What's the most surprising fact you've learned in the last couple of weeks?
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@buo - I should learn what this *means*. I once almost knew what a Kalman filter is, and I know it's extremely important. But I don't know what a phase-locked loop is.
I love ODE, so this is embarassing! There's always room for progress.
In phase locked loop output signal phase tracks input signal's phase. It's like automatic tuning, Frequencies synchronize through feedback.
Think tidal locking, or two pendelums in the same beam. I'm not sure 100% sure but I think Josephson effect is also like this.
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@Lambo got here first with my top fact, so i'll go with this one:
transit operators in the u.s. are not authorized to question the pedigree of your 'service animal.'
as long as you identify the animal as such, you are permitted to bring it on the bus.
*any* animal.
@saltywizard - what are the most crazy examples of service animals that have been recorded?
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@saltywizard - what are the most crazy examples of service animals that have been recorded?
i've heard local anecdotes about a pony on the bus, but i haven't researched national trends.
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i've heard local anecdotes about a pony on the bus, but i haven't researched national trends.
@saltywizard - I feel there should be YouTube videos about this....
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@isaackuo @drdrowland - I see, so colonizing it via air-filled balloon-like floating structures?
we will have to mine the surface for structural material
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@johncarlosbaez That distilled water is completely safe to drink (contrary to what I learned in school)!
@pschwahn - hmm, I never thought it was unsafe. It's just water, after all! But nobody ever told me otherwise. I wonder how common that belief is.
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@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
@julesh @pigworker - I don't even know what a "container" is. It's my own fault. There's this repository of computer sciency category theory terminology that's different from the mathy category theory terminology, and I've never been tempted to explore it. There must be something about it that repulses me. I guess my love of math fizzles out when it starts getting too close to computer science. I apologize.
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@pschwahn - hmm, I never thought it was unsafe. It's just water, after all! But nobody ever told me otherwise. I wonder how common that belief is.
@johncarlosbaez @pschwahn I heard this in chemistry class in school. Well, "distilled water is not for drinking" was the rule, the justification was that it lacked some of the essential stuff found in tapwater.
Presumably, it was also to prevent students from drinking the distilled water, which parents donated to the chemistry class.
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@julesh @pigworker - I don't even know what a "container" is. It's my own fault. There's this repository of computer sciency category theory terminology that's different from the mathy category theory terminology, and I've never been tempted to explore it. There must be something about it that repulses me. I guess my love of math fizzles out when it starts getting too close to computer science. I apologize.
@johncarlosbaez @julesh @pigworker Mathematicians tend to call containers "polynomial functors". David Spivak has written a lot about them under this name.
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@johncarlosbaez @julesh @pigworker Mathematicians tend to call containers "polynomial functors". David Spivak has written a lot about them under this name.
@eigil True. I'm a touch old-fashioned in this respect. I note that renaming all the things is the number one strategy when it comes to ignoring prior art. @johncarlosbaez @julesh
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@foldworks - special relativity manages to make good use of a story involving *both* twins and something akin to time travel. The Twin (Non)Paradox.
@johncarlosbaez @foldworks well akSHUallY I think you mean "general relativity" because only non-inertial reference frames could lead to the twins being different ages when reunited.
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@johncarlosbaez @pschwahn I heard this in chemistry class in school. Well, "distilled water is not for drinking" was the rule, the justification was that it lacked some of the essential stuff found in tapwater.
Presumably, it was also to prevent students from drinking the distilled water, which parents donated to the chemistry class.
@thmprover @johncarlosbaez @pschwahn
The reason I heard is that it reverses the direction of osmosis in your gut, leaching nutrients from your body instead of distributing them.
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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!
Here's my big recent surprise: the number
F = (2221564096 + 283748 sqrt(462)) / 491993569
plays a fundamental role in number theory!
For any irrational x, we define its 'Lagrange number' to be the supremum of c such that
|(p/q) - x| < 1/cq²
has infinitely many solutions for rationals p/q. So, the bigger the Lagrange number is, the easier x is to approximate by rational numbers. Quite famously, the golden ratio has the smallest possible Lagrange number, namely √5.
Here's the shocking fact: every real number ≥ F is a Lagrange number, and F is the smallest number with this property!
F is called 'Freiman's constant', because he proved this fact. His proof is 100 pages, and I don't want to read it... but some people have.
