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

by xeno6696 , Sonoran Desert, Tuesday, February 16, 2010, 21:59 (5392 days ago) @ George Jelliss
edited by unknown, Tuesday, February 16, 2010, 22:12

xeno wrote: "PI, e, and several other constants aren't approximated, they use the raw Euclidean constants and hard code it into the math coprocessor on your Pentium or Athlon CPU. When PI is needed for a calculation it simply calls the hardware-coded value, rocks and rolls. This dramatically reduces calculation time at runtime. (2 opcodes vs. a chain of function calls if we're talking C.)"
> 
> I'm afraid I just don't believe this. You will have to explain how it's done more clearly. The link you gave admits that pi to ten places of decimnals is sufficient for all practical purposes.
> -All I can do is provide some resources:
http://kakku.wordpress.com/2007/10/26/super-pi-how-fast-is-your-processor/
For one to run on your own PC-http://findarticles.com/p/articles/mi_m1200/is_v131/ai_4702871/
For the supercomputing battles of computing PI-Or just google "PI algorithms" to find hundreds of others in multiple programming languages. 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? -> I don't know why you should feel insulted when I recommend a good book. I'm glad you already have it.
> -That's why I said "almost." One cannot communicate tone over the internet!-> xeno also asks: "Also, tell me where finite maths end and analysis begins:" 
> 
> I'm just using analysis as a shorthand for mathematics based on the assumed existence of real infinities.-I'm not 100% sure of your math background, but what you call "Calculus," we call "analysis" as it pertains to analyzing the structure of functions, and since you can define anything as a function, you can't really separate "finite maths" from anything else.-[EDIT]
Or maybe you can consider that PI can be perfectly calculated when you assume a Euclidean space. Since we can do that in a computing environment, we can always get an arbitrary accuracy of PI. Does that help?

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