weekend_editor

johncarlosbaez, 16 days ago (edited 16 days ago) to random

@TruthSandwich got me interested in the vibrational modes of bells. They're not harmonics with frequencies 1, 2, 3, 4, ... times the lowest frequency: they're much more complicated! That's why bells sound clangy. This chart shows how they sometimes work.

The lowest frequency vibrations are called:

• the 'hum' (the lowest frequency)

• the 'prime' (with frequency roughly 2 times that of the hum)

• the 'tierce' (roughly 2.4 times the hum, so a minor third above the prime)

• the 'quint' (roughly 3 times the hum, so a major fifth above the prime)

• the 'nominal' (roughly 4 times the hum, so an octave above the prime)

and so on. If you think these names are illogical, join the club! One reason it's tricky is that the loudest vibration is not the lowest one: it's the 'prime'.

The numbers I just gave you should be taken with a big grain of salt. They really depend on the shape of the bell, and you'd have to be great at designing bells to make them come out as shown here. It's not like a violin string or flute, where the math is on your side.

This quote helps explain the chart:

"Modern theory separates the modes of vibration into those produced by the "soundbow" and those produced by the remaining bell "shell". The bell vibrates both radially and axially and the principal vibrational modes are shown in the diagram together with their classification using the scheme proposed by Perrin et al. This scheme consists of the mode of vibration (RIR - Ring Inextensional Radial, RA - Ring Axial, R=n - Shell driven), the number of meridians (where “m” is half the number of meridians) and the number of nodal circles (n)."

Starting to sound like orbitals in quantum mechanics!

(1/3)

cstross, 20 days ago to random

Today's writing: what if Doctor Phibes murdered and impersonated Max, owner of the KitKatKlub, in order to run an elaborate sting against Doctor Mabuse—film recap, starring Vincent Price, Diana Rigg, Charlotte Rampling, and Peter Cushing.

johncarlosbaez, 22 days ago to random

The press likes to talk about problems, so it paints everything as a problem. But some problems are better than other problems.

From here: https://archive.is/lx6CC

cstross, 24 days ago to random

From America with cash: Right-wing groups want to end abortion in the UK

A right-wing political and media ecosystem pushing a US-style anti-abortion agenda is gaining traction in the UK

https://www.opendemocracy.net/en/us-anti-abortion-culture-war-uk-stella-creasy-amendement-/

Meanwhile:

YouGov survey finds nearly 90% of Britons support abortion

https://www.msichoices.org/latest/yougov-survey-finds-nearly-90-of-britons-support-abortion-in-the-uk/

seraph, 1 month ago to random

this shit is so funny

Are you serious, X Corp? Ahoy there, welcome to roblotwitter! I assure you, there's nothing fishy going on here, so feel free to read on. Yeah, it's a "honeypot". Sorry about that. I'm not trying to apologize and get away with it, though. But when you clicked on this link, you probably thought you were looking at something like "roblox.com". Simple URL substitution can cause this kind of thing to happen, so I made this site. So let's shout it out. "Are you serious, X Corp?"

johncarlosbaez, 1 month ago (edited 1 month ago) to random

What math should you know before studying the proof of Fermat's Last Theorem? That's what this video answers.

It's pretty funny. I don't want to completely give it away, but I know a fair amount of math, and a sinking feeling spread over me as the video went on... so I'm curious when that feeling will hit you.

Eventually the guy suggests that you should really learn French... so you can read Grothendieck's 12-volume Séminaire de Géométrie Algébrique, which is thousands of pages long. But for me, even that's not the worst part!

The good news is that this guy, Anthony Vasutaro, admits it's fine to plunge in and learn stuff as needed. Even better, he is really serious about this stuff. He has a huge series of videos explaining the proof of Fermat's Last Theorem in detail.

