alt.hn

5/14/2026 at 1:00:31 PM

The Third Hard Problem

 https://mmapped.blog/posts/48-the-third-hard-problem

by surprisetalk

5/17/2026 at 3:37:00 AM

I have always called this the “one true taxonomy” problem, because whenever you sit with multiple stakeholders in a room talking about a taxonomy, you can never get to agreement, because there is no such thing as the “one true taxonomy”.

Any hierarchical taxonomy classifies on one dimension at each taxonomic level. Invariably someone wants to classify on one criteria when someone else wants to classify on another. Taxonomies that humans use aren’t multi-dimensional. So if there is a disagreement, someone wins and someone(s) has to lose.

No one is wrong; they just have different priorities or preferences or goals.

So now as an architect I never argue (and seldom discuss) taxonomies. I make two points and then bow out:

1. Whatever your taxonomy is, you need a rubric for each level. You need a procedure or set of questions that unambiguously map any $THING you encounter into exactly one bucket. Validate that competent people with no specific domain knowledge can properly classify things with your rubric; it must be repeatable by amateurs, not just experts (software is dumb).

2. Existence trumps theory. If there exists a taxonomy and rubric for what you’re classifying, you need to provide a $DARN_GOOD_REASON why this wheel needs reinventing. Personal preference and your 1% edge case probably don’t justify all the work to reinvent everything.

Then, I go back to the implementers and tell them to design in a tagging system, which is a DIY taxonomy, and except in ridiculous use cases, I can make indexes make it fast enough to let everyone overlay their own classification system.

by efitz

5/17/2026 at 5:31:50 AM

> Then, I go back to the implementers and tell them to design in a tagging system, which is a DIY taxonomy, and except in ridiculous use cases, I can make indexes make it fast enough to let everyone overlay their own classification system.

This 100x! I wish this were more common.

The key property of a tree is that there a unique path (address) for each element, which is a useful property in the implementation layer. But forcing that on users is a horribly leaky abstraction.

Ideally separate the low-level implementation from the interface, and allow users their own way to address content. I imagine object storage (with UUIDs or whatever) is often good enough for the lower layer. For the interface layer, tags are an improvement on categories (tree structure), but I think there's also room for more innovation (fuzzy matching, AI-driven interfaces, etc) that start by allowing trading-off precision for recall but then allow regaining precision by adding more approximate qualifiers to the filtering.

----

PS: Pushing this approach to 11/10...

An intriguing (crazy?) application of this idea would be: what if we did this to the concept of a codebase? Make it a database (with all the corresponding improvements over a filesystem) -- it's no longer a tree of files, and allow users to query code like "that foo which accepts a bar, frobnicates its internal state, and emits a mutated baz". Note that this might also solve the "naming things" problem.

This setup seems like a powerful abstraction for AI coding agents. All that back-end power (database >> filesystem) is something they can easily leverage, and they can also be built to robustly resolve your fuzzy queries into precise addresses, and then update the code based on your desired outcome.

by ssivark

5/18/2026 at 1:13:57 AM

There's some prior work on the codebase thing:

[Unison](https://www.unison-lang.org/docs/the-big-idea/) content addresses every definition. Kinda interesting.

A [Code Property Graph](https://en.wikipedia.org/wiki/Code_property_graph) takes a codebase and turns it into three graph representations: it's AST, a Control Flow Graph, and Program Dependence Graphs. These graphs are overlaid and shoved into a single property graph. It's a structure mainly used by some static analysis tools like [Joern](https://joern.io/)

---

This has been a topic of a lot of interest and research for me. I've been experimenting with figuring out a system inspired by these ideas, among others, to apply the same idea (shoving multiple graph representations together) to a broader set of information

by Jarwain

5/17/2026 at 1:15:00 PM

> that foo which accepts a bar, frobnicates its internal state, and emits a mutated baz

Tangential, but that reminds of the Haskell "hoogle" tool which allows searching for functions _by type_ across a large database of libraries, even by abstract types. So you might wonder "hmm what's that function that has a type structure like `t a -> (a -> t b) -> t b`?" and it'll happily tell you that it's monad `bind`

by frogulis

5/17/2026 at 4:56:18 PM

Tag Clouds were sticky tasty web goodness a few years back.

I've got a legacy tag cloud curation tool for random collections (each collection gets its own id) of URLs. It IFRAMEs each URL to present it; no whining. I've used it for classifying technical docs, photo libraries (then I used the tags to train an image classifier), and to present an analysis of a customer's web site.

It's written in Perl, and (still) runs on modern Perl. Make friends and maybe I'll toss the code your way and help you with your project.

by m3047

5/17/2026 at 9:19:55 AM

More than once I encountered a project lead (often a higher-up) spend a half day after the project kick-off to create an elaborate folder structure for the team.

