Talk:Hollow Earth/Archive 1

Project Phoenix
The entire section regarding Project Phoenix is being removed. It is a scam, cult, and/or hoax; regardless, wikipedia isn't the place for them to link to a donations page. Their website espouses scientific data that is grossly inaccurate. Its inaccuracy should be apparent even to a virtual laymen, that is, based on the accepted beliefs of the scientific community. If someone outside of the Phoenix Organizations feels it should be reworked into the article, please place it to a vote before reinserting it.

THAT IS AN OPTION AND NOT FACT.

—The preceding unsigned comment was added by 72.150.123.48 (talk) 07:49, 11 December 2006 (UTC).

explanation
I would like it very much if Steven Johnson would explain his comment that the "'topology' argument is sophistry, because [it] can be thought of as a coordinate transformation without physical consequences." Mark Miller


 * From a certain topological viewpoint, a coffee-cup is the "same" as a donut. That doesn't mean we can't distinguish between the two when we have breakfast, because there are physical consequences to the transformation from one to the other.  In the same way, saying that there is a topology-preserving transformation that sends "interior" to "exterior" of a sphere is non-controversial &mdash; but it doesn't mean that we can't distinguish interior from exterior because the physical laws for the "exterior" of the transformed system are different from the original physical laws for the actual sphere exterior.  (Note that I added an explanation to this effect in the article.)   &mdash;Steven G. Johnson 22:06, Oct 22, 2004 (UTC)

Do't the people who follow the Urantia Book believe in some kind of hollow earth, with accesses near the poles? Unless my memory is doing tricks again, they were on the outside and another civilization was on the inside surface. One dubious account has it that Admiral Byrd had found the northern entrance in 1947. A lot of this seems to belong to the fruitcake school of pseudoscience. See http://www.endtimeprophecy.net/~tttbbs/EPN-1/GroupPages/grupufos.htmlEclecticology
 * I know OF the Uranita Book, but don't know if they include a belief in a hollow earth. --Emb021 20:18, 1 February 2006 (UTC)

- Removed the following until somebody who cares makes this NPOV:
 * Martin Gardner discusses a non-falsifiable Concave Hollow Earth Theory in one chapter of his book On the Wild Side. According to Gardner, this theory states that light rays travel in circular paths, and slow as they approach the center of the spherical star-filled cavern. No energy can reach the center of the cavern, which corresponds to no point a finite distance away from Earth in the widely accepted scientific cosmology. A drill, Gardner says, would lengthen as it traveled away from the cavern and eventually pass through the "point at infinity" corresponding to the center of the Earth in the widely accepted scientific cosmology. Supposedly no experiment can distinguish between the two cosmologies. Martin Gardner does not accept the Concave Hollow Earth Theory, and suggests that the man who proposed it may have had religious motives.

"non-falsifiable"!!!! "widely accepted scientific cosmology"!!!! Yikes! --maveric149


 * I can easily imagine Martin Gardner as the central character in a native American trickster myth. This passage makes it sound as though he's having a laugh at the reader's expense. I'm only starting to grasp the Doctrine of Falsifiability, and, as I understand it, a theory that is non-falsifiable falls outside the tentacles of the scientific method.  The behaviour of light in the centre of the cavern gives a picture that is uncomfortable close to the way it behaves in the vicinity of a black hole.  The phrase "widely accepted scientific cosmology" doesn't bother me at all; I see it as nothing more than a convenient way to refer to conventional wisdom. Eclecticology
 * Yeah, I never grasped the difficulty here. But I've removed the first disputed phrase. We'd better keep "widely accepted.." 'cause this theory sure as farg ain't widely accepted. Dan 08:17, 16 Feb 2004 (UTC)

Removed:

''material below moved from "Hollow earth" article: some text that duplicated material already here removed. The rest needs some merging. ''


 * On the inside, gravity pulls things to the center of the mass of the shell. Our "up" is, therefore, their "down". The result: Inner earth people, strange birds and even prehistoric looking mamoths can walk around in the inner forests, lakes and rivers. There is, in some accounts, a central "dusty" sun that provides heat and light to this inner paradise. If true, there would be no night inside. Large entrances may be found somewhere around the north and south poles.

