Of course I read it. And all I saw was you saying that you "got dealt some shitty hands"; nothing about mental illness.

And I assumed that this "shitty hand" was something else, because if it was mental illness you were talking about and you actually understood mental illness, you wouldn't have said something so fucking stupid.

But you didn't say just anything other than that. You said they had complete control and can just pick themselves up and dust themselves off and move on. Which is a fucking stupid way to say "they aren't completely helpless" because that's not the same thing.

What you said demonstrates that you don't, so tough shit, I'm telling you that you don't. You understand your own journey, which I don't know or care about. As a generalization, as a statement intended to demonstrate understanding of mental illness and others who suffer from it, "you have complete control of how you play that hand" is stupid and wrong.

What the AC said as to why the SMBH can't explain the galaxy rotation curve -- the problem is that the curve is flat, meaning the orbital velocity doesn't decrease with distance from the center as one would expect regardless of the amount of mass at the center. See the graph on the right, here. All increasing mass at the center would do is change the values on the Y-axis. The curve shape would be the same.

As far as measuring the relativistic mass goes -- turns out that's easy! Put an object on a scale, and you are measuring its relativistic mass. Measure the gravitational force exerted on some object by another, and you are measuring it's relativistic mass. All of your everyday notions of what "mass" means and the ways in which you measure mass are measuring relativistic mass.

It's actually figuring out the intrinsic mass that's hard. And for a black hole, it's both impossible and irrelevant. The properties of a black hole do not depend at all on the intrinsic mass of whatever went into it. In fact it was proven that in General Relativity that you can't tell what made a black hole, or what has gone into it since, by observing the black hole. The resulting object is the same regardless. This is called the "no hair" theorem for what I'm sure are hilarious historical reasons.

Also light has energy which is mass in Relativistic thinking, and is moved by (and moves other things by) gravity which is due to it's energy (same as mass).

This is confusing because people think of "mass" as the things photons don't have and matter does (which is true if we mean intrinsic mass), but also think of "mass" as the thing which effects/is affected by gravity and makes objects resist acceleration, when that's actually the relativistic mass (= energy).

A photon is a quantum mechanical particle, which is a thingie which behaves kinda like a classical particle and kinda like a classical wave but not exactly like either.

However the key thing about quantum mechanics is that stuff is quantized... like particles are. So we call them particles. There is no misconception in doing so.

What you said was quite correct.

I'm not sure what they were saying. I think maybe they meant to reply to justthinkit who was actually proposing an alternative?

No. Gravity is determined by the stress-energy tensor, and the energy component is total energy, aka relativistic mass (literally, they're the same thing). Relativistic mass is the gravitational mass is also the inertial mass.

A proton's mass -- the ratio between its acceleration and the force exerted by an electric field -- is much higher than the intrinsic mass of the quarks that make it up. It's the kinetic energy of those quarks held together by the Strong Nuclear Force that gives a proton 90% of its mass. The Higgs Field only explains that last 10%.

Similarly the gravity of the sun is far greater than just the intrinsic mass of the quarks and electrons inside it. It's the sum of all energy in the sun.

If you an accelerate an object it gains energy, and therefore (E=mc^2) relativistic mass, and also therefore increased gravity.

Oh, and yes, this means photons have gravity. Not are affected by gravity (though of course they are) but exert it.

A black hole of one solar mass will take 10^67 years to evaporate from Hawking Radiation -- and this time is proportional to the cube of the mass, so think about those SMBHs out there with billions of solar masses. That's a mind-bogglingly long time. You might think it's a long time waiting in line at the Department of Transportation, but that's peanuts compared to black hole evaporation...

And that's only after the CMBR has been red-shifted into near non-existence since until then the black hole is absorbing more energy than it is losing.

Though there are in theory primordial black holes (ones created in the moments after the Big Bang) that would have a lifespan measured merely in billions of years.

"Beware of he who would deny you access to information, for in his heart he dreams himself your master".

                Commissioner Pravin Lal, "U.N. Declaration of Rights"

What I really love about this quote, aside from it being amazingly insightful, is that it always seemed to turn up just after I'd gotten done refusing to share some piece of tech I'd developed with one of my "allies" because I wanted to have every advantage when I inevitably steamrolled them. It's like Commisioner Lal knew me, man.

Spoken like someone who doesn't understand and hasn't even really thought about mental illness.

Hint: The thing you think gives you "complete control" is the thing affected by the disease.

If a tree falls in the woods and no-one is there to hear it, is the next tree to fall guilty of plagiarism?

Okay, but don't complain about a fact that even in a world where the military was managed and utilized ideally would still be true.

