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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.

I don’t think so for a minute. He’s just had a lifetime of entitlement and is now trying to minimise as much as possible the opprobrium that has finally caught up him. Nor do I think Zuckerberg is on the spectrum. He’s just talking his own book, as these guys always do.

“Astronomers have watched a dying star fail to explode as a supernova, instead collapsing into a black hole. The remarkable sighting is the most complete observational record ever made of a star's transformation into a black hole, allowing astronomers to construct a comprehensive physical picture of the process. … The discovery will help explain why some massive stars turn into black holes when they die, while others don't.” https://phys.org/news/2026-02-supernova-clearest-view-star-collapsing.html

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.]

I bake or roast sweet potatoes whole and , if there are any leftovers then they can be eaten cold the next day like a sweet . The skin should be caramelised on the outside and are very filling and easy to just grab. I think they taste better when cold(but some are better than others-recently one was so juicy that it squirted when cut with a knife)

“with the new upgrade, called Mars Global Localization, Perseverance can match its own panoramic imagery to orbital terrain maps onboard, calculate its precise position and continue along its planned route without waiting for Earth-based confirmation. An onboard algorithm performs the comparison in about two minutes and can pinpoint the rover's location to within roughly 10 inches (25 centimeters), all without assistance from human planners” https://www.space.com/space-exploration/mars-rovers/nasas-perseverance-rover-now-has-its-own-gps-on-mars-weve-given-the-rover-a-new-ability

Mandelson has now also been arrested on suspicion of misconduct in public office. So the apparent unfairness as between the two suspects has been rectified, at least.

Don't use AI as information source, use it as information processing tool. Use models with biggest context window. Atm its Gemini 3.1pro and Claude Sonet/Opus 4.6 Dont upload full pdf. Read by chapters. Develop a system promt that will force AI to support every statement with source (still can give you fake source as legit) Studding like this is not easier if that's what you are after. You quickly will realize that AI will mislead you on regular basis, so you can't just learn, no. You have to debate it then test it in relation to established basis then test it against empirical data and still the doubt in you will grow in to healthy scientific scepticism. Just treat AI as your useful but sometimes ignorant friend that you having fun debating. Get your knowledge challenged at all times and don't get lost. Good luck!

There's a significant difference between failing to recognise social cues and dismissing them with contempt. I'm not a psychologist, but I might wager a modest sum on entitlement mentality and narcissistic personality disorder. A lot going around just now it seems. Sim-post with @exchemist Sim-post with @exchemist

Passing along something Geordie posted on another forum, from an FB feed. Hypothetically, if someone was accused of having sex with goats by over 30 different people and regularly denied it, but also dropped very public hints about how much he liked to have sex with goats for decades, and ran a goat pageant to find the best looking goats, and was best friends with someone who who got convicted of fucking goats and trafficking goats to friends all over the world who also liked to fuck goats, and his name was in the classified goat fucker chronicles 5,000 times, and he wished other goat fuckers well in prison, what do you think the odds are that person is also a goat fucker?" Ragnar Blackwolf

Good point! But again - why waves in the first place? What precisely do you mean by "waves"? Do you know the general solution of the two-dimensional wave equation? [math]\dfrac{1}{c^2}\dfrac{\partial^2 \psi}{\partial t^2} - \dfrac{\partial^2 \psi}{\partial x^2} = 0[/math] [math]\psi = f(ct+x) + g(ct-x)\ \ \ \ \text{where }f()\text{ and }g()\text{ are arbitrary functions of a single variable.}[/math] Note that: [math]\dfrac{\partial \psi}{\partial t} = cf'(ct+x) + cg'(ct-x)\ \ \ \ \ ;\ \ \ \ \ \dfrac{\partial \psi}{\partial x} = f'(ct+x) - g'(ct-x)\\\dfrac{\partial^2 \psi}{\partial t^2} = c^2f''(ct+x) + c^2g''(ct-x)\ \ \ \ \ ;\ \ \ \ \ \dfrac{\partial^2 \psi}{\partial x^2} = f''(ct+x) + g''(ct-x)[/math] Thus, we see that "wave" refers to the motion of a function through spacetime rather than any sinusoidal character of the function. However, arbitrary functions can be decomposed into their sinusoidal Fourier component functions. In the case of the four-dimensional wave equation, a disturbance at each spacetime point propagates along the light cone emanating from that point. And because the wave equation is linear, superposition applies at the intersections of the various light cones, as well as any decomposition of a function into component functions. Also note that because the wave equation is a differential equation, the general solution is valid at each spacetime point, which is the basis of the Huygens-Fresnel principle.

