, in watercolor
Prompt: Additional prompt: Funny cartoon drawing of an angry bunny standing in front of a large carrot with his arms folded and an angry look: I won't give you that, it's my carrot!
Prompt: A majestic Holy Birman cat, lying on an old antique Victorian crimson couch in an steampunk style dark library room, in background many bookshelves with a lot of old books and brass steampunk artifacts like clocks, steampunk mechanical devices, clockwork instruments, steampunk weapons, whisky bottles, an old antique globe, some cobwebs, illuminated by candles, orange candlelight
Mysterious Black Cat in the Skull Field ** #CATURDAY
Model:
Realismo
Size:
1600 X 1200
(1.92 MP)
Used settings:
Prompt: A scary black cat with red glowing eyes, sitting on a pile of skulls, in an mythic enchanted tomb with cobwebs and spiders, illuminated by burning torches,
Prompt: A majestic Sacred Cat of Burma, sitting on an old antique Victorian crimson couch in an steampunk style dark dusty library room, in background bookshelf with many old books and brass steampunk artifacts like clocks, steampunk mechanical devices, steampunk weapons, an old antique globe, there are some cobwebs, the room was illuminated by candlelight and orange gas lamp,
Steampunk lab and workshop with "Overseer" ** #CATURDAY
Model:
Artflow
Size:
1152 X 864
(1.00 MP)
Used settings:
Prompt: A British Shorthair silver tabby cat, sitting on an old antique wooden table with beautiful carvings, a human skull on the table, alchemical apparatus there, in an steampunk style dark laboratory room, in background shelves with many brass steampunk artifacts, clocks, steampunk mechanical devices, clockwork instruments, steampunk weapons, an old antique globe, some cobwebs, illuminated by candles, orange candlelight, in watercolor
Dream Level: is increased each time when you "Go Deeper" into the dream. Each new level is harder to achieve and
takes more iterations than the one before.
Rare Deep Dream: is any dream which went deeper than level 6.
Deep Dream
You cannot go deeper into someone else's dream. You must create your own.
Deep Dream
Currently going deeper is available only for Deep Dreams.
