mrdk

BeaBi, 1 day ago to random German

Wer die Hamburger Initiative "Laut gegen Nazis" dabei unterstützen möchte, dem braunen Merchandising das Leben zu erschweren, findet im Artikel die Kontaktmöglichkeit :nona:

https://www.tagesschau.de/inland/laut-gegen-nazis-enness-markenrechte-100.html?at_medium=mastodon&at_campaign=tagesschau.de

#noAFD #noNazis

11011110, 3 days ago to random

xkcd on "one-bit Bloom filter" (but isn't this really a zero-bit filter?): https://xkcd.com/2934/

Also, @xkcd seems to have stopped updating a couple weeks ago; anyone know what happened or how to get it going again?

beandev, 4 days ago (edited 3 days ago) to random German

Also die #Umfrage in der Bild ist ja wieder nice geframed.

Es gibt einen Deep-link zur Umfrage, um den Bild-Müll nicht lesen zu müssen, aber die #Verbrenner-Frage trotzdem beantworten zu dürfen.

Gleich mehrere Umfragen:

Abgeschaltet: https://interactive-web.la.spring-media.de/thumbs.html?id=76fc94e8-4977-b66e-6c09-bbcf3815ea57 (404)

Hier wird wieder ordentlich gegen das Verbrenner-Aus gevotet:

https://interactive-web.la.spring-media.de/poll.html?id=8d94dc7b-0bea-9ef9-9875-4a68e6387767

Bitte rege boosten :BoostOK:

#Klimakrise 🌍🔥

ColinTheMathmo, 19 days ago to random

Technically, we're all half centaur. -- Source unknown

oblomov, 1 month ago (edited 1 month ago) to math

A curious math problem I came up with: given a target, what's the fewest digits an integer must have (in a given base) to contain all integers from 0 to the target, as substrings?

http://wok.oblomov.eu/mathesis/number-substrings/

@mathematics @math @math

e.g. for a target of 19 a candidate representative would be 1011213141516171819 in base 10, that has 19 digits. Can it be done in less, or is $\sigma_10(19) = 19$?
Can we find a general rule? Any properties of this function?

#math #maths #numberTheory #combinatorics

ProfKinyon, 1 month ago to random

Theorem: If N is a positive integer and is not a perfect square, then (\sqrt{N}) is irrational.

Proof: Suppose (\sqrt{N} = a/b) for positive integers (a,b) with no common factor greater than 1. Then (b/a = \sqrt{N}/N), and so (a/b = (bN)/a). Since the first fraction is in lowest terms, the numerator and denominator of the second fraction must be a common integer multiple, say (c), of the numerator and denominator of the first. Hence (a = cb), and therefore, (\sqrt{N} = c), that is, (N) is a perfect square. QED

I learned this proof from a one paragraph insert in the American Mathematical Monthly (vol. 115, June-July 2008, p. 524) written by Geoffrey C. Berresford. I just love it.

joshuagrochow, 1 month ago to Matrix

No one defines a #matrix as "a thing that transforms like a matrix". Why define tensors that way?

Array=numbers in a (possibly high-dim) grid
Matrix=array representation of a linear map* in a chosen basis
Tensor=array representation of a multilinear map in a chosen basis

(* or linear endomorphism, or bilinear function, but we'll get there.)

Vectors=1-tensors, but not all 1-index arrays are vectors
Matrices=2-tensors, but not all 2-ary arrays are matrices

Similarly, not all k-ary arrays are tensors. Some examples:

Christoffel symbols aren't a tensor because they aren't (multi)linear in all of their arguments.

Most "tensors" in #MachineLearning #AI aren't tensors b/c they aren't multilinear - they are just multi-dim arrays of numbers. To say an array is (or represents) a tensor is to endow it with additional multilinear structure, same as with arrays vs matrices vs linear structure.

(1/4)

#tensors #matrix #algebra

johncarlosbaez, 2 months ago (edited 2 months ago) to random

I love this picture comparing different telescopes. Space telescopes are sexy - but the really big telescopes are down here. The Overwhelmingly Large Telescope is so big you might miss it: 100 meters across. Unfortunately the European Southern Observatory wimped out and decided to build a merely Extremely Large Telescope instead.

