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Is the Universe Shaped Like a Funnel?
DrMorpheus writes "A new theory of the shape of the Cosmos posits that the Universe may be shaped like a medieval horn, according to Frank Steiner at the University of Ulm. This theory, if true, could explain several strange observations about the microwave background radiation. The Universe would be stretched out at one end into a long tube and flared out into a bell at the opposite end. The technical name for this shape is a 'Picard topology'. To quote the article, '...our Universe is curved like a Pringle, shaped like a horn, and named after a Star Trek character. You could not make it up.'"
Why do we continue to classify the shape of the Universe? Realistically, if we can not define the shape by placing it within a totally viewable package, it because useless to define it by something that we are unable to classify. Funnel? We see the outside of the funnel so that we can define the shape, but from the interior, it is just a curved or flat plane that we can only recognize by viewing from an all emcompassing view external.
:-P
Since we have no proof of anything beyond the Universe, this is just a chasing of a simple definition. Without the Universe in a 3D viewable environment and being just IT, then we can't define the shape meaningfully.
Think of it like this, we could say the work was flat, but it was not till we were able to look at it from an external view. Think being about 4 miles deep in the Earth and attempting to define the shape of the Earth.
Anyway, I shall crawl back in my hole and wait for those much smarter than me to put me in my place.
"What is the universe" and "What is the shape of the universe" are two different questions.
I don't think the universe being discussed is "everything that exists".
The shape being discussed is more technically the shape (or topological character) of the geometry of the universe we find ourselves in.
There are many kinds of shapes that are possible, some "space filling" and some not. (I am sure there is a more correct technical term from topology to describe "space filling".)
The question of shape does not address what's in the gaps if it's not space-filling.
In the Star Trek, Euclidean world, the universe is flat, the speed of light appears to be essentially infinite and there is also no physical limit to speed, and simultaneity holds.
This is clearly not the case in our universe, and locally, it's not even flat, but positively curved.
The overally curvature has been debated ever since Einstein released General Relativity, and the answer seems to vacillate between flat and negatively curved.
The article is discussing the simplest kind of negative curvature, but it is taking the discussion to extremes that I have not seen discussed before.
The trumpet shape being discussed is a two-dimensional analog of the actual case in our universe, and is clearly not space-filling.
HCG 50a = 2MASX J11170638+5455016
11h17m06.4s +54d55m02s
For enlightenment, please read Flatland by Edwin A. Abbott. A very interesting way to conceptualize life in one, two and four-dimensional worlds.
This has been a test. If this had been an actual Sig, you would have been amused.
You can determine the "shape" of a piece of space from inside it. Let me drop down one dimension and consider the shapes of surfaces. We all know that the angles at the corners of a triangle add up to 180 degreed. This, however is only actually true, when you draw your triangle on a truly flat surface. On a curved surface such as that of the Earth, the angles will add up to MORE THAN 180 degrees. Consider, for example a triangle with one vertex at the N pole, and two 90 degrees apart on the equator, with its edges made of great circles (the appropriate analogue of a straight line). All THREE angles of this triangle are right angles.
In fact, on a sphere of radius R, the sum of the angles exceeds 180 degrees by 180/pi * A/r^2, where A is the area of the triangle.
On a saddle-shaped surface, the angles of a triangle are always LESS THAN 180 degrees in a similar way.
Building on these ideas, you can define a precise notion of the shape of a surface entirely from INSIDE the surface, and extend it up to three dimensions (or more) dimensions. This is what the cosmologists are talking about when they talk about the "shape" of the universe.
The interesting thing is that in the US things are emitting tones at 120 Hz, not 60. (however, there is a Bb at ~116Hz and a B at ~123 Hz, so calling this a Bb is still pretty close). Since the current reverses direction *twice* per cycle, metal in transformers, etc. expands and contracts *twice* per cycle, generating sound at twice the current frequency. For more information, see this link on magnetostriction
"There are a dozen opinions on a matter until you know the truth. Then there is only one." - CS Lewis (paraprhase)
Imagine the graph of y = 1 / x^2 from x = 1 to x = infinity. Integrate to find the area under the line:
integral(1/x^2) = (-1/x + c)
so -1/infinity = 0
-1/1 = -1
0 - (-1) = 1
so the area under the curve is 1, even though the graph goes out to infinity.
