Ew. Apparently, #K9 got bought by Mozilla. I expect it will soon be equipped with phone home and telemetry and possibly full browser capabilities.
Anyone, what's a good mail client for Android?
@johncarlosbaez my favorite characterization of the Bernoulli lemniscate is still the one where it's the envelope of all circles centered on a hyperbola and passing through the origin:
<< “The result is an absence of checks and balances in Russia, and the decision of one man to launch a wholly unjustified and brutal invasion of Iraq,” Bush said, before wincing and correcting himself. “I mean, of Ukraine.”
The comment left the audience in an awkward silence. Then, Bush shrugged and said under his breath: “Iraq, too.” >>
Also I guess it's what Adam Curtis was criticising in "All Watched Over By Machines Of Loving Grace", which I have actually yet to watch because I'm not sure I can take much Adam Curtis, but I guess it's my duty
Copyright is the most legitimate complaint, though even it applies largely to only 20th century works, nearly all published after 1925. (There are exceptions, this is law, jurisdictions differ. But as a rule that holds.) Copyright is indeed hugely culpable for restricting rather than enabling access to works, as UC Berkeley Law Prof Pam Samuelson has said.
Quantity is the first of the red herrings. If you've a lot of something to do, and actually do want to do something with it, doing something is more likely to get you there than doing nothing. This means devising a plan, prioritising works to process, perhaps setting up processes for new aquisitions such that they're archived on arrival. Even a random sampling is better than nothing. Roughly 140 million books have ever been published, unpublished media (manuscripts, notes, etc.) expand that, but the set is finite.
I regret to inform you that the original 1994 TekWar movie is on Youtube, and that Jake Cardigan's computer was made out of two flatscreens (portrait and landscape) duct-taped together with a bunch of PVC tubing right from the beginning.
I kind of want that rig. It really would make reading PDFs a lot easier.
Let's have some fun with the Heisenberg group H! It is the group of upper triangular matrices of the form
/ 1 a c \
| 0 1 b |
\ 0 0 1 /
Muliplying two such matrices you can easily see it's a monoid, because the result is again an upper triangular matrix:
/ 1 a+A c+aB+C \
| 0 1 b+B |
\ 0 0 0 /
You can also read this thread on my blog:
Mathematicians don't hold back, more than four dimensions aren't at all a problem. It's not physics, where the poor bastards have to substantiate that they really and totally absolutely in fact do exist. And not just as degrees of freedom like, for example, position and velocity taken together, which, for a single particle, would already amount to a 3+3=6 dimensions or degrees of freedom. The name for something like that is phase- or Hilbert #space, and it's the topic of symplectic #geometry,
Do parallel lines meet at infinity?
We've been told only half the story about vectors! Orientations (of a vector) in 3-space fit onto one half of the surface of a 4-ball. The configuration space for 3-orientations happens to be 3-dimensional, but I'm getting ahead of myself.
There are more spaces than just the flat, euclidean n-dimensional spaces. After Euclid, it took 2000 years until people dared to take such things seriously, like seeing the surface of a sphere as something of its own.
I first heard about Thurston in Fall 2012 when I learned that he had passed away. Many people spoke about him in awe, and I got a nice reading suggestion, like his notes The Geometry and Topology of 3-Manifolds, best viewed in his charmed hand-written version:
There's also a TeX version, naturally freely available:
That's because he wanted people to understand! Look:
William Thurston – The Mystery of 3-Manifolds
There's Yu. I. Manin's book "Cubic Forms, Algebra, Geometry, Arithmetic".
It's not quite like Conway's "Sensual Quadratic Form", which itself kneads some strange methods and insights into a whole, but both are about discrete ideas. Manin's book is a comprehesive introduction to concepts for solving certain elliptic Diophantine equations. It discusses CH quasigroups and Moufang loops, cubic and cubic minimal surfaces, and Brauer-Grothendieck groups. Fun stuff!
/me is listening to
thanks to Sven Türpe for suggesting it.
Image of the Mandelbrot set near -1.54368901269207636157... It's the negative of:
((3*sqrt(33) + 17)^(1/3) - (3*sqrt(33) - 17)^(1/3) + 2)/3
It goes back to a problem by Omar Khayyam, who lived between 1048 and 1131! See http://oeis.org/A256099 and especially look at the pdf linked from there.
On the internet, everyone knows you're a cat — and that's totally okay.