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If you want to learn, you need to forget AI and work the problem out yourself. It sounds to me as if you have not done that. If you had, you would not be asking this question. Look up Raoult’s Law - then calculate for yourself the first part of the problem and show me how you did that. Then we can talk about the second part.

https://chemistryhelpforum.com/t/useful-latex-code-for-chemistry-equations.147266/ For those who might be interested, here is an interesting thread about LaTex / Mathml and MatthJAX in chemistry. I wonder if there is anything there we could learn for this forum ?

This wasn’t true last year when you claimed it and it’s still not. Germany’s oil imports are lower than when they started shutting down nuclear, and basically none of it is from Russia. So this is not only not a fact, it is a lie - a repetition of an untruth that was pointed out to you, yet you’ve repeated it https://www.scienceforums.net/topic/135990-anti-democratic-political-decisions-in-the-western-countries/#findComment-1290436 It’s also something whose connection to “less freedom” is unclear to me. Your survey quote lacks an actual link, but here it is https://www.cleanenergywire.org/news/two-thirds-germans-against-shutting-down-last-nuclear-power-plants-point-survey “32 percent of those surveyed were in favour of the remaining reactors continuing to run for a limited period, and an additional 33 percent were in favour of an unlimited runtime extension. Only 26 percent fully support a complete phase-out nuclear power at this point in time” So it’s the timing that’s the issue. Only a third wanted an unlimited extension. The shutdown plan predates that; it was made under Schröder and the first shutdown occurred in 2003. Merkel initially delayed it until Fukushima caused a pivot and she accelerated the plan.

Details matter here. It depends. Which humans? How were they trained? What parameters were given for the analysis?

... Not an issue apparently, see Flywheel Storage Power System Reading between the lines, the limited current scale of such installations seems due to a lack of perceived urgency rather than any significant technological limit. And the UK always has Dinorwig - it would take one monster of a flywheel to compete with that.

Today I learned that the No True Scotsman fallacy is just 51 years old (it was coined in 1975 by a philosophist Antony Flew). That Scotsman could still be alive today if he was a real person!

The story of that convict, with a bit more details (he was jailed again later) is mentioned in the Krakatoa book. Ludger Sylbaris - Wikipedia

Yes! That was why my mother, then teaching geography at the local girls' grammar school, bought the book. Plate tectonics was the new thing. She was quite excited by it and so, having a scientifically-minded boy's interest in volcanoes, I read parts of the book myself. Of course the detailed understanding of how volcanoes arise behind subduction zones has progressed hugely since then, but the principle was already there.

If someone wrote a wiki on weaponized obtuseness, this post should be in it. a) repeating an unfounded claim does not make it true, especially if you ignore a whole discussion that spawned from it. b) let me think, what else could have happened in China in the last two decades? Was it the introduction of capitalism and massive growth? No, that would be against my narrative. Clearly, they have become much more authoritarian after the death of such liberal figures like Mao. Also, again you ignored examples like Russia.

Today, after going through about one third of this book, I learned that I don't care about English kings.

I have been looking for the 2011 version but YT only has one with a handful of episodes translated into English. And I am just starting to learn Chinese. There is the 1998 version though:

I think that Google was guilty regarding our local law. (because it can easily accepted as "third eye" , it definitely follows people. And this is a guilt.)

I used to watch The 'Water Margin'. Have you seen that series? 1970's. 'Monkey', late 70's, was another.

Allowing free speech does mean that one can spout propaganda, but giving the government the power to censor or decide what the truth is, is inherently authoritarian. The problem as I see it is not the system, it’s that authoritarians exist. And to the point of the OP, if we didn’t have sociopaths we wouldn’t have a lot of the billionaires exerting influence. People are going to try and game the system, regardless of the system that’s put in place. Blaming the system is a red herring, IMO, because the problem is inherent in any population of people.

