When researchers reanalysed the gold-standard data set of the early universe, they concluded that the cosmos must be "closed," or curled up like a ball. Most others remain unconvinced.
A provocative paper published today in the journal Nature Astronomy argues that the universe may curve around and close in on itself like a sphere, rather than lying flat like a sheet of paper as the standard theory of cosmology predicts. The authors reanalysed a major cosmological data set and concluded that the data favours a closed universe with 99% certainty — even as other evidence suggests the universe is flat.
The data in question — the Planck space telescope's observations of ancient light called the cosmic microwave background (CMB) — "clearly points towards a closed model," said Alessandro Melchiorri of Sapienza University of Rome. He co-authored the new paper with Eleonora di Valentino of the University of Manchester and Joseph Silk, principally of the University of Oxford. In their view, the discordance between the CMB data, which suggests the universe is closed, and other data pointing to flatness represents a "cosmological crisis" that calls for "drastic rethinking."
In your opinion, which shape is more likely ?
(Score: 2) by DannyB on Tuesday November 05 2019, @03:17PM (3 children)
Didn't we get data sets of the early universe off the gold standard?
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(Score: 1, Funny) by Anonymous Coward on Tuesday November 05 2019, @03:51PM
Alas, data will confirm that much like US gold reserves [campaignforliberty.org] the universe is almost entirely empty.
(Score: 1, Funny) by Anonymous Coward on Tuesday November 05 2019, @05:55PM
That would explain its endless expansion (inflation) ...
(Score: 0) by Anonymous Coward on Tuesday November 05 2019, @09:13PM
Yes. It's off the gold standard and is now a fiat universe.
(Score: 1) by fustakrakich on Tuesday November 05 2019, @03:25PM (17 children)
Oh jeeze! As if the flat earthers weren't enough trouble.
The universe is just a big fluffy cloud, looks like a rabbit
La politica e i criminali sono la stessa cosa..
(Score: 5, Funny) by DannyB on Tuesday November 05 2019, @03:32PM (14 children)
The universe is a large sphere with the stars affixed to its inside.
The earth is a large flat disk in the center of the universe.
The sun and moon move in a circular pattern around the top of the disk.
The earth is on an infinite stack of turtles.
(it's turtles all the way down)
The final turtle of that infinite stack is propelled by a rocket.
The rocket moves at 9.8 m/s^2 giving us the illusion of gravity.
The rocket is powered by a perpetual motion machine so it never stops.
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(Score: 4, Informative) by DannyB on Tuesday November 05 2019, @04:08PM (3 children)
Silly skeptics would ask: how do you explain that the sun moves South in the winter?
Stupid Round Earther: the sun moves South in the winter for the same reason that birds move South for winter -- because it's warmer in the South during winter! Look at Australia where Christmas is hottest day of the year.
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(Score: 2) by JoeMerchant on Tuesday November 05 2019, @07:21PM (2 children)
The turtles have a cyclic, seasonal behavior that affects the sun's track across the sky.
The planets are even better following those crazy looping courses.
🌻🌻 [google.com]
(Score: 2) by DannyB on Tuesday November 05 2019, @07:36PM (1 child)
Epicycles.
Not the same as bicycles.
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(Score: 2) by MostCynical on Wednesday November 06 2019, @07:45AM
Hurts to ride an epicycle
"I guess once you start doubting, there's no end to it." -Batou, Ghost in the Shell: Stand Alone Complex
(Score: 1) by fustakrakich on Tuesday November 05 2019, @04:20PM (8 children)
You know you really had me, up until:
The final turtle
La politica e i criminali sono la stessa cosa..
(Score: 2) by DannyB on Tuesday November 05 2019, @05:05PM (2 children)
But not the perpetual motion machine?
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(Score: 1) by fustakrakich on Tuesday November 05 2019, @05:43PM (1 child)
Sorry 'bout that. I dismissed out of hand everything after the "final turtle", but I can believe in perpetual motion, it's the perpetual stillness that's impossible.
La politica e i criminali sono la stessa cosa..
(Score: 0) by Anonymous Coward on Tuesday November 05 2019, @06:30PM
Never say impossible, without a crapload of evidence to back that up.
(Score: 2) by maxwell demon on Tuesday November 05 2019, @06:31PM (4 children)
What's the problem? There are infinitely many turtles, and then one more, the final turtle.
