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The Third Hard Problem
- adampunk 6mo agoThis is more true as stated than people want to give credit for, usually.
- mcphage 6mo agoI thought the two hard problems were naming things, cache invalidation, and off-by-one errors?
- fragmede 6mo agoDon't race forget conditions!
- cheschire 6mo agoHis message was submitted before the memory recall completed execution.
- rectang 6mo agoAt least the title “The Third Hard Problem” is still appropriate regardless of whether you get the joke right.
- layer8 6mo agoThey are. The article is about a third hard problem.
- mcphage 6mo agoTouché :-)
- et1337 6mo agoI think all three problems are really one problem under the hood: Are these two things actually the same thing, or they separate?
- tikhonj 6mo agoReminds 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 https://people.math.osu.edu/cogdell.1/6112-Mazur-www.pdf
- card_zero 6mo agoMathematics 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.
- moi2388 6mo agoYes, I found the same and was very pleasantly surprised when I first learned about the ideas of cubical type theory.
- tonetheman 6mo ago[dead]
- aleksiy123 6mo agoOr non binary. How much are these the same and how.
- hackthemack 6mo agoI 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 https://en.wikipedia.org/wiki/Lumpers_and_splitters
- ToniDoni 6mo agoI thought it was timezones.
- aleksiy123 6mo agoUse multiple trees.
- rzzzt 6mo agoThe tree node on the UI should not only expand downwards but sideways and in-out of the screen.
- kator 6mo agoI 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.
- chaboud 6mo agoThe 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 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.
- sdwr 6mo agoThe map is not the territory!
- evmar 6mo agoOne 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 https://neugierig.org/software/blog/2023/07/dominator.html
- chrisco255 6mo agoThank you for sharing, first I've heard of this tree type.
- euroderf 6mo agoAnother interesting type of tree is the multitree. Try this very readable paper: https://interactivity.ucsd.edu/articles/In_Process/MultiTrees.pdf https://interactivity.ucsd.edu/articles/In_Process/MultiTree...
- Svoka 6mo agoPutting object into trees is basically a caching problem.
- recursivecaveat 6mo agoI was thinking it's a naming problem haha, a file path can be seen as a global/fully-qualified name really.
- deleted 6mo ago[deleted]
- jeffbee 6mo agoThe 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.
- g8oz 6mo agoThis seems optimistic.
- petersumskas 6mo agoThere are only two hard problems in computer programming: 1. Naming things 2. Cache invalidation 3. off-by-one errors
- sprayk 6mo agothere are actually 10 problems: naming things, cache invalidation, base conversions, off by one errors, and cache invalidation
- QuaternionsBhop 6mo agoBase conversions are easy, but which off by one is it? base 4 or base 6?
- sprayk 6mo ago10 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)
- deathanatos 6mo agoLength 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.
- js8 6mo agoEvery few years I watch, with amusement, our management restructuring the organizational hierarchy, allegedly because the old one didn't work.
- cgio 6mo agoMaybe allegedly so but in reality it worked once again, given there’s still management to be reorganised.
- js8 6mo agoWell, 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.
- gobdovan 6mo agoI 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.
- speed_spread 6mo agoIMO 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.
- PhilipRoman 6mo agoHard 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)
- lstodd 6mo ago
- zephen 6mo agoThe 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.
- efitz 6mo agoI 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.
- ssivark 6mo ago> 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.
- iamwil 6mo agoI 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.
- gw32 6mo agoWell 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.
- naruhodo 6mo agoFor me, the canonical example is organising images in folders vs tags.
- guardiantesla 6mo agoI 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.
- panstromek 6mo agoThis is good diagnosis of the problem. I found that often the right solution is to ditch the hierarchy and use flat structure. I wrote about this some time ago: https://yoyo-code.com/embrace-flatness/ https://yoyo-code.com/embrace-flatness/ Big insight in that article is also from https://matklad.github.io/2021/08/22/large-rust-workspaces.html https://matklad.github.io/2021/08/22/large-rust-workspaces.h... about structuring large rust workspaces as a flat list.
- phazy 6mo agoJohn 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.
- renox 6mo agoIs 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..
- RyanJohn 6mo ago[dead]
- cxr 6mo agoThis is an independent riff on an argument Ted Nelson wrote down 50 years ago (and the reason why he coined the term "hypertext"). <https://en.wikipedia.org/wiki/Computer_Lib/Dream_Machines https://en.wikipedia.org/wiki/Computer_Lib/Dream_Machines> <http://link.springer.com/10.1007/978-3-319-16925-5 http://link.springer.com/10.1007/978-3-319-16925-5>
- EGreg 6mo agoThis 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.