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

by xeno6696 , Sonoran Desert, Thursday, February 18, 2010, 01:12 (5391 days ago) @ George Jelliss

If pi is written in the intel chip as correct to 66 bits that's still way off being "exact". After all pi is a transcendental number that is expressed by a nonrecurring infinite decimal. Am I right in thinking that 66 binary digits is only equivalent to about 20 decimal digits? So there are still infinity minus twenty digits to come! If the algorithms always cut off at the same point to ensure they agree that's a bit of a cheat. Even with an accuracy of 66 bits I'm sure there are calculations that can be devised that will give an incorrect result because this is not sufficiently accurate. How about the 1000th root?-A 64-bit (double) number has a sign bit, so 2^11 possible numbers, then 52 bits for the fraction, 2^52 possible numbers. Here is where my programmer thinking masked my mathematical thinking. ...you're right. The total translation in precision only comes out to about 16 places on a 64-bit number. This was my fault for not slowing down and remembering my hardware classes. Computers think only in integral terms, you need algorithms to represent floating points. This is why floating point addition isn't necessarily commutative--you're liable for rounding errors. -But I still must ask the question--if its already predetermined that you're only going to approximate PI, how on earth can you reasonably say that any PI algorithm is accurate? Like this paper suggests:
http://mathdl.maa.org/images/upload_library/22/Hasse/00029890.di991740.99p0456b.pdf-If you use this to calculate PI to one billion places, how is anyone supposed to believe that the algorithm is actually doing what it says it does?-The only thing that makes sense is to construct a Euclidean only space and then calculate under those restrictions in order to get a standard to measure by.-(I wasn't suggesting that they were measuring algorithms by the Intel number, only trying to make the statement that good programmers don't "calculate" PI they just make a hardware call for it.)

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\"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.\"