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	<title>Comments on: AAS Post #2: Listening to the Universe</title>
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	<link>http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/</link>
	<description>I am an astronomer, writer, and skeptic. I likes reality the way it is, and I aims to keep it that way. My real name is Phil Plait, and I run the Bad Astronomy blog.</description>
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		<title>By: Keith Douglas</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/comment-page-1/#comment-9600</link>
		<dc:creator>Keith Douglas</dc:creator>
		<pubDate>Fri, 13 Jan 2006 17:44:45 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/#comment-9600</guid>
		<description>From what I know it is strictly speaking incorrect to say that space is warped by mass. Instead one should say that gravitational fields the spatiotemporal structure. After all, as Einstein himself remarked, if you remove all bodies and radiation from the universe nothing at all remains. This is a fundamental change vis-a-vis the Newtonian perspective where space and time *are* &quot;stuffs&quot;.</description>
		<content:encoded><![CDATA[<p>From what I know it is strictly speaking incorrect to say that space is warped by mass. Instead one should say that gravitational fields the spatiotemporal structure. After all, as Einstein himself remarked, if you remove all bodies and radiation from the universe nothing at all remains. This is a fundamental change vis-a-vis the Newtonian perspective where space and time *are* &#8220;stuffs&#8221;.</p>
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		<title>By: JLR</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/comment-page-1/#comment-9601</link>
		<dc:creator>JLR</dc:creator>
		<pubDate>Thu, 12 Jan 2006 01:08:45 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/#comment-9601</guid>
		<description>Irishman said:
&gt;So I donâ€™t think that attitude is particularly helpful. Okay, maybe the answer is â€œyouâ€™re just not suited to understanding astronomy, pick a new hobby,â€ but somehow thatâ€™s dissatisfying to me. Anyone interested in learning should be taught to the best of our abilities to teach them. Sometimes thatâ€™s limited by their ability to learn, and sometimes their willingness to learn. But if we donâ€™t make the effort, then it is our fault.</description>
		<content:encoded><![CDATA[<p>Irishman said:<br />
&gt;So I donâ€™t think that attitude is particularly helpful. Okay, maybe the answer is â€œyouâ€™re just not suited to understanding astronomy, pick a new hobby,â€ but somehow thatâ€™s dissatisfying to me. Anyone interested in learning should be taught to the best of our abilities to teach them. Sometimes thatâ€™s limited by their ability to learn, and sometimes their willingness to learn. But if we donâ€™t make the effort, then it is our fault.</p>
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		<title>By: Irishman</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/comment-page-1/#comment-9602</link>
		<dc:creator>Irishman</dc:creator>
		<pubDate>Wed, 11 Jan 2006 15:53:49 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/#comment-9602</guid>
		<description>And here is a graphic representation showing an object warping space-time. This example is a 3-D representation and does not use external gravity.

http://sciencebulletins.amnh.org/astro/f/gravity.20041101/essays/44_2.php

You can see a close-up of the central region here.
http://sciencebulletins.amnh.org/astro/f/gravity.20041101/</description>
		<content:encoded><![CDATA[<p>And here is a graphic representation showing an object warping space-time. This example is a 3-D representation and does not use external gravity.</p>
<p><a href="http://sciencebulletins.amnh.org/astro/f/gravity.20041101/essays/44_2.php" rel="nofollow">http://sciencebulletins.amnh.org/astro/f/gravity.20041101/essays/44_2.php</a></p>
<p>You can see a close-up of the central region here.<br />
<a href="http://sciencebulletins.amnh.org/astro/f/gravity.20041101/" rel="nofollow">http://sciencebulletins.amnh.org/astro/f/gravity.20041101/</a></p>
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		<title>By: Irishman</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/comment-page-1/#comment-9603</link>
		<dc:creator>Irishman</dc:creator>
		<pubDate>Wed, 11 Jan 2006 15:41:54 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/#comment-9603</guid>
		<description>Bill 34543 Said:
&gt;OK, so if this proton bounces a little, how will we know itâ€™s from two neutron stars halfway across the galaxy, or from a baseball being hit on Earth? Also, as big as the universe is, arenâ€™t there probably a LOT of things crashing together? Isnâ€™t this going to mean a lot of noise in the detector?

