Bitcoin : There’s a lot of people thinking that others are somewhat obsessed with Craig when we debunk what he says. Unfortunately he makes many mistakes all the time: Turing Completeness and CSW most recent interview.
People like me are surely upsetting some CSW supporters. They call us “shills” or “bitmain shills” and such nonsense when we point out CSW mistakes. Since I believe there are people out there who support CSW in good faith because they don’t have some technical background, I decided to post this.
I’ll use only the beginning of the last CSW interview to show you how he is plainly wrong and can be verified easily without knowing CS or math.
In [this interview](https://www.youtube.com/watch?v=whbzIGML1qY&feature=youtu.be&t=1m30s) CSW claims that people do not understand that *Turing Completeness is the ability to calculate any number*.
This is completely false, and it is very simple to debunk it. There are effectively real numbers which are *not* computable. That is, there are numbers that your machine cannot compute.
One known such number is [Chaitin’s constant](https://en.wikipedia.org/wiki/Chaitin%27s_constant) – Chaitin omega number.
Chaitin omega number actually defines an infinite class of transcendental numbers which are not computable. So, not only there is *at least* one real number which is not computable, *but an infinity of them* (craig missed an infinity).
*I’d like to go a bit further to debunk yet another claim, but this is more complicated so you can skip.*
***
Recall that CSW also said in that passage that people are missing the point when they say that a TM needs to have the ability to loop.
Now lets go back one step. What numbers then a TM needs to be able to compute? What means to be turing complete? It means that the machine has the ability to calculate all algebraic numbers and also some transcendental numbers, such as `e` and `π`. These we know can be computed with arbitrary degree of precision (that is, there exist an algorithm that will print the n-th digit of those numbers), but the machine may never halt and reiterate the same code if we don’t set any degree of precision.
Algebraic numbers have finite algorithms because they are the root of polynomials in one variable with rational coefficients. The polynomials are themselves finite by definition, and the operations are thus in finite amount. Those operations are computations!
So the important thing is to look at transcendental numbers.
Calculation done with them may never halt because they do not have a finite description such as algebraic numbers (the finite description of algebraic numbers is their polynomial).
Ok, I went a bit far here, but the point is that CSW is also wrong in the second claim because to compute a transcendental number one needs to loop code endlessly, since the program cannot halt in a finite description such as in the case of algebraic numbers.
For instance, a program can halt if it finds the relation x^2 = 2 and print the square root of two, even tho sqrt(2) is irrational and has an infinite non periodic decimal expansion. Such thing is not possible for π.
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Author: rdar1999
Score: 29
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