And yes, the concept "infinitely many and then one" is actually mathematically sound; it's the ordinal number ω+1.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 0) by Anonymous Coward on Tuesday November 05 2019, @07:29PM (1 child)
That's why we have to be nice to Mitch.
(Score: 2) by DannyB on Tuesday November 05 2019, @09:47PM
Maybe they're mirrored infinite reflections of the final turtle? But not Mitch. The mirrors would break.
"Minbari... Pale; bloodless. Look into their eyes and see nothing but mirrors-infinities of reflection." – A Soul Hunter
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(Score: 2) by DannyB on Tuesday November 05 2019, @09:40PM (1 child)
How about infinitely many, minus one.
Maybe you remember Jack Valenti?
He was the Motion Picture Ass. Head of America back in the day. When VCRs came out, he is the one famous for saying that the VCR is to the motion picture industry what the Boston strangler is to the woman alone. (Nevermind that VCRs became a HUGE source of income from movie rentals soon after.)
In the time soon after Napster became a thing, and about during the Gnutella daze, Jack said that copyright length should be infinite. Forget the Sonny Bono act extending copyright length. But the constitution says "for limited times", so Jack proposed that copyright be "forever minus one day".
What a jackass.
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(Score: 2) by maxwell demon on Tuesday November 05 2019, @10:47PM
Great description. ;-)
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by dry on Wednesday November 06 2019, @06:59AM
You're forgetting the Elephants.
(Score: 0) by Anonymous Coward on Tuesday November 05 2019, @07:26PM
Oh shit, that means Microsoft Azure fees.
(Score: -1) by MyOpinion on Wednesday November 06 2019, @12:21PM
.. so you can prove that the Earth is "a space globe" then.
Right?
Truth is like a Lion: you need not defend it; let it loose, and it defends itself. https://discord.gg/3FScNwc
(Score: 5, Insightful) by DannyB on Tuesday November 05 2019, @03:27PM (45 children)
Suppose the 2D flatland universe were curved in some invisible 3rd dimension into a sphere. There are two things that would be observable to flatlanders.
1. If you travel in a straight line, you will go in a "great circle" of the universe, and once you're all the way "around" the universe, you end up where you started. (sort of like politicians)
2. Put three space stations far apart, with lasers between them, forming an equilateral triangle. The angles of the two laser beams at each space station should be 60 degrees. But if the universe were curved in some invisible 3rd dimension, the angles would always be greater than 60 degrees. Because the triangle is on the surface of a sphere. Although the 3rd dimension of the sphere is not directly observable to the flatlanders. In fact, if you move the three space stations far enough apart, the angles could increase from 60 degrees to 90 degrees. Using coordinates of the Earth just for illustration, suppose one station is at the North Pole. Another is at the Equator at the prime meridian 0 degrees longitude and 0 latitude. And the other station is on the Equator at 90 degrees longitude. A triangle formed from these three points will have a 90 degree angle at each angle of the triangle.
So if our universe is curved in some un-observable 4th dimension, the same observations should apply.
Now it seems unlikely that we can travel in a great circle all the way around the universe. A telescope cannot see all the way around, because it can only see to the 13.7 billion light year limit, if the universe is 13.7 billion years old, and the universe is larger than 13.7 years (which it would be if we can see to 13.7 billion light years in opposite directions.
But we might be able to do the three space stations experiment. But the stations would have to be light years apart (maybe?). And the angle would be greater than 60 degrees -- but would be enough greater that we could reliably measure it? Doubtful IMO.
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(Score: 0) by Anonymous Coward on Tuesday November 05 2019, @03:33PM (13 children)
What if we are on the inside of the sphere? Not trying to detract from you points which are very fun to think about. Just trying to add a little nuance.
(Score: 3, Informative) by Immerman on Tuesday November 05 2019, @04:05PM (12 children)
The inside *is* the outside - the "sphere" is a two dimensional surface that you're embedded within.
If you mean inside the volume of the sphere - then you're talking about a being that is no longer a 2D flatlander and is capable of existing in 3D space - and that's not really relevant to us flatlanders unless it decides to interact with us and the 2D universe we exist in (and we'd have a devil of a time trying to make sense of it if it did)
(Score: 2) by DannyB on Tuesday November 05 2019, @04:51PM (8 children)
I like it: the inside is the outside. It is a 2D "surface" of the sphere. Just as our universe is a "3d surface" of a 4d sphere.