Lots of info at the link the BA provided in the article. From here:
http://sciencebulletins.amnh.org/astro/f/gravity.20041101/essays/45_2.php
-----
No Noise, Please!
If only it were so easy. Many, many types of competing vibrations, or noise, can jostle the test masses enough to mask the effect of a true gravitational wave.

Loggers felling trees nearby cause noise. The crash of ocean waves produce noise. â€œEven the motion of the atoms inside the mirrors are making the mirrors move,â€ says Gabriela GonzÃ¡lez, a physicist at nearby Louisiana State University.

Scientists have taken painstaking precautions to reduce the impact of noise on LIGO. The mirrors are suspended on a single thin metal wire to reduce the effects of forces other than gravity. To dampen competing vibrations, investigators constantly adjust the mirrors with the ultraprecise equivalent of a car suspension system.

Still, how do you detect a gravitational wave and not a rabbit jumping nearby? â€œThatâ€™s the $300 million question,â€ laughs GonzÃ¡lez. One way is by checking if a suspected wave coincided with a disturbance registered by other instruments on site, which look for changes in ground motion, magnetic field, power line voltage, and other aspects. Another way, GonzÃ¡lez explains, is by double-checking results with LIGOâ€™s twinâ€”a complete duplicate facility constructed in a barren scrub desert in Hanford, Washington. At 3,030 km away, itâ€™s distant enough that seismic and other disturbances wonâ€™t affect both observatories simultaneously.
-----

So the scientists are definitely thinking of the noise problem and doing everything they can to eliminate mechanical vibrations so that the gravitational wave distortions of space-time can be separated out.

And then here is a page that discusses what causes gravitational waves and why the effects we can detect come from supermassive space objects far away instead of nearby tiny objects, like people.
http://sciencebulletins.amnh.org/astro/f/gravity.20041101/essays/46_1.php
----------
Why do all those massive, exploding outer-space events get all the fun? Why is it that only &lt;i&gt;they&lt;/i&gt; can create a gravitational wave? The truth is, anything with an accelerating mass has a gravitational effect. Detecting it? Well, thatâ€™s another matter entirely.
...
&lt;b&gt;You:&lt;/b&gt;  â€œEvery time you accelerateâ€”say by jumping up and downâ€”youâ€™re generating gravitational waves,â€ says Rainer Weiss, Professor Emeritus of Physics at MIT. â€œThereâ€™s no doubt of it.â€ But just standing there wonâ€™t cut the mustard. To make a wave, your mass has to both move (have velocity) and have acceleration (change the rate of motion, direction, or both).

Still, donâ€™t get your hopes up. No matter how fast you jump, sprint, or cartwheel, the resulting warp your waves make on space is so weak that itâ€™s utterly unmeasurableâ€”perhaps  100,000,000,000,000,000,000,000 times less so than the warp made by massive exploding space objects. And LIGO has a tough enough time measuring those.

