How likely is a future without paper?

Silicon storage retention times vary substantially by type: Mask ROM should, barring abuse or sufficiently long continuous service that ion migration kills them(which would take a while, your CPU works a lot harder for most of its life and those rarely fail), last for ages. Eventually the dopants will probably thermodynamics-and-stochastic-phenomena their way around the silicon such that the structure is lost; but it’d take a very long while.

PROMs are somewhat less reliable, since writing to them involves ‘blowing’ some of the connections that were originally present in the chip in its factory state, a process that involves a certain amount of thermal and mechanical brutalization compared to mask ROMs, where the unwanted links are simply omitted during manufacture.

EPROMs, EEPROMs, and flash are less reliable still. Electrons gradually escape from the floating gate, and denser processes and multi-level cells decrease the acceptable amount of loss before it becomes impossible to tell what the intended state of the gate was. Manufacturer-alleged retention times are still usually in the decade range; but that’s hardly archival. Optical media(except the dye-based writeable/rewriteable kind, adding temperature sensitive organic chemistry to your process isn’t a longevity bonus) are likely to survive much better.

In terms of being able to read the stuff in the future, optical media have the advantage that, if you really care that much and understand the format used, you don’t need a purpose-build drive to read it. The purpose built drives are vastly better, of course, and their specialization is why you can get a $20 drive that will read back a DVD and multiple megabytes per second; but if you used an optical microscope with camera to grab an image of the pit/land structure of a disk, you could infer the data from that. Slow, ugly, and nontrivial; but very much possible.

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