Personally I'm more interested in the 'big ideas' than the actual proof. And for the big ideas, I'm finding Nigel Boston's paper quite nice:

• The proof of Fermat's Last Theorem, https://people.math.wisc.edu/~nboston/869.pdf

Beware: this is only for mathematicians! There are lots of other introductions at varying levels of intensity. No matter how little math you know, there's one that you'll enjoy.

https://www.youtube.com/watch?v=MnAvpa1oUEk

cstross, 2 months ago to random

I notice that the Odysseus commercial lander a US company just plonked on the Moon cost NASA a little over $100M.

By way of comparison, the Indian government's Chandrayaan-3 mission, the lander of which touched down in 2023, cost roughly $90M.

So private space can be more expensive than 100% government agency-run missions.

gutenberg_org, 2 months ago to science

Austrian physicist and philosopher Ludwig Boltzmann was born #OTD in 1844.

His greatest achievements were the development of statistical mechanics, & the statistical explanation of the second law of thermodynamics. In 1877 he provided the current definition of entropy, S = kB ln Ω, where Ω is the number of microstates whose energy equals the system's energy, interpreted as a measure of statistical disorder of a system. Max Planck named the constant kB the Boltzmann constant.

#science #physics

Title page to volume I and II of "Vorlesungen über Gastheorie" by Ludwig Boltzmann (1896-1898). Copy located in the Niels Bohr Library & Archives, American Institute of Physics, in College Park, Maryland.

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

How can we save the wonderful wildness of nature?

In 2017, Douglas Eger founded Intrinsic with the goal of creating "natural asset companies" (NACs). The idea is that a landowner works with investors to create a NAC that licenses the rights to the ecosystem services the land produces. If the company is listed on an exchange, a public offering of shares would provide the landowner with a revenue stream.

Sound impractical? Here's what happened. The Rockefeller Foundation kicked in about $1.7 million to fund the effort. In 2021, Intrinsic announced its plan to list NACs on the New York Stock Exchange. They filed an application with the Securities Exchange Commission (SEC).

Then the American Stewards of Liberty, a Texas group that campaigns against conservation measures, picked up on the plan. Through both grass-roots organizing and high-level lobbying, they argued that NACs were a Trojan horse for foreign governments and “global elites” to lock up large swaths of rural America, prevent mining in parks, etc. The SEC started to get tons of criticism.

A group of 25 Republican attorneys general called it illegal and part of a “radical climate agenda.” On Jan. 11 this year, the Republican chairman of the House Natural Resources Committee sent a letter demanding a slew of documents relating to the proposal. Less than a week later, the SEC gave up on allowing NACs.

This makes me think the idea actually might have been practical! Otherwise why work so hard to kill it?

The above is paraphrased from a NY Times article. You can read the whole thing for free here:

https://web.archive.org/web/20240218132637/https://www.nytimes.com/2024/02/18/business/economy/natural-assets.html

johncarlosbaez, 2 months ago to random

Today I got some questions about logic, like:

what do provability, decidability, consistency, and completeness mean?
how do we work with equality in set theory?

I don't know articles that explain topics like this to non-mathematicians, clearly and crisply, without becoming overlong or heavy with notation. Do you?

I looked around and found this "Introduction to First-Order Logic":

https://builds.openlogicproject.org/content/first-order-logic/introduction/introduction.pdf

but the very first sentence is

"You are probably familiar with first-order logic from your first introduction to formal logic."

which is basically a way of saying "fuck you - if you don't know this stuff already I won't explain it to you".

As a student I liked Boolos and Jeffrey's book "Computability and Logic":

http://alcom.ee.ntu.edu.tw/system/privatezone/uploads/Logic/20090928151927_George_S._Boolos,_John_P._Burgess,_Richard_C.

but that's more like a course than what I'm thinking of here: a collection of essays that explain different topics in plain English.

I also liked Hofstadter's "Gödel, Escher, Bach", but that's a massive quirky elaborate tale, not a simple clear explanation.

Wikipedia articles are packed with information but they aren't self-contained, clearly written essays. Articles in the Stanford Encyclopedia of Philosophy are better in some ways, but they often "show off" by including more advanced material.

