i feel like this is more a demonstration of the limits of the definitions used and how they're applied, rather than proving that the infinite knot is not the unknot.
I instantly recognized the cube tree pattern. I've been playing with variations that imply a Sierpinski Triangle (what I call a ternary cube tree). In fact, I have a new one that I've been putting many hours into. I should be posting vids (on top of the ones I've already posted) within a couple of weeks, if I can just stop tweaking the damn things.
My ternary cube tree is one that I came up with on my own with no prior hinting that such a thing was possible. That means the date of my first posting, May 24, 2015, means the concept is at least 9-years old (ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-8djZV2wtMXg.htmlsi=3ssx9b_hVoS1MfgE, with a claim that I came up with it in 2012). Though, I wouldn't be at all surprised if something out there pre-dates this. What I would be most interested to find out is if anyone came up with the Sierpinski Triangle slice before me (which has some interesting variations, ru-vid.comVzwvcMIDKjI?si=lYS-CdvBVWwi27HL).
Crap, now you've got me thinking whether I can get a smooth zoom in the one's I've done most recently with the video game, Sauerbraten (yet to be posted). Something tells me that I won't get a really clean zoom, particularly with you're finding that zoom speed is a big deal, and the video game only has constant speed. Won't free me from thinking about it though.
Looking at any one "major" site, having 6 heighbors. It's like spherical packing, but of wavefronts on the surface of the sphere. What is the frequency of the primary oscillations with respect to n? Edited: Mod 3, I see now
I just received my set of OptiDice, which inspired me to check how numerically balanced the rest of my dice were. I was shocked how other than OptiDice, every dice set has 5-8 on the same side of the d8 and 7-12 on the same side of the d12. And a few sets didn't even make sure opposite sides added to 9 or 13 (respectively)! Numerical balancing needs to become the standard.
I think if we stop naming things after people, that does more harm than good. The core problem is the naming bias, not the practice itself. Trying to give names like the "length-angle invariant" will inevitably become ambiguous when additional such invariants are discovered, and they'll also invariably lead to proliferation of acronyms, which suck. I'm also not a believer that the person's name necessarily always needs to be the very first person who discovered a concept. If someone else did important work studying, expanding, or popularizing it, that can be as important as the initial discovery.
One thing that jumped out to me is the difference between infinite processes and infinite states. 0.9... is 1 because it's not an infinite process of something writing the number 9 on end, merely approaching 1, but every single infinite 9 is already present. However, the issue with the infinite slip knot is you can't undo all of it at once. You have to undo one slip before you can undo the next. IDK if that is actually accurate, but is one of the ways I parse infinities
i liked this vid and its niche but versatile concept. the music was a little distracting for me. I can tell its intended implemented was to be non-distracting, so i thought this feedback might be helpful. not subscribed but looking forward to the next niche concept!
As someone who doesn't understand group theory at all, I love the idea that group theory links so many totally disparate concepts. Does this mean you can create a knot that retains the symmetry operations of each of the 219 space groups for 3d crystals?
After a point it all started to go over my head, but this was still a super interesting video. My non-mathematician brain enjoyed the 3D models and the colours 😁👌
I'm fairly sure that almost no mathematics is done by dead white men. Well, who knows, maybe there is an afterlife where mathematicians carry on their research for eternity. But they don't tend to share their results with the living.
Is it possible to construct an infinite slipknot of finite length? Perhaps if each cell was half the length of string compared to the previous, for example. Then isn't there an analog to Zeno's paradox wherein pulling on the string at a fixed rate for a finite amount of time will undo each successive cell in half the time of the previous, untying the knot in finite time?
Yes, it is possible to construct an infinite slipknot of finite length. (The example in the video has this property, but that is not emphasised here.) No, it is not possible to perform a "ambient" isotopy, even by undoing the next cell in half the time of the previous. This is because the fundamental group of the wild knot's complement is not the same as the fundamental group of the unknot's complement. EDIT: Here is another answer. Look at the string held by Henry at timestamp 8:47. Pretend that it is made of rubber and can stretch. He holds on to the string and you preform the supertask - you undo the k^th "bite" of the slipknot in time interval [1/2^{k+1}, 1/2^k]. If you draw the pictures, you'll find that there are 2^k points of the rubbery string that are now distance 1/2^k (say) from the wild point. So, in the limit, there are infinitely many points of the rubbery string in contact with the wild point. But an ambient isotopy can't do that...
In H3 what would be the problem with aligning the view perpendicular to the ground each frame? For every point where the user/player could be in hyperbolic space, there should be a straight line perpendicular to the ground and going through said point, right? If the ground is flat of course
I love how in the intro, the real life footage perfectly matches with the simulated footage afterwards. What I believe he did was reverse the footage of the first clip, first starting off with the 3D model in the precise position and then picking it up and turning it.
