Bay 12 Games Forum

Please login or register.

Login with username, password and session length
Advanced search  
Pages: 1 ... 240 241 [242] 243 244 ... 339

Author Topic: SCIENCE, Gravitational waves, and the whole LIGO OST!  (Read 406166 times)

i2amroy

  • Bay Watcher
  • Cats, ruling the world one dwarf at a time
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3615 on: March 28, 2016, 10:25:52 pm »

Aha! But see if you have two Mobius strips and each one has one edge than together they will have edges! Checkmate good sir!

:P
Logged
Quote from: PTTG
It would be brutally difficult and probably won't work. In other words, it's absolutely dwarven!
Cataclysm: Dark Days Ahead - A fun zombie survival rougelike that I'm dev-ing for.

Starver

  • Bay Watcher
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3616 on: March 28, 2016, 11:54:12 pm »

What.

I mean, Mobius loop, yes, Klein bottle, yes, but you lost me with the topology.  I think that's topology.  Is it topology?
I think so.  Although I'm too busy rotating and rippling a hypothetical Klein Surface in four dimensions to actually load up my internal dictionary as well.

Aha! But see if you have two Mobius strips and each one has one edge than together they will have edges! Checkmate good sir!

:P
Take a donut (or torus, if you prefer, but.... *mmmmm* donuts *slaver*) and imagine a hole in one edge of the surface, which you open up and then turn the rest of the donut inside out through, before closing it back up again...  there is no hole (it was just a topological conceit, and if you were willing to let the toroidal membrane intangibly pass through itself, intact, it would have had the same effect).  And what was the major circular axis of the torus is now the minor circular axis, and vice-versa.

No, nothing to do with Mobiuseseses, directly, but just because you see a surface edge/boundary at one point in the process doesn't mean that it exists at all points in the process.  As I'm sure you know :P :P :P

(@TheDarkStar: "edges" would be correct.  One edge from Mobius Strip 'A', one edge from Mobius Strip 'B'.  Made to touch all the way around (forced into the 4th dimension and/or allowed to separate in a carefully allowed 'exception' of continuity), such that what were edges to both strips are now just straight, edgeless, and travel sideways from any given point transitions across to the other strip, across the width of the other strip, feely transitioning across the counterpart 360 degrees 'opposite' edge position (of a full 720-degree arc/rotational symmetry of 0.5) seamlessly back across the first strip towards the original starting point....  yes, that seems to work, in my head.)
Logged

Solifuge

  • Bay Watcher
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3617 on: March 29, 2016, 01:04:43 am »

Take a donut (or torus, if you prefer, but.... *mmmmm* donuts *slaver*) and imagine a hole in one edge of the surface, which you open up and then turn the rest of the donut inside out through, before closing it back up again...  there is no hole (it was just a topological conceit, and if you were willing to let the toroidal membrane intangibly pass through itself, intact, it would have had the same effect).  And what was the major circular axis of the torus is now the minor circular axis, and vice-versa.

I believe this is what happens when you 4D-spin a Toroid (Doughnut), and look at it in 3-Space too:

It's not really accurate except when thinking of it in 3D with 4D perspective, but I usually think of the 4D Axis as In (Negative) and Out (Positive). Inward-distant things appear smaller in 3-Space representations, and Outward-distant things appear larger. It's a lossy visual metaphor as much as putting cubes on a chalkboard is, but it's why Tesseracts look like they have tiny cubes in them, etc,. and the lines and such are all just edges of the cubes that make up each 4D face/cell/whatever (which is moving "in" as it gets 4-Space distant). When very 4D-close or 4D-distant, things would appear to stretch to cover everything in 3-Space, or shrink to nothingness, (This is what happens when the doughnut flips it's shit in the animation too).

(I kinda think this is why gravity pulls things toward things too. Stuff's trying to move down a 4D slope, but can only move in 3D, so the "In" force gets deflected into 3D, the same way a billiard ball with an effectively 2D force applied collides and rolls along the 1D edge of a pool table. But that's just another half-baked attempt at conceptualizing this stuff)

Side note: I'm starting to wonder if it's possible to make a VR Game which displays 4 Spatial Dimensions projected down using Stereoscopic 3D, and wondering how much of a headache it would induce.

« Last Edit: March 29, 2016, 01:11:55 am by Solifuge »
Logged

Helgoland

  • Bay Watcher
  • No man is an island.
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3618 on: March 29, 2016, 06:49:13 pm »

Hmm, you sure we aren't saying the same thing? To use the terms as I understand them, A Mobius Loop is a non-orientable manifold of 1 dimension fewer than a Klein Bottle, yeah? Just as there's no distinction between the top and bottom of a 3D Mobius Loop, there's no distinction between the inside and outside of a true 4D Klein Bottle. In 3D, it's just warped a bit funny, due to not being able to extend the surface out/in in that direction.

