Richard Feynman once remarked something to the effect that if society collapsed and only one piece of knowledge could be preserved, the knowledge that the world consisted of tiny particles called atoms would be the most significant.
Such knowledge without the accompanying understanding of how we know this to be true would very quickly turn into a religion where the pronouncements were made and expected to be accepted on faith. It would soon dissolve into rancorous debate over the true interpretation of atoms and would further our understanding of nature no more than religion does today.
There is an amusing medieval parable of the horses teeth which is too perfect to actually be true but is a good illustration of the problem.
Consider the idea that any of the great thinkers from 1000 years and beyond would have little trouble catching up with modern politics. Our technology is more advanced but the machinations, conflicts, and fundamental struggles would largely be quite familiar. The science, however, would be entirely foreign. There is not a single thing from any of our sciences that would not be a novelty. We can look at Aristotle as offering relevant political advice but his sciences are so far off the mark that his conceptions cannot even be believed by children. To put it another way, our science has advanced while our politics remains frozen. We are limited to ideologies because in truth we have not advanced our fundamental understanding of politics more than a couple small steps.
Our scientific advances have occurred in the last 3 centuries, skewing heavily to the most recent. What is the cause?
To understand the answer to that question, we have to understand what it is that truly sets science apart from other methods of finding truth. That is: the scientific method.
How is it that the Scientific Method has managed to accomplish so much in so short a time span? Perhaps the answer will become clearer once we look at it a little closer.
The scientific method starts, as with the rest, in observing the world. The more accurate the observation the better.
The next step is to develop an hypothesis that explains this observation. Superficially this looks the same, or at least similar, as any other method but a proper hypothesis has some strict criteria.
First the hypothesis must be able to explain the observations that have been made.
It perhaps does not need to explain all observations, but it certainly cannot contradict known verifiable observations.
Second the hypothesis must make predictions about further observations that have not yet been observed.
It may be possible to come up with a new hypothesis that only explains existing observations but does so more simply than competing hypotheses. See a good discussion of Ockhams Razor
Third, the predictions must be precise enough that, if they should fail, the hypothesis will then be invalidated.
Once a candidate hypothesis has been selected it must be tested. Testing involves a deliberate attempt to break it. The principle at work here is that before one can feel confident using a building block, one must first find out how solid that block is and what it takes to break it. Note the difference between that approach and the approach employed by political, religious, and other zealotry whose primary objective is to defend their hypotheses.
It is also important to note here that the testing phase is only as good as the testing is rigorous and the subsequent observations are detailed. If either of those are lacking, the testing will not be adequate.
As an hypothesis resists continued attempts to disprove it, it can be useful in developing further hypotheses. Eventually, as confidence grows, it becomes a working provisional theory with the understanding that it has not yet been falsified. As more new hypotheses depend on an existing hypothesis, one can increasingly rely on it safe in the knowledge that it cannot easily be overturned and must be reasonably close to nature.
One of the beautiful anti-authoritarian features of this process is that other people have to choose to use the hypothesis in their own work. They have to see the value in it. From that perspective, attempting to convince people who will never use your work is then a complete waste of time. Additionally, adoption has to be voluntary. It would not be possible to coerce agreement except in a very short time frame and would ultimately prove a fruitless endeavor
It is common practice for people to describe as 'Theories' pretty much any idea that comes along. This is incorrect and is an attempt to undermine all the hard work that goes into developing formal theories. Equating theories with half-baked ideas is nothing less than an attack on science itself. The dimunition of the meaning and significance of theories is part of the larger war on science by people in the religious, business, and other communities that find that established theories are rather inconvenient for their beliefs and practices. Rather than develop alternative hypotheses the primary path forward is discrediting unfavorable ideas as being "only theories" with the implicit understanding that they are therefore just one persons opinion.
This is then matched by an attack on science from another flank from people who, wishing to aggrandize themselves, try to elevate their own ideas to the realm of the theoretical, without having to do the work necessary to get there. This two pronged attack on science is so prevallent that it is difficult to find anyone outside of the scientific community that understands what a theory is or has any respect at all for theoretical work.
My response, therefore, to those wondering what the most important thing to preserve would be is: The Scientific Method. It really is more than a method and is in fact a mental discipline. It is something that must be practised and internalized.
In importance, the next most important thing to preserve, would be the knowledge of how to make lenses because our ability to accurately observe the universe is likely the single biggest factor leading to scientific discovery and lenses give us both the telescope as well as the microscope which have each lead to massive changes in how we understand the world.
As for the fundamental change that we need politically, the question to answer it is possible to apply the scientific method to the organization of our society.
A bold task, but I believe it is possible, and I definitely believe it is worth finding out. We have reached a juncture where our political infrastructure and ideologies are preventing us from any meaningful change. We need to improve.
Although attributed to Lao Tzu, likely falsely, there is a saying: "If you do not change direction, you may end up where you are heading."
Another more poignant quote comes from Buckminster Fuller: "You never change things by fighting the existing reality. To change something, build a new model that makes the existing model obsolete."