Nice philosophy, Dave. I hate to destroy it with a few scientific facts (caution, long rap following):
1) Of course there is something like a natural recycling of organic matter in a functioning ecological system. Yet, the tree didn't absorb the poet's corpse, but it used several atoms from him, restructured in new molecules and different combinations. And it's simply impossible to follow a single atom through its history, however amusing it might turn out: e.g. one of Burns's atoms is built into a tree leaf. This leaf feeds a caterpillar, which gets eaten by a bird, and after some bacteria has taken the specific molecule apart in the bird's digestive system, the atom becomes part of some bird droppings. Following the logic above, the poet has become shit…
That's toilet philosophy indeed!
On the other hand, this recycling process also happens to inorganic matter, but on a much larger time scale. All chemical elements heavier than hydrogen have been formed by suns. After a few billion years, the sun explodes and the heavier matter is able to escape, just to form new stars, which weld even more atoms together, and so on. Our own sun is a star of the 4th or 5th generation at least. So it is safe to say we all are children of the suns and stars!
2) According to the Second Law of Thermodynamics, the total entropy of the whole universe is constantly increasing, i.e. the disorder decreases. To increase the order means to use up energy to form a more complicated order. That's why your apartment gets really messy if you don't straighten it up from time to time.
Now, the only parameter which remains the same is the total sum of matter plus energy in the universe. In more complicated elements, more energy is needed to keep the atoms together. All atoms eventually decay sooner or later into less complicated structures (the heaviest elements are often prone to become radioactive, which means decay). So, on a large time scale, not even the atoms remain the same. This becomes even more fuzzy if you further break up the scale to include quarks into your speculations…
So, whereas it seems to be the identical matter, it just isn't. It's one of an immensely huge number of look-alikes.
3) Recently, I read a nice statistics about the incredible number of different positions on a chess board after only four moves of both players (I've got no memory for numbers though). After only 10 moves, the number of possible variations equals the number of atoms on Earth (at least I think that was the statistics' analogy). If you go through the infinitely more complex possibilities of which specific atoms will form a certain body or tree, and what will become of them when they get restructured in a multitude of other matter variations, you'll certainly see that it's next to impossible that the same atoms will conglomerate in an identical combination of something which has already existed in the past.
However, you'll see extremely similar combinations, formed by different atoms. That's where our own perception is limited, even by using electron microscopes: We'll never be able to tell the difference.
4) The current cosmic theories clearly state that time is finite, at least there's a beginning. Without universe, there's no time, because time is just an inherent property of space. So time began at the Big Bang. Scientists are still very unsure about a possible end of the universe. It could be expanding forever, or the expansion could be stopped by gravitation. In the latter case, the galaxies will approach each other again and form a 'Big Crunch'. There are some interesting theories about time in a contracting universe: its direction could well be reversed in that case, meaning that results will occur
before the causes. A broken tea cup on the floor would reassemble and fly up to the table, it would be full before you pour the tea in and empty after the pouring… Quite amusing, but anyway, that'll happen (if ever) well after the last living creature's extinction.
My own favorite theory states that galaxies and time won't need to reverse their direction to create a Big Crunch. The assumed four-dimensional structure of our universe makes it possible to expand towards the original starting point, similar to someone who starts at the Earth's North Pole, walks straight onward, and never changes directions. After an unknown time factor, he reaches the South Pole, and without changing his direction, he'll move northward again, finally approaching the North Pole from the 'other side'. Earth is a three-dimensional structure, but the same analogy can be transported into the fourth dimension of the universe.
5) And I have my own philosophy about immortality. For example, Burns's poetry has existed much longer than his body. I love his poem on "Haggis, the great chieftain of the pudding clan"! (that's his, isn't it?)
Sorry for the long-winded thread. I have to continue my ramblings on the toilet, I guess…
Disclaimer: I have never studied physics and I won't claim that all my above assumptions are correct. They are thoroughly limited by my lack of knowledge. In short: they are the limits…