A 3 dimension being (like us) could pick up a left shoe from the surface of the 2d flatland, and then lay that shoe back down into the flatland universe "flipped over" making it a right shoe now!
A 4 dimensional being could pick up a person from the "3d surface" of our universe, and then put them back onto the "surface" of our universe flipped over. You would be your mirror image. Everything to you would look flipped. All of your molecules would be the "left hand" reconstruction from the same atoms. Could you digest ordinary "right handed" food? (google for left handed sugar)
A 3d person would have omniscient view of the 2d flatland universe. You could see inside of a closed safe. You could take the yolk out of an egg and put it back into the universe but outside of the shell.
Now I will point out something. Make of it what you will.
Job 11:7-9 [biblegateway.com]
Four dimensions.
Eph 3:17-19 [biblegateway.com]
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(Score: 1) by fustakrakich on Tuesday November 05 2019, @06:17PM (3 children)
That's cheating. They're putting two dimensions on the vertical axis. Trying to separate heaven from hell maybe?
La politica e i criminali sono la stessa cosa..
(Score: 2) by maxwell demon on Tuesday November 05 2019, @06:46PM (1 child)
They are doing 3D typography. You know, for letters, you have one width, but both a heigh above and a depth below the baseline. In 3D typography you obviously get another dimension, the length.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 1) by fustakrakich on Wednesday November 06 2019, @12:13AM
Oh yeah, baseline -> firmament. The other axes don't have that divider
La politica e i criminali sono la stessa cosa..
(Score: 2) by DannyB on Tuesday November 05 2019, @09:33PM
Maybe they just didn't have words to describe that many dimensions. Would we? Would such a writing translate well into another language thousands of years later? Especially Job which is much older.
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(Score: 2) by Azuma Hazuki on Wednesday November 06 2019, @03:16AM (1 child)
"Sufficiently advanced demons and/or aliens are indistinguishable from God." Think about that for a bit.
I am "that girl" your mother warned you about...
(Score: 2) by GreatAuntAnesthesia on Wednesday November 06 2019, @11:29AM
Look to Windward, Iain M Banks, 2000.
(Score: 0) by Anonymous Coward on Wednesday November 06 2019, @03:36AM (1 child)
high/deep is the same dimension ackshually
(Score: 2) by DannyB on Wednesday November 06 2019, @04:52PM
Would you have words to name four dimensions in a simple way?
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(Score: 0) by Anonymous Coward on Tuesday November 05 2019, @08:50PM (2 children)
Oh sure I guess I was just thinking what would it be like if we could measure something like an on average positive or negative curvature. If there was an on average positive or negative positive curvature I think that to mean we would be on the inside or the outside but not both. Oh, and yes I understand that the idea was that we are in the surface if a shphere not just someplace inside the clolume of it.
(Score: 2) by DannyB on Tuesday November 05 2019, @09:31PM (1 child)
If we measure a curvature, in what way is it "positive" or "negative".
Mariner 9 was a spacecraft to Mars long ago. Communication is along a straight line between Earth and Mariner 9. Due to planetary motion, that straight line eventually gets nearer to the surface of the sun. As it does, the "ping time" between Earth and Mars (eg Mariner 9) gets longer. The gravitational field of the sun warps the space. Eg, it is curved in another dimension. We can't see it in our 3D space. But we can tell that there is more "space" there because of the longer ping time. Is that space a "hill" or a "valley" in the 4th dimensional space? Can it possibly matter? Or does the question even make sense.
On flatland, suppose there were a hill in the surface. Suppose Flatlanders mark two points A and B on opposite sides of that hill. Now the flatlanders cannot see or perceive this hill in any way. But if the hill is sufficiently high, they can observe that movement from A straight to B (going over the hill) takes longer than going on a curved path (avoiding the hill) and arriving at B. In other words going "out of your way" from A to B is actually shorter than a straight line from A to B. By careful measurements, flatlanders could map out a circle around this "hill" or expanded space.
Similarly if we observed such a phenomena, we could map out a sphere around which any travel through that region is actually a longer path than going around the sphere. And if the "hill" or "valley" were infinitely tall/deep, then it is really just a black hole. If you try to make a straight line through that spherical region, there is so much space that you never make it across. If you stretched that tall hill around and merged it into another tall hill from some other part of the universe, you have a wormhole. And since this is space-time not just space, you could join the other end to another point in time as well as space. There are more than just 4 dimensions. One of the "spacial" dimensions is time.
