Since the rules are entirely reconstructed, I have to say I'm a bit skeptical of a game where a central point is keeping a count of moves up to 150. It seems too unpractical for a casual game.
Are there other known ancient games that work like this?
Yeah, I don't know about the author, but my brain spatial memory is very much tied to Euclidean geometry. The holonomy effect (view is rotated when coming back to the same point) in particular is very disorienting.
I'd say not much: you update the channel, run nixos-rebuild switch, fix all the warnings/errors due to renamed/changed options until it succeeds and you're done. If you have a database like postgres you may have to do a schema upgrade manually, since the default version is updated every 4/5 releases or so.
It's very rare to find something that prevents you from directly updating. Nixpkgs tries very hard to no require new Nix features, so it evaluates with even Nix versions from a decade ago. Also, NixOS options and packages are frequently changed, but the automatic migrations (mkChangedOptionModule, mkRenamedOptionModule, alias, etc.) are never removed in practice.
Since the binary cache has never been cleared since its creation (2002?), it should actually be easy to install a super old NixOS release and upgrading it to the latest to see what happens.
By the way, there are LTS versions of NixOS, just not officially supported. See https://docs.ctrl-os.com/.
And when it happens, that there are new Nix features used in Nixpkgs, then you can download the closure for the new Nix executable, directly from the build farm, and update your OS from this new Nix version.
> they still see the URL so they can get the content if they want it
That's incorrect, a MitM can only reveal the server hostname by inspecting the SNI during the TLS handshake, but the HTTP request, including the URL and headers, is encrypted.
No they can't. They obviously know the IP addresses, but that's not terribly useful since everything is behind a cloudflare proxy nowadays. The server hostname may provide some more information, if the server doesn't support ECH [1], but the full URL is encrypted.
If you use HTTPS they can see that you hit wikipedia (they will see you are trying to do a DNS lookup for en.wikipedia.org), but they can't see that you are viewing https://en.wikipedia.org/wiki/Hundeprutterutchebane in particular- that is only available to someone who can read the body of the HTTP request, which with HTTPS is encrypted.
I just do this for the IP ranges of Amazon, OpenAI, Huawei and other companies that run these insane crawlers: it's 100% effective and it doesn't annoy real users with a captcha or some PoW thing. There's simply no reason for them to reach my homeserver other than to scrape the hell out of it.
The breeding blanket is entirely contained inside a vacuum vessel, so there isn't any oxygen to react with. Also, the are many blanket designs, but the lithium is never present in its elemental form (precisely because it would be very reactive), but in a stable chemical bond with some neutron multiplier (like lithium-lead alloys or beryllium ceramics). In some design the lithium is even immersed in the coolant itself, which is high pressure helium, so it's not going to ignite in any reasonable way.
> breeding blanket is entirely contained inside a vacuum vessel, so there isn't any oxygen to react with
When the vessel works. If the vessel breaches, that lithium could ignite. Note a showstopper. But I suppose a risk to be thought about by the engineers (probably not by policymakers).
Commonwealth Fusion Systems plan to use lithium in salt form FLiBe, a molten salt made from a mixture of lithium fluoride (LiF) and beryllium fluoride (BeF2). It does not violently react with air or water.
Thanks. So the author's point in the linked article is wrong, it's the opposite of what they wrote. Contrary to what they say, it's indeed a bus, and it isn't the case that CSMA/CD is useless, it's that isn't enough to deal with the situation, so additions have been made to it.
Thanks for your link that helped clarifying this for me!
When you have switches that link two nodes together, for only the duration of one-way transmission you don't need CSMA/CD. We literally have no use for it. We will never have two computers transmit onto the same Ethernet wire anymore.
WiFi is different of course. However as the author wrote, your WiFi devices always go through the access point where they use 802.11 RTS/CTS messages to request and receive permission to send packets. All nodes can see CTS being broadcasted so they know that somebody is sending something. So even CSMA/CA is getting less useful.
Yes I'm only talking about wifi networks. I get that CSMA/CD itself is getting less useful, but it's because something else is doing its job, not because what it did is useless (that's why I wrote "or something similar" when I asked). Wifi is still, necessarily, a common bus where everyone talks.
CSMA/CD - Collision Detection and CA Collision Avoidance. - FYI the article is from 2017!
for Non-WiFi, we don't use CD because all is bi-dirireactional and all communication have their own lane, no needed because there will never be a collision this is down to the port level on the switches, the algorithm might be still there but not use for it.
For WiFi, CD can never be good or work, because "Detecting" is pointless, it cannot work. we need to "Avoid" so it has functionality because is a shared lane or medium. CA is a necessity, now in 2026, we actually truly don't need it or use it as much since now WiFi and 802.11 functions as a switch with OFDM and with RF signal steering, at the PHY (physical level) the actual RF radio frequency side, it cancels out all other signals say from others devices near you and we "create" similar bi-directional lanes and functions similar as switches.
The article is good and represents how IETF operates a view (opinionated) of what happens inside. We actually need an IETF equivalent for AI. Its actually good and a meritocracy even though of late the Big companies try to corrupted or get their way, but academia is still the driver and steers it, and all votes count for when Working-Groups self organized. (my last IETF was 2018 so not sure how it is now in the 2020s)
How can wifi be a star topology when all clients connect to the base station using the same airwaves? If it really were a star topology, it would also not be possible to use aircrack-ng or other tools to gather data for WPA cracking by passive listening -- that can only happen on a shared medium network.
I think the most accurate classification is that wifi emulates a star topology at OSI layer 2 on top of a layer 1 bus topology.
> My concern is that the word “elementary” in the title carries a much broader meaning in standard mathematical usage, and in this meaning, the paper’s title does not hold.