What makes modern science say the earth has a core of molten rock and metal? This article looks at various claims of the hollow earth theory including the science as if the earth is a small naturally occuring (?) Dyson sphere. (A Dyson sphere is an artifical shell built around a star.)

- is there any relation between Hollow earth and Agarthi?

--Yak 00:21, Feb 20, 2004 (UTC)

To a degree. The idea of 'hollow earth' is sometime extended to include the idea of large, inhabitable cavern world(s) under the earth's crust, which would include Agarthi. --Emb021

The article states ...direct observation refutes it... Perhaps I am not so observant because I see no direct observation that refutes the theory. 71.37.95.27 18:01, 6 October 2006 (UTC)

Recent revert
Disagreeing with one change is no justification for reverting all of them. That's rude and counterproductive--save reverting for vandalism. Edit selectively: shift the offending paragraph and leave the inoffensive changes alone. FWIW, I disagree about that move--I think that the fact that the Hollow Earth has been declared pseudoscience and has few or no current adherants has been expressed up front, which is enough to keep people from succumbing to belief in bogus theories. I think it makes more sense, and certainly reads better, to begin with descriptions of the colorful theories rather than the explanation about why these theories can't be true. The article really isn't about science. Also, when you do explain the science that refutes these views, you (or someone) might want to add a sentence about what is known of the earth's interior. --BTfromLA 05:52, 24 Jan 2005 (UTC)


 * The idea that you could stand on the inner surface of a hollow world is still a widespread misapprehension, so it is both important and interesting to counter it upfront&mdash;it changes one's whole conception of hollow Earth theories even as a matter of fantasy.  Saying that the Earth isn't hollow (an experimental fact, but not a physical law per se) has nothing to do with this fundamental misunderstanding of gravitation.  The only other change you made was to cosmetically alter the first paragraph (and to insert spelling and grammatical errors)&mdash;I didn't particularly care for these alterations (e.g. it's not clear to me that there were ever "scientific" claims of a hollow Earth in any meaningful sense of the word), so I didn't see any point in keeping them. &mdash;Steven G. Johnson 07:58, Jan 24, 2005 (UTC)


 * "Scientific" claims (however you'd care to phrase that) are a necessary condition for pseudoscience. --BTfromLA 04:52, 25 Jan 2005 (UTC)

500 miles thick?!

 * Edmund Halley in 1692 (Philosophical Transactions of Royal Society of London) put forth the idea of Earth consisting of a hollow shell about 500 miles thick . . . In 1818, John Cleves Symmes, Jr. suggested that the Earth consisted of a hollow shell about 800 miles (1,300 km) thick . ..

500 miles is in the same order of magnitude as the distance from London to Dublin. It's maybe a third the width of Europe. Surely no one could have been so ignorant as to propose such a width? &mdash;Simetrical (talk) 10:48, 29 July 2005 (UTC)


 * Sorry, maybe I'm just dense but if you're going to believe that the Earth is hollow anyway, why should you worry about figuring out logical dimensions? 209.7.198.2 15:19, 1 August 2005 (UTC)

Because while maybe you'd find it plausible that the Earth is hollow a few hundred years ago&mdash;after all, who'd actually dug below a few hundred feet?&mdash;basic arithmetic has been known for quite some time.

Oh, and by the way, please sign and date your messages by typing four tildes: ~. This makes it easier to keep track of who's saying what in a conversation. Thanks, and welcome to Wikipedia! &mdash;Simetrical (talk) 04:13, 2 August 2005 (UTC)

It seems to me that this is irrelevant. All that matters is whether or not Edmund Halley put forth the idea or not. If you have solid evidence that he didn't; then I suggest you edit the article to reflect the facts. --JiFish(Talk/Contrib) 11:23, August 2, 2005 (UTC)

Evidently, a planet-sized body cannot rely on bending stiffness of the outer shell to maintain its shape under gravitational attraction, so presumably shape would be maintained by internal gas pressure, rather like a soap bubble. If, as appears to be claimed, the interior vents to the atmosphere, the pressure must be equal to sea level pressure on the outside. The absence of a gravitational field within the interior implies an absence of hydrostatic pressure, so the pressure must be uniform throughout at about 10^5 N/m^2. The pressure is presumably balanced by tensile stress in the crust, having a maximum stress of about 3×10^6 N/m^2. Balancing the pressure force and tension in the skin, we have, for the thickness:
 * $$t=\frac{pR}{2\sigma}$$

where R is the radius of the Earth (≈6.37×10^6 m), p is the gas pressure and $$\sigma$$ is the maximum tensile stress of the surface rock. This yields a thickness of 106km. Based on the idea of a soap bubble, the 500-1000km estimates aren't too bad.

