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Undecidability, Uncomputability, and Unpredictability Essay Contest
December 24, 2019 - April 24, 2020
Contest Partners: Fetzer Franklin Fund, and The Peter and Patricia Gruber Foundation
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What Is “Fundamental”
October 28, 2017 to January 22, 2018
Sponsored by the Fetzer Franklin Fund and The Peter & Patricia Gruber Foundation
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Wandering Towards a Goal
How can mindless mathematical laws give rise to aims and intention?
December 2, 2016 to March 3, 2017
Contest Partner: The Peter and Patricia Gruber Fund.
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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation
Media Partner: Scientific American

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How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American
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It From Bit or Bit From It
March 25 - June 28, 2013
Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American
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Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
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Is Reality Digital or Analog?
November 2010 - February 2011
Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American
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What's Ultimately Possible in Physics?
May - October 2009
Contest Partners: Astrid and Bruce McWilliams
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The Nature of Time
August - December 2008
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RECENT POSTS IN THIS TOPIC

Neil Bates: on 5/19/20 at 1:11am UTC, wrote Dear Dr. Davies, Your essay addresses the question establishing this...

Rajiv Singh: on 5/18/20 at 11:42am UTC, wrote Dear Paul Davies, > ... which is to say that the originating event, or...

Peter Jackson: on 5/18/20 at 8:33am UTC, wrote Paul, Nice essay. I do like your fundamental thinking, as you may see from...

Vladimir Fedorov: on 5/18/20 at 7:08am UTC, wrote Dear Paul, I greatly appreciated your work and discussion. I am very glad...

John Schultz: on 5/17/20 at 21:56pm UTC, wrote Dear Professor Davies It seems to me that you have accidentally made a...

gerry : on 5/17/20 at 21:18pm UTC, wrote last attempt to send image

Gerry: on 5/17/20 at 21:07pm UTC, wrote I hope the attached image is visible.

Gerry Klein: on 5/17/20 at 21:05pm UTC, wrote Hello Paul, What size T-shirt do you wear? The formula that represents...


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FQXi FORUM
September 19, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: An Undecidable Universe by Paul Davies [refresh]
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Author Paul Davies wrote on Apr. 24, 2020 @ 13:36 GMT
Essay Abstract

The status of the laws of physics is one of the great foundational questions of science. Many theoretical physicists working on fundamental problems tacitly assume that the laws are infinitely precise, immutable, universal and eternal mathematical relationships, occupying the ontological basement of reality. In cosmology, transcendent laws are often invoked to explain the origin of the universe from nothing as a lawlike physical process. There is, however, a contrarian concept, deriving from the field of computation, and exemplified by Rolf Landauer’s hypothesis that as idealized mathematical relationships cannot be implemented in the real universe they should not be invoked as fundamental laws; real computations always involve imprecision and uncertainty. Even on a cosmic scale the observable universe will have a finite computational capacity. John Wheeler famously championed the notion that the laws of physics are ultimately mutable and imprecise. These considerations of Landauer and Wheeler suggest a new source of unknowability in the universe deriving from limitations on computational power, and invite a reformulation of the halting problem of the theory of computation.

Author Bio

Paul Davies is Regents’ Professor of Physics at Arizona State University and Director of the Beyond Center for Fundamental Concepts in Science. His research spans the origin of the universe, the origin of life, quantum gravity, SETI and cancer evolution. He is the author of 32 books and many research papers. Davies holds three honorary doctorates and Fellowship of University College London. He was awarded the Templeton Prize, the Royal Society’s Faraday Prize and The Kelvin Medal of the UK Institute of Physics. He is a Member of the Order of Australia and has an asteroid named after him.

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David Brown wrote on Apr. 24, 2020 @ 14:34 GMT
"... the laws of physics determine what can be computed ..." (page 3).

The Koide formula uses square-root(mass) in a formula involving the masses of electron, muon, and tauon.

