In reality, Germany became entirely dependent on Russian gas, oil and coal.

For all that talk of dependency preciously little happened when Russia closed the valves. There’s press reports about BASF going into gas saving mode but that’s a bit misleading – actual gas saving mode would be to change their processes on a fundamental level (they have plans and infrastructure for that), what they did do is to use the flexibility in their standard processes to not rely on gas as precursor where there’s more readily available options – as they’ve been doing for literal decades, depending on market prices they’re using more of this, or more of that. They pulled a lever over to one side, they didn’t build a whole new set of levers to pull.

Germany ended up having more gas reserves at the end of the winter than usual because people were quite mindful when heating their homes, mindful as in “it doesn’t need to be t-shirt temperature in here, 20C suffices”, not as in “let’s heat our homes like English pensioners”. Gas prices actually sunk, presumably due to lower demand companies invested in things like waste heat recycling.

The whole concept of Wandel durch Handel relied on the assumption that economical entanglement makes war ruinous, and thus states are heavily disincentivised to be belligerent. You can now interpret that in two ways: a) It didn’t stop Russia, therefore, it failed or b) it succeeded in ruining Russia’s economy because all their what ball bearing companies went belly-up during entanglement, German ball bearings being cheaper (not necessarily unit price, you also have to take lifetime, service costs etc. into account) and now they have severe shortages (that’s simplifying quite a bit but that’s the net effect).

In the end there’s only one thing to take away: Policy can’t influence non-rational actors. All you can ensure is that if an actor becomes irrational they’re shooting themselves in the foot.

Why is basic arithmetic so sacred that it must not be besmirched?

It isn’t. It’s convenient. Toss it if you don’t want to use it. What’s not an option though is to use it incorrectly, and that would be insisting that 0.999… /= 1, because that doesn’t make any sense.

A notational system doesn’t get to say “well I like to do numbers this way, let’s break all the axioms or arithmetic”. If you say that 0.333… = 1/3, then it necessarily follows that 0.999… = 1. Forget about “but how do I calculate that” think about “does multiplying the same number by the same number yield the same result”.

catches people because using arithmetic properly leads to an incorrect understanding of repeating decimals.

Repeating decimals aren’t apart from decimal arithmetic. They’re a necessary part of it. If you didn’t learn 0.999… = 1, you did not learn decimal arithmetic. And with “necessary” I mean necessary: Any positional system that supports expressing rational numbers will have repeating digits. It’s the trade-off you make, by fixing the divisor (10 in our case), to make numbers easily comparable by size, because no number can divide any number cleanly because there’s an infinite number of primes. Quick, which is the bigger number: 38/127 or 39/131.

Any notational system has its awkward spots. You will not get around awkward spots. Decimal notation has quite few of them, certainly fewer than Roman numerals where being able to do long division earned you a Ph.D. If you can come up with something better be my guest, I already linked you to a starting point.

0.999… has no smallest digit, thus the carry operation fails to roll it over to 1.

That’s where limits get involved, snatching the carry from the brink of infinity. You could, OTOH, also ignore that and simply accept that it has to be the case because 0.333… * 3. And let me emphasise this doubly and triply: That is a correct mathematical understanding. You don’t need to get limits involved. It doesn’t make it any more correct, or detailed, or anything. Glancing at Occam’s razor, it’s even the preferable explanation: There’s a gazillion overcomplicated and egg-headed ways to write 1 + 1 = 2 (just have a look at the Principia Mathematica), that doesn’t mean that a kindergarten student doesn’t understand the concept correctly. Begone, superfluous sophistication!

(I just noticed that sophistication actually shares a root with sophistry. What a coincidence)

Someone using only basic arithmetic on decimal notation will conclude that 0.999… is not 1.

Doesn’t pass scrutiny, because then either 0.333… /= 1/3 or 3 /= 3 (or both). It simply cannot be the case when looking at the whole system, as opposed to only the single question 0.999… ?= 1 and trying to glean something from that. Context matters: Any answer to that question has to be consistent with all the rest you know about the natural numbers. And only 0.999… = 1 fulfils that.

Why are you making this so complicated?

They’ve definitely done that before, dunno if it was deliberately. They must have somewhat of an idea how long it takes for nocebo to kick in with the local village idiots, if it’s short enough it could actually be a rather good idea to make waiting a bit a general policy. Tank some mild capital and opportunity cost to prevent having to battle in court and the town newspaper? Sounds like a win to me.

