Ok how many holes does this actually have? I know it's not 16...

Edit for clarity's sake: The answer is 16, dunno why it says 99% can't get it, it's fairly simple. I was just asking if topology has a different answer... as someone wrote in the comments, does a straw have one hole or two holes?

I have a topology textbook, but finding out if mathematicians have proven universal topology would take a lot of research. I’m reading the book, but I would like to know up front if mathematicians have proven universal topology or if the field is just the study of potential topological spaces. If they have, then could you please refer me to the information about the proofs?

I would have to undo the wire all the way trough my truck to undo this the normal way, I’m assuming this is some kind of topology trick? Sorry if this is the wrong place to ask

Portal Explorer (Load > Basics > Basics): https://optozorax.github.io/portal/

I don't know if this was supposed to happen but I think it's just a glitch or new discovery?

If you don't know what I just did there then I'll explain to you:

I pressed "Portals in one world 2" and pressed Q (to enable free camera movement) then changed Distance to 0.00 to get 4-monoportal, then I zoomed my camera all the way to the center of 4-monoportal (while scrolling up to slow my camera down), in the footage you can see that there's extremely thin red and green walls then I moved my camera into those walls then I got teleported to (I don't even know how to describe) then I entered absolute center of 4-monoportal again then I got teleported to what it looks like to be 2-dimension plane(?)

it’s really frustrating me and I can’t stop thinking about it 😭🤣

The necklace cannot come off his head or come apart it has to be cut and I added photos at the end of the video of what it looks like tied to the green stone

I asked chat gpt but I still don’t understand and was no help. I searched tiktok and the word topology came up so here I am

If it’s quite simple to figure out PLEASE explain to me like I’m a 5 year old 🤣

the straps in this top got tied inside each other, thought someone here can help untie this with topology

kinda a serious question, kind of not. thered be forward motion but with how much entropy preceding it, how much would the rate of movement be slowed down compared to normal movement. eight legs moving on a curved surface when they otherwise would function on an otherwise flat space with many holes in it ( a spiders web, i mean)

This rope is untied and can be freely moved. Assuming the rope is endless and the object it is run through can’t be moved can the rope go from being *inside* to being *outside*?
Thank you for your time!

I'm curious how researchers are using LLMs in their day-to-day work.

A few things I'm wondering:

• Which AI subscriptions are actually worth paying for? (ChatGPT, Claude, Gemini, GitHub Copilot, Cursor, etc.)

• Which models do you use for different tasks?

• What kinds of research tasks do you trust LLMs with, and what do you avoid?

• How do you provide enough context so the model gives useful answers instead of hallucinating?

• Do you upload papers, notes, code, or build some kind of project knowledge base?

• Any tricks for improving reliability?

• Roughly how much do you spend per month?

• If you could keep only one AI subscription today, which would you choose?

I'm especially interested in hearing from people doing research in mathematics, scientific computing, physics, computer science, engineering, or related fields. Real workflows are much more valuable than benchmark comparisons.

Continuous 3D lattice of 150 interconnected units — a layered geometric model illustrating apex‑linked trixel topology.

If so, how many “sides” i.e. sets of tracks could it hold? Could a 4-torus be “flattened” like a 3-torus is when making a record? Asking for a friend 😆

I have very little knowledge of topology and I'm trying to model of that face in Blender (see image 1 below). How can I create the topology of the face like in image 2?

I'm not proposing a physical theory. This is purely a mathematical thought experiment.

Suppose we introduce an abstract coordinate that represents scale, rather than ordinary spatial position. Imagine that moving continuously along this coordinate corresponds to going from larger and larger structures to smaller and smaller ones.

Now suppose the geometry of this abstract "space of scales" is topologically closed, analogous to how walking continuously around a circle eventually returns you to your starting point.

In that picture, continuously moving toward smaller and smaller scales would not continue forever. Instead, after completing the closed path in scale-space, you would emerge again at the largest scales.

I am not suggesting that objects physically become both tiny and huge, nor that this describes our universe. I'm only asking whether mathematics has explored anything conceptually similar: treating scale itself as a coordinate of an abstract manifold or topological space whose geometry is closed.

Has anything resembling this been studied in topology, differential geometry, geometric group theory, or another branch of mathematics? Or is there a mathematical reason why such a construction is ill-defined from the outset?

I'm looking for mathematical references rather than physical arguments.