Younger me wondered: "Don't they have more important things to do? Why do they never delegate such a menial and boring task, especially when the structure is kind of obvious"

Today it makes total sense to me. Even if it looks obvious no one has the exact same hierarchy in mind. It was fast for them to materialize the hierarchy themselves than to convince anyone about it in every detail. Some things just can't be delegated.

by weinzierl

5/17/2026 at 12:45:18 PM

That’s a good name! I often resort to “there are many ways to slice a cake”, less sophisticated blunt gets the point across.

by designerarvid

5/17/2026 at 1:00:31 AM

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.

by chaboud

5/17/2026 at 1:49:49 PM

The map is not the territory!

by sdwr

5/17/2026 at 2:25:57 AM

There are only two hard problems in computer programming:

1. Naming things 2. Cache invalidation 3. off-by-one errors

by petersumskas

5/17/2026 at 5:49:46 AM

Length 3 lists always feel better, and my favorite formulation of this is,

  There are only three hard problems in computer science:

  1. Naming things
  2. Cache invalidation
  3. Off-by4. Multi-threading
  -one errors.

by deathanatos

5/17/2026 at 7:29:44 PM

My favorite version of this but is like "An engineer has one problem he decides to solve with multi-threading. Now problems. has two he"

by llbbdd

5/17/2026 at 2:29:06 AM

there are actually 10 problems: naming things, cache invalidation, base conversions, off by one errors, and cache invalidation

by sprayk

5/17/2026 at 2:34:10 AM

Base conversions are easy, but which off by one is it? base 4 or base 6?

by QuaternionsBhop

5/17/2026 at 4:16:46 AM

10 base 2 is 2 base 10. i gave four unique hard problems. and now typing this out i see that I was off by 1 (or two)

by sprayk

5/17/2026 at 11:57:52 AM

Off-by-two is a subset of all possible off-by-one errors.

by rzzzt

5/17/2026 at 5:05:00 PM

All off-by-one errors can be reproduced by producing an off-by-one error of some other off-by-one error.

by m3047

5/17/2026 at 12:03:16 AM

I think all three problems are really one problem under the hood:

Are these two things actually the same thing, or they separate?

by et1337

5/17/2026 at 12:18:18 AM

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

by tikhonj

5/17/2026 at 8:31:06 AM

Mathematics is all just explanations for why this is really that. If it didn't have to respect its human audience, and their failure to grasp similarities, the whole edifice could be one implicit statement. (After all, since this is really that, there is no this or that.) So mathematics is about people.

by card_zero

5/17/2026 at 1:41:08 AM

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

by hackthemack

5/17/2026 at 2:43:06 AM

Wow, thanks for that, TIL! I’m definitely a code lumper.

by et1337

5/17/2026 at 1:45:09 AM

"Ambiguity is the enemy", as a rule of thumb, has helped me

by hexasquid

5/17/2026 at 12:48:39 AM

Or non binary. How much are these the same and how.

by aleksiy123

5/17/2026 at 12:43:40 AM

[dead]

by tonetheman

5/17/2026 at 3:00:31 AM

I have a deep distrust of hierarchies, because they keep you trapped into a single model that keeps extending its authority, usuall without anyone explicitly deciding that it should do so. For example, the file system: once it was deemed hierarchy is the main metaphor for navigation, the structure persisted and was reused for organisation, ownership, access control and governance. And it became infrastructure we cannot easily remove before we could even question if it was right or not. And once it dominated, non-hierarchical things were retrofitted as glue, e.g.: symlinks, aliases, shortcuts... also, when's the last time you've used a tag?

The webs are so much more malleable, but they're also not free. All the 'good enough's you were that a hierarchy that was taking care of implicitly are now your responsibility to model precisely and make sure they're performant as well. Look at ReBAC, for example. It gives you expressive power, but it also forces you to reason precisely about relationships, graph traversal, consistency, and cost. Strikingly similar is GraphQL.

Interestingly, source code is hierarchical, but compiles almost immediately to a graph IR and most analysis and optimisations happen there. But almost nobody looks at a CFG/SSA graph directly. You author in a hierarchical manner, yet the operational substrate is a malleable graph.

by gobdovan

5/17/2026 at 5:50:38 AM

> before we could even question if it was right or not

But we could. Early filesystems didn't have heirachy. They'd sometimes support a single level of organization by treating a prefix of the filename as directory, but nothing below that. We looked at that and considered heirarchy better.

What you lament is that we stopped with heirarchy. You wish for something more general, and that you have received. With hardlinks and ACL the filesystem is freed from its shackles of heirarchy. Most people don't need that most of the the time.

The strict heirarchy sits as the third step of a complexity ladder. The reason we stopped there, in most cases, is that it's enough complexity.

by delusional

5/17/2026 at 12:01:52 PM

You're overfitting on the filesystem example. My point is model lock-in.

