Actually, according to our good friend wikipedia, Toronto is still 8th by metre area population in NA.
It makes a difference whether you are asking about the population of the city, or the population of the metro area, the city plus surrounding areas that are not in the same political unit.
Physical theories are confirmed by evidence, and well confirmed by large amounts of of evidence... but confirmation is not exactly the same as proof
Who's replicated the Higgs?
The Higgs discovery was done by two groups, working independently and doing different experiments, although using the same accelerator, so that's a good start.
I would not call the Higgs discovery well confirmed, though; not yet. You definitely want to keep on doing experiments to nail this one down more confidently.
I doubt many scientists believe that you can prove any scientific theory true.
In general, this is correct: you can prove a scientific theory false, but never prove it true. (You can prove mathematical theories true. But mathematical theories require assumptions, called postulates. To prove that a mathematical theory is true in the real world, you would need to find a way to prove the postulates true.)
Physical theories are confirmed by evidence, and well confirmed by large amounts of of evidence... but confirmation is not exactly the same as proof
The summary was wrong: Physicists Peter Higgs and Francois Englert did not win the Nobel Prize for discovering the Higgs Boson. They (along with some others) predicted it, but didn't discover it. (More accurately, they won the Nobel for elucidating the Higgs mechanism of symmetry breaking as a means for massless particles to acquire mass). This was a deduction (deducing that a particular field would lead to symmetry breaking with particular properties, from the mathematics of field theories), not an induction (fitting a model to theories).
What impacts them are the policies the party they vote for enact. So yes they vote Republican and Republican policies hurt them.
The point is that, in terms of voting for governorship of their state, the poorest ten states don't vote Republican. They vote equally Republican and Democratic.
No, I just said consider the source when reading the numbers. If you blindly accept them, fine with me.
That would be wise... except you apparently didn't consider the source; you just were looking for an excuse to say "I don't believe these numbers". Did you even read the source material? The source was an organization with the explicit objective "to find the uninsured around the country and persuade them to sign up for health insurance." Quoting from the article: "the groups have little incentive for bias because skewed numbers would complicate efforts to find the uninsured and target outreach resources."
1. I see plenty of anecdotal stories that support many views.
Well, you were the one making up anecdotal stories-- I was just listing what I'd heard from people I know. Except you didn't even have actual anecdotes from real people-- you were just making up a hypothetical, "maybe people did not want or feel they needed health care." Yeah, right. Maybe some people do prefer to rely on emergency rooms, paid for by taxpayers, if they get catastrophically sick. I do not consider this an optimal solution.
People hear what they listen for. Numbers from objective studies are what I'd pay attention to.
To the contrary. When presented with numbers, your response was "Its not that hard to play with numbers to make any point you want. "
Translation: any time you see numbers that don't support what you already have decided, you say they're not 'objective'. Great strategy: ignore anything you don't like.
...The fact that many of the (very optimistically estimated) number of those who were added to O-Care rolls did not want or feel they needed it should be considered as well.
I personally know several people who were able to get insurance under Obamacare but didn't have it before. Not one says that they "did not want or feel they needed" insurance. What they say is, "Thank God, this is saving my life."
However, even if what you said was true: what you are implying is that there is a body of people who previously were saying "I don't want or need insurance, because if I get sick I'll go to a hospital that is legally is not allowed to turn me away, and the taxpayers will pay for it," -and they are now paying for their own health care. That's a win for the taxpayers.
In other cases, such as ones I am very familiar with, previously covered spouses were forced to move to their own plan if their work provider had coverage available. This means that although a new health care subscriber can now be counted, that person was already covered
That's not the way the number of uninsured is counted. That would count as a wash: neither an addition nor a reduction to the number of uninsured.
... More often than not, it is the large urban populations that shift state's support bias to liberal, and it is those same urban areas that hold the most desperate and dependent populations of the truly underprivileged.
Sorry, the belief that poverty is an urban phenomenon is another myth. It's a myth that's pervasive among liberals and conservatives, but simply not true. There are actually more poor and underprivileged people in rural America. You're right about urban areas being liberal and rural conservative, but wrong about being able to attribute that to "dependent populations of truly underprivileged": the greatest use of food stamps, as a percentage of population, in poor rural areas, not urban areas.
.... Its not that hard to play with numbers to make any point you want.
But you don't have to do that, because it's even easier to simply say "Those numbers don't support my political bias, so they are wrong."
