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OK. I see. Why didn't you just say that was your answer from the beginning, instead of giving it piecemeal? You had this 'question' all ready with the answer and all. Then you ask a question pretending not to know the answer. The answer is kinda obvious TBH. You can find about infinitely many possibilities to do that. I gave you one that's pretty obvious too. About as obvious as the fact that \( \sqrt{2} \) is irrational, which you haven't proved either. Yes, that's a result in number theory too, and you're resting your answer on shoulders of giants. (pi)rational cannot give you a rational is pretty obvious to me too. Proving it rigorously is another matter. You, though, for some reason, don't like the argument. You prefer yours, (which is to come pretty soon.) You reappear then in intervals of less than one minute declaring that your answer is the answer, and it's simpler than everybody else's. Your answer in every step is, of course, flawed unless you provide the looping argument which is your final effect. Then you pull the rabbit out of the hat that you've been silent about for the whole conversation. Voilá! --Applause. 👏👏👏 To me, it's been a considerable amount of time down the drain. I have better things to do. Cute. Thank you.

Potentially. In many areas we have got extremely high test positivity rates, but that is also skewed by the fact that quite a few areas have been switching to symptom-only testing. But all evidence still point to the fact that we undertest more than we did before. Not necessarily. The issue is that due to increasing vaccinations, the baseline susceptibility of the population shifts. I.e. we do see more vaccinated folks getting infected, but since the vaccine still prevents more serious damage, it might appear milder. What we need to check is basically the outcome among the unvaccinated, but as the number is getting smaller, it is also getting more biased. We have generally more unvaccinated among the younger population, for example, who generally have better outcomes. So we would need to look at unvaccinated folks in an age matched cohort. However, we do not have the data (yet). It would also be important to figure out risk among the elderly, especially if vaccine protection wanes. Moreover, the lung studies were conducted on animal models. So why they provide clues, it is not entirely clear whether it can be translated directly to humans. And especially elderly people are difficult to simulate in animal models. Together, I would still be somewhat more careful in declaring Omicron less virulent, so far we are looking at milder outcomes, but it may not (solely) because of the properties (i.e. virulence) of the virus, but external factors (vaccination, age) are almost certainly contributing. I am fairly certain that we will get an update relatively soon. Yes, there is always underreporting. The reported clinical cases are always the minimum known numbers. Depending on testing situation, testing strategies and also willingness to get tested the accuracy of reports has likely varied quite a bit. There is evidence that we have more underreporting than before, though.

Given that the movie Soylent Green is set in 2022, this news story seemed rather apt. (CNN quickly revised the headline, btw, hence the screenshot)

Studiot: It's a response to your rudeness, calling my example of water is wet as from a "recognized authority.". It seemed directed at me, given that those were my words and not a quote from SEP. The example was mine. You brought the incivility and the blowback is what you got. The fact that you took my example with extreme literalness (yes of freaking course you would need a handful of molecules to understand interactions and bonding) in order to nitpick at that rather than address the main point of the example, suggested you simply wanted something to pick on. And strong and weak emergence are the terms generally used in philosophy of science, and in particular disciplines where they are at issue. The fact that you pay a subscription (for a website that has no paywall) is nice, but has zero relevance to the topic. I hope the definition of types of emergence was useful to other members, who have more open minds. PS - Looking back at my post, I note the quote from SEP was in a different font, followed by the URL. Which was then followed by my own comments. Clearly indicated with a different font.

You can get the OS off the MS site when you need it. The license no. is embedded in the pc and will be read during installation.

Two points: You are picking at an example while missing the conceptual point of defining weak emergence. If the example has technical problems, fine, whatever. Did you bother to read the SEP article? Second, "recognized authority"?? WTF is this rude snarkiness about? Did someone piss in your oatmeal? I am not a chemist, nor have made such claims. If deriving wetness from micro-constituents doesn't work for you, then just pick another example. Gas pressure, tornadoes, whatever floats your boat, brother. If there is some secret grudge thing here, just PM me, okay? Otherwise, back the fuck off and lose the attitude.

Yes, it answers it. If we know that logπ2 is irrational. I got a simpler proof, without that knowledge: r=sqrt(2)sqrt(2) , s=sqrt(2).

Ah, OK. Yes, that can happen. Studiot gave an important clue, I think. Think Euler. I think you will agree that \( \log_{\pi}2 \) is irrational. Take \( r=\pi \) and \( s=\log_{\pi}2 \). Then, \[ r^{s}=\pi^{\log_{\pi}2}=2 \] The fact that \( \pi^{x} =2\) cannot be solved with x rational should be easy to prove by contradiction. Edit: Actually, I don't think it's 'easy', it's a somewhat elaborate result of number theory.

The maximum mass for a neutron is star is ~2.17 solar masses, and one that massive would have a radius of ~15 km. The event horizon for a BH with that mass is ~6.43 km, and has a photon sphere at ~9.65 km. At the surface of the Neutron star, escape velocity would be ~ 0.463 c and orbital velocity would be ~0.33 c, both well short of c.

You can't reverse engineer an emergent phenomenon and, conversely, you can't predict the outcome of an emergent phenomenon from its component parts. Ultimately, emergence has a strong unpredictable element about it.

This Zeno paradox is deeper than any of the others and was not properly answered for 150+ years after the others. The other Zeno paradoxes rely on sequences of integers and their reciprocals. This one relies on something deeper. The solution came after it became necessary to integrate many functions that could not be integrated by the Riemann integral, commonly taught in high school today. As you likely know, the Riemann integral is the sum of lots of small rectangles that make up the area under a curve. In fact it is the limit as the width of these rectangles ten to zero. But Zeno's question is what happens when that limit is reached ie the width is zero? The generalisation the the Riemann integral was introduced by Lebesgue (1875 - 1941) adn this ushered in what today is known as measure theory. https://en.wikipedia.org/wiki/Henri_Lebesgue The other approach to this issue was also developed in the first half of the 29th century by Paul Dirac and is known as the Dirac Delta function.