You can pull the same trick with sufficiently "narrow" functions in 3D too, but I'm not doing a 3D integration in this comment box with no maths symbols.
Well, it's quite easy. Let's go one dimension lower, and think about an in one direction infinitely long strip of paper (like an toilet paper strip that begins somewhere but never ends), which is getting narrower fast enough.
:-)). But since it's getting narrower, on the next meter, it just has an area of 1/2 square meter. On the next meter, it's area is just 1/4 square meter, and so on, on each meter half the area of the previous meter.
... ...
On the first meter, it has, say, an area of one square meter (yes, that's quite large for toilet paper
Now, how large is the total area? Well, let's look at it (I'm ommiting the square meter unit for brevity):
The first meter has, as I said, an area of 1.
The first 2 meters have an area of 1+1/2 = 1.5.
The first 3 meters have an area of 1+1/2+1/4 = 1.75.
The first 10 meters have an area of 1+1/2+...+1/512 = 0.998046875.
As you see, as you add up the area meter by meter, the total area gets arbitrary close to 2, without ever reaching it. Therefore the total area is just 2 square meters.
Or to see it differently: When cutting the first meter off, the resulting strip looks exactly the same, just half as narrow. Therefore it has half the area of the original strip, the other half being the cut off first meter, which, as we know, has one square meter. Therefore the whole area is 2 square meters, which clearly is finite.
The Tao of math: The numbers you can count are not the real numbers.
This is just a hunch, but I bet "Picard topology" is named after Emile, not Jean Luc.
http://alternatives.rzero.com/
When you double the frequency, it's the same note - just one octave higher.
i.e. if 60Hz is Bb, so is 120, 240, 480, etc....
The only reason we have the rights we have is that people just like us died to gain those rights. -- Cheerio Boy
What do we mean by the topology of the Universe?
We sort of mean the 'shape'. It is easy to talk about 2 dimensional surfaces in a three dimensional universe - planes, spheres, funnels, etc. But the Universe has 3 (large) dimensions, not 2, so it is much harder. Normally, we think of the universe as a 3 dimensional equivalent to a plane - that is, in space, straight lines are straight, never curve back on themselves, and go on forever. Another common topologies which arise naturally from gravity theory are 'spherical' - where parallel lines eventually cross, and you can see the back of your head. The group in questions is proposing that the Universe is a 3d analog to the surface of a horn. Others have proposed 3d analogs to the surface of a doughnut....
How can one possibly determine what this shape is?
If the Universe is actually curved in some way, then light coming from distant objects will be bent on its way to us, distorting the images. For the global topology of the Universe, one wants to use the largest, most distant thing you can look at. The Universe is expanding and cooling. Light takes time to travel, so if you look far enought away, you can look far enough back in time to when the whole Universe was filled with a hot H-He plasma. This is called the Cosmic Microwave Background (CMB). Most recent topology studies have looked at the statistics of the fluctuations of this distant plasma for distortion in the image from what is predicted.
So, is this true?
Could be.... but the evidence is not compelling. The anomalies they are looking at are of rather low statistical significance, and the idea that the universe is just 'straight/flat' and boring still fits pretty well. And unfortunately, for the large scale stuff, the data isn't going to get any better. The problem is, we only have one Universe, and COBE and WMAP have measured the large scales as well as can be measured. The small scale distortions have more potential given upcoming experiments like Planck, and the WMAP year2 data.
To make this explanation less confusing, you might say the Universe is in three dimensions what the Earth's surface is in two. I don't mean to be a pedant, it's just your explanation might not have made sense to someone unfamiliar with the idea, since the Earth is a three-dimensional object.
I found the meaning of life the other day, but I had write-only access.
Basically, the shape of the universe determines what happens to "parallel" lines as they stretch across huge distances.
The universe is not infinitely large by definition. General relativity describes how the size and age of the universe are related and quite possibly finite. This relates to the "big bang" and the question of whether it will be followed by a "big crunch."