&lt;b&gt;Spinning Aircraft Carrier:&lt;/b&gt; Only &lt;i&gt;enormous&lt;/i&gt; amounts of motion at &lt;i&gt;enormous&lt;/i&gt; speeds from &lt;i&gt;enormous&lt;/i&gt; masses can produce a ripple that LIGO could detect. â€œTo rival here on Earth the strength of gravitational waves from a supernova in the center of our galaxy,â€ suggests Mike Zucker, the head of LIGOâ€™s Livingston facility, â€œyouâ€™d need to take an aircraft carrier and spin it, end over end, a thousand times a second.â€ Not very likely.
----------</description>
		<content:encoded><![CDATA[<p>Bill 34543 Said:<br />
&gt;OK, so if this proton bounces a little, how will we know itâ€™s from two neutron stars halfway across the galaxy, or from a baseball being hit on Earth? Also, as big as the universe is, arenâ€™t there probably a LOT of things crashing together? Isnâ€™t this going to mean a lot of noise in the detector?</p>
<p>Lots of info at the link the BA provided in the article. From here:<br />
<a href="http://sciencebulletins.amnh.org/astro/f/gravity.20041101/essays/45_2.php" rel="nofollow">http://sciencebulletins.amnh.org/astro/f/gravity.20041101/essays/45_2.php</a><br />
&#8212;&#8211;<br />
No Noise, Please!<br />
If only it were so easy. Many, many types of competing vibrations, or noise, can jostle the test masses enough to mask the effect of a true gravitational wave.</p>
<p>Loggers felling trees nearby cause noise. The crash of ocean waves produce noise. â€œEven the motion of the atoms inside the mirrors are making the mirrors move,â€ says Gabriela GonzÃ¡lez, a physicist at nearby Louisiana State University.</p>
<p>Scientists have taken painstaking precautions to reduce the impact of noise on LIGO. The mirrors are suspended on a single thin metal wire to reduce the effects of forces other than gravity. To dampen competing vibrations, investigators constantly adjust the mirrors with the ultraprecise equivalent of a car suspension system.</p>
<p>Still, how do you detect a gravitational wave and not a rabbit jumping nearby? â€œThatâ€™s the $300 million question,â€ laughs GonzÃ¡lez. One way is by checking if a suspected wave coincided with a disturbance registered by other instruments on site, which look for changes in ground motion, magnetic field, power line voltage, and other aspects. Another way, GonzÃ¡lez explains, is by double-checking results with LIGOâ€™s twinâ€”a complete duplicate facility constructed in a barren scrub desert in Hanford, Washington. At 3,030 km away, itâ€™s distant enough that seismic and other disturbances wonâ€™t affect both observatories simultaneously.<br />
&#8212;&#8211;</p>
<p>So the scientists are definitely thinking of the noise problem and doing everything they can to eliminate mechanical vibrations so that the gravitational wave distortions of space-time can be separated out.</p>
<p>And then here is a page that discusses what causes gravitational waves and why the effects we can detect come from supermassive space objects far away instead of nearby tiny objects, like people.<br />
<a href="http://sciencebulletins.amnh.org/astro/f/gravity.20041101/essays/46_1.php" rel="nofollow">http://sciencebulletins.amnh.org/astro/f/gravity.20041101/essays/46_1.php</a><br />
&#8212;&#8212;&#8212;-<br />
Why do all those massive, exploding outer-space events get all the fun? Why is it that only <i>they</i> can create a gravitational wave? The truth is, anything with an accelerating mass has a gravitational effect. Detecting it? Well, thatâ€™s another matter entirely.<br />
&#8230;<br />
<b>You:</b>  â€œEvery time you accelerateâ€”say by jumping up and downâ€”youâ€™re generating gravitational waves,â€ says Rainer Weiss, Professor Emeritus of Physics at MIT. â€œThereâ€™s no doubt of it.â€ But just standing there wonâ€™t cut the mustard. To make a wave, your mass has to both move (have velocity) and have acceleration (change the rate of motion, direction, or both).</p>
<p>Still, donâ€™t get your hopes up. No matter how fast you jump, sprint, or cartwheel, the resulting warp your waves make on space is so weak that itâ€™s utterly unmeasurableâ€”perhaps  100,000,000,000,000,000,000,000 times less so than the warp made by massive exploding space objects. And LIGO has a tough enough time measuring those.</p>
<p><b>Spinning Aircraft Carrier:</b> Only <i>enormous</i> amounts of motion at <i>enormous</i> speeds from <i>enormous</i> masses can produce a ripple that LIGO could detect. â€œTo rival here on Earth the strength of gravitational waves from a supernova in the center of our galaxy,â€ suggests Mike Zucker, the head of LIGOâ€™s Livingston facility, â€œyouâ€™d need to take an aircraft carrier and spin it, end over end, a thousand times a second.â€ Not very likely.<br />
&#8212;&#8212;&#8212;-</p>
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		<title>By: Irishman</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/comment-page-1/#comment-9604</link>
		<dc:creator>Irishman</dc:creator>
		<pubDate>Wed, 11 Jan 2006 15:12:24 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/#comment-9604</guid>
		<description>Maybe, but that&#039;s not the limit of the use of the metaphor.  These same examples are used to convey the information to anyone interested in the topic, be it someone trying to get a career in astronomy and cosmology, or just some layperson who has a hobbyist interest in knowing about the universe.  So I don&#039;t think that attitude is particularly helpful.  Okay, maybe the answer is &quot;you&#039;re just not suited to understanding astronomy, pick a new hobby,&quot;  but somehow that&#039;s dissatisfying to me.  Anyone interested in learning should be taught to the best of our abilities to teach them.  Sometimes that&#039;s limited by their ability to learn, and sometimes their willingness to learn.  But if we don&#039;t make the effort, then it is our fault.

