3 ms·

Turing conpleteness is not associated with crativity or intelligence in any ateaightforward manner. One cannot unconditionally imply the other.

by gmueckl 7mo ago

marcus_holmes 7mo ago
after all, CSS is Turing Complete ;) https://stackoverflow.com/questions/2497146/is-css-turing-complete https://stackoverflow.com/questions/2497146/is-css-turing-co...
vidarh 7mo ago
No, but unless you find evidence to suggest we exceed the Turing computable, Turing completeness is sufficient to show that such systems are not precluded from creativity or intelligence.
- thesz 7mo ago
  I believe that quantum oracles are more powerful than Turing oracles, because quantum oracles can be constructed, from what I understand, and Turing oracles need infinite tape. Our brains use quantum computation within each neuron [1]. [1] https://www.nature.com/articles/s41598-024-62539-5 https://www.nature.com/articles/s41598-024-62539-5
  - vidarh 7mo ago
    There's no evidence to suggest a quantum computer exceeds the Turing computable.
    - thesz 7mo ago
      The difference is quantum oracles can be constructed [1] and Turing oracle can't be [2]: "An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an entity unspecified by Turing "apart from saying that it cannot be a machine" (Turing (1939)." [1] https://arxiv.org/abs/2303.14959 [2] https://en.wikipedia.org/wiki/Turing_machine
      - vidarh 7mo ago
        This is meaningless. A Turing machine is defined in terms of state transitions. Between those state transitions, there is a pause in computation at any point where the operations takes time. Those pauses are just not part of the definition because they are irrelevant to the computational outcome. And given we have no evidence that quantum oracles exceeds the Turing computable, all the evidence we have suggests that they are Turing machines.
        thesz 7mo ago
        > This is meaningless. Turing machines grew from the constructive mathematics [1], where proofs are constructions of the objects or, in other words, algorithms to compute them. [1] https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)#Constructive_mathematics Saying that there is no difference between things that can be constructed (quantum oracles) and things that are given and cannot be constructed (Turing oracles - they are not even machines of any sort) is a direct refutation of the very base of the Turing machine theoretical base.
  - deleted 7mo ago
    [deleted]
- jibal 7mo ago
  That's an irrelevant strawman. It tells us nothing about how create such a system ... how to pluck it out of the infinity of TMs. It's like saying that bridges are necessarily built from atoms and adhere to the laws of physics--that's of no help to engineers trying to build a bridge. And there's also the other side of the GP's point--Turing completeness not necessary for creativity--not by a long shot. (In fact, humans are not Turing complete.)
  - vidarh 7mo ago
    No, twisting ot to be about how to create such a system is the strawman. > Turing completeness not necessary for creativity--not by a long shot. This is by far a more extreme claim than the others in this thread. A system that is not even Turing complete is extremely limited. It's near impossible to construct a system with the ability to loop and branch that isn't Turing complete, for example. >(In fact, humans are not Turing complete.) Humans are at least trivially Turing complete - to be Turing complete, all we need to be able to do is to read and write a tape or simulation of one, and use a lookup table with 6 entries (for the proven minimal (2,3) Turing machine) to choose which steps to follow. Maybe you mean to suggest we exceed it. There is no evidence we can.
    - thesz 7mo ago
      > A system that is not even Turing complete is extremely limited. Agda is not Turing-complete, yet it is very useful.
  - jibal 7mo ago
    P.S. everything in the response is wrong ... this person has no idea what it means to be Turing complete. > all we need to be able to do is to read and write a tape or simulation of one An infinite tape. And to be Turing complete we must "simulate" that tape--the tape head is not Turing complete, the whole UTM is. > A system that is not even Turing complete is extremely limited. PDAs are not "extremely limited", and we are more limited than PDAs because of our very finite nature.
    - 7mo ago

Turing conpleteness is not associated with crativity or intelligence in any ateaightforward manner. One cannot unconditionally imply the other.

by gmueckl 7mo ago

Turing conpleteness is not associated with crativity or intelligence in any ateaightforward manner. One cannot unconditionally imply the other.

marcus_holmes 7mo ago

after all, CSS is Turing Complete ;) https://stackoverflow.com/questions/2497146/is-css-turing-complete https://stackoverflow.com/questions/2497146/is-css-turing-co...

vidarh 7mo ago

No, but unless you find evidence to suggest we exceed the Turing computable, Turing completeness is sufficient to show that such systems are not precluded from creativity or intelligence.

thesz 7mo ago
I believe that quantum oracles are more powerful than Turing oracles, because quantum oracles can be constructed, from what I understand, and Turing oracles need infinite tape. Our brains use quantum computation within each neuron [1]. [1] https://www.nature.com/articles/s41598-024-62539-5 https://www.nature.com/articles/s41598-024-62539-5
- vidarh 7mo ago
  There's no evidence to suggest a quantum computer exceeds the Turing computable.
  - thesz 7mo ago
    The difference is quantum oracles can be constructed [1] and Turing oracle can't be [2]: "An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an entity unspecified by Turing "apart from saying that it cannot be a machine" (Turing (1939)." [1] https://arxiv.org/abs/2303.14959 [2] https://en.wikipedia.org/wiki/Turing_machine
    - vidarh 7mo ago
      This is meaningless. A Turing machine is defined in terms of state transitions. Between those state transitions, there is a pause in computation at any point where the operations takes time. Those pauses are just not part of the definition because they are irrelevant to the computational outcome. And given we have no evidence that quantum oracles exceeds the Turing computable, all the evidence we have suggests that they are Turing machines.
      - thesz 7mo ago
        > This is meaningless. Turing machines grew from the constructive mathematics [1], where proofs are constructions of the objects or, in other words, algorithms to compute them. [1] https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)#Constructive_mathematics Saying that there is no difference between things that can be constructed (quantum oracles) and things that are given and cannot be constructed (Turing oracles - they are not even machines of any sort) is a direct refutation of the very base of the Turing machine theoretical base.
- deleted 7mo ago
  [deleted]
jibal 7mo ago
That's an irrelevant strawman. It tells us nothing about how create such a system ... how to pluck it out of the infinity of TMs. It's like saying that bridges are necessarily built from atoms and adhere to the laws of physics--that's of no help to engineers trying to build a bridge. And there's also the other side of the GP's point--Turing completeness not necessary for creativity--not by a long shot. (In fact, humans are not Turing complete.)
- vidarh 7mo ago
  No, twisting ot to be about how to create such a system is the strawman. > Turing completeness not necessary for creativity--not by a long shot. This is by far a more extreme claim than the others in this thread. A system that is not even Turing complete is extremely limited. It's near impossible to construct a system with the ability to loop and branch that isn't Turing complete, for example. >(In fact, humans are not Turing complete.) Humans are at least trivially Turing complete - to be Turing complete, all we need to be able to do is to read and write a tape or simulation of one, and use a lookup table with 6 entries (for the proven minimal (2,3) Turing machine) to choose which steps to follow. Maybe you mean to suggest we exceed it. There is no evidence we can.
  - thesz 7mo ago
    > A system that is not even Turing complete is extremely limited. Agda is not Turing-complete, yet it is very useful.
- jibal 7mo ago
  P.S. everything in the response is wrong ... this person has no idea what it means to be Turing complete. > all we need to be able to do is to read and write a tape or simulation of one An infinite tape. And to be Turing complete we must "simulate" that tape--the tape head is not Turing complete, the whole UTM is. > A system that is not even Turing complete is extremely limited. PDAs are not "extremely limited", and we are more limited than PDAs because of our very finite nature.
  - 7mo ago