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(Score: 2) by Immerman on Wednesday November 06 2019, @02:24AM
The inside and outside of a sphere both have positive curvature, negative curvature is not so straightforward.
A plane has zero curvature - simultaneously shoot two projectiles (in frictiononless vacuum, etc) parallel to each other across the surface, a short distance apart, and their paths will forever stay the same distance apart
A sphere has positive curvature - do the same thing, and the paths of the projectiles will eventually cross
A hyperbolic "saddle" has negative curvature - do the same thing, and the paths of the projectiles will diverge
Hyperbolic space is profoundly weird. As a visualization aid of 2D hyperbolic space, some projections of hyperbolic space onto a flat plane as drawn by Escher, using one of the more common mathematician's visualization transforms: http://www.josleys.com/show_gallery.php?galid=325 [josleys.com]
The figures are all the same size, but there's an infinite distance between the center of the circle and the rim. If you were to follow parallel lines extending from each side of the black X, you will see that the farther you travel, the more figures there are that can fit between the lines - the more space there is between those lines. And that's true no matter where in the drawing you start - all points in space are still equivalent, the center point is just where you happen to be looking from.
I've heard that hyperbolic space can actually be useful for describing some aspects of Relativity, but I don't really know anything more about that.
(Score: 2) by mhajicek on Tuesday November 05 2019, @03:36PM (3 children)
Another thing, there would be a lensing effect on very far away objects, making them appear larger. At the extreme, a star at the opposite position would appear in every direction, like a cosmic background.
The spacelike surfaces of time foliations can have a cusp at the surface of discontinuity. - P. Hajicek
(Score: 2) by ikanreed on Tuesday November 05 2019, @03:41PM
The unstated assumption of that being that the "opposite" point is within our lightcone.
(Score: 4, Informative) by DannyB on Tuesday November 05 2019, @04:20PM (1 child)
Making that easier to grasp, from the North pole, you would see the South pole no matter what direction you looked. If you had a telescope that could see halfway around the universe. But the light from that part of the universe may have not, and in fact may never, reach us.
Another thought. If the universe is expanding, think of it as though the sphere is like a balloon being inflated. No matter where you are on the sphere, all other galaxies appear to be moving away from you. If it were not so, then only from Earth would all other galaxies appear to be moving away from us. But from elsewhere, you would not observe that ALL galaxies are moving away. If it turns out that all galaxies are moving away, no matter where in the universe you observe from, then clearly the sphere of the universe is being inflated. Or rather, it is the space that is expanding -- stretching things in it. (It's 3D space curved into a 4D sphere. We are unaware of the "curvature" in a hidden dimension unless we measure it.)
If the space stretches things in it, then consider this. The Big Bang was the sphere of the universe (in a higher dimension than 3D) expanding. That is why the space is still stretching. The Big Bang must have been the brightest thing in the universe. So why don't we see this brilliantly bright light when we look anywhere in the sky? Because as the space has stretched for 13.7 billion years, those waves of light have also stretched -- making them have a longer wave length and thus lower frequency -- to be observed as the cosmic microwave background radiation.
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(Score: 4, Informative) by maxwell demon on Tuesday November 05 2019, @06:53PM
Well, we don't really see the afterglow of the big bang, we see the afterglow of the phase where the plasma got cold enough to form atoms, that was about 380 thousand years after the big bang. When the universe was filled with plasma, it wasn't transparent, so no light from the actual big bang is left.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by ikanreed on Tuesday November 05 2019, @03:36PM (10 children)
I have an objection to your analysis of seeing "all the way around". Namely that light intensity in flatland would follow an inverse linear relationship with distance(akin to our inverse square law) and would fade to imperceptible at... some unspecified distance, presumably smaller than the universal sphere we're inventing.
(Score: 2) by DannyB on Tuesday November 05 2019, @04:25PM (4 children)
Light fades to imperceptible because fewer and fewer photons reach the telescope.
Suppose someone were to expose a camera with its shutter open for a long time to a dark part of the sky which has no stars or light? Wouldn't you gradually collect an image? It's not that the photons cease. It's just that there are fewer and fewer of them. But if you were to collect them for a long enough time, you might form a Hubble Deep Field image.
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(Score: 2) by ikanreed on Tuesday November 05 2019, @04:40PM (3 children)
That's where the classic problem of "the signal is less than the variance in the noise" arises where even the most thorough statistical methods only give you "Maybe there's something?" even with large durations of observation.
