Problems of Unbounded Scope
Very frequently, engineers will set their sights on some large, abstract, grand problem. They will then convince themselves that some far simpler approximation of the problem is in fact equivalent to the vast problem. They produce a solution, proclaim the vast problem “solved”, and begin congratulating themselves.
Google created search engines, where information could be retrieved via a collection of keywords. They “solved” “search”. It is however a serious mistake to take this too literally.
More recently, we have gained LLMs, which often can be rather useful as a search engine. The kinds of questions that can be asked, and the detail of the responses, is much greater. Nevertheless, while LLMs can answer more complex and nuanced questions than Google, I find that they generally seem to be comparable to someone with an encyclopedic memory but who doesn’t think deeply about what any of this knowledge means or how it may be connected.
Of course, “search” can be defined even more broadly and abstractly.
For example, if we are seeking knowledge and answers, a text query of any kind will often be a rather poor and limited tool for finding unknown unknowns. How do you write a query for something you don’t know you’re looking for? Random discovery is often a better tool for at least this problem even if it is not particularly efficient.
How does one approach random discovery? Wikipedia seems somewhat better at this than Google or LLMs, in that one can very easily wander through links and rather quickly discover unexpected knowledge only distantly related to their original subject of interest. There is also no real “algorithm” filtering this discovery based on your typical habits, only your natural curiosity and the proximity of unexpected details to the things you were looking for.
A conventional print encyclopedia may have its own advantages that have been lost in the digital age, in that its volumes or table of contents may be organized by category, forming an atlas for the high-level arrangement of knowledge. Wikipedia is a vast iceberg, its true depths are not obvious from the surface, and it’s hard to comprehend or anticipate what it does and does not contain. An encyclopedia, a shelf of books in comparison, may be organized by subject in a way that categorizes all contained knowledge and gives some impression of roughly how much is there. There may be many surprises on a small scale, but for the most part a reader can quickly grasp the range of knowledge represented and their own knowledge or ignorance of it.
Of course, a simple list of categories may not reveal much structure, and some graph-based atlas may be an even more fine-grained tool.
We must also keep in mind that the sum of human knowledge is not and never will be complete. There are things we don’t understand, questions we have not answered, and no amount of searching the archives will locate such answers. You may instead be forced to search the world, something that Google and LLMs are not well-optimized for.
Most people spend at least some part of their lives – the unlucky ones perhaps a very long time – lost and in search of meaning, purpose, or inspiration. A text query isn’t very effective at resolving this. Some combination of religious experiences and life struggles will often prove a much better tool, though even this is only so effective. Religions and the meaning they offer have been subject to change, adaptation, and innovation over time, and presumably further innovation in the frameworks we use to guide people toward meaning should be possible. I personally suspect however that the generator functions – the ideas that motivated and produced these religious texts – have largely been lost, and that much of the decline of religion is the result of no longer understanding why people for so long placed such immense value in these ideas and frameworks, or how why some died out and others successfully spread to billions.
Some questions are reducible to math and are computable. Some may be in principle computable, but require mathematics that has not been developed yet, perhaps only in some distant or indefinite future. Others may require knowledge of the world that may or may not be possible to gather, or facts of history that have been lost to time. Some questions – whether they can be formalized or not – may simply be intractable or incomputable.
Not everything that is computable is something we presently know how to compute, and not everything we know how to compute is something we know how to productively apply. There is an infinite tower of complexity classes called the Polynomial Hierarchy, of which nearly all algorithms humans write fall into just the bottom couple levels, overwhelmingly only the first. Presumably the higher levels are increasingly more powerful and theoretically more useful, but we today have very little idea of what any of it is good for. Even then, the Polynomial Hierarchy is only a small part of the wide array of known complexity classes, which presumably are only a tiny part of all possible classes.
Ultimately, ambition is a skill. The actual range of possible achievement is for all intents and purposes infinite – both unfathomably vast in scale and even more vast in variety. Finding things that are bold enough to be worth doing while still remaining achievable in the present day is not a trivial problem. It’s best not to harden your goals in life too early, as with more time and experience you can often see even greater and more worthy goals. Of course, we stand on the shoulders of giants – we are able to catch rockets out of the sky not because we have bigger brains than people of the past (brain sizes actually declined after the introduction of agriculture), but because we have the advantage of centuries and millennia of accumulated knowledge. Our map of what is possible and how to get there is ever-expanding.
Ultimately, we should recognize that the problems we are working with today will seem but mere toys to people centuries or millennia from now, who will work with vastly more general and powerful tools than anything we can imagine today. On one hand there’s a humility in that, in knowing that we can only achieve things that are in a certain sense rather small and nearby. On the other hand, it also tells us that beliefs that a given hard problem is “solved” should not be taken too seriously, as most important and general problems in fact have effectively infinite scope.
Human imagination is actually a very limited thing, much more limited than we often assume, and something we should aim to expand and improve. Telling ourselves that hard problems are “solved” when they are not only serves to halt imagination of anything greater.
The hard problems are never truly over.
This has been a more philosophical article today. I’m hoping to have some more technical articles out soon, including another Bzo Dev Log once I can get a few more things done.