Hey, they did it! People have known for a long time that in 4 dimensions you can pack equal-sized balls so that each touches 24 others. In 2008 someone showed that's the best you can do. But in April this year, three mathematicians showed there's essentially just 𝑜𝑛𝑒 𝑤𝑎𝑦 you can accomplish this!

This way is easy to describe. Take the points whose coordinates are all integers, together with those whose coordinates are all integers plus 1/2. Use each of these points as the center of a ball of radius 1/2. Then each ball touches 24 others. This pattern is called the 𝗗𝟰 𝗹𝗮𝘁𝘁𝗶𝗰𝗲.

The new result shows that if you pack equal-sized balls in 4 dimensions so that each touches 24 others, you're 𝑓𝑜𝑟𝑐𝑒𝑑 to create a version of the D4 lattice - possibly rotated, translated and/or rescaled.

This sort of thing is hard to show: it took a lot of fancy math and two weeks of calculation on a standard desktop computer. I believe only other dimensions where we know a result like this are 1, 2, 8 and 24. In dimension 3 it's just false: you can pack equal-sized balls so that each touches 12 others, and this is the best you can do, but there are uncountably many different ways to do it!

arxiv.org/abs/2404.18794

Optimality and uniqueness of the $D_4$ root system

We prove that the $D_4$ root system (the set of vertices of the regular $24$-cell) is the unique optimal kissing configuration in $\mathbb R^4$, and is an optimal spherical code.

^arXiv.org

I'm a little puzzled at the salience that is being given to the Apple conclusions on #LLM #reasoning when we have lots of prior art. For example: LLMs cannot correctly infer a is b, if their corpora only contain b is a. #Paper: arxiv.org/abs/2309.12288

#AI #MachineLearning #logic

The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"

We expose a surprising failure of generalization in auto-regressive large language models (LLMs). If a model is trained on a sentence of the form "A is B", it will not automatically generalize to the reverse direction "B is A".

^arXiv.org

Remember this? Where ministers belonging to the biggest party in government were hellbent on deporting a sick child before his application could be approved but their coalition partners effectively vetoed it meaning the kid and his family got asylum?

ruv.is/english/2024-10-09-yaza…

Well, it’s looking like this pissed that party’s MPs off to such an extent that the government has collapsed, meaning we’re about to have an election about the same time as the Americans.

Yazan and family receive asylum in Iceland - RÚV.is

Yazan Tamimi and his parents received asylum in Iceland yesterday. Last month they were scheduled to be forcibly removed to Spain, but the Minister of Justice stopped the deportation after an intervention by the Minister of Social Affairs.

^RÚV

A la vuelta de la manifestación por #viviendadigna me he encontrado con Francisco Aijon, el padre de uno de #Los6DeZaragoza y hemos estado hablando un poco.

Están intentando presionar al #psoe a través de #sumar para ver si hacen algo, pero por lo que comenta no hay mucha esperanza.

Cago en todo.

Que asco de vida.

Se pueden hacer muchas cosas inteligentes desde el prisma tecnocrático, regulatorio y fiscal para atajar el problema de la vivienda. Y a cualquier burócrata le tiran las ganas de ir por ahí, porque aprecia la elegancia de la intervención mínima.

Pero al ser tan listos, también hay un gran margen de error.

A veces no hay que ser tan listos. Llega con actuar con seriedad, consistencia y proporcionalidad (a un gran problema, una gran solución).

Mi solución tonta al problema de vivienda: construcción financiada por las AAPP, parque permanente de alquiler con contratos de largo plazo (10, 15 años), a coste más 10%, el 10% se invierte en construir o adquirir más vivienda.

Which Global Superpower do you trust most to maintain a mutual peace and invest in a sustainable future?

#Mastodon

• USA (22%, 8 votes)
• China (77%, 28 votes)
• Russia (0%, 0 votes)

One thing I still like about twitter is their 'spaces'. What would be a good open source alternative to that?

I accept it won't (easily) integrate to Mastodon's web UI, which would be ideal, but I am looking for as low a barrier as possible:

- No new apps, so Mumble drops out
- Web UI
- No account
- Audio-only

Any suggestions?

Etiquette tip

If you go somewhere posh and you're worried about using the wrong knife or passing the butter incorrectly and other such 'rules', remember:

Those who matter don't notice; those who notice don't matter.

Took me almost 50 years to learn that.

Phishing emails look exceptionally good these days. I got a few that looked completely legitimate. My email spam didn't even catch them

Please remind yourselves, your family, & friends that if something seems SHOCKING in email, especially related to your banks or Venmo/PayPal accounts, close the email and look in your app or web account.

Do not click links. Do not call any listed phone numbers. Open your account and check there first

If something is still wrong, call the number in the app

Ich will garantiert nicht protzen oder angeben, das ist überhaupt nicht in meiner Natur.

Aber gerade wurde mein demnächst erscheinendes neues Album als "Die beste neue #Musik des Jahres, die ich bisher gehoert habe!" bezeichnet, und ich muss zugeben:

Das tut einfach gut.

Ich *brauche* es nicht, ich lebe nicht dafür, aber:

Es tut einfach so verdammt gut.

Im Herzen drin.

Wenn mal was zurück kommt.

Und wenn es dann auch noch so etwas ist.

Danke.

❤️

The last time I made a video about #Ableton, it was to do with Note, their iOS music-making app.
This video is an Ableton-first, in which I bring you their newest piece of hardware, #AbletonMove.
It ships with a web-based screen-reader and I've been enjoying it for many months.
It uses sounds from Note, but in a hardware form.
32 poly-aftertouch pads, four tracks of midi (or samples,) 8 knobs, USB-C for power and controlling Ableton Live and a USB-A port for connecting class-compliant midi devices, should you wish to trigger it from a keyboard.

Please be advised that screen-reader support is currently an experimental feature and is not fully fleshed out.
Not all aspects of the experience are as desired and there are a few kinks, but it is very much better than nothing whatsoever, and I am extremely thankful to the team that made this possible.

Ableton themselves are not talking about this screen-reader function in any of their literature, but I think it's important enough that it deserves recognition, and to bring an accessible groove-box to blind people in this way.

#InspiredBySound - Let's Move! (Ableton Move Accessibility Overview) youtu.be/p8IbinbOhY4
#Accessibility #ScreenReader

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