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Author | Topic: Objective reality | |||||||||||||||||||||||
New Cat's Eye Inactive Member |
Gawsh, an explanation on where and how they were wrong would've been an interesting read.
I thought I'd done that.
Well you didn't.
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cavediver Member (Idle past 3643 days) Posts: 4129 From: UK Joined: |
Do you have any actual arguments against the point of view that I have expressed? What arguments? That because Pi is not like a tiger, it is obviously not "objective reality", where-as titilation obviously is. Forgive me, but I just prefer to laugh at that rather than argue with it. You seem worringly attached to your beliefs here, hence the justifable comparison with a religious faith. Myself, I'm still on a long journey trying to understand this existence, and I rather debate and argue it with others of similar curiosity. You, in this thread at least, don't fit that bill. Sorry. Edited by cavediver, : No reason given.
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cavediver Member (Idle past 3643 days) Posts: 4129 From: UK Joined: |
Well you didn't. Yes, it's strange. From all of Dr A's claims of having shown, demonstrated, and explained, I must be missing half of his posts.
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Dr Adequate Member (Idle past 284 days) Posts: 16113 Joined: |
What arguments? That because Pi is not like a tiger, it is obviously not "objective reality", where-as titilation obviously is. Forgive me, but I just prefer to laugh at that rather than argue with it. You may indulge yourself however you choose, so long as it doesn't hurt anyone.
You seem worringly attached to your beliefs here, hence the justifable comparison with a religious faith. And hence the justifiable comparison to your fanatical belief in the existence of cheese. It worries me.
I'm still on a long journey trying to understand this existence, and I rather debate and argue it with others of similar curiosity. Feel free. But apparently you don't want to debate with me because I actually have a point of view. This is both your loss and mine. Edited by Dr Adequate, : No reason given.
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cavediver Member (Idle past 3643 days) Posts: 4129 From: UK Joined: |
then that would lead us to also consider the ratio pi as objective, even if we think of numbers as merely useful fictions. I'm interested in this point. Are you treating the ratio Pi as something more "real" other than your fictional numbers, or is it as much a fiction as say the integers?
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Dr Adequate Member (Idle past 284 days) Posts: 16113 Joined: |
Well you didn't. I thought that I had, but I guess sometimes I'm a bit gnomic. So what didn't you understand? I'm happy to fill in the gaps for anyone who is genuinely interested. Edited by Dr Adequate, : No reason given.
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Dr Adequate Member (Idle past 284 days) Posts: 16113 Joined: |
Yes, it's strange. From all of Dr A's claims of having shown, demonstrated, and explained, I must be missing half of his posts. Again, I'm happy to fill in the gaps. What didn't you understand? Edited by Dr Adequate, : No reason given.
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nwr Member Posts: 6408 From: Geneva, Illinois Joined: Member Rating: 5.1 |
cavediver writes:
I am distinguishing between ratios and numbers.Are you treating the ratio Pi as something more "real" other than your fictional numbers, or is it as much a fiction as say the integers? If I say that my window is 30 inches wide, then I am using the number 30 as part of my representation of the width. But I could represent the width in centimetres, or in hand spans, or in some other unit. The numbers used would be different, depending on the unit used. The width is a quantity (in this case a length quantity), and the use of numbers to represent it is a convenience of our choice. Likewise, I say that a ratio is a quantity, though in this case it is a dimensionless quantity. But I still distinguish between the quantity (i.e. the ratio) which is not a fiction, and the number we use to represent it (which is a fiction). Roughly speaking, numbers are names that don't actually name anything, and they are fictions precisely because they don't actually name anything. Having names that don't name anything is very useful, for we can transfer those names to wherever we want to use them. Mathematics works because we have chosen highly systematic naming systems for such uses, and the rules of mathematics are the laws of system for those naming systems. Presumably a different intelligent civilization might come up with a very different systematic naming scheme, so might not have anything that corresponds to our numbers. But ratios that arise from idealizing empirical methods would likely be shared, so the pi as a ratio might be known to that civilization, even if they don't use anything that is quite the same as our numbers.
