FTR, I don't see how platonism answers my question about pi better than non-platonist views. It's just pure curiosity for me. And yes, this is a bit of a deviation from the OP topic, but since this is still about maths, whatever. I will get to reading your response soon, polymath, but I do want to try and see if I can answer Rahn's questions first just in the hopes that maybe I can make more clear my state of mind regarding this.
My answer to this is "yes and no". While there are certainly infinite digits to 1/3, I can sort of see a clear enough pattern here and appreciate that, by splitting the set of real numbers between 0 and 1 into three equal subsets, the cutting points are going to have to be values with infinite digits to allow for that, but there is nevertheless an "orderliness" to it anyway, since it's the same value occupying the decimal values and when you look at 2/3, it's 0.666666... and 3/3 = 0.999999 (which is also 1), pattern here being that the decimal value is jumping by 3.
Perhaps for you this understanding should easily be applied to numbers like pi, but I don't see it the way you seem to be seeing it.
I didn't say it's not beautiful. I find such numbers very fascinating actually but won't say no to the thinking that it nevertheless appears to contain random sequences of digits that seem to have no clear pattern to them. That's what I mean by "messy".
No, I don't find it strange that all four sides of a square are equal in length. The square, by definition, must have four sides equal in length. The concept of a square, while based initially on observations of approximate squares, is easily defined as such. With pi, it's not like people historically made basic observations and were like "hey, let's equate pi to some complicated value just because it's intuitive". Rather, pi had to be discovered via certain calculations and then over time (with further understanding and technology) refinements continue to be made to the value to make it more and more precise. This is the bit that's fascinating me, that a number discovered in that way and is key to many of the problems solved just happens to be this really "messy" (to me) sort of number.
To be clear, I am not saying there is any hard problem here. I do suspect the answer lies in the definitions being used ultimately. Something about them seem to be leading to such strange (to me) numbers, but I don't know what the specific explanation(s) is/are or whether I am even qualified to ever comprehend the answers.
Ok, time to now read and try to digested what polymath has responded with.
(June 16, 2020 at 7:44 am)Rahn127 Wrote: Do you find 1/3 to be messy ?
If you cut a pie into 3 equal pieces, does each person have 1 piece of pie or do they have .3333333333333333333333333 pieces of the whole pie ?
My answer to this is "yes and no". While there are certainly infinite digits to 1/3, I can sort of see a clear enough pattern here and appreciate that, by splitting the set of real numbers between 0 and 1 into three equal subsets, the cutting points are going to have to be values with infinite digits to allow for that, but there is nevertheless an "orderliness" to it anyway, since it's the same value occupying the decimal values and when you look at 2/3, it's 0.666666... and 3/3 = 0.999999 (which is also 1), pattern here being that the decimal value is jumping by 3.
Perhaps for you this understanding should easily be applied to numbers like pi, but I don't see it the way you seem to be seeing it.
Quote:Pi isn't messy in my opinion. It's complex. It's beautiful.
It contains the words to every novel ever written.
(That last one may not be true, but it sounds good)
I didn't say it's not beautiful. I find such numbers very fascinating actually but won't say no to the thinking that it nevertheless appears to contain random sequences of digits that seem to have no clear pattern to them. That's what I mean by "messy".
Quote:Also do you find it strange that all four sides of a square are equal in length ? I mean what are the odds that all four sides just happen to be equal ? That sounds like it was designed by some higher power to be that way. What things can you name in nature are exactly the same length on all four sides ?
No, I don't find it strange that all four sides of a square are equal in length. The square, by definition, must have four sides equal in length. The concept of a square, while based initially on observations of approximate squares, is easily defined as such. With pi, it's not like people historically made basic observations and were like "hey, let's equate pi to some complicated value just because it's intuitive". Rather, pi had to be discovered via certain calculations and then over time (with further understanding and technology) refinements continue to be made to the value to make it more and more precise. This is the bit that's fascinating me, that a number discovered in that way and is key to many of the problems solved just happens to be this really "messy" (to me) sort of number.
To be clear, I am not saying there is any hard problem here. I do suspect the answer lies in the definitions being used ultimately. Something about them seem to be leading to such strange (to me) numbers, but I don't know what the specific explanation(s) is/are or whether I am even qualified to ever comprehend the answers.
Ok, time to now read and try to digested what polymath has responded with.