It's just as possible that I don't get the distinction you're pointing out here, though. I'm in no way classically-trained, and my grasp of formal terminology is pretty sparse.
Naah, both the Möbius strip and the Klein bottle are two-dimensional manifolds - they locally look like the two-dimensional real plane, after all. What's important is that they are abstract objects - they're separate from their embedding into three- or four-dimensional space. What you're calling 'warped a bit funny' is the observation that the Klein bottle cannot be properly embedded into three-dimensional space; trying to do so comes at the price of self-intersection. It's very important that the self-intersecting object you get no longer is a Klein bottle, or even just a manifold at all!
It's rather counterproductive to cling to this sort of visualization anyway. Here is a more elegant way to think about Klein bottles and Möbius strips, which makes several of the glueing statements in the thread fairly easy to see:
Spoiler (click to show/hide)

'Morally', as my topology prof would say, the comparison between Möbius strip and Klein bottle that you make is correct. However it's hard to make it rigorous: You're looking at the boundary of the Möbius strip, but the Klein bottle does not have a boundary. The better comparison is: Just as you cannot distinguish front and back of a Möbius strip, you cannot distinguish between the inside and the outside of a Klein bottle - that's basically what non-orientability is. In fact that's precisely what you see if cut out a piece of a Klein bottle that looks like a Möbius strip, as in the spoiler above. Generalizing this, a surface is non-orientable iff you can embed a Möbius strip into it, and I think similar statements hold in higher dimensions.
The whole orientability thing gives rise to a lot of interesting topology - look into differential topology and the transversality theory in particular if you want more of this ;)
Logged
The Bay12 postcard club
Arguably he's already a progressive, just one in the style of an enlightened Kaiser.
I'm going to do the smart thing here and disengage. This isn't a hill I paticularly care to die on.

Furtuka

  • Bay Watcher
  • High Priest of Mecha
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3619 on: April 05, 2016, 11:34:49 am »

http://news.yale.edu/2016/04/04/chasing-after-prehistoric-kite-runner

Fossil of ancient ocean arthropod discovered that carried its young by tethering them to its body and having them just trail along after it
Logged
It's FEF, not FEOF

Cryxis, Prince of Doom

  • Bay Watcher
  • Achievment *Fail freshman year uni*
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3620 on: April 05, 2016, 07:27:21 pm »

Take a donut (or torus, if you prefer, but.... *mmmmm* donuts *slaver*)

Logged
Fueled by caffeine, nicotine, and a surprisingly low will to live.
Cryxis makes the best typos.

Solifuge

  • Bay Watcher
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3621 on: April 06, 2016, 04:00:24 pm »

http://news.yale.edu/2016/04/04/chasing-after-prehistoric-kite-runner

Fossil of ancient ocean arthropod discovered that carried its young by tethering them to its body and having them just trail along after it

Cool! My Mom used to do this to my sibs and I when we were kids too.
Logged

Levi

  • Bay Watcher
  • Is a fish.
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3622 on: April 12, 2016, 01:25:04 pm »

Logged
Avid Gamer | Goldfish Enthusiast | Canadian | Professional Layabout

Aklyon

  • Bay Watcher
  • Fate~
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3623 on: April 12, 2016, 02:02:07 pm »

So whose going to power the lasers?
Logged
Crystalline (SG)
Sigtext
Quote from: RedKing
It's known as the Oppai-Kaiju effect. The islands of Japan generate a sort anti-gravity field, which allows breasts to behave as if in microgravity. It's also what allows Godzilla and friends to become 50 stories tall, and lets ninjas run up the side of a skyscraper.

Starver

  • Bay Watcher
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3624 on: April 12, 2016, 03:27:08 pm »

So whose going to power the lasers?
Sister Miriam?
Logged

Gentlefish

  • Bay Watcher
  • [PREFSTRING: balloon-like qualities]
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3625 on: April 12, 2016, 07:28:20 pm »

Sounds like they're earth-based, being shot at the laser sails. Considering the fact that they said they'd reach 0.2c in a matter of minutes, it's not unlikely.

This is really really cool though. Although, they never did give us how long it would take at 0.2c to get to alpha centauri.

Cthulufaic

  • Bay Watcher
  • whats a touhou
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3626 on: April 12, 2016, 07:37:43 pm »

Sounds like they're earth-based, being shot at the laser sails. Considering the fact that they said they'd reach 0.2c in a matter of minutes, it's not unlikely.

This is really really cool though. Although, they never did give us how long it would take at 0.2c to get to alpha centauri.
I read a similar article that said around 24 years, and then another 4 for us to actually receive any data from it.
Logged

PTTG??

  • Bay Watcher
  • Kringrus! Babak crulurg tingra!
    • View Profile
    • http://www.nowherepublishing.com
Logged
A thousand million pool balls made from precious metals, covered in beef stock.

Aklyon

  • Bay Watcher
  • Fate~
    • View Profile
Re: SCIENCE, Gravitational waves, and the whole LIGO OST!
« Reply #3629 on: April 17, 2016, 08:47:42 am »

Time for new circuits?
Logged
Crystalline (SG)
Sigtext
Quote from: RedKing
It's known as the Oppai-Kaiju effect. The islands of Japan generate a sort anti-gravity field, which allows breasts to behave as if in microgravity. It's also what allows Godzilla and friends to become 50 stories tall, and lets ninjas run up the side of a skyscraper.
Pages: 1 ... 240 241 [242] 243 244 ... 339