What's the most surprising fact you've learned in the last couple of weeks?
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What's the most surprising fact you've learned in the last couple of weeks? I don't mind if it's quite technical. I just want to hear what you folks are being surprised by!
Another thing that surprised me was that viruses, organisms that are not supposed to be alive, still “talk” with each other.
Magnus (@magnus@mastodon.world)
Attached: 1 image Viruses are not alive, but they talk with each other. https://www.cell.com/cell/fulltext/S0092-8674(26)00227-8
Mastodon (mastodon.world)
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What's the most surprising fact you've learned in the last couple of weeks? I don't mind if it's quite technical. I just want to hear what you folks are being surprised by!
@johncarlosbaez pigs can breathe through their butt!?
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@pozorvlak A container is a strictly positive functor, generalising the notion of "algebraic signature". For any such F, its free monad F* gives you the F-terms, seen as containers over sets of variables, where Kleisli arrows X -> F* Y are simultaneous substitutions from variables in X to F-terms over Y. Klesli extension then gives you the action of such a thing on terms in F* X.
Now, indeed, morphisms F -> G in the category of containers correspond exactly to natural transformations from F to G, i.e. parametrically polymorphic functions in forall X. F X -> G X. (There is a representation theorem which gives a more concrete definition of container morphism.) Anyhow, joyously, -* is a monad on containers. A Kleisli arrow is some F -> G*, "compiling" F-operations to G-terms. Kleisli extension then gives you a compositonal F* -> G* compiler for whole F-terms. Instead of "variables and substitution", you get "operations and compilation".
So you can take some F -> G*, Kleisli extend to get an F* -> G*, then instantiate at 0 to get a recursive function in F* 0 -> G* 0 operating only on closed F-terms. If you let me test this function, I can reverse-engineer the Kleisli arrow you got it from.
If, e.g., you take F = G = (X -> 1 + X2), making F* 0 and G* 0 the type of unlabelled binary trees, I will need at most 4 tests to recover your F -> G* (or in degenerate cases, another which gives the same function), and they are the simplest 4 trees you can think of!
@pigworker @johncarlosbaez oh, clever! Describing it as "compilation" makes a lot of sense.
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@bornach @johncarlosbaez two literary ones:
- there's a Spanish equivalent of Shakespeare and I've never heard of him before today: https://mathstodon.xyz/@mjd/116532678297823850
- Ann Radcliffe's "The Mysteries of Udolpho", the book parodied by Jane Austen's "Northanger Abbey", has been continuously in print since 1794 and made Radcliffe £500. That's almost as much as Austen's total lifetime earnings of £684.Here's my two:
1. Octopus arms can coordinate among themselves because are connected by special nerves that do not visit the brain, and (the surprising part) each arm is not connected to the adjacent ones but to the arms _three_ away.
2. Japanese has unvoiced vowels. Until yesterday I would have told you confidently that unvoiced vowels are definitionally impossible.
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Here's my two:
1. Octopus arms can coordinate among themselves because are connected by special nerves that do not visit the brain, and (the surprising part) each arm is not connected to the adjacent ones but to the arms _three_ away.
2. Japanese has unvoiced vowels. Until yesterday I would have told you confidently that unvoiced vowels are definitionally impossible.
@johncarlosbaez Oooh, here's another one I learned just yesterday: There was a well-known abstract expressionist painter, Charles Florian Cajori, who as you no doubt guessed, was the grandson of famous historian of mathematics Florian Cajori.
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What's the most surprising fact you've learned in the last couple of weeks? I don't mind if it's quite technical. I just want to hear what you folks are being surprised by!
The last couple of weeks? Learning is what drives me, a week is quite a long time!
There are two things I learned from your posts: Donella Meadows' nine leverage points were quite engaging. Didn't talk about it much on-line, because there's so much to say! I found it to be a hopeful perspective, well worth any dread caused by talking about big problems. People I told about it mostly liked it!
The other is that I now have a picture of the 600-cell! I always felt, nah, that's too complicated, let's stick to the smaller ones. And then your explanation of @jasonhise's happened, and @henryseg showed off his models. That's so cool, now what do I do with it?
It's sort of on-topic for me, because I have been eyeing little facts about rendering hyperbolic spaces for a while. Since @Number_Cruncher reignited my interest in Coxeter-Dynkin diagrams, and all that comes with it. I think I owe them a shader for hyperbolic Coxeter groups. Sorry, been busy...
For one, I have now practical experience optimizing compressed data size by rewriting the uncompressed source. That's quite an odd thing to do, but I learned a ton about what my code actually needs to do. Oh and if you ever want to submit a shader you wrote to a demo competition, I might have something for you.
The other obsession that got lots of time was to write an ocaml module for conformal geometric algebra. That alone is a very beautiful subject! I want it to output math kernels for shaders. In the end I learned that typed-tagless-final is the name for the concise style to represent syntax trees I didn't dare to use, thanks @JacquesC2 for writing about it years ago!
