Notices by John Carlos Baez (johncarlosbaez@mathstodon.xyz), page 6

@kevinrns - I agree with you. When I talk about the collapse of civilization I'm talking about climate change. But if we could break free from the grip of the super-rich we could tackle that. Already last year we added 50% more renewable energy last year than the year before. China added enough solar to power more than 50 million homes.

What's that country smaller than Cuba?

@detritus - it's true that *more energy* won't save, only *less carbon emitted*. But the revolution in solar power is having some effects. Carbon emissions are dropping in the US and EU, as even this somewhat old chart shows (that trend is continuing). Unfortunately that trend was overshadowed by China's skyrocketing emissions. So I'd say our future depends a lot on what the Chinese and Indians do.

@kevinrns

@detritus - No, the decline in US carbon dioxide emissions is not due to COVID. If you actually look at the graph you'll see US carbon emissions have been dropping since 2007, with little wiggles. They've dropped 20% since 2007 - and we expect them to keep dropping!

There was indeed a plunge during COVID, and it bounced back in 2023. But US carbon dioxide emissions in 2023 were 4,778 megatonnes, down 20% from the peak in 2007, namely 6016 megatonnes. Carbon emissions are expected to drop in 2024.

Too bad this information isn't more widely known! For data up to 2022 go here:

https://www.statista.com/statistics/183943/us-carbon-dioxide-emissions-from-1999/

and for more recent data go here:

https://www.eia.gov/outlooks/steo/report/total.php

@kevinrns

If our civilization collapses, extraterrestrial archeologists can look at this and be impressed. Three satellites following the Earth in an equilateral triangle, each 25 million kilometers from the other two. Each contains two gold cubes in free-fall. The satellites accelerate just enough so they don't get blown off course by the solar wind. The gold cubes inside feel nothing but gravity.

Lasers bounce between each cube and its partner in another satellite, measuring the distance between them to an accuracy of 20 picometers: less than the diameter of a helium atom! This lets the satellites detect gravitational waves — ripples in the curvature of spacetime — with very long wavelengths, and correspondingly low frequencies.

It should see so many binary white dwarfs, neutron stars and black holes in the Milky Way that these will be nothing but foreground noise. More excitingly, it should see mergers of supermassive black holes at the centers of galaxies as far as... the dawn of time, or whenever such black holes were first formed. (The farther you look, the older things you see.)

It may even be able to see the "gravitational background radiation", the thrumming vibrations in the fabric of spacetime left over from the Big Bang. This radiation was created before the hot gas in the Universe cooled down enough to become transparent to light. So it's older than the microwave background radiation, which is the oldest thing we see now.

It's called LISA - the Laser Interferometric Satellite Antenna. And we're in luck: ESA has just decided to launch it in 2034.

I cannot tell you about anything interesting today, because I'm rushing to finish a grant proposal that might help other people get paid to do something interesting.

Soon I will see if I can upload an .xslx file without buying Excel. Wish me luck.

The music director of Leipzig died in 1722, so the city council held an audition for his replacement. The winner was Georg Philipp Telemann. He went back to Hamburg, where he worked, and demanded a raise. They gave him the raise, so he stayed in Hamburg.

Next they tried to hire Christoph Graupner, one of the foremost composers of the day. He worked in Darmstadt, but the city wouldn't let him go. Back then you often needed permission from your employer to get a new job.

One of the Leipzig city councilors said: "Since the best men cannot be obtained, we must make do with the mediocre."

So they hired Johann Sebastian Bach.

Big news in bug math. This is the first year since 1803 when both 13-year cicadas and 17-year cicadas will emerge from the ground simultaneously in the US!

13 and 17 are both prime. It's believed cicadas evolved to have prime-number life cycles to avoid predators that emerge more frequently, like once every 4 years or 5 years or... whatever. By showing up infrequently, with a prime number life cycle, they can starve out those predators.

And since 13 and 17 are both prime and 13 × 17 = 221, both kinds of cicadas emerge simultaneously only once every 221 years. And

1803 + 221 = 2024

so now they'll both emerge simultaneously and we'll have 𝑙𝑜𝑡𝑠 of cicadas!

Also, this year the two kinds can interbreed! Maybe they're be fruitful and multiply... and we'll get 221-year cicadas. 😆

The last time the Northern Illinois Brood’s 17-year cycle aligned with the Great Southern Brood’s 13-year cycle, Thomas Jefferson was president.

https://www.nytimes.com/2024/01/19/science/cicadas-emergence-broods.html

"To compensate for the shortcomings caused by its degeneration, some cheese makers resort to supplementing P. camemberti with a second species of fungi: Geotrichum candidum, also selected for its white, cottony texture.

