What Would the View Be Like From Within a Black Hole?

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If you fell into a black hole, would you be engulfed in darkness? Could you see out beyond the event horizon? Are there wormholes inside black holes? Do black holes give birth to baby universes? Believe it or not, these questions may have been answered. Andrew Hamilton from the University of Colorado and Gavin Polhemus have created a video showing what falling into a Schwarzschild black hole might look like to the person falling in. The two researchers warn that based on our experience in the 3D world, we might imagine that falling through the horizon would be like falling through any other surface. However, they say, it’s not. And likely, a person falling into the black hole would be able to see outside of the event horizon.

“When an observer outside the horizon observes the horizon of a black hole,” the researchers say, “they are actually observing the outgoing horizon. When they subsequently fall through the horizon, they do not fall through the horizon they were looking at, the outgoing horizon; rather, they fall through the ingoing horizon, which was invisible to them until they actually passed through it. Once inside the horizon, the infaller sees both outgoing and ingoing horizons.”

As you might expect, this work has created a lot of interest, and the servers hosting the videos has already crashed once, but now has been put on a new server. Watch several different videos. along with written commentary here.

While this work is great fun to watch and delve into, it also has great scientific merit. Calculating what the universe looks like from inside a black hole is an important exercise because it forces physicists to examine how the laws of physics behave at a breaking point. For example, near the singularity, the observerโ€™s view in the horizontal plane is highly blueshifted, but all directions other than horizontal appear highly redshifted.

Also, the principle of locality is severely tested inside a black hole. This is the idea that a point in space can only be influenced by its immediate surroundings. But when space is infinitely stretched, as physicists think it is at the heart of a black hole, the concept of “immediate surroundings” doesn’t make sense. So the concept of locality begins to lose its meaning too.

And that provides an interesting “thought laboratory” in which physicists can ask how ideas such as quantum mechanics and relativity might break down.

It also provides some other entertaining results. For example, space is so heavily curved inside a black hole that ordinary binocular vision would be no good for determining distances, says Hamilton. But trinoculars might work.

Read the paper here.

Sources: Technology Review Blog

56 Replies to “What Would the View Be Like From Within a Black Hole?”

  1. Interesting…most of the commenters are more wrapped up in what somebody might say — sharpening their “rididule” knives.

    Might this “thought laboratory” be over the top even for the crew that believes a “point” exists in space when pure mathematicians will tell you a point is an abstract concept.

    The article states: “Calculating what the universe looks like from inside a black hole is an important exercise because it forces physicists to examine how the laws of physics behave at a breaking point. For example, near the singularity..”

    “Singularity”, also known as “infinite density” which means exactly what? “Infinite” can’t be quantified, it’s fudge factor.

    Or it might remind them how ridiculous all the “black hole” paraphernalia real is.

    “While this work is great fun to watch and delve into…”

    Okay, fun, yes and entertaining.

    But “it [the video] also has great scientific merit.

    Hmmm?

    The scientists are self-contradictory: “Examine how the laws of physics behave at a breaking point.”

    If the laws of physics breakdown, then there is no way to know how the “physics behaves” by its own definition.

    I’m sure it fun, but as “chewing gum for the eyes” and not much more.

    And sure astronomy should be fun and even fanciful at times, but dressing up a video fun house mirror as science reveals how off-track “modern” astronomy has become.

  2. Dave-c’mon=lets not make this a ————–
    GET READY FOR A RUMBLE-IN THIS CORNER-< SBC WITH HIS PATENTED “GRAVITY SLAM” VS OIM WITH HIS UN-ORTHODOX ‘ ELECTRO CHOKE-HOLD’ -get you popcorn, peanuts===Lol.
    Anyway, this will just have to be a thought
    thinking- I would not like to find out.!!!!!

  3. awww star-grazer, can we please have a rumble? Those one sided reason-vs-idiot catfights are soooo entertaining! Come on Oils, give us your latest rant against the gravitists! Lets see the Master(y) at work, bringing us another entertaining smackdown!

  4. I think its more entertaining that you can “see” a coordinate system when you are inside a black hole. I didn’t know that! ๐Ÿ˜€

    And after OiM has given us his great thought, Anaconda will appear to tell us that this video proofs the destruction of GR. Just because this seems to be so ridiculous!

