The problem with trees is that the are a dimensional reduction, an aggregation; taking a problem without directionality and applying a useful/functional hierarchy.
So a tree is a way to take a high dimensionality graph and make it usefully lower dimensionality, but, given the aforementioned proof, that reduction is going to go from being a lossless compression to a heuristic. So any interesting problem (at least, any problem interesting to me) is only going to be aided (read: not solved exhaustively) by that hierarchy.
I'm okay with this. Being okay with this has been one of the most freeing things over the last 20 years of my career. Accept inaccuracy, and find usefulness in your data structures.
My brother - wise in the ways - once said "programmers are obsessed with trees".
It's true.
Spare yourself - when you find your mind has been taken over and you have become obsessed by some sort of tree problem/challenge, snap out of it, go do something useful that will make you much happier than the "I kinda got it to do what I wanted", but knowing in your heart it never worked as nicely as you would have hoped outcome.
Reminds me of my favorite math essay: "When is one thing equal to some other thing?"
It's a great question, much deeper and more interesting than it seems. The essay suggests thinking in terms of isomorphisms (relative to the structure you care about) rather than equality in some absolute sense, and I've found a fuzzy version of that to be a really useful perspective even in areas that can't be fully formalized.
I wonder whether the author deliberately avoided ontology? That's what comes to mind when I read this. The age-old debate between taxonomy and ontology.
The problem with trees is that the are a dimensional reduction, an aggregation; taking a problem without directionality and applying a useful/functional hierarchy.
And that's a problem because Aggregability is NP-Hard: https://dl.acm.org/doi/abs/10.1145/1165555.1165556
So a tree is a way to take a high dimensionality graph and make it usefully lower dimensionality, but, given the aforementioned proof, that reduction is going to go from being a lossless compression to a heuristic. So any interesting problem (at least, any problem interesting to me) is only going to be aided (read: not solved exhaustively) by that hierarchy.
I'm okay with this. Being okay with this has been one of the most freeing things over the last 20 years of my career. Accept inaccuracy, and find usefulness in your data structures.
My brother - wise in the ways - once said "programmers are obsessed with trees".
It's true.
Spare yourself - when you find your mind has been taken over and you have become obsessed by some sort of tree problem/challenge, snap out of it, go do something useful that will make you much happier than the "I kinda got it to do what I wanted", but knowing in your heart it never worked as nicely as you would have hoped outcome.
One nice tool for analyzing maps as tree is dominator trees. I wrote a bit about it here: https://neugierig.org/software/blog/2023/07/dominator.html
I think all three problems are really one problem under the hood:
Are these two things actually the same thing, or they separate?
Reminds me of my favorite math essay: "When is one thing equal to some other thing?"
It's a great question, much deeper and more interesting than it seems. The essay suggests thinking in terms of isomorphisms (relative to the structure you care about) rather than equality in some absolute sense, and I've found a fuzzy version of that to be a really useful perspective even in areas that can't be fully formalized.
https://people.math.osu.edu/cogdell.1/6112-Mazur-www.pdf
Or non binary. How much are these the same and how.
I thought it was timezones.
Putting object into trees is basically a caching problem.
I was thinking it's a naming problem haha, a file path can be seen as a global/fully-qualified name really.
I thought the two hard problems were naming things, cache invalidation, and off-by-one errors?
Don't race forget conditions!
His message was submitted before the memory recall completed execution.
At least the title “The Third Hard Problem” is still appropriate regardless of whether you get the joke right.
Use multiple trees.
I wonder whether the author deliberately avoided ontology? That's what comes to mind when I read this. The age-old debate between taxonomy and ontology.
This is more true as stated than people want to give credit for, usually.