Koide formula, Wikipedia

Is there some plausible way of introducing some concept of Koide uncertainty that uses square-root(mass) and justifies the Koide formula in terms of new physics?

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Jenny Wagner wrote on Apr. 24, 2020 @ 16:43 GMT
Professor Davies,

thanks a lot for this highly interesting and informative essay!

When you write in your last sentence that the fate of the universe is undecidable, is it necessary to base all considerations on a potentially occurring big bang? Would it make sense to start at our current state today? That may result in the same statement about the undecidable future (which seems utterly reasonable, at least to me), if we find an appropriate definition of relative computational uncertainty w.r.t. an arbitrary state and not necessarily to the big bang. Starting at our current state, could we then make statements whether we the existence of the big bang is decidable or not?

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Lachlan Cresswell wrote on Apr. 25, 2020 @ 05:25 GMT
Dear Professor Davies,

A most interesting and challenging essay!

Early on you state: “What manner of entity are the laws of physics? Where do they come from? What is their ontological status? Physicists divide into two camps. One camp regards the laws as convenient formalizations that humans have invented to organize observational and experimental data. The other camp regards...

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Irek Defee wrote on Apr. 25, 2020 @ 09:09 GMT
Dear Prof. Davies,

Your arguments for tying the fate of the Universe with undecidability and theory of computation are very interesting. The remaining issue is how come all this is as it is and where it came from. In my essay I sketch arguments that the origin of the Universe is buried in the uncomputability with special TOE which kind of complements your thoughts on the fate:

https://fqxi.org/community/forum/topic/3508

Best regards,

Irek

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Chidi Idika wrote on Apr. 25, 2020 @ 12:59 GMT
Professor Davies,

I enjoyed reading your lucid essay. I have just two questions, sir.

(1) You spoke of Lloyd’s limit as an upper bound for bit/entropy. But it seems to me that Landauer’s limit actually is a lower bound and possibly an alternative way to phrase Lloyd’s limit. Am I wrong on this?

One implication would be that in electromagnetism, for instance, we think of speed of light as the upper limiting speed of physical information. Yet there is, I think, the credible possibility that this too can be rephrased as some lower bound — perhaps some Majorana qubit or mass gap. It is conceivable then that, this way, general relativity in principle agrees more with Landauer’s limit (and with quantum mechanics).

Yet we can combine the two limits so that we have as our model actually a holographic event horizon (say, a beat frequency or harmonic oscillator or wave function). This simply is the way I think of a “mind” — as a unique holographic event horizon.

It would be akin to remodelling the un-decidable rather as the natural unit system of physical information.

(2) Now, what possibility does this hold, in your opinion, for a practical definition life itself?

Namely, is not life mathematically speaking the number basis (imaginary unit) and physically speaking the quantum vacuum (holographic event horizon)?

Implied would be that coupled, with its amplitudes or interference pattern or so-called Hawking radiation, every mind is actually a unique arrow of time (Einstein’s space-time manifold or light cone).

It seems to me that such a model will agree entirely with Everett’s many-worlds interpretation.

What you have termed the un-decidability of the universe might just be, put conversely, the free will.

I crave your invaluable judgement on these two questions, sir.

Chidi Idika (forum topic: 3531)

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Michael James Kewming replied on Apr. 25, 2020 @ 20:41 GMT
(1) no, Landauer’s principle is only a limit on dissipative computation.

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Chidi Idika replied on Apr. 28, 2020 @ 17:38 GMT
In my opinion the black-body cavity of Planck's quantum theory is actually a bridge between dissipative and non-dissipative systems. Otherwise why speak of its radiation spectrum?

That is, the energy you require to build up bits of information into a complex system only go in as the binding energy. Same energy is what you account for as the ionization energy of which the Landauer limit perhaps constitutes the threshold.

The point thus is that overall one has a standing wave or so-called black-body cavity; and which may in turn model the self-referencing state of Godel's theorem.

Or isn't it?

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Charles John Sven wrote on Apr. 25, 2020 @ 18:17 GMT
Greetings Professor Paul Davies:

Without a clear picture of creation then perhaps your last statement is prescient.

