I like this one as it asks to form an image and asks about clarity. The image is about hearing. So it crosses both parts.
Another example would be to form an image of a telemarketer on the telephone. Change the accent. Introduce line distortion.
For me it's in the middle. Happy birthday is clear to visualise and I can follow the tune. it's not very vivid but it's like I'm singing to myself with my mouth shut. I don't have a mental "visual" image of the song by default. When changing it the imagery appears a bit more but the focus is on the sound. I can easily change it to children's voices, the unix greybeards is more difficult as it requires me working out what they would sound like including spatial echoes from the auditorium. I find the resulting image (which is clearer than the children) is amusing.
I'm not envious of the people who have an inescapable inner voice. I think it would hinder my thoughts, the speed of it, and the ability to think abstractly. It's not totally baseless, because I can force myself to have an inner voice, but it's a conscious effort. Sometimes useful if I need to clarify my thoughts. On the same note, not having a inner voice makes it really difficult sometimes to put my emotions and thoughts into words.
But I'm really jealous about anyone that can clearly conjure images, "videos", and sounds in their mind, I feel like I have a big disadvantage if I want to learn to draw, 3D model, or play an instrument.
Now change this image of happy birthday so that it's now a childrens choir singing it. Now change it so its by a bunch of cynical unix grey beards singing it in a convention.
How easy was it to change this image? Did changing it affect the clarity?
For my favorite songs, I can recall it perfectly... But I don't hear it at all as if I was hearing it in real life. In fact, I don't know how to describe how vivid it is. Maybe I don't hear it at all? But I can sing these songs (out loud) without a problem.
However, I seem to be incapable of changing some elements about it. I can't seem to be able to make it faster, slower, change the singer, or the instruments. But, when I sing it out loud, I can of course modify it.
For "Happy birthday" (well, in my native language), it's really weird. Because I don't have a specific song in mind, I can follow the words, the tune, but I don't "feel" the voice of a specific singer. And I'm incapable to change this recall to different voices, like children or grown men. But if I listen to a version sung by these people, I can recall it after (until I forget).
Thanks again for these questions, I was aware of my lack of inner voice, my difficulties of a "inner sight" (that's a whole other can of worms), but I never applied this interrogations to a "inner hearing".
In parallel of my studies, I created some years ago on the side an interactive app for generating and coloring L-Systems : https://epholys.itch.io/lsys . It's a bit rough, but I created a lot of interesting trees (all here : https://imgur.com/a/0Rx7uln) and included them as a zip file alongside the app.
The Euler equations neglect viscosity.
> They also assume that fluids are “incompressible,” meaning that under the rules of the Euler equations, you can’t squeeze a fluid into a smaller space than the one it already occupies.
The Euler equations are compressible flow equations.
---
These two mistakes could have been corrected had the author read the first sentence of the wikipedia page about the Euler equations.
The TL;DR is that there are two papers that show that under many assumptions, simplified versions of the Euler equations (which are already a big simplification), blow up.
https://arxiv.org/abs/1904.04795https://arxiv.org/abs/1910.14071
> The Euler equations are not a literal description of a real-world fluid. They include several nonphysical assumptions. For example, the equations only work if internal currents within a fluid don’t generate friction as they move past each other. They also assume that fluids are “incompressible,” meaning that under the rules of the Euler equations, you can’t squeeze a fluid into a smaller space than the one it already occupies. > [...] > These unnatural provisos led the mathematician and physicist John von Neumann to quip that the equations model “dry water.” To model the motion of a more realistic fluid with internal friction (or viscosity), researchers use the Navier-Stokes equations instead.
So it seems they know what they are writing about, at least more than you supposed.
(As opposed to the non-dangerous way which means writing safe code to begin with and mentioning unsafe as the exception)