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# How Big is the Universe?

Eratosthenes method is not even remotely close to being "a very similar method" to using non-Euclidean geometry, which wasn't even invented until something like 2000 years later.

posted by DU at 10:56 AM on July 24, 2012 [2 favorites]

While there are different sizes of infinity (there are more real numbers than integers), the flat infinite universe would have the same size as the hyperbolic infinite universe.

posted by justkevin at 11:57 AM on July 24, 2012 [1 favorite]

Well, that screws with my day. I always thought you could usually see the curve because that's where the horizon is. No?

By the way, Literary Studies major here.

posted by cjorgensen at 12:06 PM on July 24, 2012

Well, from what I understand, the universe is great big. And comparatively, we're just tiny little specks. Specks, oh, about the size of, say, Mickey Rooney.

posted by Rev. Syung Myung Me at 1:04 PM on July 24, 2012

In case anyone is confused, think of this: there are an infinite number of whole numbers, right? And there are an infinite number of even (divisible by 2) whole numbers, yes? But there are only half as many even numbers as whole numbers. So not all infinities are the same.

posted by echo target at 8:42 AM on July 25, 2012

Post

# How Big is the Universe?

July 24, 2012 10:48 AM Subscribe

How Big is the Universe? Measured with a protractor. Lots of Pictures!!!

*A surface of negative curvature has any three points form a triangle whose three angles sum to less than 180°, and again, knowing the distances and measurements of all three angles allows you to calculate the radius of curvature.*

In practice, the very first calculation of the circumference of the Earth — dating to the 3rd Century B.C. — used a very similar method, again reliant on simple geometry.

In practice, the very first calculation of the circumference of the Earth — dating to the 3rd Century B.C. — used a very similar method, again reliant on simple geometry.

Eratosthenes method is not even remotely close to being "a very similar method" to using non-Euclidean geometry, which wasn't even invented until something like 2000 years later.

posted by DU at 10:56 AM on July 24, 2012 [2 favorites]

I now believe the earth is shaped like a pringle.

posted by elizardbits at 10:58 AM on July 24, 2012 [1 favorite]

posted by elizardbits at 10:58 AM on July 24, 2012 [1 favorite]

And they said we were crazy to let Frito-Lay and Oscar Meyer to underwrite science curricula!

I just wish they'd decide whether the atomic weight of bolognium was "delicious" or "snacktacular."

posted by Earthtopus at 11:01 AM on July 24, 2012 [1 favorite]

I just wish they'd decide whether the atomic weight of bolognium was "delicious" or "snacktacular."

posted by Earthtopus at 11:01 AM on July 24, 2012 [1 favorite]

Excellent article! Thanks, Yellow.

posted by benito.strauss at 11:35 AM on July 24, 2012

posted by benito.strauss at 11:35 AM on July 24, 2012

Be advised: it is recommended that one listens to this when reading such materials.

posted by Algebra at 11:41 AM on July 24, 2012 [1 favorite]

posted by Algebra at 11:41 AM on July 24, 2012 [1 favorite]

ok, so let me see if i got this...if it's positively curved like a (hyper(hyper?(hyper??))) sphere, then it's finite in extent, and if it's (perfectly) flat, then it's infinite.

what if it's negatively curved? would that make it

posted by sexyrobot at 11:47 AM on July 24, 2012

what if it's negatively curved? would that make it

*more*than infinite? what? how?posted by sexyrobot at 11:47 AM on July 24, 2012

*what if it's negatively curved? would that make it more than infinite? what? how?*

While there are different sizes of infinity (there are more real numbers than integers), the flat infinite universe would have the same size as the hyperbolic infinite universe.

posted by justkevin at 11:57 AM on July 24, 2012 [1 favorite]

This is cool and all, but I originally read it as

posted by WidgetAlley at 11:57 AM on July 24, 2012 [2 favorites]

*How Big is the Universe? Measured with a pteorodactyl.*And everything's just totally downhill after that.posted by WidgetAlley at 11:57 AM on July 24, 2012 [2 favorites]

Ok, the number at the end, mind blown. 0.0001% visible at the moment.

posted by Hactar at 12:02 PM on July 24, 2012

posted by Hactar at 12:02 PM on July 24, 2012

*...cannot measure the curvature of the Earth from any known location on the surface of the planet.*

Well, that screws with my day. I always thought you could usually see the curve because that's where the horizon is. No?

