Here's an argument that I'm sure will give my philosopher of physics collaborator Jacob Barandes the fits. The conclusion will be that there are vastly many complex structures smaller than a proton, right here in our region of spacetime, populated by vastly many scientific and philosophical observers. Look at that drop of water running from the faucet to the drain. Within it are many tiny people, living many tiny lives.
[Cancer can go hang. I'll keeping fly my weird philosophical speculations on this blog as long as I can. Naturally, I'm hoping to land in the long statistical tail, so that the field won't be rid of me anytime soon.]
Assumption 1: The universe is infinite.
The observable portion of the universe, of course, is not infinite. It extends a only minuscule 46 billion light-years in every direction from us. But there's no reason to think the universe ends exactly at the observational horizon, with us at the center! How inelegant and un-Copernican that would be.
An infinite universe is slightly more elegant than one with an edge. (Why would there be an edge? What would happen there?) And current physical estimates also tend to suggest that at the largest scales, the universe is spatially flat, rather than looping back upon itself in a closed but edgeless geometry. Lots of theoretical physicists think infinitude is a good guess. In any case, I will assume it.
Assumption 2: If the universe is infinite, complexity recurs at large scales.
This assumption is less standard and harder to justify, but not, I think, wholly implausible. Imagine zooming out and out and out so that our galaxy becomes a speck, less than a speck, less less less than less than less of a speck; keep zooming.
It might be that once you've zoomed out far enough, every scale looks smooth and boring -- that things simplify at large scales and zooming further out yields only more featureless simplicity. But it might instead be that complexity reappears at some larger scales, generating structures as intricate as those at our familiar scale. Given infinitude, we can keep zooming out until we find those scales. My second assumption is that however far we zoom out, there will always be larger scales at which complexity reappears.
Such complexity could arise from large-scale interactions among processes governed by the laws we already know. Or it could arise from phenomena we're familiar with but don't yet understand (such as dark matter or dark energy). Or it could arise from unfamiliar processes with measurable effects only at enormous scales. Compare: If we were proton-sized, we'd have difficulty detecting gravity, which accumulates noticeably only at macroscopic scales. There is no guarantee -- nor indeed any particular reason -- to think that all physical laws must operate at scales we can readily detect.
Assumption 3: If the universe is infinite and complexity recurs at large scales, so do life and intelligence.
I see no reason to suppose that the evolutionary processes that produced life and intelligence on Earth could occur only at our scale. Evolution by natural selection requires patterns that reproduce with stable heritable variation and differential reproduction rates depending on that heritable variation. If complexity recurs at large scales, some of these scales will plausibly host complex processes capable of sustaining evolution over long time periods, producing entities approximately as intelligent as we are.
Since we have infinitude to play with, if one otherwise complex level for whatever reason can't host stable evolutionary processes like we see on Earth, forget that level and keep going up.
Now let this evolution run until we have scientific and philosophical observers.
Putting Assumptions 1-3 together suggests that there are infinitely many cosmic observers, capable of philosophy and science, vastly larger than we are, whose worlds contain us as tiny parts -- far tinier relative to them than a proton is relative to us. There's no particular reason to think their sensory organs or scientific equipment could detect events at our scale, which would be to them sub-sub-sub-sub-microscopic.
Assumption 4: Given Assumptions 1-3, it would be an un-Copernican coincidence if we happened to occupy the smallest scale hosting intelligent observers.
According to the Copernican Principle in cosmology we should assume as a default -- pending contrary evidence -- that we don't occupy any particularly special position in the universe, such as its exact center. To dwell at the very lowest, most fundamental level would make us special in an un-Copernican way. Why should we, of all the infinitely many observers at infinitely many scales, be so lucky as to occupy the foundation?
Copernican reasoning thus gives us grounds to think that if there are larger philosophical and scientific observers there are also smaller ones.
Now if we had good reason to rule out life-supporting complexity at smaller scales, we'd know that we are at the lowest level. But our failure to detect complexity at smaller scales doesn't establish its absence. As I mentioned above, there's no particular reason to think all scientific laws operate at scales we can measure or perceive.
Thus, Assumptions 1-3, plus a plausible application of the Copernican Principle and the absence of a reason to think we do dwell at the lowest level, invite the conclusion that within that tiny droplet falling toward the drain are realms of complexity far too small for us to register, populated by vastly many tiny tiny lives and tiny tiny philosophers and scientists, gazing out across their portion of the droplet, wondering what exists beyond the reach of their senses and equipment.
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