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Passions in Poetry

Chasing Shadows

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Stephanos
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0 posted 11-18-2003 09:48 PM       View Profile for Stephanos   Email Stephanos   Edit/Delete Message      Find Poems   Click to visit Stephanos's Home Page   View IP for Stephanos

Philosophers have long been accused of chasing shadows right?  Actually I think this may be more about physics.

Regardless, I found this posted elsewhere, and thought you guys might have fun with it.

quote:
consider a simple three-membered set and consider whether it is clear, true and consistent.

I will begin by assuming that the following ideas are clear and require no explanation. I'm taking the words in their ordinary usage, not as a physicist might understand them:

The skyscraper is casting a shadow.

That is the skyscraper's shadow.

John is standing in the skyscraper's shadow.

At this moment, the length of the skyscraper's shadow is exactly half of the skyscraper's actual height.

Now for the set of propositions:

1) If an object casts a shadow, then light is falling directly on that object.

2) An object cannot cast a shadow through an opaque object.

3) Any shadow is a shadow of something.

Most people concede that the set (1,2,3) is clear, that is, (1) is clear, (2) is clear and (3) is clear, that (1,2,3) is true, that is, (1) is true, (2) is true, and (3) is true, and that the conjunction of (1), (2) and (3) is consistent. (As it happens, the conjunction of (1), (2) and (3) is formally consistent, whether anyone concedes that or not. That much, at least, is not a matter of opinion.)

What may we deduce from (1,2,3)? Not much, for (1,2,3) is a snare and a delusion. If the conjunction (1,2,3) is clear, then it is not true, and if it is true, then it is not clear, i.e., if it's true, then the propositions cannot mean what they seem to mean.

I have a large conifer in my backyard that casts a long and broad shadow on a clear day. From time to time a cardinal flies past the conifer, through its shadow. Now at a precise moment, when a cardinal is flying past the conifer, there is an area on the lawn that, had the confier been absent, there would still have been a shadow cast by the cardinal. Call the area comprised by the shadow that would have been cast by the cardinal if the conifer did not exist A.

What is casting the shadow on A? It cannot be the cardinal, for (1) says that's not possible. It cannot be the tree, for (2) says that's not possible. It must be something, for (3) says so. So what is casting the shadow on A?



We needed something to jumpstart this forum again!

Stephen.

[This message has been edited by Stephanos (11-18-2003 09:52 PM).]

Not A Poet
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1 posted 11-19-2003 11:31 AM       View Profile for Not A Poet   Email Not A Poet   Edit/Delete Message      Find Poems   Click to visit Not A Poet's Home Page   View IP for Not A Poet

The conifer by difraction, the short answer to a long question.
Magic Solias
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2 posted 11-19-2003 06:04 PM       View Profile for Magic Solias   Email Magic Solias   Edit/Delete Message      Find Poems  View IP for Magic Solias

Common sense.  Since there is no light that can reach the cardinal to cast the shadow, no shadow could be cast by it.  But because there is no light, there is "shadow" (absense of light) when the cardinal is in a zone absent of light.  So none of the propositions 1,2,3 are actually wrong.

Magic Solias

"we dream to love and love to dream"

Essorant
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3 posted 11-19-2003 08:30 PM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

If there were no motes of light in the shadow wouldn't the cardinal be invisible?
The shadow still has light and this therefore must cast the shadow for the cardinal.

[This message has been edited by Essorant (11-19-2003 08:31 PM).]

Essorant
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4 posted 11-20-2003 12:32 AM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

ZZZzzzzzzzzz    

Stephanos
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5 posted 11-20-2003 01:47 AM       View Profile for Stephanos   Email Stephanos   Edit/Delete Message      Find Poems   Click to visit Stephanos's Home Page   View IP for Stephanos

Personally I think #2, "An object cannot cast a shadow through an opaque object", is suspect.

It is misleading. If there is one light source, then an object CAN cast a shadow that engulfs any smaller opaque object, including the surface on the other side of that opaque object. Shadow is simply the abscence of light ... which transcends opaqueness. The concept of "opaque" only makes sense in the assumed presence of light.


Stephen.

Essorant
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6 posted 11-20-2003 10:23 AM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

Stephen

But engulfing doesn't mean penetrating the object.  If shadows could penetrate opaqueness where would they land at all?
hush
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7 posted 11-20-2003 02:37 PM       View Profile for hush   Email hush   Edit/Delete Message      Find Poems  View IP for hush



Listen to you guys, talking all smart-like.