By the way, Literary Studies major here.

posted by cjorgensen at 12:06 PM on July 24, 2012

There's always a point in these kinds of articles where I'm happily reading along and then realize I'm not understanding it any more. This also happens every time I try to finish

posted by Curious Artificer at 12:44 PM on July 24, 2012 [4 favorites]

*A Brief History of Time*.posted by Curious Artificer at 12:44 PM on July 24, 2012 [4 favorites]

Metafilter: realize I'm not understanding it any more.

posted by herbplarfegan at 12:48 PM on July 24, 2012 [1 favorite]

posted by herbplarfegan at 12:48 PM on July 24, 2012 [1 favorite]

*How Big is the Universe?*

Well, from what I understand, the universe is great big. And comparatively, we're just tiny little specks. Specks, oh, about the size of, say, Mickey Rooney.

posted by Rev. Syung Myung Me at 1:04 PM on July 24, 2012

I had the exact same experience as Curious Artificer. So, I came here to read some comments, see if that would jump-start some understanding.

And understanding obliterated. Thanks, Metafilter!

posted by Terminal Verbosity at 1:08 PM on July 24, 2012 [1 favorite]

*While there are different sizes of infinity ...*And understanding obliterated. Thanks, Metafilter!

posted by Terminal Verbosity at 1:08 PM on July 24, 2012 [1 favorite]

You have to actually use the word "puny" if you're going to reference that song.

posted by Curious Artificer at 1:17 PM on July 24, 2012 [1 favorite]

posted by Curious Artificer at 1:17 PM on July 24, 2012 [1 favorite]

hmmmm...would gravity be stronger in a negatively curved universe. like, would G be bigger?

posted by sexyrobot at 1:57 PM on July 24, 2012

posted by sexyrobot at 1:57 PM on July 24, 2012

I understood everything except the part where looking at the cosmic microwave background radiation allowed us to conclude that the universe is flat. Anyone care to comment?

Actually, I think I'm also having trouble understanding how sending out three objects into space would allow us to determine the curvature of space.

posted by SugarFreeGum at 2:37 PM on July 24, 2012

Actually, I think I'm also having trouble understanding how sending out three objects into space would allow us to determine the curvature of space.

posted by SugarFreeGum at 2:37 PM on July 24, 2012

The three object form a triangle. Each of the three objects measures the angle it sees between the other two, and then we add them up.

Example: Three people start at the North Pole. One stays, and two of them head off at 90° to each other. Let's image they walk all the way to the equator, (although they don't necessarily know that). North Pole guy still sees 90° between them, and each of the equator guys sees 90° between North Pole guy and the other equator guy, as in this picture.

90° + 90° + 90° = 270°.

On a flat surface you know that the angles of a triangle add up to 180°. Because we got a different number than 180°, we know that the surface of the Earth is curved, and because it's greater than 180°, we call the curvature

If you did this on the surface of a Pringle, or on a horse saddle, the angles would add up to less than 180°. That curvature is called negative.

(Why we call one way of being curved positive and the other negative, and not vice-versa, comes from the mathematical formula for curvature, and it isn't obvious to the natural human eye.)

posted by benito.strauss at 2:53 PM on July 24, 2012

Example: Three people start at the North Pole. One stays, and two of them head off at 90° to each other. Let's image they walk all the way to the equator, (although they don't necessarily know that). North Pole guy still sees 90° between them, and each of the equator guys sees 90° between North Pole guy and the other equator guy, as in this picture.