  5. Interesting stuff, but if our current understanding of physics breaks at the event horizon how can we look beyond?

    Is the gravity at the absolute centre of a black hole stronger that it is at the Event Horizon? I think it should be, but then is there any way of knowing..

    The speed of light is a finite speed of about 186,000 miles per second.

    To curve space to the point of being parallel or infinitely curved is well…. infinite…Aaarrrggh

    It boggles the mind and great fun it is too.

  6. @ Sci-Fi Si

    Interesting stuff, but if our current understanding of physics breaks at the event horizon how can we look beyond?

    The physics break down at the singularity, not at the event horizon. It’s just that beyond the event horizon things start to get even more inconceivable than they used to be “in front of” the event horizon.

  7. Have you people noticed that on this science site you see these ads about 2012 the end of the world, now I see an ad promoting scientology… Next probably an ad for EU?

  8. DrFlimmer- You’ve mistakenly given ammo to OIM, despite the fact SBC ‘tag team’ members will use eye gouge, cheap shots,other dirty tricks-OIM will emerge thru the Black Hole and rise up like the WWE ‘Undertaker’ as he will say the videos is ridiculous and made by ‘inmates committed to an asylum for the criminally insane’ IMHO, humans will NEVER find out what really happens once at the singularity, (NEVER I realize, is a strong word, but such thinking will be just that , a think journey)
    As more powerful ‘puters are created, simulations inside a black hole will be truly awesome.!!!! Well, I better get out of Dodge,Lol.

  9. @ Olaf

    Since I use firefox I have that great tool included named “AdBlockPlus”… it blocks most of the banners!

  10. @ star-grazer

    Never say never ๐Ÿ˜‰

    Probably physicist will come up with a theory of quantum gravitation which should prevent us from a singularity. Since space and time start to fluctuate at very “compressed” scales it non-sense to speak of a dot or a singularity in a quantum world. It is a possibility that we can avoid the singularity in the future – but future will tell….

    (Probably this is even more ammo…. we will find that out, too….)

  11. DrFlimmer- You are correct, perhaps far into the future, far more will be found out about the great Universe we are in . You are a Scholar and a Gentleman.
    Take care

  12. @ Astrofiend:

    Astrofiend states: “I think you’ll find Anaconda that not many physicists strongly believe that a singularity is truly physical.”

    Hmmm?

    Astrofiend clarifies the, above, quote with the following sentence:

    “More like they are using it as a working concept because we have not yet developed a fully viable and self-consistent theory of quantum gravity as of yet that can fully probe these enigmatic regions.”

    There is a problem: Quantum mechanics and General Relativity are inconsistent with each other.

    Astrofiend states: “…or that of some discredited crank…”

    Astrofiend, your appeal to civil discussion rings hollow when you drop that bouncing betty into the party.

    Judging by your past comments (the only thing I have to go on), any argument that is offered against the “black hole” hypothesis is likely to be judged by you as being from some “discredited crank”.

    Yes, there are explanations for observations that have been attributed to aspects of General Relativity. And, yes, I have an opinion. Gravity exists, no doubt about that, but is not based on geometry, or space-curvature, rather gravity is intrinsic to matter — exactly how it operates has yet to be revealed.

    Perhaps, only then will gravity be able to be quantiized.

    Astrofiend presents my [Anaconda’s] statement: “If the laws of physics breakdown, then there is no way to know how the “physics behaves” by its own definition.”

    And Astrofiend responds: “is preposterous.”

    No, not at all. Scientists don’t claim physical laws breakdown, a priori, based on a mathematical hypothesis, which is what astrophysicists have done with both “black holes” and the “big bang”.

    Rather, scientists state they don’t understand the physical laws and will make observations & measurements to understand, describe, and explain physical laws. Scientists generally proceed on the basis that physical laws are constant at all locations in the Universe.

    That’s why Einstein didn’t believe in so-called “black holes”. Einstein clearly stated in his theory that the physical laws of the Universe are the same at ALL locations in the Universe. So-called “black holes” and the “big bang” specifically rely on physical laws being set aside.

    There is an arrogance present when a hypothesis based on a priori, mathematical equations attempts to trump the recognized principle in science that the physical laws of the Universe are immutable and constant.