This is clearly nonsense, because there is no evidence that the surface rock is everwhere in tension. The pressure would be the same either side of the crust so there can be no net pressure force acting on the shell. Without some excess of internal pressure over external, the bubble will simply collapse - end of story.Gordon Vigurs 11:15, 27 July 2006 (UTC)

Regardless of if you think it is nonsense or not, real scientists (unlike yourself) due subscribe to this theory. Something may not be widely accepted and still be right. Fact of the matter is, Congress wouldn't have funded Admiral Byrd's expeditions to Antarctica/North Pole had there not been something there to address. America wasn't the only country interested in finding out about these areas as well. 129.21.144.217 16:24, 27 October 2006 (UTC)

Jules Verne
Verne never argued fr a hollow earth, rather his book deals with an earth penetrable to far greater depths than hitherto believed, and with the existence within the earth of immense cavern pockets capable of sustaining breathable atmosphere at surface temperatures, with flowing water, vestigial weather, and independent bio-mass. --SockpuppetSamuelson 10:59, 15 August 2005 (UTC)

Depends on how you use the term "hollow earth". Some writers speak of 2 basic 'hollow earth theories'. The 'liberal theory', which postulates the idea of the earth being a hollow shell with a mini-sun at the center; and the 'conservative theory', which postulates large, habitable caves, in the earth's crust. Verne's work, as well as the ideas of Agharta, Shaver, etc, falls into this later group. --Emb021


 * How do partisan politics play into this discussion? Sorry if I am ignorant but I don't understand the use of "liberal/conservative" to describe these theories.Stovetopcookies 23:03, 7 November 2006 (UTC)
 * What does partisan politics have to do with the terms liberal and conservative? Liberal=open-minded, generous. Conservative= avoiding excess, cautious. yeah, those terms seem to fit here all right. Rihk 03:32, 10 November 2006 (UTC)

Gravity
"Newton's law of gravity mathematically implies a gravitational force of zero everywhere inside a spherically symmetric hollow shell of matter, regardless of the shell thickness"

My understanding is that the net effect of gravity would only result in a zero force at the exact center of the sphere.


 * Your understanding is wrong; the force is zero anywhere inside the sphere. (This is a classic freshman physics problem, by the way.)

Also, "regardless of the shell thickness" is an issue. For a simple example, assume that the earth has a small hollow in the center (a bubble in the inner core, for example) of one km in diameter. We wouldn't even notice the difference, not would miners who dig down in to the crust.


 * We wouldn't notice the difference outside the sphere. However, inside the bubble, which is what the article describes, the gravity would be zero. &mdash;Steven G. Johnson 15:01, August 17, 2005 (UTC)


 * ... If the bubble has the same center as the Earth. Otherwise, there would be some gravity.--Bloodstained Agar 09:31, 29 November 2005 (UTC)

It wouldn't be a spherically symmetric hollow shell otherwise, now, would it? &mdash;Simetrical (talk) 01:37, 30 November 2005 (UTC)

Gravity should be away from the center towards a concentric sphere ad infinitum
The gravity should be outwards inside the sphere towards a cocentric circle around the center. The gravity should be away from the center. The 'heaviest part' of the earth should be a smaller sphere sharing the same center. The size could perhaps be computed by moment of inertia? but this is for inertia. (moment for gravity?)--Jondel 02:28, 30 November 2005 (UTC)


 * Nope. —Steven G. Johnson 02:46, 30 November 2005 (UTC)

If you are dead center, you'd float. At the surface of the bubble you could stand(?)--Jondel 02:50, 30 November 2005 (UTC)

Shouldn't the gravity vary from zero at the center and increase towards the bubble surface and 'under ' the bubble surface towards the co-centric sphere?--Jondel 03:00, 30 November 2005 (UTC)


 * Nope. In a concentric spherical bubble within a spherical mass, the gravity is zero everywhere within the bubble.  (This is a standard freshman physics result and can be found in many undergraduate textbooks.)  —Steven G. Johnson 03:42, 30 November 2005 (UTC)

