Very interesting article. I don’t understand, however, how shorthanders used typewriters for short-writing. The figure on p.168 (above fig. 9) is not explanative.
The numbers above the words indicate which finger (index, middle, ring) is used to press a key, the letters below indicate the hand (left or right). Basically a precursor of touch typing that doesn't use the little fingers and doesn't always use the same finger for the same key.
The actual shorthand would be written on paper, with the typewriter being used to expand it to a more readable form.
Then shouldn't $280 became $280\times 10^15 = $280000\times 10^12 = $280000tn dollars? Why $81tn ? Even if the currency is Brazil real, it should evaluate to about 48,000 trillion USD.
I don’t understand why one should define a month by partitioning the orbit into twelve equiangular sectors (relative to the centre of the orbit). Shouldn’t the orbit be partitioned into twelve parts with (roughly) equal travel times?
Yep. We ship in little bits and bobs from China constantly to keep our enormous manufacturing center running here in the USA. This is going to be horrible for us.
There are a few channels on YouTube where someone's tasked with fixing a laptop or some small electronic thing. They pull it open, find some tiny little circuit that won't go, dissolve the solder, and put a new tiny little circuit in to save a perfectly good device from the landfill.
I hope they can still afford their tiny little circuits and tiny little solder dissolving things with more expensive shipping.
It doesn't require linear algebra to understand the paper or how the algorithm works, but it does require linear algebra to understand why the algorithm works. In general, since the induced 1-norm of a stochastic matrix S is exactly equal to 1 but not smaller than 1, the mapping x↦Sx is NOT a contraction. Neither convergence of the power method nor uniqueness of fixed point are guaranteed. (If there are multiple fixed points, there are multiple inconsistent rankings.)
In the paper, the significance of the so-called "damping factor" is not clear. However, with linear algebra, we know that the damping factor makes the stochastic matrix positive rather than merely nonnegative. Hence the Perron eigenvalue is "simple" (i.e. of multiplicity one), the Perron vector is unique and the power iteration must converge to it.
That's easier explained using fixed-point theory: The damping factor makes the mapping x↦Sx into an actual contraction (on the space of probability distributions). Not to mention that it has a simple common-sense justification (you don't want to get stuck in a subnetwork that only links to itself, or drown out a subnetwork that has more outlinks than inlinks).
There is probably some gain from understanding the algorithm specifically as a Markov chain iteration (if nothing else, it provides a great example for Markov chain iteration), but I think it's perfectly possible -- and easier -- to understand it as a fixed-point iteration on a compact space. And I am someone who does algebra for a living and normally explains everything algebraically if ever possible...
I feel like the four-color theorem automated proof is much more 'human-readable' than the proofs done with automated theorem provers. Because with the four-color theorem, there is a human readable proof that says "if this finite set of cases are all colorable, then all planar graphs are colorable". And then there is some rather concrete code that generates all the finite cases, and finds a coloring for them. Every step in there makes sense, and is fully understandable. The fact that the exhaustive checking wasn't done by hand doesn't mean its hard to understand how the proof works, or what is 'actually going on'.
For a general theorem prover, reading the code doesn't explain anything insightful about why the theorem is true. For the 4 color theorem, the code that proved it actually gives insight in how the proof works.
“...find partners to trade spots in critical classes after they filled up”.
I am not from the USA and I don’t understand the context. What does “trade spots” mean? Does it mean that if I have registered to course A but not course B and my friend have registered to course B but not course A, we can swap our registered courses in the official registration system?
I assume it means that at the start of the semester or just days before it starts that if class A and B are both full but I am enrolled in class A but wanted to drop it and get in class B and you are in class B and wanted in class A then we could swap enrollments.
That's that the poster's app would allow. I assume that right now it is like a seat on a plane or something: If I drop there is an opening and it is first come first serve to fill the slot. So there's no way to assure that you get my old spot. But the poster's app would allow that.
I don't understand. How can this prevent someone from feeding an AI generated image to a "zero-knowledge-proof-whatever" hardware/software module to create a so-called self-proclaimed "verified" real image? This is not a sarcasm but a genuine question.
