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Post by StuartG on May 22, 2011 22:47:38 GMT 1
? is it bad maths, maths modelling reality, or what? StuartG
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Post by nickcosmosonde on May 23, 2011 3:25:28 GMT 1
Is there any reason it should?
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Post by StuartG on May 23, 2011 8:49:21 GMT 1
Well I think so, a circle has a circumference and radius/diameter that from my point of view should be fixed in relation to one another, but they are not exactly, when You try to work out the relationship it seems very fuzzy and seemingly goes on forever. Is it that the maths is exactly right and is just mimicking what's really happening in reality and the matter that represents the circumference is in fact that fuzzy at its boundary. Cheers, StuartG
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Post by eamonnshute on May 23, 2011 10:23:00 GMT 1
What do you mean by "exactly"? Pi does have an exact value, although it consists of an infinitely long string of digits.
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Post by marchesarosa on May 23, 2011 11:16:29 GMT 1
"Pi does have an exact value, although it consists of an infinitely long string of digits"
This is a very strange definition of "exact", Eamonn.
Pi is just a ratio between circumference and diameter, isn't it? It is an invariant "relationship" rather than an exact number.
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Post by StuartG on May 23, 2011 13:39:27 GMT 1
Dear Aim'nShoot Hardy exact is it? 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 exact light 299 792 458 m s-1 Cheers, StuartG
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Post by eamonnshute on May 23, 2011 14:09:14 GMT 1
What do you mean by exact? Exactly what? Is one third (=0.33333333...) exact?
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Post by StuartG on May 23, 2011 16:15:48 GMT 1
Really I was hoping that someone might say that it points to say, a physical reality, such that, when a circumference of some matter is examined at that miniscule level the matter would not be that precise in its boundary. I'll just have to settle for an 'irrational' number. Cheers, StuartG
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Post by marchesarosa on May 23, 2011 20:52:36 GMT 1
Well, I can fold a piece of paper or a piece of string into thirds, but not into 0.3333r, Eamonn.
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Post by speakertoanimals on May 23, 2011 22:06:40 GMT 1
To those who REALLY are perturbed that pi is irrational, most interesting numbers are irrational!
So, take two unit lines, place at ninety degrees, what is the distance between the ends?
Easy, you say, root 2. Except that is an irrational number!
Now take 4 unit lines, arranged in a cross, and join ends (to make a square). Length is 4 times root 2, irrational again.
Perhaps you can see where I'm going -- add more unit radii, join ends, using 4, then 8, then 16 etc etc. In the limit of an infinite number, the length you end up with 2 pi, and since it started as irrational when we just had 4, no real surprise if it keeps going that way.
So we see that even the simplest 2D construction we can think of (2 lines at right angles) leads to irrational numbers, so why should we be surprised if more complicated ones (like drawing circles) do too?
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Post by StuartG on May 23, 2011 22:15:17 GMT 1
Not surprise, more disappointment. It's not 'pretty' enough! StuartG I found the same decimalising time, mostly irrational outcomes.
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Post by speakertoanimals on May 24, 2011 12:35:10 GMT 1
Did you really mean that 1/3 isn't the same as 0.3 recurring...............
Else it's a daft statement.
Except pretty boring, since 1/3 is just yet another rational number. but as I said before, take even the simplest geometric construction in 2D (two equal length lines at right angles), and the irrational come storming in.
Okay, it upset the greeks a bit, but surely we have got over that now?
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Post by marchesarosa on May 24, 2011 13:26:51 GMT 1
One third is another ratio, isn't it? 0.3r is just a number. No they are not the same thing as far as I can see. One can arrive at the answer 0.3r by any (infinite) number of arithmetic calculations. But one third is one third is one third. It has a "meaning" independent of arithmetic.
Am I being too sophisticated for you, STA?
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Post by speakertoanimals on May 24, 2011 13:57:47 GMT 1
Nope, they are EXACTLY the same. 0.333 ISN'T the result of an infinite number of calculations at all, you can work out it is recurring before you start.
Take a half, to be simple. In binary base, that's 0.1 In decimal, 0.5
Why? Because 1/2 is the same as 5/10.
Or a third. Let's work in base 3. So, 1, 2, 3 in base 3 is 1, 2 and 10
4,5 ,6 would be 11 (a three and a one), 12 (a three and a two ones), then 20, 21, 22, 100 and so on. Like binary, just one more symbol.
Same goes for fractions
Rather than 1, 1/10, 1/100, 1/1000 as we have in decimal numbers, in binary fractions we have 1/2, 1/4, 1/8, 1/16 and so on.
Hence in base 3, a third is just 0.1, but 0.3333 recurring in base 10, or 0.0101010101................... in binary
The recurring thing just tells you that in SOME basis, the number can be written as a non-recurring fraction. Because what it really means is that it can be written as p/q, where p and q both whole numbers. Hence in base q, just get p q'ths, like 0.1 in base 3.
Except rational or irrational has a MEANING independant of the base you choose to write numbers down with. A third is 0.33333....., is 1/3, is 0.1 (base 3), and so on. Same number, different basis.
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Post by marchesarosa on May 24, 2011 14:21:23 GMT 1
You are willfully misunderstanding my point, STA.
O.3r is just a figure that can be produced by any number (infinite or thereabouts) of arithmetic processes - addition, subtraction, multiplication etc, not simply the division of one by three that you are concerned with. There is nothing special about about it. It is the offspring of many promiscuous parents.
"One third" is an invariant ratio AND it has a meaning independent of your arithmetic.
You may believe that the concept of "one third" is somehow equivalent to 0.3r but your reasoning would be circular, or something like that.
Which came first, thirds or decimals? I think thirds have some sort of epistemological priority, myself. Your arithmetic is just contingent.
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