4 ms·

'Next-Level' Chaos Traces the True Limit of Predictability

83 points by pseudolus 2y ago

deleted 2y ago
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fuck_google 2y ago
[dead]
jonahbenton 2y ago
Wild to me that pieces like this ignore Wolfram and specifically his computational irreducibility. Much more precise rendition of the equivalent but less robust concept undecidability. The key insight he arrives at is that predicting/modeling a system is itself a computational process and the ability of a modeler to make computationally less expensive predictions is dependent both on their own computational capability and the nature of the computation. It is very neat and precise and systematic. "Next level" chaos is just more poor imprecise metaphor.
- ironSkillet 2y ago
  This is a popular science article, not a scientific paper.
- drdeca 2y ago
  Does he have any theorems about this?
- UltraSane 2y ago
  Has he published any peer reviewed papers on it?
  - markisus 2y ago
    Here is his 1984 article published in PRL in which he highlights that cellular automata can be realized as physical systems and therefore computational intractabilities will manifest in models of physics. https://content.wolfram.com/sw-publications/2020/07/undecidability-intractability-theoretical-physics.pdf https://content.wolfram.com/sw-publications/2020/07/undecida...
    - brookst 2y ago
      Honest question: isn’t that the same thing as saying that computers use phyisical processes, so all programs are physical processes, so all concepts of intractability in programming also apply to physics? It’s all just electrons, right?
      - criddell 2y ago
        If you're going to be reductive, you might as well go all the way and say it's all just fluctuations and perturbations of quantum fields, right?
        weard_beard 2y ago
        You lost me at, "What exactly is a phase change? Why can't we predict all possible states of matter and why do we keep discovering new ones? Can high energy particles form bonds with themselves or each other? Could you build a nucleus of neutrinos surrounded by a photon cloud to construct macro scale matter? Why isn't there a periodic table of high energy particles that we've discovered thus far with clear categories of properties and principles (even if incomplete or contradictory) that we teach in schools to challenge our students?
    - UltraSane 2y ago
      That isn't his physics project.
- nathan_compton 2y ago
  Arguably it is Wolfram who has ignored the state of knowledge, which is not to entirely disparage his ideas.
andrewflnr 2y ago
> In a paper published in Nature in 2015, they proved that the spectral gap problem is equivalent to the halting problem (opens a new tab) — and therefore undecidable. If someone handed you some complete description of the material’s particles, it would either have a gap or not. Hold up. This is experimentally findable, right? Did they just invent a physical halting oracle? ...Hmm. The paper[0] is paywalled, but the abstract mentions aperiodic tilings. This might be a situation where the undecidability only holds if the material is actually infinite, in which case its significance is little more dubious. Still cool, but not practical-halting-oracle cool. [0] https://www.nature.com/articles/nature16059 https://www.nature.com/articles/nature16059
- Legend2440 2y ago
  It's not an oracle. 'equivalent to the halting problem' just means 'your system is a turing machine'. >Even if someone attempted to build one of the machines depicted in these blueprints, however, researchers point out that undecidability is a feature of physical theories and cannot literally exist in real experiments. Only idealized systems that involve infinity — an infinitely long tape, an infinitely extensive grid of particles, an infinitely divisible space for placing pinballs and rubber ducks — can be truly undecidable.
  - andrewflnr 2y ago
    It's a property that can be measured in finite (constant?) time, that's determined by a halting-complete problem. Unless I drastically misunderstood, and except for the whole finite-size thing.
    - rstuart4133 2y ago
      I didn't understand the think completely (I suspect you would have to read the page) but they do mention a Turing machine with an infinite tape several times, then they say they used the quantum states of a finite sized system to emulate that tape. That makes sense. You can always in principle determine if a finite system halts (although resource constraints mean you may not be able to do so in practice). So their system must be able to contain an infinite amount of information despite being finite in size. But that does mean they are assuming an infinity lurks within every qubit. I didn't realise we understood quantum so well we can confidently make that assumption.
cgio 2y ago
> Cubitt put undecidability on a collision course with large quantum systems in 2012. Nominative determinism…
- jayhoon 2y ago
  https://www.dr-qubit.org/qubit.html https://www.dr-qubit.org/qubit.html Toby Cubitt's website
- brookst 2y ago
  I prefer “aptronym” but yeah.
deleted 2y ago
[deleted]