> Elementary functions typically include arbitrary polynomial roots, and EML terms cannot express them.
If you take a real analysis class, the elementary functions will be defined exactly as the author of the EML paper does.
I've actually just learnt that some consider roots of arbitrary polynomials being part of the elementary functions before, but I'm a physicist and only ever took some undergraduate mathematics classes.
Nonetheless, calling these elementary feels a bit of stretch considering that the word literally means basic stuff, something that a beginner will learn first.
No. It's code for the thickest, densest book on the subject that you're ever gonna not read, as it actually assumes you're experienced in the subject and goes into everything except intro level topics.
I guess you're right, I was probably mislead this whole time. I went through my old analysis class book [1] and there doesn't seem to be an explicit definition of elementary functions. The best I can find is this paragraph (I translate from italian):
> The elementary functions of analysis, that is powers, roots, exponentials, logarithms and their inverses, functions obtained from the former by arithmetic operations or composition, admit the limit f(p) for x → p, for any p in their set of definition. The study of such functions, which is not limited to the sole real functions of real variable, is carried out naturally in the setting of metric spaces.
That said, I'm relatively sure that a definition was given in class and it didn't include arbitrary roots: despite being notoriously difficult, the exam didn't require students to draw the graph of any elementary function including implicitly-defined algebraic roots.
I picked up another one of the old recommended books [2] and it seems to be similarly vague; while the book currently taught in my university [3], gives this definition:
> The following functions (from ℂ to ℂ) are called the elementary functions of the Analysis:
> 1) Rational functions (integral or fractional)
> 2) Algebraic functions (explicit or implicit)
> 3) The exponential function
> 4) The logarithm function
> 5) All those functions that can be obtained by combining a finite number of times the functions of kind 1)...4).
So, roots of arbitrary polynomials implicitly defined are indeed considered elementary. I never knew this.
So, I did a bit of research and I wasn't going crazy: there are apparently two competing definitions of "elementary" in use [1]:
> the class of functions [...] is what I would call exponential-logarithmic functions or EL functions; that is, they are the functions that can be expressed using some finite combination of constant functions, the identity function, exp, log, composition, and arithmetic operations (+−×÷). Some authors call this class of functions elementary functions, but that term is now more commonly used in a different sense, which includes algebraic functions.
Evidently my professor was in the exponential-logarithmic camp.
The definition of "elementary function" typically includes functions which solve polynomials, like the Bring radical. The definition was developed and is most fitting in algebraic contexts where algebraic structure is meaningful, like Liouvillian structure theorems, algorithmic integration, and computer algebra. See e.g.
There appears to be a typo in that example; I assume "Essentially elementary functions are the functions that can be built from ℂ and f(x) = x" should say something more like "the functions that can be built from ℂ and f(x) = y".
Not a typo! Think of f(x) = x as a seed function that can be used to build other functions. It's one way to avoid talking about "variables" as a "data type" and just keep everything about functions. We can make a function like x + x*exp(log(x)) by "formally" writing
f + f*(exp∘log)
where + and * are understood to produce new functions. Sort of Haskell-y.
jargon are words being used that don't carry the typical laymen definition, but a specific one from the domain of said jargon.
If a written piece is intended for an audience who knows the jargon, then it's fine to use jargon - in fact it's appropriate and succinct. If it was intended for the laymen, then jargon is inappropriate.
But it seems you're lamenting that this jargon is wrong and that it shouldn't be jargon!?
I don't know if I read this right, but I thought it's proven that "elementary functions" can't solve 5th degree or higher polynomial, so I'm confused how it's interpreted if elementary functions also include arbitrary polynomial roots. Or is it different elementary functions?
That theorem is not formulated about "elementary functions".
It says that polynomial equations of the 5th degrees or higher cannot, in general, be solved using "radicals".
While something like "polynomials" or "radicals" has a clear meaning, which are the "elementary functions" is a matter of convention.
The usual convention is to include all algebraic functions and a few selected transcendental functions.
In "all algebraic functions", are included the rational functions, the radicals and the functions that compute solutions of arbitrary polynomial equations.
Some conventions used for "elementary functions" describe the expressions that you can use to write such "elementary functions", in which case not all algebraic functions are included, but only those written by combining rational functions with radicals.
For an algebraic function that computes a solution of a general polynomial equation, which cannot be expressed with radicals, you cannot write an explicit formula, but you can write the function only implicitly, by writing the corresponding polynomial equation.
So the difference between the 2 kinds of conventions about which are "the elementary functions" is usually based on whether only explicitly-written functions are considered, or also implicit functions.
So the argument of the post is basically “this definition of elementary functions includes functions without closed form expression, and thus we cannot express these elementary functions with eml”, or sth more (that there exist elementary functions with closed form expressions that cannot be expressed by eml)?
FWIW I never thought that functions without closed form expressions were considered elementary functions, but i guess one could choose to allow this if they wanted
The term 'elementary function' doesn't really have a single universally agreed on strict definition.
Definitions are either a bit fuzzy, or not universally agreed on.
Though interestingly https://en.wikipedia.org/wiki/Elementary_function says "More generally, in modern mathematics, elementary functions comprise the set of [...]". Though at least Wikipedia thinks that 'modern mathematics' has a consensus; of course, there's no guarantee that whoever you are talking to uses the 'modern mathematics' definition that Wikipedia brings up.
In math elementary usually means fundamental or foundational not elementary school. The root word is element and the relationship to “simple subject” is tangential and more related to its teaching the elemental topics for a lifetime education than definitionally cross discipline.
Are there other known ancient games that work like this?
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