“…one arrives at a startling eschatological conclusion: not only is the fate of the universe undecided, it is actually undecidable.”

Consider a picture of creation based on common 3D physics without resorting to mathematical assumptions as a Richard Feynman study as presented in my essay– Common 3D Physics Depicts Universe Emerging From Chaos.

Regards

Charles Sven

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John David Crowell wrote on Apr. 25, 2020 @ 19:18 GMT
Dear Paul. I enjoyed your essay. I thought you described the pathway of how physics and cosmology arrived at where they are today very well. I believe your summary statement: “... not only is the fate of the universe undecided, it is actually undecidable” is logical based on the current fundamental/foundational “beliefs” in science, philosophy and mathematics that went into the...

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Harrison Crecraft wrote on Apr. 25, 2020 @ 20:29 GMT
Dear Dr. Davies,

I enjoyed your clear and succinct essay. You state that physicists divide into two camps. One camp regards laws as convenient formalizations that humans have invented to organize observational and experimental data. The other camp regards the laws as ‘fundamental.’ You then continue that fundamental laws “are an idealization that cannot even in principle be tested....

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Baruch Garcia wrote on Apr. 30, 2020 @ 18:37 GMT
Great essay! I agree with your thesis of the undecidability of physics. However, I believe we are missing one crucial ingredient - quantum mechanics.

Wheeler's "It from Bit" and "mutability" is often understood, as you say, "vague deliberations" however, in his unpublished notebooks, he was looking for a connection between undecidability and quantum mechanics in a much more lucid way. Both undecidability and QM set epistemological limits on what we can know. His "higgledy-piggledy" world is built on quantum mechanics, on what he calls "elementary acts of observation."

So we have a triangle between math, philosophy, and physics. Math: Undecidability, Philosophy: Epistemological limits, Physics: Quantum mechanics.

While discussing the philosophy of physics is essential, we don't want to miss out on the physics which actually proves this point. My essay, "Undecidability as a framework for Quantum Theory and Spacetime" posted on this forum, describes Wheeler's vision on the physics side if you wish to read more. The last section agrees with your essay, so the two go together nicely.

In short: Excellent essay, I agree 100%, but don't forget about the quantum-undecidability connection!!

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Alyssa Adams wrote on Apr. 30, 2020 @ 22:42 GMT
Hi Paul!

Great essay! I wonder if there's some space in-between these two camps of thought. For biology, it seems that objects like proteins change what they can possibly interact with depending on their sequence and how they've folded. Viruses are only able to propagate their genetic information if a "successful" genetic mutation is able to reproduce in a host. Failed mutations lead to malformed viruses, which are unable to propagate and continue in the evolutionary state space.

With examples like these, do you think some "laws" are intrinsic to the physical configuration of a system? Should these laws be thought more of a map that guides a system through a particular state space, or a causal landscape between possible states? And if so, would you think that our idea of physical laws is more a way to represent successive state transitions in a way that is compressible to a few symbols? Also if so, then how can we make predictions about some transition from any arbitrary state to another arbitrary state? I'd be curious to know what you think! I talk about these ideas in my essay as well, so I'd also be very curious to know what you think of those too!

Cheers!

Alyssa

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Vladimir Rogozhin wrote on May. 1, 2020 @ 18:33 GMT
Dear Paul,

You have raised in your extremely important essay many questions and problems that truly confirm that fundamental science is in a deep crisis of understanding.

Understanding is the event of “grasping the structure” (G. Gutner “Ontology of mathematical discourse”). "Grasp" of what structure? The original, ontological - that structure, which is the basis of knowledge...

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Rodney Bartlett wrote on May. 3, 2020 @ 06:28 GMT
Dear Prof. Davies,

When I was browsing through this contest's entries and saw the name Paul Davies, I wondered if this could possibly be the well-known physicist. I decided it must be someone who just happens to have the same name. Then I clicked on your entry's title and read your bio. You ARE the famous physicist, after all.