Many of the poorest and most rural states in the country tend to favor Republican politicians.
The link is to a 2011 article, which states the following:
Most of the 10 poorest states in the country are Republican. Mississippi is the poorest... followed by Arkansas, Tennessee, West Virginia, Louisiana, Montana, South Carolina, Kentucky, Alabama and North Carolina.
The economics of a state is more impacted by what party holds the governorship and statehouse, not by what party they voted for for president. Looking at the governorship of each of those states http://upload.wikimedia.org/wi... you see that the parties of the governors of the states listed are, respectively, Republican, Democratic, Republican, Democratic, Republican, Democratic, Republican, Democratic, Republican, Republican.
I would assert precisely the opposite. "trade-offs to preserve compatibility and interoperability" do not cripple the functionality to users-- failures to engineer compatibility and interoperability is what cripples functionality.
The number of times that there's been a new feature and I've said "oh, excellent, it's true that my old files no longer work, but this is so wonderful I don't care" has been very close to zero. The number of times there's been a new feature and I've said "those assholes, I have twenty thousand files that don't work any more, what in the world were those idiots thinking?" is decidedly not zero.
I'm not sure to what extent Tesla innovated to create the cars they have, but certainly they made the first EV that people actually wanted to have for reasons other than it being an EV or hybrid.
The Tesla Roadster made electric cars cool, in that it was a car for the ultra-top end market, people who otherwise would be buying a Lotus or Ferrari. So, it was an existence proof that you could make an EV that contended with top-end sports cars.
It was also one of the first mass market EVs that doesn't look like utter crap (the Honda Civic hybrid being the other one).
Actually, Leaf is the top selling EV on the market right now. If you count electric cars with gasoline backup, Volt would be on the list.
Tesla doesn't make a mass-market EV yet; their Model S right now is rather a luxury car rather than something for the average buyer. While I'd love to have one... I don't think Tesla comes anywhere close to being "the first" in the way of mass market EVs. There are a lot of electric cars out there, both mass-market and otherwise.
This is just typical politics in the aerospace industry. It's so critical to national defense infrastructures that it tends to develop more cruft on its surface than others despite dealing with such incredibly interesting high tech. Also, US congressional budgets have been starving the budgets for the projects dealing with basic scientific research and study, which is a shame.
I would prefer to see NASA bet on all three horses so you have better odds of one of winning the race!
I would too, but they haven't been given the budget to do so. In fact, congress has been demanding the opposite: it had previously been very insistent that NASA needs to downselect to just one.
It's quite a victory that they managed to keep on funding two options.
Interesting! I first heard that idea from David Brin, who was proposing it as something to be used for disasters. http://davidbrin.wordpress.com... Maybe the governent of Hong Kong qualifies as a disaster.
As I understand it GR does *not* factor in the energy within the gravitational field as creating it's own "secondary" field
It is built into the theory. This is why GR is a nonlinear theory-- which is precisely what makes it so difficult to solve.
- if it did gravity would no longer follow the inverse-square law near singularities,
Correct. Gravity only follows inverse square law in the weak-field limit. Orbits in 1/r2 potentials are ellipses. Orbits in Schwartzschild geometry are not ellipses. Right there you know that Einsteinian gravity differs from Newtonian 1/r2 gravity.
I actually would like to spend some time to elucidate how it is that nonlinearity in GR means that it incorporates the effect of gravity on gravity-- but I'm afraid I just don't have the time to spare at the moment.
... Bottom line, we have Einstein himself on record saying he chose to ignore the energy in a gravitational field as "double counting", are you really going to argue the point with his ghost?
Not only would I not argue, I would agree with him. Since the gravitational effect of gravity is already accounted for in general relativity, it would be double counting to count it again.
But, of course, everybody wants to buy the cheapest ones, not ones tested to long lifetime.
People buy the cheapest because they don't trust the 'rating' on the package. They know it will die 'early' anyway so they might as well be cheated out of $5 rather than $10.
Yep. That's a vicious circle, of course, a feedback look that results in a "race to the bottom."
As I said, what is needed is a good (and trustworthy) rating agency to test and qualify the bulbs.
As for the stability of a dust cloud - if it's "stationary", certainly. But how about if it were orbitting an ancient neutron star or other massive non-luminous object in an organized manner? A "lynch pin" as it were to impose order on what would otherwise devolve into a chaotic system and collapse.