83 points by pseudolus 2y ago

deleted 2y ago

[deleted]

fuck_google 2y ago

[dead]

jonahbenton 2y ago

Wild to me that pieces like this ignore Wolfram and specifically his computational irreducibility. Much more precise rendition of the equivalent but less robust concept undecidability. The key insight he arrives at is that predicting/modeling a system is itself a computational process and the ability of a modeler to make computationally less expensive predictions is dependent both on their own computational capability and the nature of the computation. It is very neat and precise and systematic. "Next level" chaos is just more poor imprecise metaphor.

ironSkillet 2y ago
This is a popular science article, not a scientific paper.
drdeca 2y ago
Does he have any theorems about this?
UltraSane 2y ago
Has he published any peer reviewed papers on it?
- markisus 2y ago
  Here is his 1984 article published in PRL in which he highlights that cellular automata can be realized as physical systems and therefore computational intractabilities will manifest in models of physics. https://content.wolfram.com/sw-publications/2020/07/undecidability-intractability-theoretical-physics.pdf https://content.wolfram.com/sw-publications/2020/07/undecida...
  - brookst 2y ago
    Honest question: isn’t that the same thing as saying that computers use phyisical processes, so all programs are physical processes, so all concepts of intractability in programming also apply to physics? It’s all just electrons, right?
    - criddell 2y ago
      If you're going to be reductive, you might as well go all the way and say it's all just fluctuations and perturbations of quantum fields, right?
      - weard_beard 2y ago
        You lost me at, "What exactly is a phase change? Why can't we predict all possible states of matter and why do we keep discovering new ones? Can high energy particles form bonds with themselves or each other? Could you build a nucleus of neutrinos surrounded by a photon cloud to construct macro scale matter? Why isn't there a periodic table of high energy particles that we've discovered thus far with clear categories of properties and principles (even if incomplete or contradictory) that we teach in schools to challenge our students?
  - UltraSane 2y ago
    That isn't his physics project.
nathan_compton 2y ago
Arguably it is Wolfram who has ignored the state of knowledge, which is not to entirely disparage his ideas.

andrewflnr 2y ago

> In a paper published in Nature in 2015, they proved that the spectral gap problem is equivalent to the halting problem (opens a new tab) — and therefore undecidable. If someone handed you some complete description of the material’s particles, it would either have a gap or not. Hold up. This is experimentally findable, right? Did they just invent a physical halting oracle? ...Hmm. The paper[0] is paywalled, but the abstract mentions aperiodic tilings. This might be a situation where the undecidability only holds if the material is actually infinite, in which case its significance is little more dubious. Still cool, but not practical-halting-oracle cool. [0] https://www.nature.com/articles/nature16059 https://www.nature.com/articles/nature16059

Legend2440 2y ago
It's not an oracle. 'equivalent to the halting problem' just means 'your system is a turing machine'. >Even if someone attempted to build one of the machines depicted in these blueprints, however, researchers point out that undecidability is a feature of physical theories and cannot literally exist in real experiments. Only idealized systems that involve infinity — an infinitely long tape, an infinitely extensive grid of particles, an infinitely divisible space for placing pinballs and rubber ducks — can be truly undecidable.
- andrewflnr 2y ago
  It's a property that can be measured in finite (constant?) time, that's determined by a halting-complete problem. Unless I drastically misunderstood, and except for the whole finite-size thing.
  - rstuart4133 2y ago
    I didn't understand the think completely (I suspect you would have to read the page) but they do mention a Turing machine with an infinite tape several times, then they say they used the quantum states of a finite sized system to emulate that tape. That makes sense. You can always in principle determine if a finite system halts (although resource constraints mean you may not be able to do so in practice). So their system must be able to contain an infinite amount of information despite being finite in size. But that does mean they are assuming an infinity lurks within every qubit. I didn't realise we understood quantum so well we can confidently make that assumption.

cgio 2y ago

> Cubitt put undecidability on a collision course with large quantum systems in 2012. Nominative determinism…

jayhoon 2y ago
https://www.dr-qubit.org/qubit.html https://www.dr-qubit.org/qubit.html Toby Cubitt's website
brookst 2y ago
I prefer “aptronym” but yeah.

deleted 2y ago

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