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  1. Re:Question for the Physics doctorates on Hubble Captures Colliding Galaxies · · Score: 2
    The trouble isn't collisions between stars themselves, but between the interstellar medium in the two colliding galaxies. The space between stars is filled with gas and dust (albeit at densities which are many orders of magnitude lower than what you find in any terrestrial environment); when galaxies collide, the gas should probably behave in some interesting ways -- shocks, ionization fronts, etc. I won't even guess what that would do to any given place in one of the galaxies, on average, but my hunch is it wouldn't be good. :-)

    As a side note, people have tried to create maps of the "acceleration vectors" of galaxies in the local universe, but not by studying motions over time -- rather, you look at the density distribution of matter and try to infer a potential and acceleration field. Yes, it's a little sketchy.

  2. Re:Electoral College vs. Parliamentary Democracy on Slashback: Palmistry, Lecture, Quid Quo Pro · · Score: 2
    It is an odd system -- the primary rationale which functions today is that it forces a candidate to have relatively broad geographic appeal. If the President were elected via a straight popular vote, very large majorities in a few states could win the election, even if a candidate lost (narrowly) over most of the country. The electoral college system forces a candidate to carry several states -- it's still possible to lose in a majority of states and win the election, since the number of electors allotted to each state varies, but the system is not as potentially lopsided as it could be with a straight popular vote.

    Of course, it's debatable whether the fix (EC) is worse than the problem.

    BTW, it's maybe worth mentioning that the question of how a representative democracy ought to work has found different answers in the US, depending on when you asked the question. Once upon a time, for instance, the public voted only for delegates to the House of Representatives; those representatives elected the members of the Senate. (This was changed by amendment to the Constitution.)

  3. die, dead horse on Slashback: Palmistry, Lecture, Quid Quo Pro · · Score: 5
    This is a topic which has been hashed out again and again on these threads, but my tolerance has mysteriously vanished, leaving in its place a sudden, urgent desire to stand on a soapbox.

    IMHO, there is only one reason to cast a vote for anyone, ever : you believe that vote will have some net positive effect. Furthermore, a reasonable addendum might be that you should probably cast the vote which you think will have the greatest positive effect. That is, cast the vote which will make the world "best" according to whatever metric you like. This is assuming that you don't find the very act of voting for a particular candidate inherently immoral. So the question for prospective Nader (or Browne, Hagelin -- I'm mangling the spelling here, sorry) voters is just this: do you believe that the greatest good is accomplished by voting for Nader, possibly winning the Green Party more than 5 percent of the popular vote, hence guaranteeing that they will receive money in the 2004 elections, and hence maybe, eventually contributing to having more than a two-party system in this country? Do you think that the simple message sent by a vote for Nader -- loosely translated, perhaps, as "the major parties are completely ignoring issues of very real importance to me" -- in conjunction with the above possibilities for funding in later elections, are more important than the possible consequences of a Bush victory?

    This is something about which reasonable people may differ. I happen to think that the best outcome can be accomplished by voting for Gore -- that is, I think I like the results of voting for him more than the likely results of voting for any other candidate. Your results may vary.

    What complicates the decision is that estimate of the likely effect of casting a particular vote -- and that's where this "wait until the last minute" idea comes in. If you live in a state which is absolutely certain to go to one or the other of the major candidates, what is the net effect of casting a vote for one of those candidates? The way I see it, very little -- it sends no strong message, has no effect on who governs or what their policies are, etc. A vote for a 3rd-party candidate, however, might still have a net positive effect -- particularly with respect to the funding in 2004 issue. Waiting until you have the best sense of the effect your vote will have -- if such an estimate is ever possible -- can only make the decision easier.

  4. Re:Scientific papers on line on Sweet, Sweet Mathworld Is Gone · · Score: 2

    yeah, I don't have any clue how the copyright issues apply to scientific papers. But in astronomy and astrophysics, it's getting to the point where I'm quite surprised when I need a paper that isn't online. This site, for instance, will let you do searches over the contents of many journals, stretching back almost a century in some cases, and then get the papers you need either in scanned or fully electronic form. (Interestingly enough, the "electronic refereed journal" version of many articles requires your institution to have purchased access -- that is, ApJ online isn't accessible to everyone. But the scanned versions don't have such restrictions -- at least not that I'm aware of.)