I don't know what you mean by "in an organized manner." You mean, what if a superior civilization put each grain of dust on exactly such a trajectory that dust/dust interactions don't destabilize the cloud? OK.
As for ordinary, non-"organized" dust clouds, if there is any interaction between dust grains, and no internal source of energy to keep it from collapsing, a dust cloud large enough to be self-gravitating is unstable.
As for new physics for a "solid" object of that mass - we wouldn't even have to go very far. All we have to do is [proposes altered version of General Relativity]....
That would be new physics. General Relativity does, of course, account for the gravitational energy of gravitational fields; that's why it's nonlinear. On the face of it, your proposed revision to general relativity's equations violates conservation of energy. There may be some way to avoid that-- but if you do, this is new physics.
I got a 3 pack of LED lights to play with about a year ago from Feit. No problems with those, although it's still too early to tell how I'll fare. The light is a little more directional than the CFLs but I like the color temp better.
You can get directional or non-directional LED bulbs. I like the fact that you can get directional LEDs: for applications like overhead can lights, this nearly doubles the effective brightness. But most of the LED lamps you buy take deliberate measures to be non-directional, to make them screw-in replacements for incandescents
Color temperature is something you can pick. I like the "daylight" color personally--5000K-- but my wife prefers the warmer color temperatures, down in the 2700K range.
The Department of Energy had a pretty rigorous test regimen set up for testing LED bulbs. http://www.lightingprize.org/6... What is needed is a good (and trustworthy) rating agency to test and qualify the bulbs.
But, of course, everybody wants to buy the cheapest ones, not ones tested to long lifetime.
For what it's worth, I have about 60 LED bulbs in my house, from about fifteen maufacturers. So far, four have failed.
Further - no viable light bulb replacements will work with dimmer switches (Which my house has many).
That was true five years ago-- these days it seems all of then are rated to work with dimmers . I have some Philips LED bulbs on a dimmer in the dining room-- they work fine.
Density is not the determinant a black hole. Large black holes have very low densities.
From the size and mass, we can rule out pretty much all the other possibilities. (Small but massive dust clouds are gravitationally unstable.) So if it's not a black hole, it must be something else, and that something else is either new physics, or a manifestation of old physics that we've been insufficiently clever to figure out yet.
Please describe what an earth without form and void is supposed to mean. He created a void?????
Well, of course, that's not actually what Genesis said. What Genesis said was that the earth was tohu v' bohu. ( -- let's see how/. does with Hebrew). So, what you're really asking is, what does it mean for the Earth to be bohu? He created a bohu? (Or maybe bohu was already there?)
My personal explanation, the author went with bohu simply because it was a good rhyme with tohu. When you're a poet, sometimes you just have to go with the easy rhyme.
How is it at odds with observations? We've (indirectly) observed some of objects consistent with our theories of how black holes would behave, but to the best of my knowledge we've never observed the *formation* of such an object.
The headline-- Black holes don't exist-- is at odds with our observations: we see things that appear to be black holes.
The actual summary is not at odds with our observations: the summary says that stellar collapse doesn't form black holes, and we don't have observations to say know how the black holes we seem to be observing were formed.
Now, you could go on and ask whether the things that we see which we are interpreting as black holes might be something else. But that would require a new theory that could explain how the massive, compact objects we see could exist, and not be a black hole. I don't believe that, at the moment, we have any other candidates.
With that said, of course we can't see a black hole itself. But we can see the stuff orbiting it, and that can tell us its mass and size, which is enough to tell what it is.
The headline-- black holes don't exist-- is at odds with the actual article.
The article doesn't say the mathematicians said that black holes don't exist: it says they showed black holes aren't formed by the collapse of massive stars. Black holes such as the ones at the nuclei of galaxies may very well be formed by other processes.
--even if it were true that black holes don't exist, by the way, it doesn't solve the problem of the incompatibility of general relativity with quantum mechanics. At best it would solve the black hole information paradox; but since it still incorporates Hawking radiation in the solution, it doesn't even solve that.
Slashdot Mirror
Actually, according to our good friend wikipedia, Toronto is still 8th by metre area population in NA.
It makes a difference whether you are asking about the population of the city, or the population of the metro area, the city plus surrounding areas that are not in the same political unit.
Cities: Toronto is fourth largest: https://en.wikipedia.org/wiki/...
Metropolitan Areas: Toronto is eighth largest: https://en.wikipedia.org/wiki/...