Last year, I sent you an email for some reason (I simply can't remember what it was about). Anyway, you wished me the best. One example of my best is my entry in this contest, NON-COMPUTABILITY AND UNPREDICTABILITY ARE SO YESTERDAY: WITH COMPUTABLE AND PREDICTABLE COSMIC STRUCTURE, PLUS IMPLICATIONS FOR MATHEMATICS AND SCIENCE, new paradigm

Your "Undecidable Universe" seems to be the exact opposite of my COMPUTABLE AND PREDICTABLE COSMIC STRUCTURE. Your entry appears to be an excellent example of compatibility with the present interpretation of science's data while my entry seems to be compatible with a new paradigm … a fresh way of understanding that data. If I may borrow from the inside-front-cover of your 1991 book "the matter myth" (cowritten with astrophysicist John Gribbin), this new paradigm can be stated as

"(Future) developments at the frontiers of science are challenging our views about ourselves and the nature of the cosmos as never before."

Nevertheless, I sincerely wish you the best. Whichever of our entries ends up closest to the science accepted in a thousand years, we both have the same purpose - to enjoy the pursuit of scientific truth.

Rodney (Bartlett)

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Jason W Steinmetz wrote on May. 3, 2020 @ 21:49 GMT
Your essay was informed, intelligent and interesting. Of course, I am familiar with your work so I expected nothing less. Even when I disagree with your fundamental assertions you make an intelligent argument what is worth considering.

What I found most interesting is that, as I read many different essays by many different authors, each one is trying to espouse some idea or concept that is in one way or another beyond what has been established. Whereas your essay is a informed survey of the fundamental ideas, concepts and questions that surround this difficult topic.

Thus, my only complaint would be that I would like to have seen a more robust rebuttal of Platonism. Of course, that just identifies me as one of those authors...

You wrote: "By combining these deep insights, one arrives at a startling eschatological conclusion: not only is the fate of the universe undecided, it is actually undecidable."

Death to Laplace's Demon!

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Member Daniel Sudarsky wrote on May. 12, 2020 @ 21:25 GMT
This is certainly a very interesting essay, however, I find myself a bit baffled by a certain recurring theme that I consider disturbing, and that is the implicit anthropocentricity of some of the ideas.

To exemplify my concern let us focus on a topic that appears prominently in the essay:

Gödel's lesson, regarding the undecidability of the truth values ...

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Gemma De las Cuevas wrote on May. 15, 2020 @ 08:24 GMT
Dear Prof. Davies,

Thank you for writing this essay. I wonder if you are familiar with the work "Machines, logic and quantum physics" by Deutsch, Ekert and Lupacchini, where they argue that it is the physical laws what determine what is computable. So I guess they would agree with the first part of your claim that "the laws of physics determine what can be computed, and computability determines what can be the laws", but not with the second one. I was wondering what your standpoint on that work was.

Thank you and best regards,

Gemma

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Member Rick Searle wrote on May. 16, 2020 @ 14:53 GMT
Dear Prof. Davies,

I have been enjoying your books since I was a teenager (which means for a very long time)and greatly enjoyed your essay here.

It made me wonder if physicist should heed the advice of Nicolas Gisin and abandon the infinities of the reals?

https://www.nature.com/articles/s41567-019-0748-5

Best of luck in the contest!

Rick Searle

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Gerry Klein wrote on May. 17, 2020 @ 21:05 GMT
Hello Paul,

What size T-shirt do you wear? The formula that represents the Universe, the only Universe you know where all is in motion and all is motion is the equation of motion. For more info please see my 4 contest entries especially the 2008 one.

V=S/T

Thanks, all the best,

Gerry

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Gerry wrote on May. 17, 2020 @ 21:07 GMT
I hope the attached image is visible.

