#hyperbolic

[keepingitneutral]

Sinfonía Verde, Península de Osa, Costa Rica,

Courtesy: Studio Saxe

[r4v3nzcr0ws]

is anyone else terrified to admit what their gender is? im scared im gonna walk into a room and say im a transmasc girl and then get publically executed

[things-from-strings]

found some old yarn, decided to turn it into a hyperbolic plane ✨️🏳️‍🌈🧶

3 dc in each st around; i'm liking what's happening so far✨️👌

[iamadequate1]

Of all the things my human eyeballs have seen, "It's transphobic to not like Izzy!!" is one of the worst of all

[darkwingsnark]

DUCKVEMBER DAY 07: Torpid Duck

I had a tamagotchi as a kid, and I saw this goober often.

I like Kuchipatchi, but it's kinda messed up that the 97' US website used to say 'hey, you don't want your pet to end up like THIS'.

RUDE. He's just a little guy.

[geometrymatters]

Anti-de Sitter space stack of hyperbolic discs

A gravitational field has negative energy and may be represented in terms of hyperbolic space with negative curvature.

[mathhombre]

Line Bundles on Complex Tori

That's the hexagonal tiling honeycomb by Roice Nelson. John Carlos Baez is working through a series on these beautiful infinite spaces.

Order 5 cubic honeycomb.

Coxeter showed there are 15 regular hyperbolic honeycombs.

Fun article in a good series. Highly recommend if it's at all of interest.

[maxdibert]

I couldn't help but burst into laughter when that person failed to come up with a logical argument against your claims and suddenly out of nowhere, decided to insult you by calling Snap an incel. It was so random and irrelevant!

Honestly, people really need to grow up.

Yeah, like, she seems to think that calling Snape an incel in the middle of a tantrum because other people don’t like her OTP is something that’s going to bother me. I mean, I just play along because when it’s over, I want her to tell me what she’s smoking—it must be some incredible mushrooms lol.

[isomorphismes]

Hadamard knew in 1898 that negative curvature and simply connectedness for surfaces embedded in 3-space force uniqueness of geodesics joining two points—implying that any segment of geodesic is also a shortest path.

But there is a long way toward the modern statement: “on any complete abstract Riemannian manifold of ≥0 curvature of any dimension, curvature is the quotient of its universal covering by a discrete group of isometries.”

Marcel Berger, Riemannian Geometry during the Second Half of the Twentieth Century

-------

Hadamard, 1898 being Les surfaces à courbure opposées et leurs lignes géodésiques

[sarenth]

On "Angry Gods" and Reactivity

I have seen both TikTok and Tumblr go back and forth on the subject of whether the Gods are angry or not.  I think this rhetoric has some seriously dangerous aspects to it. Sometimes the Gods do get angry at humans. Sometimes They get angry at us as a because we have the capacity to be fucking brilliant, kind, and we choose to be mean-spirited and make harmful choices. The problem is that people…

[mathart]

A 5-4 tiling of anti-deSitter space with Calabi-Yau manifolds rotating in CP-4

[daily-public-domain]

Day 367: Penrose Tiling

link

–This image is part of the public domain, meaning you can do anything you want with it! (you could even sell it as a shirt, poster or whatever, no need to credit it!)–

[alliterative-endlessknot]

The #ConnectedAtBirth #etymology of the week is SOVEREIGNTY/HYPERBOLIC/ OVERBEARING #wotd #sovereignty #hyperbolic #overbearing

[silly-plush-corner]

Watching through the CodeParade Hyperbolica devlogs and feeling the same giddiness I felt wearing that miku skirt

[mclaricepoetry-art]

(via "Hyperbolic Energy" Cap for Sale by CanvasQuill) 💥💚Hyberbolic Energy in Neon Green💚💥 for the ones who live life LOUD and in technicolor. subtle? never heard of her. hyberbolic is the vibe when you’re too much and proud of it. lime green? yeah, it’s basically screaming, and we’re here for it. this is for: the people who are always extra (in the best way)

anyone who thinks neon is a personality trait

repping bold energy, no apologies

grab it on hoodies, stickers, and whatever else you wanna slap your personality on. link in the post. let’s make subtle a thing of the past.

[geometrymatters]

Tatyana O. Sharpee’s work in the realm of geometric cognition—a field dedicated to understanding how the brain interprets and represents spatial information—has yielded groundbreaking insights into how our minds map the world around us. Continuing her previous argument for hyperbolic geometry in neural circuits, the recent paper, co-authored with Huanqiu Zhang, P. Dylan Rich, and Albert K. Lee, sheds light on the hyperbolic geometry of hippocampal spatial representations.

The hippocampus, a crucial part of the brain involved in memory and spatial navigation, houses ‘place cells’—neurons that fire when an animal is in a particular location. The geometry of these spatial representations, however, has remained largely unknown. Breaking new ground, Sharpee and her team reveal that the hippocampus does not represent space according to a linear geometry, as might be expected. Instead, they discovered a hyperbolic representation.

We investigated whether hyperbolic geometry underlies neural networks by analyzing the responses of sets of neurons from the dorsal CA1 region of the hippocampus. This region is considered essential for spatial representation and trajectory planning.

Imagine holding a map of your city. A linear representation would be akin to the map’s scale, where an inch on paper corresponds to a fixed number of miles in reality. A hyperbolic representation, in contrast, changes the scale depending on where you are on the map. The implications of this discovery are profound. A hyperbolic representation provides more positional information than a linear one, potentially aiding in complex navigation tasks.

This hyperbolic representation isn’t static—it dynamically expands with experience. As an animal spends more time exploring its environment, the spatial representations in its brain expand. The expansion is proportional to the logarithm of time spent exploring, suggesting our brains continually refine our spatial maps based on our experiences. As we spend more time in an area, our mental map of that area becomes more detailed and expansive. This dynamic updating could be crucial for efficiently navigating familiar environments.

Continue Reading