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.
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 jumped to a similar conclusion right away and popped over here to comment only to find you have beaten me to the punch. I use to keep a work wiki page of common problems the team encounters over and over again.
Years ago, I stumbled upon the "idea" was already debated in other fields long before programming. Lumpers and Splitters.
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 first chapter of this waves away the fact that hierarchical filesystems are now useless, but it is still a fact. There is no more reason to organize your files than there is to drive around in a chariot. It is hard to map one domain to the other, but it is also not necessary. With AI indexing and recall it's less necessary than it has ever been.
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.
There are only two hard problems in computer programming:
1. Naming things 2. Cache invalidation 3. off-by-one errors
there are actually 10 problems: naming things, cache invalidation, base conversions, off by one errors, and cache invalidation
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
I jumped to a similar conclusion right away and popped over here to comment only to find you have beaten me to the punch. I use to keep a work wiki page of common problems the team encounters over and over again.
Years ago, I stumbled upon the "idea" was already debated in other fields long before programming. Lumpers and Splitters.
https://en.wikipedia.org/wiki/Lumpers_and_splitters
"Ambiguity is the enemy", as a rule of thumb, has helped me
Or non binary. How much are these the same and how.
One nice tool for analyzing maps as a tree is as a dominator trees. I wrote a bit about it here: https://neugierig.org/software/blog/2023/07/dominator.html
I thought the two hard problems were naming things, cache invalidation, and off-by-one errors?
At least the title “The Third Hard Problem” is still appropriate regardless of whether you get the joke right.
Don't race forget conditions!
His message was submitted before the memory recall completed execution.
I thought it was timezones.
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 first chapter of this waves away the fact that hierarchical filesystems are now useless, but it is still a fact. There is no more reason to organize your files than there is to drive around in a chariot. It is hard to map one domain to the other, but it is also not necessary. With AI indexing and recall it's less necessary than it has ever been.
This seems optimistic.
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.
Use multiple trees.
This is more true as stated than people want to give credit for, usually.