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If we were limited to observing the shadow of a tree without the possibility of ever seeing the actual tree, what are some approaches that could be employed in order to determine its true nature. How could we ever know about its DNA, photosynthesis process, or its rough surface?

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  • Even when we saw the tree itself, we saw it in our mind. This link does not address your question, but it does address the typical subject-object problem. rugwig.blogspot.com/2013/10/…
    – Gordon
    Sep 3, 2017 at 23:27
  • We couldn't seems to be the obvious answer.
    – user20253
    Sep 4, 2017 at 13:30

3 Answers 3

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I believe that when the observation is limited to the projection, part of the information about the original object is lost. Therefore, it will not be possible to determine with any certainty the nature of the tree. The statistical methods used for the determination of the hidden parameters from the observed ones prevent the complete certainty about a single result.

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As has been mentioned already: "When the observation is limited to the projection, part of the information about the original object is lost." That is inevitable. A two-dimensional picture cannot convey the complete information of a three-dimensional space. Nevertheless the problem can be overcome by projections under different angles as is usually applied in modern medical applications like X-ray and NMR. There it is possible to see the structure of human bodies, for instance the brain in three dimensions.

In order to investigate the tree we had to observe its shadow at different times and if possible cast by different sources.

DNA would be out of reach for shadow research.

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How could we ever know about [the tree's] DNA, photosynthesis process, or its rough surface?

If one shadow of the tree is the only information available to an observer, any further detail is lost.

However, if there are comparisons available, a lot of detail might be teased out about the tree. Is there available a shadow of a known object, such as a car, a building, a mammal or a bird? Can the tree itself be viewed in different colored light, or when lit from different angles?

It happens a lot that some unknown quality can be estimated only by looking at something else, comparing the two, and then making an uncertain decision. You just go with what you got.

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