Prompt: A vibrant, jewel-toned, highly detailed, and polished image with fluid, organic textures, soft and ethereal lighting, and a luminous, dreamlike aesthetic. A mathematical diagram on a black background illustrates Euler's Formula and Euler's Identity, along with a unit circle representation. The formula "e^(iα) = cos α + i sin α" is in bright green text with "Euler's Formula:" aligned vertically to the left. The unit circle in the complex plane is white, with yellow horizontal and vertical arrows labeled "Re" and "Im" respectively. The origin is "0". Points "i" and "e^(iφ) = cos φ + i sin φ" are marked on the unit circle with white dots. A white line extends from the origin to "e^(iφ)". Teal dashed lines project to the axes, labeled "cos φ" and "sin φ". An angle "φ" is marked. At the bottom, "e^(iπ) + 1 = 0" in blue text, with "Euler's Identity:" aligned vertically to the right. The entire scene is set against a teal sphere centered on a black background, encased within two golden circles that intersect vertically and horizontally. To the right of the sphere, a white text box with "e^(i*pi) = -1" appears to hover. A thin, golden, undulating wave-like structure emanates horizontally from the sphere, resembling a 3D sine wave. All elements have a metallic sheen, creating a symmetrical composition with a central focal point.
Prompt: F = ma,
the force of intention,
motion born from will,
the universe where push comes to shove
the collision of thought and matter,
fermion and boson.
Prompt: Synchronization of time between Earth and the Moon, with the Earth-Moon barycenter as the focal theme. Depict Earth and the Moon in the foreground: Earth vibrant with clouds and continents, and the Moon contrastingly barren and rocky. Visualize the barycenter as a glowing point of energy beneath Earth's surface, with orbit lines or beams connecting it to the Moon to suggest their gravitational balance.
Integrate futuristic clocks or hourglasses, floating between Earth and the Moon, interconnected by ethereal beams of light to symbolize synchronized timekeeping. Subtle mathematical symbols or equations should blend into the starry background or clock designs to reflect the computational efforts involved. Use deep blues, purples, and silvers to evoke cosmic harmony, with smooth flows of light reinforcing the connection between these celestial bodies. Aim for a mood of wonder and curiosity, celebrating the beauty of the universe and the scientific achievements that unite time across space.
Inspirations; (1) Artists: Chesley Bonestell for grand, scientific space art; Alex Grey for glowing, symbolic imagery; M.C. Escher for mathematical and surreal balance. luminous drama of Greg Rutkowski; atmospheric sci-fi landscapes of Andreas Rocha. (2) Styles: abstract & dreamlike Surrealism; tech-driven Futurism; visual metaphors of Symbolism. (3) Techniques: glowing, luminescent detailing to emphasize energy flows, photorealistic precision for celestial bodies, and geometric patterns to highlight balance and mathematical harmony.
Prompt: The ability of an AI model to process and understand long, complex prompts, giving equal weight to all parts, is often associated with the following concepts:
1. Long-Context Understanding:
Context Window: This refers to the amount of text the model can process at once. Larger context windows enable the model to consider more information from the prompt, leading to more comprehensive understanding.
Attention Mechanisms: These mechanisms allow the model to focus on the most relevant parts of the prompt, even when it's long and complex.
2. Enhanced Model Architectures:
Transformer-based Models: Models like GPT-4, which are based on the transformer architecture, are particularly adept at handling long-range dependencies and complex relationships within the text.
3. Advanced Training Techniques:
Large-Scale Training: Training the model on massive datasets exposes it to a diverse range of prompts and responses, improving its ability to handle complex inputs.
Fine-tuning: This involves training the model on specific tasks or datasets, allowing it to specialize in certain types of prompts and responses.
It's important to note that the specific techniques and capabilities that enable a model to process long, complex prompts can vary depending on the model's architecture, training data, and the specific implementation. However, the general principles of long-context understanding, advanced model architectures, and effective training techniques are key to achieving this capability.
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 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
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.
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.
