Complex concepts explained through analogy

[60moo]

Let's face it - most people don't understand scientific concepts, let alone understand ideas relating to quantum physics or astronomy. Yet pretty well everybody has at least some fascination for the Universe.

Even with my very limited knowledge, I've derived some satisfaction attempting to describe certain ideas - otherwise not easy to grasp - to those who want to understand, through analogy e.g.

Q: How can there be no centre to the Universe?
A: Just as there's no centre to the surface of a sphere.

Q: Surely there was a time before the Big Bang?
A: Think of it in the same way there's no north of the North Pole...

So, what analogies do you use to help "explain" certain concepts about our Universe to the layman?

[Beyond]

You mentioned the concept of there being no center to the universe. I should think that a Donut might make a good analogy. It also has no center. One could use it like a snapshot in time of a young Universe expanding outward. As time went on, the emptyness of the center would follow and would be like the center of the Donut - round. The really good part of using the Donut as an anology is that if you find you are wrong, or that you are hungry, you can eat the analogy

[Chris Peterson]

You mentioned the concept of there being no center to the universe. I should think that a Donut might make a good analogy. It also has no center. One could use it like a snapshot in time of a young Universe expanding outward. As time went on, the emptyness of the center would follow and would be like the center of the Donut - round. The really good part of using the Donut as an anology is that if you find you are wrong, or that you are hungry, you can eat the analogy :!: :D

No, that's not a good analogy! It's almost certain to make people think the Universe is toroidal, or that there is (or was) a center, and now it's empty. Neither of those is close to the truth. The best way I know to teach the shape of the Universe is to play the Flatland game. Start with a circle, and put some ants along the edge. As the circle gets larger, the ants get farther apart, but the point of expansion isn't on the line (universe) the ants occupy. Now you can move up to a balloon. Ants walking on it have two dimensions of freedom instead of one, but otherwise things work the same- the balloon gets larger, the ants' 2D universe gets larger, but the expansion is about a center which is outside that universe. Hopefully, with those examples as a start, people can now understand how this can be taken up one more dimension, to the universe we live in. We have three dimensions of freedom, and a universe that, as in the analogies, is growing outward from a center that isn't part of our accessible space. It isn't that there isn't a center to our universe, it's just that it doesn't exist as a 3D point.

[Beyond]

So does that mean the Universe did not expand in all directions until after inflation?

[Chris Peterson]

So does that mean the Universe did not expand in all directions until after inflation?

It expanded four-dimensionally from the first instant (before and after inflation). You could think of the center point as being at (0,0,0,0), which is where it still is. Unfortunately, since t no longer equals zero, that's a point we are unable to see... it doesn't exist in the three-dimensional universe we have access to, any more than the center of a balloon exists in the two-dimensional universe its surface occupants have access to. We see space getting larger, but we don't see the center of expansion.

[Beyond]

Ok, time for me to "EAT" my Donut. At least it's better than eating Crow - No feathers

[Beta]

I've sometimes compared atoms to bells. A bell has a characteristic set of frequencies, and will resonate if hit with sound of a frequency close to one of its own. A loud crash will make a bell hum a little, at its own pitch. So the sun hits the atmosphere with a big loud chord of WHITE! and oxygen atoms all over the sky go *blue* *blue* *blue*.

Reading about the "center of the universe"question, it occurs to me that the trunk of a tree might be a good analogy. The bark of the tree is the present-day universe. The wood inside represents the past, where the bark used to be. The tree (and the bark) began long ago, when the bark was somehow all at the center. The bark is getting bigger with time, scars and marks are getting farther apart, but where is the center of the bark?

Richard Feynman had a beautiful analogy to describe physics: imagine the gods are playing chess and every now and then we get to see part of the board, and we're trying to learn the rules just from that. We notice the basic patterns first, like the tendency of the number of pieces to diminish over the course of a game. Later we notice more subtle patterns; for example, if at one point in a game there's only one black bishop on the board, and it's on a black square, then if we see the board later we will see either no black bishop or a black bishop on a black square. This may lead us to a theory of how a bishop moves around. Then after seeing glimpses of millions of games, we see the impossible: there was only one black bishop, it was on a black square, then later in the same game we see that there's one black bishop on the board and it's on a white square. So no matter how much we loved our theory about bishops, it was wrong (or at least incomplete) and we have to accept that fact and try again to figure out what's going on.

[Chris Peterson]

I've sometimes compared atoms to bells. A bell has a characteristic set of frequencies, and will resonate if hit with sound of a frequency close to one of its own. A loud crash will make a bell hum a little, at its own pitch. So the sun hits the atmosphere with a big loud chord of WHITE! and oxygen atoms all over the sky go *blue* *blue* *blue*.

Not bad.

Reading about the "center of the universe"question, it occurs to me that the trunk of a tree might be a good analogy. The bark of the tree is the present-day universe. The wood inside represents the past, where the bark used to be. The tree (and the bark) began long ago, when the bark was somehow all at the center. The bark is getting bigger with time, scars and marks are getting farther apart, but where is the center of the bark?