Sigh....

inthehands, 2 months ago to random

There’s a lot to chew on in this short article (ht @ajsadauskas):
https://www.bbc.com/worklife/article/20240214-ai-recruiting-hiring-software-bias-discrimination

“An AI resume screener…trained on CVs of employees already at the firm” gave candidates extra marks if they listed male-associated sports, and downgraded female-associated sports.

Bias like this is enraging, but completely unsurprising to anybody who knows half a thing about how machine learning works. Which apparently doesn’t include a lot of execs and HR folks.

1/

cstross, 3 months ago to random

Infosys enjoyed a boom in UK government invoices in 2023

Tech services biz Infosys enjoyed a 49 percent increase in its invoices from the UK government for 2023, according to research figures.

(Infosys was founded by the Prime Minister's father-in-law and his wife is a major shareholder.)

https://www.theregister.com/2024/02/13/infosys_uk_government_contracts/

cstross, 3 months ago to random

MAD CONSPIRACY THEORY: JFK, as POTUS, had access to the FTL drive of the saucer that crashed at Roswell.

FTL implies time travel. So it's a time machine.

He saw his 2nd term would be dominated by the Vietnam War turning to shit, so he assassinated himself to trigger a grandfather paradox then bumped off Elvis and replaced him then lived happily ever after.

This is as plausible as the current Taylor Swift nonsense, amirite?

gutenberg_org, 3 months ago to books

English author, poet, mathematician and photographer Charles Dodgson was born #OTD in 1832. Within the academic discipline of mathematics, Dodgson worked primarily in the fields of geometry, linear and matrix algebra, mathematical logic, and recreational mathematics, producing nearly a dozen books under his real name. To promote letter writing, Dodgson invented "The Wonderland Postage-Stamp Case" in 1889.

Books by Lewis Carroll at PG:
https://www.gutenberg.org/ebooks/author/7

#books #lietrature

Photo of Alice Liddell taken by Lewis Carroll (1858) Lewis Carroll - The Life and Letters of Lewis Carroll, p. 80 Alice Liddell as a beggar-maid (from the story of Cophetua). Supposed tear hole or ink-blot in photo digitally removed. This was first published in Carroll's biography by his nephew: Collingwood, Stuart Dodgson (1898) The Life and Letters of Lewis Carroll, London: T. Fisher Unwin, pp. p. 80
Title page of The Life and Letters of Lewis Carroll (Rev. C. L. Dodgson) by Collingwood, which is available at PG: https://www.gutenberg.org/ebooks/11483

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

My mom grew up in rural Michigan in the 1940s, when almost everyone was a churchgoer and people used lots of euphemisms when swearing. So instead of the exclamation "God!" they'd say "gosh!" Instead of "hell!" they'd say "heck!" And though the exclamation "holy Moses!" isn't taking the Lord's name in vain, even that sometimes got watered down to "holy moly!"

So I loved this joke:

Q: What happens to people who don't believe in gosh?
A: They go to heck.

But yesterday something else happened to remind me of all this. A computer science student whose native language is not English wrote that they were going to a "heckathon". That's a great name for a hellishly hectic programming event!

cstross, 4 months ago to random

I am currently sleeping 11-12 hours overnight … and needing a 2 hour afternoon nap as well. And that's WITH the SAD lamps!

lilithsaintcrow, 4 months ago to random

“‘Impossible’ to create AI tools like ChatGPT without copyrighted material, OpenAI says.”

Then fucking pay for it honestly or fucking perish, you fucking grifters.

https://www.theguardian.com/technology/2024/jan/08/ai-tools-chatgpt-copyrighted-material-openai

johncarlosbaez, 4 months ago to random

Imagine the gravitational equivalent of a hydrogen atom. This would be two particles bound by their gravitational attraction, described by a quantum-mechanical wave function.

Alas, nobody has ever seen such a thing. But why not?