Once a system commits to one hierarchy, it becomes very hard to introduce another authoritative model. Not only you cannot have alternative models with equal authority, you do not even get a clean parallel hierarchy later; you get the first hierarchy, now ossified, plus workarounds around it. On the other hand, webs are harder to reason about and more expensive to operate, but they can produce hierarchies 'on-demand' and you can get rid of them as easily as you've established them. Ergo, a ton of different programming languages just compile to LLVM IR.

by gobdovan

5/17/2026 at 6:17:40 PM

Here is my take using the city as a metaphor.

All physical things have to be arranged in a linear fashion, this is pauli exclusion principle writ large.

A type of mereological nihilism is true, so hierarchy is real but in a weak emergence sense.

When I am standing on a street corner in a city, I can walk into a building and then navigate into a room inside that building and pick up a piece of paper inside.

Or I can walk down the street and as I pass landmarks, I will pass things in order, this is also a perceived hierarchy, because my starting position and movement are bound by time, I will always have a fixed order of experiences from any x,y coordinate.

So everything bounded by time and space acts as an emergent hierarchy via movement for a specific loci.

The paper can be moved however, and that same piece of paper sitting in the drawer at an attorneys office means something very different than when its sitting in the approved licenses cabinet in an offical government building.

Semantic meaning is first class but its an entirely different dimension than other types of meaning and due to pointers it isn't bound by pauli exclusion.

When people start thinking about the semantics of objects in computer programs they often become confused, because the semantic representation of the object follows semantic ontology laws not physical object ontology.

People can fuck this up in either direction and think physical laws apply to semantic meaning or physical meaning applies to semantics.

by fellowniusmonk

5/18/2026 at 12:54:04 AM

Yeah, that's part of it. But I'd argue that once you look at a city, you look at constructions administratively designed by men, with their preference for hierarchies. Try to hierarchically describe to someone instructions to pick a random leaf in a dense tree (ironically, we use them as a metaphor for hierarchical organisation) and see how far you could go in the same way you could point them out to pick a paper in the city.

Not in a position to argue about physics, but I could think of quite a few things that are better described as web-like phenomena rather than hierarchical ones, electricity in a complex circuit comes to mind.

by gobdovan

5/17/2026 at 4:21:10 AM

IMO hard links are underused in filesystems. You can have the same file / dir appear in different places under different names. Once linked, app doesn't have to care and runtime cost is zero.

by speed_spread

5/17/2026 at 9:26:49 AM

Hard links suffer from the general issue of there being two styles of writing to a file - open(2)/write(2) vs rename(2). Depending on the internals of each program you use to update the file, you will get very different results.

This is one of the ugliest parts of POSIX design, making idioms like -o /dev/null and file attributes unpredictable (I've had a server run out of disk space because a root-owned process used rename-style writing on /dev/null)

by PhilipRoman

5/17/2026 at 11:19:14 AM

That was breakdown on a different level: your server process had no business of renaming stuff and it still did that. POSIX had nothing to do with this.

by lstodd

5/17/2026 at 5:28:09 PM

I'd agree if POSIX provided something like an open() flag which made the changes visible atomically, but as it stands, the rename() idiom is the mainstream way of durable file writing, so it is commonly used. Practical example using busybox sed: (GNU sed detects this case and refuses to overwrite)

  / # stat /dev/null
    File: /dev/null
    Size: 0          Blocks: 0          IO Block: 4096   character special file
    ...
  / # sed -i 's/foo/bar/' /dev/null
  / # stat /dev/null
    File: /dev/null
    Size: 0          Blocks: 0          IO Block: 4096   regular empty file
    ...

by PhilipRoman

5/17/2026 at 4:08:05 PM

It's the fundamental idiom of how to do atomic file replacement. The sever process had better be doing that over editing a text file in a way that could leave it invalid if the process OOMs mid edit, or another process is reading it while it's being written.

by jmalicki

5/16/2026 at 11:57:59 PM

I thought the two hard problems were naming things, cache invalidation, and off-by-one errors?

by mcphage

5/17/2026 at 1:06:27 AM

At least the title “The Third Hard Problem” is still appropriate regardless of whether you get the joke right.

by rectang

5/17/2026 at 12:02:02 AM

Don't race forget conditions!

by fragmede

5/17/2026 at 1:11:23 AM

His message was submitted before the memory recall completed execution.

by cheschire

5/17/2026 at 3:36:46 PM

They are. The article is about a third hard problem.

by layer8

5/17/2026 at 9:00:27 AM

John Ousterhout has also written about this in A Philosophy of Software Design:

The most fundamental problem in computer science is problem decomposition: how to take a complex problem and divide it up into pieces that can be solved independently.

by phazy

5/17/2026 at 4:17:19 AM

Well elucidated. This problem has irked me for years in the form of multiple inheritance. When it's disallowed (like Java, unfortunately), trying to reduce a directed graph structure to a single dominant hierarchy is quite the bothersome choice.