Radio telescopes are even bigger. The 305-meter dish at Arecibo is famous. In 2020 scientists decided to shut it down after it was damaged by a hurricane and two earthquakes and two important cables snapped. But before they could even shut it down, more cables snapped and the support structure, antenna, and dome assembly fell into the dish, destroying the whole thing.

Luckily in 2016 the Chinese had built an even larger radio dish in Guizhou: the Five-hundred-meter Aperture Spherical Telescope, or FAST. It's the largest one shown here. But in Russia there's a radio telescope 576 meters across - not a dish, but a bunch of separate structures.

And then there's the xkcd cartoon....

(1/2)

BartoszMilewski, 2 months ago to random

I wonder if there are cases of mathematical synesthesia. When you'd see mathematical equations or diagrams in color (or smell, taste?). I've heard of people seeing numbers as colorful, but what about higher levels of abstraction?

mrdk, 2 months ago to mathematics

I got interested again into “transformed addition” (which is not its real name, if it has one). This is a method to define a new addition-like (+_f) operations on the reals via a function ( f \colon \mathbb R \to \mathbb R ) the requirement that

[ x +_f y = z ]

is equivalent to

[ f(x) + f(y) = f(z). ]

An example is ( +_{\log} ), which is equivalent to multiplication.

Now I have found that

[ x +_{\arctan} y = \frac{x + y}{1 - x y},]
which is nice. But is there any use for this operation, especially outside trigonometry?

And has anyone developed a general theory of “transformed addition”? What is its real name?

#Mathematics #Algebra

BartoszMilewski, 2 months ago to random

I wonder if it makes sense to consider fractional logic. For instance if you have a fractional 1/3 inference rule, you'd have to use it three times to consume its premise once.

johncarlosbaez, 3 months ago (edited 3 months ago) to random

Hey! Please sign this petition - it could make a real difference:

https://www.change.org/p/urge-duke-university-to-reconsider-closing-their-herbarium

Duke University want to close its herbarium, a massive collection of 825,000 plant specimens. The Dean of Natural Sciences gives this reason: "we are a university with limited resources". But Duke has an endowment of $11.6 billion - and this is a key resource for studying biodiversity!

“There are no herbariums that could absorb something like this,” said Kathleen Pryer, the director of the herbarium. “I’m very concerned that it will end up in a warehouse somewhere and become forgotten.”

14,306 people have signed the petition to stop this. Can you help bring it up to 15,000?

Or if you want to read more first:

https://web.archive.org/web/20240224094530/https://www.nytimes.com/2024/02/21/science/duke-herbarium.html

I'll quote a bit:

"Herbariums have been a mainstay of biology for centuries. Botanists return from expeditions with dried leaves, flowers, stems and seeds, which are then stored for posterity. Some specimens have even been the basis for naming new species.

But herbariums are also valuable because they include plants collected over long stretches of time, helping scientists track the impact of humans on the environment. Some collections have shown that plants have shifted their ranges as the planet has warmed, for example.

The collections have become even more useful as technology has advanced. With improved DNA sequencing, researchers have begun to extract genetic material from dried plant specimens, tackling old scientific questions such as the origin of the world’s crops.

Botanists are far from finished documenting the diversity of plants. And every year, they identify new species that need to be stored because many are already threatened with extinction."

christianp, 3 months ago to random

This wave of spam after all that discussion of the opt-out bridge thing is really thought-provoking

dmm, 5 months ago to science

This paper describes the predatory bacterium Vampirococcus lugosii, which preys on members of the bacterial species of the genus Halochromatium [1].

This thing is incredible. For example: Vampirococcus lugosii has a severely reduced genome, something like 1.3 Mbp, and lacks the genes which code for many of the standard biosynthetic metabolic pathways (e.g. phospholipid synthesis, amino acid synthesis, and nucleotide synthesis). Yet it is somehow still alive.

How does this work?