Inside and outside are terms that only have meaning when you divide the universe into parts. When talking about the universe, as you point out, there is no sense in speaking of that which is "outside."
Now, write a book.
I'm just asking for an offtopic mod here, but I'd just like to chime in on something:
A sax is a woodwind, as I'm sure you know, because its sound originates in the wooden reed in the mouthpeice (just like other woodwinds like clarinets and oboes, both of whose bodies can be wood, plastic or other materials), whereas all brass instruments have their sound originate in a brass or otherwise metallic mouthpeice.
This is the same reason that a piano is considered a string instrument (since the sound originates in the vibrating string) as opposed to a percussion instrument (due to the hammers inside that hit the strings) even though it mechanically seems similar to the xylophone.
"Stumble before you crawl"
Or, in other words, space is curved.
Here is the original paper.
http://xxx.uni-augsburg.de/abs/astro-ph/0403597
Shows you that you really need to know what you are talking about if you want to make an intelligent comment about this paper.
Close, but no cigar.
It's 120Hz in the US, and 100Hz in Europe.
The sound is based on the _amplitude_ of the signal, and there are two peaks and two zeroes for each cycle, hence the hum has twice the frequency of the mains source.
Ask any geeky guitarist/bassist.
FP.
Also FatPhil on SoylentNews, id 863
Check out the actual article, the "Picard" topology is named after E. Picard who proposed it (presumably in 1884, ref 18).
3 59 7.pdf
http://arxiv.org/PS_cache/astro-ph/pdf/0403/040
actually, (61.74/60) is less than (60/58.27), not the other way round, but you are right to say that this makes 1.74 a smaller percentage of 60 than 1.73 is of 58.27.</nitpick>
frequency is a continuous property of a wave... whether you choose to select linearly or logaritmically spaced points is up to you. over large scales (i.e. multiple octaves or decades), it is generally more useful to choose logarithmically spaced points, because you want to treat low octaves with the same number of points as high octaves. over small ranges (here only 3.47 Hz or about 5.78% of the nominal 60 Hz), it makes sense to deal with linearly spaced points, because the imbalance between octaves cannot come into play. in this case, if you played the B-natural against 60 Hz and then played the B-flat against 60 Hz, the resulting beat frequency signals would sound essentially the same, as the difference between them would be only 0.01 Hz.
I've read one to many Hawking books.....
The darkness... controls the music. The music... controls the soul.
And by the way, it's named after Emile Picard from 1884, not Jean-Luc from the 25th century.
Sound waves are displacement of matter, not just air.
If corporations are people, aren't stockholders guilty of slavery?
idpispopd
- Some of the models are closed curves that are finite in size - the typical analogy is a 4-space hypersphere with a 3-d surface that the Universe maps onto, similar to the way the 2-d surface of the Earth is wrapped around a 3-d sphere and doesn't have edges. But that's not the only model. (The string-theory and membrane-theory folks add another half dozen dimensions to the mix, but the big dimensions can still mostly follow that model.)
- Some of the models say "no, it's not curved, it's flat, maybe a bit bumpy but it's really infinite".
- Some of the models say it's the opposite of a closed curve - these typically look saddle-shaped or horn-shaped, because instead of the curvature in the x direction and the curvature in the y direction both going the same way, they're going the opposite way.
A lot of this stuff tends to be related to models about how much matter and energy the Universe has - is there enough mass to make it close in on itself or not, and do we need to postulate lots of as-yet-undiscovered "dark matter" to make it heavier, or enough even-less-defined "dark energy" to blow it apart?Bill Stewart
New Fast-Compression-only CPR http://preview.tinyurl.com/dy575ks
You are arguing about terminology. In spherical geometry, an arc of the equator, line of longitude, or any other great circle is a straight line, according to mathematicians. (When they want to be precise, they call it a "geodesic".) It has the property of being the shortest path between two points in the sphere, as well as being a straight path between those points (in the sense that it parallel-propogates its own tangent vector). In short, mathematicians have a more general definition of "straight line" than you do, which reduces to your definition if the space in which the line exists is flat.
Some of your questions may be answered in this FAQ or this one.