Fun fact: The -gh endings of many English words share a proto–Indo European root with that enclitic¹ -que in Senatus Populusque Romani. I remember being skeptical of this when I first heard it assuming that the person was arguing for a shared Latin heritage until I dug in and discovered that it actually went back to PIE.²
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1. For the non-linguists here, an enclitic is a suffix added to a word that either functions as a separate word (here -que means “and”) or as a grammatical modifier like the possessive ’s in English.
2. Proto–Indo European for those of you who don’t do acronyms.
This piqued my interest with the -gh endings, so I did a little investigation. What I found wasn't "many", apparently the only really attested example in Modern English is "through" and pretty much every other instance has died out. With a side note that the -kWe ending, also became "hw-" prefixes in English question words and possibly also the ge- prefix on collective nouns (also long since lost in English, but still present in German) which no survives only in the "i" in "handiwork", originally "hand geworc".
Of course, I only did a cursory examination, so there might be other examples not mentioned in the articles I found, but that's what I learned in about half an hour. Still, very cool fun fact, thanks!
It seems this -que was already a relic at that time, or maybe sort of literary, because it coexisted with et (as in etc, et cetera, &c), which still exists e.g. in French. Or maybe one is from antic Latin and the other is from "vulgar"/late Latin ?
There were a number of different ways to write and in Latin. The Vulgate Bible, apparently unhappy with all the vav-connectives in its Hebrew sources uses them all.
It's an open question whether the Veneti themselves were ethnically Slavic though. We know of the earlier Gallic Veneti, which were a Celtic seafaring tribe that settled multiple locations along the European coastline. The Italian region Veneto and the city Venice can also trace their names to an ancient group called "Veneti", and they seem to have spoken a mix of Italic and Celtic. In contrast, the Slavic language seems to have originated much further east.
A 2012 study has suggested that Venetic was a relatively conservative language significantly similar to Celtic, on the basis of morphology, while it occupied an intermediate position between Celtic and Italic, on the basis of phonology
The most archaic Slavic hydronyms are found here, along the middle Dnieper, Pripet and upper Dniester rivers [..] inherited Common Slavic vocabulary [includes] well-developed terminology for inland bodies of water (lakes, river, swamps) and kinds of forest (deciduous and coniferous), for the trees, plants, animals and birds indigenous to the temperate forest zone, and for the fish native to its waters
The fact that the Slavic language seems to have developed inland but the Veneti mostly settled coastal areas puts a big question mark under the Veneti == Slavs link.
There are Germans from Slavic / protoslavic descent in North-Eastern Germany aside from the small Slavuc speaking minorities. Some location names and family names (Wend, Wenden, etc) are very telling in this regard. I like this direct link to ancient history.
The scale and distances of migrations throughout Europe in the 4th-5th centuries are hard to comprehend, as well as the rapid transformation of the societies of the groups that migrated. It has the same feel to me as a major geological event, like the breaking apart of Pangea.
Research on this topic has been very active since the late 2000s (before that scholars on the topic had been very few). It seems that the scale of the migrations are much better understood now (100k-300k people over 3 centuries).
But as you say, the rapid transformation of the societies of the groups that migrated at the time is very hard to comprehend, but also the changes of those where they migrated, in cases where it was more of a fusion than an invasion / displacement.
I think it is a very interesting point to offer to those in Europe minimizing the current migration waves (often for noble reasons of reducing racism and countering far right ideologies). It's no use denying that welcoming tens of millions of people from other cultures over a few decades has and will have very deep social and political effects.
I have left comments on HN and Reddit and then found them rolled into Google's AI search summarizer OR the knowledge box with _extreme rapidity_ such that when I went, mere moments later, to go re-check some fact I had cited, I found my own comment at the top of the results, repeated back to me, but with authority and gravitas, ensconced in the austere trappings of the knowledge box.
Isn’t there a performance cost though with runtime binding of functions? (I’ve not looked too closely at Swift since the first couple of years when Objective C compatibility was essential, so maybe that’s less of a default than it was in the early days).
Runtime binding only occurs for Objective-C interop.
Swift functions are bound at compile time when statically known. Dynamic dispatch is done through vtables for native Swift classes, and through witness tables for protocol existentials.
I used to do things like this when I was a kid (less extreme, never more than a single sheet of paper), where I would create some natural features: a lake shore or river, maybe a freeway or two or a railroad and then start platting out a subdivision in the open spaces. It was a delightfully meditative practice and maybe I should start doing it again.
