Such an event on the contrary would probably prompt the most able country left to seek to become the leader (technically and politically) by taking the opportunity to best those left in a worse state.
If you wanted to let a society recover from technological collapse then you would merely need a list of possible inventions ordered by the date of their invention. 3D CAD models with micrometer tolerances are not useful to such a society anyway.
There's ideas that can survive long after devices turn to dust. The germ theory of disease. The Staff system. Ops planning. Cross-fertilization and hybridization. Optics. With these ideas, the devices can be recreated, and in a better sequence that we accidentally created them the first time.
Methane hydrates largely seem to be frozen in tundra and on the seafloor. Even accessing them tends to precipitate release. Liquids are far more fungible than either solids or gasses, and methane hydrates tend to be the latter transforming wantonly to the former with very little in-between. Sort of the worst of all possible worlds.
Also a tremendously worse greenhouse gas, though not quite so long-lived as CO2. Centuries rather than millennia.
Methane Hydrate can be 'harvested' by drilling, then pumping a little warm water down the hole, then piping the gas into the harbor where the city enjoys endless free natural gas.
The most productive wells and fields tended to be heavy initial producers. Among the most prolific single wells I'm aware of is the First Oil Well of Bahrain:
https://en.wikipedia.org/wiki/First_Oil_Well,_Bahrain
Drilled in 1931, initially flowing at 9,600 bbl/day, peaking at 80,000 bbl/day, and (as best I can make out still producing at 35,000 bbl today, 89 years after first oil.
Contrast with stripper and marginal oil wells, producing 10-15 bbl/day, or less.
But even a stripper well produces a liquid, which stays a liquid (modulo condensate and NGLs). You can pump liquid from the ground, and store it in loosely-covered tanks. It will flow through nonpressurised or lightly-pressurised pipelines.
Methane hydrates are solids which sublime to gas. You can't pump solids. You can't store gas in unenclosed containers. Piping requires pressurisation, cooling, or both. This is done, yes, but gas remains generally more problematic than oil. Whilst not an intractable problem, it's a more technical, constrained, limiting, and expensive prospect.
Something tells me that "a little warm water" becomes a more complex prospect at deep-sea depths, pressures, and temperatures.
The amount of fuel required to smelt iron and produce high-quality steel (a technique only perfected in the 1860s -- previous high-quality steels such as Damascus and Japanese tamahagane were forged rather than smelted, with the iron and carbon impurities literally hammered out, often by hand. Water- or wind-driven trip-hammers could help with this.
Given the mass of raw wood needed to produce charcoal used in both iron and gunpowder production, the embodied mass of wood represented in an age-of-sail ship of the line (typically 72 cannon, half of which would be engaged in a broadside) rivalled or exceeded the mass of the ship itself.
That's not "the cannon and powder weighed more than the ship", but "the fuelwood consumed in producing these weighed more".
Britain, never particularly lush in forests, had stripped itself bare, and relied on imports from Sweden and the Americas to build and fuel its ships. Coal, particularly coked coal, was a game-changer. Even today, 15% of all coal use is "metalurgical", which is to say, coked coal used in steel production, not merely providing fuel to the fire, but chemically bonding with iron.
And that's just steel.
The concentrations of ores from which other metals are smelted are tremendously reduced from pre-industrial times. Copper (virtually all electric transmission and motors), gold and silver, numerous vital and strategic minerals (look up the "Harbord List", dating to WWI, of strategic minerals, now encompassed in the US Strategic Mineral Reserve and successor programmes), and more.
If we can avoid shutting off the grid entirely, some elecrical substitution may suffice. Aluminium smelting is virtually fully electrically-based, and steel recycling (which doesn't require coal) can and does run in electric arc furnaces.
Vaclav Smil's books on energy, Energy and Civilisation, and materials, Making the Modern World, are very strongly recommended.
A collapse is never binary (unless you are talking about planetary collapse where life does not recover at all anytime soon). It's actually very hard to even imagine circumstances where the whole body of knowledge we have would be completely lost. Even with 10% of the knowledge and existing machinery left, we could pretty much rebuild everything in a matter of centuries.
They have fusion reactors for every housewife, godlike metallurgy and rocket engines, but they can't make advanced computers no matter how hard they try after an interstellar nuclear civil war put an end to interstellar trade and, thus, complex economies and long supply chains.
Such things require enormous societal organisations to work, and that requires period of civility, prosperity, and material security to make people with brains to do things like that and not to scramble to work on better bomb shelters.
After few generations of people living caring about only basic necessities, the society went into downward spiral because the less scientists and engineers there were, the less were available to teach the next generation of them, and maintain advanced manufacturing equipment.
Despite the basic knowledge of science still being there, there were nobody with hands on skills and material capacity to make complex manufacturing equipment even after a period of relative prosperity 300 years later.
It's like asking a average random engineering or physics PhD to make AMSL 3500 EUV scanner. He will have a basic idea how the thing works, but it will take him more than a lifetime just to make a single part of it if he were to work alone without societal and material facilities for making something so complex.
So long as you understand the basic principles, you could make an integrated circuit using hand-drawn acetate or glass sheets and some really simple optics. Or ignore integrated circuits and make stuff from discrete components which you made yourself. You only need to care about making complex EUV scanners much, much later on.