(Score: 0) by Anonymous Coward on Tuesday November 05 2019, @05:33PM (1 child)
That just means you need better detectors with less noise.
(Score: 2) by ikanreed on Tuesday November 05 2019, @05:38PM
A truism, but also really fucking hard.
(Score: 1) by nitehawk214 on Tuesday November 05 2019, @08:03PM
Correct, this is precisely what the cobe, wmap, and planck telescopes have imaged:
http://www.jon.fysik.su.se/planck.html [fysik.su.se]
"Don't you ever miss the days when you used to be nostalgic?" -Loiosh
(Score: 2) by maxwell demon on Tuesday November 05 2019, @06:59PM (4 children)
It would only fade linearly as long as you are still close enough to be approximately Euclidean. Indeed, when looking from the pole, as soon as the object passes the equator, it would start getting brighter again, as the rays are bound towards each other (think of a looking glass for analogy). Indeed, a point source at the other pole would be about as intense as a light source right in front of your eye.
That's of course assuming that there is no absorption on the way of the light; anything in between the light source and your eye will take away light in the same way as in a flat space.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by ikanreed on Tuesday November 05 2019, @07:29PM (3 children)
I think it's safe to say any world with emission and no absorption would be unbelievably bright eventually.
(Score: 2) by maxwell demon on Tuesday November 05 2019, @07:45PM (2 children)
Plasma is a damn good absorber. That's the point.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by maxwell demon on Tuesday November 05 2019, @07:47PM
Oops, ignore that post; I somehow thought you had answered another post of mine.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by DannyB on Tuesday November 05 2019, @09:18PM
Plasma is a lot hotter than modern LCD sets, which are also much cheaper.
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(Score: 2) by PiMuNu on Tuesday November 05 2019, @03:53PM (3 children)
Good idea. Now, all we have to do is wait for the light to propagate between those space stations.
(Score: 2) by DannyB on Tuesday November 05 2019, @04:29PM (2 children)
It might take even longer for the space stations to get to their positions to begin the experiment.
What if a triangle of space stations, with their lasers going, began expanding away from each other? The triangle gets bigger and bigger. The measurement of the angle of the lasers is watched to observe an increase from 60 degrees. Suppose one space station remains close to our solar system, but the other two are moving away.
Geez . . . what am I saying? I need to get back to writing stupid jokes and smart alek comments.
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(Score: 3, Interesting) by PiMuNu on Tuesday November 05 2019, @05:53PM (1 child)
It's a cute idea, but I think to measure anything you need to have spaceships O(the size of the universe) apart. Which takes O(the age of the universe) to achieve. It might be challenging to do the analysis, because to transmit the results will also take O(the age of the universe).
(Score: 2) by DannyB on Tuesday November 05 2019, @07:39PM
I mentioned that there might be a slight time lag in order to set up the experiment.
I did take into account the transmit time by suggesting that one of the stations remain near our solar system and the other two move away from it in an ever expanding triangle.
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(Score: 2) by captain normal on Tuesday November 05 2019, @04:11PM (1 child)
"Flatland: A Romance of Many Dimensions" is available at Project Glutenberg.
https://www.gutenberg.org/files/201/201-h/201-h.htm [gutenberg.org]
To me it is ridiculous that so called "scientists" would limit their thinking to only 3 dimensions.
When life isn't going right, go left.
(Score: 2) by DannyB on Tuesday November 05 2019, @04:31PM
I enjoyed the paperback in the 1990s or maybe 1980s. To long ago enough to remember clearly.
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(Score: 2) by Immerman on Tuesday November 05 2019, @04:21PM
>But we might be able to do the three space stations experiment.
Maybe eventually, but probably not. Assuming the circumference of the hypersphere is equivalent to the diameter of the observable universe (i.e. everything we see is unique, and there's nothing we can't see), you're talking a hypersphere 28 billion light-years around. Even if your triangular instrument spanned the entire galaxy, 100,000 ly across, it would still only span about 1.3/1,000ths of a degree of the hypersphere's surface. That'd be like trying to measure the curvature of the Earth by looking at the sum of angles of a triangle 50 feet across. You're so far below the noise threshold (unevenness of the Earth's/universe's surface) as to make the endeavor pointless.