I also think that sometimes the ones using the metaphor don&#039;t fully grasp the intent of the metaphor, and misuse it.  That doesn&#039;t help anyone, either.  Part of the problem is one of memory. We hear this brilliant metaphor that helps us grasp a concept, but we don&#039;t commit the full details of the metaphor to memory, only the concept.  Later we try to share that metaphor with someone else because it was so meaningful to us, but our lack of grasping the fullness of the metaphor leads us to miss some of the details and thus misdirect the person we are trying to help.

I don&#039;t know what the fix is, other than trying to pay more attention ourselves when we hear good metaphors to the actual context and intent, and trying to remember those elements along with the concept.  Also, helping correct others when we hear them misunderstand or misuse a metaphor.</description>
		<content:encoded><![CDATA[<p>Maybe, but that&#8217;s not the limit of the use of the metaphor.  These same examples are used to convey the information to anyone interested in the topic, be it someone trying to get a career in astronomy and cosmology, or just some layperson who has a hobbyist interest in knowing about the universe.  So I don&#8217;t think that attitude is particularly helpful.  Okay, maybe the answer is &#8220;you&#8217;re just not suited to understanding astronomy, pick a new hobby,&#8221;  but somehow that&#8217;s dissatisfying to me.  Anyone interested in learning should be taught to the best of our abilities to teach them.  Sometimes that&#8217;s limited by their ability to learn, and sometimes their willingness to learn.  But if we don&#8217;t make the effort, then it is our fault.</p>
<p>I also think that sometimes the ones using the metaphor don&#8217;t fully grasp the intent of the metaphor, and misuse it.  That doesn&#8217;t help anyone, either.  Part of the problem is one of memory. We hear this brilliant metaphor that helps us grasp a concept, but we don&#8217;t commit the full details of the metaphor to memory, only the concept.  Later we try to share that metaphor with someone else because it was so meaningful to us, but our lack of grasping the fullness of the metaphor leads us to miss some of the details and thus misdirect the person we are trying to help.</p>
<p>I don&#8217;t know what the fix is, other than trying to pay more attention ourselves when we hear good metaphors to the actual context and intent, and trying to remember those elements along with the concept.  Also, helping correct others when we hear them misunderstand or misuse a metaphor.</p>
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		<title>By: JLR</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/comment-page-1/#comment-9605</link>
		<dc:creator>JLR</dc:creator>
		<pubDate>Wed, 11 Jan 2006 01:32:11 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/#comment-9605</guid>
		<description>Irishman said:
&gt;That is what makes the bending sheet metaphor and the expanding balloon metaphor and the expanding raisin cake metaphor so difficult to use. People who donâ€™t accept the premise will argue the periphery of the metaphor, the details that are irrelevant to the concept that is the intent of the model. Thatâ€™s also why itâ€™s hard to teach with those models, because some people canâ€™t grasp the concept youâ€™re trying to convey out of the extraneous details.&gt;