90° + 90° + 90° = 270°.

On a flat surface you know that the angles of a triangle add up to 180°. Because we got a different number than 180°, we know that the surface of the Earth is curved, and because it's greater than 180°, we call the curvature

**positive**.If you did this on the surface of a Pringle, or on a horse saddle, the angles would add up to less than 180°. That curvature is called negative.

(Why we call one way of being curved positive and the other negative, and not vice-versa, comes from the mathematical formula for curvature, and it isn't obvious to the natural human eye.)

posted by benito.strauss at 2:53 PM on July 24, 2012

I don't get to see as many lady parts as I would like to, but by means of inference from experience I can

posted by quoquo at 3:25 PM on July 24, 2012

*know*what I'm missing. Isn’t science wonderful?posted by quoquo at 3:25 PM on July 24, 2012

We are so teeny.

I don't recall seeing any statements that all the dark energy and dark matter are out "there" (wherever "there" may be). I think they are in every interstice, it's just we can't detect them. So 22% of what's between your head and your toes is dark matter, and 74% of it is dark energy. (But I'd love to be corrected by anyone who know better.)

posted by benito.strauss at 4:39 PM on July 24, 2012

I don't recall seeing any statements that all the dark energy and dark matter are out "there" (wherever "there" may be). I think they are in every interstice, it's just we can't detect them. So 22% of what's between your head and your toes is dark matter, and 74% of it is dark energy. (But I'd love to be corrected by anyone who know better.)

posted by benito.strauss at 4:39 PM on July 24, 2012

OK, dragging out ye olde cosmologie memories, so apologies if I fuck up anything. I spend more time in particle physics these days.

First, the local curvature does not necessarily map to the global properties of the space. The Universe could be flat and finite (torus - exactly like the game-space in Asteroids) or flat and infinite (plane). I think you can have both closed and infinite as well, though I don't have a good picture for what that looks like.

It used to be thought the curvature did relate to the end-fate of the Universe in a one-to-one mapping: positive curvature was closed: expansion will cease and the Universe will recollapse at some point, negative was open: expansion will never stop and the Universe will expand on forever, reaching in a maximum entropy, very cold state; flat is the border-line case: Universe will never quite stop expanding but would get arbitrarily close, still ending in cold death though.

Discovery of dark energy removes this connection. With this addition, the curvature of the Universe is unconnected to the end-fate, as the dark energy will drive us to continual expansion regardless. A cosmological constant (which dark energy is at least doing a very solid impression of) forces us to live in de Sitter space-time, which expands forever regardless of the local curvature.

Now, as to the question from SugarFreeGum on the measurement of CMB and why this tells us about curvature. What you'd like is to know both the physical size of a standardized ruler that's far away, and then how big it appears in the sky. From this, you can get the curvature, using the arguments about how angles add that the link discusses. (they have a nice picture too at the CMB part, so go look at that).

The CMB is a snapshot of the Universe at the moment when it cooled enough for electrons to combine with protons to form electrically neutral atoms. Prior to this, photons could not propagate very far, as they were continually hitting electrons, being reabsorbed, emitted, and so on. Afterwards, they generally moved off, and the expansion of the Universe red-shifted the photons from the eV-scale energies (10^-6 m wavelength) they had at the time to the microwave wavelength they have today. Thus the Cosmic Microwave Background (CMB). This occurs when the Universe was about 300,000 years old.

Now, when we look at the CMB, we see many hot and cold patches (though the fluctuations are on the order of 1 part in 10^5, so very small). What is causing these? Remember that the Universe today is much larger than the Universe way back when. This, combined with the finite speed of light, means that today we are looking back at many "causal volumes:" volumes of space that were small enough so that there wasn't enough time for light to propagate outside of them, so they could not be affected by stuff happening further away (of course, if I draw two causal volumes next to each other on the sky, a point on the edge is in both. This argument about causality really refers to the center of each patch, and I get to pick the centers as I divide up the sky - the way the analysis works is by picking every possible set of centers, but ignore that for this discussion).