OK. Thank you for replying. Then, a little above the bubble surface, things should float (0 g)? At the bubble surface or just below, things have weight (?) they rest, or fall away from or towards the center(?). I hope I'm not taxing your patience. --Jondel 04:11, 30 November 2005 (UTC)


 * Inside the bubble, things float. Outside the bubble, gravity pulls towards the center of the sphere. —Steven G. Johnson

And if you're only partway inside the bubble, gravity would apply proportionally. If your feet were an inch into the inner surface of the sphere, for instance, a tiny little bit of net gravity would be exerted on them. If all of you was below the surface (where the outside of the sphere is understood to be "down"), the gravitational pull would be greater. If you were entirely outside the sphere, you would be pulled toward it. Of course, the precise amounts of force would depend on the masses and distances involved. &mdash;Simetrical (talk) 04:12, 1 December 2005 (UTC)

Has the shell theorem, or any such "standard freshman physics result," been demonstrated empirically anywhere? Or is this simply "utextbook physics" of a theoretical nature, that undergraduates are expected to memorize? —The preceding unsigned comment was added by Gordon_Vigurs (talk • contribs) 2006-07-26 04:55 (UTC)

Whilst I agree with the sentiments, this wasn't my comment Gordon Vigurs 09:31, 27 July 2006 (UTC)

Since I have been accused of making a comment, I think I shall do so. The 'freshman exercise' considers the force on a particle within the spherical shell. The problem is symmetrical about a line joining the centre of the shell to the particle, so we only need to consider the component of gravitational force in this direction. This is made up of the attraction of infinitesmal annular rings centred on this axis. Integrating over the whole sphere, the result is zero net force everywhere within the spherical shell. Now, although the particle remains in equilibrium under the gravitational attraction of the shell, the individual infinitesmal parts of the shell experience a net force of attraction in the direction of the particle. We cannot seriously invoke elastic forces to hold a planetary-sized object's shape, so what is it that keeps the shell intact? By implication, the shell cannot be stable. Gordon Vigurs 18:12, 28 July 2006 (UTC)

How might one go about testing or demonstrating the shell theorem? Does the weightlessness result depend on perfect concentricity and/or the centrality of the hollow? If I go into a cave, or if I dig a hole in the ground and make it nearly a perfect bubble, why am I not necessarily weightless? I have dug a fairly large underground hole that was close to being spherical but I did not float. I have also visited many caverns without ever floating. What part of the theory am I misunderstanding? 160.253.0.248 21:09, 5 December 2005 (UTC)


 * The hole has to be at the center of the earth&mdash;the theorem only applies to concentric spherical shapes&mdash;so I doubt any of the caves you've visited go that deep. =)  The shell theorem is pretty central to the description of planetary motion and many other gravity-related phenomena (and equivalent results appear elsewhere, e.g. in electromagnetism), so yes, it has been extensively tested.   —Steven G. Johnson 22:31, 5 December 2005 (UTC)

The point is that if the hole is at the center of the Earth, there's equal mass in all directions, so gravitational pull is equal in all directions. Intuitively, you might think that you should have to be in the center of the hole as well; however, if you do the math, you'll figure out that in fact this isn't the case. And yes, Newton's law of $$F_g = \frac{M_1M_2G}{D^2}$$ has been empirically proven to be an excellent approximation of gravitational force when you're reasonably far away from massive objects such as stars. Obviously no one has made an enormous planetlike shell and tried to float in it, but the result of zero gravity inside a shell is a straightforward result of Newton's law (I don't know the exact proof offhand, but I'd guess it involves a fairly basic application of definite integrals). I'm not quite sure whether the same result holds true if the shell has an impossibly great density, such that relativity would be the only way to get accurate measurements of the gravitational attraction, but I'd guess it would—possibly Steven here knows.