Perhaps here is a method to weed out folks that should take a different career path.  Maybe people that can&#039;t grasp the concept(s) will be better served and serve in fields and areas in which such concepts are not relevant.  I remember reading somewhere that intelligence is comprised of maybe a hundred different abilities, and we all have varying combinations and degrees of them.
I had the same problem trying to explain to some people about the &quot;Flatlanders&quot;.  Some readers here may have heard of &#039;em.  A 2D world containing 2D people that have no experience of 3D reality.  It&#039;s a tool to show how we, in our 3D universe, have trouble visualizing other dimensions that may be around us.  A fellow might try to argue with the Flatlander&#039;s concept, saying something to the effect of &quot;that&#039;s impossible because they couldn&#039;t have a circulatory system because they would be cut to pieces&quot;.  Please, ignore details irrelevant to the concept.</description>
		<content:encoded><![CDATA[<p>Irishman said:<br />
&gt;That is what makes the bending sheet metaphor and the expanding balloon metaphor and the expanding raisin cake metaphor so difficult to use. People who donâ€™t accept the premise will argue the periphery of the metaphor, the details that are irrelevant to the concept that is the intent of the model. Thatâ€™s also why itâ€™s hard to teach with those models, because some people canâ€™t grasp the concept youâ€™re trying to convey out of the extraneous details.&gt;</p>
<p>Perhaps here is a method to weed out folks that should take a different career path.  Maybe people that can&#8217;t grasp the concept(s) will be better served and serve in fields and areas in which such concepts are not relevant.  I remember reading somewhere that intelligence is comprised of maybe a hundred different abilities, and we all have varying combinations and degrees of them.<br />
I had the same problem trying to explain to some people about the &#8220;Flatlanders&#8221;.  Some readers here may have heard of &#8216;em.  A 2D world containing 2D people that have no experience of 3D reality.  It&#8217;s a tool to show how we, in our 3D universe, have trouble visualizing other dimensions that may be around us.  A fellow might try to argue with the Flatlander&#8217;s concept, saying something to the effect of &#8220;that&#8217;s impossible because they couldn&#8217;t have a circulatory system because they would be cut to pieces&#8221;.  Please, ignore details irrelevant to the concept.</p>
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		<title>By: Irishman</title>
		<link>http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/comment-page-1/#comment-9606</link>
		<dc:creator>Irishman</dc:creator>
		<pubDate>Tue, 10 Jan 2006 17:22:02 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/badastronomy/2006/01/09/aas-post-2-listening-to-the-universe/#comment-9606</guid>
		<description>Bill 34543 Said:
&gt;Also a comment on the stretched sheet example. It always comes with gravity. A ball rolls along the sheet and when it comes to the depression, it rolls in. Duh! GRAVITY made it roll in. How about an example of space being warped by mass, that does NOT involved gravity in the explanation? Putting gravity into the explanation is circular. Or so it seems to me

You raise a difficult issue, something inherent to using metaphors and models to represent effects that aren&#039;t directly observable.  Bending of space time is such a difficult thing for us to conceptualize, thus the need for a model. The problem is that the model or metaphor is constrained by the rules of our everyday life, but it is those rules that make conceptualizing the effect so difficult in the first place.  Those rules define our common experience. They are &quot;how the world works&quot; at the level we experience it.  So when we look at something beyond everyday experience, such as gravity bending space-time, or the expanding universe, we&#039;re dealing with effects that doesn&#039;t conform to everyday rules that we can easily see.  Metaphors and models are attempts to explain it, conceptualize it, put it in a context that we can conceptualize.  Of course, that&#039;s the inherent flaw, that the model or metaphor is inherently misleading and therefore, maybe our understanding is flawed.  Certainly, if you scrutinize the metaphor too closely you can find flaws.  The trick is to understand what you&#039;re trying to get out of the model and ignore the details that detract when they don&#039;t conflict with the elements you&#039;re trying to grasp.

That is what makes the bending sheet metaphor and the expanding balloon metaphor and the expanding raisin cake metaphor so difficult to use.  People who don&#039;t accept the premise will argue the periphery of the metaphor, the details that are irrelevant to the concept that is the intent of the model.  That&#039;s also why it&#039;s hard to teach with those models, because some people can&#039;t grasp the concept you&#039;re trying to convey out of the extraneous details.

What the metaphor is attempting to explain is the warping of the fabric caused by mass. More mass causes a larger depression. The depression affects the path of objects rolling in a straight line nearby.  Yes, this model is using external gravity to provide a downward force against a 2-D plane of fabric of &quot;space-time&quot;, bending into a 3rd dimension.  The reality is a 3-D space-time, and the warping is not caused by an external force, but by the object itself compressing space-time around it.  We might think of it as a 3-D space being curved in a 4th dimension.  But humans can&#039;t very well see 4 dimensions, so we have to simplify and then extrapolate. The problem is I can&#039;t come up with any other example that demonstrates a curvature caused by a presence, at least nothing that can be visualized any easier.  And nobody else seems to be able to, either.