Not the person you replied to, but like them, I too liked to draw imaginary maps when I was a kid, mainly of medieval towns. I also tend to like the world-building aspects of strategy games, arguably more than the actual strategy parts.
Cities: Skylines have been in my wishlist since shortly after it came out but I never got around to playing it until about a month ago, and... didn't like it at all. It felt too "micro-manage-y" (for the lack of a better word) while also having the pressure of the ticking time.
Needless to say, I was very disappointed after looking forward to it for ~10 years.
I actually had the same experience as you (own it, played it only a bit for similar reasons), but FWIW I believe there is a sandbox mode to just play around in.
Another chill medieval town building game is Manor Lords. It has some management but overal is laid back.
Oh you just reminded me of the joy of making maps for D&D. I only ever played two or three times, but I had notebooks full of detailed maps of dungeons, cities, whole continents.
I don’t think I’ve ever worked with anyone in engineering who I would consider degenerate aside from the occasional crypto supporter. Even 30% seems like a scary high percentage of degenerate engineers.
What’s interesting is that while most cars imported into Mexico (except for those from the NAFTA region) face stiff tariffs or outright bans (if you move to Mexico from the US you can only bring your car if it was manufactured in Mexico/Canada/US, other cars are not allowed at all), but electric cars have no tariff at all which means that, e.g., Chinese EVs are widely available there. The BYD Seal sells for MXN888000 in its AWD/big battery configuration which translates to USD51,184¹ which is comparable to the Tesla Model 3 price in Mexico (and a bit lower than the equivalent price in the US). Mexico is going at the EV transition with a two-pronged strategy: Building a domestic industry and encouraging imports at the same time. This seems to be the exact opposite of the US strategy.
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1. Worth noting two key differences between the Mexican and American car buying experience: First, prices are fixed. There’s none of this negotiating with the dealer about the price or upselling you on undercoating stuff. You can look on the website and know what the price is. Second, instead of sales tax, Mexico uses VAT to achieve the same purpose. As a result, the price you see for a product is going to be the actual price you pay walking out the door and not the price before sales tax (at my current residence, the total sales tax is currently 10%). As a consequence, some things that might appear to be slightly more expensive in Mexico, depending on where you live, may actually be slightly cheaper.
There’s a bit of hand-waving in the jump to 2n choose n solution, which I suppose is fine, and my ex–math teacher brain really wants to have a proper proof or at least solid reasoning rather than “it follows the pattern” based on three observations.
But I am reminded of how during my engagement 24 years ago, my future father-in-law raised an issue of being able to determine whether they were getting the full amount of sandpaper on large rolls that they were paying for. I was able to simplify the question a bit to one that treated the rolls as if they were simple concentric rolls of a specified thickness and from there could turn it into the good old Gaussian sum formula times 2π to get the length. The engineers working for the company came up with the same solution, but instead of using n(n-1)/2 they did the summation with multiple rows in excel.
You can go down or right at any point. To go in bottom-right corner, you need n down steps and n right steps. In how many ways can you arrange n things on type A and n things of type B? In C(2n, n). The problem is about modeling, once you model it correctly, you get the definition of combinations.
C(2n, n) isn’t about permutations, but choosing subsets of a set without order, but as I’ve thought about it, the model here is that there are 2n moves to be made and you need to choose n of them to be down (or right, depending on your preference).
Which suggests another approach to the solution; you have 20Ls and 20Rs which can appear in any order so it’s a permutation with repetition problem and thus 40!/(20!20!)
That approach has the advantage that it’s easily adapted to non square rectangular grids (n+m)!/(n!m!)
That theoretical wait time doesn’t usually end up being so long. Between borrowers returning things early, people on the wait list giving up and most importantly, the library deciding that the current inventory is insufficient, the wait times usually are much less than that (I’ve observed this with books and other materials at my local library and the wait on in-demand times is never as long as the queue would imply).
But we can check out a Netflix Roku, and the wait time really is what it says on the tin + a bit more; which works out to about once a year, which is about what we need ...
Hmm, my library had a T-Mobile wireless hotspot available and the wait time on the hold was less than what was expected. It ended up being rather fortuitous as the first half of 2020 corresponded to the beginnings of the dissolution of my marriage and I spent that time living in a mostly unfurnished house with no internet and I got the hotspot just before everything shut down in March and it enabled me to have internet for a couple months while the library was closed.
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1. For the non-linguists here, an enclitic is a suffix added to a word that either functions as a separate word (here -que means “and”) or as a grammatical modifier like the possessive ’s in English.
2. Proto–Indo European for those of you who don’t do acronyms.
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