I like that one. It loses a little over the balloon because you have a cylinder instead of a sphere, but I don't think that matters much. It is probably helpful to emphasize that the little tree cosmologists trying to understand their universe live on the bark, and the only directions they are aware of are on that surface... outward or inward for them are the same as time.

[Beyond]

So does that mean the Universe did not expand in all directions until after inflation?

It expanded four-dimensionally from the first instant (before and after inflation). You could think of the center point as being at (0,0,0,0), which is where it still is. Unfortunately, since t no longer equals zero, that's a point we are unable to see... it doesn't exist in the three-dimensional universe we have access to, any more than the center of a balloon exists in the two-dimensional universe its surface occupants have access to. We see space getting larger, but we don't see the center of expansion.

Then is it not also true that we do not actually see Expansion itself - just it's effects on the things around us that we can see and the same would be said of all the "forces" that there are -- That we cannot see them with our 3-Dimentional vision because they are all in the 4th-Dimention or beyond, and in order to see the forces that act upon everything daily, we would have to borrow from a science fiction show called Star-Trek and in particular Commander Jordy LaForge's visor that is portrayed as picking up 3, 4 or more Dimentions. Has anyone ever done any kind of serious experimenting in this area?

[Chris Peterson]

Then is it not also true that we do not actually see Expansion itself - just it's effects on the things around us that we can see and the same would be said of all the "forces" that there are -- That we cannot see them with our 3-Dimentional vision because they are all in the 4th-Dimention or beyond...

We genuinely see expansion of the Universe. We just don't see it in all its dimensions, although we are perfectly capable of understanding it in higher dimensions, as well as devising experiments that let us indirectly observe it in higher dimensions. This is really a limitation of our natural senses, not of our understanding. (When you blow up a balloon, the surface is genuinely expanding, so if you are a 2D being living on that surface, you genuinely observe real expansion, but only in two of the three dimensions that the balloon exists in.)

and in order to see the forces that act upon everything daily, we would have to borrow from a science fiction show called Star-Trek and in particular Commander Jordy LaForge's visor that is portrayed as picking up 3, 4 or more Dimentions. Has anyone ever done any kind of serious experimenting in this area?

I don't think it is possible to see beyond our three spatial dimensions. That would require time travel, which I don't think is possible. People have devised clever visualizations to help people "see" four-dimensional objects. I don't know... does this help you visualize a four-dimensional cube?

[Beyond]

So what you are saying then is that we partially see expansion at work, but because our brains are not physically capable of defining it past the 3rd dimention, they round off our visual perception to the 3rd dimention and so we do not actually realize that we ARE seeing the force that IS causeing all things to expand, because without a referrence to what it looks like in the 4th dimention, we cannot make a distinction between the expansion and what is being expanded in the 3rd dimention that we are in.

The cube is rather neat, but i don't know if it would help me visualize the 4th dimention at all. I think i would have to get a glimpse of something that i actually knew was in the 4th dimention for my brain to have an actual referrence of 4th dimentional activity as a base of understanding to apply to what i see in this 3rd dimention and even then it just may not work. It may help people who are really good at abstract ideas, though.

[Beyond]

That particular cube to me, looks like a regular cube in motion going from a small cube to a big cube to a small cube cycle. What would be the 4th dimentional part? The size change?
What would the complete 4 dimentional cube look like at rest?

[Chris Peterson]

So what you are saying then is that we partially see expansion at work, but because our brains are not physically capable of defining it past the 3rd dimention, they round off our visual perception to the 3rd dimention and so we do not actually realize that we ARE seeing the force that IS causeing all things to expand, because without a referrence to what it looks like in the 4th dimention, we cannot make a distinction between the expansion and what is being expanded in the 3rd dimention that we are in.

Trying to parse that sentence exceeded my stack depth <g>.

Have you read Flatland? Even if you have, read it again. And also read Planiverse. Those two books can really provide a lot of insight into this whole business of visualizing higher dimensions. What we are seeing is a 3D cross section of the 4D universe. Think about what a Flatlander sees when you set a sphere on his universe- a point, then as you pass the sphere through, he sees a circle that mysteriously gets larger or smaller. All he can see is the cross section of the sphere and his flat universe. A 4D sphere exposes a cross section to a 3D space in exactly the same way. If a 4D sphere were passed through our universe, we'd see a solid sphere apparently changing size. Not expanding or contracting, but simply changing size. It would seem impossible. And to a 4D being watching us, our entire volume would be accessible. They could reach inside and remove your appendix without breaking your skin- just as you could reach inside a 2D being (from a direction they aren't aware of) and pull out an internal organ. If you put their appendix next to them, they'd just feel it disappear from inside and reappear outside their body.

[Chris Peterson]

That particular cube to me, looks like a regular cube in motion going from a small cube to a big cube to a small cube cycle. What would be the 4th dimentional part? The size change?
What would the complete 4 dimentional cube look like at rest?

We can't see the entire 4D cube, we can only see a cross section where it intersects our 3D space. Think about a planar universe- everything looks like some sort of polygon. When you set a cube on that plane, you get a square. But depending on how you orient the cube, and how deep you place it, it could look like a lot of different shapes. What the tesseract animation is trying to show is the 3D cross section of a 4D cube as it passes through 3-space, presenting a sequence of 3D cross sections.

