MigL

It has nothing to do with 'spinning' the death toll, JC. His policies, such as pressuring State Governors to re-open, and lack of policies, such as not making medical supplies available to certain States, have led to the situation in the US. Canadians and Americans are generally very similar, and our own response has been far from perfect. Yet Canada, with 1/10 of the American population, has 42x less infections. And 23x less deaths

Pandering to every group, and further sub-dividing society.

I'm not sure about the floating part, but there are other substances that expand when frozen solid. Silicon and Gallium ( used in semiconductors ) come to mind, but I'm sure there are others. Has to do with the way molecules aggregate into the solid crystal structure taking up more space than freely moving molecules. It is fortunate that ice floats for Earth based life, meaning seas and oceans don't freeze from the bottom up, and aquatic life is possible. But this wouldn't be necessary on a planet where the temperature doesn't drop below 00 , or where the prevailing liquid has a wide temperature range liquid state. We are limiting our criteria of life, to life 'as we know it'. But there are certainly arguments for life based on other chemistries. Carbon based life is suited to temperatures where water is liquid, but at much higher temperatures sulfur based or even silicon based life might be possible ( sulfur and silicon don't form as many compounds as carbon, but they are prolific in their bonding ).

Welcome Rinakra. Looking forward to learning a few things from you.

I ran my own 'model' also. Against : 1 - Don't like his domestic policy. 2 - Don't like his foreign policy. 3 - Don't like where the Country is headed. 4 - Don't like his lack of coronavirus response. 5 - Don't like him personally. For : 1 - The ability of some Americans to wallow in their ignorance continues to surprise me. That's 5 against re-election, and one slim hope for D Trump's re-election. So I give him 5 to 1 odds. My coding is not as pretty ( last time I coded anything elaborate, was using FORTRAN, though I dabbled in assembly, Forth, Pascal and various flavors of Basic ), but gives similar results. What do you think INow ?

This is quite ridiculous ... If you have a ruler ( a one dimensional line with numbers on it ) all you need is one number to specify any position on it. If you have a sheet of graph paper ( 2 dimensional numbered grid lines ) you need two numbers to specify any position on it. It is a simple mental jump to imagine a height above that sheet of graph paper with the same grid lines. That is the third dimension, and you now need three numbers to specify a location in that space above the sheet of graph paper. And should you want to assign variables to a specified location, you can call them x, y, and z. Dimensions are simply the directions you can move in a given space. Back and forth, side to side, and up down for 3 dimensional space.

I don't care; I still want a History forum. I ( and CharonY ) are constantly having to sneak in historical tidbits into other forums. Please, please, please.please, ...

Me too. No vision in my left eye. Have to keep my eye moving to get any sense of depth perception while driving, or else the bird dropping on the windshield looks like a boulder in the middle of the road,

All of Newton's equations of motion were derived using calculus. As a matter of fact, he invented the calculus for just that purpose. ( also, independently, by G Leibniz ) Newtonian mechanics, while not as 'sophisticated as Lagrangian or Hamiltonian mechanics, can still calculate the 'fall 'of an artillery shell at several miles distance, or even enable putting a rocket in lunar orbit. So, I would say, quite useful. Your criticism of calculus, on the other hand, totally useless.

Ah, but I did... Part implies fractional cause, not the whole cause. And a quick look at the OP shows that we are both wrong about the intent of the OP The OP seems to imply barriers within academia. And also comments that some forum members make about other ( new ? ) members who may not have had the opportunity for an equivalent education. I chose to address the second option, in my first post, and gave examples of forum members who have done well through a good attitude and hard work ( including the O Poster in the Physics forums ), and gave advice regarding the attitude to have , on this forum, to get some learning opportunities out of it. It went in different directions after that. Perhaps you are correct, it wouldn't be the first time I failed to make myself understood by someone.

Have you caught Dimreepr disease ? Don't leave me hanging; can you give a more elaborate answer/opinion ? Sure, there are anecdotal stories where some motivated but disadvantaged kid can't get an education. But there are also many where motivated but disadvantaged kids do get an education ( my story for one, in a previous post ). So, if we agree on the disadvantaged part, maybe we should start questioning the 'motivation' ( or lack thereof ) part.

And all I'm saying is that removing 'barriers' only gets you part way there. I think the bigger challenge is making people want an education. To paraphrase Venus Flytrap... Education is not being forced on anyone. It's yours for the taking, but you have to want it. complementary lesson about atoms with each viewing.

I'm still not sure what you are asking for, since you keep throwing different scenarios out. If you are asking about the limit formulation of a derivative ( with x cannot equal 0 ) that is introductory differential calculus, so I find it hard to believe you've been doing it for 20 years. If we define f(x) to be a function of x, the derivative function of f at x is given by: df (x) = lim h→0 { f(x + h) − f(x) }/ h If the limit exists, f is said to be differentiable at x, otherwise f is nondifferentiable at x. If y = f(x) is a function of x, then we also use the notation dy/dx to represent the derivative of f. You should also note that dy and dx are not numbers but differentials. Sorry about the lack of LaTex.

I agree with your points about poverty levels, CharonY, and even I would like to see free ( or at least subsidized ) education for all who want it. But that wouldn't solve the problem of bad attitude, and not putting forth the effort. On the other hand, someone like Markus ( and I don't know his financial situation or why he didn't obtain a formal education ) with good attitude and self driven work/effort managed to become the leading expert on GR on two different Forums I've participated in ( equalled only by Dr.Rocket ) The first cause for concern was a 1965 report by a Democrat D Moynihan. https://en.wikipedia.org/wiki/African-American_family_structure It is areal phenomenon, not imaginary. But its cause is rooted in systemic poverty of Black Americans.