  5. not necessarily a dichotomy, but still troubling on Why Does The Universe Exist? · · Score: 2
    As I think the comments here have demonstrated, many people find it possible to "believe" in both inflation and the existence of a deity. Sure, it's impossible to reconcile a belief that the Universe is 6,000 years old (a la strict literal interpretation of the Bible) with observation, but no big surprise there. More interesting, IMHO, is the question of what a Creator is left to do in a Universe governed by physical law : do you believe in a Planner God, who designs the laws by which the Universe will function and then leaves it alone? Or do you find the idea of such a remote Deity repellent; do you insist on your God being an interventionist one, deeply passionate, answering the prayers you say each night? Both beliefs have rich philosophical pedigrees, and of course people have tried to reconcile the two ("God is outside of time," etc.), but the question still holds merit.

    Personally, I think that if you want to call yourself a Believer (of whatever religion you choose), you can't just say "I'm a creationist," or "God handles everything," and leave it at that. The facts are there, and are pretty hard to dispute : I could go on at length about this, but the Inflationary Big Bang is supported by many different observations, and no other theory has emerged (or is likely to emerge, IMNSHO) which can say the same. (Examples: the existence of a CMB, and the fact that it has the spectrum of a perfect blackbody at 2.7 K, to within one part in 10^5 or so, everywhere in the sky; the existence of a Hubble flow; etc.) You can't just ignore these things : you must find a way to reconcile them with your faith; if that makes your picture of God, and the way God functions, more complicated ... well, so be it.

    And we haven't even touched on what is maybe the most fundamental thing, which is that it might be impossible for any scientist (or anyone who thinks scientifically) to believe absolutely, without doubt. Richard Feynman has discussed this all (much more eloquently) in some of his books, but the gist is this: that doubt is the very nature of science. You never, ever, ever say "I am absolutely sure of this one thing"; you say, "I am almost certain; I am 99.99999 percent certain," etc. And this is a profound thing, because for a simply religious person it is just "there is a God"; for a deeply scientific person, it must be "I am almost certain there is a God." You are never quite sure, cannot ever be quite sure -- no matter how much you would like to believe, no matter how many times you have felt like a Deity exists, the doubt is still there.

  6. Re:Candidates need to win only 8 states on Politics, Assassination, and Debates · · Score: 2

    but the situation could be even worse (though arguably more unlikely) in a straight popular vote. that is, by pulling huge majorities in a geographically limited area, a candidate could capture the presidency while completely ignoring the concerns of a large chunk of the country. the electoral college system isn't perfect, but it does manage to strike a minimal balance between representation by geography and representation by population.

  7. regional issues and the EC on Politics, Assassination, and Debates · · Score: 2
    actually, the idea that voters on one side of the country wouldn't know what was up on the other has been exploited in prior elections. In 1820 (I think -- sorry I don't have an almanac handy), one of the major political parties of the day planned to field not one candidate but several, based in different geographic regions of the country. So in Georgia, they might say, "Joe, he's our man!"; in Maine, "Bob, he's our man!"; etc. This was, IMHO, a totally brilliant plan : each of the candidates could be tailored to a particular region, could garner large majorities of the vote unburdened by national concerns. It was also, obviously, a total bastard plan, since the eventual idea was to have the party candidates all meet, decide on which candidate would be the "true" candidate, and cede their delegates to that one candidate. Alas, none of this worked, because of squabbling internal to the party.

    Presumably you couldn't do this today, since people would figure out pretty quickly what was up. (Imagine if the "democratic" candidate for Pres. was Bill Bradley in the Northeast, and Gore elsewhere? Or if the Republican were McCain in the NE and Bush elsewhere?) But I thought it was an interesting idea.

    Note, also, that the intent of the EC was also in part to force the winning candidate to have appeal which subsumed geographic lines -- if you went by a straight popular vote, overwhelming majorities in only a few states could decide the election.

  8. Re:Heh on Astronomers Find Black Hole At Milky Way's Center · · Score: 2
    yeah, that's not a great choice of comparison for distance. the radius of a one solar mass black hole is about 3 km, and it just scales linearly with mass, so you're looking at no more than 8 million km for a 2.6 million solar-mass BH. By comparison, the radius of our Sun is about 700,000 km, and the Earth orbits at about 150 million km from the Sun.

    of course, the above numbers are upper limits on the radius; a BH can always be *smaller* than the Swarzschild radius, but never larger.

