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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 28 Jun 2019
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      Replying to @MathObsessed @Grady_Booch @aatishb

      The assumption that something can execute an algorithm with infinitely many operations in a finite number of steps leads to contradictions. This is why most mathematicians seems to have become constructivists after Gödel and Turing. Constructive math is computation.

      1 reply 0 retweets 0 likes
    2. Ernest Lebedev‏ @MathObsessed 28 Jun 2019
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      Replying to @Plinz @Grady_Booch @aatishb

      I didn’t mean that it is a limitation in terms of number of operations, what I meant is: irrational numbers are not “incomputable”. They just cannot be represented as a floating point number with exact precision. Computers have rough time with numbers when it comes to precision

      1 reply 0 retweets 0 likes
    3. Grady Booch‏Verified account @Grady_Booch 28 Jun 2019
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      Replying to @MathObsessed @Plinz @aatishb

      I know what uncomputable is, but I don’t know what you mean by incomputable.

      4 replies 0 retweets 0 likes
    4. Ernest Lebedev‏ @MathObsessed 29 Jun 2019
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      Replying to @Grady_Booch @Plinz @aatishb

      What I was trying to say is: modern computers have “architecture” which limits them severely to imprecise floating point operations. With this limitation you can’t compute irrational numbers precisely, I think.

      1 reply 0 retweets 0 likes
    5. Joscha Bach‏ @Plinz 29 Jun 2019
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      Replying to @MathObsessed @Grady_Booch @aatishb

      The implication of Gödel and Turing’s proofs is that an infinite precision hypercomputer cannot be built, not just in our universe, but in any language.

      1 reply 0 retweets 0 likes
    6. Ernest Lebedev‏ @MathObsessed 29 Jun 2019
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      Replying to @Plinz @Grady_Booch @aatishb

      Correct me if I am wrong, please, but our computers operate based on a state machine principle. If you calculate each decimal point step by step you will never get a precise irrational number. However, as I implied: modifying architecture to allow irrationals can change the plot

      2 replies 0 retweets 0 likes
    7. Joscha Bach‏ @Plinz 29 Jun 2019
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      Replying to @MathObsessed @Grady_Booch @aatishb

      How do you propose to integrate an infinite amount of information in a finite number of implementable operations?

      1 reply 0 retweets 0 likes
    8. Ernest Lebedev‏ @MathObsessed 30 Jun 2019
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      Replying to @Plinz @Grady_Booch @aatishb

      Not at all proposing that :) Again, I am trying to explain that the concept of floats is limiting since infinity is unattainable. People added fractions to natural numbers. In the same way: add irrational fractions to floats. As a concept, not as a “special” float

      1 reply 0 retweets 0 likes
    9. Joscha Bach‏ @Plinz 30 Jun 2019
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      Replying to @MathObsessed @Grady_Booch @aatishb

      How do you implement the value of an irrational number?

      2 replies 0 retweets 1 like
    10. Ernest Lebedev‏ @MathObsessed 30 Jun 2019
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      Replying to @Plinz @Grady_Booch @aatishb

      Well, that is another point :) I am not educated enough to propose something valuable, I am afraid. I was just into this particular conversation and my reasoning suggests that having floats only is a limitation, because maths, for example, are purely logical yet more abstract

      1 reply 0 retweets 0 likes
      Joscha Bach‏ @Plinz 30 Jun 2019
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      Replying to @MathObsessed @Grady_Booch @aatishb

      The argument is that classical mathematics pretends that a function and the value it returns are =, but Gödel/Turing show that this only works if the function terminates after finitely many steps, so classical math semantics have to be replaced by constructivism (computation).

      10:37 AM - 30 Jun 2019
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        2. Ernest Lebedev‏ @MathObsessed 30 Jun 2019
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          Replying to @Plinz @Grady_Booch @aatishb

          Computers are machines and have obvious limitations. This is why human mind is so different, I think. Humans can come up with an idea of irrational numbers - machines cannot, I believe. IF machines rely on pure logic as they are today

          1 reply 0 retweets 0 likes
        3. Grady Booch‏Verified account @Grady_Booch 30 Jun 2019
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          Replying to @MathObsessed @Plinz @aatishb

          Coming up with the idea of an irrational number is very different than calculating an irrational number. The former is a matter of abductive reasoning; the latter is provably incomputable in this universe.

          1 reply 0 retweets 2 likes
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        1. Ernest Lebedev‏ @MathObsessed 30 Jun 2019
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          Replying to @Plinz @Grady_Booch @aatishb

          I may be unaware of something but that doesn’t downgrade maths to constructivism IMO. I don’t think that infinity by definition can be achieved by a finite number of steps. And since an irrational number is an infinite fraction, of course you cannot compute it as a precise float

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        1. Ernest Lebedev‏ @MathObsessed 30 Jun 2019
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          Replying to @Plinz @Grady_Booch @aatishb

          I am not sure if we’re on the same page... Are you talking about Godel’s theorem of incompleteness? Like there are statements within a formal system that are not deductible by pure formal logic? And Turing theorem about finite inputs?

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