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That's wonderful, as long as the styles that prefer lavish illustration and marginalia on fat glossy paper all have affluent parents who can fork out $50-100 per, and drive them to school. These books are lovely to look at, but they'd be difficult for a poor family to buy and the student to carry back and forth to school on foot and the bus. Once you get to college or university, the prices and heft become truly crippling. https://www.wiley.com/en-ca/General+%26+Introductory+Chemical+Engineering-c-CG00

What Captain Renault said. And PEBKAC reminds me, when I did IT work back in the early nineties, we had a cat who liked to play with our desktop at home when we stepped away from it. Things would be weird onscreen when you returned. Though the cat had another name, I started calling him Pebkac. And that caught on, and he was Pebkac for the rest of his mischief-filled life.

Not proved, according to this: "In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero-point energies of quantum fields are “real.” On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents. … I have presented an argument that the experimental confirmation of the Casimir effect does not establish the reality of zero-point fluctuations. Casimir forces can be calculated without reference to the vacuum ... . The vacuum-to-vacuum graphs (See Fig. 1) that define the zero-point energy do not enter the calculation of the Casimir force, which instead only involves graphs with external lines. So the concept of zero-point fluctuations is a heuristic and calculational aid in the description of the Casimir effect, but not a necessity." Casimir effect and the quantum vacuum R. L. Jaffe Phys. Rev. D 72, 021301(R) – Published 12 July 2005

I'm shocked, shocked I tell you, that not all news sites in the world do things the same way. It's almost like they act independently.

Surely it's because the short leg on tables and chairs is getting shorter . Merry Christmas everyone! 🙂

No, that wasn't the reason. They are perfect in all respects: this 'imperfection' is solely in the eye of the beholder. https://www.youtube.com/watch?v=AdbPWoMsdIs (and I wish you'd let up on that painting school joke)

At smaller scales dark matter doesn't really play that much of a role. It's when you get to the region of galactic haloes when it starts to kick in. That's why you don't consider it when solving problems like, eg., the perihelion of Mercury. It's very sparse and apparently nucleates around the galaxies, but at very long distances in comparison with atomic matter. As there are no collisions, it doesn't fall anywhere near the galactic centres in any significant amount. Einstein's equations OTOH seem to me to be formulated as some kind of compromise --a brilliant and predictive one to be sure. The Einstein tensor does not saturate all the possible geometric degrees of freedom. The other degrees of freedom are coded in the Weyl tensor. They can also be generalised in several ways, like including torsion, complexifying them... They seem so inviting for generalisation. Although this is nothing but a hunch. It also has to be said that the attempts have been many, and nobody so far seems to have been able to extend Einstein's predictions significantly. As to primordial BHs, it's very appealing. But how big can they grow before there would be noticeable effects? I don't think you mean dark matter haloes are made up of SMBHs. We would have seen them already by their lensing effects. Plus the masses would be so out there. I'm probably just expressing my preferences. We really need the data James Webb will provide.

I would guess that it's a combination of two things. Firstly, that humans are a freakish development, and that intelligent life that has comparable technology is very very unlikely. If you accept that humans are a one in a million freak, then look at what the Earth would be like without us. Chimps and Bonobos would be top of the technology tree. Dolphins and Orcas might match them for intelligence. And that would be it on Earth. Human numbers at one point dropped to the low thousands, it would easily have happened that we went extinct. So but for one freakish species, even this Earth would have been totally unable to communicate with other worlds. It's entirely possible that life would never again produce intelligence on the human scale. It might just hit a ceiling time after time, and we are total freaks. The other factor is the huge distances involved in trying to communicate. If there are technologies out there in the Milky Way, they are probably far too distant to ever be able to get a signal through. After all, we are only just now able to detect a shadow on a star, caused by a planet, at these distances. No imaginable technology could match the scale of that type of signal.

Yes they do.

Two versions of Bach's Prelude No.1 Gives me chills this one: