654 karma · joined October 24, 2015
On the other hand, I like that it actually handles pressure, though even the thinnest pen size is rather thick at the default zoom level and kind of hard to write with.
I also wonder if anyone actually experimented with microwaving their dinner at 10GHz or if that was just an educated guess. X-band magnetrons for radars are widely available though, so I would not be surprised if that was coming from practical experience...
Also note that other languages often support non-ASCII identifiers as well --- for example, `σ` is a completely valid identifier name in Python (though it is more restrictive than Julia, `σ²` is not valid in Python and yet is valid in Julia). It even works in C, but that might just be a GNU extension.
For example, I know that if I want to declare a computer peripheral to the customs, there is a good chance to get the correct TARIC code in the chapter that literally starts with "Nuclear reactors"...
Especially as otherwise, those parts would just get sold to the car manufacturers and would be used to make ethically questionable products.
This seems unlikely for the reasons you listed. Since USB is a polled bus and has shared bandwidth, implementing the flow control is likely very beneficial in case the bus can't temporarily handle the full Ethernet speed.
So, a USB-to-Ethernet gizmo just monitors its internal Ethernet-to-USB queue and if it starts to overflow, it attempts to flow control the switch. But, if no USB host is connected, no USB data requests ever arrive, the queue overflows and never gets cleared...
There may also be some WoL/USB remote wakeup stuff at play, which may be why these ICs do not drop the link on USB host disconnect by default. In fact, I wonder if messing with those settings on the host side could remediate the issue...
Say we live in an n-dimensional vector space V and have an endomorphism f : V -> V. Now, we consider the pullback [1] f* : Λⁿ(V) -> Λⁿ(V) induced by f on the vector space of n-linear alternating forms Λⁿ(V) on V.
This is just an endomorphism on Λⁿ(V). However, Λⁿ(V) is one-dimensional, hence necessarily invariant under f*. This means f* has an eigenvalue (!). This eigenvalue is what we usually call the determinant of f.
This is completely independent of any choice of basis, orientation, or an inner product.
[1] That is, given an element w ∈ Λⁿ(V) and an arbitrary n-tuple v₁, ..., vₙ of vectors from V, we have (f*w)(v₁, ..., vₙ) = w(f(v₁), ..., f(vₙ))
https://www.youtube.com/watch?v=GbqA9Xn_iM0&list=PLPH7f_7Zlz...
Notably, it treats QM with much more rigor than is usual in introductory courses, so having a nontrivial mathematical background is not an obstacle.
I am still surprised that this is not more common. Even a biology-grade binocular microscope for 100$-ish makes a huge difference.
In differential geometry, we traditionally parametrize curves by a parameter "t" and think of it as "time", so the parametrization allows us to "walk along" a curve. This is very intuitive geometrically of course.
But in relativity, we also have a "time" coordinate (or at least a timelike unit-length tangent vectors), which then completely oposes this geometric intuition about curves.
Of course now physicists decide to rename well-established concepts and start calling "arc length parametrization" by "proper time parametrization", which makes it sound like it is something special, while it, as far as I can tell, has no actual physical meaning.
This will always end up being slower than a plane wave in the same material, usually only somewhere between 10%-90% (and this also depends on the wavelength) of the free-space group velocity.
Meaning we have to be very careful about treating our projective transformations as linear maps, as they are, in fact, nothing like that.
Of course people doing graphics often pick a section of the projective space ("last component is 1"), then map that onto R^3 and off they go, sort of ignoring the "planes at infinity" and praying for the best. This is messy but I do not see a better way.
The last edition also contains chapters on stuff like dual spaces and quotient spaces, which are important yet very often missing in other textbooks.
That being said, his reliance on C/R in about half the book could be a problem for people with CS background. Like, what if I want to compute determinants of linear maps which are over Z_2? There are also no chapters on number wrangling (like the gaussian elimination and friends), which is a big plus in my view but possibly a problem for others.
And even if they did believe you it was not cocaine, I would still assume they would not be happy about someone importing a prescription drug.