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gerry wrote on May. 17, 2020 @ 21:18 GMT
last attempt to send image

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John S Schultz wrote on May. 17, 2020 @ 21:56 GMT
Dear Professor Davies

It seems to me that you have accidentally made a strawman of the Reals. Your arguments against infinite precision in measurement, seem quite solid, but they have nothing to do with continuity or uncountability or any property unique to the Reals. They would seem to pertain equally to the Algebraics and (yes) even the Rationals.

You quote Chaitin “All measurements and observations yield only rational numbers.” Okay…, but in the context of your paper would it perhaps be clearer to say “All measurements and observations yield only truncated rationals” or some other such wording? One cannot, of course, get an infinity of digits by measuring something, and if some theory has numbers with an infinity of digits, doesn’t it exhibit the identical “infinite precision” problem?

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Vladimir Nikolaevich Fedorov wrote on May. 18, 2020 @ 07:08 GMT
Dear Paul,

I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

"There is, however, a contrarian concept, deriving from the field of computation, and exemplified by Rolf Landauer’s hypothesis that as idealized mathematical relationships cannot be implemented in the real universe they should not be invoked as fundamental laws; real computations always involve imprecision and uncertainty. Even on a cosmic scale the observable universe will have a finite computational capacity. John Wheeler famously championed the notion that the laws of physics are ultimately mutable and imprecise. These considerations of Landauer and Wheeler suggest a new source of unknowability in the universe deriving from limitations on computational power, and invite a reformulation of the halting problem of the theory of computation".

While the discussion lasted, I wrote an article: “Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus”, due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 “Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability”.

I hope that my modest results of work will provide you with information for thought.

Warm Regards, `

Vladimir

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Peter Jackson wrote on May. 18, 2020 @ 08:33 GMT
Paul,

Nice essay. I do like your fundamental thinking, as you may see from mine, suggesting some better fundamental laws! They do indeed lead to a more coherent 'cyclic' cosmological model.

You may have seen Wolframs recent update to Lloyd at 10^116, but more importantly I find is the Elementary Length at 10^-93, consistent with a recent SUB-matter gravity paper of mine (cited in the essay). The link to Wolfram is arxiv.org/abs/2004.08210 (most interesting from p.360), but I hope you'll read & score my essay first. As ours are close, and to avoid yet more 1's, I hope you equally like mine to allow the gentlemanly approach!

Time now runs out so I'm very glad I got to yours.

Very best regards

Peter

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Rajiv K Singh wrote on May. 18, 2020 @ 11:42 GMT
Dear Paul Davies,

> ... which is to say that the originating event, or process, is treated as lawlike, and not as an unexplained initial condition.

I suppose the idea of "A lawlike origin" has been traversed by researchers in many different ways, particularly in the sense, what could create those laws. Even mathematical origin has run into problems, what mathematics must be...

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Neil Bates wrote on May. 19, 2020 @ 01:11 GMT
Dear Dr. Davies,

Your essay addresses the question establishing this contest more directly than almost all of the other essays (including mine), and it does so in very efficient and readable way. It is important to delve into the problem of to what level of precision we could know laws of physics, either with actual physical machines of calculation, or even with ideal mathematical constructs. For comparison, I recommend the essay by Ian Durham (https://fqxi.org/community/forum/topic/3555), which includes discussion of the issue of computation and numbers.

However, two observations: First, the laws of physics are mostly more about conceptual issues like conservation, symmetry, basic power laws etc, than precise numbers: altho those do come up in physical constants and some parameters of particles etc. Maybe there, the relevance of these issues is greater.

Also, I personally don't think the constraints of computation are necessarily a constraint on the universe itself, since we don't know "how it works." If a concept like Wolfram's constructivism from simple elements is valid, then it certainly matters to both how things happen, and how we can know it. Yet maybe the match would be even better than trying to perfectly model a continuous system.

Finally: you and others might find my essay interesting. I discuss the limitations on realistic models of "superluminal signalling" to explain the correlations of entanglement. I'll be frank: it could use more votes on this last day. Pardon inactive link.

https://fqxi.org/community/forum/topic/3548

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