Ask HN: Why does DNA have only 4 nucleotides?

I was eating with my dad, who is a biophysicist, and he brought up an interesting question for which I haven't found an answer. I thought maybe someone on HN would have heard something more.

Why, after billions of years of evolution, do we still have ALL known organisms still have 4 nucleotides? Yes, Uracil is used in RNA but it encodes the same information, ie why is it always base 4? How come a 5th nucleotide has never appeared, or any nucleotide become less prevalent?

It seems interesting that the genetic code is base 4. And are there really only 20 amino acids?

Several thoughts (from someone with only intro-level biology, fwiw):

1. I think a lot of biological why's might be fundamentally un-answerable except for "pure statistical randomness." That's just the branch that evolution happened to fall towards.

2. Or perhaps it is answerable. In terms of costs and benefits, it could be that the cost of the additional complexity in replication, transcription, translation and all the tasks DNA serves outweighs the error-reduction that is possible with additional base pairs (either by allowing triplets/quadruplets/etc or by allowing greater redundancy in mapping to proteins). There are probably diminishing returns in error reduction after having two base pairs.

What is the basis of your question? Are you interested in why those particular changes have not yet occurred? Or are you looking for the answer to why further error reduction methodologies have not yet been incorporated into our cellular mechanics, as mentioned by brianchu?