Some of those regions were slightly overdense compared to the Universe as a whole, and those were slightly hotter. Some were underdense, and so colder. Remember also that the size of a causal patch increases over time; today for example, it's the size of the visible Universe, much larger than way back at the moment of decoupling (when the CMB took it's snapshot of the Universe).

Let's examine one of those patches. Let's say it's overdense. Then the stuff inside starts to undergo gravitational collapse, heating the photons in the patch. Those hot photons will then push the material back apart, cooling the material a bit. However, that takes time to occur. Roughly speaking it takes about as much time to occur as it would take for light to pass from one side to another. So, the hottest (or coldest) patches on the sky are exactly the size of a causal patch at the CMB decoupling time where material had time to fall in and heat up but not enough time to "rebound" and cool.

So, by looking around at the CMB, and figuring out the what the angular size is of the spots with maximum variation from the smooth background, you can determine precisely how big a causal patches from time of the CMB decoupling appears today. So we know the angular size. We can also use this argument about infall of material to determine the physical size of the patch back then. So we have our ruler. Then we can figure out what the geometry of the Universe must be. Tada, we have a measurement of the flatness of the Universe.

This is usually stated in terms of the normalized energy density Omega, where Omega = 1 is a completely flat Universe. Using the WMAP satellite's measurements of the CMB angular power spectrum (the fancy way of saying the amount of hotness/coldness of patches of a particular size in the CMB), we get Omega between 0.98 and 1.08. We can do much better by combining a bunch of different experiments and requiring that they agree (that is, that the Universe has the same energy density no matter how you measure it. This appears to be a good assumption, which tells us about

the consistency of our theory).

benito.strauss: those are densities averaged over huge volumes. In our local region (the inner-ish Milky Way) baryons dominate. For example, on average there is about one dark matter particle per coffee cup (assuming DM particles weigh about as much as a silver atom or so).

posted by physicsmatt at 6:21 PM on July 24, 2012 [8 favorites]

First, the local curvature does not necessarily map to the global properties of the space. The Universe could be flat and finite (torus - exactly like the game-space in Asteroids) or flat and infinite (plane). I think you can have both closed and infinite as well, though I don't have a good picture for what that looks like.

It used to be thought the curvature did relate to the end-fate of the Universe in a one-to-one mapping: positive curvature was closed: expansion will cease and the Universe will recollapse at some point, negative was open: expansion will never stop and the Universe will expand on forever, reaching in a maximum entropy, very cold state; flat is the border-line case: Universe will never quite stop expanding but would get arbitrarily close, still ending in cold death though.

Discovery of dark energy removes this connection. With this addition, the curvature of the Universe is unconnected to the end-fate, as the dark energy will drive us to continual expansion regardless. A cosmological constant (which dark energy is at least doing a very solid impression of) forces us to live in de Sitter space-time, which expands forever regardless of the local curvature.

Now, as to the question from SugarFreeGum on the measurement of CMB and why this tells us about curvature. What you'd like is to know both the physical size of a standardized ruler that's far away, and then how big it appears in the sky. From this, you can get the curvature, using the arguments about how angles add that the link discusses. (they have a nice picture too at the CMB part, so go look at that).

The CMB is a snapshot of the Universe at the moment when it cooled enough for electrons to combine with protons to form electrically neutral atoms. Prior to this, photons could not propagate very far, as they were continually hitting electrons, being reabsorbed, emitted, and so on. Afterwards, they generally moved off, and the expansion of the Universe red-shifted the photons from the eV-scale energies (10^-6 m wavelength) they had at the time to the microwave wavelength they have today. Thus the Cosmic Microwave Background (CMB). This occurs when the Universe was about 300,000 years old.

