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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 27 Jun 2019
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      Replying to @aatishb

      All the irrational numbers are actually uncomputable functions. You have to express them as algorithms that require infinitely many steps to run. As a result, nothing in the universe can be caused by an irrationally numbered value. Reality is all decorated integers.

      10 replies 7 retweets 53 likes
    2. Ernest Lebedev‏ @MathObsessed 28 Jun 2019
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      Replying to @Plinz @Grady_Booch @aatishb

      On the contrary, friend. You’re making a big mistake by not understanding that an irrational number can easily be a result of a function. The thing that appears as “uncomputable” to you is merely a limitation of modern computer architecture. You are just a bit confused :)

      1 reply 0 retweets 1 like
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. 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
    9. 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
    10. 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
      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?

      2:27 AM - 30 Jun 2019 from Cambridge, MA
      • 1 Like
      • Jakob Berg
      2 replies 0 retweets 1 like
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        2. 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
        3. 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).

          3 replies 1 retweet 1 like
        4. 3 more replies
        1. Ernest Lebedev‏ @MathObsessed 30 Jun 2019
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          Replying to @Plinz @Grady_Booch @aatishb

          Not saying that maths are perfect to reflect the reality, just saying that computers imply pure logic and maths is pure logic, therefore extension the field of computations from just floats seems reasonable to me

          0 replies 0 retweets 0 likes
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