Not really, they’d need to triple their numbers.

Numbers on the far left are misleading as Die Linke is bleeding members to the BSW but the BSW is taking their sweet time handing out membership cards, double-checking every single applicant. Reportedly they have a backlog of at least 8000 applicants or such and at least 20k people generally interested. Wagenknecht is at least 70% tankie so it doesn’t surprise that they’re doing a vanguard thing.

I get that ever model is wrong, but some are useful.

There is nothing wrong about decimal notation. It is correct. There’s also nothing wrong about Roman numerals… they’re just awkward AF.

Basic decimal notation doesn’t work well with some things, and insinuates incorrect answers.

You could just as well argue that fractional notation “insinuates” that 1/3 + 1/3 = 2/6. You could argue that 8 + 8 is four because that’s four holes there. Lots of things that people can consider more intuitive than the intended meaning. Don’t get me started on English spelling.

Terms.

There! Syntax. We went over this. Seriously, we did, and, no, I got the last word.

I suggest you check some Maths textbooks, instead of listening to a Physics major.

I can check any textbook from any discipline. You know what? I could even ask my school teachers. Because I’m not American and I wasn’t taught shit that doesn’t match up with what professionals are doing.

You’re just another yank drunk on jingoism, “We do it like that, therefore, it is right”.

https://www.youtube.com/watch?v=lLCDca6dYpA

…oh wait I remember that Unicody user name. It’s you. Didn’t I already explain to you the difference between syntax and semantics until you gave up. I suggest we don’t do it again but instead, you review the thread.

Also it’s not like “getting food is easier” is the only hypothesis out there as to why we settled down. Another one, IMO much more in line with human nature, is that we figured out how to ferment beer and for that reason planted buttloads of grain.

Simlocks have completely vanished from the market at least here in Germany, mostly because carriers don’t care if you use your subsidised bonus phone with a different card – you’re still locked into a contract with two years or such minimum duration. Even those contracts have gotten rare though I think most people right-out own their phones and then make a separate contract.

0.999… = 1 requires more advanced algebra in a pointed argument,

You’re used to one but not the other. You convinced yourself that because one is new or unacquainted it is hard, while the rest is not. The rule I mentioned Is certainly easier that 2x/x that’s actual algebra right there.

It’s as if all math must be regarded as infinitely perfect, and any unbelievers must be cast out to the pyre of harsh correction

Why, yes. I totally can see your point about decimal notation being awkward in places though I doubt there’s a notation that isn’t, in some area or the other, awkward, and decimal is good enough. We’re also used to it, that plays a big role in whether something is judged convenient.

On the other hand 0.9999… must be equal to 1. Because otherwise the system would be wrong: For the system to be acceptable, for it to be infinitely perfect in its consistency with everything else, it must work like that.

And that’s what everyone’s saying when they’re throwing “1/3 = 0.333… now multiply both by three” at you: That 1 = 0.9999… is necessary. That it must be that way. And because it must be like that, it is like that. Because the integrity of the system trumps your own understanding of what the rules of decimal notation are, it trumps your maths teacher, it trumps all the Fields medallists. That integrity is primal, it’s always semantics first, then figure out some syntax to support it (unless you’re into substructural logics, different topic). It’s why you see mathematicians use the term “abuse of notation” but never “abuse of semantics”.

The teacher couldn’t possibly fathom marking “mega” right for students who had only context from the classroom and also marking “yotta” right for students who had done independent research.

That is child abuse. Literally. The way my teachers worked, presumably because they learned how to deal with the situation when actually studying pedagogics (a thing we require of teachers here) is to give an extra point because you want to encourage kids to figure things out on their own.

https://en.wikipedia.org/wiki/Rewriting

…if that’s too heady do note that if you have a heap of four marshmallows and a heap of five marshmallows then that’s the same as having a heap of five marshmallows and a heap of four marshmallows. To have a heap of nine marshmallows, you first have to turn them into a single heap. That’s reducing the number of heaps from two to one and that’s a hand-wavy way to justify the term.

That’s like asking a fusion researcher whether the reactor needs to reach 100 million Celsius or Kelvin, isn’t it.

