Refutation of the \"Language-Only\" Interpretation of Math (The limitations of science)

by xeno6696 , Sonoran Desert, Wednesday, February 17, 2010, 02:52 (5395 days ago) @ George Jelliss

xeno wrote: "PI, e, and several other constants aren't approximated"
> 
> and now offers a programme to run on my computer. This states:
> "it takes 37.510 seconds to calculate 1M digits of PI"
> So it does not contain pi, it has to calculate it to an approximation. 
> -Right, but all these different algorithms calculate the same exact identical value of PI! There is a standard, like a meter, that computer scientists use in order to verify the accuracy of a PI-computing algorithm, otherwise, you could just write a code that spits out a random sequence of integers, and call it PI. Obviously this doesn't happen, or nations and corporations wouldn't spend literally billions of dollars on computing a value deemed "approximation only." -You probably won't believe me still, but the only thing I can do is show you a snippet of assembler code that I use when I need PI in C programs. -
inline double PI()
{
 double x; 
 __asm
 {
 fldpi; 
 fstp x;
 }
 return x
}
 
Intel has a hard-coded value on x87 processors, the commmand "fldpi" takes the hard-coded value and pops it into the processor's L1 cache, fstp copies it to real memory. The value on Intel's chip is a 66-bit number, but since the memory address of a double is 64bits, truncation occurs but the value you get for PI is considered wholly accurate for the entire piece of memory, 64 bits or PI to 2^64 - 1 places. Assembly language is considered "machine language" so there is no faster way to get a value for PI. The value for PI that they get is done by the method I've talked about previously--asserting a "pure Euclidean space" and letting it fly. I don't know what else to tell you, this is everything I know! Short of getting an electron microscope and finding the binary representation of PI on the chip fab I don't know what to tell you. -To me, an approximation means that there would be some ambiguity, that if you tried to get the same result twice, there would be a variation. I showed you those other computer algorithms to demonstrate that there is no variation in this. All these various algorithms are computing the same value. Maybe you're familiar with Ramanujan/Hardy's formula for PI? One method for calculating PI that we're taught is an exact value for PI is Machin's formula, but it is an expensive call (even in C) so we use the above assembler method to get the same result. --
> xeno: "In all instances, the accuracy of the algorithms are compared to 
> the Euclidean ideal, otherwise how could they tell which one was more 
> accurate than the others?"
> 
> Sorry, there is no comparison going on here. The fact that one method of calculating pi is equivalent to another has to be shown by theory.
> -Again, all I can do is point you to where I've pointed you. All the algorithms you find "approximate" (in your words) the exact same carbon-copy value of PI. I've given you a snippet of assembler code and spoken as far as all my training in computers can possibly take me on this question. -> you ask: "I'm not 100% sure of your math background"
> 
> You may get a better idea from this section of my website:
> 
> http://www.mayhematics.com/m/m.htm
> 
> It's far from complete, and it's unlikely I will ever find time to complete it now, but the sections on Generalities and Numbers may help.

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"