robryk @robryk@qoto.org

@freemo @zpartacoos @Electronics

> portable emergency battle

:D

> it even tells you the internal battery voltage of each of the 4 parallel cells separately

What do you mean by parallel here?

@freemo That's caused by qoto's CSP:

```
content-security-policy
base-uri 'none'; default-src 'none'; frame-ancestors 'none'; font-src 'self' https://qoto.org https://maxcdn.bootstrapcdn.com; img-src 'self' https: data: blob: https://qoto.org; style-src 'self' https://qoto.org https://maxcdn.bootstrapcdn.com https://miy.pw https://hcaptcha.com https://*.hcaptcha.com 'nonce-/wSZXEg7p+TWzLScbGBBUA=='; media-src 'self' https: data: https://qoto.org; frame-src 'self' https: https://hcaptcha.com https://*.hcaptcha.com; manifest-src 'self' https://qoto.org; connect-src 'self' data: blob: https://qoto.org https://storage.gra.cloud.ovh.net wss://qoto.org; script-src 'self' https://qoto.org https://maxcdn.bootstrapcdn.com https://hcaptcha.com https://*.hcaptcha.com; child-src 'self' blob: https://qoto.org; worker-src 'self' blob: https://qoto.org
```

That you can just change. If it's really that MathJax is loading something from somewhere else, and you find that acceptable, then adding that somewhere else to style-src would work.

@freemo I also get lot of CSP errors: `Content Security Policy: The page’s settings blocked the loading of a resource at inline (“style-src”).` that point at MathJax.js:19:16737 and thereabouts.

@freemo For me it never actually displays a rendered version even for a moment, but sometimes (when I refresh the whole page) it displays the raw, unrendered version instead, and that version is not replaced by anything for at least ~30s.

@freemo MathJax issue: https://qoto.org/web/statuses/107122108820756990 renders as lots of whitespace and broken text in 3 column view for me. Screenshot attached.

When I look at the DOM, I see lots of spans with font size of 800%~900%.

I was slightly wrong. In actuality, \(I = C_1^T*J*C_1 + C_2^T*J*C_2\) for some \(C_{1,2}\). I should write it up fully, which I'll do soon (tm).

An easy way to see why the original was wrong is that this is the difference between \((a^T+b^T)M(a+b)\) and \(a^TMa+b^TMb\). I could have also been clued in by the impossible properties I claimed C has in [1].

Why the standard way to describe rotational inertia of a body is to specify its moment of inertia matrix?

Moment of inertia matrices are somewhat weird: not every symmetric semipositive-definite matrix is a valid moment of inertia matrix (note that there can be no body that has nonzero moment of inertia about exactly one of its principal axes).

Moment of inertia matrix is expected to satisfy I_{around e} = e^T*I*e [0]. At the same time I_{around e} = \sum m_i*r_{perp to e}^2 = \sum m_i*(r_{b1}^2+r_{b2}^2) where b1 and b2 are some orthogonal basis of the surface perpendicular to e.

This creates a natural idea: if we define J := \sum m_i*r_i^T*r_i, then I = C^T*J*C (see [1] for value of C), _and_ every semipositive definite J corresponds to an object that could possibly exist.

So, why don't we use this J instead of I? I think it is less confusing, and seems to be way better e.g. if we're numerically trying to find a moment of inertia that optimizes for something.

[0] So I = \sum m_i*||r_i||^2*Proj_{perp to r_i}^T*Proj_{perp to r_i}

[1] C = \sum_{i != j}e_i^T*e_j (btw. it's not immediately obvious to me that this definition is invariant wrt orthonormal base change, and if you have a succinct description of why it is so, I'd appreciate seeing it)

@Pat @freemo "Very quickly" still leaves an observable portion of the stream where this hasn't happened yet:

If you open your tap just a little bit, you'll notice that the stream narrows downward, and at some point breaks into droplets.

The narrowing obviously is caused by the water still accelerating: the total volume-based flow of water is conserved, so the crosssectional area of the stream is inversely proportional to the speed.

Also note that terminal velocity of a stream should be much higher than that of a droplet, because only viscous friction slows it down (as opposed to having to move the air "sideways" too).

@freemo So your hypothesis is just that the heights are scaled up due to high viscosity, not that the effect will never happen? (I can see how viscosity can change the time required, but can't see how it can affect whether the whole thing happens at all.)

Actually, I might be able to predict how viscosity, vertical air speed, initial radius, and maybe something else (density?) too affect the distance just by dimensional analysis. Hm~ figuring out how those parameters and liquid-air surface tension affect the height sounds like a nice problem, solutions to which can be verified: I can adjust many of these parameters by e.g. mixing up various concentrations of soap in water, and should be able to measure them independently. If by some amount of luck I find enough time and will to do it, will be sure to write it up.

When a vertical stream of liquid is high enough, usually the stream starts to fragment into drops. The standard explanation for that that I believe is that the falling liquid is sped up, so the stream narrows, and at some point the stream is narrow enough that droplets are a lower energy state from a surface tension POV.

I today noticed that streams of my shower gel either never fragments into drops, or they require a height that I cannot provide before that happens.

@pbx One would hope that browsers would provide the expected tooltips for dates enclosed in a <time> tag (https://developer.mozilla.org/en-US/docs/Web/HTML/Element/time). Alas, my Firefox seems to ignore those tags.

Imagine a ball (of uniform density) rolling on a horizontal plane without slipping. Due to its symmetry its angular speed in the reference frame of the plane will remain constant over time if it's not disturbed[1]. Its angular speed has three components. What I found surprising (but is obvious if we present it this way) is that by only nudging the ball horizontally you can't get it to spin around the vertical axis: so, horizontal nudges allow one to explore only a 2d subspace of the 3d space of the angular speeds.

tl;dr I got surprised by a consequence of the fact that while rotations around different axes do not commute, infinitisemal rotations (and thus angular speeds) do commute.

[1] If its density was not symmetric, it could undergo precession and nutation.

@freemo I'm somewhat confused by this aspect of safety. Would doing the longer (for air) profile using EAN be just as (un)safe as doing the profile for air with air? (I'm trying to figure out if this is safer just because there is a risk that's ~proportional to time spent underwater, or if there's something specific that e.g. makes slower deco less well understood.)

@freemo Is the "safely" part due to nitrogen narcosis, something else, or both?

@freemo So technically some Trimixes could be available (the ones where the ratio of nitrogen to oxygen is at least 4:1, so they can be mixed out of air, nitrogen and helium)?

@freemo Well, gases enriched in oxygen don't help with the second problem :)

For sake of pure curiosity: do you know if there are issues with supply of anything other than air, or anything that has higher oxygen concentration than air?

@freemo Can't, or that deco would be infeasibly long?

@freemo Then you might find https://www.swiss-divers.ch/informationen/tauchplaetze/zuerichsee-tauchplaetze/ useful. Disclaimer: I have no clue how accurate that is.

@freemo I don't know. But this is where he worked for most of his life, where his experiments to create the model were executed, and where first dives using his tables happened (Lake Zürich is more than 100m deep in the deepest point).

@freemo You reminded me that I wanted to write to the street naming commission, because it's kinda weird that there's no Bühlmann's street in Zürich.