Let\'s consider two spherical chickens by Tommaso Bolognesi

Dear Akinbo Ojo,

I introduced the character of Prof Priss for two reasons: (i) to provide a third example of the effectiveness and reliability of mathematical laws in describing the physical world (after the examples from acoustics and knot theory), and (ii) as an opportunity to briefly discuss Tegmark's conjectures on the mathematical universe and to speculate on their possible future developments, as embodied in the Priss-Goedel-Priss theorem.

I understand that Tegmark's conjecture does not address the continuous vs. discrete issue (which, by the way, was the subject of the 2011 Essay Contest), and is open to both. His mathematical structures may be continuous or discrete, or, I believe, even include both continuous and discrete pieces; and all these structures are 'real'. Because the discrete/continuous discussion is not central in the Mathematical Universe, Priss does not take a position about this issue. Rather, he focuses on an aspect - the Self-Aware Subsystems - that I find intriguing in Tegmark's work, and makes it the subject of his theorem.

In conclusion, I don't know how Priss would answer your three interesting questions. My personal take on them is, in brief:

1. I regard infinity and infinite divisibility as logical constructions of the mind, not corresponding to physical reality, which is finite in all respects. 'Atoms of spacetime' are sufficient for building a very rich universe.

2. If these atoms are all there is, you do not need separating walls: they are separate by definition, like the integer numbers: what is there between 2 and 3?

3. Does the bottom mathematical structure, or algorithm, exist eternally? Under the computational universe conjecture, space and time emerge as the computation unfolds, so in a way there is no time before the computation starts, and the question would be meaningless. Whether mathematical structures exist 'before' the birth of the universe, or 'out' of time... I confess that I find these questions too difficult, or unattractive, or both.

Ciao

Tommaso

Dear Joe Fisher,

thank you for pointing out the typos. Actually, I did write "could't" with a missing "n" - but I don't see errors in "lethal".

Regards

Tommaso

Dear Sophia,

thanks for your support. It balances the painful '1' that I got as 4th (and last) score from a community member - a score I would not even assign to an essay written by a spherical chicken. Anyway, the algorithmic universe conjecture is indeed looked at with much skepticism by most FQXi citizens (not all, fortunately!). But the essay also includes some light discussion on a possible, long term, positive development of the Mathematical Universe Conjecture, in the form of a theorem that was not meant to be totally bizarre. I plan to be still around in 2031 to check out the details of its proof...

Regards

Tommaso

Hi,

a few people, including Konrad Zuse, Ed Fredkin, Stephen Wolfram, Seth Lloyd, Hector Zenil (the last three are FQXi members) have proposed convincing arguments in support of the idea that the peculiar mix of order and chaos that we observe in the physical universe might be understood as the manifestation of the emergent properties of a computation. Interesting nature-like phenomena can be observed in the spontaneous computations of simple programs, including periodicity, self-similarity, pseudo-randomness, emergent 'particles', self-reproduction.

Of course something that "is" cannot be the unfolding of a computation; but people disagree on attributing the same existential status ("is") to the past and the (unknown) future of the universe. What may be valid for a rather unstructured, infinite spacetime, may not be valid for one pullulating of evolving biospheres...

Regards

Tommaso

Dear George,

if the Priss-Goedel-Priss theorem is right, then the mathematical structure that corresponds to the physical universe is made up of sets and functions (as in Tegmark's MUH), and the latter are total and computable, hence they can be implemented by Turing machines (conputable) that are guaranteed to terminate on each output (total). Now, I am not completely sure about what you mean when you write "do you worry about the halting problem?". I see two possible interpretations of your words.

1. You allude, perhaps humorously, to our own existence, or life span, which, according to this view, should also terminate, without hope for some eternal existence. If this is what you intended, I just observe that there is of course no direct connection between the guaranteed termination of the computations of those defining functions and the presumed termination of our lives. The implied gap is indeed as large and obscure as the gap that separates the static universal mathematical structure envisaged by the MUH and the accidents of the history of the universe that have led to, say, the evolutionary biosphere. This is, in my opinion, one of the weak points of the MUH.

2. Alternatively, you might have intended that the 'existence' of undecidable problems/functions is undeniable (e.g. the halting problem), and it would be unwise to 'rule out' them from our 'real' universe. Well, Priss would question the above terms 'existence' and 'real': he thinks that these functions do not 'exist' in the 'real' universe - the one where SAS arise - and do not contribute to its definition.

In any case, the boss of the agency clarifies, later in the story, that a model of computation that is Turing-universal must include partial computable functions, that are undefined/divergent for some input. Priss's universe, then, would not be based on Turing-universality, which is probably one of the reasons why the agency boss disagrees with him...

Thanks for your comments. Ciao!

Tommaso

PS

I'll read your essay a second time before commenting.

Lorraine,

who wrote the code? This is a question that I carefully avoid :-} But I am in good company with many people who refuse to answer the similar question 'Who wrote wrote the Einstein equations, or the Schroedinger equation'. ('Einstein and Shroedinger'? Sure, but that is not the point.) The question you pose is of course about who decided that the physical universe should obey those laws. Many people do not feel too frustrated for not being able to answer this question, about the origin of laws expressed in continuous mathematics, but feel just happy when they discover those laws. Switching to another form of math, algorithms and maybe discrete math, should not change that attitude...

Regards

Tommaso