[Beyond]

Thanks! It seems as though I've learned something. Now all i have to do is figure out how to find out what i just learned in a way that i can understand it.
Isn't Science wonderful? We really need an asperin smiley

[Beyond]

Chris Peterson wrote "trying to parse that sentence exceeded my stack depth <g>"
After a trip to WikipediA -- could you please explain that statement in very basic english?
Thank you!

[Chris Peterson]

Chris Peterson wrote "trying to parse that sentence exceeded my stack depth <g>"
After a trip to WikipediA -- could you please explain that statement in very basic english?
Thank you!

Sorry, it's a programming term. A stack is a sort of temporary storage area, and when we try to understand a complex sentence, we actually use something a little like it in our brains.

[Henning Makholm]

What the tesseract animation is trying to show is the 3D cross section of a 4D cube as it passes through 3-space, presenting a sequence of 3D cross sections.

If so, it would start from nothing, pass through a sequence of shapes, and then contract to nothing, rather than repeat cyclically.

I understand it as being a central projection of a 4D cubic wireframe onto a 3D hyperplane, while the 4D cube rotates in place. (Then, the 3D image is centrally projected onto a 2D plane to create the 2D array of pixels that actually show up on our monitors).

[The Code]

I've sometimes compared atoms to bells. A bell has a characteristic set of frequencies, and will resonate if hit with sound of a frequency close to one of its own. A loud crash will make a bell hum a little, at its own pitch. So the sun hits the atmosphere with a big loud chord of WHITE! and oxygen atoms all over the sky go *blue* *blue* *blue*.

Not bad.

You forgot little old me Nitrogen

http://mb-soft.com/public/bluesky.html

tc

[Beta]

You forgot little old me Nitrogen

Damn... For years I've thought the sky was blue because of resonance with the atomic spectrum of oxygen, based on a conversation I had years ago. Now that I hunt around I see that everyone says it's Rayleigh scattering, and that the size of the molecules is what matters, not the spectra. I'm not entirely convinced yet, but I'll have to reexamine my ideas and probably throw away my analogy as pretty but false. Well, that's science for you.

[Chris Peterson]

Damn... For years I've thought the sky was blue because of resonance with the atomic spectrum of oxygen, based on a conversation I had years ago. Now that I hunt around I see that everyone says it's Rayleigh scattering, and that the size of the molecules is what matters, not the spectra. I'm not entirely convinced yet, but I'll have to reexamine my ideas and probably throw away my analogy as pretty but false. Well, that's science for you.

The analogy is not false. Rayleigh scattering is still an atomic resonance phenomenon. If your analogy was so specific as to suggest that photons of a specific wavelength were simply being absorbed because of a match between their own and certain atomic orbital energy levels, that would be a problem. But at the quantum level, scattering still involves the absorption and re-emission of photons, so your loose analogy is fine. As others have noted, including other gases as well as oxygen would improve it.

[Ann]

The code linked to a page where a physicist said this about the color of the Sun:

it appears to us to be a bright yellow, almost white color.

But what about the white color of clouds?

Clouds include little condensed droplets of water. These droplets are a LOT bigger than atoms, and so they are not as transparent as oxygen or nitrogen gas. Therefore, ALL light colors tend to reflect off of those cloud droplets. During the day, that means that the light reflected off them appears bright white.

All the colors of the "bright yellow, almost white" Sun reflect off the cloud droplets, and therefore clouds look white. Shouldn't the clouds look "bright yellow, almost white" if they really reflect the color of the Sun?

Ann

[Chris Peterson]

All the colors of the "bright yellow, almost white" Sun reflect off the cloud droplets, and therefore clouds look white. Shouldn't the clouds look "bright yellow, almost white" if they really reflect the color of the Sun?

Maybe you have a better idea what this physicist means by "bright yellow, almost white". That makes no sense to me. Pretty much by definition, "bright yellow" means a saturated yellow, and "bright white" means unsaturated.

Clouds are white for the same reason sunlit snow is white: the scattering particles don't preferentially scatter any particular visible wavelength, so you get both scattered direct sunlight (which has a faint yellow cast after passing through the atmosphere) as well as scattered blue sky light. The two are thus added back together, giving the original white color of the sunlight itself. Clouds can certainly show color casts if they aren't uniformly lit by both the sun and the blue sky.

[Ann]

All the colors of the "bright yellow, almost white" Sun reflect off the cloud droplets, and therefore clouds look white. Shouldn't the clouds look "bright yellow, almost white" if they really reflect the color of the Sun?

Maybe you have a better idea what this physicist means by "bright yellow, almost white". That makes no sense to me. Pretty much by definition, "bright yellow" means a saturated yellow, and "bright white" means unsaturated.

Thanks, Chris. Now I know what "white" is. It is unsaturated yellow!



The adventures of Snow Unsaturated Yellow?

Ann

[geckzilla]

Oh Chris, you've left your participle dangling and Ann is all over it now.