An Undecidable Universe by Paul Davies

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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?

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

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

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 selected, and what provides physical existentialism to that. Also, mathematics is arbitrary to the extent that it depends on axiomatic system selected, and there cannot be any limit to what can be selected. So, even the discovery of mathematical relations (theorems) are contingent on the arbitrariness of axioms. A totally different viewpoint is required now; one such possibility of creation is discussed in the essay, Mother of all Existence, that shows even pure lawlessness or random exchanges between null reality and existence can create a physical universe or function like the known universe.

> In addition, the (ultimate, fundamental) laws are taken to be infinitely precise mathematical relationships.

One of the reasons that infinite precision is opted is because changes do occur upon interaction with definite results, and if interactions are non- deterministic, then how does a definite consequence arise? Moreover, entirely deterministic function with finite quantized states can only be cyclic over eternity, and continuum like infinity is indeterminate as discussed in the essay. Moreover, a deterministic universe (function) cannot come into and go out of existence, that would require an arbitrary jump, and the function cannot switch from one set of laws to another as may be required even in case of a priori Platonic existence (though I am not sure of the term Platonic). A limited indeterminism is the only path of rescue for creation, and it is possible to argue that limited indeterminism may arise when underlying reality is a continuum, but the permissible observable transitions are in quanta.

Rajiv

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