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My Take on the Limitations of Scientific Knowledge

  1. Jul 13, 2015 #1
    Imagine an intelligent ant living in a sealed glass tank, with nothing inside but sand and himself, for his entire existence. He has the intelligence of a human but no way to escape, and nothing to see outside of the glass tank. The temperature never changes, the air is static, the source of light is homogenous, isotropic, and unclear in origin. This intelligent ant could still formulate many laws of physics. The projectile motion of grains of sand, as well as their inelastic collisions, could lead to Newton's laws of motion. He could stack sand and discover geologic facts such as angle of repose, relative hardness between quartz and micas, and basic sedimentary properties. Perhaps rubbing against the sand could induce static charge and lead to very rudimentary electrostatics experiments. The ant could see sand being broken down continuously and be led to speculations of indivisible atoms, and whether or not they exist, just as the Greeks were. Perhaps by stackting sand grains very carefully the ant could discover basic things about diffraction of the little scattered visible light he receives. But surely it is obvious that the vast majority of contemporary physics will be forever inaccessible to the ant. Sure, he has sillicon, but he has no way to dope it, no way to drive it into depletion, and no other circuit components to combine it with. He has no means of power generation, no organic compounds to burn for fuel, nothing to forge into a Small Hadron Collider. He will never know of gamma rays, muons, plasma oscillations, dark matter, neutrinos, nuclear reactions, fermions and bosons, oscilloscopes, lasers, supernovae, the cosmic microwave background, or so many other cornerstones of human knowledge. How can we expect him to discover Maxwell's equations with no real electrodynamics? How about the Schrodinger equation? How can one arrive at the Friedman equations with no stars? Continuity with no transport processes? Where does the Minkowski metric arise in a box in a box of sand, where even Newton's universal law of gravitation never has to be derived, since F = mg will forever suffice? Even if the ant is a brilliant armchair mathematician who spends all his time writing in the sand, he would look at these equations as beautiful but unphysical and indistinguishable from other classes of functions and exotic algebras in terms of their explanatory power. We can safely say that the ant will never figure out that he lives in something called an "old lady's basement," his tank was created by something called a "glassmaker", which is a type of something called a "person", which is a type of something called a "mammal", that lives on something called a "planet" inside something called a "solar system" that is in something called a "galaxy" that is in something called a "universe" that is governed by all of these universal equations that reduce to those that he is familiar with in the right limits. Thus:

    -If the ant were of the opinion that the only way to advance scientific knowledge is empirically, then he will never learn anything that doesn't apply to his tank. Will this lead to the origins of the universe? It's unspeakably unlikely.

    -If the ant were of the opinion that a-priori research without experimentation can produce knowledge, he has no way to verify it, and many if not infinitely many competing models would have equal applicability. After all, all reality has to do to satisfy the ant's inquisition is produce a tank full of sand. Will the ants speculations produce an accurate description of the universe? Again, the answer is that it's unspeakably unlikely.

    Yet we as humans find ourselves within our own tank of sand. Some inflation models speculate that the observable universe could be as small as 10^-23 of the entire universe - which more or less means our search for knowledge amounts to trying to figure out what an avocado is by forever looking at one hydrogen atom bound inside that avocado. Yet even if the entire universe were contained within the observable one, theres no guarentee that everything in here will be measurable. Again, there could be laws of physics that are essential to a complete description of reality that we will never be able to probe, because their energy scales are too high, or because there are types of matter that do not interact with ours, or etc. In short, we are limited by the applicability of physics to our observations - there could be existing laws of physics that will never be applicable to any situation we can produce, yet that are essential to understand the large scale structure of reality. A not-so-bold person might even say that this is far more likely than not.
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  3. Jul 13, 2015 #2


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    And yet, since the tank is perfectly isolated from the rest of the world, it constitutes the entirety of the universe for the ant, and any laws that might be accessible only from outside are of no concern to her.
    The ant would do best to develop as good an understanding of its environment as she can, and not waste her time on speculation about in principle untestable regimes.
  4. Jul 13, 2015 #3
    So it wouldn't bother you as an ant to know your knowledge is forever incomplete and approximations to unknowable things? I get your pragmatism, it's basically the only thing you can do. But surely you think that many if not most cosmologists seek a complete description of the universe?

    Also, the ant thanks you for the free sex change.
    Last edited: Jul 13, 2015
  5. Jul 13, 2015 #4


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    Cosmologists are scientists too - their descriptions of the universe must be testable, which means at least a partial overlap with the observable part we inhabit.

    As to whether this lack of extended knowledge bothers me - my tank is so huge and full of mysteries neither me nor any other ant will be able to understand in our lifetimes, that worrying about there being even more knowledge out there, that's by definition perfectly useless to us, seems a bit silly.
  6. Jul 13, 2015 #5
    Yes that's pretty much the canonical response to threads such as this, and why they get derailed on whether or not string theories merit consideration. But let us not go there.

    It's just strange to me that the typical response is "do not seek a complete description of reality, be entertained by what you can see."
  7. Jul 13, 2015 #6


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    How would you ever know if you're describing 'reality' if you can't test it?
  8. Jul 13, 2015 #7
    You wouldn't ever know, that was one of my points. If it had sufficient explanatory power and elegance, it might be reasonable, though. Or would it? And is it even likely that we'd arrive at such a theory?
  9. Jul 13, 2015 #8


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