Thanks. Last time I related that story, someone just couldn't believe that a class was harder with Maple doing the grunt work. They assumed I just hadn't taken much math so it was the hardest by default. Then tried to impress me with their standard engineering math curriculum.

Well then you have a problem because while it may be argued that the ends justify the means, that argument falls apart when the means contradict and thus prevent the ends.

All-out-war is over because the political goals of war have changed. You simply cannot fight a war of "liberation" without respecting the civilians. And this was self-evident in the years of complete and utter failure in Iraq. Sure, we didn't engage in "all out war" against a poorly understood collage of insurgent forces because that's a completely ineffective way to fight an insurgency unless you're willing to go the Roman or Mao Tse Tung route and use genocide. Which would have resulted in us "winning" for a definition of "winning" completely different than what we started with. The warfare equivalent of flipping the chessboard. Good job. You "won". Slow clap.

So instead we tied our soldiers' hands with rules of engagement while simultaneously maintaining a flippant attitude toward colateral damage -- enough to "look nice in the papers" back home, but definitely not the ones in Iraq. This was because the people in charge, like you, really would have rather engaged in all-out war but knew they couldn't because of politics at home.

The result was unsurprisingly ineffective as the ranks of insurgents swelled with angry former-civilians (many of whom were former-army, but don't get me started on that).

A lot of people credit The Surge with turning Iraq around, but while a component it was actually the least important part of what changed. Petraeus' real genius was in not only using force even more judiciously than before -- the opposite of what you would do -- but also in fully engaging the civilian population. He didn't treat them as though they were basically the enemy that he couldn't shoot because it looked bad on CNN. He treated them as if they were already allies that required help. He took "winning hearts and minds" seriously, and it worked. When the area of Iraq Petraeus was in charge of stabilized like none of the rest of Iraq had, they put him in charge of the lot so his demonstrably effective (and not coincidently completely unlike your) strategy could benefit everywhere. And it did. Only in the environment created by this new strategy could the additional troops put in have been effective.

You know what the REALLY sad part is? The part that really causes comments like yours make the bile swell up in my throat?

It's that when we began in Afghanistan, the people did support us. Unlike the Iraqi people who felt betrayed by us after Desert Storm, the Afghan people still thought of us as the folks who helped them kick out the Russians. With no love lost for the Taliban, they were actually on our side. At first.

Thanks to years of idiotic management, that flippant attitude towards collateral damage you embody, and years of neglect due to being focused on Iraq, we lost both literal and figurative ground in Afghanistan. We squandered our advantage. Pissed it away. Turned the people against us.

And then some dweeb comes along and says the people "will never support us". As if it was always this way. As if it's their fault, instead of ours. Gee, maybe we should just stop worrying about killing them. That would probably fix it.

So fucking sad.

To make it clear how big a difference it is, let's look at the ratio of the mass of the body in question to the mass of the rest of the objects in its orbit (discounting direct satellites).

Of the planets Neptune happens to have the lowest such ratio. It outmasses everything else in its orbit by a factor of over 10,000.

Meanwhile Pluto is outmassed by the other objects in its orbit by more than a factor of ten. It is less than 10% of the mass in its orbit.

That's a five order of magnitude difference. "Clearing the orbit" isn't precisely defined... and it doesn't need to be. You don't need a precise definition of where exactly on the beach the ocean begins to know that Asia and North America are separated by the Pacific Ocean.

And I suspect that such a large distinction isn't a cosmic accident, and that other star systems of sufficient age will show a similar trend. Unfortunately it's going to be a long time before we can test this hypothesis.

The sun will become a white dwarf, which is a post-stellar remnant made of electron-degenerate matter (where the electromagnetic repulsion is not sufficient to hold electrons apart against gravity, and instead they're held apart by the Pauli Exclusion Principle) about the size of the earth. Before that, when it ends its Red Giant phase, it will shed much of its mass in novas. Which are gentle events only in comparison to a supernova. "Explosion" is quite fair. Certainly nobody in the solar system watching would say, Crocodile Dundee style, "That's not an explosion..."

The most difficult math course I ever took was my first college math course, Calc II with Maple. Why yes, use of the symbolic calculus program Maple was so important to the class it was in the name. We took our tests at a workstation with Maple on it.

When my adviser suggested I take this version instead of normal Calc II, I didn't hesitate because I naively assumed this would make the class easier.

Turns out that when you remove the time it takes to do the actual mechanics of taking integrals and derivatives, you can instead focus on problems where the difficulty is figuring out how to set up that integral and derivative. Which is much harder than following some rules by rote.

That's why Feynman Diagrams were such a big deal -- they actually allowed physicists to figure out how they should be applying the equations of quantum mechanics to a specific problem. It let them figure out what to calculate. How wasn't the challenge.