Now, when we look at the CMB, we see many hot and cold patches (though the fluctuations are on the order of 1 part in 10^5, so very small). What is causing these? Remember that the Universe today is much larger than the Universe way back when. This, combined with the finite speed of light, means that today we are looking back at many "causal volumes:" volumes of space that were small enough so that there wasn't enough time for light to propagate outside of them, so they could not be affected by stuff happening further away (of course, if I draw two causal volumes next to each other on the sky, a point on the edge is in both. This argument about causality really refers to the center of each patch, and I get to pick the centers as I divide up the sky - the way the analysis works is by picking every possible set of centers, but ignore that for this discussion).

Some of those regions were slightly overdense compared to the Universe as a whole, and those were slightly hotter. Some were underdense, and so colder. Remember also that the size of a causal patch increases over time; today for example, it's the size of the visible Universe, much larger than way back at the moment of decoupling (when the CMB took it's snapshot of the Universe).

Let's examine one of those patches. Let's say it's overdense. Then the stuff inside starts to undergo gravitational collapse, heating the photons in the patch. Those hot photons will then push the material back apart, cooling the material a bit. However, that takes time to occur. Roughly speaking it takes about as much time to occur as it would take for light to pass from one side to another. So, the hottest (or coldest) patches on the sky are exactly the size of a causal patch at the CMB decoupling time where material had time to fall in and heat up but not enough time to "rebound" and cool.

So, by looking around at the CMB, and figuring out the what the angular size is of the spots with maximum variation from the smooth background, you can determine precisely how big a causal patches from time of the CMB decoupling appears today. So we know the angular size. We can also use this argument about infall of material to determine the physical size of the patch back then. So we have our ruler. Then we can figure out what the geometry of the Universe must be. Tada, we have a measurement of the flatness of the Universe.

This is usually stated in terms of the normalized energy density Omega, where Omega = 1 is a completely flat Universe. Using the WMAP satellite's measurements of the CMB angular power spectrum (the fancy way of saying the amount of hotness/coldness of patches of a particular size in the CMB), we get Omega between 0.98 and 1.08. We can do much better by combining a bunch of different experiments and requiring that they agree (that is, that the Universe has the same energy density no matter how you measure it. This appears to be a good assumption, which tells us about

the consistency of our theory).

benito.strauss: those are densities averaged over huge volumes. In our local region (the inner-ish Milky Way) baryons dominate. For example, on average there is about one dark matter particle per coffee cup (assuming DM particles weigh about as much as a silver atom or so).

posted by physicsmatt at 6:21 PM on July 24, 2012 [8 favorites]

I tried the benito.strauss method (above), using pteradactyle to make sure I got all my proportions right. Let me know when you find out what's under the turtles.

posted by mule98J at 6:45 PM on July 24, 2012

posted by mule98J at 6:45 PM on July 24, 2012

Thanks for stepping in, physicsmatt. Can you indicate how we would know about "local" variations in dark matter density? Just give me the key words and I'll go confuse myself. Thanks.

posted by benito.strauss at 7:39 PM on July 24, 2012

posted by benito.strauss at 7:39 PM on July 24, 2012

benito.strauss, we know the general structure of the Galactic dark matter density profile (i.e. how much dark matter is where) from the rotation curves of the stars as they move around the Galactic center (look at the galaxy rotation curves subsection in the wikipedia dark matter article). The Particle Data Group's (PDG) review article on dark matter has every bit of gory detail. From their cite 6, the local density is 0.39 GeV/cm^3, which for a 100 GeV dark matter particle translates into 0.004 dark matter particles per cm^3, or 1 per 250 cm^3, which is a bit more than one per coffee cup, but close enough.

There's a bit of uncertainty here, since these numbers derive from averaging the motion of stars in a large section of the local Milky Way and make some assumptions about a smooth dark matter halo (that is: dark matter density depends only on radius). Really, there should be local substructure: little halos of dark matter, streams of torn-apart halos that fell in and got ripped apart by the tides of the Galaxy, things like that. We could be living in a some-what over- or under-dense region, but as far as we can tell this either can't deviate too much from this result, or be too large on the Galactic scale.