I live in a University town. The majority of kids are immigrants, who realize the value of education. Rich affluent kids, ( with no socially imposed barriers ) just want to go to College to party. There are certainly some barriers to education, but want and encouragement are big factors in getting one. The 5 year old black kid that MSC mentions, might have a chance at an education IF his dad was home to encourage him. If his dad was home, he might not be on his own most of the time, and might not have to drop out to get a job, or worse , join a gang. I was an immigrant child in 1968, and my parents worked day and night to make sure we kids got a University education. ( although now that I think about it, I could have become a plumber, and made a lot more money ) First generation immigrant kids work very hard to make sure they don't have to live the life their parents did. Second generation, not so much. Do you think its a coincidence that lately, Colleges and Universities are filled with Middle Eastern, North African, South Asian and east Asian students ? I'm not sure about the US, but in Canada, visible minorities make up over 30% of 1st year students. https://higheredstrategy.com/visible-minority-participation-in-university-studies/ A much higher percentage than is present in the general population.

You should have said that to begin with. There would have been a lot less confusion. Limits approach a limiting value; they never actually reach it.

Still not sure what exactly you mean by x cannot equal zero. Are you talking about limits ( as x -> 0 ) ?

Yes it does cut both ways; I never said it didn't. I've known plenty of people who had no 'barriers' to obtaining the best 'money is no object' education. Yet their 'everything should be handed to me' attitude allowed them to not even try, and they drop out halfway through 1st year University. There are many barriers to an education, or expanding our knowledge; the worst ones are of our own making.

Why is it always barriers imposed by, or the fault of society, when someone fails ? What part does personal responsibility play in this ? Markus Hanke taught himself GR ( and many other aspects of Physical Science ). It was not provided for him, but he wanted it and he got it. Barriers did not hinder him. You, yourself, have displayed a questioning attitude. One of the best ways to learn about things you know little about. Yet others come here with the attitude that what little knowledge they have , is all there is. They ask no questions, but make conjectures and proclaim results which more learned members quickly dismiss. And yet their attitude, not barriers, allows them to double down and insist they are right ( until they are banned ). A good attitude, and a willingness to learn, go a long way in these days of internet access and on-line courses.

There are two long range forces, gravitational and electromagnetic, and two very short range forces, color and weak ( flavor ). As far as we know, Dark Matter interacts with all other matter, including itself, gravitationally, but does not interact via the Electromagnetic force at all ( or only extremely weakly ). That means we cannot detect it by electromagnetic means ( no visible, radio, infrared, uv, x-ray or even gamma emissions ), but its gravitational interactions with matter and itself, will produce 'falls' or orbits around its center of gravity. It could also be captured by BH event horizons when it intercepts them. Dark Matter particles may get very close to each other, or even collide, but, since they don't interact via the color force, they will not clump together like quarks in nucleons, or protons and neutrons n the nucleus due to residual. And since they don't interact electromagnetically, they won't clump like electrons and protons in atoms. So I see very little chance of being able to localize a large enough mass of Dark Matter that it would be able to collapse to a BH. One type of neutrino is being investigated as a candidate for Dark Matter, so there is the possibility that it also interacts via the weak ( flavor ) interaction, but again, this interaction does not produce bound states.

And I though Zap and his YouTube friend had done a good job of explaining. OK, one more time... The Earth is orbiting the Sun at a radial distance of 150 million km. We now start compressing the Sun. When it is half its current size, the Earth still feels the same gravitational attraction and remains in orbit at 150 Mkm. When it is one tenth of its current size, the Earth still orbits at 150 Mkm, and feels the same gravity. When it is 1/1000 of its current size, the Sun still has the same mass, and the Earth is still orbiting at the same radius of 150 Mkm, so it still feels the same gravity. However, when the Sun is compressed past its Schwarzschild radius, 2GMsun/c^2 , or about 6 km across, it is enclosed by an event horizon, which means that, for the mass of the sun, a 3 km radial separation requires an escape velocity faster than the speed of light. https://en.wikipedia.org/wiki/Schwarzschild_radius IOW, the event horizon goes black because no light can reach us any longer. Yet the Earth is still happily orbiting at 150 Mkm, and feeling the same gravity. So, to recap, if our Sun was a Black Hole, at the current distance from the sun we would feel exactly the same gravity as we currently do. If we were to move closer to the Sun, since as a Black Hole it is vastly smaller, we would feel an increase in gravity, until we get to about 3 km radial separation, at which point no force in the universe could keep us from falling into the event horizon ( its gravity would be THAT strong ). Yes, mass is directly proportional to Schwarzschild radius, but I'm not sure I follow or understand the rest of your questions. Please re-phrase or clarify.

What's really sad is that, centuries later, you still don't understand it. Maybe you should have some humble pie with your Thanksgiving dinner; ask proper questions and stop being so derisive.

Sure came in handy for I Newton.

As Joigus says, the gravity produced by a BH is no different than from any other equivalent mass. If expansion can overcome the gravity of galaxy clusters, it can similarly overcome the gravity of a BH composed of the masses of the equivalent number of stars in that galaxy cluster. There is no upper limit on BH size. There is only a limit to how much you can feed them. Once they 'eat' all close by mass via their accretion disc, they can't overcome farther out stable orbiting material, and stop growing. Direct collapse, however,without going through star lifetimes, is a totally different mechanism.

Lesson to be learned … Dye your hair. ( nobody looks good with white hair, and the flies really show )