So what can be done to save Camembert? Should producers return to a “wild” population, similar to P. camemberti, and restart the long process of domestication? Could they resort to genome editing technologies in order to counter the accumulation of mutations or the loss of specific genes with a given desirable function? “People in the industry sometimes ask us whether it’s possible to modify a gene and allow a strain to sporulate in greater quantities,” Giraud reveals, quickly adding that this would not solve the problem: “Genome editing is another form of selection. What we need today is the diversity provided by sexual reproduction between individuals with different genomes.”

A species that is genetically similar to P. camemberti, called Penicillium biforme, also found in cheese because it is naturally present in raw milk, possesses an incredible genetic and phenotypic diversity. This opens up the possibility of inoculating Camemberts and Bries with P. biforme. If cheese lovers want to keep enjoying these products, they will have to learn to appreciate greater diversity in flavour, colour and texture, perhaps even among cheeses from a single source. And, who knows, thereby contribute to enriching our gastronomic heritage."

Below you can see P. camemberti, which is white, and P. biforme, which is green. Look yummy?

I got all this from here, where you can also read about the Roquefort crisis:

https://news.cnrs.fr/articles/french-cheese-under-threat

(2/2)

Camembert is an endangered species! It relies on a mold that had lost the ability to reproduce sexually... and now, thanks to inbreeding, this mold has also lost the ability to reproduce using spores. Roquefort is also in trouble, but for Camembert it's worse:

"The world over, this other symbol of French gastronomy is inoculated exclusively with one single strain of Penicillium camemberti, a white mutant that was selected for Brie cheeses in 1898 and Camemberts in 1902.

The problem is that ever since then the strain has been replicated by vegetative propagation only. Until the 1950s, Camemberts still had grey, green or in some cases orange-tinged moulds on their surface. But the industry was not fond of these colours, considering them unappealing, and staked everything on the albino strain of P. camemberti, which is completely white and moreover has a silky texture. This is how Camembert acquired its now-characteristic pure white rind.

Year after year, generation after generation, the albino strain of P. camemberti, which was already incapable of sexual reproduction, lost its ability to produce asexual spores. As a result it is now very difficult for the entire industry to obtain enough P. camemberti spores to inoculate their production of the famous Norman cheese.

Worse still, while the Roquefort PDO (Protected Designation of Origin) standard retains a degree of microbial biodiversity, the PDO specifications for Camembert require farmers and other producers to use P. camemberti exclusively."

What to do about it? Switch to eating American cheese, or Velveeta? Read on....

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@phiofx - "do these constraints reflect some generic feature of our neural network topology?"

I don't think it's our neural network topology: I think the common features of music between culture traces its way back to the math of vibrations, overtones and resonance. The octave and perfect fifth having the simplest frequency ratios, namely 2 and 3/2, gives them special physical properties. The major third, with frequency 5/4, is also important.

It surprised me at first how similar western music is, in its basics, to Carnatic and Hindustani music. All of them prominently feature 7-tone scales contained in the 12-tone chromatic scale, and the favorite 7-tone scale is always the one that contains a frequency, the frequencies 3/2 and 2/3 times that, and the frequencies 1, 5/4 and 3/2 times all those. This forms 3 "triads" shown below in the key of C in western music notation.

@skarthik

I don't post much about serious math here anymore. But here's a little piece of category theory connected to music. I dreamt this up thanks to a comment from @skarthik.

In Carnatic music there are 72 seven-note scales called 'Melakarta ragas'. By cyclically permuting the notes of a Melakarta raga you sometimes get another Melakarta raga. This process is called 'graha bhedam':

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

This would give an action of the group ℤ/7 on the set of Melakarta ragas... except sometimes when you cyclically permute the notes of a Melakarta raga you 𝑑𝑜𝑛'𝑡 get another Melakarta raga, since there are constraints on which 7-note scales count as Melakarta ragas. So we only have some sort of partially defined group action. Let's make up a definition:

Let's say a 'partial group action' of a group 𝐺 on a set 𝑋 is a partially defined map

𝐺×𝑋→𝑋
(𝑔,𝑥)↦ 𝑔𝑥

such that:

1. for all 𝑥∈𝑋, 1𝑥 is defined and equal to 𝑥.
2. If one of (𝑔ℎ)𝑥 and 𝑔(ℎ𝑥) are defined, then so is the other, and they are equal.

Now the interesting thing is that any partial group action gives a groupoid where

• the objects are elements of 𝑋
• a morphism 𝑔:𝑥→𝑦 is an element 𝑔∈𝐺 with 𝑔𝑥 = 𝑦
• the composite of morphisms 𝑔 and ℎ is their product in the group 𝐺.

