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

by xeno6696 , Sonoran Desert, Monday, February 15, 2010, 21:33 (5396 days ago) @ George Jelliss

xeno wrote: "I do hate that you dismiss pure math like that"
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> I don't dismiss pure maths only the infinitist type.
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> xeno: "99% of computer science both exists because of and relies upon many of these "fantasy objects."" 
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> You won't find e or pi or root-2 in a computer anywhere, only approximations to them. If you blow up any computer graphics that appear to show circles, you will find that they are in fact polygons.
> -You are wrong here--you're confusing numerical computation with graphical representation. -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.) -The computation of PI to an arbitrary precision is an open field within computer science, and if you did some digging you'd find that several big labs are also involved in calculating it out--including Intel. It is Euclid's PI that they are comparing their algorithms against. -http://www.cs.berkeley.edu/~ejr/GSI/2000-spring/cs267/assignments/assignment1-results/flab/-IN regards to computer graphics, they use matrix maths to represent 3-dimensional (or higher) objects. You are correct in the department of triangles--but that was a Euclidean result itself, right in the Elements. My overall point was that these matrix representations are still manipulating Euclidean objects in a Euclidean space. -This is irregardless of whether the graphics in question are rendered via shading, 3d projection, or raytracing. -> xeno: "Fibonacci relations by themselves are responsible for some of the best search algorithms"
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> That's probably quite correct, but it's finite maths, not analysis.
> -Not probably. 
http://comjnl.oxfordjournals.org/cgi/content/abstract/39/4/331
http://en.wikipedia.org/wiki/Polyphase_merge_sort-As you mentioned Knuth, you'd also be aware that in the book "The Art of Computer Programming" he discusses a tape-drive implementation of a mergesort algorithm that explicitly used Fibonacci. Fibonacci also works as a worst-case upper bound on the Euclidean Algorithm. -Also, tell me where finite maths end and analysis begins: You can take a derivative of the binomial theorem and derive further results relevant to "finite maths" and computing. When I took Combinatorics the professor consistently demonstrated how by using the operations of calculus we would regularly derive new results, and how they applied to computing. Combinatorics is supposed to be a "finite math," but in the words of that professor, "No mathematician can tell you what the difference is between discrete math and other math. The one who does wins a Fields Medal." Maybe one of you?" Probably not, I'll be 35 before I'm done with college. But I'd love to hear your answer!-Generally speaking, "finite math" tends to restrain itself to integer math, but the lines are far too murky to claim that with certainty. -> Stirling's numbers (of the second kind) count the number of ways of partitioning a set of n into k subsets. Bell numbers are the sum of these. But this again is finite maths.
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> I recommend the book "Concrete Mathematics" by Graham, Knuth and Patashnik.-Almost insulting: I start my Master's in Computer Science this summer. I've owned "Concrete Mathematics" since my first semester after calculus. I already have the background here. I'm not talking out of my ass.

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\"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.\"