Personally, my mind is so full of correlations and cranial nerves that as far as complex thought goes, I'd say I'm slightly more useful than a potato, yet not quite as capable as say, a slug.

And, essentially, I've got nothing to say, but I just miss this forum so durn much I thought I'd peek in and add some frivoloity.
jbouder
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8 posted 11-20-2003 02:40 PM       View Profile for jbouder   Email jbouder   Edit/Delete Message      Find Poems  View IP for jbouder

Hush:

At least your poetry is better than that of the Vogons.

Stephen:

Since "A" doesn't really exist, how can anything cast a shadow on it?

Jim
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9 posted 11-20-2003 10:53 PM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

Does anyone know where Brad has been?
Stephanos
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10 posted 11-21-2003 12:20 AM       View Profile for Stephanos   Email Stephanos   Edit/Delete Message      Find Poems   Click to visit Stephanos's Home Page   View IP for Stephanos

Essorant: "But engulfing doesn't mean penetrating the object.  If shadows could penetrate opaqueness where would they land at all?"

You're right.  Engulfing does not mean penetrating ... that's why the word penetrate is the wrong word to use when speaking of shadow (the absence of light).  Think about it in terms of a complete shadow.  In the absence of light, nothing is visible.  Everything just seems as part of the shadow.  So to think of a shadow "penetrating" or "not penetrating" an opaque object is wrongheaded.  Shadow does not penetrate opaqueness ... it takes it away.  In a complete shadow, there is no such thing as opaque.  

So the bird on the other side of the conifer is not being "penetrated" by the shadow of the conifer... the bird and everything beyond it, is engulfed in the absence (or at least a lesser amount) of light.

I just found it helped me out if I imagined the conifer blocking out ALL the light ... this helps us to realize what the true nature of a shadow is, which is the absence of something.  Seeing this is the case, it would make sense to speak of LIGHT not being able to penetrate opaque objects, but not shadow.

Did I make myself clear, or confuse everyone?  These things are difficult to articulate.




Hush,

We could use a potato and a slug instead of the conifer and the cardinal if it would make it easier for ya.     Yeah, I miss this forum too.  Why do you think I'm posting such a portentous topic?




Jim:  "Since "A" doesn't really exist, how can anything cast a shadow on it?"


Ha.  You really want to take this one to a new level don't you?  We'll have to accept this "area" by pure inference eh?  


I'm beginning to get a headache.


Stephen.

        

[This message has been edited by Stephanos (11-21-2003 12:29 AM).]

Essorant
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11 posted 11-21-2003 01:17 AM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

{edited)

I decided I wouldn't get started about non-existance again lol.

I better get to bedfordshire.
Hope your headache goes away quickly, Stephen

Essorant


[This message has been edited by Essorant (11-21-2003 01:33 AM).]

jbouder
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12 posted 11-21-2003 09:28 AM       View Profile for jbouder   Email jbouder   Edit/Delete Message      Find Poems  View IP for jbouder

Well, if we suppose "A" exists, then I would rephrase the question, "What is obstructing the visible light from shining on Point A."  The answer would be the conifer.  If the conifer wasn't there, it would be the bird.

Pete's answer was better, but I think is more or less saying the same thing.

Jim
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13 posted 11-21-2003 01:01 PM       View Profile for Deep_Inside   Email Deep_Inside   Edit/Delete Message      Find Poems  View IP for Deep_Inside

just think what would happen if the cardinal passed on the other side of the conifer. the cardinal would then be casting a shadow on the conifer and then there is no light for the conifer to cast a shadow but this means there is an absent of light continuing onto the ground so if the cardinal pass thought the shadow he is then passing thought a absent of light from the main light source (in this case the sun)and witch then continues onto the ground.
now you can still see the cardinal because there is light being cast onto the cardinal that is being bounced from another abject this is being hit with said light source. so with this reasoning the 123 formula is still correct.

and if this is just a bunch of crap i have no idea of whats going on here :goffy:
eor
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14 posted 11-21-2003 01:45 PM       View Profile for eor   Email eor   Edit/Delete Message      Find Poems  View IP for eor

the sun is at a differnt angle than before, either earlier or later in the day, so therefore when the bird flys through the place where the shadow once was the birds shadow appears, there for not casting a shodow through an opaque object.  in short it's morning or dusk.

"So what befalls the flawless?
Look what I've built, it shines so beautifully now watch as it destroys me."

Essorant
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15 posted 11-21-2003 06:39 PM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

If we were to imagine each shadow as being a different colour would there be a different colour at all for this cardinal inside the conifer's shadow?  There is light inside the shadow still, so shouldn't this draw some shadow off the cardinal, and show if it were a different colour?