    “But black holes exist, the big bang happened, if the physical laws have to be set aside to preserve these ideas…well, I guess the physical laws will have to be put aside.”

    So says the “modern” astronomer.

    Astrofiend states: “Physicists probed this region where physics broke down…”

    No, they realized they didn’t understand the physics.

    Something “modern” astronomy has yet to face up to.

  13. @ DrFlimmer
    “Probably physicist will come up with a theory of quantum gravitation which should prevent us from a singularity.”

    As Oils would say, use a big magnet and suround your spacecraft with plasma and everything is solved! LOL

    @ DrFlimmer
    “Since I use firefox I have that great tool included named “AdBlockPlus”โ€ฆ it blocks most of the banners!”

    Yes I could do that, but does it no scare you that creationists, 2012 people and Scientology put ads on a scientific site?

    Even Youtube scientific and evolution movies are infected with 2012 ads and creationists ads. ๐Ÿ™

  14. I think you’ll find Anaconda that not many physicists strongly believe that a singularity is truly physical. More like they are using it as a working concept because we have not yet developed a fully viable and self-consistent theory of quantum gravity as of yet that can fully probe these enigmatic regions. Clearly you don’t like the idea of black holes – yeah we get it. You bang on about it at every chance. Show me some quantitative analysis to back your arguments. Anything actually, that is not merely your opinion or that of some discredited crank, but a well reasoned mathematical and phenomenological argument that demonstrates where GR fails before the black hole solution comes into play.

    Also, your statement…

    “The scientists are self-contradictory: “Examine how the laws of physics behave at a breaking point.”

    If the laws of physics breakdown, then there is no way to know how the “physics behaves” by its own definition.”

    …is preposterous. Physicists always probe the regions where laws or theories begin to break down. Not after the point they break down – where they break down, and the lead-up to this point. It is one of the most valuable methods for understanding what needs to be done next.

    Take electromagnetism and Galilean relativity. It was demonstrated that one of these sets of laws was wrong – they were inconsistent. Physicists probed this region where physics broke down, and eventually Einstein discovered (with others) that Galilean relativity broke down in the high speed limit. Special relativity was born. Likewise with GR stemming from the disagreement between Newtonian gravity and special relativity. Likewise quantum electrodynamics stemming from non-relativistic quantum mechanics and field theories. The list is literally endless – this is how physics moves forward. So it is with GR and QM in the strong field limit. Where does this physics break down and how? That is the key question, and the answer will provide a tremendous leap forward in our state of knowledge. If we didn’t find out where laws fail, in which circumstances, then we would literally be stuck back with Aristotle’s world view. To suggest otherwise represents a serious misunderstanding of a key part of the scientific process, particularly in physics.

    As an aside, I’m sick to death of all of the BS that goes on on this site these days, and I’m going to make a concerted effort not to get involved in tit-for-tat pettiness. I’ll be restricting myself to strictly scientific stuff or talking points, unless there is a wanton howler that needs smashing. Mostly because I have no interest in all of the negativity.

  15. Well said astro. You are right about the pettiness on here, and I have started to become a bit too keen to ridicule the trolls who infest this site, so i guess im partly to blame for that.

    But without some form of forum moderation on here, the trolls and the people who ridicule them will just carry on. As has been suggested in the past, maybe it would be best to move the comments area on here to a link to the BAUT forums, where effective moderation already exists, and all of the Universe Today articles have a forum topic thread for discussion about each article.

    I think that would be easy to implement, and it would solve all the problems that we have here.

  16. Astrofiend,

    Well said. Unfortunately it’s wasted on Anaconda. He doesn’t understand that he doesn’t understand science and how it’s practised.

    Maxwell,

    The PC/EU topic has been discussed on BUAT and from what I gather such discussions have been banned. We can see the reasons why.