Urban Agglomertions: Toronto is number five: https://en.wikipedia.org/wiki/...
So I rate the original claim,
Toronto is Canada's largest city, the fourth largest in North America
, as True.
Physical theories are confirmed by evidence, and well confirmed by large amounts of of evidence... but confirmation is not exactly the same as proof
Who's replicated the Higgs?
The Higgs discovery was done by two groups, working independently and doing different experiments, although using the same accelerator, so that's a good start.
I would not call the Higgs discovery well confirmed, though; not yet. You definitely want to keep on doing experiments to nail this one down more confidently.
Large amounts of evidence only confirms a theory if the evidence is independent.
Yep. That's why you want independent confirmation. Replication is what makes science.
Never rely on scientific results until they're independently confirmed.
I doubt many scientists believe that you can prove any scientific theory true.
In general, this is correct: you can prove a scientific theory false, but never prove it true. (You can prove mathematical theories true. But mathematical theories require assumptions, called postulates. To prove that a mathematical theory is true in the real world, you would need to find a way to prove the postulates true.)
Physical theories are confirmed by evidence, and well confirmed by large amounts of of evidence... but confirmation is not exactly the same as proof
The summary was wrong: Physicists Peter Higgs and Francois Englert did not win the Nobel Prize for discovering the Higgs Boson. They (along with some others) predicted it, but didn't discover it. (More accurately, they won the Nobel for elucidating the Higgs mechanism of symmetry breaking as a means for massless particles to acquire mass).
This was a deduction (deducing that a particular field would lead to symmetry breaking with particular properties, from the mathematics of field theories), not an induction (fitting a model to theories).
What impacts them are the policies the party they vote for enact. So yes they vote Republican and Republican policies hurt them.
The point is that, in terms of voting for governorship of their state, the poorest ten states don't vote Republican. They vote equally Republican and Democratic.
No, I just said consider the source when reading the numbers. If you blindly accept them, fine with me.
That would be wise... except you apparently didn't consider the source; you just were looking for an excuse to say "I don't believe these numbers". Did you even read the source material? The source was an organization with the explicit objective "to find the uninsured around the country and persuade them to sign up for health insurance." Quoting from the article: "the groups have little incentive for bias because skewed numbers would complicate efforts to find the uninsured and target outreach resources."
1. I see plenty of anecdotal stories that support many views.
Well, you were the one making up anecdotal stories-- I was just listing what I'd heard from people I know. Except you didn't even have actual anecdotes from real people-- you were just making up a hypothetical, "maybe people did not want or feel they needed health care." Yeah, right. Maybe some people do prefer to rely on emergency rooms, paid for by taxpayers, if they get catastrophically sick. I do not consider this an optimal solution.
People hear what they listen for. Numbers from objective studies are what I'd pay attention to.
To the contrary. When presented with numbers, your response was "Its not that hard to play with numbers to make any point you want. "
Translation: any time you see numbers that don't support what you already have decided, you say they're not 'objective'. Great strategy: ignore anything you don't like.
...The fact that many of the (very optimistically estimated) number of those who were added to O-Care rolls did not want or feel they needed it should be considered as well.
I personally know several people who were able to get insurance under Obamacare but didn't have it before. Not one says that they "did not want or feel they needed" insurance. What they say is, "Thank God, this is saving my life."
However, even if what you said was true: what you are implying is that there is a body of people who previously were saying "I don't want or need insurance, because if I get sick I'll go to a hospital that is legally is not allowed to turn me away, and the taxpayers will pay for it," -and they are now paying for their own health care. That's a win for the taxpayers.
In other cases, such as ones I am very familiar with, previously covered spouses were forced to move to their own plan if their work provider had coverage available. This means that although a new health care subscriber can now be counted, that person was already covered
That's not the way the number of uninsured is counted. That would count as a wash: neither an addition nor a reduction to the number of uninsured.
... More often than not, it is the large urban populations that shift state's support bias to liberal, and it is those same urban areas that hold the most desperate and dependent populations of the truly underprivileged.
Sorry, the belief that poverty is an urban phenomenon is another myth. It's a myth that's pervasive among liberals and conservatives, but simply not true. There are actually more poor and underprivileged people in rural America. You're right about urban areas being liberal and rural conservative, but wrong about being able to attribute that to "dependent populations of truly underprivileged": the greatest use of food stamps, as a percentage of population, in poor rural areas, not urban areas.
