Learn about the earliest use of infinity we’ve found; and vampire-like sea slugs that absorb other organisms’ attributes. The earliest mathematical use of infinity was found in a reused prayer book by Briana Brownell Reviel Netz. (2021). The Diagrams as Floating Bodies by Reviel Netz of Stanford University. Archimedespalimpsest.org. http://archimedespalimpsest.org/about/scholarship/method-infinity.php NOVA | Infinite Secrets | Working with Infinity | PBS. (2021). Pbs.org. https://www.pbs.org/wgbh/nova/archimedes/infinity.html Lloyd, R. (2009, February 17). Idea of Infinity Stretched Back to Third Century B.C. Livescience.com; Live Science. https://www.livescience.com/3336-idea-infinity-stretched-century.html The Archimedes Palimpsest Project. (2021). About the Archimedes Palimpsest. Archimedespalimpsest.org. http://archimedespalimpsest.org/about/ Some species of nudibranchs can absorb other organisms' attributes like vampires by Grant Currin Jonny Thomson. (2021, July 9). Nudibranchs: psychedelic body snatchers of the deep. Big Think; Big Think. https://bigthink.com/surprising-science/nudibranchs-strange-body-snatchers-ocean Goodheart, J. (2018, May 9). How Sea Slugs Steal the Defenses of Their Prey. Si.edu. https://ocean.si.edu/ocean-life/invertebrates/how-sea-slugs-steal-defenses-their-prey Nudibranchs: psychedelic thieves of the sea. (2017). Nhm.ac.uk. https://www.nhm.ac.uk/discover/nudibranchs-psychedelic-thieves-of-the-sea.html Nudibranchs (2016). National Geographic. https://www.nationalgeographic.com/animals/invertebrates/facts/nudibranchs-1?loggedin=true Follow Curiosity Daily on your favorite podcast app to learn something new every day withCody Gough andAshley Hamer. Still curious? Get exclusive science shows, nature documentaries, and more real-life entertainment on discovery+! Go to https://discoveryplus.com/curiosity to start your 7-day free trial. discovery+ is currently only available for US subscribers.
Learn about the earliest use of infinity we’ve found; and vampire-like sea slugs that absorb other organisms’ attributes.
The earliest mathematical use of infinity was found in a reused prayer book by Briana Brownell
Some species of nudibranchs can absorb other organisms' attributes like vampires by Grant Currin
Follow Curiosity Daily on your favorite podcast app to learn something new every day with Cody Gough and Ashley Hamer. Still curious? Get exclusive science shows, nature documentaries, and more real-life entertainment on discovery+! Go to https://discoveryplus.com/curiosity to start your 7-day free trial. discovery+ is currently only available for US subscribers.
Find episode transcript here: https://curiosity-daily-4e53644e.simplecast.com/episodes/infinity-in-a-used-prayer-book-and-vampire-like-sea-slugs
CODY: Hi! You’re about to get smarter in just a few minutes with Curiosity Daily from curiosity-dot-com. I’m Cody Gough.
ASHLEY: And I’m Ashley Hamer. Today, you’ll learn about the surprising place researchers found the earliest mathematical use of infinity; and how some species of sea slug absorb the traits of other organisms like vampires.
CODY: Let’s satisfy some curiosity.
Have you ever found something important in an old possession? Well, it was probably nothing like what researchers found in a used prayer book. Buckle up, because this is quite the story.
It starts back in 1906, when historian Johan Ludvig Weiberg made a startling discovery: As he was examining a Byzantine prayer book written in 1229, he noticed that several pages contained writing underneath its current contents. And as a historian, he recognized the text: it was from an ancient manuscript by Archimedes that was written around 225 BCE, 1000 years earlier. Weiberg was examining the oldest surviving copy of the book.
See, back in the day, books were often reused. Books like that ancient manuscript were usually made from sturdy parchment, so it was possible to take a knife and scrape off the old ink without damaging the book itself. That’s exactly what had happened.
This strange book is now called the Archimedes Palimpsest, and it contains a total seven books of the work of Archimedes. And thanks to modern imaging technology, even more of its secrets have been revealed.