  17. “Even mainstream scientists admit that at singularities the โ€˜laws of physicsโ€™ break down. It would be more accurate to say that their own theories break down.” — David Pratt, natural philosopher, 2005

    “…the ‘Schwarzschild singularities’ do not exist in physical reality.” — Albert Einstein, mathematician, 1939

    “I am inclined to think that physicists will not be satisfied in the long run with this kind of indirect description of reality, even if an adaptation of the theory to the demand of general relativity can be achieved in a satisfactory way. Then they must surely be brought back to the attempt to realise the programme which may suitably be designated as Maxwellian: a description of physical reality in terms of [electromagnetic] fields which satisfy partial differential equations in a way that is free from singularities.” — Albert Einstein, mathematician, 1931

    “…in the present state of our experimental knowledge, nothing entitles us to suppose that singular points (in four dimensions) may exist in the Universe.” — Marcel Brillouin, mathematician, January 1923

  18. “Personally I have better questions to deliberate on.”

    Ok, then. You can go off and deliberate whatever you want, and we’ll stay here and deliberate on what we want.

  19. The Birkeland-current that is supposedly powering our Sun (according to EU) should generate a large magnetic field, a compass in that field would point at the Sun.

    My compass pointed roughly at the magnetic north pole of Earth, every single time i tested.

    EU failed the compass test, EU fails.

  20. We understand that there should be laws of physics that work everywhere. Unfortunately, we don’t know what those laws are. General relativity is a very good approximation to the true laws of physics except at locations of extreme curvature, like the the center of a black hole and the big bang.

    When people say “the laws of physics break down at the singularity,” what they should say is “the laws we know, general relativity and quantum mechanics, are poor approximations of the true, unknown laws of physics once the curvature gets too large.”

    The scientific community realizes that we don’t have the final theory. Pushing current theories to their limits is the best way I know to get some insight into the true physics.

    None of this changes the fact that general relativity is an excellent approximation to the true laws of physics practically everywhere in the universe. You can accept predictions of general relativity with confidence as long as they don’t involve curvatures that are huge. For example, the horizon of a black hole is a prediction you can trust, even though the central region is mysterious.

  21. It doesn’t matter how it looks like, one thing for sure is our body or our technology will not able to stand with the G force, and smash into a tiny atom or electron. One can imagine a high speed spinning centrifuge that compress all materials toward the wall. If light also can’t escape from the G-force, a space ship will enter and come out as ashes if the wormhole does exist.

  22. @ Olaf:
    The ads are placed by Google, using a script which searches the page for keywords and selects ads which the script “believes” may interest readers of the page. It’s a way for UT to pay its expenses, so it can carry on bringing you the news. I enjoy the fact that the owners of those Web Sites pay UT, even though most of the readers of UT are not interested in conspiracy sites. You might click on those ads to increase the revenue for UT… at the expense of those sites. I do it a lot.

    This simulation is of course pure conjecture, a play with mathematics – but I find it entertaining, and I see it as a great effort towards making better models for understanding what goes on “out there”.
    I see “The laws of physics break down” as an unfortunate way of saying things. For myself, I translate it as “We have no model to explore and explain what we observe”.

    People quoting D. Pratt, take note, please: There are some countries where he would go to jail for some of his (to certain groups of people) highly offensive published material! O.K., that’s on subjects other than Physics (he seems to try to set himself up as “rebel expert” on many things he reads about)… but still: Quoting Pratt discredits people who quote him.

  23. @ Solrey:

    Your analysis is poetic in its simplicity and eloquent reasoning.

    The balance between your own reasoning and prose and the supporting quotes you provide illuminates the subject.

    The fact that these intertainment videos get carried as serious science suggests “modern” astronomy knows that “popularizing” the message is important, and in our “pop’ culture, it is important. But for serious scientific observers and serious scientists alike, they reveal a problem.

    @ Gavin Polhemus: “General relativity is a very good approximation to the true laws of physics except at locations of extreme curvature, like the the center of a black hole and the big bang.”

    Space is not a physical object (space is the absence of physical objects), neither is time. General Relativity assumes both as physical objects, this assumption creates problems in analysis.

    In an ironic way, I hope these kinds of videos are continued to be treated as serious science because it makes the job easier for people who question “modern” atronomy’s connection with reality.

    Why?

    Because if “modern” astronomy promotes this kind of easily demonstrated conjecture as serious science what does it say about the rest of its menagerie of exotica?

    Particularly, when an alternative theory which employs a fundamental state of nature, electromagnetism, has no stable of exotic menagerie at all.

    Why the stable of exotics?

    Only one reason I can figure out: The gravity “only” model fails to explain the large structures of the Universe without them.