The weightlessness theorem only applies perfectly to situations where the concentricity and sphericity are perfect (and where no other masses exist). It applies imperfectly to imperfect situations, with the imperfection of the result proportional to the imperfection of the setup. If you dig a hole, the imperfection of the setup is near-total (concentricity is completely out the window, by a factor probably of millions), and so the results are equally imperfect (negligible reduction in gravitational pull). &mdash;Simetrical (talk) 05:10, 6 December 2005 (UTC)


 * Does the theorem have any requirements regarding motion by the sphere, like, say, Earth's daily rotation? Also, how would all this relate to a situation like the climactic scene of Contact, in which Ellie is weightless inside the sphere, but her chair isn't because it's attached to the sphere itself? (Did they get it right?) —Darrell M. 144.81.62.177 18:44, 15 December 2005 (UTC)


 * The theorem has nothing to do with motion. (In Newton's model of gravity, gravitational force changes instantaneously as masses move around, so only the relative positions matter.  This is modified by general relativity, but the corrections are probably negligible here.)  Rotation does introduce centrifugal forces if you rotate with the surface, as mentioned in the article, but these are pretty small (1/300 of Earth gravity at the equator).  I haven't seen Contact, so I have no idea about the scene you describe.  —Steven G. Johnson 21:33, 15 December 2005 (UTC)


 * About the scene in Contact: First of all, there's no way that the mass of the spherical pod could possibly have enough mass to exert noticeable gravity, even if the spherical-shell theory is assumed to be incorrect. Secondly, the pod itself is an advanced artifact that appears to open wormholes, so it must itself have a very bizarre gravitational field when running. If you've got gravity control, there's nothing to say you can't bend it so the perceived gee is zero for a five foot wide interior of the pod and 20g for one inch away from the skin. Further discussion of this probably belongs in Talk:Contact_(film)... or outside WP altogether. --Rpresser 16:58, 27 July 2006 (UTC)

BTW, there are many discoveries that the center rotates faster than the earth surface. I can find sources on the web. Please watch Contact starring Jodie Foster.--Jondel 08:28, 16 December 2005 (UTC)


 * That's for the real Earth. We are talking about the fantasy Earth of a rotating rigid shell. —Steven G. Johnson 18:17, 16 December 2005 (UTC)


 * How stable is a hollow shell, which is so large that elastic forces are negligible, under gravity? Gordon Vigurs 08:55, 26 July 2006 (UTC)


 * How can an object larger than, say 100km across, possibly be rigid? It must be made of solid unobtanium! Gordon Vigurs 14:01, 29 July 2006 (UTC)


 * Or Skrith? Lance Tyrell81.145.241.242 (talk) 16:43, 6 January 2008 (UTC)

Centrifugal force
Would not the centrifugal force of the earth's rotation result in a gravitational force inside the sphere toward the wall of the "bubble" as it has been previously called? It would appear to me that the gravitational force would be at its maximum at the equator because that is the area of the highest linear velocity, and the gravitational force would decrease dramatically as one gets closer to the poles. Stovetopcookies 23:05, 7 November 2006 (UTC)\

--==__==--


 * -- Well, considering Newton was talking about a completely enclosed space, how does this support the fact? The earth is not a bubble, there are ways to enter through the "holes at the poles"; therefore, the earth is not a complete sphere. Instead, the earth is a pseudo-sphere (for the lack of a better term). My pseudo-sphere has a regular spherical body, but a semi-straight cut at the poles: Like the circular beads of a necklace. Would this not be enough to leak some atmosphere in, just as well, atmospheric pressure would be taken into consideration. Atmospheric pressure varies depending on how close or how far you are away from the earth. So, if we are to believe in nature and all the natural things that happen: ie, tornadoes, earthquakes, plate techtonics, and mountains, then pressures would vary inside the earth as well. This pressure would also create enough of a wind, and with wind you need weights, weights would lead to some sort of gravity (probably in an incorrect order); therefore, the earth potenially has gravity within. Remember, bubbles have no holes: the earth does. I do agree if the earth was completely and utterly enclosed that Newtons law would apply; however, I do not believe it does in this case. Besides, this is just a small piece of the theory puzzle. From my understanding, and forgive my ignorance by omitting this comment in its entirety, the atmosphere is what is keeping us from being flung out into the open space is it not? Therfore with a misdirection (for the lack of a better term) of the atmosphere not containing the effect that it would on the outside since we are dealing with the inside that is shielded by the earths crust, would that not pull toward the surface? How would we really be able to tell, the systems (atmospheric pressure, gravity, etc.) in which we are dealing with are so large. Consider this to be against the "freshman physics problem". :citation needed?:

