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Physicist: Do the defects of real numbers open the door to free will in physics?

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From Emily Conover at ScienceNews, describing the work of physicist Nicholas Gisin:

Gisin — known for his work on the foundations and applications of quantum mechanics — takes issue with real numbers that consist of a never-ending string of digits with no discernable pattern and that can’t be calculated by a computer. Such numbers (for example, 1.9801545341073… and so on) contain an infinite amount of information: You could imagine encoding in those digits the answers to every fathomable question in the English language — and more.

But to represent the world, real numbers shouldn’t contain unlimited information, Gisin says, because, “in a finite volume of space you will never have an infinite amount of information.”

Instead, Gisin argues March 19 on arXiv.org, only a certain number of digits of real numbers have physical meaning.

And the implications for free will?

But if the world is described by numbers that have randomness baked into them, as Gisin suggests, that would knock classical physics from its deterministic perch. More.

It is fair to ask, at what price? Readers?

Real numbers: A real number is a number that can be found on the number line. These are the numbers that we normally use and apply in real-world applications.

See also: Researchers: Neuroscience has not “disproved” free will: “To be clear, we’re not taking a position on free will,” Dubljevic says. “We’re just saying neuroscience hasn’t definitively proven anything one way or the other.”

Can we build a computer with free will?

and

How can we believe in naturalism if we have no choice?

8 Replies to “Physicist: Do the defects of real numbers open the door to free will in physics?

  1. 1

    Determinism hasn’t been on the perch—oh, at least since Poincare discovered chaos around 1910. And clearly by 1920 when Dmitri Egorov and Nikolai Luzin founded the Moscow school of mathematics as a religious attempt to topple the Communist empire. http://www.hup.harvard.edu/cat.....0674032934
    We physicists had to wait for Lorenz to show us his famous butterfly curve in 1970, but surely a mathematician would know these details?

  2. 2
    Nonlin.org says:

    Gisin confuses data with information: http://nonlin.org/biological-information/

    Also, this is wrong:
    “Standard classical physics, the branch of physics that governs the everyday, human-sized world, leaves no room for free will.”

    This too:
    “After some number of digits, for example, the thousandth digit, or maybe even the billionth digit, their values are essentially random.”

  3. 3
    polistra says:

    This is unbelievably superficial. Digits are not numbers.

    Nature doesn’t care if we write a number or not.

    Circumference over diameter is the same whether we write the result in binary or decimal or Babylonian base-60.

    Even our perception doesn’t need digits. We can see and USE sines and cosines and hypotenuses for drawing and carpentry and plumbing without any digits at all.

  4. 4
    PaV says:

    I think Gisin is onto something. His discussion on boundary condition and determinism, which, as ‘Robert Sheldon’ points out, flows from chaos theory, or, rather, flows into chaos theory.

    However, I believe he’s pointing to something very profound–no pun intended, when he compares the ‘infinite’ dimensionality of the real numbers–as in, our ‘real’ world, and the ‘finite’ information content (think here of degrees of freedom) of actual space. A volume of actual space can NOT have an infinite information density–which means that ‘space’ itself cannot supply these ‘infinite’ degrees of freedom. Something, or Someone, else must do so.

    Oh, as the Physics community inches closer to the answer to so many questions!

  5. 5
    kairosfocus says:

    Folks, way back, my dad used telephone numbers as poor man’s random number tables. That’s because there is no correlation between names and number assignments. That clash of two deterministic schemes was sufficient to create effective randomness. Similarly, the determined structure of a circle clashing with that of the usual place value notation schemes creates the lack of correlation that is famously present in the digits of pi. Likewise for say that value of x, e, such that area under 1/x between 1 and e is unity. A similar thing happens with chaos and the effective randomness of a fair die: eight corners, twelve edges and roughness suffice to create effectively random outcomes. Shuffling of a deck of cards and spinning a roulette wheel are similar, too. Relevant power series do have transfinite numbers of terms [a decimal number is a compressed power series], and we may be surprised in our calculations, but that does not mean that any given term in the series is not perfectly determined. Determined is not equal to calculable by us or by the observed cosmos turned computer. However, that infinite depth does bridge to a phil-theol question: does an omniscient God know any arbitrary digit of pi, and does the determinism generating the digit then end in some form of compatibilism, wholly determined but free in some sense as not externally compelled? I suggest, compatibilism utterly fails as it undermines rational responsible freedom. I further suggest that an omniscient God cannot be a mechanical, material entity, once he knows something like any arbitrary digit of pi, no matter how trivial that seems to be. KF