    And if we have to make up exotics to keep the model going — well…necessity is the mother of invention.

  24. Anaconda said;
    “No, they realized they didn’t understand the physics.”

    Against the Jackasses of yourself and OilisMastery, and all those absolute twits at Thunderbolts.Info (Now forever Dunderbolts.Info)
    True words were never spoken.
    Well done. You are beginning to see the light for what it is.
    Clearly the only people lost in black holes are the EU mob!

    Oh, is it true, that EU now belief magnetic field have THREE poles. Positive, Negative and Daft!

    Thank God it is April’s Fools Day – a days designed for you kind. You should go celebrate!

  25. It is quite impossible to create a singularity and the inside face of any event horizon is totally reflective to any photons. You cannot see beyond any event horizon.

  26. @ Solrey:

    I think you hit the nail on the head: Pure mathematicians have thoroughly infiltrated and dominated the astrophysical field.

    Pure mathematicans are not physical scientists. Many have little respect for the rigors and limitations of physical experimentation. As Lawrence B. Crowell put it: Many astrophysical graduates can’t get jobs in astronomy — what do they do — they become computer programmers because of their mathematical skills, so they go to work creating “computer code” which as long as its internally consistent, can be completely arbitrary, yet will work just fine.

    Pure mathematicians have reached the end of their road in astronomy and the road they have built is full of pot holes and structural defects.

    And architect has more connection to and respect for the physical sciences than many astrophysicists.

    Why?

    Because an architect can’t ignore the physical laws of nature unless he wants to see his building/structure collapse.

  27. Chris said;
    “It is quite impossible to create a singularity and the inside face of any event horizon is totally reflective to any photons. You cannot see beyond any event horizon.”

    So are you saying there are photons inside a black hole then? Based on this bold assumption, and reading you past comments, do you think there are magnetic fields too?
    Based on the EU models, then you think at the very centre of the
    black hole is a ‘null-field’ and not any central singularity?

  28. Utter nonsense. When will “scientists” stop using artwork to promote their “theories” and do real science. Garbage, rubbish, utter crap!

  29. It’s interestiong to speculate what might be and to imagine possibilities, but realize this. In time all things are possible, only not all things are probable. I’m sure the radiation around and inside any blackhole would be enough to instantly fry you if you were any where near it.

  30. This article is more scientific fiction presented as scientific fact. There are no measurements that even suggest such conjecture exists. But the authors did get their names publicized … that may well be their objective.

  31. Feenixx,

    “There are some countries where he would go to jail for some of his (to certain groups of people) highly offensive published material! O.K., that’s on subjects other than Physics”

    Like what? That’s a serious accusation.

  32. When it comes to cosmology, sound science has been usurped by abstract math. It seems that most cosmologists these days are better suited at programming video games than doing any real science. Actually, many physicists do become software programmers.
    Math is an important tool, no doubt, but it doesn’t hold the answers to our questions.

    Most of the cosmology articles I read these days sound more like they were written by L. Ron Hubbard, where something purely made up in somebodys head develops a religious following. And woe to those who question their reasoning.

    There is a theory based on sound science utilizing all those wacky things like labs, experiments, comparative analysis and even math. But most of you don’t want to hear about it because you seem to be more comfortable with, and entertained by, science fiction rather than science fact. Even Einstein said “As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality.”
    He also said “”Black holes are where God divided by zero.”
    LOL

    Tesla said something relative to this article:
    “Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.”

    And this:
    “Einsteins relativity work is a magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king… its exponents are brilliant men but they are metaphysicists rather than scientists.”

  33. @anaconda
    Thanks. Isn’t it ironic that skeptics call EU/PC theory pseudoscience yet thoroughly embrace the “science” of what amounts to a video game?

    It’s like thinking one is a rockstar because they’re good at Guitar Hero.
    Or on the other hand, actually being able to play a real guitar for an audience yet knowing that you’re no rock star.
    Illusion vs. Reality.

  34. @ Joe Hanford;

    I’ve read it. Is say sweet nothing of your EU rubbish.

    Why give you a summary when you could understand it nor believe anything it says?

    Note: Looks like yet another EU crackpot has joined the fray! The Thunderbolts.Info managementโ€™s current new plan to discredit current accepted theory and investigation. Expect more of this to come.

