What's the most surprising fact you've learned in the last couple of weeks?

[foldworks@mathstodon.xyz]

@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

[jannem@fosstodon.org]

@johncarlosbaez
That we don't adjust our viewing distance of pictures according to the focal length. But we do adjust it according to the physical size of the image - but only imperfectly. Smaller images are viewed relatively further away than larger images.

So the rule that ~50mm (45° FoV) is a "normal" focal length is only true for larger images. When viewed on smartphones the "normal" is more like 150mm or so.

[isaackuo@spacey.space]

@johncarlosbaez The fourth Doctor always had a companion ending in "ah", except for the one story where he didn't have any companion at all (The Deadly Assassin).

[pozorvlak@mathstodon.xyz]

@johncarlosbaez I knew that auto manufacturers were forbidden from selling direct to consumers across much of the US thanks to lobbying from car dealerships, and that Tesla had fought this. But I only learned today that the workaround Tesla used in New Mexico was to sell from Indian reservations.

[bornach@vis.social]

@pozorvlak @johncarlosbaez
Learned this from https://youtu.be/GREaEG_0Xcw

[pozorvlak@mathstodon.xyz]

@bornach @johncarlosbaez me too!

[chemicaleyeguy@mstdn.science]

@johncarlosbaez Surprised to learn on #MayThe4th that *both* #GeorgeLucas and #StanleyKubrick were inspired by Canadian avant-garde collage filmmaker Arthur Lipsett, who was mentored and recommended to the National Film Board of #Canada by Group of Seven co-founder Arthur Lismer. https://en.wikipedia.org/wiki/Arthur_Lipsett

[maxpool@mathstodon.xyz]

@johncarlosbaez

Ancient Rome consumed lots of oil and they didn't reuse the large Dressel 20 amphora barrels. Monte Testaccio in Rome is a 'trash mountain' made of 53 million broken olive oil amphorae.

Monte Testaccio - Wikipedia

(en.wikipedia.org)

[pigworker@types.pl]

I learned that the free monad construction, which iterates any container to give you a term monad, is itself a monad on containers, and that its Kleisli arrows determine a class of recursive functions over tree-like data. Moreover, if someone offers to let you test such a function but withholds the Kleisli arrow which generated it, you can recover their secret by a pleasingly small amount of perturbation testing.

[glocq@mathstodon.xyz]

@johncarlosbaez There is no recorded case of schizophrenia in anyone congenitally blind. No one knows why.

[pozorvlak@mathstodon.xyz]

@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.

[maxpool@mathstodon.xyz]

@johncarlosbaez

Maybe the most surprising fact I learned just few hours ago and wrote down is that hybrid car engines don't use Otto cycle. I never thought of that.

ma𝕏pool (@maxpool@mathstodon.xyz)

I just learned something new about hybrid cars: traditional gasoline cars with internal combustion engines using the Otto cycle are only about 25% efficient. Hybrids use a modified engine using the Atkinson cycle, which achieves roughly 40% efficiency, the Toyota Sienna in the video 41%. This increased thermal efficiency is the primary reason for their superior fuel economy. https://www.youtube.com/watch?v=KnUFH5GX_fI #cars #hybrids

Mathstodon (mathstodon.xyz)

[rioda@mastodon.bida.im]

@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".

[bartoszmilewski@mathstodon.xyz]

@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)

[julesh@mathstodon.xyz]

@johncarlosbaez @pigworker I learned the same thing but the other way round (this is not a coincidence, we were in the same place when it happened). I knew this operation was a monad but didn't know it was the free monad monad

Said in terms of just polynomial functors, the operation p* defined as the least fixpoint of p*(y) = y + p(p*(y)) (that's the least fixpoint of an endofunctor on Poly) is both a monad -* on Poly, and also has the property that p* is a monad on Set for every p

[pozorvlak@mathstodon.xyz]

@pigworker @johncarlosbaez

> I learned that the free monad construction, which iterates any container to give you a term monad, is itself a monad on containers,

Makes sense - "free" things are usually left adjoint functors, and "forgetful . free" gives a monad.

> and that its Kleisli arrows determine a class of recursive functions over tree-like data.

Wait, what? A Kleisli arrow would be a natural transformation f -> Free g where f and g are endofunctors; how does that give you a recursive function? Co-Kleisli arrows, sure...

> Moreover, if someone offers to let you test such a function but withholds the Kleisli arrow which generated it, you can recover their secret by a pleasingly small amount of perturbation testing.

SORCERY

[magnus@mastodon.world]

@johncarlosbaez

I was surprised to learn that there are small cleaner ants that clean bigger ants of a different species.

If one insect wants help with cleaning, why choose another smaller insect of the same family? One could imagine so many other willing arthropods.

Magnus (@magnus@mastodon.world)

Attached: 1 image Did ants learn this from cleaner fish? There are small ants that clean big ants without meeting any agression, just like small cleaner fish can clean sharks. https://onlinelibrary.wiley.com/doi/10.1002/ece3.73308

Mastodon (mastodon.world)

[arsatiki@wandering.shop]

@johncarlosbaez India now has a larger share of new battery electric cars (out of all new cars sold) than USA

[lambo@openbiblio.social]

@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.

[pait@mastodon.social]

@johncarlosbaez That of the heat the human body loses, 50% is by radiation.

Then 30% by convection, and 20% by evaporation of sweat, the latter being highly variable. Very little by conduction, unless the person is immersed in water.

I did not think radiation would amount to that much.