[This message has been edited by Essorant (11-21-2003 08:36 PM).]

Not A Poet
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16 posted 11-21-2003 09:27 PM       View Profile for Not A Poet   Email Not A Poet   Edit/Delete Message      Find Poems   Click to visit Not A Poet's Home Page   View IP for Not A Poet

But the color of a shadow is determined solely by the object on which it is cast. It is in no way related to the color of the object casting it.

Essorant
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17 posted 11-21-2003 09:59 PM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

Yes, I wasn't referring to the colours of the objects.  We could call a conifer's shadow a mist of purple, and a cardinal's a mist of green.  Would there be any hues of green in the purple?  Any shade of the cardinal at all?


[This message has been edited by Essorant (11-21-2003 10:26 PM).]

Not A Poet
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18 posted 11-21-2003 11:51 PM       View Profile for Not A Poet   Email Not A Poet   Edit/Delete Message      Find Poems   Click to visit Not A Poet's Home Page   View IP for Not A Poet

There could be green if the shadow is on grass but the purple is a stretch. If the thing cast is truly a shadow then its color will be determined by whatever it is cast upon. In this case green if on grass, some brown if on dirt and gray (usually) if on concrete. Now if that tree happened to be translucent, sort of like darkly colored glass, so that it reduced the light but still passed some through then the color of its "casting" would be affected byt its own color. But then it really would not be a shadow either.

When the bird flies into the area between the tree and its shadow, where it receives no direct light then it appears to not cast a shadow. In fact though, there is still light in that zone, diffracted light bending around the tree and reflected light from any number of other sources. Depending on the relative intensity of all these secondary light sources, the bird may actually cast a shadow or even several shadows. But the location of those shadows will be determined by the light sources. It may even be on the dark side of the tree. To the naked eye, however, any such shadows will almost surely be indistinguishable as the secondary light is usually very weak compared to the primary light and the secondary sources are usually arrayed so as to light any shadows resulting from each other.

Thanks for bringing this up Stephen. A worthy discussion indeed.

Essorant
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19 posted 11-22-2003 12:41 AM       View Profile for Essorant   Email Essorant   Edit/Delete Message      Find Poems   Click to visit Essorant's Home Page   View IP for Essorant

Not A Poet
Thank you.  It does make more sense to me now; despite a bit of a headache  

[This message has been edited by Essorant (11-22-2003 12:42 AM).]

Ron
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Pete, I think Essorant's original point about color wasn't meant to be taken literally, but was rather a "thought experiment" that could indeed be useful to differentiate between otherwise indistinguishable shadows.

In my opinion, the fallacy, as usual, lies in the original propositions, and is essentially the same old trick of trying to determine how much a hole in the ground weighs. A hole, of course, doesn't really exist, except as a handy way to talk about the absence of something. Same with a shadow. Proposition 2 talks about an object "casting a shadow" as if a shadow is something that really exists. It doesn't, but rather just denotes an absence of light. By rewording Proposition 2, its truth value easily devolves into silliness.

2) An object cannot block more light through an opaque object?

Pete's first answer was, I think, both the most correct AND the most revealing by what it failed to say.

What about the millions of dust motes that are floating between the source of light (our sun) and the tree/bird/ground upon which we see the "lack of light" we call a shadow? We know light can't pass through the motes, so shouldn't we see millions of tiny shadows? If a plane flew two miles overhead, between the sun and the tree, shouldn't we see its shadow?

The answer, as Pete indicated, is that we don't think of the dust motes as blocking light, but rather we say the light has been diffused. Another way of saying the same thing is to call the light a wave. If we put a big rock four or five feet from the shore line into the ocean, we don't end up with a complete absence of water behind the rock when a wave comes in. Rather the wave of water hits the rock, then bends (or diffuses) around it. The big rock is just a dust mote compared to the vastness of the ocean, and we'll see very little evidence of its existence by measuring the volume of water at the shore line.

Change the rock to a boulder and move it only a foot from the shore line. It is now like the tree, and there will be noticeably less water behind the boulder than in front of it. The wave of water has more to bend around, and less time to do it. But if you put a paper bag holding your lunch directly behind the boulder, the result will STILL be a very soggy sandwich.