  9. not too relevant in this case on Astronomers Find Black Hole At Milky Way's Center · · Score: 2

    What you say is true, but this isn't what the group mentioned in the article was doing. More germane, maybe, is that another way of "detecting" BHs, and actually quantifying how massive they are, is to look at the motions of objects around them -- if, eg, stars are moving very quickly, then the mass around which they orbit must be quite large. The technique described in the Nature article sorta, kinda, has to do with this, but the goal was (I think) to pinpoint position more than anything else. We were already pretty sure Sag A was a black hole.

  10. Re:high redshift galaxies, etc. on Plans To Peer At A Black Hole's Event Horizon · · Score: 1
    This sounds like a troll, but I'll bite.

    Excuse me? I don't want to start a flamewar here, but I didn't use the term "daydreaming" anywhere in my post. I can only suppose you're talking about the fact that I called the NGST slogan "hokey PR" -- I called it this not because the NGST is unjustified scientifically, but because it struck me as a silly slogan. I'm a graduate student in astrophysics, for chrissakes.

  11. high redshift galaxies, etc. on Plans To Peer At A Black Hole's Event Horizon · · Score: 3

    The formation of galaxies is definitely a topic of major research interest; one of the major science missions of the Next Generation Space Telescope is to probe "the era when galaxies were young" (as the hokey PR material used to say). Keep in mind, though, that the problem is not just one of building a bigger telescope, but of building a telescope that is sensitive in the right wavelength regimes : the farther away from us you look (and hence the farther back in time you're probing), the more "redshifted" things become; their light is shifted to longer and longer wavelengths. So to probe the early galaxies, NGST has to be sensitive in the infrared region of the spectrum -- which brings up a whole slew of complicated design problems. (The Earth glows in the IR, for one thing, so a near-Earth orbit isn't practical -- the NGST will be nowhere near us, and hence impossible to service once it goes up.)

  12. OT, or not OT on Startup Claims 16.8M Pixel Camera Sensor · · Score: 2
    ouch. a little overly dismissive of 35mm, don't you think? :-) certainly it has real flaws -- and you're right in suggesting that anybody who could seriously consider blowing $5,000 for a serious digital camera could also consider going for some beefy large-format view camera -- but things are hardly as clear-cut as you make them out to be here.

    yeah, you have to use slow-ass films to get good resolution. but for a lot of applications, this isn't a big deal -- I take a lot of pictures of outdoor scenes, and Velvia (ISO 50) works just fine for sizes up to 16x20ish. clearly large-format is superior, but not everyone wants to drag a large-format system with them. For outdoor photography, this is a serious issue -- the weight of a decent view camera with lenses, etc, is in the 50 lb.+ range; contrast this with a digital camera (or 35 mm, or even medium-format) system, and you might be willing to sacrifice some resolution to save your back.

    the real advantage of large-format, IMHO, and the thing that will keep them around for the foreseeable future, is the perspective control they allow you. admittedly, tilt lenses exist for 35mm -- and I haven't tried them -- but they seem a poor substitute.

    Just my 2 cents. :-) I do agree with you that the comparison between film & digital is usually pretty meaningless, unless you define a particular target usage; for the professional landscape photographer, who doesn't care about weight (because he has a llama to carry his gear or something -- I'm not even kidding about the llama, John Fielder does this) and doesn't have to pay for his own film, digital clearly loses to large format. For the amateur who shoots snapshots and posts one out of every ten on the Web, and ditches the rest, digital is easily the right way to go.

  13. die, dead horse on Baby Black Hole With Big Appetite · · Score: 2
    There have been some good replies to this already, but hey! clarify, clarify, clarify.

    Re: formation. When a star is in the happy, go-lucky stages of its life (the Main Sequence, when its burning Hydrogen into Helium in its core), and even a little later, its structure is set largely by the balance of gravity against ordinary gas pressure. (Take the term "ordinary" loosely here.) Later on, as material in the core of the star becomes very tightly packed, etc, that core becomes electron degenerate -- what's holding it up is the tendency of electrons to dislike rather intensely being crammed next to other electrons. (Again, I'm grossly simplifying things here, but what the hell.) This, in turn, leads to all kinds of interesting things -- for one, the conductivity of electron-degenerate matter is extremely high, so it tends to be largely isothermal; for another, degenerate matter is just plain weird : when you pile more mass onto the degenerate core, the damn thing gets smaller! So you see the normal cycle of compression-expansion is screwed up, and strange things can happen. The degeneracy will actually be broken multiple times in the life of the star, as the core eventually reaches its ignition temperate (in massive enough stars : and remember, because its isothermal, the whole thing reaches the ignition temp. more or less at the same time -- which is why you get the so-called "Helium flash" or "carbon flash").