Here&#039;s a thought.  Think of a large magnet in the center of a table. Now roll a  small iron sphere across the table near  the magnet.  In this example, gravity is only constraining the sphere to move in the plane of the table, not affecting the pull in any way.  Now the magnet is having an effect on the sphere without touching the sphere. That is the magnetic field lines.  The sphere gets effected because as it passes through the field lines, the iron molecules try to align, and thus wiggle the field lines.  But what are magnetic field lines?  Can you see them?  Does this example help you visualize the mass making the change to the surroundings?  Or is this such an imaginary game itself that it needs its own metaphor to explain it?</description>
		<content:encoded><![CDATA[<p>Bill 34543 Said:<br />
&gt;Also a comment on the stretched sheet example. It always comes with gravity. A ball rolls along the sheet and when it comes to the depression, it rolls in. Duh! GRAVITY made it roll in. How about an example of space being warped by mass, that does NOT involved gravity in the explanation? Putting gravity into the explanation is circular. Or so it seems to me</p>
<p>You raise a difficult issue, something inherent to using metaphors and models to represent effects that aren&#8217;t directly observable.  Bending of space time is such a difficult thing for us to conceptualize, thus the need for a model. The problem is that the model or metaphor is constrained by the rules of our everyday life, but it is those rules that make conceptualizing the effect so difficult in the first place.  Those rules define our common experience. They are &#8220;how the world works&#8221; at the level we experience it.  So when we look at something beyond everyday experience, such as gravity bending space-time, or the expanding universe, we&#8217;re dealing with effects that doesn&#8217;t conform to everyday rules that we can easily see.  Metaphors and models are attempts to explain it, conceptualize it, put it in a context that we can conceptualize.  Of course, that&#8217;s the inherent flaw, that the model or metaphor is inherently misleading and therefore, maybe our understanding is flawed.  Certainly, if you scrutinize the metaphor too closely you can find flaws.  The trick is to understand what you&#8217;re trying to get out of the model and ignore the details that detract when they don&#8217;t conflict with the elements you&#8217;re trying to grasp.</p>
<p>That is what makes the bending sheet metaphor and the expanding balloon metaphor and the expanding raisin cake metaphor so difficult to use.  People who don&#8217;t accept the premise will argue the periphery of the metaphor, the details that are irrelevant to the concept that is the intent of the model.  That&#8217;s also why it&#8217;s hard to teach with those models, because some people can&#8217;t grasp the concept you&#8217;re trying to convey out of the extraneous details.</p>
<p>What the metaphor is attempting to explain is the warping of the fabric caused by mass. More mass causes a larger depression. The depression affects the path of objects rolling in a straight line nearby.  Yes, this model is using external gravity to provide a downward force against a 2-D plane of fabric of &#8220;space-time&#8221;, bending into a 3rd dimension.  The reality is a 3-D space-time, and the warping is not caused by an external force, but by the object itself compressing space-time around it.  We might think of it as a 3-D space being curved in a 4th dimension.  But humans can&#8217;t very well see 4 dimensions, so we have to simplify and then extrapolate. The problem is I can&#8217;t come up with any other example that demonstrates a curvature caused by a presence, at least nothing that can be visualized any easier.  And nobody else seems to be able to, either.</p>
<p>Here&#8217;s a thought.  Think of a large magnet in the center of a table. Now roll a  small iron sphere across the table near  the magnet.  In this example, gravity is only constraining the sphere to move in the plane of the table, not affecting the pull in any way.  Now the magnet is having an effect on the sphere without touching the sphere. That is the magnetic field lines.  The sphere gets effected because as it passes through the field lines, the iron molecules try to align, and thus wiggle the field lines.  But what are magnetic field lines?  Can you see them?  Does this example help you visualize the mass making the change to the surroundings?  Or is this such an imaginary game itself that it needs its own metaphor to explain it?</p>
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