(Score: 3, Interesting) by Mojibake Tengu on Tuesday November 05 2019, @04:29PM
It could be much more right angles all the way around:
https://en.wikipedia.org/wiki/Pentagramma_mirificum [wikipedia.org]
This principle above can be easily extended to 4th dimension within
https://en.wikipedia.org/wiki/120-cell [wikipedia.org]
Respect Authorities. Know your social status. Woke responsibly.
(Score: 0) by Anonymous Coward on Tuesday November 05 2019, @05:14PM (1 child)
I have proof! My penis is so long it is constantly proding me in the back. So now you know.
(Score: 2) by DannyB on Tuesday November 05 2019, @05:21PM
Black holes are infinitely deep.
Amazon might have a portable one.
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(Score: 2) by JoeMerchant on Tuesday November 05 2019, @07:37PM (2 children)
And, there's the key. All indications are that our furthest observers (is it Pioneers or Voyagers now?) are still so close together that any observation of such curvature is well under the accuracy of the available measuring instruments.
🌻🌻 [google.com]
(Score: 2) by DannyB on Tuesday November 05 2019, @09:16PM (1 child)
Yep. I agree.
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(Score: 2) by JoeMerchant on Tuesday November 05 2019, @09:26PM
Next, instead of theoretical flatlanders on a globe on your desk, put your flatlanders on the surface of the Earth and make them blind, they only get their information from propagating sound waves... kind of like our relativistic limits with the speed of photons in our space.
It would only take 32 hours for an atmospheric sound wave to travel the circumference of the Earth, but that starts to give some perspective on how that's going to mess with attempting measurements to detect curvature.
🌻🌻 [google.com]
(Score: 2) by inertnet on Tuesday November 05 2019, @08:26PM (2 children)
That's a nice idea, but I'd use 4 stations that form a regular tetrahedron.
(Score: 2) by DannyB on Tuesday November 05 2019, @08:53PM (1 child)
Care to elaborate why?
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(Score: 3, Interesting) by inertnet on Wednesday November 06 2019, @10:54PM
Late response because I've been away.
Your triangle example would register curvature in 2D space, but in 3D space it would only work for one plane of reference. Adding a 3rd station would allow this constellation to measure in 3D.
(Score: 2) by looorg on Tuesday November 05 2019, @06:32PM (19 children)
I thought it was endless, a shapes imply there is an edge. Where is the end/edge of the universe? While not likely to have a visit from humanity any time soon what would happen if we went there?
(Score: 2) by maxwell demon on Tuesday November 05 2019, @07:04PM (8 children)
No, it doesn't. The surface of the Earth is (approximately) a sphere (clearly a shape). But it has no edge (no matter how far you travel, you never will fall over the edge of the Earth).
The Tao of math: The numbers you can count are not the real numbers.
(Score: 0) by Anonymous Coward on Wednesday November 06 2019, @02:15AM (1 child)
You do go off the edge of the Earth if you go UP.
(Score: 2) by Immerman on Wednesday November 06 2019, @02:34AM
Yes, but you have to evoke a 3rd dimension to leave the 2D surface.
The analog for going "off the edge of the universe" would be traveling through the 4th (or higher) dimensions, possibly encountering other 3D universe "surfaces" along the way. Or perhaps only perceiving a continuous metamorphosis of our own.
(Score: -1) by MyOpinion on Wednesday November 06 2019, @12:26PM (5 children)
It looks and measures level.
Are you claiming it is not?
Truth is like a Lion: you need not defend it; let it loose, and it defends itself. https://discord.gg/3FScNwc
(Score: 2) by maxwell demon on Wednesday November 06 2019, @01:56PM (4 children)
Level? What do you mean with that?
The Tao of math: The numbers you can count are not the real numbers.
(Score: -1) by MyOpinion on Wednesday November 06 2019, @02:11PM (3 children)
Literal sense: horizontal, planar, level.
Are you claiming it is not?
Truth is like a Lion: you need not defend it; let it loose, and it defends itself. https://discord.gg/3FScNwc
(Score: 2) by maxwell demon on Wednesday November 06 2019, @02:29PM (2 children)
Horizontal and planar are not synonyms.
The Tao of math: The numbers you can count are not the real numbers.
(Score: -1) by MyOpinion on Friday November 08 2019, @04:36PM (1 child)
Horizontal and planar, or horizontal and flat: Level.
I do not see why you seem so confused of this: is level not level in your mind?
How about in your everyday experience?
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(Score: 2) by maxwell demon on Friday November 08 2019, @06:50PM
In my mind, level is something you achieve. And I interpreted your three-word list as three supposed synonyms, of which the first two however weren't synonyms.