This problem is of immense interest to theorists and experimentalists looking for dark matter in direct detection experiments (that is, experiments looking for dark matter hitting atoms in very sensitive detectors), since if the local density is larger or smaller than expected, that will greatly change their expected rate of signal. Would really suck if we're in a 100 ly void of dark matter, wouldn't it? Also, those streams and substructures could potentially change the energy dependence of the observations in the experiments, which could make it easier or harder to distinguish from background. There are computer programs (N-body simulations) that construct simulated galaxies and run them from the Big Bang till today to try and figure out what the average spiral galaxy dark matter looks like. There's still a lot of work to be done in the simulations, and the Milky Way has some annoyingly unusual quirks (the Magellanic Clouds, for example), so this will take a while. But we're getting there.

So yeah, I'm bad at keywords apparently.

posted by physicsmatt at 8:13 PM on July 24, 2012 [3 favorites]

There's a bit of uncertainty here, since these numbers derive from averaging the motion of stars in a large section of the local Milky Way and make some assumptions about a smooth dark matter halo (that is: dark matter density depends only on radius). Really, there should be local substructure: little halos of dark matter, streams of torn-apart halos that fell in and got ripped apart by the tides of the Galaxy, things like that. We could be living in a some-what over- or under-dense region, but as far as we can tell this either can't deviate too much from this result, or be too large on the Galactic scale.

This problem is of immense interest to theorists and experimentalists looking for dark matter in direct detection experiments (that is, experiments looking for dark matter hitting atoms in very sensitive detectors), since if the local density is larger or smaller than expected, that will greatly change their expected rate of signal. Would really suck if we're in a 100 ly void of dark matter, wouldn't it? Also, those streams and substructures could potentially change the energy dependence of the observations in the experiments, which could make it easier or harder to distinguish from background. There are computer programs (N-body simulations) that construct simulated galaxies and run them from the Big Bang till today to try and figure out what the average spiral galaxy dark matter looks like. There's still a lot of work to be done in the simulations, and the Milky Way has some annoyingly unusual quirks (the Magellanic Clouds, for example), so this will take a while. But we're getting there.

So yeah, I'm bad at keywords apparently.

posted by physicsmatt at 8:13 PM on July 24, 2012 [3 favorites]

oops, I guess I didn't completely answer the question. There are efforts under way to measure more accurately the local motion of stars relative to the Galactic center, which can be used to determine the gravitational potential through which the stars move, and thus the dark matter density in the local volume of space. This is difficult for (at least) three reasons:

1) You need a bunch of stars to do this, and that means going progressively further out from the Sun. But the further out you go, the less sensitive you are to small variations.

2) You need to know local motions very well. In addition to the observational issues of measuring stellar motion relative to the Sun, you need to translate that into motion around the Galactic center, which is apparently difficult to determine precisely.

3) We're locally dominated by baryons, and this techniques measures the sum of baryonic and dark matter contributions. So once you figure out the potential, you need to know the location of the baryons, and subtract their contribution. Fortunately, baryons glow (directly or indirectly), so we can make a decent map of where most of them are around here.

I'm hitting the edge of my knowledge, as this is something we need an observer to really answer. I think the LSST Collaboration is going to be providing a survey of the local stars among its science objectives, so this might be a place to start looking for more information. Suffice to say, its an area of very active interest at the moment.

posted by physicsmatt at 8:31 PM on July 24, 2012 [4 favorites]

1) You need a bunch of stars to do this, and that means going progressively further out from the Sun. But the further out you go, the less sensitive you are to small variations.

2) You need to know local motions very well. In addition to the observational issues of measuring stellar motion relative to the Sun, you need to translate that into motion around the Galactic center, which is apparently difficult to determine precisely.