  35. OilIsMastery Says:
    “I thought you worship Einstein as an infallible omniscient demigod so how can his analysis be wrong?”

    I worship no one. It is science not religious hocus-pocus via fault dogma and faith. The only analyst whose wrong here is plainly you and your jackass EU nit-wits friends.

    Are you are also member of that ridiculous Dunderheads.Info cult?) I thought it was registered s a fringe religion as a tax dodge. Go figure? Science – you have no clue!

    Note: Looks like yet another EU crackpot has joined the fray! The Thunderbolts.Info managementโ€™s current new plan to discredit current accepted theory and investigation. Expect more of this to come.

  36. To Crumb,
    The sun is absolutely not a nuclear furnace, it is more aptly a florescent light bulb.

    You can stay on the titanic all the way or you can jump off and very cooly say ‘ I always knew EU to be true’

    Current cosmology theory is a disaster. If you don’t see this, than keep on sipping the kool aid. More over arching math will be coming forward soon to prop up the failed theories that you embrace.

  37. Sal, you need to chill out. I’m certainly no fan of EU, PU, EC, AWT , Thunderbolts, etc. I was simply seeking comment on the paper posted with the computer animations, which is what this article is about. What are your views of the related paper?

  38. @40_octaves
    “The sun is absolutely not a nuclear furnace, it is more aptly a florescent light bulb.”

    What? Then how come florescent lights are not hot and shine by a rarefied gas?

    I think when they induced the convulsive therapy with you, they just turned up the current too high!

    Fried brains – that all EU proponents in a nutshell!

    Note: Looks like yet another EU crackpot has joined the fray! The Thunderbolts.Info managementโ€™s current new plan to discredit current accepted theory and investigation. Expect more of this to come.

  39. mr. crumb.

    every thread i have read today in this forum contains you arguing with the “EU” people.
    you’re a long time poster here and respected. why not just let it go? you’re hurting your reputation.

  40. I don’t know what u people are trying to say, its like…a rocket scientist convention explosion in my brain, just like the universe, it’s fun to pretend to understand sometimes eh?

  41. pantzov said
    “every thread i have read today in this forum contains you arguing with the โ€œEUโ€ people.
    youโ€™re a long time poster here and respected. why not just let it go? youโ€™re hurting your reputation.”

    EU continues to be been banned blog site after blog site floor the disruption they cause. They are effective eliminated from Wikipedia in editing, and now they target popular sites of Universe Today or even attack childrens’ sites to spread their almost religious-driven agenda.

    What do you do? Well you could put up with the deception and fraudulent tactic by an organised group, or do something about it. Surgical strikes is exactly how these people work, whose sole aim is to produce sufficient doubt to reject general tenets of science.
    Argue with them and you get non-sensible illogical arguments. You lose.
    Argue with scientific theory or using the scientific method. You lose.
    Argue sensibly, then they attempt discredit you – even off topic. You lose.
    Let them have their way and ignore them, we all lose.

    So should you prefer I just walk away or take the fight to them?

    Until some reasonable form of group moderation, I prefer the latter.

    Thanks for you concern.

  42. It is sad that comments here have little to do with the actual work presented. Some of this is rather interesting IMO. The Reissner-Nordstrom one is has the infinte pulse of light at the second horizon. For a physical black hole, not one which is a classical “eternal black hole,” or a configuration variable on the vacuum, this infinte pulse of light involves all the field theoretic data which composed the black hole. In effect this is in the classical sense the singularity.

    Lawrence B. Crowell

  43. @ND

    Mainly some (but not all) of his writings about health issues, especially his essays about HIV and AIDS.
    Apart from this: many (but not all) of his essays make references to unavailable information, giving rise to the suspicion that he possibly invented it. Citing his work as a source in a paper which will be reviewed by a peer or a teacher is likely to cause problems for the author.

    While many “fringe philosophers and scientists” appear to be involved for commercial considerations, and many more just because it’s “so cool and alternative”, I see David Pratt, motivated (very strangely) by a spiritual path, as dangerous for some groups of vulnerable people.

  44. I realise my last post is totally off topic – that’s why I did not elaborate on the issue when I first mentioned it.
    ND asked for clarification, I would have supplied it in a personal message, if I had a log-in account.
    My apologies to UT.

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