Kevin and Ron, I think the issue gets down to this difference that began with the Greek mathematicians, between the world as experienced and the world abstracted mathematically, the world of ideal forms. You can say that this stick is two inches long but your measurement is limited by the precision of your ruler. There is a difference between the 2x4s you put into your construction plans and the 2x4s that go into the walls. A handy man friend of mine claims to be 32nd inch carpenter. So that all the boards he cuts are within a tolerance of 32nd of an inch of the abstract specifications in his plans.
In a motorcycle engine tolerances are specified to within 1000ths of an inch. Thin films used in the manufacturing of microprocessors have tolerances measured in billionths of a meter. But these tolerances are simply measures of the allowed differences between the real and the ideal worlds. In short this is rounding error. It is this distinction that caused many to assume the ideal world was of prime importance and the real world is a sloppy copy. What Mandelbrot illustrated is that the length you get when you measure anything in the real world is a function of the instruments you use to measure with. Those instruments in effect determine how much rounding error you are willing to tolerate. What quantum mechanics shows is that no matter what instrument you choose to use, you lose. It is in principle impossible to make infinitely precise measurements. This is not just a matter of faulty instruments or technique. It is built into the nature of matter itself as we currently understand it. Case ----------------------------------------------------- Kevin, "You assume a truth where there is none." That’s exactly my point ..although admittedly my Terms are rather clumsy "ƒ(x) + ƒ(y) does not always equal ƒ(x+y) where the intent is the function that rounds to the nearest whole number". In that way ƒ = (y) in that they are both the function of the limit. (x) + (x) does not allways equal ƒ. (x) + (x) may equal ƒ(x) , (x) + (x) may equal ƒ(y). (x)+(x) may equal 0 It all Depends on the "values" of "x" in realtion to an assumed limit...It's all variable, the closest we can get to Precision is an assumed limit with an assumed "mean" and that depends on the value of the measurement In relation to the intent of the subject with the object. The emphisis I'm making is that ƒ is not an absolute value ...that the value [(x) + (x)] is the The "real" value and not absolute. Only when a limit to perception/precision is applied is anything Useable and senseable. I'm seeing paralells to Bohrs philosophy. Is [(x) + (x)] the function Of Quality? Please let me know if I am overlooking something. Thanks, -Ron ------------------------------------------------ Hello Ron, > The statement is, "2 + 2 = 5 for very large values of 2." It's a joke > about rounding and estimating. <snip> > math is meaningless until an absolute is assumed.you have to have a > cut-off To precipitate a round then you may reach an absolute 1. but > does reality have a cut-off point To cause a rounding? Averaging is > the closest we can come to any kind of precision. Ron, I see your approach to the math as saying ƒ(x) + ƒ(y) = ƒ(x+y) where ƒ is the function that rounds to the nearest whole number. So if x = 2.4 then ƒ(x) = 2. And if y = 2.3 then ƒ(y) = 2. And if x + y = 4.7 then ƒ(x + y) = 5. In this way your approach can say 2 + 2 = 5. But look at your assumption. You assume a truth where there is none. ƒ(x) + ƒ(y) does not always equal ƒ(x+y) where ƒ is the function that rounds to the nearest whole number. I also see in your approach a misapplication of tolerances. In other words the statement 2 + 2 = 5 is a misapplication of 2±½ + 2±½ = 4±1. Notice how the two ±½s combine to become ±1. So 2.4 + 2.3 = 4.7 is conveyed as 2±½ + 2±½ = 4±1 not 2 + 2 = 5. Hope this helps. Kevin moq_discuss mailing list Listinfo, Unsubscribing etc. http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org Archives: http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/ http://moq.org.uk/pipermail/moq_discuss_archive/
