alteregoivy
I know how evolution works and why it works. I also know it's been proven that you can make very complex protein compounds just by simulating the conditions of Earth at the dawn of our planet.
Just being a little nitpicky here, but they aren't really "complex" protein compounds by my understanding. The Miller-Urey experiments simply demonstrated that organic matter (amino acids and the building blocks of life) can be produced from previously inorganic matter when applying electricity to certain chemicals under the right conditions (likely the same conditions that Earth used to be like). This is a huge step in developing a workable theory on abiogenesis (the origins of life), but we still have yet to fully create life from scratch. Now we just need to find a way to get these building blocks working together.
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What I don't understand is what evidence (if any) there is to prove that DNA can arise from those conditions and begin to self-replicate.
The important thing to recognize here is that none of this needs to be proven in order to demonstrate evolutionary theory as valid. There is already an overwhelming heap of evidence that shows that evolution is occurring now and has been occurring for a long time. How the process first started is irrelevant and unnecessary with regards to verifying the theory. If a creationist keeps insisting that it is necessary to point out how it first started in order to prove it, then you can simply point out then that the creationist must not believe that the moon exists since no one really knows where it came from and how it fell into Earth's orbit.
This is a common tactic by fundamentalists. The creationist is basically conflating two different things: Abiogenesis and Evolution. Evolution addresses how life has diversified over time, NOT the origins of life.
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I also don't understand how DNA can then jump to making a single-celled organism.
DNA is fairly complex and doesn't just form out of the blue. Most scientists believe that more primitive and strictly RNA-based organisms like certain forms of bacteria were likely the first living organisms. They were not like other single-celled organisms that we have now which are modern eukaryote cells with an endoplasmic reticulum, Golgi apparatus, and various organelles. It wasn't until later when DNA was acquired and developed, and since DNA is more stable than RNA, this is what allowed more complex organisms to form. Beyond that, I don't know any of the specifics or details of how it happens, so you'll probably need to pick up a biology book that talks about the origins of self-replication if you want anything more.
sweatdrop