  6. 6
    Fnarb says:

    Aren’t there two kinds of ‘incomputable’ reals? (1) Those which can be computed to arbitrary finite precision by a finite Turing machine, which contain a finite number of bits of information which varies as the Kolmogorov complexity of the number, such as the base of the natural logs or pi, and (2) those which must remain unknown, such as: assuming a uniform distribution of their canonical representations, what portion of all Turing machines halt on every input? Since halting is recursively undecidable, God presumably knows this number, but we don’t. In either case, the fact that humans don’t know such reals in their entirety does not seem to me to indicate that they contain ‘infinite information’. Moreover, ‘unknown to humans’ and ‘free’ are vastly different concepts.

  7. 7
    groovamos says:

    Nonlin Gisin confuses data with information:

    Just visited your site and posted. I think the confusion started with your assertion that “data” is everywhere but “information” somehow is not.

    So you have a distinction between how data is quantified and how information is quantified? What is your unit of measure of each? How much is 1 datum? How much “data” is in a pebble?

    So it would be good explain your theory that data are everywhere in nature.

    And I will break the news to you after seeing your essay: Shannon considered entropy to be information. If you examine a perfectly compressed text file, the number of bits in the file is equal to the total entropy therein.

  8. 8
    bornagain77 says:

    as to this claim from the article:

    But to represent the world, real numbers shouldn’t contain unlimited information, Gisin says, because, “in a finite volume of space you will never have an infinite amount of information.”

    Richard Feynman disagrees with him:

    Richard Feynman, in his role in developing Quantum-Electrodynamics, which is a mathematical theory in which special relativity and quantum mechanics are unified,,,

    Theories of the Universe: Quantum Mechanics vs. General Relativity
    Excerpt: The first attempt at unifying relativity and quantum mechanics took place when special relativity was merged with electromagnetism. This created the theory of quantum electrodynamics, or QED. It is an example of what has come to be known as relativistic quantum field theory, or just quantum field theory. QED is considered by most physicists to be the most precise theory of natural phenomena ever developed.
    http://www.infoplease.com/cig/.....ivity.html

    ,, Richard Feynman was only able to unify special relativity and quantum mechanics in quantum electrodynamics by quote unquote “brushing infinity under the rug” by a technique called Renormalization.

    THE INFINITY PUZZLE: Quantum Field Theory and the Hunt for an Orderly Universe
    Excerpt: In quantum electrodynamics, which applies quantum mechanics to the electromagnetic field and its interactions with matter, the equations led to infinite results for the self-energy or mass of the electron. After nearly two decades of effort, this problem was solved after World War II by a procedure called renormalization, in which the infinities are rolled up into the electron’s observed mass and charge, and are thereafter conveniently ignored. Richard Feynman, who shared the 1965 Nobel Prize with Julian Schwinger and Sin-Itiro Tomonaga for this breakthrough, referred to this sleight of hand as “brushing infinity under the rug.”
    http://www.americanscientist.o.....g-infinity

    In the following video, Richard Feynman rightly expresses his unease with “brushing infinity under the rug.” in Quantum-Electrodynamics:

    “It always bothers me that in spite of all this local business, what goes on in a tiny, no matter how tiny, region of space, and no matter how tiny a region of time, according to laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out. Now how can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one stinky tiny bit of space-time is going to do?”
    – Richard Feynman – one of the founding fathers of QED (Quantum Electrodynamics)
    Quote taken from the 6:45 minute mark of the following video:
    Feynman: Mathematicians versus Physicists – video
    https://www.youtube.com/watch?v=obCjODeoLVw

    I don’t know about Richard Feynman, but as for myself, being a Christian Theist, I find it rather comforting to know that it takes an ‘infinite amount of logic to figure out what one stinky tiny bit of space-time is going to do’:

    “Why should it take an infinite amount of logic to figure out what one stinky tiny bit of space-time is going to do?”
    – Richard Feynman

    John1:1
    “In the beginning was the Word, and the Word was with God, and the Word was God.”

    of note: ‘the Word’ in John1:1 is translated from ‘Logos’ in Greek. Logos is also the root word from which we derive our modern word logic
    http://etymonline.com/?term=logic

    The reason why I find it rather comforting is because of John 1:1, which says “In the beginning was the Word, and the Word was with God, and the Word was God.” ‘The Word’ in John 1:1 is translated from ‘Logos’ in Greek. Logos also happens to be the root word from which we derive our modern word logic.

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