Today I learned that the fake snow, used on the set of 'The Wizard Of Oz' was actually fluffy Asbestos fibers. Veritasium just dropped another video on the history, use, dangers, and attempts to regulate the use of Asbestos. These are my favorite kinds of videos produced by Veritasium. Turns out the spray-on insulation protecting the steel structure of the World Trade Center buildings was impregnated with Asbestos, which was then pulverized in those huge dust clouds, as the buildings came down. To this date, more than twice as many people have died from 'asbestosis' ( pulmonary fibrosis related to Asbestos exposure ) and related cancers, than in the original event, from simply breathing the resulting dust.

What was the background of their upbringing? Is it ok for 40. 50, 60 year old millionaires and billionaires to fuck 12, 13, 14 year olds and then blackmail, even kill them, to keep their silence? Children that age in developed nations are not considered to have sexual autonomy, especially with people that could be their grand and great grandparent. I'm not interested in the facts of each case, the principle of protecting naive/disadvantaged children from elder abuse supersedes all that. There is no circumstance, with consent or not, where a child can be sexually available to a person several times their age.

There is so much wrong with what you've written. You are talking about pubescent and prepubescent GIRLS like they should be self aware and be sexually familiar.

Consent laws protect children in these instances, or are supposed to, unless the men are shielded by other men who see nothing wrong with having sex with children.

Well, no, not really. Switzerland is a different country. And this is basically the same argument as before, about the timing of something vs the underlying sentiment; I see you omitted the paragraph that follows your quote, that shows the result of a vote to prohibit new construction. These lame “arguments” are rather tedious. You’ve obviously convinced yourself of something, but it’s not based on any facts you’ve shared.

Yes, and it's a classic joke, which I first heard as a teenager, and not in a vaccine context. It went something like: Doctor: Your baby has jaundice. Mother: I want a second opinion. Doctor: Okay. Your baby is ugly!

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 ?

No, AJB was a former, higly respected member of this forum. I havent found that to be the case. While D Lincoln explains when and how the Higgs was found, for example, 'Physics Explained' delves into how the Higgs field/mechanism works, how it gives rise to mass and the detected particle, all with a 'simplified' mathematical model. Check it out ... Just what I needed, another cat video. Like I already don't spend half of my internet time watching cat videos. As a former owner of two cats that I adored, I'm resisting the idea of getting another, as putting the previous ones 'to sleep' after 15 and17 years were two of the most difficult decisions I've had to make.

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.

That is my broader point though, hidden authoritarianism can be exemplified by arbitrary application of rules to certain people. That is what we are seeing in the US, where ICE and border control seemingly arbitrarily accept or reject various levels of proof of citizenship. In a broader sense, this arbitrariness has always existed at borders as the agents there can legally deny you entry except when you are a citizen, I believe. I.e. you do not need a full-on gestapo moment, but there built-in vulnerabilities, even in not fully autocratic systems. The main difference in my mind is how these vulnerabilities are being exploited. After all, in the US in theory you always had to prove your legal status if you are not a citizen. But generally you wouldn't be stopped on a random basis. But it was always fully in their power to do so in public places. Edit: with regard to OP and this point here specifically, the broader issue is that authoritarianism is not binary. Even in an otherwise liberal (as in free) system, there are necessary restrictions as well as vulnerabilities. How free a given society is depends not only on whether the whole structure is authoritarian or not, but rather on how the many individual components, ranging from the bureaucracy, law enforcement, judiciary, but also voter decisions decide to run things and what restrictions and safeguards we put into place and how we decided to enforce those. The slide in authoritarianism in Weimar, but also many other countries in recent times was often not after a coup and a massive restructuring of the system. Instead, they are characterized by continuous undermining of safeguards on all levels. In the given example, offline paperwork would only provide benefits, if they are robust safeguards forcing for example law enforcement to accept them. Yet much of it still lies in the discretion of the officer. And again, in the US we can see how fast the discretion can change.

