Q_Goest, you raise some interesting points, but I'm not completely sure what your position on the argument in the original post is. Specifically, if you disagree with the conclusion, it would be helpful to me if you could explain at what point you think the argument breaks down.
As far as...
Actually the property of the rationals you are describing when you say that "between any two rationals (or indeed, any two real numbers) is another rational" is the property of the rationals being dense in the space of all real numbers. And this is equivalent to the existence, for any real...
It seems like we're getting stuck pretty early on in the argument. Namely, people don't seem to agree that the human brain could be simulated by a computer. That is, it seems like you don't even agree that a simulation of the functional properties of the brain is possible, let alone that such...
The Turing machine has to run if we want to know its state at some future point. But its future state is determined, independent of our knowledge. In any case, I'm not sure you accept my premise that a consciousness could be simulated on a Turing device. If you do accept it, we can continue...
What I mean is, what exactly is the absurd conclusion? And what does it imply, ie, which of the four steps in the argument are wrong? Are you saying human consciousness can't be simulated on a Turing machine? It doesn't seem necessary to have all the machinery of QM and GR to simulate a human...
Maybe. Can you elaborate on how this argument would run?
In any case, I agree, it is more than possible that our universe cannot be simulated on a Turing machine. However, I still believe (hope?) that it is described in some mathematically precise way. Maybe everything follows from a...
argument that all computable universes are "real"
I haven't been on this forum in a while, and I'm sure this kind of thing has been talked about many times, but I thought I'd bring it up again so I could discuss it with you guys. Here's my argument.
Start with a human being named John. He...
hamster,
I'm not sure what you mean. Are P(x) and Q(x) supposed to be polynomials? According to mathematica, the indefininte integral contains logs, and is very complicated.
jgens,
I'm not sure I understand exactly what you're saying, but I'm skeptical of your method since you don't...
I've just found that, for all a>0:
\int_0^\infty \frac{a (x^2 - 1)^2 - 2 x (x + a)^2}{(x + a)^3 (a x + 1)^3} dx = 0
This can be found by brute force, but there must be a simpler way to show it.
One can check (say, by graphing the function), that:
f(x) = sin(x) + cos(x) + csc(x) + sec(x) + tan(x) + cot(x)
is never zero. So finding the minima of |f(x)| can be done by looking at all the local minima and maxima and seeing which is closest to zero.
If you define u = sin(x)+cos(x)...
Ok, well let me give the integral I'm interested in:
\int_{-1}^1 dx \frac{e^x}{x+b} \tan^{-1} \left( \frac{\sqrt{1-x^2}}{x+a} \right)
here a is some arbitrary real number greater than 1, and b is picked so that at x=-b the argument of inverse tan is i (explicitly it's b=(a^2+1)/2a). This...
Is there a way to perform a contour integral around zero of something like f(z)/z e^(1/z), where f is holomorphic at 0? If you expand you get something like:
\frac{1}{z} \left( f(0) + z f'(0) + \frac{1}{2!} z^2 f''(0) + ... \right) \left( 1 + \frac{1}{z} + \frac{1}{2!} \frac{1}{z^2} + ...