The particles couldn't be charged, since then the electromagnetic force would swamp the gravitational force. But suppose we used neutrons! We can work out the Bohr radius of two gravitationally bound neutrons, ignoring the nuclear force between them, and...

...well, I'll leave it as a puzzle: is it very large, or very small?

If it's very small, then of course the nuclear force would swamp the gravitational force, and that would explain why we don't see "gravitational atoms" made of 2 neutrons.

But if it's very large, then on average the neutrons would be quite far apart, so the nuclear force between them might really be negligible: that force goes to zero much faster than the inverse square law obeyed by gravity. So then things get more interesting!

johncarlosbaez, 4 months ago (edited 4 months ago) to random

You may have seen this Jedi math trick: take something that makes sense with real numbers and try it with complex numbers. Weird yet useful things happen.

For example it turns out that imaginary time is 1/temperature. Hawking used this to compute the temperature of black holes.

An easier example is that the exponential function applied to an imaginary number gives you the trig functions sine and cosine.

Indeed, if ω is any complex number, exp(iωt) is a function of time that oscillates at a frequency equal to the real part of ω, and decays exponentially at a rate equal to the imaginary part of ω. So we can think of ω as a complex frequency! Its real part is an ordinary frequency, while its imaginary part is a decay rate.

Thus, in music it makes sense to consider tuning systems where the frequency ratios are complex. I haven't yet found anything interesting to do with this thought. But it makes sense to have notes that oscillate but also decay.

Here's a dumb idea. Nobody knows Bach's original well-tempered scale. In 1977, Herbert Anton Kellner had a wacky suggestion: the beats in the major third (which is close to a frequency ratio of 5/4, but not quite) should have the same frequency as those of the perfect fifth (which is close to 3/2, but not quite).

This led him - the derivation is too long to fit in the margin of this post - to the 'Bach equation':

F⁴ + 2F - 8 = 0

where F is the frequency ratio of the perfect fifth. He got a solution

F ≈ 1.495953506

for the perfect fifth. But it also has a negative solution, and two complex solutions that aren't real. Do these mean anything?

Maybe you can come up with a better idea about complex tuning systems....

johncarlosbaez, 4 months ago (edited 4 months ago) to random

For my Christmas present this year I hope Santa fixes this website - or shuts it down. This symbol does not mean "approximately equal to" - that's

≈

This symbol means "isomorphic to", or "congruent to". I cannot stand another year with this misinformation ruining my Google searches.

https://www.fileformat.info/info/unicode/char/266f/index.htm

𝐍𝐚𝐫𝐫𝐚𝐭𝐨𝐫: 𝐁𝐮𝐭 𝐭𝐡𝐞 𝐩𝐫𝐨𝐛𝐥𝐞𝐦 𝐠𝐨𝐞𝐬 𝐝𝐞𝐞𝐩𝐞𝐫 𝐭𝐡𝐚𝐧 𝐁𝐚𝐞𝐳 𝐭𝐡𝐢𝐧𝐤𝐬. 𝐑𝐞𝐚𝐝 𝐨𝐧!

johncarlosbaez, 4 months ago (edited 4 months ago) to random

Yes, this guy is playing Scottish folk music in a pub on Christmas eve... on a bouzouki! This instrument jumped from Greece to Ireland in the 60s, but now it's used in Scottish folk music too.

We're having a great evening. I hope you are too.

For more on the Irish bouzouki, try this:

https://en.m.wikipedia.org/wiki/Irish_bouzouki

lednabwm, 5 months ago to random

Hmmm....🤔 🤣😂🤣😂🤣

siderea, 5 months ago (edited 5 months ago) to random

There are two problems that are coming for Mastodon of which apparently an awful lot of people are unaware. These problems are coming for Mastodon not because of anything specific to Mastodon: they come to all growing social media platforms. But for some reason most people haven't noticed them, per se.

The first problem is that scale has social effects. Most technical people know that scale has technological effects. Same thing's true on the social side, too.

🧵

CC: @Gargron