This construction is famous for ordinary group actions:

https://ncatlab.org/nlab/show/action+groupoid

but it works fine for partial group actions!

So, there's a groupoid of Melakarta ragas. The Wikipedia article shows that Carnatic music theory is concerned with the connected components of this groupoid: that is, bunches of Melakarta ragas related to each other by graha bhedam.

One reason we can't have Trump as president: he operates as a gangster. Today's bomb threat to the judge in his bank fraud trial is just the latest example. Two weeks ago, after the Colorado Supreme Court ruled him ineligible to run for office because of the insurrection he led, they got hit with death threats. And many in the Republican party have fallen in line because of such threats - see below!

People not following the news may not realize how big a problem this is.

It works like this: Trump threatens that judgements against him will cause havoc... and his more unhinged supporters fill in the details. It's called 'stochastic terrorism' - and it's not just chatter. Republican attacks against the Speaker of the House eventually led a guy to break into her house: not finding her home, he broke her husband's skull with a hammer. Earlier, right-wingers plotted to kidnap the governor of Michigan, but were stopped by the FBI.

It's horrific. If we don't stop Trump by making him lose this election, we're going to have a mob boss in charge of the USA.

For more details, read on!

(1/n)

https://www.vox.com/23899688/2024-election-republican-primary-death-threats-trump

Here are 41 cases of violence before May 2020 in which the perpetrator explicitly said they were supporting Trump. I don't know if this has been updated more recently. It's easy to look up that 1,265 people have been charged with crimes connected to the January 6th insurrection, and 467 have been sent to prison so far. But I'm more interested in the use of death threats and attacks to punish Trump's opponents.

ABC News could not find a single criminal case filed in federal or state court where an act of violence or threat was made in the name of President Barack Obama or President George W. Bush.

(2/n)

https://abcnews.go.com/Politics/blame-abc-news-finds-17-cases-invoking-trump/story?id=58912889

These days I'm digging into the math of 'just intonation' - one of the most popular tuning systems in the late Middle Ages and early Renaissance. The idea here is that all frequency ratios should be products of the primes 2, 3 and 5. In this article I explain why it became more popular than the earlier Pythagorean system which only used the primes 2 and 3.

Basically, it seems that around 1300 English musicians started writing music that relied heavily on the frequency ratio

5/4 = 1.25

Pythagorean tuning approximates this by

81/64 = 1.265625

but that's sort of annoying. So, the English system spread into Europe - perhaps helped by the Hundred Years’ War (1337–1453), when northern France was sometimes occupied by the English.

The math of this tuning system goes a lot deeper than I explain here... but that's why this is only Part 1!

One problem is that people who know math jargon often don't know music jargon, and vice versa. So, if you want to use the concepts of "free commutative monoid" and "major triad on the fourth", you either have to explain both concepts, explain one and alienate one audience while boring the other... or explain neither and alienate almost everyone. There are a few people who write about music theory assuming you know both math and music jargon. They publish it in serious journals. But they are talking to very few people, I'm afraid! That's a pity, since the stuff is so cool. So I'm pulling my punches and trying to be really gentle.

https://johncarlosbaez.wordpress.com/2023/10/30/just-intonation-part-1/

Perth-based composer Alan Lamb makes music from the resonance of wires.

At the age of 5, he remembers his nanny putting her ear to the telephone poles to "hear the sound the world made". Later he had a recurring dream, in which the sound of a sustained major sixth emanated from a train which descended distant hills and then ran through the air above where he was standing.

Pursuing these memories, in 1974 he constructed devices to amplify the upper harmonics of nylon and catgut threads. Later he got the idea of using wires suspended in magnetic fields and of 'strumming' them using pulsed electric currents. The device produced interesting sounds - but he was not yet satisfied.

One night in the summer of 1975, during a holiday in Scotland, he pulled to the roadside to sleep in his in his van. Later he was awoken by the sound of another major sixth - but this time it was not a dream. He had stopped beside telephone wires which sang throughout the night, the sound waxing and waning with the wind! Hearing the wires sing, Lamb felt emotionally transported and became determined to record their music.

Later he returned to Australia to pursue postgraduate research into neurobiology. As his progressed, he continued to feel deeply frustrated in his attempts to record the music of wires.

A breakthrough occurred in 1976 when he visited the Great Southern Region of Western Australia. He found a half-mile stretch of abandoned telephone wires... all singing softly in the wind. Lamb was able to buy them for just $10 - and thus began his musical career.

He's now considered one of the founders of "dark ambient" music.

(1/2)

https://www.youtube.com/watch?v=WnlNbb8eric

@textproof - on the shows I'm talking about you should take a strong opinion and defend it vigorously but not define your terms.