Note that I'm not a native speaker of English; it tremendously helps if you use full sentences.
Anyway, I think I now understand what you are trying to say: That “level” means “horizontal and planar”.
On my experience: Well, where I live, the Earth is certainly not very planar ;-)
But what I know from personal experience, and what is not compatible with a flat Earth, but fully with a spherical Earth, is the fact that from the top of a mountain you see much further than from near the bottom (but high enough to look over local obstacles).
Of course, from the surface itself, a curvature radius of over 6300 km is damn flat, flat enough that you won't recognize any difference from a plane with your naked eye unless you can see over huge distances.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by DannyB on Tuesday November 05 2019, @09:02PM (9 children)
If the Universe is Infinite
I never thought the universe could be endless. If it were, then there would be infinite repetition of everything. Somewhere else there would be an exact copy of the earth. In fact an infinite number of exact copies.
Consider. The digit expansion of PI continues endlessly. Somewhere within those digits you will find a 5. Then later another 5, then more, and in fact an infinite number of 5's.
If you look, you can find a 59, and another 59, and in fact an infinite number of 59s. Although this infinity is smaller than the infinity of the previous paragraph. (I think there is a Numberphile video about different infinities on YouTube.)
In fact, a pattern 592, or 5926, etc can be found infinite times. In fact, any large integer will occur within the digits of PI, and will then re-occur, an infinite number of times.
Like an infinite universe. There are an infinite number of H20 molecules. Form a more complex molecule and you'll find an infinite number. Now combinations of molecules, like an amino acid, a protein, a base pair of DNA, a strand of DNA, an entire organism. Or a collection of molecules that make up a particular grain of sand on the beach. An infinite number of times, in an infinite universe, there will be an identical arrangement of molecules to form that same identical grain of sand. Or to form identical mountain ranges. Or identical planets.
Now the bigger pattern you look for, the further you have to look to find it. But, hey, if the universe is infinite.
If the Universe is NOT Infinite
What happens? Do you run into a brick wall? Does it have a sign in English saying "this is the end"? A more sensible fixed size universe is that it curves around on itself four dimensionally into a hypersphere. A 4d sphere.
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(Score: 2) by dry on Wednesday November 06 2019, @07:39AM (2 children)
Someone actually calculated the average distance in an infinite universe it would be before you got an exact copy of the Earth, including us, and also an exact copy of the Milky Way, they were bloody big numbers, something like 4 to the googol to the googol to the googol, when measured in metres. IIRC, it was based on the plank unit and there being only so many possible combinations.
(Score: 2) by deimtee on Wednesday November 06 2019, @02:01PM
I think that was Tegmark.
If you cough while drinking cheap red wine it really cleans out your sinuses.
(Score: 2) by DannyB on Wednesday November 06 2019, @04:58PM
That is interesting.
Mind boggling that there would be an infinite number of copies at such average intervals.
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(Score: 2) by maxwell demon on Friday November 08 2019, @06:58PM (5 children)
While pi is assumed to be normal, it AFAIK has not been proved. So for all we know, after the 101,000,000-th digit, there might be no more digit 5. It's unlikely, but not impossible.
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by DannyB on Friday November 08 2019, @07:17PM (4 children)
That thought has crossed my mind long ago. But seems unlikely. The more those kinds of restrictions are introduced, the more it starts to resemble a repeating fixed pattern maybe.
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(Score: 2) by maxwell demon on Friday November 08 2019, @08:13PM (3 children)
That doesn't follow. You can have a string that avoids the 5, but contains all the other numbers randomly.
Also, there's nothing that says that pi won't eventually go into some pattern (again, unlikely, but not impossible). The only pattern that we can exclude is an exact repetition of the very same string of digits with nothing in between (because that would make a rational number, which we know pi isn't).
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by DannyB on Friday November 08 2019, @08:36PM (2 children)
I was just about to point out the rational number thing.
If you never go into "rational number" repetition of digits, then it seems (intuitively -- gut feeling) impossible to suddenly permanently exclude a digit like 5. But I know of know proof. There would still be an infinite number of repetitions of patterns of digits without 5. But then again, the more restrictions get added to what can appear, the more this (seems to) move more towards a "rational number" style repeating digits. But I am NOT a mathematician. And I don't pretend to be one on TV.
