What stuff? Don't you get it? We're interested in generating trees. We care if the trees are unique. We care that the trees are correct. That is pretty much all we care about. In general, for the task of generating a tree for a 100 amino acid, highly conserved protein, over 20 organisms, you can generate a maximally parsimonious tree by brute force; heck, I can usually do it by inspection. But having a program certainly helps.
If I were doing bioinformatics research, I'd care about the scalability and computability of my algorithms. I'm not. I'm trying to show freshman students who often don't know what DNA is when the class starts, how the DNA of various species can be used to generate a tree of life.
Interesting. Is there a fractional relaxation?
I don't know, and care less.
Again, this is the icky proof-by-example, I talked about. One of the reasons we hate this sort of thing is that it makes you reinvent the wheel everytime. Just show it works for all proteins. Or, better yet, for all strings on a fixed alphabet.
Who's we? You and the small subset of other pure mathematicians with a chip on their shoulder about the real world?
As far as I'm concerned, mathematics is a tool for the sciences. We're happy to have mathematicians work out the gory details of algorithmic computability, on the admittedly over optimistic hope they might come up with something useful.
Proof by inspection.
Who's we? You and the small subset of other pure mathematicians with a chip on their shoulder about the real world?
The real world is a special case.
As far as I'm concerned, mathematics is a tool for the sciences.
And that is why you fail, young padawan.
Mathematics is all things. It is all that we know. There are three forms of learning: Mathematics, experimentation, taxonomy.
Mathematics is the highest form. It encompasses all high-order knowledge. Information in mathematics reverberates a thousand-fold across all sciences. Or to put it simply: I know everything, I just don't know what you choose to call it.
The next level is experimentation. While essential, it's intellectually lower on the scale.
Taxonomy just gives names to stuff and many economists have made a very good living at that.
We're happy to have mathematicians work out the gory details of algorithmic computability,
That is not mathematics. That is computer science. But they're good people.
'Twere not for the pure mathematicians and theorists, a lot of applied folks would still be trying to invent perpetual motion machines. A lot of the mathematicians' best work is in heading people off from dead ends, too.
Cheers!
You really hit the nail on the head here.