I have been interested in Seth Lloyd's cosmological model (which proposes that the universe is a some kind of quantum computer or at least similar to it: https://en.wikipedia.org/wiki/Programming_the_Universe, https://arxiv.org/abs/quant-ph/0501135) since long ago.

I was wondering if this model could be completely compatible with Tegmark's Mathematical Universe Hypothesis, in the sense that Lloyd's model would propose all the universes proposed by Tegmark

I have found some evidence that suggest that this is the case:

I found a short review that Lloyd made about Tegmark's book "Our Mathematical Universe":

"In Our Mathematical Universe, renowned cosmologist Max Tegmark takes us on a whirlwind tour of the universe, past, present—and other. With lucid language and clear examples, Tegmark provides us with the master measure of not only of our cosmos, but of all possible universes. The universe may be lonely, but it is not alone."

Besides, Lloyd's model does not only propose the existence of computable universes, as it is indicated here: https://arxiv.org/pdf/1312.4456.pdf. (In that article it is suggested that he agrees that uncomputability exists in physics.)

So, could Lloyd's cosmological model be able to "produce" all universes (hence all mathematical structures) proposed by Tegmark? Is LLoyd's model only compatible with our set of laws? Or is it compatible with any set of laws (any set of mathematics)?

PS: I am not asking whether Tegmark allows other types of mathematics to exist, but we have to be careful and distinguish between his two main hypotheses:

The Computational Universe Hypothesis (where he proposes the existence of only computable and finite structures) and the Mathematical Universe Hypothesis (where he proposes the existence of all mathematical structures computable or not).

He first proposed his Mathematical Universe Hypothesis. The Computable Universe Hypothesis was built later to avoid some problems that his original idea had with Gödel's incompleteness theorems. But Tegmark did not rule out his original hypothesis and he still considers it.

When my question asked about the difference between Lloyd's and Tegmark's models, I was thinking about the Mathematical Universe Hypothesis and not only about the Computable Universe Hypothesis (it is quite obvious that Lloyd's model could produce all universes present in the Computable Universe Hypothesis, but this is not so clear for the Mathematical Universe Hypothesis)


  • Hi, welcome to Philosophy SE. Tegmark seems to suggest that his mathematical universes are finitist, in which case they can be "implemented" on any Turing machine, not even a quantum computer, see Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics? But that is not saying much, and nothing specifically about Lloyd, who wants universe to be "uncomputable".
    – Conifold
    Jul 12, 2019 at 17:41
  • @Conifold A quick glance at the above Wiki link shows that Lloyd believes the world to be simulable by a quantum computer. That would make it computable. As I understand it, quantum computers can not compute anything a classical Turing machine can't. All they can do is compute certain problems more efficiency. But the class of computable functions is the same for quantum and classical computers.
    – user4894
    Jul 12, 2019 at 19:24
  • "I will show that answers to some of the most basic questions concerning physical law are in fact uncomputable" says Lloyd. Since Tegmark's finitist laws come from Godel complete structures, they are computable. But this is irrelevant to your question. If computers can simulate Lloyd's uncomputable math they can certainly simulate Tegmark's.
    – Conifold
    Jul 12, 2019 at 19:45
  • @Conifold Thank you for your comment. I think that Lloyd proposes some kind of (quantum) computer capable of producing uncomputable features. For example, In Digital Physics wikipedia page (en.wikipedia.org/wiki/Digital_physics), it is indicated that Lloyd's model could not only produce a discrete but analogue/continuous ontology.
    – Maribel
    Jul 12, 2019 at 21:36
  • @Conifold As for Tegmark, it is right that he proposes the existence of finite and computable mathematical structures, but this is one of his two main hypothesis. The other hypothesis, which was published before his Computational Universe Hypothesis, proposed the existence of all mathematical structures (computable or not; finite or infinite). This is known as the Mathematical Universe Hypothesis. In my question, I was rather referring to this particular hypothesis.
    – Maribel
    Jul 12, 2019 at 21:36


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