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(Score: 2) by maxwell demon on Friday November 08 2019, @09:17PM (1 child)
Your gut feeling is wrong. The following is an irrational number, despite only using two digits:
0.101001000100001000001000000100000001000000001…
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by DannyB on Monday November 11 2019, @03:22PM
Excellent example. Thanks.
If PI were to end up with something similar eventually, I wonder if it can ever get out of such a pattern.
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(Score: 2) by Thexalon on Tuesday November 05 2019, @07:17PM (4 children)
The shape of the universe doesn't give a damn about my opinion. Evidence determines the right answer, not my opinion.
The only thing that stops a bad guy with a compiler is a good guy with a compiler.
(Score: 0) by Anonymous Coward on Tuesday November 05 2019, @08:34PM (2 children)
No evidence allows an approximate model. There is no right answer.
(Score: 2) by Thexalon on Tuesday November 05 2019, @08:41PM (1 child)
Then the right answer is "I don't know (yet)".
The only thing that stops a bad guy with a compiler is a good guy with a compiler.
(Score: 2) by DannyB on Tuesday November 05 2019, @09:12PM
That is the right answer. "I don't know." I've believed since soon after college it is an (at least) 4D sphere (of space -- not even counting time which is yet another dimension).
I've pointed out possible "experiments" in this thread. But there are other evidences that our 3D space IS warped in a 4th dimension.
Remember Mariner 9, a spacecraft sent to Mars? The straight line between Mariner 9 and the Earth sometimes gets nearer and nearer to the sun's surface as the two planets (Earth, Mars) move. When that line gets near the sun, the length of that line gets much longer. This is because space is warped near the sun due to the large gravitational field of the sun. There is "more space" there. This is evidenced by the higher "ping time" between Earth and Mariner 9 when the direct signal path is near the sun. There is a "hill" (or valley) of space there. Oh, and time moves more slowly the deeper you get into a gravity well. Which also fits with the longer ping time.
I don't know if I should mention gravitational lensing.
If our 3d space curves in another (4th) dimension, then a sphere would be a sensible shape, but not necessarily the true shape. And the answer may be unknowable.
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(Score: -1) by MyOpinion on Wednesday November 06 2019, @12:33PM
So what evidence is there for a large-scale convexity of the oceans?
Truth is like a Lion: you need not defend it; let it loose, and it defends itself. https://discord.gg/3FScNwc
(Score: 1, Disagree) by Anonymous Coward on Tuesday November 05 2019, @07:37PM (3 children)
Keep going in a straight line and you'll catch up to yourself due to Einsteins theory of special relativity.
(Score: 0) by Anonymous Coward on Tuesday November 05 2019, @08:37PM
thanks worf
(Score: 2) by DannyB on Tuesday November 05 2019, @09:13PM
Exam papers need to be a Möbius Strip.
TIME IS UP.
Put your pencils down. Turn your papers over.
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(Score: 2) by Webweasel on Wednesday November 06 2019, @03:38PM
This, recruits, is a 20-kilo ferrous slug. Feel the weight! Every five seconds, the main gun of an Everest-class Dreadnought accelerates one to 1.3 percent of light speed. It impacts with the force of a 38-kiloton bomb. That is three times the yield of the city buster dropped on Hiroshima back on Earth. That means: Sir Isaac Newton is the deadliest son-of-a-bitch in space! (...) I dare to assume you ignorant jackasses know that space is empty! Once you fire this hunk of metal, it keeps going 'till it hits something! That can be a ship, or the planet behind that ship. It might go off into deep space and hit somebody else in ten thousand years. If you pull the trigger on this, you are ruining someone's day, somewhere and sometime!
Priyom.org Number stations, Russian Military radio. "You are a bad, bad man. Do you have any other virtues?"-Runaway1956
(Score: 1) by Sulla on Tuesday November 05 2019, @08:27PM
When a galaxy retires does it move to the universal equator? I need to know which galaxy is in the position of Florida so I can avoid it.
Ceterum censeo Sinae esse delendam
(Score: 2) by hendrikboom on Wednesday November 06 2019, @12:17AM (1 child)
So... The matter density appears to be about 5% higher than the matter density at which the universe would be flat.
What no one is saying is what radius of curvature is consistent with this oversupply of matter.
(Score: -1) by MyOpinion on Wednesday November 06 2019, @12:30PM
Need to ask, what is your definition for "the universe"?
Truth is like a Lion: you need not defend it; let it loose, and it defends itself. https://discord.gg/3FScNwc