One mechanism that Vampirococcus uses is to get these raw materials from its prey. An example of this are the nucleotides that Vampirococcus lugosii gets by chopping up the DNA that it sucks out of its prey. And amazingly, Vampirococcus lugosii uses a CRISPR-Cas system and various restriction enzymes to accomplish this. See the image for a cartoon of this system.

Predatory microbes.

Crazy.

---

Description of “Candidatus Vampirococcus lugosii”]

Lugosii after Bela Lugosi (1882–1956), who played the role of the vampire in the iconic 1931’s film “Dracula”. Epibiotic bacterium that preys on anoxygenic photosynthetic gammaproteobacterial species of the genus Halochromatium. Non-flagellated, small flat rounded cells (500–600 nm diameter and 200–250 nm height) that form piles of up to 10 cells attached to the surface of the host. Gram-positive cell wall structure. Complete genome sequence, GenBank/EMBL/DDBJ accession number PRJNA678638.

#biology #vampirococcuslugosii

References

[1] "Reductive evolution and unique infection and feeding mode in the CPR predatory bacterium Vampirococcus lugosii", https://www.nature.com/articles/s41467-021-22762-4

ColinTheMathmo, 5 months ago to random

Quote:

"Let me emphasize this: inmates took advanced math just for fun."

https://www.ams.org/journals/notices/201911/rnoti-p1821.pdf

mrdk, 5 months ago to fediverse

Today is John Mastodon Day: On this day one year ago, a journalist misunderstood some facts and created the person of “John Mastodon” of them (https://web.archive.org/web/20221216232836/https://www.mediaite.com/opinion/hypocrisy-and-fear-all-the-way-down-at-twitter). On that day, the Fediverse got a new meme, a patron saint and a running gag at the same time.
Let us all celebrate it!

#JohnMastodonDay #JohnMastodon #Fediverse

fractalkitty, 5 months ago (edited 5 months ago) to Haiku

I composed haiku without words and coded visuals to meditate, contemplate, and entrance.

Live View: https://haiku-without-words.netlify.app/

Code: https://github.com/fractalkitty/haiku-without-words

Codepen: https://codepen.io/fractalkitty/pen/ZEwNMEv?editors=0010

#haiku #music #meditation #decemberAdventure

mrdk, 5 months ago to mathematics

Yesterday was the 150th birthday of set theory. On 7th December 1873, Georg Cantor wrote a letter to his friend and colleague Richard Dedekind in which he showed that the set of integers is smaller than the set of real numbers, even if both sets are infinite.
This started a development that soon began to change mathematics: first by showing that infinite numbers are something one can meaningful talk about and that sets are a helpful tool for that, and then — most importantly! — through the possibility to build complex structures from nested sets, set theory gave mathematics the freedom to create arbitrary mathematical objects at will, whenever needed.
Before set theory, almost all mathematical objects were “something like numbers and functions” or “something like geometrical figures” or a mixture of both as in analytic geometry. The first discipline that does not fit into this schema must be topology: It cannot even be thought without sets. But even something like algebra has profited immensely from the ability to create arbitrary mathematical objects.

The birthday of set theory should therefore be celebrated by mathematicians all over the world. 🎂

(One of the people who discovered that in contrast to most other mathematical disciplines, set theory has a birthday, was @rudytheelder, but there is also Herbert Meschkowski, who in 1973 published a book in German with the title „Hundert Jahre Mengenlehre” that uses the same idea.)

#Mathematics #SetTheory

fractalkitty, 6 months ago to random

Drying and in poor lighting, but obviously requires two signatures because it has no orientation. Will seal and post better pics tomorrow.

Anyone else have tree and circle obsessions?

Acrylic, 15x30in

#mathart

Same painting with the blue circle on the bottom left and now in portrait orientation
Same painting with the red/orange circle on the bottom left and now in portrait orientation
Same painting in flipped landscape orientation.

dpiponi, 6 months ago to random

As I photograph my electronic book reader using my handheld supercomputer/communication device I can't help wonder what kind of world a sci-fi writer imagined in which there are neural interfaces to spaceships with hyperdrives but adjusting your watch is an unsolved problem.