.... Its not that hard to play with numbers to make any point you want.
But you don't have to do that, because it's even easier to simply say "Those numbers don't support my political bias, so they are wrong."
The final sentence of the summary is misleading.
Many of the poorest and most rural states in the country tend to favor Republican politicians.
The link is to a 2011 article, which states the following:
Most of the 10 poorest states in the country are Republican. Mississippi is the poorest... followed by Arkansas, Tennessee, West Virginia, Louisiana, Montana, South Carolina, Kentucky, Alabama and North Carolina.
The economics of a state is more impacted by what party holds the governorship and statehouse, not by what party they voted for for president. Looking at the governorship of each of those states
http://upload.wikimedia.org/wi...
you see that the parties of the governors of the states listed are, respectively, Republican, Democratic, Republican, Democratic, Republican, Democratic, Republican, Democratic, Republican, Republican.
I would assert precisely the opposite. "trade-offs to preserve compatibility and interoperability" do not cripple the functionality to users-- failures to engineer compatibility and interoperability is what cripples functionality.
The number of times that there's been a new feature and I've said "oh, excellent, it's true that my old files no longer work, but this is so wonderful I don't care" has been very close to zero. The number of times there's been a new feature and I've said "those assholes, I have twenty thousand files that don't work any more, what in the world were those idiots thinking?" is decidedly not zero.
I'm not sure to what extent Tesla innovated to create the cars they have, but certainly they made the first EV that people actually wanted to have for reasons other than it being an EV or hybrid.
The Tesla Roadster made electric cars cool, in that it was a car for the ultra-top end market, people who otherwise would be buying a Lotus or Ferrari. So, it was an existence proof that you could make an EV that contended with top-end sports cars.
It was also one of the first mass market EVs that doesn't look like utter crap (the Honda Civic hybrid being the other one).
Actually, Leaf is the top selling EV on the market right now. If you count electric cars with gasoline backup, Volt would be on the list.
Tesla doesn't make a mass-market EV yet; their Model S right now is rather a luxury car rather than something for the average buyer. While I'd love to have one... I don't think Tesla comes anywhere close to being "the first" in the way of mass market EVs. There are a lot of electric cars out there, both mass-market and otherwise.
Wasn't the HL-10 the spacecraft that Steve Austin crashed in?
no, that was the M2-F2.
Spectacular video of the crash, though.
http://www.airspacemag.com/ist...
This is just typical politics in the aerospace industry. It's so critical to national defense infrastructures that it tends to develop more cruft on its surface than others despite dealing with such incredibly interesting high tech. Also, US congressional budgets have been starving the budgets for the projects dealing with basic scientific research and study, which is a shame.
I would prefer to see NASA bet on all three horses so you have better odds of one of winning the race!
I would too, but they haven't been given the budget to do so. In fact, congress has been demanding the opposite: it had previously been very insistent that NASA needs to downselect to just one.
It's quite a victory that they managed to keep on funding two options.
Interesting! I first heard that idea from David Brin, who was proposing it as something to be used for disasters.
http://davidbrin.wordpress.com...
Maybe the governent of Hong Kong qualifies as a disaster.
As I understand it GR does *not* factor in the energy within the gravitational field as creating it's own "secondary" field
It is built into the theory. This is why GR is a nonlinear theory-- which is precisely what makes it so difficult to solve.
- if it did gravity would no longer follow the inverse-square law near singularities,
Correct. Gravity only follows inverse square law in the weak-field limit. Orbits in 1/r2 potentials are ellipses. Orbits in Schwartzschild geometry are not ellipses. Right there you know that Einsteinian gravity differs from Newtonian 1/r2 gravity.
I actually would like to spend some time to elucidate how it is that nonlinearity in GR means that it incorporates the effect of gravity on gravity-- but I'm afraid I just don't have the time to spare at the moment.
... Bottom line, we have Einstein himself on record saying he chose to ignore the energy in a gravitational field as "double counting", are you really going to argue the point with his ghost?
Not only would I not argue, I would agree with him. Since the gravitational effect of gravity is already accounted for in general relativity, it would be double counting to count it again.
But, of course, everybody wants to buy the cheapest ones, not ones tested to long lifetime.
People buy the cheapest because they don't trust the 'rating' on the package. They know it will die 'early' anyway so they might as well be cheated out of $5 rather than $10.
Yep. That's a vicious circle, of course, a feedback look that results in a "race to the bottom."
