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John Carlos BaezJ

johncarlosbaez@mathstodon.xyz

@johncarlosbaez@mathstodon.xyz
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Recent Best Controversial

  • Good news!
    John Carlos BaezJ John Carlos Baez

    @ChrSt - I know what you mean. It may not come as quick as 2028, but the technology seems real. Companies have been working on it for decades:

    "Still, like any advance at the cutting-edge of electrical or electronic technology, solid-state cells are really, really hard to take from the lab to production EVs. For every 100 promising lab tests of batteries in general, perhaps one will advance to a prototype line—and fewer yet into high-volume production. Toyota learned that lesson 15 years ago, when it couldn’t produce the lithium-ion cell it chose for the third-generation 2010 Toyota Prius—and had to revert to its tried-and-true, 15-year-old nickel-metal hydride cells.

    Toyota has long been a proponent of solid-state cells. It has said it believes EVs will not be suitable for mass adoption until solid-state batteries arrive. But even mighty Toyota has struggled to get solid-state cells into production. It first showed a prototype solid-state cell 15 years ago, in December 2010. Through most of the 2010s, it said it would put solid-state cells into production by 2020. In late 2023, the company announced that date had slipped to 2027. "

    https://www.caranddriver.com/features/a63306863/solid-state-batteries-evs-explained/

    Uncategorized

  • Good news!
    John Carlos BaezJ John Carlos Baez

    @arsatiki - I don't mind 2030. As you get older time seems to go faster. Since I'm old, to me 2030 is almost the same as 2028.

    Uncategorized

  • Good news!
    John Carlos BaezJ John Carlos Baez

    @isocat - no, because it's the NOT SUFFICIENTLY ROUNDED conversion. 1000 kilometers has one significant digit - it's clearly a rough estimate. Claiming the car goes 621 miles is bullshit. Does it always conk out on mile 622?

    Uncategorized

  • Good news!
    John Carlos BaezJ John Carlos Baez

    @lluad - but also because the writer doesn't get the idea of "significant figures". It's like when a reporter hears a tree is 300 meters tall and reports that it's 11811.0236 inches tall. (Okay, I'm exaggerating.)

    Uncategorized

  • Good news!
    John Carlos BaezJ John Carlos Baez

    @arsatiki - I may be overoptimistic, but things are looking better now in various ways:

    "EVs with semi-solid-state batteries are already rolling out in China, albeit in small numbers. Customers can buy and drive them today, thanks to early adopters such as Nio and the state-backed SAIC Motors that invested in the tech early. In the West, Mercedes-Benz and BMW are testing solid-state batteries, and Stellantis is planning to begin trials next year.

    Japanese and Korean automakers are also working on this tech, but they’ve been tight-lipped about their plans. In 2022, Nikkei reported that Toyota held the highest number of solid-state battery patents, followed by Panasonic and Idemitsu."

    https://insideevs.com/news/771402/every-solid-state-battery-ev/

    Uncategorized

  • Good news!
    John Carlos BaezJ John Carlos Baez

    I'm trying to figure out how the new solid-state batteries work. So far I'm getting this:

    They use a solid lithium sulfide-based electrolyte - a glassy ceramic material made using Li₂S and P₂S₅, which combine to form various lithium thiophosphates like Li₃PS₄, Li₇P₃S₁₁ and Li₄P₂S₆. The resulting sulfide glass has a high conductivity for Li⁺ ions, comparable to liquid electrolytes. The Li⁺ ions hop through the disordered sulfide lattice via vacancies and interstitial sites.

    The hard part: the glassy material should be soft enough to keep contact with the electrodes as it expands and contracts during charge-discharge cycles, and not crack. Toyota claims to have solved this problem.

    https://oilandenergyonline.com/articles/all/toyotas-breakthrough-solid-state-batteries/

    (Nerdy nitpick: this article says the new car's range is 621 miles. Can you guess why they give such a precise figure?)

    (2/2)

    Uncategorized

  • Good news!
    John Carlos BaezJ John Carlos Baez

    Good news! By 2028, Toyota expects to make electric cars with a 1000 kilometer (600 mile) range with batteries that can be charged in just 10 minutes!

    They're using 'solid-state batteries'. Currently a lot of car batteries use an organic solvent with a dissolved lithium salt. The new solid-state batteries replace that flammable liquid with a glassy material containing compounds of lithium, sulfur and phosphorus. They charge faster, they have 10 times the energy density, and don't easily catch on fire. But they are tricky in various ways.

    Toyota wants to win the race, and they've teamed up with a Japanese oil company that will manufacture the battery material. But Mercedes-Benz and other companies are also in the race. The activity in China is particularly intense, as you'd expect.

    https://electrek.co/2026/02/09/big-oil-is-betting-big-on-toyota-to-win-the-solid-state-battery-race/

    (1/2)

    Uncategorized

  • Math is everywhere.
    John Carlos BaezJ John Carlos Baez

    The Meso-American Long Count identified any day by counting how many days passed since the world was created. This count is more or less in base 20, except that the second “digit” is in base 18, since they liked a year that was 18 × 20 = 360 years long. So,

    7.16.6.16.18

    would mean

    7 × 144,000 + 16 × 7,200 + 6 × 360 + 16 × 20 + 18 = 1,125,698 days

    after the world was created. But if the first digit was 8 instead of 7, the date would be 144,000 days later.