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cavediver Member (Idle past 3643 days) Posts: 4129 From: UK Joined: |
I am distinguishing between ratios and numbers. Yes, that is what I thought. But I can generate the integers in a number of ways that are blatently dimensionless. Topological winding numbers for example. How would you classify these in the sense of our present discussion?
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Dr Adequate Member (Idle past 284 days) Posts: 16113 Joined: |
Could we at least fill in the ontological status of math as an afterthought?
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nwr Member Posts: 6408 From: Geneva, Illinois Joined: Member Rating: 5.1 |
cavediver writes:
Winding numbers give you integers, though there might be some exotic way of getting non-integer values there. And pi is not an integer.But I can generate the integers in a number of ways that are blatently dimensionless. Topological winding numbers for example. A question that I remember thinking about many years ago, was how do we know that the integer 3, as obtained in counting, is the same 3 as we get in measurement? Or, to put it differently, how can we know that the integers are a subset of the reals? The correct answer, I think, is that this is a matter of executive fiat. We get the integers by an idealization of counting. It is a method where we start with one and build up combinatorially. We get the reals from geometry. We think of a line as a continuum, and we divide it up. It isn't obvious that these give rise to the same numbers. The Greeks and the Egyptians had different ways of dealing with these. Our current way of looking at them comes from Arabic notation. Roughly speaking, we forced the two systems to be the one system. With that forcing, we get all of the problems of the infinite that bother the constructivists. As a pragmatist, I don't personally have a problem with it - it seems to work well. But I don't think it is a forgone conclusion that intelligent alien civilizations would similarly force measuring and counting into a single system. And if they don't so force them, then ratios would be part of the measuring system rather than part of the counting system. In that case pi might show up as an equivalence of different dimensionless ratios, so pi as a ratio would still be important. But it might never be reduced to the form of a number.
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nwr Member Posts: 6408 From: Geneva, Illinois Joined: Member Rating: 5.1 |
Dr Adequate writes:
Ontological status is an aspect of ontology.Could we at least fill in the ontological status of math as an afterthought? Ontology is a branch of metaphysics. Metaphysics is nonsense. But then, I am agnostic toward analytic philosophy (the religion of the academy).
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AnswersInGenitals Member (Idle past 151 days) Posts: 673 Joined: |
That the biggest possible circle ever wouldn't allow us to scientifically measure the pi ratio down to the 50th decimal place... That biggest possible circle wouldn't allow us to measure pi at all since the circumference/diameter of a circle only equals pi in a flat (Euclidian) space, which our universe isn't on a large scale. For example, on the surface of a sphere the largest possible circle has a C/D = 2. Thus, C/D = pi is a very contingent result, i. e., is true of certain realities and not of others. On the other hand, even if we had never stumbled on the fact that C/D = pi in the locally flat part of the universe we live in we would have still discovered pi, and been able to calculate it to arbitrary precision in other contexts. For example: 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ......... = pi/4. This is true anywhere in our universe and anywhere in any universe.
...but we can still calculate what it(pi) precisely is shows that not every objective thing can be scientifically investigated. The precision with which we can calculate (or measure) something has absolutely nothing to do with its ability to be subjected to scientific investigation. Or am I misunderstanding you.
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cavediver Member (Idle past 3643 days) Posts: 4129 From: UK Joined: |
how can we know that the integers are a subset of the reals? An excellent question - I think we see clues to an intimate connection in my previously mentioned winding numbers - think of the Cauchy residue formula and the Gauss Bonnet formula. Here the very continuum based geometry forces upon us the integers. But I'm drifting asleep, so this will have to be continued tomorrow. Good night!
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AnswersInGenitals Member (Idle past 151 days) Posts: 673 Joined: |
We get the integers by an idealization of counting. It is a method where we start with one and build up combinatorially. We get the reals from geometry. We think of a line as a continuum, and we divide it up. It isn't obvious that these give rise to the same numbers. But what if space and time are actually discrete, which they almost certainly are. Then all measurements, if done properly, would yield integer results similar to the way that a mass of real stuff can be stated as an approximate real number denoting weight or a precise integer denoting the precise number of molecules of the stuff.
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