#curvature

[wikinley]

Offshore windpark in front of the Belgian coast perfectly shows the earth's curvature.

[art-of-mathematics]

I know I have drawn this shape so often already, but the process of drawing it is so soothing.

And for that, I have drawn a kind of step-by-step guide how to draw that shape in the top of this drawing:

(from left to right: ) [sorry in advance if I make it sound more complicated than it actually is. If you want to draw it, I would advice you to focus more on these illustrations rather than on my gibberish-text.]

1. draw a 2-dimensional Cartesian plane - or, in other words: just draw a cross like depicted

1.1. mark 2 points on the y-axis/vertical line with same distance to the coordinate origin, then mark 2 points on the x-axis/horizontal line with the same distance to the coordinate origin. (The markings on the y-axis need to be farther away from the origin than the markings of the x-axis)

2. connect the 4 marked points like depicted above. This is a function plot of a tractrix. (it has two mirror symmetry axes. )

3. draw an ellipse and connect the two markings on the x-axis. This becomes a kind of "belt" for the pseudosphere (4th picture)

4. part the ellipse into whatever-amount-you-want of partings (like you would cut a cake) and slightly mark these.

5. now imagine you cut that shape horizontally on the outer surface. (In the 5th picture I depicted that with red-ish pen across the pseudosphere. ) -

6. then the cut shape needs to be "(shape) shifted". For that we use a set of marked points we did in step 4). Furtherly, we "cut" the ellipse open, and push one end of it to the top, and the other end to the bottom. (depicted in picture 6 )

7. Then we connect the rest to get that shape:

[knotty-et-al]

Pseudosphere and dini surface

^ Visualization about the transformation of a pseudosphere into a dini surface.

v Pseudosphere

[blairelythere]

Sculpting my ass so I can sit on the faces of my lovers (and haters) 💗✨️

[th3-0bjectivist]

“Terra Panoramic” - Acrylic paint on canvas

[whats-in-a-sentence]

But the question of whether the Energizer Bunny could move forever in one direction and vanish into the darkness, or would one day circle around and catch you from behind – whether space goes on forever or wraps back like a video screen – is still completely open.¹⁴

14. So far, we've focused exclusively on the curvature of three-dimensional space – the curvature of the spatial slices in the spacetime loaf. However, although it's hard to picture, in all three cases of spatial curvature (positive, zero, negative), the whole four-dimensional spacetime is curved, with the degree of curvature becoming ever larger as we examine the universe ever closer to the big bang. In fact, near the moment of the big bang, the four-dimensional curvature of spacetime grows so large that Einstein's equations break down. We will discuss this further in later chapters.

"The Fabric of the Cosmos" - Brian Greene

[thethirdbear]

[art-of-mathematics]

Pseudosphere transforming into Dini surface (WIP)

Here is a gif to what I try to depict:

Great website:

[screampotato]

Original photo by Apostolos Vamvouras

I'm fascinated by curves, surfaces and space.

[fashionfotorecccluse]

Spacetime

[raurquiz]

#happybirthday #lindahamilton #actress #sarahconnor #theterminator #terminator2 #judgmentday #darkfate #dantespeak #HillStreetBlues #BlackMoonRising #BeautyandtheBeast #MissinginAmerica #HomebyChristmas #Chuck #Defiance #LostGirl #Curvature #EasyDoesIt #ResidentAlien #Claws

[marcospevensie2]

[sciencesolutions]

[whats-in-a-sentence]

If all the matter and energy in the universe were to be smeared uniformly throughout space, and if, after this was done, there turned out to be more than the so-called critical density of about .00000000000000000000001 (10^-23) grams in every cubic meter* – about five hydrogen atoms per cubic meter – Einstein's equations would yield a positive curvature for space; if there were less than the critical density, the equations would imply negative curvature; if there were exactly the critical density, the equations would tell us that space has no overall curvature.

* Today, matter in the universe is more abundant than radiation, so it's convenient to express the critical density in units most relevant for mass – grams per cubic meter. Note too that while 10^-23 grams per cubic meter might not sound like a low, there are many cubic meters of space out there in the cosmos. Moreover, the farther back in time you look, the smaller the space into which mass/energy is squeezed, so the denser the universe becomes.

"The Fabric of the Cosmos" - Brian Greene

[thebigboyshop]

The Curvature series exclusively at The BIG Boy Shop!

For the Thick inda hips Women...