3) We're locally dominated by baryons, and this techniques measures the sum of baryonic and dark matter contributions. So once you figure out the potential, you need to know the location of the baryons, and subtract their contribution. Fortunately, baryons glow (directly or indirectly), so we can make a decent map of where most of them are around here.

I'm hitting the edge of my knowledge, as this is something we need an observer to really answer. I think the LSST Collaboration is going to be providing a survey of the local stars among its science objectives, so this might be a place to start looking for more information. Suffice to say, its an area of very active interest at the moment.

posted by physicsmatt at 8:31 PM on July 24, 2012 [4 favorites]

*While there are different sizes of infinity...*

In case anyone is confused, think of this: there are an infinite number of whole numbers, right? And there are an infinite number of even (divisible by 2) whole numbers, yes? But there are only half as many even numbers as whole numbers. So not all infinities are the same.

posted by echo target at 8:42 AM on July 25, 2012

Thanks as usual, physicsmatt. I certainly appreciate the fuller explanation; I just asked for keywords in case you didn't have a lot of time.

Am I right in thinking that the only way we know anything (currently) about dark matter is through its effect on visible (i.e. baryonic?) matter. So if there was a galaxy out there made completely of dark matter, we'd only ever know about it through its contribution to the universal total amount of dark matter, and if some visible matter passed it by? (I've got no good basis for arguing that such a thing exists. I'm just postulating stuff here.)

posted by benito.strauss at 9:17 AM on July 25, 2012

Am I right in thinking that the only way we know anything (currently) about dark matter is through its effect on visible (i.e. baryonic?) matter. So if there was a galaxy out there made completely of dark matter, we'd only ever know about it through its contribution to the universal total amount of dark matter, and if some visible matter passed it by? (I've got no good basis for arguing that such a thing exists. I'm just postulating stuff here.)

posted by benito.strauss at 9:17 AM on July 25, 2012

echo target: that's not the greatest example, since both infinities you mentioned are the same infinity: it's called aleph_0. What this means is that you can come up with an algorithm to match an integer with an even integer and never run out of either. So there are the same number of even numbers and even and odd numbers (even though one is a subset of the other). There are also the same number of rational numbers (numbers that can be written as ratios of integers) as integers.

There are, however, other larger infinities (aleph_1 and so on). The number of real numbers (rational+irrational) numbers is infinitely larger than the number of rational numbers (and thus of integers), for example. Actually there are infinitely more real numbers between 0 and 1 than there are integers.

Warning: this subject drove Cantor mad, so if you start seeing Lovecraftian horrors on the periphery of your vision after a while, step slowly away from the set theory.

benito.strauss: we know of dark matter only through its gravitational effects at the moment. Either from effects on rotation curves of bound objects (galaxies or galaxy clusters), the expansion rate of the early Universe (CMB power spectrum and Big Bang Nucleosynthesis), or gravitational lensing (where we 'see' dark matter that is backlit by light from a far-off source by the bending of the light caused by the gravity of the dark matter).

If there were dark matter "galaxies," they could show up as sources of gravitational lensing, in addition to coming in to the total dark matter energy density we determined from the early Universe constraints.

In some sense, we already see such objects (the aforementioned gravitational lensing does occur). Furthermore, if you look at cold dark matter N-body simulation, you find that there should be a huge number of dark matter halos from galaxy-sized down to solar-system sized. Some of these contain large number of baryons in the form of gas, so these halos have stars and are the normal galaxies, satellite galaxies and dwarf galaxies we see around us. Many of them presumably do not contain significant gas and so are invisible to us.

However, none of these dark halos would look like spiral galaxies. They would be big, fluffy roughly spherical objects. The reason is that dark matter does not interact with itself very strongly (if at all). It certainly has no long range forces other than gravity with significant strength (i.e., no electromagnetism or "dark" electromagnetism). Without such forces, dark matter cannot self-scatter, and more importantly, it can't radiate energy and cool. This means that it can't form compact objects like stars and planets. So, sadly, there are no dark solar systems with dark aliens looking at their dark CMB and wondering about the missing 5% of the Universe which is us. I was very sad when I figured that out.