You see, @johncarlosbaez, you're still important to me, and I miss our conversations!
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Another thing that surprised me was that viruses, organisms that are not supposed to be alive, still “talk” with each other.
Magnus (@magnus@mastodon.world)
Attached: 1 image Viruses are not alive, but they talk with each other. https://www.cell.com/cell/fulltext/S0092-8674(26)00227-8
Mastodon (mastodon.world)
@magnus - Cool! People say viruses are not alive because they don't metabolize independently, but I disagree with that criterion.
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What's the most surprising fact you've learned in the last couple of weeks? I don't mind if it's quite technical. I just want to hear what you folks are being surprised by!
@johncarlosbaez Red deer is not the same as roe deer.
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@Dyoung - wow, cool! I just knew the normal distibution maximizes entropy for a given mean and variance.
It would be cool if these facts are connected.
@johncarlosbaez I feel somehow they must be. It's interesting how many roads there are that lead to the Gaussian!
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@johncarlosbaez Red deer is not the same as roe deer.
@otacke - I don't know enough about these deer to be surprised! They sound like European or British deer to me. Do they have overlapping ranges?
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Roland Bulirsch (https://en.wikipedia.org/wiki/Roland_Bulirsch), one of the two people who wrote a numerical analysis textbook I frequently refer to (https://doi.org/10.1007/978-0-387-21738-3), as well as someone who wrote quite a bit on the subject of elliptic integrals, was apparently a gym buddy of Arnold Schwarzenegger. Bulirsch, along with their other gym friends, took up a collection to help Schwarzenegger emigrate to America.
@tpfto
Interesting!This fits with what I've heard in the 1980s: That he occasionally appeared in police TV movies playing muscular men. (I've never seen him appear, or maybe I just didn't recognize him because I've not been in his lectures. In the year I had numerics lectures, they were given by C. Reinsch.)
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What's the most surprising fact you've learned in the last couple of weeks? I don't mind if it's quite technical. I just want to hear what you folks are being surprised by!
@johncarlosbaez I may cite two:
- that the wave particle duality and the complementary principle are old fashioned ways of talking, that in modern quantum mechanics is preferred to talk about superposition and collapse of the wave function.
- the concept of eusociality, a high level form of sociality, where individuals take care of the offspring of others... Edward O. Wilson says that we humans have a weak form of eusociality (Wikipedia).
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@johncarlosbaez That a certain crystal structure of some material can suddenly not be produced anymore, a so called "disappearing polymorphism". I learned this from a recent episode of the "Veritasium" YouTube series. I was stunned, I still am. It seems we still do not really know how this happens. It is being hypothesized that a very tiny crystal is enough to "infect" the material to the effect of losing its polymorphism. There's also a very nice Wikipedia article about this.
@Lambo - yes, this is amazing!
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@johncarlosbaez "Identical twins do not have the same fingerprints however, because even within the confines of the womb, the fetuses touch different parts of their environment, giving rise to small variations in their corresponding prints and thus making them unique." https://en.wikipedia.org/wiki/Twin#IdenticalTwins
@foldworks - Wow! I'm not completely surprised because I didn't think fingerprints are stored genetically... it would take a lot of genes to store that information, and for what purpose? But it's interesting to hear how fingerprints get formed.
This paper is cool:
N. Hirokawa, Y. Tanaka, Y. Okada and S. Takeda, Nodal flow and the generation of left-right asymmetry, Cell 125 1 (2006), 33-45.
It reports on detailed studies of how left-right asymmetry first shows in the development of animal embryos. It turns out this asymmetry is linked to certain genes. About half of the people with a genetic disorder called Kartagener's Syndrome have their organs in the reversed orientation. These people also have immotile sperm and defective cilia in their airway. This suggests that the genes controlling left-right asymmetry also affect the development of cilia! And the link has recently been understood...
The first visible sign of left-right asymmetry in mammal embryos is the formation of a structure called the "ventral node" after the front-back (dorsal-ventral) and top-bottom (anterior-posterior) symmetries have been broken. This node is a small bump on the front of the embryo.
It has recently been found that cilia on this bump wiggle in a way that makes the fluid the embryo is floating in flow towards the left. It seems to be this leftward flow that generates many of the more fancy left-right asymmetries that come later.
How do these cilia generate a leftward flow? It seems they spin around clockwise, and are tilted in such a way that they make a leftward swing when they are near the surface of the embryo, and a rightward swing when they are far away!
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@foldworks - Wow! I'm not completely surprised because I didn't think fingerprints are stored genetically... it would take a lot of genes to store that information, and for what purpose? But it's interesting to hear how fingerprints get formed.
This paper is cool:
N. Hirokawa, Y. Tanaka, Y. Okada and S. Takeda, Nodal flow and the generation of left-right asymmetry, Cell 125 1 (2006), 33-45.