    The Olmec's other calendar, the Tzolkʼin, uses a 260-day cycle. Here each day gets its own number and name: there are 13 numbers and 20 names. And the rock the Stirlings found had inscribed not only the last four digits of the Mesoamerican Long Count, but also the Tzolkʼin day: 6 Etz’nab.

    Here’s why 7 was the only possible choice of the missing digit. Because the last four Long Count digits (16.6.16.18) are fixed, the total day count must be

    B × 144,000 + 117,698.

    for some B. But

    144,000 = 0 mod 20,

    and there are 20 different Tzolkʼin day names, so changing B by one doesn't change Tzolkʼin day name.

    On the other hand, there are 13 different Tzolkʼin day numbers, so adding one to B adds

    144,000 ≡ –1 (mod 13)

    days to the Tzolkʼin day number. This means that after the day

    7.16.6.16.18 and 6 Etz’nab

    the next day of the form

    N.16.6.16.18 and 6 Etz’nab

    happens when N = 7+13. But this is 13 × 144,000 days later: that is, roughly 5,094 years after 32 BC! Far in the future!

    So, while 32 BC seemed awfully early for the Olmecs to carve this stone, there’s no way they could have done it later. (Or earlier, for that matter.)

    For a fuller story, read my blog article!

    (2/2)

    https://johncarlosbaez.wordpress.com/2026/02/12/stela-c/

    Uncategorized

  • Math is everywhere.
    John Carlos BaezJ John Carlos Baez

    Math is everywhere. Here's a tale where a bit of number theory let a couple of archeologists, Marion and Matthew Stirling, figure out that the Olmec civilization was incredibly old.

    The Stirlings found the stone here in Mexico, and guessed that the date written on it was 7.16.6.16.18. In the calendar used by the Olmecs and other Central American civilizations, this corresponds to September 3, 32 BC.

    But the first digit was missing from this part of the stone! All the Stirlings actually saw was 16.6.16.18. And the first digit was the most significant one! If it were 8 instead of 7, the date of the stone would be much later: roughly 362 AD, when the Mayans were in full swing.

    The Stirlings guessed that the first digit must be 7 using a clever indirect argument.

    The Olmecs and Mayans used two calendars! In addition to the calendar I just mentioned, called the Mesoamerican Long Count, they also used one called the Tzolkʼin. This uses a 260-day cycle, where each day gets its own number and name: there are 13 numbers and 20 names. And inscribed on this stone are not only the last four digits of the Mesoamerican Long Count digits, but also the Tzolkʼin day: 6 Etz’nab.

    This is what made the reconstruction possible!

    (1/2)

    Uncategorized

  • INCOMING political earthquake, courtesy of Rep. Thomas Massie:
    John Carlos BaezJ John Carlos Baez

    @MJmusicinears - that story is fake. Here's the truth:

    https://wsbt.com/news/nation-world/reps-khanna-and-massie-review-unredacted-epstein-files-at-doj-amid-transparency-push

    Uncategorized

  • Chaco Canyon should be called Choco Canyon, because researchers have found traces of *chocolate* in cups found at this site dating back to 1000 - 1125 AD.
    John Carlos BaezJ John Carlos Baez

    @dougmerritt - the use of honey suggests they weren't insane.

    Uncategorized

  • Chaco Canyon should be called Choco Canyon, because researchers have found traces of *chocolate* in cups found at this site dating back to 1000 - 1125 AD.
    John Carlos BaezJ John Carlos Baez

    For more on parrots and scarlet macaws at Chaco Canyon:

    https://archaeologymag.com/2025/12/ancient-puebloans-macaws-ceremonial-use/

    "Chaco Canyon saw occupation from the mid-9th to the mid-12th centuries, which also coincided with the growth of what eventually became monumental masonry pueblos, known as Great Houses. While macaw and parrot remains have intrigued researchers for decades, the last analysis of them was published more than half a century ago. This study reexamines that old material using modern zooarchaeological methods and contextual reconstruction.

    The reanalysis identified the remains of 45 birds from five different sites within the canyon. Most of them were scarlet macaws, with a small number of thick-billed parrots, a species that is not native to the region, and provide evidence of long-distance acquisition. Most of the birds were found in the Great Houses, particularly Pueblo Bonito, the largest and most studied Chacoan building. There, archaeologists found dozens of macaws in large plastered rooms, which often included thermal features, indicating a deliberate effort was put into keeping the birds warm in a harsh environment.

    Many of the rooms showed clear signs that live birds had been held inside for long periods. Researchers observed thick layers of droppings, food debris, and what looked like perches, which provides proof that macaws lived in these spaces rather than just being put there for a short time or processed. Individuals ranged widely in age from juveniles to those over the age of twenty, which points to long-term care rather than short-lived use."

