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Incompleteness, Undecidability, and Uncertainty

Discussion in 'Physical & Life Sciences' started by J_B_, Jan 10, 2021.

  1. J_B_

    J_B_ Active Member

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    I made an offhand comment here, but now it's going to bug me. I might as well get it out of my system.

    It seems to me that if science were necessarily tied to mathematics in an existential way, a scientific incompleteness theorem would simply be an extension of the mathematical one (i.e. Godel). However, that seems impossible to establish.

    Maybe something based on measurement, as in physics' uncertainty principle, would be a more realistic possibility. That is, maybe some measurement in biology (etc.) would imply a biology uncertainty principle.

    What do you think? Is there, maybe, an incompleteness, undecidability, or uncertainty principle for sciences other than physics?
     
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  2. Speedwell

    Speedwell Well-Known Member

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    It depends on what you are looking for wiggle room for.
     
  3. J_B_

    J_B_ Active Member

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    Maybe I don't understand you, but I don't see how. It either is or it isn't. My gut says an incompleteness/uncertainty principle applies to all the sciences, but as I said in the other thread, I have no idea how it would work. Godel & Heisenberg were smarter than I'll ever be.
     
  4. Speedwell

    Speedwell Well-Known Member

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    Godel's incompleteness theorems apply to axiomatic formal systems--which science is not.
     
  5. J_B_

    J_B_ Active Member

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    Noted.
     
  6. Ophiolite

    Ophiolite Recalcitrant Procrastinating Ape

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    What would be the function, or benefit, or application of such a principle?
     
  7. J_B_

    J_B_ Active Member

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    The same as Godel is for math or Heisenberg is for QM.
     
  8. Ophiolite

    Ophiolite Recalcitrant Procrastinating Ape

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    Heisenberg's principle, as I understand it, is description or interpretation of observations within QM theory. I am unclear as to how you see this in some ways different from other observations/interpretations within the field. Consequently I cannot yet see the relvance to an analagous "thing" in other sciences.
     
  9. J_B_

    J_B_ Active Member

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    Google is a wonderful thing. I had no idea this existed.

    Uncertainty principle of genetic information in a living cell | Theoretical Biology and Medical Modelling | Full Text

    The date was 2005, so I'm gonna check the followup.
     
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  10. J_B_

    J_B_ Active Member

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    Apologies for the frenetic pace, but in checking publications that referenced the above paper, I found this:

    Unsolvable Problems of Biology: It Is Impossible to Create Two Identical Organisms, to Defeat Cancer, or to Map Organisms onto Their Genomes

    I think it's fascinating that someone is claiming unsolvable problems in biology. How widely the idea is known or accepted is a different matter.
     
  11. Ophiolite

    Ophiolite Recalcitrant Procrastinating Ape

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    Useful. The abstract alone has given me two things:
    • A clear(er) picture of what you were driving at
    • An explanation for why I was having some difficulty in getting your drift: I consider absolute certainty to be a silly idea and in geology (my field of expertise) issues are so 'macro' that the uncertainty you are interested in doesn't arise (in any meaningful way [thus far{to the extent of my knowledge}])
     
  12. J_B_

    J_B_ Active Member

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    I'm glad it helped. You can tell me if this changes anything for you.

    https://www.journals.uchicago.edu/doi/abs/10.1086/629321
     
  13. FrumiousBandersnatch

    FrumiousBandersnatch Well-Known Member

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    Why is this so notable? Living systems are dynamic, in continual flux, and that includes their genomes.

    Heraclitus was aware of this principle around 500BC...
     
  14. J_B_

    J_B_ Active Member

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    I love to explore and discover the world. It fills me with a sense of wonder. A facet of my sense of wonder is that I wish others would share it with me. Yet, when I mention such ideas, or ask questions about them, the response is much too often (as here), 'Meh.' That saddens me.

    I've often wondered if my own field might be constrained by an uncertainty principle, but, as I said, had no idea how to approach it. These papers, recently found*, sparked a thought regarding the general approach that may be at play here. It was especially important to find both the biology and geology papers. Why? Because one question niggling at me was: What facet makes simple confidence levels (something long known in science) rise to the level of an uncertainty principle? Now I have an answer.

    My first impression is that the case presented by the biology papers is a significant finding; the case presented by the geology paper, while worthy of publication, is just a small step in the understanding of uncertainty in geology.

    Still, I would like to hear the opinion of @Ophiolite on that.

    - - -

    *Just as my recent discoveries of Kauffman, Longo, etc. opened up some fascinating new territory regarding the nature of first principles.
     
  15. Ophiolite

    Ophiolite Recalcitrant Procrastinating Ape

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    Interesting. Since you are focused on a search for some Uncertainty Principle you see the geology paper as "a small step in the understanding of uncertainty in geology".

    Since I'm focused on the development of our geological knowledge I see it as progress in the use of geothermometry and a review of some of the constraints on its reliability.

    As the paper is behind a paywall I don't know if there is anything in it to justify the title. Based on the abstract alone, that title "The Granulite Uncertainty Principle: Limitations on Thermobarometry in Granulites", is either a tongue in cheek dig at physicists, or a desperate measure to get more readers. I don't think it speaks to your search.

    There's fifty years of development in techniques since I studied them as an undergraduate. Vast improvements in analytical methods, extensive field work and detailed laboratory studies have led to more accurate, more precise and more revealing data, but at the boundaries we are making assumptions and testing them. That's what the paper is about.
     
  16. J_B_

    J_B_ Active Member

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    I defer to your expertise.

    Sorry. There was always the chance that you had access, given you work in the discipline. Regardless, thanks for taking a look.

    Maybe my wording didn't connect with you, but this is exactly what I was trying to say. Thanks for confirming.
     
  17. essentialsaltes

    essentialsaltes Stranger in a Strange Land

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    Some star in some distant galaxy has the most planets around it. (There could be ties.) We will never know how many planets it has. There are all sorts of things we can never know. But this kind of incompleteness is not very interesting, I think.
     
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  18. Ophiolite

    Ophiolite Recalcitrant Procrastinating Ape

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    I'm retired and my work deviated from geology to engineering decades ago. I've revisted geology as a hobby over the last twenty five years, but I make do with text books and such papers as are accessible.
    There is no need to apologise. The abstract gave me new information that will inform my future reading and literature searches.
     
  19. FrumiousBandersnatch

    FrumiousBandersnatch Well-Known Member

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    We all have our own interests. I just found it odd that you would be captivated by the fact that biology is messy and uncertain - when those are its characteristic features...

    It's not really an uncertainty principle like Heisenberg's Uncertainty Principle, which defines an important uncertainty relation, it's just the uncertainty of dynamic systems. I'm generally wary of taking the name of a specific concept and repurposing it for vaguely similar situations; I'm not having a pop at you, but at the people who want an eye-catching title for their article or paper.

    I suppose it could be significant to geneticists, but I'd expect them to be well aware of the effect of mutations when comparing or duplicating sequences...

    I'm probably getting cynical in my dotage ;)
     
  20. Brightmoon

    Brightmoon Apes and humans are all in family Hominidae.

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    That struck me as a little odd too! that they’d want to propose a type of ur-organism when even a biological concept such as species is blurry , Let alone individuals. Also the cells inside multicellular organisms doing different jobs means that some DNA is shut off
     
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