SK

@sk607
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52 Posts

Metronomes started randomly synchronize after a short period of time as they influence each other through the side-to-side motion of their shared base.

Source: UCLA Physics & Astronomy
https://demoweb.physics.ucla.edu/content/160-spontaneous-synchronization

Mathematics has never ever been adversarial until now. The fact that mathematicians may freely assume good faith of all their fellows is what has made the review of both non-mechanised and mechanised mathematics tractable.

"Autoformalisation" is a buzzword for a new kind of mathematics that is inherently adversarial. Whether a result is a theorem or an "exploit" (hahaha) will take immense amounts of energy to determine.

I don't think that people are really understanding how absolutely crucial the non-adversarial nature of mathematics has been, and how the loss of the good-faith assumption could actually lead to mathematics being set back hundreds or even thousands of years. It's existential.

There is a full universe behind that wonderful new Artemis II "Night Marble" view of Earth.

Here's a breakdown of the stars (and one planet) in the field of view. Look at us! Just a planet hanging out in space.

Annotation by Rodrigo GonzΓ‘lez Peinado. Orientation set with north at the top.

#space #science #nature #Artemis2

During thunderstorms, electric discharges in the air cause trees to glow with an ultraviolet aura. You can't see it with your eyes, but researchers have finally managed to measure it & recreate it in the lab.

https://news.agu.org/press-release/thunderstorms-conjure-ghostly-coronae-in-treetops-observed-outdoors-for-the-first-time/ #science #nature

The ability to make complex distinctions with high accuracy after ingesting a sufficient amount of training data is a signature feature of machine learning algorithms. But humans also have this ability, even if they are not always consciously aware of it. One of my favorite illustrations of this is the learned ability to determine (qualitatively) the temperature of water from its sound, which almost all of us have acquired purely through training data: https://www.youtube.com/watch?v=Ri_4dDvcZeM

We even have the learned ability to accurately predict the next word in a sentence, even when we do not understand the semantic content of the sentence itself. Some (rather frustrated) examples of this occur in the later stages of the classic "Who's on first?" sketch: https://www.youtube.com/watch?v=r9t097tbeT0

You Can Hear The Difference Between Hot and Cold Water

YouTube

What Americans die from vs. what's reported in the media

by @ourworldindata

Here is my presentation from today at COS on:

"The sorry state of scientific publishing and how we could move to an open and resilient infrastructure"

https://jekelylab.github.io/COS_goes_FOSS_publishing.html#/title-slide

#publishing #foss #openscience #opensource

It's sad to see the decay of science information online.

For the 30th anniversary, NASA posted hi-res Voyager images and in-depth details.
For the 35th, lo-res images and in-depth details.
For the 40th, a cartoon and a short blurb, along with a dead link.

#tech #history #nasa

Some geometry problems are easy to state but hard to solve! For any triangle, can an ideal point-sized billiard ball bounce around inside in a π‘π‘’π‘Ÿπ‘–π‘œπ‘‘π‘–π‘ trajectory - a path that repeats?

The answer is "yes" for acute triangles, and this has been known since 1775. It's also "yes" for right triangles. But for obtuse triangles, nobody knows!

In 2008, Richard Schwartz showed that the answer is "yes" for triangles with angles of 100Β° or less. He broke the problem down into cases and checked each case with the help of a computer. Then progress was stuck... until 2018, when Jacob Garber, Boyan Marinov, Kenneth Moore and George Tokarsky showed the answer is "yes" for triangles with angles of 112.3Β° or less.

Beyond that we're stuck.... except for triangles with all π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™ angles (measured in degrees). For them too the answer is "yes".

The picture here is from

George Tokarsky, Jacob Garber, Boyan Marinov, Kenneth Moore, One hundred and twelve point three degree theorem, https://arxiv.org/abs/1808.06667

and for more check out this article on Quanta:

https://www.quantamagazine.org/the-mysterious-math-of-billiards-tables-20240215/

One Hundred and Twelve Point Three Degree Theorem

It has been known since Fagnano in 1775 that an acute triangle always has a periodic billiard path, namely the orthic triangle. It is currently unknown whether every obtuse triangle has a periodic path. In 2006, Schwartz showed that every obtuse triangle with obtuse angle at most 100 degrees has a periodic path. The aim of this paper is to show that every obtuse triangle with obtuse angle at most 112.3 degrees has a periodic path using a computer assisted proof.

arXiv.org