As I said, what is needed is a good (and trustworthy) rating agency to test and qualify the bulbs.
...
As for the stability of a dust cloud - if it's "stationary", certainly. But how about if it were orbitting an ancient neutron star or other massive non-luminous object in an organized manner? A "lynch pin" as it were to impose order on what would otherwise devolve into a chaotic system and collapse.
I don't know what you mean by "in an organized manner." You mean, what if a superior civilization put each grain of dust on exactly such a trajectory that dust/dust interactions don't destabilize the cloud? OK.
As for ordinary, non-"organized" dust clouds, if there is any interaction between dust grains, and no internal source of energy to keep it from collapsing, a dust cloud large enough to be self-gravitating is unstable.
As for new physics for a "solid" object of that mass - we wouldn't even have to go very far. All we have to do is [proposes altered version of General Relativity] ....
That would be new physics. General Relativity does, of course, account for the gravitational energy of gravitational fields; that's why it's nonlinear. On the face of it, your proposed revision to general relativity's equations violates conservation of energy. There may be some way to avoid that-- but if you do, this is new physics.
I got a 3 pack of LED lights to play with about a year ago from Feit. No problems with those, although it's still too early to tell how I'll fare. The light is a little more directional than the CFLs but I like the color temp better.
You can get directional or non-directional LED bulbs. I like the fact that you can get directional LEDs: for applications like overhead can lights, this nearly doubles the effective brightness. But most of the LED lamps you buy take deliberate measures to be non-directional, to make them screw-in replacements for incandescents
Color temperature is something you can pick. I like the "daylight" color personally--5000K-- but my wife prefers the warmer color temperatures, down in the 2700K range.
The Department of Energy had a pretty rigorous test regimen set up for testing LED bulbs.
http://www.lightingprize.org/6...
What is needed is a good (and trustworthy) rating agency to test and qualify the bulbs.
But, of course, everybody wants to buy the cheapest ones, not ones tested to long lifetime.
For what it's worth, I have about 60 LED bulbs in my house, from about fifteen maufacturers. So far, four have failed.
Further - no viable light bulb replacements will work with dimmer switches (Which my house has many).
That was true five years ago-- these days it seems all of then are rated to work with dimmers . I have some Philips LED bulbs on a dimmer in the dining room-- they work fine.
Density is not the determinant a black hole. Large black holes have very low densities.
From the size and mass, we can rule out pretty much all the other possibilities. (Small but massive dust clouds are gravitationally unstable.) So if it's not a black hole, it must be something else, and that something else is either new physics, or a manifestation of old physics that we've been insufficiently clever to figure out yet.
Please describe what an earth without form and void is supposed to mean. He created a void?????
Well, of course, that's not actually what Genesis said. What Genesis said was that the earth was tohu v' bohu. ( -- let's see how /. does with Hebrew). So, what you're really asking is, what does it mean for the Earth to be bohu? He created a bohu? (Or maybe bohu was already there?)
My personal explanation, the author went with bohu simply because it was a good rhyme with tohu. When you're a poet, sometimes you just have to go with the easy rhyme.
What, Argentina can't just click on google maps to find pools, they need drones?
How is it at odds with observations? We've (indirectly) observed some of objects consistent with our theories of how black holes would behave, but to the best of my knowledge we've never observed the *formation* of such an object.
The headline-- Black holes don't exist-- is at odds with our observations: we see things that appear to be black holes.
The actual summary is not at odds with our observations: the summary says that stellar collapse doesn't form black holes, and we don't have observations to say know how the black holes we seem to be observing were formed.
Now, you could go on and ask whether the things that we see which we are interpreting as black holes might be something else. But that would require a new theory that could explain how the massive, compact objects we see could exist, and not be a black hole. I don't believe that, at the moment, we have any other candidates.
With that said, of course we can't see a black hole itself. But we can see the stuff orbiting it, and that can tell us its mass and size, which is enough to tell what it is.
The headline-- black holes don't exist-- is at odds with the actual article.
The article doesn't say the mathematicians said that black holes don't exist: it says they showed black holes aren't formed by the collapse of massive stars. Black holes such as the ones at the nuclei of galaxies may very well be formed by other processes.
--even if it were true that black holes don't exist, by the way, it doesn't solve the problem of the incompatibility of general relativity with quantum mechanics. At best it would solve the black hole information paradox; but since it still incorporates Hawking radiation in the solution, it doesn't even solve that.