I believe I've already told you about the baby tiger that my niece had for about a year. Before she became a magician at the Greg Frewin Theater, she was part of the act and choreographer, and G Frewin included tigers into his stage act. On one occasion I was invited backstage and got to pet Boomer, an 800 lbs tiger, that has since passed. What I found incredible was that if you scratch them behind the ears, they 'purrr' just like household cats, yet the frequency is so low and loud, it actually vibrates the floorboards.

OK, then [math]\frac{xy}{2}=\frac{1}{\sin 2\beta}[/math].

Mr President; someone has suggested a name for the new Ballroom. https://en.wikipedia.org/wiki/Orangery

The Riemann curvature tensor in one dimension does not vanish but rather is undefined. It has no components in 1D.

If you like a little math with your science, try 'Physics Explained' also. When I first started watching him, I thought ( hoped ) it was AJB.

Good channel, with clear explanations addressing some fairly counterintuitive concepts in science. I like the interviews with the public, where Derek shows common misunderstandings. LOL. Sometimes one forgets how much...orange there was ca. 1970.

See all his dinner guests did a runner.

There is a lot of contradicting information in lit, and it mostly depends on what you measure. The few things where most studies agree is that digital reading is different from paper, so lessons are not easily transferable. There are some studies on screen use, but the papers cover a lot of ground and include e.g. simulating driving and measures other than fatigue. A recent study has combined ambient lighting mode with screen color temperature and dark vs light mode. Generally speaking, they found that indicators of fatigue were higher when reading in light mode and with screen color temps in the lower (warmer) range. Other studies have looked at alertness and onscreen tasks it seemed that blue was advantageous for folks to find stuff effectively. Whether that plays into fatigue was not tested.

Excuse me, but it is 1,1,1,2,3,5... https://en.wikipedia.org/wiki/Alkane#Isomerism

Don't usually watch random YouTube videos, but there are some channels I follow. Most are Military aviation related. Some that may be of interest to Forum members are 'Pax Americana' and 'Perun', which deal with Military policy, and for the 'scientists' among us, 'Physics Explained' and 'Veritasium'.

I think the police did feel endangered, some suffered severe injuries. In fact, some police officers offered testimony to that effect during the inquiries. In other situations it would most likely have ended in bloodshed (in the US, that is). There was some deliberate intention not to further escalate. IIRC there were orders from leadership not to e.g. use teargas or other means to use tear gas and other means. As a whole the situation appeared to have set up to support Jan 6 rioters and one might also add that quite a few in the police force might have felt sympathetic to them (before they were being pummeled that is). Ultimately, they only opened fire once and there have been quite a few discussions regarding police actions against, say, black folks or BLM protesters in comparison.

Just came up in (I think it is called) my feed. This seems very genuine.Most of the other stuff that appears in my feed is pure crap and is ai generated (so that I click on it a lot less lately)

Old Soviet joke: A man goes to a news stand every day and looks at just the front pages of all the newspapers. The guy behind the stand asks him what he's looking for. "An obituary". "But comrade, obituaries aren't on the front page!" "The one I'm looking for will be."

LOL. Brilliant. And how amazing that the 47th is able to always wrap himself in the glory of others. I guess that's the magic that happens when you courageously overcome bone spurs. I'm hoping the Mark Carney virus is highly contagious.

“We know from theory that most of the mass in the universe is expected to be dark matter, but it’s difficult to detect this dark material because it doesn’t emit light. Cloud-9 gives us a rare look at a dark-matter-dominated cloud.” The object is called a Reionization-Limited H I Cloud, or "RELHIC.” The term “H I” refers to neutral hydrogen, and “RELHIC” describes a natal hydrogen cloud from the universe’s early days, a fossil leftover that has not formed stars. … The cloud may eventually form a galaxy in the future, provided it grows more massive — although how that would occur is under speculation. If it were much bigger, say, more than 5 billion times the mass of our Sun, it would have collapsed, formed stars, and become a galaxy that would be no different than any other galaxy we see. If it were much smaller than that, the gas could have been dispersed and ionized and there wouldn't be much left. But it’s in a sweet spot where it could remain as a RELHIC. https://science.nasa.gov/missions/hubble/nasas-hubble-examines-cloud-9-first-of-new-type-of-object/