What’s the orientation of the Rope Trick hole?

The Rope Trick spell specifies

Holding one end of a 60-foot or shorter rope causes the other end to rise up until the rope is fully perpendicular to the ground. At the high end, a portal opens to an extradimensional space into which eight medium or smaller creatures can fit by climbing up the rope. The rope can also be dragged up into the space to hide the entrance and the portal itself is invisible.

Spells and attacks are unable to enter or exit the extradimensional space, but those within can see out of it as through a 3 by 5 foot window centered over the high end of the rope.

If everything inside the extradimensional space has not exited beforehand, it will fall out when the spell ends.

Our group has been playing under the assumption that the window is positioned vertical relative to the ground plane, because that’s the way most windows we see are positioned. This would mean that you climb into the hole as if on top of a cliff edge at the end of the rope and you then have a view of the world as if you’d be looking out of any normal building window.

However, this seems to be in contradiction with popular depictions on the internet.

The difference would be surprisingly relevant to some standard strategies we have been employing.

How is the Rope Trick portal positioned relative to the ground plane/gravity/the rope?

Sony Vaio Duo 11 touchppad and screen orientation not working on Ubuntu 19.04

I recently installed Ubuntu 19.04 on my Sony Vaio Dduo 11 ultrabook. Complete spec: https://www.cnet.com/products/sony-vaio-duo-11-svd11215cyb-11-6-core-i7-3517u-8-gb-ram-256-gb-ssd-qwerty/

The touchpad has 3 buttons (right click, left click, middle for scrolling). None of them work, but I can move the cursor using the touchpad.

The switch for automatic screen orientation also doesn’t work (when I press it – it is just like the super key.)

I tried:

apt upgrade && apt dist-upgrade.  kevin@mypc:~$   uname -a Linux mypc 5.0.0-20-generic #21-Ubuntu SMP Mon Jun 24 09:32:09 UTC 2019 x86_64 x86_64 x86_64 GNU/Linux 

Findng resources for this ultra book is pretty difficult. In Windows 10, the touchscreen buttons work fine, even before I install any driver.

Any help on this problem will be appreciated.

Questioning Pillars of Object Orientation

In this talk at DDD Amsterdam ’18, on The Systemics of the Liskov Substitution Principle, Romeu Moura says

you have object orientation when you have

  1. encapsulation
  2. decoupling
  3. coherence
  4. cohesion

And when someone asked about “Interface”, which is documented as a “Pillers of Object Orientation” in many computer science textbooks along with “Polymorphism and Abstraction”, he says

inheritance is there to help these four

Can anyone please tell me where I can find a document or a book reference claiming Romeu Moura is correct?

Can we approximate harmonic maps which are a.e. orientation-preserving with maps which preserve orientation globally?

Let $ \mathbb{D}^n$ be the closed unit disk, and let $ f:\mathbb{D}^n \to \mathbb{R}^n$ be harmonic; suppose that $ n \ge 2$ , and that $ \det df >0$ a.e. on $ \mathbb{D}^n$ .

Are there harmonic maps $ \omega_n: \mathbb{D}^n \to \mathbb{R}^n$ , such that $ \det d\omega_n >0$ everywhere on $ \mathbb{D}^n$ , and $ \omega_n \to f$ in $ W^{1,2}( \mathbb{D}^n,\mathbb{R}^n)$ ?

Change orientation in androidx86

How can I fully rotate my screen and not only resize it like in the picture?enter image description here

In already tried several rotation apps in the play store. I tried via root shell the commands: wm size, settings put system accelerometer_rotation 0 and settings put system user_rotation 0 both are working fine on my phone, but not on my tablet.

unoriented bordism with twisted orientation

The computation of the unoriented bordism group of the point $ N_*=\Omega_*^O$ is a classic result.

I would like to know a related bordism group, where we specify the twisted fundamental class $ [M]\in H_d(M,\mathbb{Z}^w)$ as part of the data. More precisely, I would like to consider the pairs $ $ (M, [M]\in H_d(M,\mathbb{Z}^w)) $ $ where $ \mathbb{Z}^w$ is the coefficient system twisted by $ w_1(M)$ ; I then call two $ (M,[M])$ and $ (M’,[M’])$ bordant when there is $ (N,[N]’)$ such that $ \partial N=M \sqcup M’$ where the twisted orientation of $ N$ induces that of $ M$ and $ M’$ , as in the case of oriented bordism.

Most probably this is well known to the experts…

Prove that every undirected graph has some orientation that is a Directed Acyclic Graph.

Prove that every undirected graph has some orientation that is a Directed Acyclic Graph.

I understand that in graph theory, an acyclic orientation of an undirected graph is an assignment of a direction to each edge (an orientation) that does not form any directed cycle and therefore makes it into a directed acyclic graph. Every graph has an acyclic orientation. But I’m not sure how to prove it. Any help would be appreciated!

Orientation on manifolds

I am trying to understand the definitions here. In many books an orientation on a manifold is an assignment to affix $ +1$ and $ -1$ to classes of (tangent) basis. It is proven in nearly every differential geometry book that connected manifolds admits exactly two orientations.

Here is what I don’t get, since you are assigning only $ \{\pm 1\}$ , how can it make sense to talk about anything but more than or fewer than two orientations? It only otherwise make senses to talk about not oriented right?

Removing the connectedness, can you even talk about, say three orientations?