Though part of me - the worst part - would like to join the clever crowd who endlessly pontificate and interview each other, I'm held back by my intense aversion to publicly talking about:

1) consciousness
2) free will
3) string theory and other theories of everything
4) are mathematical objects real?
5) is reality a simulation?
6) interpretations of quantum mechanics
7) quantum computers
8) large language models, machine learning, AI

and most other topics that the "digiterati", the "intellectual dark web", and other quasi-scientific talking heads enjoy bloviating about. I'd much rather curl up with a good solid book on the life cycle of lichens, or the organizational structure of car repair shops.

A report from an executive of DuckDuckGo attending the antitrust lawsuit against Google:

"Google likely alters queries billions of times a day in trillions of different variations. Here’s how it works. Say you search for “children’s clothing.” Google converts it, without your knowledge, to a search for “NIKOLAI-brand kidswear,” making a behind-the-scenes substitution of your actual query with a different query that just happens to generate more money for the company, and will generate results you weren’t searching for at all. It’s not possible for you to opt out of the substitution. If you don’t get the results you want, and you try to refine your query, you are wasting your time. This is a twisted shopping mall you can’t escape.

Why would Google want to do this? First, the generated results to the latter query are more likely to be shopping-oriented, triggering your subsequent behavior much like the candy display at a grocery store’s checkout. Second, that latter query will automatically generate the keyword ads placed on the search engine results page by stores like TJ Maxx, which pay Google every time you click on them. In short, it's a guaranteed way to line Google’s pockets."

I hope we'll see more evidence proving or disproving this, since September 28, the court established a process allowing the Justice Department to publish more information about this case.

https://www.wired.com/story/google-antitrust-lawsuit-search-results/

The University of Pennsylvania is acting proud of Katalin Karikó now that she's won a Nobel. But they kicked her out of her research assistant professor job when she insisted on doing the work that won her that prize:

"She recalls spending one Christmas and New Year’s Eve conducting experiments and writing grant applications. But many other scientists were turning away from the field, and her bosses at UPenn felt mRNA had shown itself to be impractical and she was wasting her time. They issued an ultimatum: if she wanted to continue working with mRNA she would lose her prestigious faculty position, and face a substantial pay cut.

”It was particularly horrible as that same week, I had just been diagnosed with cancer,” said Karikó. “I was facing two operations, and my husband, who had gone back to Hungary to pick up his green card, had got stranded there because of some visa issue, meaning he couldn’t come back for six months. I was really struggling, and then they told me this."

"While undergoing surgery, Karikó assessed her options. She decided to stay, accept the humiliation of being demoted, and continue to doggedly pursue the problem. This led to a chance meeting which would both change the course of her career, and that of science."

Elsewhere she recalled:

“I thought of going somewhere else, or doing something else. I also thought maybe I’m not good enough, not smart enough."

She's now an adjunct in UPenn's neurosurgery department. Will they fast-track her for tenure now that she has a Nobel, or just live with the shame?

Both quotes here come from interesting stories. The first is from here:

https://www.wired.co.uk/article/mrna-coronavirus-vaccine-pfizer-biontech

The second is from here:

https://billypenn.com/2020/12/29/university-pennsylvania-covid-vaccine-mrna-kariko-demoted-biontech-pfizer/

Wow! I just learned that Isaac Newton wrote a treatise about music theory, comparing just intonation with equal tempered scales!

This was in 1643, when he was 22: the year he fled Trinity College to avoid the Great Plague, went to the countryside, invented calculus, and discovered a prism can recombine colors of light to make white light.

This great new video about Newton's never-finished treatise is probably the most pleasant way to learn about this stuff.

One reason Newton's work is amazing is that while an equal tempered scale - one with notes equally spaced - is standard now, it was very unusual in Newton's time. Much more common was just intonation, where the frequency ratios are simple fractions.

Another reason Newton's work is amazing: he compared just intonation not only to a 12-tone equal tempered scale, but also to equal tempered scales with 15, 19, 20, 24, 25, 29, 36, 41, 51, 53, 59, 100, 120 and 612 notes! He discovered that the 12, 53, 120 and 612 note scales work especially well.

The 53-note equal tempered scale actually goes back to the Chinese music theorist Jing Fang (78–37 BC), who discovered that a series of 53 just fifths is very nearly equal to 31 octaves. Later the same observation was made by Nicholas Mercator. (No, not the guy with the map, another Mercator: the one who invented natural logarithms.)

I don't know if Newton could have known of Mercator's work - but he *was* influenced by Descartes's Compendium Musicae.

https://www.youtube.com/watch?v=83ytb6AWRAk