What kind of secrets? Oh, how about the fact that Archimedes made the earliest-ever discussion of actual infinity? That means that humans were talking about these complex concepts 2,000 years before previously thought.
See, there are two kinds of infinity: potential and actual. Before the book was found, historians thought that Archimedes and his contemporaries only contemplated potential infinity.
Archimedes’ work focused on mathematical measurements of various kinds of shapes. And, here, potential infinity pops up in geometry quite often. For example, imagine a square. Now, imagine you draw a diagonal line from one corner to another. How long is that line compared to the side of the square? Even though it seems like an easy question to solve, the answer is surprisingly complex. The answer is the square root of two… which is an irrational number that can’t be expressed by a simple fraction. Instead, to get the answer, you need to perform an infinitely long calculation.
This is an example of potential infinity. It’s called potential because it extends a finite number again and again in a sort of race to get to infinity.
But actual infinity is what you need in modern mathematics. It deals with things that are actually infinite, like the number of points on a line. It’s also what underpins calculus, which was only created in the 1600s. But the manuscript showed that Archimedes had explored actual infinity too, using an interesting mixture of pure mathematics and physics.
So far, scientists and historians are still discovering the contents and relevance of the manuscripts, but even in modern mathematics, infinity stumps us. There are lots of unproven theorems about the relative scales of different kinds of infinities and how they relate to each other. Let’s hope it doesn’t take another 2,000 years to get it right.
CODY: Hope? Maybe we should say a prayer… like, from a used prayer book. That contains the earliest mathematical use of infinity we’ve ever found. Just sayin’
Nudibranchs [NOO-dih-branks] may not be famous by name, but you’ve definitely seen pictures of these vibrantly colored sea slugs. Don’t let their soft bodies fool you: nudibranchs are voracious predators. And it turns out that they get more than food from their prey. Some nudibranchs have figured out how to eat stinging sea creatures and use their weapons for their own purposes. Yes — like Rogue from X-Men, or the popular video game character Mega Man.
The group of nudibranchs that evolved this slick move are called aeolids [EE-uh-lids], and they’re among the small group of predators that chow down on jellyfish, sea anemones, and other members of the phylum cnidaria [FYE-lum nye-DARE-ee-yuh]. That’s no small feat because cnidarians [nye-DARE-ee-ins] have special cells that deliver venom through tiny harpoons called nematocysts [NEM-uh-tuh-sists]. Cnidarians use their stinging cells to hunt prey and to defend themselves.
And they’re pretty effective! Unless a cnidarian is trying to fend off an aeolid [EE-uh-lid].
Aeolids have a sly way of keeping cnidarians [nye-DARE-ee-ins] from stinging them. As they begin their meal, they coat the stinging cells in a special slime. Aeolids are slugs, after all! With the cnidarian’s defenses neutralized, an aeolid is free to gobble up its prey, including the venom and tiny harpoons.
That’s when things get interesting. Most of the nematocysts are digested and pooped out like normal, but some of the immature ones wind up in special pouches that stick out of the aeolid’s back like tiny fingers. Once they’re safely stowed away, the developing nematocysts get everything they need to develop into fully functional stinging cells. Once they’re fully developed, the protrusions become fingers of doom, complete with venomous harpoons the aeolid can deploy at will.
That’s not the only way nudibranchs have evolved to steal and use parts of their prey. Some coral-eating species have figured out how to steal algae and stow it away in the very same type of structures that stick out of the nudibranch’s back. Once there, the algae do what algae do: turn sunlight into sugars. Most of the energy goes back into the algae, but the host gets its cut, too. Some nudibranchs get about 25 percent of their total energy this way. As for the algae, they don’t seem to mind. Some studies suggest they reproduce more quickly inside the nudibranch than they would have out in their normal habitat.
That’s nudibranchs for you — beautiful, slimy, shrewd businessmen of the sea.
Let’s recap today’s takeaways
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ASHLEY: Today’s writers were Briana Brownell and Grant Currin.
CODY: Our managing editor is Ashley Hamer.
ASHLEY: Our producer and audio editor is Cody Gough.
CODY: [AD LIB SOMETHING FUNNY] Join us again tomorrow to learn something new in just a few minutes.
ASHLEY: And until then, stay curious!