by gw32

5/17/2026 at 5:03:50 AM

I doubt there would exist a perfect taxonomy for everything. Taxonomies are subjective to individuals but somehow can be (ahem! AI) mapped relative to someone else’s preference taxonomy. What efficiency and meaning each individual (or organization or community) yields would be completely different.

by guardiantesla

5/17/2026 at 12:13:49 AM

I thought it was timezones.

by ToniDoni

5/17/2026 at 12:47:14 PM

Is there an OS whose primary FS is a taggedFS? It'd be interesting to hear from the users if this is nice to use or not..

by renox

5/17/2026 at 4:05:44 AM

I think I've always called this "Ontology is hard". It's genuinely useful when it's used as a tool for clarification. It's constraining when it's used as a tool for modeling.

by iamwil

5/17/2026 at 4:49:22 AM

For me, the canonical example is organising images in folders vs tags.

by naruhodo

5/17/2026 at 2:47:21 AM

Every few years I watch, with amusement, our management restructuring the organizational hierarchy, allegedly because the old one didn't work.

by js8

5/17/2026 at 4:45:15 AM

Maybe allegedly so but in reality it worked once again, given there’s still management to be reorganised.

by cgio

5/17/2026 at 9:11:15 AM

Well, tell that to my management, that it's a pointless endeavor. The structure of (required) social relations in the workplace is a graph; so there will always be some flaw when trying to conform this into a tree.

by js8

5/17/2026 at 1:10:32 AM

Putting object into trees is basically a caching problem.

by Svoka

5/17/2026 at 1:14:37 AM

I was thinking it's a naming problem haha, a file path can be seen as a global/fully-qualified name really.

by recursivecaveat

5/17/2026 at 12:50:50 AM

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.

by kator

5/17/2026 at 3:35:55 AM

The article veers from saying computers are different, to saying they should be different but maybe aren't, back to how special they are:

> The next time you sit down to an empty design doc and don’t know where to start, be kind to yourself. You’re solving a hard problem.

This supposed hard problem in computing has always been with us, in real life. Which he admits multiple times, e.g.:

> Yet Victorian-era gentlemen might have pondered the same questions while sorting letters as we do while sorting virtual paper.

He appears to claim that the sole organizing principle in real life is the hierarchy, but, of course, that computers and ideas are different:

> Hierarchies are so natural to us that they ... [work] for physical objects that can be in only one place at a time. Ideas and information, however, resist taxonomies. They form intricate webs that penetrate rigid boundaries.

This distinction of physical vs. virtual requirements doesn't hold up under any sort of rigorous analysis. As he admits, hierarchies are not always ideal in physical space -- do we organize parts and supplies separate from tools, or place them next to their probable job sites?

And of course, the "in only one place at a time" is certainly true for any given group of atoms, but we have become adept at making fungible copies of atoms for many things. I might have drywall screws or 33 ohm resistors in multiple cached locations, and I have soldering irons and screwdrivers and pliers on more than one workbench.

One thing that is true is that we can usually add non-hierarchical groupings to information more easily than we can to groupings of atoms.

Another thing that is true is that we already often do so whenever the convenience outweighs the various costs.

And the third thing that is true is that this, also, is not much different than the physical world, where we routinely both break our hierarchies and create copies of things when needed.

by zephen

5/17/2026 at 2:16:14 PM

This an issue of growing ontologies and taxonomies.

I have found that the best answer I have is:

1) Gossip and use the existing ontology and add new items only if genuinely needed

2) Combine synonyms, sometimes using vector embedding and cosine similarity during search

The insight is that trees are not a storage constraint but a traversal consequence — any walk through a graph starting from a given node produces a tree as a byproduct, and different starting points or orderings produce different trees from the same underlying structure. Rather than forcing a choice of canonical hierarchy at write time (the dentist-bill-goes-in-which-folder problem), you store the graph and let the tree emerge lazily from context: whoever is querying, from wherever they enter, gets the tree that is relevant to them, and no connections are sacrificed to produce it.

In general, federated systems have this quality emerge. For example, in OpenStreetMap, one group can label Nagorno Karabakh, the other Artsakh, and no one has to fight Google etc.

by EGreg

5/17/2026 at 12:47:24 AM

Use multiple trees.

by aleksiy123

5/17/2026 at 11:59:47 AM

The tree node on the UI should not only expand downwards but sideways and in-out of the screen.

by rzzzt

5/17/2026 at 1:27:04 AM

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.

by jeffbee

5/17/2026 at 1:32:29 AM

This seems optimistic.

by g8oz

5/16/2026 at 11:47:29 PM

This is more true as stated than people want to give credit for, usually.

by adampunk

5/17/2026 at 1:11:50 PM

[dead]

by RyanJohn