To see the same phenomenon in yet a different way, change the cardinal into a fat little hummingbird and have it hover an inch or two from the ground. The hummer will be surrounded in the shadow of the conifer, as was the cardinal, but the tree hasn't blocked ALL the light, any more than the boulder blocked all the water from our paper bag, so of course, we can still see the bird. Unlike the cardinal, who flew high enough to allow the remaining light to diffuse, the hummingbird hovering two inches from the ground will cast its own deeper shadow within the shadow of the tree.
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21 posted 11-22-2003 11:23 AM       View Profile for Midnitesun   Email Midnitesun   Edit/Delete Message      Find Poems  View IP for Midnitesun

OK, so you made me stop and think about this one.
I lived in the Interior of Alaska for six years, and even in the coldest darkest winter nights I walked in the woods near my cabin. I had to constantly be aware of movement (think Moose) as well as the depth/solidity of the snowpack. Aknowledging the variations of a shadow's DEPTH and INTENSITY often meant survival.
Even in a seemingly lightless environment, and with poor natural vision, I saw many shades of shadow once my eyes became accustomed to the darkness. The darkness rarely hid even the smallest of objects, though more than once I mistook a branch for something more sinister. LOL, I think I need another cup of java to put this all in perspective.
Thanks for waking me up today.
River
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22 posted 11-22-2003 06:42 PM       View Profile for River   Email River   Edit/Delete Message      Find Poems  View IP for River

my brain hurts. i don't have an answer. just thought i would share that with everyone, lol.

                - River
Stephanos
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23 posted 11-24-2003 04:24 PM       View Profile for Stephanos   Email Stephanos   Edit/Delete Message      Find Poems   Click to visit Stephanos's Home Page   View IP for Stephanos

Stephen said : "Personally I think #2, "An object cannot cast a shadow through an opaque object", is suspect.  It is misleading. If there is one light source, then an object CAN cast a shadow that engulfs any smaller opaque object, including the surface on the other side of that opaque object. Shadow is simply the abscence of light ... which transcends opaqueness. The concept of "opaque" only makes sense in the assumed presence of light. "


Ron said:  "In my opinion, the fallacy, as usual, lies in the original propositions, and is essentially the same old trick of trying to determine how much a hole in the ground weighs. A hole, of course, doesn't really exist, except as a handy way to talk about the absence of something. Same with a shadow. Proposition 2 talks about an object "casting a shadow" as if a shadow is something that really exists. It doesn't, but rather just denotes an absence of light. By rewording Proposition 2, its truth value easily devolves into silliness.

2) An object cannot block more light through an opaque object?
"


We're saying the same thing here, right?





Ron: "The answer, as Pete indicated, is that we don't think of the dust motes as blocking light, but rather we say the light has been diffused. Another way of saying the same thing is to call the light a wave."


Yeah, but I think that the initial problem can be approached best by imagining absolute light and shadow, rather than sunlight.  Perhaps imagining a the conifer and cardinal in a completely dark world, with a large laser beam shining down on the conifer.  Your statements about diffusing light is interesting, but a secondary issue to the fallacy of proposition #2 isn't it?


My headache IS starting to go away.    


Stephen.

[This message has been edited by Stephanos (11-24-2003 04:26 PM).]

Not A Poet
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24 posted 11-25-2003 02:36 PM       View Profile for Not A Poet   Email Not A Poet   Edit/Delete Message      Find Poems   Click to visit Not A Poet's Home Page   View IP for Not A Poet

As Ron (I believe) pointed out, as shadow is not a "thing" in and of itself. Instead, it is the absence of light. In the everyday world, it really is an area of reduced light which we perceive as a darker spot. I think this fact effectively invalidates proposition #2.

Since our venue was outside, we were implicitly talking of the everyday world, not lasers. When you walk outside and look at the sun (hopefully through very dark glasses) you are seeing direct light. When you look any other direction, you are still seeing that same light but indirectly. Everything in our environment, even the air and Ron's dust motes, interacts with that sunlight, most commonly by reflecting it or refracting (bending) it. As a result, our eyes and everything we see are actually receiving light from all around. So even in a dark shadow, there is still some light. The reason the shadow appears dark is that the direct sunlight is so much stronger than all that ambient light that the area surrounding the shadow is so much lighter by contrast.

Ron also brought out another fact that could stand more discussion. The closer the shadow is to the object casting it, the denser it will become. The reason is that the object is also blocking some of that ambient light as well as the direct sunlight. As it gets closer to its shadow, there is less ambient light able to reach the shaded area. Thus the shadow gets darker.

And, although it can be extremely useful, it really is not necessary to consider the wave nature of light to understand these facts. Thinking of it as rays of photons will yield the same results. Of course that does require relativity to explain why the photons turn or the light seems to bend. But I find the concept of relativity easier to grasp than wave mechanics.

Pete
 
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