    I've veering wildly off-topic here, so back to the point: eventually, if the star is massive enough, even electron degeneracy pressure isn't enough to hold up the star against the crushing pull of gravity. The core collapses -- the electrons fuse with protons to form a big soup of neutrons, which can exert an even more impressive form of degeneracy pressure. (The core-collapse process, as you might imagine, is pretty dramatic: remember that this is an awful lot of mass we're talking about here. There is a rebound off the neutron-degenerate core, plus an outgoing flood of neutrinos which were produced in the p-e fusion into neutrons -- a truly stupendous amount of energy is released, and we call it a Supernova.) And (you can probably see this coming) if the remnant core is massive enough, even neutron degeneracy pressure isn't enough. But we know of no force in the universe that can stop the collapse after that : the object collapses indefinitely, to a singularity.

    But the Black Hole, it should be mentioned, comes into being long before all the mass is concentrated in a single point : a BH can be said to exist the moment an event horizon exists -- that is, the instant the density of matter in a region is so great that the escape velocity from that region is greater than the speed of light.

    God, that was a long answer to a short question. To top it all off, the supermassive BHs in the cores of galaxies may be totally different beasts -- nobody is entirely sure how they form, though certainly there is a long process of merging and growing before they attain their current (billion-M_sun) masses.

    2.3.4 : I don't really have the energy to answer these very completely anymore. :-) But very "briefly." 2: black holes don't suck, any more than normal matter does. If our sun were magically replaced by a black hole, our orbit wouldn't change one bit. (Of course, we wouldn't have too long to appreciate that fact, since we would miss rather dearly the lack of sunlight.) A BH is "different" from a normal object, attraction-wise, only once you get pretty darn close to the thing. So yes, they will eventually stop growing. 3: people use "size" sloppily, but I usually mean the radius of the event horizon. This is really the only definable radius for a BH; it is related to the mass by a well-known formula. Some people also use "size" interchangeably with "mass" -- there are certainly more or less massive BHs. 4: no. :-) but you're actually hitting on some real points here -- to an outside observer, and supposing certain other things, it would like someone falling into a BH was taking an infinite amount of time to do so; in fact the Russian term for BHs was, IIRC, "frozen star," for precisely this reason. read Kip Thorne's book, called -- I think -- "Black Holes and Time Warps," for a good discussion of this sort of thing.

    Hope this helps.

  14. not really infinite density, either on Baby Black Hole With Big Appetite · · Score: 2
    It's really more well-defined to talk about the event horizon as being the boundary of the black hole. In this context, it makes sense to talk about the density of a black hole in the usual sense -- and in fact, this leads to some interesting (and perhaps non-intuitive) results. A classic for-instance : the density of a black hole actually drops as you crank the mass up. That is, supermassive black holes are much, much less dense than stellar-size ones. (And the tidal forces near the event horizon are much, much smaller -- so you could, in theory, take a spaceship and cruise very close to the event horizon of a supermassive BH without being ripped into shreds by the tidal forces.)

    Just so ya know. ;-)

  15. superexpense? on Green Bank Telescope Goes Live · · Score: 2

    A particle accelerator of the class that would actually be useful today would cost orders of magnitude more money than this telescope. Plus, I'd argue that there is always need for more telescopes -- getting time on any major scope is hard as hell (spoken like the bitter grad student I am), and there are a lot of things out there to look at. :-)

  16. a different list, from slightly less-drunk people on Physics Problems For The New Age · · Score: 3
    Last year, Physics World did a poll of working physicists on (among other things) what the ten greatest unsolved problems in physics are. The answers they got are no more definitive than the list posted here, obviously, but interesting nonetheless; the top 10 (as reported in this old PhysNews update from the AIP) were
    • quantum gravity
    • understanding the nucleus
    • fusion energy
    • climate change
    • turbulence
    • glassy materials
    • high-temperature superconductivity
    • solar magnetism
    • complexity
    • consciousness

    note that the definition of "physics" being used here is pretty broad. :-)

  17. porn grad on Online Rights And Real World Censorship? · · Score: 2
    ah, how right you are. when I was an undergrad at Rice, there was this Chinese guy (a grad student in CS there) who would come into the computer labs where we were working and, for hours on end, gaze intently at porn. we're talking full-screen action here, and this with people milling all around him. some friends and I found the guy's webpage once, and it had some line like "I like beautiful girls. Especially new girls," which ... wow.

