Regarding Nathan’s experience, chances are that the experiment was the famous Miller-Urey one where some amino acids were created (among other useless and detrimental stuff), which are the building blocks for proteins. This experiment has numerous problems, but at best it could only be like saying, “We’ve made bricks! Now we can be confident that mansions can be randomly assembled.”

I read through that DNA –> RNA –> Ribosome –> Protein process again and was almost able to comprehend the sheer magnitude such a coincidence. Almost.

Proteins are made up of folded chains of amino acids.
There can be any one of 20 different amino acids at any given position.
The arrangement of the amino acids makes all the difference as to the successful folding and final function of the protein.
Only a limited number of arrangements will do anything meaningful (much like a limited number of arrangments of letters will spell a sentence).
The possible combinations of amino acids in just a short protein is trillions of times larger than the number of atoms in the universe.
The simplest known life in the history of the earth consists of hundreds of proteins.
Proteins will not self-assemble — at least not into long (polypeptide) chains.
Ribosomes are required to assemble proteins.
Ribosomes need messenger RNA to tell them what to assemble.
Messenger RNA gets its instruction from DNA.
Numerous other helper proteins and molecules are required to support the DNA –> RNA –> Ribosome –> Protein process.

How does raw chemistry randomly and incrementally assemble into such a complex cellular system without intelligent design?

The Necktie Paradox – A situation in which it is actually in both men’s interests to wager their neckties. It seems like it would be 50/50, or favored for one of the men, but counterintuitively it is in fact in both of their interests.

The Sleeping Beauty problem – This one is a bit too long to explain, but it’s really not that complicated. Check out the link to see what I mean.

You can find a good list of paradoxes here. I haven’t had a chance to research all of them, but the ones I’ve looked at are pretty cool.

Off the top of my head I can think of the Benford paradox, or the first-digit paradox I think it’s also called. It states that the number 1 is much more likely show up as the first digit in datasets, number 2 is less likely, number 3 even less likely, on down to number 9 which is the least likely to show up as the first digit. It’s very counterintuitive because naturally we think that it should be an even distribution, a 1/9 chance that each digit should show up first (we’re talking random datasets here, like a dataset containing the heights of buildings for example).

The coolest thing about this law is its use in insurance fraud, accounting fraud, and any other instance where someone could make a fraudulent dataset. Most people tend to evenly distribute numbers when they’re coming up with false data, but if you analyze their numbers using Benford’s law you can prove that the numbers where falsely created. According to the law 1 should show up about 33% of the time and 9 should only show up 5% of the time, whereas their data most likely has both 1 and 9 showing up around 10% of the time.

I’m not an expert on this law and it’s been a long time since I’ve studied it, so I could be way off on some of this. You can find out more here.

I’ll post more counterintuitive puzzles as I come across them.