Hi Sabine I think you have written a strong, clearly written essay that is aligned with the programme of which the competition is a part. It's nice that, after further analysis of the problem, you end on an optimistic note rather than the opposite conclusion mid way.
There are a couple of places where I disagree with what is written.
1. "If a strongly emergent theory existed, it would imply that "more is different" as Anderson put it [4]. Your behavior, then, would not just be a consequence of the motion of the elementary particles that you are made of. It would mean that believing in free will would be compatible with particle physics. It would mean that reductionism is wrong." The last sentence is not a logical consequence of the earlier statements. Reductionism is looking at what something is and from that how it functions. That is the limit of its inquiry. It does not provide information about how it came to be if that is not via self assembly. Disassembling a clock and working out the function of the mechanism is not a failure because it does not explain how the parts came to be manufactured and how they came to be assembled. We know for the latter occurrences machines or people are needed. Human behaviour is not solely a function of the individual but the environment, and others. External and larger than the executive functioning of the brain alone. Emergence is looking at the how does this come to be not the detail of what is it and how it functions. I like the example of a bird's egg shell. yes the porous structure of calcium carbonate explains what it is and how it can allow case exchange , while keeping contamination out. It does not explain how it comes to be which requires the functioning reproductive anatomy of a bird. Termite mounds and nests of the Edible-nest swiftlet are other good examples of mom self assembling structures. The existence and form of which can not be explained from their constituents alone.
Reductionism and emergence have different explanatory power related to different kinds of inquiry and can not be said to fail when they do not do the job of the other.
2. "The argument - which I have made myself many times - goes like this. We know stuff is made of smaller stuff. We know this simply because it describes what we see. It's extremely well-established empirical knowledge and rather idiotic to deny. No one has managed to cut open a frog and not find atoms" S.H. No one has ever cut open a frog and found atoms unless this is a new meaning of found , where someone can be completely unaware of something and be said to have found it.The inside of the frog that is found is the same scale of resolution as the external surface of the frog that was seen. That the material aspect of the universe is packed inside itself not just at a singular scale or small range of resolution ( as our unaided eyes provide) is an important difference between products of signal processing and independently existing material things.
Kind regards Georgina