    He was known as Porn Grad.

  18. a defense of the automobile, from a cyclist on Why Do We Still Use Gasoline? · · Score: 2
    okay, a disclaimer: I bike to work every day, walk around town for most errands, and generally use my car about once a week. when I go on long trips, I take the bus to the airport.

    but allow me to play devil's advocate here: I would really, really miss my car if I didn't have it. the key thing to me (don't laugh) is shopping for groceries -- this turns out to be a real pain in the ass when you have to lug your bags of groceries (and cases of Dew, etc.) back on the bus (or on a trailer off your bike). there are other examples, but let's focus on this one.

    hogwash, you interject. people in, say, France don't use a car when they go grocery shopping; neither did we, a hundred years ago. ah, but here's the rub: people in france don't use Safeway. they buy their bread and cheese in the morning, meat for that day's meal, a nice big bottle of wine (yay, stereotypes!) ... you get the idea. Point is, people in a lot of other countries go shopping with a regularity that boggles the American mind: the idea of going to the grocery store once every 3 or 4 weeks (as I am fond of doing) is a peculiarly American one. Condemn it if you like, but the point remains: to get people to get rid of their cars, you wouldn't just have to convince them to take a bike to work; you also have to convince them to change, in a thousand little subtle ways, the way they conduct other aspects of their lives. My picayune example is a grocery store, but you could find plenty of others.

    It's also worth mentioning that some solutions to the above-mentioned problems (again using our example: in a lot of cities, companies exist which will do your grocery shopping for you! for a nominal fee, of course) are precluded in certain segments of the population, delineated by lines of both geography and socio-economics. No one in Amherstdale, West Virginia is likely to open a grocery-delivery service anytime soon. And if they did, it would take a long, long time to convince people they could afford it (even given the money they're saving by not using their cars). No bus lines in Amherstdale, either, I'm afraid, which brings us to the other big issue : the scale of the United States today is vastly different from that of most other countries (and from the scale of our own country of 100-plus years ago). People in the US are spread out, have family all over the place, like to go to the beach on weekends; if they live in a few major metropolitan places, you can get them on a train or something, but that's simply not an option in large chunks of the country, and (IMHO) never will be. Decry the large-scale-loving USA populace if you want, but again the fact remains: you'd have to change another facet of people's lives to get them to give up their cars.

    Having said all this, of course, I'll still push for people to give up their cars for all but occasional use. But I'd wager the internal combustion engine has a long and happy future ahead of it in the US. ;-)

  19. that's what they WANT you to think ;-) on IBM Constructs New Fastest Computer · · Score: 1
    do you really think they'd tell you about all the mad Quake sessions? or the parallelized porn-surfing?

    nuclear simulations, my ass.

  20. a backwards argument for abolition on IBM Constructs New Fastest Computer · · Score: 2
    If you want to argue that nuclear weapons should be abolished, fine, I applaud you. But our government is nowhere near such an abolition. Given that, it makes absolutely no sense to simply "trust" that weapons built twenty years ago will function perfectly if we "need" them. That is, given that nuclear weapons are still very much a part of our strategic arsenal, it would be utterly foolish for us not to guarantee (at least to the extent possible) that they still work. That's the point of the "Stockpile Stewardship" program. In the context of a society with nuclear weapons, there are two real alternatives -- spending oodles of money just to keep them around, plus having everybody hate us for having such power, but NOT KNOWING if they're actually going to do us any good or not; or actually periodically doing above-ground tests to see how the weapons are holding up. I find the simulations a more palatable option than either of these.

    Sorry to rant a little. My point is just this: argue all you want that we shouldn't have nukes; write your congressmen, campaign on Capitol Hill, etc. I wish you luck. But until that day comes, it makes sense for us to do this sort of simulation.