...and I've completely derailed yet another physics thread, as this is supposed to be about how we measure the curvature of the Universe. I swear that's just as interesting as dark matter and infinities.

posted by physicsmatt at 10:05 AM on July 25, 2012 [3 favorites]

There are, however, other larger infinities (aleph_1 and so on). The number of real numbers (rational+irrational) numbers is infinitely larger than the number of rational numbers (and thus of integers), for example. Actually there are infinitely more real numbers between 0 and 1 than there are integers.

Warning: this subject drove Cantor mad, so if you start seeing Lovecraftian horrors on the periphery of your vision after a while, step slowly away from the set theory.

benito.strauss: we know of dark matter only through its gravitational effects at the moment. Either from effects on rotation curves of bound objects (galaxies or galaxy clusters), the expansion rate of the early Universe (CMB power spectrum and Big Bang Nucleosynthesis), or gravitational lensing (where we 'see' dark matter that is backlit by light from a far-off source by the bending of the light caused by the gravity of the dark matter).

If there were dark matter "galaxies," they could show up as sources of gravitational lensing, in addition to coming in to the total dark matter energy density we determined from the early Universe constraints.

In some sense, we already see such objects (the aforementioned gravitational lensing does occur). Furthermore, if you look at cold dark matter N-body simulation, you find that there should be a huge number of dark matter halos from galaxy-sized down to solar-system sized. Some of these contain large number of baryons in the form of gas, so these halos have stars and are the normal galaxies, satellite galaxies and dwarf galaxies we see around us. Many of them presumably do not contain significant gas and so are invisible to us.

However, none of these dark halos would look like spiral galaxies. They would be big, fluffy roughly spherical objects. The reason is that dark matter does not interact with itself very strongly (if at all). It certainly has no long range forces other than gravity with significant strength (i.e., no electromagnetism or "dark" electromagnetism). Without such forces, dark matter cannot self-scatter, and more importantly, it can't radiate energy and cool. This means that it can't form compact objects like stars and planets. So, sadly, there are no dark solar systems with dark aliens looking at their dark CMB and wondering about the missing 5% of the Universe which is us. I was very sad when I figured that out.

...and I've completely derailed yet another physics thread, as this is supposed to be about how we measure the curvature of the Universe. I swear that's just as interesting as dark matter and infinities.

posted by physicsmatt at 10:05 AM on July 25, 2012 [3 favorites]

matt, I owe you many beers. (I believe the payment schedule for explaining physics goes, over time, as: beer, beer, beer, beer, Doctorate, beer, beer, beer.

posted by benito.strauss at 10:18 AM on July 25, 2012 [1 favorite]

posted by benito.strauss at 10:18 AM on July 25, 2012 [1 favorite]

While I cannot speak to the size of the universe, on the question of whether you can measure the circumference of the Earth from local data the OP is just plain wrong.

Doing such measurements is a popular pastime among physics hobbyists, and I remember when I had access to Dad's current issues of

Both methods yielded results within 5% of the accepted value.

posted by localroger at 3:58 PM on July 25, 2012 [1 favorite]

Doing such measurements is a popular pastime among physics hobbyists, and I remember when I had access to Dad's current issues of

*The Physics Teacher*seeing at least two articles about such experiments. One group shot a laser across the surface of a frozen lake for a distance of a couple of miles and measured the height of the beam above the ice at the ends and middle. Another measured the difference between the time of final sunset over a calm lake at the bottom of a fire escape, and then again after a mad dash to the top. (They also used trigonometry to calculate the height of the fire escape for bonus points.)Both methods yielded results within 5% of the accepted value.

posted by localroger at 3:58 PM on July 25, 2012 [1 favorite]

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posted by Edison Carter at 10:56 AM on July 24, 2012