I think it's that assumption is the problem. Most social systems are predicated on having enough net contributors to provide for net recipients, but with a declining population the ratio of contributors/recipients can get small. There may be solutions to this, but current social systems will likely fail if left unchanged. That doesn't mean the only solution is population growth, but we do need to do something
I can't say for sure about the Wang terminal keyboards, but what you're describing sounds a lot like a mechanism from some IBM Model B keyboards (usually called Beamsprings). I have an IBM 5251 keyboard that has a solenoid that hammers the side of the metal case whenever you type, and I've heard that it was added as users would have been used to typewriters and wanted to know for sure when they had registered a keypress
So honestly I don't quite remember if I encountered this with the Wangs, or if I'm recalling my Dad telling me about it from his experiences.
If the latter then odds are that it was either a machine from Wang and in that case most likely the 2200, or otherwise it will have most probably been equipment associated with the Gamma 10 from De La Rue Bull, or possibly the Ferranti Pegasus - both of which I know he worked with.
Of course, he might have been telling me a third-party anecdote in which case it's possible the IBM Display Station was the machine in question.
That all said, last time I was discussing this with someone they mentioned that the 2200's terminal had a "solenoid" trace on its PCB so it's quite possible that this really was the relevant device. Last time I personally had hands on a live 2200 was about 1993 though, so I really can't be sure.
There's a chap in the Netherlands with a Wang 2200 museum - perhaps I should just write to him and ask :D
I haven't looked at any court documents, but the WSJ article from Wednesday reported that "Last year, Google sued the anonymous operators of a network of more than 10 million internet-connected televisions, tablets and projectors, saying they had secretly pre-installed residential proxy software on them... an Ipidea spokeswoman acknowledged in an email that the company and its partners had engaged in “relatively aggressive market expansion strategies” and “conducted promotional activities in inappropriate venues (e.g., hacker forums)...”"
There was also a botnet, Kimwolf, that apparently leveraged an exploit to use the residential proxy service, so it may be related to Ipidea not shutting them down.
Not to avoid the point of the article, but GroupMe is sometimes used for academic purposes. In the 2010s I used it in school for clubs, sports, and group activities, so that may be why it wasn't blocked.
To prove something is transcendental we would need to know how to compute it exactly, and I’m struggling to see how that would come up frequently in a physics context. In physics most constants are not arbitrary real numbers derived from a formula, they’re a measured relationship, which sort of inherently can’t be proved to be transcendental
It's probably possible to use timestamps, but I suppose you would have to handle ties in more places, with sequence numbers you only break ties once. It appears that the FIX specifications allows up to microsecond precision, but given the volume of messages it's still likely a problem. It's also easier to work with integer sequence numbers than timestamps, but that's also a small consideration.
I'm almost surprised that Gemini 3 uniquely has this problem. I would have expected that responses from any LLM that require complex math notation would almost certainly be LaTeX heavy, given the abundance of LaTeX source material in the training data. I suppose it is a flaw if a model can't avoid LaTeX, but given that it is the standard (and for the foreseeable future too) I don't know what appropriate output would look like. For "pure" mathematics or similar topics I think LaTeX (or system that represents a superset of LaTeX) is the only acceptable option.
I get that the author wanted to explore constraint solvers, but why can't you use a greedy algorithm for this problem? Sort the inventory slots by how much bundle space they consume, and insert the cheapest slots. The only way I see this failing is with multiple bundles, but in practice in Minecraft (which is admittedly not really part of the constraint problem) bundles only help when you have many distinct items but a large number of items occur only a few items. In that case it isn't hard to find combinations that fill each bundle completely by only inserting all of a given item (as opposed to inserting only part of an inventory slot) since many items will have only 1 or 2 copies.
I opt for the greedy strategy in most game play scenarios for pretty much the reasons you described here. I was considering making a mod to perform this action for me and was looking for a more "correct" solution but greedy is way simpler and just as effective for most cases.
If you greedily fill bundles by first inserting all weight-4 items (pearls, etc.) in any order into a single bundle, moving to a new bundle each time the current one gets full, then inserting all weight-1 items (sticks, etc.) in any order in the same way, the solution you get will use an optimal number of bundles, and also leave an optimal amount of free capacity in the final bundle. (It helps to notice that every bundle except the last must be completely full with no wasted space, since both 4 and 1 divide 64.)
If you do the same, but add all weight-1 items before adding all weight-4 items, you'll still get a solution using the same (optimal) number of bundles, but you may use more capacity in the final bundle than needed -- e.g., if you have 61 sticks and 1 pearl, and add them in that order, the first bundle wastes 3 slots and the second uses 4 slots (vs. no wasted space in the first bundle and just 1 slot used in the second if adding in the reverse order).
OTOH, if you mix adding items of different weights (while staying with the approach of only ever adding to the current bundle if there's room, and if not, moving to a fresh bundle) then you can arrive at a suboptimal number of bundles. E.g., adding 61 sticks, 1 pearl and 3 dirt in that order will require 3 bundles instead of the optimal 2.
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