[edgythoughts]

What If Gravity Is Just an Emergent Illusion 2025

What If Gravity Is Just an Emergent Illusion 2025

Gravity—it's something we all experience every second of our lives. It keeps us grounded, governs the orbits of planets, and shapes the very structure of the universe. But what if this seemingly fundamental force isn't fundamental at all? What if gravity is not a "real" force, but rather an emergent illusion arising from something deeper—like entropy, information, or quantum entanglement? This idea, while radical, is gaining attention in theoretical physics circles. It challenges the conventional view of gravity first laid out by Isaac Newton and later reshaped by Albert Einstein. In this blog, we'll explore the speculative hypothesis that gravity may be emergent, examine the scientific reasoning behind it, and consider the astonishing implications this theory could have on our understanding of reality. The Classical View: Gravity as a Fundamental Force Before diving into the speculative realm, it helps to first understand what gravity has traditionally meant in science: - Isaac Newton described gravity as a force that acts at a distance between two masses. - Albert Einstein revolutionized this with General Relativity, stating that gravity is the curvature of spacetime caused by mass and energy. Both of these models treat gravity as a fundamental interaction—something built into the fabric of the universe. But as physicists probe deeper into the nature of space, time, and quantum mechanics, questions have emerged that challenge this long-held belief. The Radical Shift: Gravity as Emergent An emergent phenomenon is something that arises from the interactions of more basic components but doesn’t exist as a fundamental feature on its own. For example, temperature is an emergent property—it arises from the motion of atoms but isn’t a property of individual atoms. The idea that gravity might be emergent suggests it arises from microscopic processes that we don’t yet fully understand. Here's what that could mean: 1. Gravity might be the result of entropy, the measure of disorder in a system. 2. It may emerge from the information content of space, in line with holographic principles. 3. It could even be tied to quantum entanglement, a strange phenomenon where particles are deeply connected across space. This isn’t science fiction—it’s science speculation based on serious mathematical models. One Leading Proposal: Erik Verlinde’s Entropic Gravity Dutch theoretical physicist Erik Verlinde proposed in 2011 a theory called “entropic gravity.” His hypothesis states that gravity is not a fundamental force, but an emergent one resulting from thermodynamic principles. In this framework: - Gravity comes from the tendency of systems to maximize entropy. - When matter moves, it changes the distribution of information in space. - This shift creates what appears to us as a “gravitational force.” Verlinde’s idea is backed by mathematical models and even explains some aspects of galaxy rotation without needing dark matter—a major bonus if proven correct. However, it remains controversial and is far from accepted by the wider physics community. Read more about entropic gravity here: https://en.wikipedia.org/wiki/Entropic_gravity

Quantum Entanglement and the Fabric of Spacetime Another perspective on emergent gravity arises from quantum information theory. Some physicists believe that spacetime itself—and hence gravity—emerges from the entanglement of quantum particles. This is tied to the "holographic principle," which suggests that all the information inside a volume of space can be described by information encoded on its boundary. In simple terms, what we see in three dimensions might actually be a projection of two-dimensional information—just like a hologram. If gravity is an emergent result of how this quantum information behaves, then it means: - Gravity isn't pulling us down. It's the result of space adjusting itself to maintain the informational equilibrium. - Black holes might not be gravity wells in the traditional sense but extreme distortions in this information landscape. This theoretical approach is still under development, but it's changing how we view gravity and the cosmos. Further reading: https://en.wikipedia.org/wiki/Holographic_principle Implications: If Gravity Is Emergent, What Changes? If gravity isn't fundamental, it raises profound questions: 1. What replaces gravity in the list of fundamental forces? - The Standard Model includes electromagnetism, strong nuclear, and weak nuclear forces. - Gravity might be downgraded to a “macro-scale effect,” not a true interaction. 2. Can we manipulate or even “turn off” gravity? - If it's emergent, could we develop technology to alter the conditions that produce it? - Sci-fi ideas like anti-gravity might edge closer to reality. 3. What about dark matter and dark energy? - Emergent gravity models have attempted to explain galaxy behavior without invoking dark matter. - If successful, this would be a massive paradigm shift in cosmology. 4. What does this mean for our understanding of time and space? - If spacetime arises from information, perhaps time and distance are also illusions—or at least not fundamental. Why It Matters The search for a unified theory of physics has long been the holy grail for scientists. Einstein sought to merge gravity with electromagnetism. Today’s physicists are trying to merge gravity with quantum mechanics in a "Theory of Everything." The emergent gravity hypothesis offers a radical pathway toward this goal. If gravity isn’t a force like the others but a result of deeper, hidden processes, then perhaps those underlying systems are where the true laws of nature reside. This would mean everything we’ve believed about how the universe functions would need reevaluation—from the movement of galaxies to the sensation of weight we feel on Earth. Conclusion: A Beautiful Illusion? The idea that gravity might be an illusion—something that seems real but is born from deeper, unseen processes—is both unsettling and inspiring. It challenges our intuition and the way we experience the world. However, science progresses by challenging assumptions. Whether or not emergent gravity turns out to be the final answer, exploring these ideas pushes the boundaries of human understanding. By peering behind the veil of what we assume to be true, we might just uncover the most fundamental truths of the universe. — You might also enjoy reading our other blogs: - What If Time Was a Physical Substance 2025 https://edgythoughts.com/what-if-time-was-a-physical-substance-2025 - What If We Could Merge Minds via Quantum Networks 2025 https://edgythoughts.com/what-if-we-could-merge-minds-via-quantum-networks-2025 Read the full article