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Plinz's profile
Joscha Bach
Joscha Bach
Joscha Bach
@Plinz

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Joscha Bach

@Plinz

FOLLOWS YOU. Artificial Intelligence, Cognitive Architectures, Computation. The goal is integrity, not conformity.

San Francisco, CA
bach.ai
Joined April 2009

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    1. Joscha Bach‏ @Plinz 22 Sep 2018
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      Gödel and Turing: we cannot use classical mathematics to build an interpreter that runs classical mathematics Church and Turing: we can use constructive mathematics to run constructive mathematics Minsky and Turing: we can use constructive mathematics to run classical mathematics

      8 replies 22 retweets 95 likes
    2. Venkatesh Rao‏ @vgr 22 Sep 2018
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      Replying to @Plinz

      This seems important and interesting but I think I need an essay length explanation. Is there one?

      1 reply 0 retweets 5 likes
    3. Joscha Bach‏ @Plinz 22 Sep 2018
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      Replying to @vgr

      no, I only just realized it, and I have ADHS so may not write the essay

      1 reply 0 retweets 7 likes
    4. Joscha Bach‏ @Plinz 22 Sep 2018
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      Replying to @Plinz @vgr

      basic train of thoughts: Gödel's incompleteness theorem (and Turing's subsequent adaptation to computational machinery) shows that mathematics itself is incomplete. that was a shock: mathematics is the domain of all formal languages, but mathematics cannot be generated using them

      2 replies 0 retweets 12 likes
    5. Joscha Bach‏ @Plinz 22 Sep 2018
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      Replying to @Plinz @vgr

      there is a small branch of mathematics that only accepts statements as true that have actually been constructed. constructive mathematics turns out to be identical to computation. Church and Turing demonstrated that computation contains itself, i.e. we can compute all computers

      3 replies 0 retweets 10 likes
    6. Joscha Bach‏ @Plinz 22 Sep 2018
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      Replying to @Plinz @vgr

      constructive mathematics is not time-less like classical math. a function that has not been computed yet does not have a defined value. pi is a function, not a number. the axiom of choice does not hold. true infinities and continua cannot be constructed

      3 replies 0 retweets 8 likes
    7. Joscha Bach‏ @Plinz 22 Sep 2018
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      Replying to @Plinz @vgr

      construction means that there has to be a machine that can perform the actual computations. in the strong, intuitionist form, we must actually run the proof, i.e. we need to compress it into a form that actually runs on our machine (which leads to a small foundational crack)

      3 replies 0 retweets 8 likes
    8. Joscha Bach‏ @Plinz 22 Sep 2018
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      Replying to @Plinz @vgr

      since we cannot know that our interface to the machine is entirely coherent, we may always have to bracket our theories into a residual probability that a bit flipped somewhere in the proof making machine or its verification machine or the interpretation of the verification, etc

      1 reply 0 retweets 5 likes
    9. Joscha Bach‏ @Plinz 22 Sep 2018
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      Replying to @Plinz @vgr

      the main claim of AI and cognitive science however is that the brain is a computer, and because all the mathematics we need to account for run on our brains, we can build something that can satisfy all desires a classical mathematician can hope to fulfill with a finite automaton

      2 replies 1 retweet 6 likes
      Joscha Bach‏ @Plinz 22 Sep 2018
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      Replying to @Plinz @vgr

      this is where Penrose disagrees: Penrose believes that the mind and by extension the universe are implemented in non constructive mathematics. (that should imply that he thinks that QM is the wrong foundation for physics, since it is a [slightly hyper]computational model)

      11:39 PM - 22 Sep 2018
      • 5 Likes
      • Tim H Venkatesh Rao AQ Cole Hudson зануда, душноват
      4 replies 0 retweets 5 likes
        1. New conversation
        2. Joscha Bach‏ @Plinz 22 Sep 2018
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          Replying to @Plinz @vgr

          there is good hope though; the program of constructive analysis in math seems to be successful, and there does not seem to be any obvious limit to the capacities of computer algebra systems

          1 reply 0 retweets 3 likes
        3. Joscha Bach‏ @Plinz 22 Sep 2018
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          so, basically, the solution is: while we cannot build math in math, and computation is much weaker than math, every bit of math that we will ever come across will have been built by computation

          3 replies 1 retweet 9 likes
        4. 17 more replies
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        2. Carlos E. Perez‏ @IntuitMachine 23 Sep 2018
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          Replying to @Plinz @vgr

          This is indeed curiously interesting. Are there formulations of QM that are based on constructive mathematics? In fact, how often do proofs in physics assume an excluded middle?

          1 reply 0 retweets 0 likes
        3. Joscha Bach‏ @Plinz 23 Sep 2018
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          Replying to @IntuitMachine @vgr

          t‘Hooft has written up some of his work on that (in his “cellular automaton interpretation of qm”)

          0 replies 0 retweets 0 likes
        4. End of conversation
        1. New conversation
        2. James Torre‏ @jpt401 22 Sep 2018
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          Replying to @Plinz @vgr

          In what way is quantum mechanics hypercomputational?

          1 reply 0 retweets 0 likes
        3. Joscha Bach‏ @Plinz 23 Sep 2018
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          Replying to @jpt401 @vgr

          the actually computable stuff is all functions from int to int. classical physics is real to real, and qm is real to complex and back to real

          0 replies 0 retweets 1 like
        4. End of conversation
        1. New conversation
        2. зануда, душноват‏ @GolerGkA 22 Sep 2018
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          Replying to @Plinz @vgr

          But isn't mind and universe NP-complete? The whole mapping of classical to constructive math breaks up because of P!=NP

          1 reply 0 retweets 0 likes
        3. Joscha Bach‏ @Plinz 23 Sep 2018
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          Replying to @GolerGkA @vgr

          what

          1 reply 0 retweets 0 likes
        4. 2 more replies

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