Nick @internic@social.cleverlibre.org

@dpiponi - wow, and it's a real closed field! That means it becomes algebraically closed when you throw in 𝑖. But what's cool about real closed fields is that they have exactly the same first-order properties as the real numbers! Also, the first-order theory of real closed fields is complete and decidable! Also, there is an algorithm that, given any first-order formula in the language of real closed fields, produces an equivalent quantifier-free formula! A lot of this is the work of Tarski. Details here:

https://en.wikipedia.org/wiki/Real_closed_field

Well, shit
A lovely, simple yet useful little vector artwork program I've used to make T-shirt designs on my phone has:
Changed its name and logo
Pivoted to being "a tool to empower marketing teams"
Bloated up to over a half a gig in size, mostly stupid advertising templates
Breathlessly announced new "online collaboration" features, presumably to do a Figma
...and is now constantly nagging me to "Create an account and login"

I wrote an implementation of the Levi-Civita field in Haskell.

https://github.com/dpiponi/lcfield

I also added an interesting (I think) application. I wrote a little Runge-Kutta ODE solver and used it to solve d²x/dt²=-ω²x at ω=1 over the reals. I then used the LC-field to deform the equation to d²x/dt²=-ω²x at ω=1+ε. As a result, the RK solver doesn't just give you x at the end of your time period, it gives you a Taylor series for x as a function of ε which allows you to quickly compute the result of varying ω without having to rerun the solver.

An application of this kind of method can be found here: https://www.bmtdynamics.org/pub/papers/ApoDA09/ApoDA09.pdf
where used to find the probability of Apophis wiping out humanity or some such thing. (Actually, the LC-field is overkill, that paper just used the ring of truncated formal power series. My power series code would have worked just as well too. But it's fun to play with new toys.)

It's so long since I last wrote any Haskell I found myself using a C++-ism at one point. I wrote:
int main = do ...

Do I know any screen reader users who have successfully completed advanced math coursework? If so, I would like to meet with you. Boosts requested

A fatal flaw in the "be really hard on yourself as the mechanism to achieve" plan is that even when you achieve you absolutely cannot believe it, because you've really overtrained being hard on yourself. You see a systematic undervaluing that robs you of true information about your work.

So, one of the hallmarks of maladaptive high achievement I look for, as a psychologist studying productivity, is inability to really celebrate.

Please don't use the Stylish browser extension and userstyles.org. They're both owned by an advertising company, paywall basic features, and also this https://robertheaton.com/2018/07/02/stylish-browser-extension-steals-your-internet-history/

Use the "Stylus" browser extension instead. It's a fork of Stylish before they added the invasive tracking and paywalls. https://userstyles.world/ is also a community-ran alternative to userstyles.org, use that instead for sharing your styles.

#userstyles #userstyle #stylish #stylus

Our work on the theoretical foundations of results reproducibility is out at #RSOS and is open access. We dissect the relationship between open science, replication experiments, and reproducible results and challenge many deep-seated assumptions. We specifically show why meaningful replications need to be based on deeper theoretical understanding and stronger empirical foundations.
https://royalsocietypublishing.org/doi/10.1098/rsos.221042

@grimalkina Yeah, it definitely is an issue here within the #Mastodon community (I am not sure why). I know #Misskey & #Pixelfed are friendlier & seems more celebratory while Mastodon is more…political…I guess that would be the correct word.

Across about ten things this week, I'll say this: mastodon has a real toxic reply guy culture going on and it is exhausting to receive this EVERY SINGLE TIME you dare say something that gets attention, as a marginalized female scientist. Worse to me tbh than typical trolling because it is so deeply rooted in credibility deficit "know your place" patterns. You all are worse than birdsite for me, where I have nearly five times more followers. Definitely thinking about leaving.

Fix your hearts.

2 hours ago, Department of Condensed Matter Physics @ MFF UK #Praha reported (on Twitter, unfortunately), that they are taking their #LK99 samples out of the furnace after 6 hours at 925°C.

It would be exciting if one of the first confirmations of this discovery would be done in my hometown, which used to be European capital of #Alchemy for a brief period during #Renaissance times..

WHERE ARE MY X BUCKS, MUSKIE

https://www.theverge.com/2023/8/4/23820859/x-twitter-ad-sharing-payment-unpaid-delay-elon-musk

Can you roll a ball with exactly enough energy to reach the top of a dome, and have it reach the top in a finite amount of time?

I'm going to idealize the hell out of this problem so we can easily study it using math. So: no friction, no air resistance... in fact, NONE of the sneaky stuff you're probably thinking about!

The problem is still tricky. For an ordinary dome the answer is *no*. If the ball has just enough energy to make it to the top, it rolls slower and slower as it gets near the top, in such a way that it never reaches the top.

But if the dome has a carefully chosen shape, the ball can reach the top in a finite time! This was pointed out by the philosopher John D. Norton, so it's called "Norton's dome".

For a full explanation go here:

https://sites.pitt.edu/~jdnorton/Goodies/Dome/

Thanks to @SylviaFysica for pointing this out!

Norton was mainly interested in another freaky feature of his dome. Say you start with a ball at rest on top of the dome. Then there are many solutions of Newton's law

F = ma

In one the ball remains at rest on top of the dome. But in others, it starts to roll down the dome in some arbitrary direction! Moreover it can start rolling at any time.

If you change the shape of the dome ever so slightly, this probably won't work. It needs to be crafted with perfect accuracy. So this is basically just a mathematical curiosity.

Math folks will realize what's going on: not every first-order differential equation has a unique solution given its initial value. But Norton, being a philosopher of physics, manages to make this a lot more exciting than a typical textbook treatment of the Picard–Lindelöf theorem. 🙃

Here's the math:

https://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem#Example_of_non-uniqueness

@alexwild I have a bit of nostalgia for the time that Yahoo was trying to keep all pages in a defined categorised tree.

Now I can't even get Amazon to return search results related to or even containing the words in my search string.

Once again I see people talking about how Mastodon needs quote posts and full text search “right now" but is "opposed." Both features are on the road map (https://joinmastodon.org/roadmap) at the highest priority.

The actual problem is resources (money and/or qualified volunteers), which no one seems to talk about. People talk about Mastodon like it's equivalent to companies with billions in VC money, like the only barrier to implementing features is the desire to do so. The barrier is staffing.

Some of the best academic advice I ever got was "A paper is never really done, at some point you just have to set it free."

And yet...I find myself with a nearly-done paper that I just keep making more and more plots for! Someday I'll set it free, but not today, apparently.

Two things that make me cray-cray:

1) people who confuse kindness and mercy with weakness;

2) people who confuse values and beliefs with strongly-held (and usually very tenuous) personal convictions about nearly everything under the Sun.

Someone close to me once said the secret to happiness is to lower your expectations, or to limit the number of things you feel really strongly about.

I don't completely subscribe to this point of view. To me happiness has more to do with severely limiting the number of things I consider myself an expert on, and even then trying really damn hard to pretend I don't know anything about those subjects all day long.

https://www.youtube.com/watch?v=1ATJhCIeaqo