>This same argument seems to imply that virtually everything should be expensive

Non-zero doesn’t mean “unaffordable” or “expensive”.

> The hard part is looking into the future…

The hardest part is to understand that the content we want to preserve carries more valuable information about us than about itself.

Scientific knowledge can be discovered again, it’s not something to worry about. The preservation shapes the future views of us, leaving the trace in the history of those who preserve, their life and their experiences. Maybe they just needed to accept their mortality and irreversible flow of time?

I don't know. Scientific knowledge is expensive to rediscover. It requires a lot of false starts and often involves a great deal of luck/randomness. Historically, periods of flourishing are often associated with the rediscovery or importing of large collections of wisdom. For example revivals of ancient works or the introduction of works from afar due to newly developed trade routes. If ideas were easy to rediscover, we shouldn't expect those events to have much impact.

There is certainly a cost of storing data, and cost should enter the equation. But we're losing a lot of data for reasons other than cost and we don't have a reasonable way of assigning a value to the lost data.

My point is, we are engaging in a very unnatural process, trying to preserve something against the second law of thermodynamics. We are going to lose the data and things are going to break no matter what. We cannot change the nature, but we can accept it.

> We are going to lose the data and things are going to break no matter what. We cannot change the nature, but we can accept it.

If man was content with the nature of things he would never fly, or go to the moon, or any of the other myriad accomplishments humanity has made. If we can preserve clay tablets from thousands of years ago we can find some way to keep the information we produce today for posterity.

I’m not arguing with that. We can and we will preserve some information. We must not be obsessed with saving everything. Imagine the humankind in a million years from now; if we pick 10 most important facts about each century, that will be a hundred thousand facts to remember. Maybe we develop abilities to know and use them all, but from a modern human perspective that’s already too much. Now, can you reduce the XXI century to 10 facts? How much of those zettabytes of information would be worth keeping for a million years? For ten thousand years? For a thousand years?

I can't imagine an archaeologist or historian studying e.g. Pierre de Fermat ever saying, "Good thing we have so few documents and artifacts! That way we know what was really important to him."

What's the proof for Fermat's Last Theorem again? Doesn't matter, it was just a footnote anyway so let's not bother preserving it. It doesn't matter that it took our smartest minds 358 years of trail and error to rediscover the proof. It can always be discovered again.

We don’t know if the proof did exist. The complexity of the one we have is an indication that he did not tell the truth, whether that was a genuine mistake, a joke or something else. For sure it wasn’t the longest time gap between a problem statement and a solution.

Yes, rebuilding civilization from scratch would be a difficult task, taking centuries if not millennia, if no knowledge is preserved. However we do preserve it and do spend considerable effort, what cannot be said about our culture and individual experiences.

Maybe the complexity of the one we have is an indication that we haven't rediscovered it. We discovered a worse one. Maybe it will take our smartest minds another 350 years to rediscover his. If preserving data was easier in the 1600s we could just grep through Fermat's hard drive and we would know for sure!

Let's keep making preservation easier, and preserving as much as we can. Maybe much of it is worthless, but I guarantee there's at least one document we think is worthless today, that historians 500 years from now will be glad we preserved anyway.

Simple. Store everything. I give you an example: the clay tablets written in cuneiform discovered at Ur. They were disposed of by Sumerians, possibly because they have fulfilled their purpose and were simply thrown away. They deal with important things like commercial transactions, but also unimportant things like a personal letter or a poem. This unimportant things pretty much taught all we know about the Sumerian language: syntax, vocabulary, regional variations, etc. In archaeological terms, a refuse is a huge treasure trove, precisely because no one chose what to throw away. Everything is there. It's entirely up to the archaeologist to comb and come up with an interpretation.