Or signed integers because overflow is undefined. It could do the left-hand computation in two’s complement and the right hand in sign-magnitude, leading to different results. Or, as it’s undefined, it could brew you some coffee and serve it with an aspirin.

This is the flawed system, there is no method by which 0.999… can become 1 in here.

Of course there is a method. You might not have been taught in school but you should blame your teachers for that, and noone else. The rule is simple: If you have a nine as repeating decimal, replace it with a zero and increment the digit before that.

That’s it. That’s literally all there is to it.

My issue lies entirely with people who use algebraic or better logic to fight an elementary arithmetic issue.

It’s not any more of an arithmetic issue than 2/6 == 1/3: As I already said, you need an additional normalisation step. The fundamental issue is that rational numbers do not have unique representations in the systems we’re using.

And, in fact, normalisation in decimal representation is way easier, as the only case to worry about is indeed the repeating nine. All other representations are unique while in the fractional system, all numbers have infinitely many representations.

Instead of telling those people they’re wrong, focus on the flaws of the tools they’re using.

Maths teachers are constantly wrong about everything. Especially in the US which single-handedly gave us the abomination that is PEMDAS.

Instead of blaming mathematicians for talking axiomatically, you should blame teachers for not teaching axiomatic thinking, of teaching procedure instead of laws and why particular sets of laws make sense.

That method I described to get rid of the nines is not mathematical insight. It teaches you nothing. You’re not an ALU, you’re capable of so much more than that, capable of deeper understanding that rote rule application. Don’t sell yourself short.

EDIT: Bijective base-10 might be something you want to look at. Also, I was wrong, there’s way more non-unique representations: 0002 is the same as 2. Damn obvious, that’s why it’s so easy to overlook. Dunno whether it easily extends to fractions can’t be bothered to think right now.

The problem goes away easily once we understand the limits of the decimal system, but we need to state that the system is limited!

But the system is not limited: It has a representation for any rational number. Subjectively you may consider it inelegant, you may consider its use in some area inconvenient, but it is formally correct and complete.

I bet there’s systems where rational numbers have unique representations (never looked into it), and I also bet that they’re awkward AF to use in practice.

This is a workaround of the decimal flaw using algebraic logic.

The representation has to reflect algebraic logic, otherwise it would indeed be flawed. It’s the algebraic relationships that are primary to numbers, not the way in which you happen to put numbers onto paper.

And, honestly, if you can accept that 1/3 == 2/6, what’s so surprising about decimal notation having more than one valid representation for one and the same number? If we want our results to look “clean” with rational notation we have to normalise the fraction from 2/6 to 1/3, and if we want them to look “clean” with decimal notation we, well, have to normalise the notation, from 0.999… to 1. Exact same issue in a different system, and noone complains about.

By definition, all sufficiently advanced mathematics is isomorphic to witchcraft. (*vaguely gestures at numerology as proof*). Also Occam’s razor has never been robust against reductionism: If you are free to reduce “equal explanatory power” to arbitrary small tunnel vision every explanation becomes permissible, and taking, of those, the simplest one probably doesn’t match with the holistic view. Or, differently put: I think you need to look more broadly onto Occam’s razor :)

Avoiding other plants to take root, in particular ones with deep roots as they would form weak points in the dense felt-like root system grass has. Also ease of inspection.

There’s about a millennium of engineering experience in those dikes… and plenty of historical compromises. Like, we knew back in the middle ages that flat profiles secured by grass are the most stable and secure but they require massive amounts of material so it was necessary to use inferior dikes with vertical faces made of wood planks. Most recent notable innovation is sand cores and ditches behind the dike to manage seepage water (behind meaning on the land side, always confuses them tourists), and some minor alterations to geometry to improve the way waves hit it.

We probably knew that sheep were good for dikes before we built them as, at least in principle, dikes are nothing but a warft with a hole in the middle and we’ve built those since time immemorial.

And in case you’re wondering yes we’re raising them quite a bit higher in anticipation of sea levels rising. Completely uncontroversial decision, only question was whether to rise the dikes very high, or use the same budget to raise them not as high, but wider, so that they can easily be made even very higher in the future. We went with the latter option, which is kinda optimistic and pessimistic at the same time.

One night I dreamt about the new C standard. It was a tome of ten thousand pages, in dense, tiny, font, three columns of text on each page, and it was all headings and sub-headings interspersed with nothing but either “undefined” or “implementation-defined”.