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At New Scientist: Fuzzy law threatens mathematics

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We are asked, how many grains of sand can you take away from a heap and still call it a heap?

At some level, we think, the world must be precisely defined. Underpinning its workings, in the end, are the laws of physics, which are expressed using cast-iron mathematical equations that admit no vagueness.

I’m not so sure that’s the case. I think I have uncovered a fundamental physical law that is itself vague. The implications could be far reaching, potentially casting doubt on the ability of conventional mathematics to provide us with a full description of the universe – but also perhaps opening entirely new avenues to even better physical theories.

Eddy Keming Chen, “The fuzzy law that could break the idea of a mathematical universe” at New Scientist (subscription required)(subscription required)

New Scientist — as a culture — would probably always been happier joining the war on math, and this sounds like a way of testing the waters. But we shall see.

Paper. (open access)

See also: The progressive war on science takes dead aim at math

9 Replies to “At New Scientist: Fuzzy law threatens mathematics

  1. 1
    polistra says:

    I thought this was already part of the broad understanding of real science, not a new “law”. Anyone who measures things for a living knows that measurement can never be precise, and the act of making a measurement always changes the object being measured. This has nothing to do with Heisenberg or “quantum” quackery.

    When a set of objects appears to be discrete and countable, that’s just an arbitrary decision for convenience. The previous item is a perfect example. When the fungus invades the ant and becomes an organ, do you count two species or one? When bacteria are part of our gut microbiome, do you count a trillion creatures or one?

  2. 2

    For those of you who are wondering what this New Scientist paper is all about, here’s the arXiv version of Eddy Chen’s philosophical ramblings.
    https://arxiv.org/pdf/2006.05298
    He’s dealing, of course, with the pre-Socratic paradoxes of Heraclitus and Parmenides. In a way, this is also the same issue as Plato’s forms and Aristotle’s categories. Except he’s updated “forms” to “physics”. I don’t want to imply that old paradoxes are stale, but they aren’t exactly earth-shattering either.

  3. 3
    Querius says:

    How black does a color have to be to call it black (https://en.wikipedia.org/wiki/Vantablack), how clean does a surface have to be to call it clean, how many buildings have to be burned and looted before the media stop calling it mostly peaceful?

    However, some of these questions have actually been settled by U.S. law!

    According to ABC News, the average chocolate bar contains eight insect parts. Anything less than 60 insect pieces per 100 grams of chocolate (two chocolate bars’ worth) is deemed safe for consumption by the Food and Drug Administration.

    You can now safely strike that one off the list.

    Many other questions like this can be answered by the U.S. law and keep mathematics safe for now! For example, did you know that tomatoes are classified as vegetables by California law? This was decreed so that ketchup could count as a vegetable in the “meals” served in public school cafeterias.

    Our worries are finally over!

    -Q

  4. 4
    PaV says:

    There’s a link in Chen’s paper to this paper by John Bell, and I think Chen is just picking up where Bell leaves off. I think Bell’s paper is more accessible and straightforward.

  5. 5
    PaV says:

    BA77:

    Having read most of the paper I cited up above, I would highly recommend you read it. John Bell has a special place in all the deliberations about QM and the measurement problem.

  6. 6
    bornagain77 says:

    PaV, yes he does have a special place. And, as far as I know, his inequality(s) has consistently been violated in many experiments testing for it under many differing conditions. Which, last time I checked, is certainly not the result that he was hoping for:

    Einstein vs quantum mechanics … and why he’d be a convert today – June 12, 2014
    Excerpt: John Bell, a physicist working at CERN, took Einstein very seriously and wanted to develop a hidden variable theory along the lines Einstein suggested.
    He examined the states Madame Wu had created, but on looking closely at their predictions for some small adjustment of measurements, he came across a startling result.
    According to quantum mechanics, finding such a hidden variable theory would be impossible. The results of measurements in the laboratory would be different for Einstein’s hidden variables and quantum mechanics.
    This meant that quantum mechanics was simply wrong, or else that any hidden variable theory enabling a completion of quantum mechanics would have to allow a “spooky-action-at-a-distance”.
    Back to the lab
    In a nutshell, experimentalists John Clauser, Alain Aspect, Anton Zeilinger, Paul Kwiat and colleagues have performed the Bell proposal for a test of Einstein’s hidden variable theories. All results so far support quantum mechanics. It seems that when two particles undergo entanglement, whatever happens to one of the particles can instantly affect the other, even if the particles are separated!
    https://theconversation.com/einstein-vs-quantum-mechanics-and-why-hed-be-a-convert-today-27641

    Of related note,

    Quantum physics says goodbye to reality – Apr 20, 2007
    Excerpt: Many realizations of the thought experiment have indeed verified the violation of Bell’s inequality. These have ruled out all hidden-variables theories based on joint assumptions of realism, meaning that reality exists when we are not observing it; and locality, meaning that separated events cannot influence one another instantaneously. But a violation of Bell’s inequality does not tell specifically which assumption – realism, locality or both – is discordant with quantum mechanics.
    Markus Aspelmeyer, Anton Zeilinger and colleagues from the University of Vienna, however, have now shown that realism is more of a problem than locality in the quantum world. They devised an experiment that violates a different inequality proposed by physicist Anthony Leggett in 2003 that relies only on realism, and relaxes the reliance on locality. To do this, rather than taking measurements along just one plane of polarization, the Austrian team took measurements in additional, perpendicular planes to check for elliptical polarization.
    They found that, just as in the realizations of Bell’s thought experiment, Leggett’s inequality is violated – thus stressing the quantum-mechanical assertion that reality does not exist when we’re not observing it. “Our study shows that ‘just’ giving up the concept of locality would not be enough to obtain a more complete description of quantum mechanics,” Aspelmeyer told Physics Web. “You would also have to give up certain intuitive features of realism.”
    http://physicsworld.com/cws/article/news/27640

    “hidden variables don’t exist. If you have proved them come back with PROOF and a Nobel Prize.
    John Bell theorized that maybe the particles can signal faster than the speed of light. This is what he advocated in his interview in “The Ghost in the Atom.” But the violation of Leggett’s inequality in 2007 takes away that possibility and rules out all non-local hidden variables. Observation instantly defines what properties a particle has and if you assume they had properties before we measured them, then you need evidence, because right now there is none which is why realism is dead, and materialism dies with it.
    How does the particle know what we are going to pick so it can conform to that?”
    per Jimfit
    http://www.uncommondescent.com.....ent-548632

  7. 7
    Truthfreedom says:

    Hi Bornagain77.

    Materialism is dead. Finally, irretrievably. Please visit thread:
    https://uncommondescent.com/academic-freedom/is-the-usa-going-over-the-edge-as-we-speak/#comment-711623
    Posts #232, #246, #249, #293 (the “map” gimmick).

    Materialism’s epistemological blunder can not be salvaged.

    Seversky is crying tears of bitterness.

    We won. 🙂

    Aristotle and the soul are back.

  8. 8
    Querius says:

    And so is Determinism.

    L1.4 Photons and the loss of determinism
    MIT OpenCourseWare lecture, Prof. Barton Zwiebach
    https://www.youtube.com/watch?v=8OsUQ1yXCcI

    Photons + polarizing filter -> hidden variables?? -> Bell’s Inequality! -> experimental proof :. each photon behaves probabilistically, not deterministically.

    -Q

  9. 9
    Truthfreedom says:

    Thanks for the input, Querius! 🙂

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