  21. enh? they're still around on IBM Constructs New Fastest Computer · · Score: 2
    and being used for solving problems. sure, they're not in the news (because they're not the fastest anymore), but that doesn't render them any less valuable.

    Blue Mountain (at LANL), for instance, was on the order of 6,000 RS10K processors; if you hunt around enough, you can still find the webpages about it at the Lab. (Again, I'm lazy. Sorry. :-)

  22. cost, and the future of large observatories on Ask Chris McKinstry About Giant Telescopes, Etc. · · Score: 2

    Given the enormous startup cost of a 100-m class scope ($1 billion-ish), and the truly stunning operating costs (many thousands of dollars per night), do you think such scopes will continue to be developed by, eg, university consortiums? Or do you think we will have to develop a new funding/use model? My point is that very, very few schools can contemplate even being a part of a project like OWL, nor (in the current political landscape) does it seem likely that governments will be eager to dish out funds for very many such scopes. Given these conditions, do you doubt that there will ever be more than one or two instruments of this size, do you suspect that universities will band into larger and large consortiums, or do you imagine industry (for some reason which escapes me at the moment) taking interest in such a project and providing funds?

  23. slightly OT: unintended consequences on Two Scoops Of Wearable Computers · · Score: 2
    Re: your comment about useful videophones.

    There's this great bit in Infinite Jest where Wallace talks about the rise and fall of, essentially, videophones. It's hilarious and insightful and I can't begin to do it justice here, but a sketch goes something like this: videophones (in this mildly futuristic book) shattered the illusion most people enjoyed while talking on the phone; namely, that the person on the other end of the line was giving them his/her full and undivided attention. When you talk on the phone, you can be doing whatever -- picking your nose, watching TV, drying yourself off after a shower -- but somehow it never occurs to you that the person on the other end of the conversation could be doing exactly the same set of activities, could be devoting exactly the same miniscule portion of their thought to your conversation. Videphones (in Wallace's world) shattered this illusion -- you could now see exactly how bored the other person was, could tell they'd just gotten out of the shower, etc. -- and in addition tended not to project exactly the sort of image people wanted to project; ie, people always looked a little wan or something on their vidphone-screens, leading to huge problems of self-image and belonging, etc. This leads to all sorts of interesting consequences, like people buying masks representing the sort of face they wanted to project, and then eventually the advent of tableaux that would project an image of an actor, seated in a tastefully decorated room of the sort you would like people to think you own, listening thoughtfully to whatever the other person had to say. And so on, and so on.

    Good stuff. Infinite Jest (by David Foster Wallace) is, IMHO, one of the best and most entertaining books published in the past decade, and is chock-full of this sort of thing; highly recommended.

    I did say it was OT. :-)

  24. Re:I dunno about that on Classified Data Missing From Los Alamos · · Score: 2
    This incident notwithstanding, security is pretty damn tight at LANL (I worked there briefly). This vault is "behind the fence," and in a particularly secure area; among other things, you have to go through a gate which uses your handprint as an authentication scheme. You have to have a "Q" clearance (the DOE equivalent of Top Secret/SCI) to get anywhere near this place.

    Point is, it would be very, very difficult for someone who was not supposed to have access to get it -- but you can never totally protect against either insider espionage jobs or people being stupid. Los Alamos is particularly prone to both of these problems because a) it does work that a lot of people care quite a bit about, and b) it's friggin' huge.

  25. Re:Black Holes aren't so ...massive? on Black Holes' Growth Measured · · Score: 2
    Note, though, that when most people talk about "black holes" they're referring to the whole shebang -- ie, not just the singularity but the region of spacetime around it, extending out to the event horizon. It makes no sense to talk about only the singularity, since it is perpetually hidden ("nature abhors a naked singularity"). Just to be picky. :-)

    Also, note that in principle one could use the bending of light around a massive black hole to estimate its mass. (You've no doubt heard all about such "gravitational lenses," but less well-known is the fact that it's possible to get a mass estimate from such objects by looking at precisely how the light "bends.") This sort of measurement has been done for, eg, clusters of galaxies, but the masses involved are far, far larger than those in even supermassive BHs -- it's also a difficult measurement, fraught with possible errors.

    just my 2 cents. :-)