The printing press? Why are you bringing up this straw man from the 15th century? I never suggested that all technology encroaches on freedom and control. I pointed to particular technology, indicating how they are making us vulnerable to authoritarianism. One technology I didn't mention because, although it poses a substantial risk to our freedom and privacy, it also exposes the evil actions of overlords, is the proliferation of cameras. The thing about a lot of technology is that it provides us with benefits that results in us accepting the technology into our lives only to find that the technology can also be used against us. It perhaps should worry us that we voluntarily carry a tracking device with us wherever we go. And that tracking device could also be a listening device. That may be paranoia, but can any of you say for certain that a mobile phone is not acting as a listening device? That's a problem with much of technology: the users of the technology cannot know exactly how it works. Australia has recently banned under-16-year-olds from accessing social media. Many people support this as social media can be a dangerous place for children. But the consequence of this is that all (adult) Australians now have to somehow identify themselves to use social media. At present, a VPN may be able to get around the age-verification process. But as more countries adopt age-based restrictions on accessing the internet, and as VPN detection becomes more effective, VPNs will become less effective as a means to bypass age-verification. Gradually, we are finding that our ability to use the internet anonymously is being eroded away. I'll admit to some resistance to new technology based on a natural desire to maintain the status quo. But I can see the benefits of particular technology. And I can also see the dangers of particular technology. About 30 years ago, I was a believer of the idea that a fair society should be run by computers. But since then, having experienced glimpses of what such a society would be like, I no longer believe in a society run by computers. The fundamental problem with dealing with computers is that one can't negotiate with them. For example, a few years ago, I wanted to create a new Outlook email account. However, before I could do that, I had to prove that I was not a robot. But due to the arms race between producing tasks that robots can't solve, and producing robots that can solve such tasks, the requirement that ordinary humans are able to solve the tasks was forgotten. Unable to solve the task, I had to abandon creating a new Outlook email account and go with Gmail instead. Subsequently, Microsoft realised their mistake and reverted back to something that doesn't require a savant to solve. Usually, the option of an alternative task is provided (for the visually impaired), but for some reason this didn't work. Whether AI will make computers easier to negotiate with is hard to say, but I suspect that AI will be more idiosyncratic to deal with. Are you mocking me?! Computers were fine, albeit expensive, when only nerds had them. But now that every man and his dog have them, criminals now see computers as a lucrative avenue to rip people off. And now we all have to use security software that we are forced to trust, ensure that all our software has the latest updates (hoping those updates don't crash our system), treat with suspicion all our online (and other) communication, etc. The notion of authoritarianism isn't limited to governments. Private enterprise also has authoritarian tendencies in their quest for increasing profit. And criminals use scare tactics to extract money from people. And it seems that the more technology we have, the more vulnerable we are to people who want to take advantage of us.

The intrinsic properties of a manifold depend entirely on the manifold itself without any reference to a higher-dimensional embedding manifold (a coordinate transformation is an embedding of a manifold into a manifold of the same dimension). The distance between two points of a manifold depends on the path between the two points. That is, for the expression: (ds)2 = guv dxu dxv ds is not an exact differential (there does not exist a function s(..., xu, ...) for which ds is the differential). This btw is why there is no absolute time in relativity. If ds were an exact differential, then: [math]ds = \dfrac{\partial s}{\partial x^u} dx^u[/math] and therefore: [math](ds)^2 = \dfrac{\partial s}{\partial x^u} \dfrac{\partial s}{\partial x^v} dx^u dx^v[/math] [math]g_{uv} = \dfrac{\partial s}{\partial x^u} \dfrac{\partial s}{\partial x^v}[/math] But the RHS of this expression, as a matrix, has zero determinant, contrary to the requirement that the metric tensor is invertible. [If the above LaTeX doesn't render, please refresh browser.]

Interesting that the BBC article has a paragraph uncritically praising the anti-nett zero stance of Reform Party's Richard Tice. A little research shows that the author, Justin Rowlett has a significant oil company share holding in his portfolio. It is not a balanced piece of journalism.

Except I don’t think it is madhouse politics, at least not the part of the UK government. The issue of rewiring the grid for distributed power generation, as opposed to the legacy system of a small number of large central generating stations, is hardly a new one: it has been flagged for years now. The madhouse stuff is coming from those right wing parties who cynically see an opportunity to turn combatting climate change into a party political issue, which is depressing beyond belief. For all his (many) faults, Bozo at least did not do that. It seems to me that regional pricing might be a good, market-driven solution, provided it is set up in a way that does not cut the legs from under existing investments or unduly penalise populations currently without good access to renewable generation.