In research labs around the world, we make stuff almost completely from scratch all the time. It's costly in terms of labour, and it's doing low volumes with lower tolerances. But it is making real, working stuff. In thousands of companies, research findings are developed into manufacturable products, with a lot of additional development work, optimising and refining.
We already know you can go from most concepts, to research, development and production. We've done it, and will continue to do it, in every field we can think of. I think to assert that we couldn't reinvent every one of the technologies humanity has discovered and developed fails to recognise just how resourceful and ingeneous we can be if we have the drive and opportunity. It might be that some technologies would be harder to reinvent, or would take longer to reinvent, but we're a capable lot and I'd bet we could get up to speed quite quickly given a few hints about what was possible. There are thousands of manufacturing techniques from the last century which we have lost the capability to use. Material quality changes, loss of knowledge and skills through retirement, fires, water damage etc. But we could regain each of them if the need was there. Look at FOGBANK for a recent example of a capability which was lost and regained. It takes time, money and resources, but it's possible.
The main thing we have in today's world which a collapse would eliminate is effectively limitless energy, and redeveloping that would be far harder than any individual technology. They would lack the more easily exploitable resources we already exhausted, and it would take time to overcome that hurdle through additional technological advances. But that is not a hard barrier. They would have to develop alternative sources and work out different strategies. This might delay things, but it wouldn't stop them entirely. We had sophisticated civilisation before the discovery of coal and oil, and electricity. Wind, water, solar and wood were widely used for mechanical and heating purposes long before electricity was discovered.
Yes, in the universe, they can easily make microelectronics on technology level of twentieth century eighties.
The main idea is that they have no hope to make anything remotely approaching even 21st century "advanced tech" level, without an actual civilisation that had few decades of peace and prosperity to allow for civilisation-wide supply chains, knowledge sharing, and economy.
You could load the entirety of Wikipedia onto an e-reader and power it with almost no electricity.
Data centers are basically bunkers and there is a tremendous amount of replication occurring.
If anything I think we're likely to leave by far the largest accumulation of knowledge in history, regardless of how bad things get.
All encrypted at rest. Lose those keys and the data is gone...
With interruptions in the provisioning of everything from the electricity required to parts for power management, cooling, air handling, networking, memory, disks, CPU, etc., the half-life of such centres would likely be on the order of a few years, even assuming local power.
Talent is probably the biggest factor.
Even absent greater civilisational collapse, a multi-billion-dollar-a-year income company such as Google can barely keep the lights on for a given project for 5-8 years, if that. Many startups fail even faster.
I wonder what a datacenter would look like 10,000 years from now if no one did anything to it. obviously it wouldn't be powered but I'm thinking there would be recoverable data.
There are no hard lines between civilizations of course, but societies that agree on common standards for a number of things sounds like one of the better definitions I can come up with.
What is your definition of a civilization then? As far as i know there is no "global" culture, you can live in many different places and have a totally different everyday life experience.
It's easy to envision that a lot of knowledge will be conserved somewhere.
Software of various kinds might be lost, since we usually don't print them out. But the theory required to re-implement them are all available on paper, sitting in a library somewhere. A book on algorithms and data structures will be far more useful to a future civilization than raw source code for a hardware architecture that won't even exist anymore.
Although I have a background in logic programming and I study logic-based machine learning for my PhD, I find that I often have trouble to understand important terminology - and I mean "important" in the sense that entire papers are based around it, but take it for granted that the reader is very familiar with the terms, what they mean, and how they're used.
For example, I recently struggled with the following terms: "finite axiomatization", "explanation-based learning", "constructive induction", "knowledge-level learning", "weakest preconditions", and others.
I eventually managed to get on top of those terms, sufficiently to read and understand the papers that used them. I did this by searching online for an explanation ("finite axiomatization" is used in mathematical logic) and by digging in the literature for terms that were defined in previous works. I found all of that material online, of course- and where I couldn't find a copy online, I basically had to "wing it" and hope I grokked it right. Searching for anything published even in a major AI conference or journal before the 1990's is a big pain and even university libraries seem to lack physical or electronic copies.
To conclude- yes, there are going to be various works left behind if civilisation collapses. But a lot of them are going to be like maps without the key. The people surviving us will be able to read them, but not able to understand them, because they will miss key knowledge, that is currently spread around hundreds of thousands of sources that only experts in niche sub-fields are even aware of.
Which in turn assumes that you have real work to do. One of the earliest civilian computing systems was a payroll calculator - which is only useful if payroll is a problem you need to have solved, which in turn is only necessary if your economy is complex enough to need payroll calculations at significant scale, and human "calculators" aren't available.
The point is that the Greeks and the Romans had the IQ to invent modern technology. The Greeks especially also had the philosophical background.
But neither had the politics or the economics.
Modern computing is a political phenomenon, not just a scientific one. It exists because it solves certain economic and political problems, and there's no reason to assume that a different culture would have identical problems - even if it could understand the theory.
I'm a big fan of house solar for that reason. In the short term, there's every reason to prefer big solar installations run by power companies interested in every last percentage of efficiency and willing and able to maintain it well, but for disaster prep it's great to have as many independent islands that can run to some degree in an isolated mode as possible.
(Although I'd be a lot happier if house solar was more conveniently integrated into the house system. Then again, if the grid was down in the long term there's a lot of people who could tweak the solar installation to be the primary house power in not too much time or effort. Even in their current form it's a lot better than nothing. The difference between one powered outlet and zero powered outlets is pretty big.)