    (3/3)

    Uncategorized

  • Chaco Canyon should be called Choco Canyon, because researchers have found traces of *chocolate* in cups found at this site dating back to 1000 - 1125 AD.
    John Carlos BaezJ John Carlos Baez

    For more on chocolate at Chaco Canyon:

    https://www.nps.gov/chcu/learn/historyculture/pre-columbian-chocolate-discovered-at-chaco.htm

    "From 2004-2007 a University of New Mexico (UNM) research project re-excavated the trenches first dug in Pueblo Bonito’s middens under Neil Judd in the 1920s. Of the hundreds of thousands of pot sherds that were recovered, archaeologist Patricia Crown selected five for her research. She is a ceramics specialist at UNM’s Department of Anthropology. She designed the project, and W. Jeffrey Hurst from The Hershey Center for Health and Nutrition performed the research. They chose five pot sherds for organic residue analysis, three of which were likely from cylinder jars. The pieces date to between 1000 and 1125 AD based on their decorative styles.

    Only the three sherds most likely from cylinder jars exhibited trace theobromine, a conclusive indicator of cacao or chocolate. The implications of this find are extraordinary. The cacao plant grows only in certain tropical climates, and the nearest possibility for Chaco is Central Mexico. We already know the Chacoan people traded with Mesoamerican cultures for exotics like copper bells and scarlet macaws, but cacao suggests a more ritual connection than other Mesoamerican goods. In some Maya ceremonies a cacao beverage was frothed by pouring the liquid from one vessel to another. Likewise, the cacao found at Chaco was probably in liquid form because the residue had absorbed into the clay itself. Further, the limited distribution of the cylinder jars could be evidence that only an elite or small segment of the population consumed the beverage."

    (2/3)

    Uncategorized

  • Chaco Canyon should be called Choco Canyon, because researchers have found traces of *chocolate* in cups found at this site dating back to 1000 - 1125 AD.
    John Carlos BaezJ John Carlos Baez

    Chaco Canyon should be called Choco Canyon, because researchers have found traces of *chocolate* in cups found at this site dating back to 1000 - 1125 AD.

    This is amazing: Chaco Canyon is in a dry part of New Mexico, 1900 kilometers north of where cacao grows. But the cups look like those that Mayans used for chocolate-drinking rituals! And archeologists have also found remains of parrots and macaws in Chaco Canyon. This suggests enormous trading routes.

    (1/3)

    Uncategorized

  • Here's a tale of how nature triumphs in the end.
    John Carlos BaezJ John Carlos Baez

    Ecologist Alison Anastasio visited a former US Steel South Works site in Chicago. She expected to find “all crap plants” — common invasive weeds. To her surprise she spotted little bluestem and three species of native milkweed. She already knew she didn't want a career as an academic scientist. But she came up with the idea of forming a group to study this ecosystem: “a dream team of people I wanted to work with.”

    She knew Laura Merwin from the University of Chicago, and later she met Lauren Umek, a project manager for the Chicago Park District. She invited them to brunch to pitch her idea to research plants growing on slag. Not for any obvious career goal. Just from sheer curiosity.

    Merwin and Umek were excited to join her project - a “reverse side hustle,” since it involved a lot of work, but cost money. And thus the Slag Queens were born.

    Their first paper, “Urban post-industrial landscapes have unrealized ecological potential,” was published in Restoration Ecology in 2022. It argues that slag fields don't need to be fixed. They have ecological value in and of themselves. And land managers should forget whatever ecosystem was there before. Instead, they should look to more exotic ecosystems as a guide, like the dolomite prairies of Illinois, where magnesium-rich rock near the surface makes it hard for ordinary plants to thrive. Slag too is rich in magnesium.

    The Slag Queens are continuing their revolutionary work even now! For more, start here:

    • Carrie Gous, The beauty of slag, https://mag.uchicago.edu/science-medicine/beauty-slag

    Some of what I just wrote is a paraphrase of this article.

    (2/2)

    Uncategorized

  • Here's a tale of how nature triumphs in the end.
    John Carlos BaezJ John Carlos Baez

    Here's a tale of how nature triumphs in the end.

    Steel mills dumped molten slag in parts of Chicago and nearby areas. The slag hardened in layers up to 15 feet deep. These places became barren wastelands. Other industries dumped hot ash and cinders there.

    But eventually the steel mills closed.

    The deep layers of hard, toxic material were not friendly to plants. Cottonwoods are usually 30 meters tall or more. In the slag fields, stunted cottonwoods grow to just 2 meters.

    But rare species that could handle these conditions began to thrive. The lakeside daisy, a federally threatened species lost to Illinois for decades, turns out to grow taller on slag than on topsoil! The capitate spike-rush, last recorded in Illinois in 1894 and considered locally extinct, was rediscovered growing on slag.

    And more! Native prairie grasses like little bluestem. Native milkweeds. Even tiny white orchids called sphinx ladies' tresses.

    A team of women ecologists began studying these unusual landscapes. They call themselves the Slag Queens.

    (1/n)

    Uncategorized
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