There's a lot more crazy stuff about the set of all Lagrange numbers. A tiny bit is here:
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Here's my big recent surprise: the number
F = (2221564096 + 283748 sqrt(462)) / 491993569
plays a fundamental role in number theory!
For any irrational x, we define its 'Lagrange number' to be the supremum of c such that
|(p/q) - x| < 1/cq²
has infinitely many solutions for rationals p/q. So, the bigger the Lagrange number is, the easier x is to approximate by rational numbers. Quite famously, the golden ratio has the smallest possible Lagrange number, namely √5.
Here's the shocking fact: every real number ≥ F is a Lagrange number, and F is the smallest number with this property!
F is called 'Freiman's constant', because he proved this fact. His proof is 100 pages, and I don't want to read it... but some people have.
There's a lot more crazy stuff about the set of all Lagrange numbers. A tiny bit is here:
@johncarlosbaez
Somehow I missed this in the past. It's believable, but not particularly intuitive. -
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 learned in Korea recently that North Korea is much more worried about the influence of K-Culture (music, drama, etc) than about military interventions or poverty. And that (South) Korea is the number one per capita consumer of garlic.
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Here's my big recent surprise: the number
F = (2221564096 + 283748 sqrt(462)) / 491993569
plays a fundamental role in number theory!
For any irrational x, we define its 'Lagrange number' to be the supremum of c such that
|(p/q) - x| < 1/cq²
has infinitely many solutions for rationals p/q. So, the bigger the Lagrange number is, the easier x is to approximate by rational numbers. Quite famously, the golden ratio has the smallest possible Lagrange number, namely √5.
Here's the shocking fact: every real number ≥ F is a Lagrange number, and F is the smallest number with this property!
F is called 'Freiman's constant', because he proved this fact. His proof is 100 pages, and I don't want to read it... but some people have.
There's a lot more crazy stuff about the set of all Lagrange numbers. A tiny bit is here:
@johncarlosbaez It looks like the continued fraction expansion of the Friedman constant has period 66754.
Simple continued fraction of Freiman's constant
The quadratic irrational $\frac{2221564096+283748\sqrt{462}}{491993569}$ is known as Freiman's constant and arises in the theory of continued fractions. I'm curious as to its simple continued frac...
MathOverflow (mathoverflow.net)
It would be nice if there is a geometric interpretation of this constant.
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@saltywizard - I feel there should be YouTube videos about this....
@johncarlosbaez @saltywizard
Shhh don't tell anyone yet, but soon we will run a public experimental instance of @peertube at @tibhannover , inviting researchers to publish explain videos about virtually everything, spreading those right here on the Fediverse... So please keep your good ideas in mind! (TIB - same place where we run the full backup of arXiv etc) -
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 Stretching the “couple of weeks” timeframe a bit, but I haven’t been able to stop thinking about the first paragraph of this article:
Katherine Rundell · Consider the Greenland Shark
I am glad not to be a Greenland shark; I don’t have enough thoughts to fill five hundred years. But I find the very...
London Review of Books (www.lrb.co.uk)
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@johncarlosbaez I learned in Korea recently that North Korea is much more worried about the influence of K-Culture (music, drama, etc) than about military interventions or poverty. And that (South) Korea is the number one per capita consumer of garlic.
@jer_gib - both surprising! I wonder if the North Koreans would eat just as much garlic if they could afford it.
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@johncarlosbaez Stretching the “couple of weeks” timeframe a bit, but I haven’t been able to stop thinking about the first paragraph of this article:
Katherine Rundell · Consider the Greenland Shark
I am glad not to be a Greenland shark; I don’t have enough thoughts to fill five hundred years. But I find the very...
London Review of Books (www.lrb.co.uk)
@normalmode - Wow! For those who don't click:
"In 1606 a devastating pestilence swept through London; the dying were boarded up in their homes with their families, and a decree went out that the theatres, the bear-baiting yards and the brothels be closed. It was then that Shakespeare wrote one of his very few references to the plague, catching at our precarity: ‘The dead man’s knell/Is there scarce asked for who, and good men’s lives/Expire before the flowers in their caps/Dying or ere they sicken.’ As he wrote, a Greenland shark who is still alive today swam untroubled through the waters of the northern seas. Its parents would have been old enough to have lived alongside Dante; its great-great-grandparents alongside Julius Caesar. For thousands of years Greenland sharks have swum in silence, as above them the world has burned, rebuilt, burned again."
