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Natural Science Forum / Physics / Relativity / June 2005pi and numbers 2
I started a new thread because this is such a busy list and I don't know if old stuff gets looked at. So I am having a problem thinking why pi should be "irrational" I know this is probably basic math but I can't get my head around why an obviously real physical thing like a circle should be explained by a number that doesn't really exist. Help to get head around appreciated. am "Irrational" numbers are just as real as rational numbers. It's easy to prove that the square root of 2 is irrational. You should start there. Dear am: > I started a new thread because this is such a busy list > and I don't know if old stuff gets looked at. It does. > So I am having a problem thinking why pi should be > "irrational". I know this is probably basic math but I > can't get my head around why an obviously real > physical thing like a circle should be explained by a number > that doesn't really exist. "Irrational" doesn't mean what you think it means. Rational means that a number can be expressed as a ratio of two integers (1/3, 29/64, 4/1). Irrational means it cannot. Irrational does not mean that the number does not exist. > Help to get head around appreciated. URL:http://mathforum.org/dr.math/faq/faq.integers.html David A. Smith > I started a new thread because this is such a busy list and I don't know > if old stuff gets looked at. > So I am having a problem thinking why pi should be "irrational" > I know this is probably basic math but I can't get my head around why an > obviously real physical thing like a circle should be explained by a > number that doesn't really exist. There is your problem right there - it 'really exists' in exactly the same way as any number 'really exists'. Numbers are simply objects in mathematical systems - there relation to 'reality' comes when they are contained in models whose correspondence to what it is modeling is made explicit in the model. For example the diagonal of a square of unit size is root 2 which is irrational - would you seriously contend that when measured its length to extremely good accuracy would not be found to be root 2? Thanks Bill > Help to get head around appreciated. > > am >>I started a new thread because this is such a busy list and I don't know >>if old stuff gets looked at. [quoted text clipped - 10 lines] > root 2 which is irrational - would you seriously contend that when measured > its length to extremely good accuracy would not be found to be root 2? So we can count things. but there is something odd about measuring things ? because you can never arrive at a definate accurate length ? thanks am > >>I started a new thread because this is such a busy list and I don't know > >>if old stuff gets looked at. [quoted text clipped - 13 lines] > So we can count things. but there is something odd about measuring > things ? because you can never arrive at a definate accurate length ? So? The HUP also has an impact as well. Bill > thanks > > am Dear am: >>>I started a new thread because this is such a busy >>>list and I don't know if old stuff gets looked at. [quoted text clipped - 17 lines] > > So we can count things. But NOT with 100% accuracy, in most practical cases. A count is a measurement, as is itself subject to uncertainty. Examples would be counting photons with the VLBA, counting cars on a stretch of road, etc. > but there is something odd about measuring things ? Yes. The "odd" is located between "reality" and "measurement". > because you can never arrive at a definate > accurate length ? In a finite period of time, probably not. David A. Smith <snip> >>So we can count things. > [quoted text clipped - 11 lines] > > In a finite period of time, probably not. I always liked arithmetic but never went very far with it. I do have a memory of my first maths lesson. The teacher wrote up on the blackboard 1+1=2 and I distinctly remember thinking No no no that is not right. then this huge wave of sadness when I decided Ok I will go along with your way. I remember thinking it is not like that but the exact sense of it I cannot recall. It was something to do with the life in things and that by counting them the life was belittled or something. So I'm trying to think now was there something in the childish happiness with the world that I can use to figure out WTF is going on. regards am Dear am: ... >>>because you can never arrive at a definate >>>accurate length ? >> >> In a finite period of time, probably not. > I always liked arithmetic but never went very far > with it. I do have a memory of my first maths > lesson. The teacher wrote up on the blackboard > 1+1=2 and I distinctly remember thinking No no > no that is not right. I felt the same way when exposed to cursive writing. > then this huge wave of sadness when I decided > Ok I will go along with your way. I remember > thinking it is not like that but the exact sense of > it I cannot recall. It was something to do with the > life in things and that by counting them the life > was belittled or something. I took Evelyn Wood speed reading in high school. I was over 900 words per minute with "acceptable" comprehension. Haven't used it since, since the writer *struggles* with each word. If it takes such time to commit, no need to rush to consume. > So I'm trying to think now was there something in > the childish happiness with the world that I can > use to figure out WTF is going on. Try Buddhism. You may be balking at the symbolism that "stands for" (or is raised up by consciousness to keep you away from) reality. David A. Smith > Try Buddhism. You may be balking at the symbolism that "stands > for" (or is raised up by consciousness to keep you away from) > reality. Actually thinking about it somemore I think the feeling was "Oh sh.t! playtimes over". am Dear am: >> Try Buddhism. You may be balking at the symbolism >> that "stands for" (or is raised up by consciousness to >> keep you away from) reality. > > Actually thinking about it somemore I think the feeling > was "Oh sh.t! playtimes over". Ah. ;>) David A. Smith |
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