It reports on detailed studies of how left-right asymmetry first shows in the development of animal embryos. It turns out this asymmetry is linked to certain genes. About half of the people with a genetic disorder called Kartagener's Syndrome have their organs in the reversed orientation. These people also have immotile sperm and defective cilia in their airway. This suggests that the genes controlling left-right asymmetry also affect the development of cilia! And the link has recently been understood...
The first visible sign of left-right asymmetry in mammal embryos is the formation of a structure called the "ventral node" after the front-back (dorsal-ventral) and top-bottom (anterior-posterior) symmetries have been broken. This node is a small bump on the front of the embryo.
It has recently been found that cilia on this bump wiggle in a way that makes the fluid the embryo is floating in flow towards the left. It seems to be this leftward flow that generates many of the more fancy left-right asymmetries that come later.
How do these cilia generate a leftward flow? It seems they spin around clockwise, and are tilted in such a way that they make a leftward swing when they are near the surface of the embryo, and a rightward swing when they are far away!
@johncarlosbaez It's kind of 'obvious in hindsight', but I didn't know it until considering a hypothetical in a murder mystery.
Are twins the worst plot device in some stories, after time travel? (And I *like* some stories featuring twins or time travel
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@johncarlosbaez It's kind of 'obvious in hindsight', but I didn't know it until considering a hypothetical in a murder mystery.
Are twins the worst plot device in some stories, after time travel? (And I *like* some stories featuring twins or time travel
)@foldworks - special relativity manages to make good use of a story involving *both* twins and something akin to time travel. The Twin (Non)Paradox.
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The last couple of weeks? Learning is what drives me, a week is quite a long time!
There are two things I learned from your posts: Donella Meadows' nine leverage points were quite engaging. Didn't talk about it much on-line, because there's so much to say! I found it to be a hopeful perspective, well worth any dread caused by talking about big problems. People I told about it mostly liked it!
The other is that I now have a picture of the 600-cell! I always felt, nah, that's too complicated, let's stick to the smaller ones. And then your explanation of @jasonhise's happened, and @henryseg showed off his models. That's so cool, now what do I do with it?
It's sort of on-topic for me, because I have been eyeing little facts about rendering hyperbolic spaces for a while. Since @Number_Cruncher reignited my interest in Coxeter-Dynkin diagrams, and all that comes with it. I think I owe them a shader for hyperbolic Coxeter groups. Sorry, been busy...
For one, I have now practical experience optimizing compressed data size by rewriting the uncompressed source. That's quite an odd thing to do, but I learned a ton about what my code actually needs to do. Oh and if you ever want to submit a shader you wrote to a demo competition, I might have something for you.
The other obsession that got lots of time was to write an ocaml module for conformal geometric algebra. That alone is a very beautiful subject! I want it to output math kernels for shaders. In the end I learned that typed-tagless-final is the name for the concise style to represent syntax trees I didn't dare to use, thanks @JacquesC2 for writing about it years ago!
You see, @johncarlosbaez, you're still important to me, and I miss our conversations!
@RefurioAnachro - Why don't we have so many conversations anymore? I figured you either got bored of what I'm talking about or got too busy with other things.
I'm glad you have a better picture of the 600-cell now. One thing *I* want to do now is better understand all the fancy stuff about the geometry of the 600-cell that's on Wikipedia. That article has grown a lot since I last saw it:
A lot is written in ways that I have trouble quickly understanding. But some gems stand out, e.g.:
"The 600-cell can also be partitioned into 20 cell-disjoint intertwining rings of 30 cells, each ten edges long, forming a discrete Hopf fibration which fills the entire 600-cell."
and others seem like they could be great if I understood them. As a hobby I may try to understand this stuff and fit together the mental pictures.
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@johncarlosbaez
Our worm-like ancestors were cyclops. When they decided to start swimming, the central eye squeezed out two side eyes and was itself reduced to the pineal gland that to this day regulates our circadian cycle.
Our modern vision evolved from an ancient one-eyed worm creature
The now extinct worm-like animal first lost paired eyes, then re-evolved them.
The Conversation (theconversation.com)
@BartoszMilewski - wow, yikes! I didn't know that.
The eye, or should I say "a kind of eye", has evolved many times independently. You're making me want to understand not just the history of *our* eyes but *all* these eyes.
I'll have to read this:
• Bhattacharya, Stagg, Donlon and Hardy, Evolution and development of complex eyes: a celebration of diversity, https://pmc.ncbi.nlm.nih.gov/articles/PMC7578360/
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@johncarlosbaez a historical bit, for a change: I was very shocked to learn that the few italian places that have "Romano" in their name, derive that not from "Roma" and "romano" as one might expect, but from quite the opposite: during the long war between the (Roman) Empire and the Langobards, those places took name from the upper class of the Langobards, i.e. the arimanni; "Romano", in the names of these places, comes from arimanni, not from "Roma" and "Romano".
@rioDa - surprising indeed! I bet even the modern residents of some of these places would be surprised.
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@Heterokromia - wow, I didn't even know I had methanogenic archaea in my gut! I take statins. Is it bad to kill ones methanogenic archaea?