P.S.- Would size and rotational speed not play a role in smaller models when taking into consideration atmospheric pressure, or would they not sustain the requirements for any atmosphere at all to be present? If no sustainable atmosphere, then one has to uderstand that the earth does have one, bubble or not, gravity would have to apply. Furthermore, in this open space (space) how can we actaully tell how fast we are moving when we have no stationary objects to measure from? The Earths rotational speed could only be a comparison to the speeds of other objects that are also moving around in space. 66.79.234.139 08:39, 11 January 2007 (UTC) John


 * "I do agree if the earth was completely and utterly enclosed that Newtons law would apply;" Stop. The "shell theorem" would not apply, but there is no reason that Newton's laws wouldn't. The Hollow Earth look like a bubble, so its gravitiy look like the bubble's one. There would be some special effects near the hole, for sure (for exemple, one could fall through the pole's hole, but after a while inside the bubble, it would just float.) I don't know exactly what would happen in this Hollow Earth, but I doubt that it would just work as easy.Kromsson 20:06, 6 July 2007 (UTC)


 * "the atmosphere is what is keeping us from being flung out into the open space is it not?" Nope. Further more, Archimede thrust lifts everything a bit, and it is caused by the weight of the atmosphere.Kromsson 20:05, 6 July 2007 (UTC)

Requested move
Hollow Earth → hollow earth – Capitalization fix.

Survey

 * Add *Support or *Oppose followed by an optional one-sentence explanation, then sign your opinion with  ~


 * Support. jareha (comments) 01:05, 29 April 2006 (UTC)

Read ETIDORHPA

Discussion

 * Add any additional comments

So what exactly is wrong with the current spelling? Article names normally begin with a capital letter, and Earth in this case is the name of the planet and is thus properly capitalised as well. int19h 05:13, 29 April 2006 (UTC)
 * You're right, I'll withdraw this request. Not sure why I blanked and thought Earth should've been "earth". Must've been the lowercasing of hollow earth in the first paragraph that threw me off. That said, we should fix the rather schizophrenic capitalization of the phrase throughout the article. jareha (comments) 05:48, 29 April 2006 (UTC)


 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Voyage hollow Earth
Under External Links, there is a reference to http://www.voyagehollowearth.com/, Journey to the North Pole and Beyond - 24 day Trip, June 26, 2006 - July 19, 2006. Expedition aboard the IceBreaker YAMAL.

Checking the indicated link shows that the date is 2007 in stead of 2006.

Either the Date in this article is wrong, or the date has been changed on the external website in the mean time. This would make that website look like a fake.


 * I just went there and I got a message saying the site is no longer active. And I wanted to go, too.  )-:  Stovetopcookies 23:29, 7 November 2006 (UTC)

Fictional Worlds based on the Hollow Earth
I am deleting this section, whose present contents were:
 * Dinotopia
 * Hyrule (Legend of Zelda)
 * Land of Oz (Wizard of Oz)
 * Middle Earth (Lord of the Rings)
 * Mushroom Kingdom (Super Mario Brothers)
 * Narnia
 * Zion (The Matrix)

I find no connection to any of these worlds and the Hollow Earth theory. Dinotopia is an island, the Hyrule page give no such indication, Middle Earth was not located in the Earth's interior, etc. --Ogdred 22:15, 8 September 2006 (UTC)

I agree, especially concerning the Hyrule reference. I was like "what!?" At the very least, I could give the benefit of the doubt and think of Termina, the other fictional Zelda world. My reason being that the beginning of the game features enormous, seemingly bottomless caverns that could conceivably be a hollow earth.

Narnia was a parallel universe accessible through a wall behind a bookshelf, if I remember correctly. As for Dinotopia, I do beleive it was referred to as an island, but I suppose the misconception could arise from Jules Verne's Journey to the Center of the Earth in which there were large caverns where dinosaurs still lived.

Stovetopcookies 23:13, 7 November 2006 (UTC)

Should that television commerical where the Dodge Nitro drops through the earth, passing by fantasic underground worlds, ending up at an asian village, be included?

If memory serves, Dinotopia was an island on the INNER SURFACE of the earth. In the book, of course; te movie was corrupted to near unrecognizability. —Preceding unsigned comment added by 209.78.16.118 (talk) 01:12, 24 March 2008 (UTC)