So you agree that an irrational relation is expressing the act of approximating an A as if it were many small B's? That it is explicitly an incommensurate relation that we use because it makes things convenient and manageable for our human minds?webolife wrote:No, I understand... I was just summarizing your logic.
Phi
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Re: Phi
Physicist: This is a pen
Mathematician: It's pi*r2*h
Mathematician: It's pi*r2*h
- webolife
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Re: Phi
Not really. I see phi and pi, etc. as real numbers in the universe. I see our attempt to measure them with incommensurate devices as requiring that we approximate their values for our own convenience. The same goes with trying to measure any "rational" number. We are always limited to some standard of precision. But I understand what you are trying to say. Theoretically there are countable numbers of whatever objects in the universe. So you don't like describing patterns of them with convenient numbers like pi, phi, etc. I just don't agree with your conclusion, that these therefore have no physical significance.
Truth extends beyond the border of self-limiting science. Free discourse among opposing viewpoints draws the open-minded away from the darkness of inevitable bias and nearer to the light of universal reality.
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Re: Phi
webolife wrote:Not really. I see phi and pi, etc. as real numbers in the universe.
We don't "measure pi". We measure an object. The hypothesis might be a circle, which is described as having equal length and height and as having a width that never varies the same over two consecutive finite distances in the direction of length and vice versa. THIS is what you see as something "real in the universe". You are hypothesizing the existence of an object with these characteristics and calling it a circle. The circle is in your head, it is a concept. Then you try to quantify the circle so you can compare it to something in reality, something you physically measure. You do so by approximating it as a n polygon. When you measure something in reality and get a number that is extremely close to what you got for an n-polygon you use this as evidence to support your hypothesis. However you can never prove the hypothesis because you cannot quantify something infinitely.webolife wrote:I see our attempt to measure them with incommensurate devices as requiring that we approximate their values for our own convenience.
This is important! It is the scientific method! You are hypothesizing an object (hypothesis), describing it conceptually (theory), then providing observational evidence (we measure numbers that look like a high order polygon that *could be* what we described as a circle). Quantification is the last step. We don't measure pi, we measure objects. Pi just refers to the fact that we can successively approximate a circle, pi is just a symbol that expresses our approximation method in compact form.
Physicist: This is a pen
Mathematician: It's pi*r2*h
Mathematician: It's pi*r2*h
- webolife
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Re: Phi
Well then, yea for pi, if it allows us to do these things, thereby helping us realise the physical significance of universal patterns.altonhare wrote:webolife wrote:Not really. I see phi and pi, etc. as real numbers in the universe.We don't "measure pi". We measure an object. The hypothesis might be a circle, which is described as having equal length and height and as having a width that never varies the same over two consecutive finite distances in the direction of length and vice versa. THIS is what you see as something "real in the universe". You are hypothesizing the existence of an object with these characteristics and calling it a circle. The circle is in your head, it is a concept. Then you try to quantify the circle so you can compare it to something in reality, something you physically measure. You do so by approximating it as a n polygon. When you measure something in reality and get a number that is extremely close to what you got for an n-polygon you use this as evidence to support your hypothesis. However you can never prove the hypothesis because you cannot quantify something infinitely.webolife wrote:I see our attempt to measure them with incommensurate devices as requiring that we approximate their values for our own convenience.
This is important! It is the scientific method! You are hypothesizing an object (hypothesis), describing it conceptually (theory), then providing observational evidence (we measure numbers that look like a high order polygon that *could be* what we described as a circle). Quantification is the last step. We don't measure pi, we measure objects. Pi just refers to the fact that we can successively approximate a circle, pi is just a symbol that expresses our approximation method in compact form.
I didn't mean "measuring pi", I meant measuring objects characterized in their patterns by relationships such as pi and phi.
I'm quite tired of this debate, so if you want the last word, so be it.
Truth extends beyond the border of self-limiting science. Free discourse among opposing viewpoints draws the open-minded away from the darkness of inevitable bias and nearer to the light of universal reality.
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Re: Phi
Alton, thank you for this explanation of whole numbers. A friend has been trying to explain this concept of reality to me but I just didn't get it, even though I use it in everyday life--when I can't find a ruler to use inches to measure a distance, I use a certain length of string, or something else convenient to represent a 1 (something), I never use a zero (nothing). I finally get it.The smallest number we use can be set to 1 and everything else scaled up from there so that we work only with whole numbers.
jtb
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