What Is the One Fact Humanity Needs to Know?
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From that one insight, the entire rest of the scientific method flows; from there, science itself, and math, and pretty much the ~10 answers that didn't include this idea in it.
Fantastic! Is that original?
It came from a slightly different source for me, but a similar one. Imagine you're thrust back in time 200-400 years, and let's just stick you in England or something where you've got a University and a willing audience to learn. How do you transfer as much knowledge as possible, as quickly as possible? Well, as much as I think the Prime Directive of Star Trek is a bit of a crock as a moral principle [1], as a descriptive principle we can see there's some truth to it today, if we look around with open eyes... simply transferring knowledge without transferring the ability to develop it yourself, or, if you prefer, transferring wisdom, is a dangerous thing to do, and tends not to produce lasting results. So I asked myself what my thesis would be, what's something short and simple that I would repeatedly hammer on? And that's what I came up with.
I would also do that thing that some of the best teachers do, where they tell you "I'm going to deliberately screw up derivations in class, it's on you to catch them", to try to avoid being treated as personally reliable myself. (The "Dark Ages" are widely misunderstood and were not the barren wasteland of knowledge advancement the popular conception has of it, but I do think you could make a good case that they were indeed slowed down by over-privileging Aristotle and the other such classical authors for too long.)
[1]: Specifically, it leaves a rich space of options between "completely leaving the society in poverty to their own devices" and "just blunder in and start selling tech with wild abandon" completely unexplored. It's a great dramatic device, I really have no problem with it within the show itself, but it doesn't travel out of that context well.
>Imagine that Archimedes invented a temporal telephone ("chronophone" for short) which lets him talk to you, here in the 21st century...
> If you say something that is considered obvious in your home culture, it comes out of the chronophone as something that is considered obvious in Archimedes's culture...
>if you say "The Earth circles the Sun" it comes out of the chronophone as "The Sun circles the Earth". It doesn't matter that our civilization is right and their civilization is wrong - the chronophone takes no notice of facts, only beliefs and cognitive strategies. You tried to transmit your own belief about heavenly mechanics, so it comes out as Archimedes's belief about heavenly mechanics.
IMHO “If civilisation was destroyed,” given current environmental status (exhausting resources, pollution, rising sea levels and temperatures, almost 75% of species gone extinct in the last century), as well as our unsustainable economy, corrupted political leaders, and proliferated nuclear weapons (still) powerful enough to fully obliterate mankind (if not the whole of life on Earth), it would most likely be due to ourselves.
So the best bits of information I would pass on to survivors would be those that would allow them not to repeat our mistakes: "take care of the environment, and don't make war to each other; do this with the utmost diligence - keep in mind it's a really tough job; so tough in fact, that we failed, and all of our advanced technology, with all of our wisdom, wasn't enough to prevent our collapse."
Edit: I understand my answer is perhaps OT (in the sense that it's not scientific information) but nevertheless if we want to maximise the survivors' chances...to survive, I would rather ensure they do not make our mistakes; because if we assume they'd have their own history and evolution (as a civilisation), just like we did, then we might assume as well, that they would make mostly similar discoveries, so there's no point in telling them in advance what they are going (sooner or later) to find out by themselves anyway.
Half the reason we have what we have today is fighting over finite natural resources. You eliminate the pressure of overpopulation, you eliminate a massive reason to fight in the first place.
I think this is the most important thing to learn, because it would spare the future from a lot of suffering and give future people leisure time to think about the world and discover things for themselves. However, I don't like that this is a bit of knowledge that doesn't easily allow humans to verify it.
Instead, I would tell them that one can see many tiny things some of which make us ill, but not the tiniest of them, by staring through a tiny water droplet.
Item #2 would, I think, be a statement on the periodic table that can easily be verified using minimal technology, again with a hint that there are even smaller things.
Because Einstein said: 'God does not play dice', he wanted to express that just because there's a probability of measuring something doesn't mean reality itself is built upon probabilities.
My second was the Haber process, a simple reaction that produces fixed nitrogen. With that a simple agricultural society could escape subsistence.
As a free bonus, this stuff automatically gives you an idea of microbes which should lead to lenses, microscope, telescopes, and, ideally, another scientific enlightenment.
It's also hard to get proper experimental controls, especially without modern technology and sanitation. And the process of empirically proving the relationship between specific pathogens and diseases is complicated!
https://en.wikipedia.org/wiki/Koch's_postulates
So I guess my concern is that people could have a lot of seemingly compelling experiences that might make them reject the germ theory (or think it was only applicable to a minority of infectious diseases), even after having been told about it in detail.
P.S. Ok, I see now that the context is science and reconstructing civilization.
Perhaps the acronym is a bit less pertinent, then. Perhaps not. Even in scientific and technical fields, I see too much attitude and salesmanship that disregards it, to the detriment of those who blindly buy in to the pitch.
TANSTAAFL -- even if you're very bright.
This would be especially important if Cataclysm was man-made.
With no oil, people will just deal with the limitations of low wattage electrics until they get better battery and generation tech. Arguably, you could have a 19th century type society with a nuclear reactor; both uranium and graphite can be mined with simple tools.
Also, I wonder what a very religious scientist would answer.
You can also follow random Wikipedia article links and find, for example, laureate Joseph Rotblat saying "I am not a particularly religious person, and this is the reason for my agnosticism".
The other one is at the other side of the world...
(assuming civilization is not destroyed at once but in slow phases)
- Michael Faraday
So I would rather go with something that took a very long time to be understood and was absolutely necessary to create any civilization. For example number 4, basic hygiene. Or agriculture: "you can grow edible plants on purpose by planting their seeds in the ground and watering them". The scientific method is not very useful if you have to spend your life hunting and gathering to survive.