Re: Daily "Check In" Thread For Us
Posted: Sun Mar 29, 2020 5:02 pm
Google confirms.
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https://www.gyroscopicinvesting.com/forum/viewtopic.php?t=10540
I know that Einstein's said that if observations didn't agree with his theory, that meant the observations are wrong.Smith1776 wrote: ↑Sun Mar 29, 2020 4:59 pmWell if you perfectly understand i then you should easily understand the use of the Ramanujan Summation.Libertarian666 wrote: ↑Sun Mar 29, 2020 4:55 pm
"[L]egitimate" and "divergent series" also don't belong in the same sentence without a negating qualifier.
But i is another matter. That is easily understood as being on a number line perpendicular to the normal one, and you don't need any divergent infinite series tricks to use it.
And of course it is also key to the "most beautiful equation", so I'll give it a pass on being "imaginary".
If these physics textbooks I'm looking at are wrong in using that result, then we ought to tell them.
Ok, I get it now.Libertarian666 wrote: ↑Sun Mar 29, 2020 5:08 pm You can get any result you want if you rearrange terms in a non-convergent infinite series: https://en.wikipedia.org/wiki/Riemann_series_theorem
Newtonian physics is not incorrect. If you use the formulas for general relativity in non-relativistic scenarios they simplify to Newton's formulas. They're 100% correct. Relativity theory is just an extension, not a correction.Libertarian666 wrote: ↑Sun Mar 29, 2020 5:04 pm
I know that Einstein's said that if observations didn't agree with his theory, that meant the observations are wrong.
But as someone who isn't Einstein, it's obvious to me that if a theory comes up with an obviously incorrect result such as the Ramanujan Summation does, then the theory is incorrect.
That doesn't mean it doesn't have any value. To take the most famous example, we know that Newtonian physics is incorrect, but it is still very useful in many applications. You just have to know where it produces incorrect results and not try to use it there.
Newtonian physics is in fact incorrect in all cases. It just appears to be correct in everyday macroscopic life because we can't detect the differences between it and real physics. With sufficiently precise instruments (barring quantum limitations) that is not true.Smith1776 wrote: ↑Sun Mar 29, 2020 5:12 pmNewtonian physics is not incorrect. If you use the formulas for general relativity in non-relativistic scenarios they simplify to Newton's formulas. They're 100% correct. Relativity theory is just an extension, not a correction.Libertarian666 wrote: ↑Sun Mar 29, 2020 5:04 pm
I know that Einstein's said that if observations didn't agree with his theory, that meant the observations are wrong.
But as someone who isn't Einstein, it's obvious to me that if a theory comes up with an obviously incorrect result such as the Ramanujan Summation does, then the theory is incorrect.
That doesn't mean it doesn't have any value. To take the most famous example, we know that Newtonian physics is incorrect, but it is still very useful in many applications. You just have to know where it produces incorrect results and not try to use it there.
That is true for some values of "=" and "sum".Libertarian666 wrote: ↑Sun Mar 29, 2020 5:04 pm I already extended an olive branch by saying you're correct in saying that the sum of all positive integers isn't -1/12 in traditional maths. Why can't we do the same by just admitting it has legitimate uses in theoretical maths? I mean, there is literally coursework on this stuff being handed out as university assignments.
Now we're in Newtonian physics is incorrect territory.Libertarian666 wrote: ↑Sun Mar 29, 2020 5:22 pm
Newtonian physics is in fact incorrect in all cases. It just appears to be correct in everyday macroscopic life because we can't detect the differences between it and real physics. With sufficiently precise instruments (barring quantum limitations) that is not true.
No problem. Good luck with your homework.Smith1776 wrote: ↑Sun Mar 29, 2020 5:30 pmNow we're in Newtonian physics is incorrect territory.Libertarian666 wrote: ↑Sun Mar 29, 2020 5:22 pm
Newtonian physics is in fact incorrect in all cases. It just appears to be correct in everyday macroscopic life because we can't detect the differences between it and real physics. With sufficiently precise instruments (barring quantum limitations) that is not true.
Holy moly we're off on the deep end. I see what I'm dealing with here. No more productive conversation is going to be had on this topic, so I won't be responding anymore to this particular subject.
I'll just be getting back to homework with infinite sequences, series, and yes, the Ramanujan Summation.
We saw that movie on an airplane. Very interesting!
Yes, that's the way I first heard it, also. But it was from my older brother's LP, not a CD. Here's the script:Xan wrote: ↑Sun Mar 29, 2020 9:09 pm This is abuse!
https://www.youtube.com/watch?v=ohDB5gbtaEQ
Edit: oh. The version I'm more familiar with from a CD has the fellow walking into the wrong room, which turns out to be "abuse" where he just gets yelled at. Apparently that wasn't part of the original TV sketch.
I've seen that. It's so great. And his voice hasn't changed!Mountaineer wrote: ↑Mon Mar 30, 2020 6:29 am ...
Neil diamond is posting a video of himself singing “Sweet Caroline" with the lyrics…
”hands…washing hands…don’t touch me…I won’t touch you…"
I hope this doesn't sound snide, because I don't mean it that way at all, I'm just genuinely curious.
It is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.stuper1 wrote: ↑Mon Mar 30, 2020 11:45 amBy the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.
You say the magic is really in i, but that's not so clear to me. We defined i as the square root of -1. We defined pi as the ratio of circumference to diameter. We defined e as the natural logarithm of 1. To me, it seems that we "invented" all of these things, or maybe a better word is "discovered". Then, the magic is that when they are combined in a certain way, which nobody had even thought of when the original definitions were made, instead of getting a nonsense irrational-number result like say 4.6239281394821..., we get an absolute whole number of -1.Xan wrote: ↑Mon Mar 30, 2020 11:57 amIt is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.stuper1 wrote: ↑Mon Mar 30, 2020 11:45 amBy the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.
As Kronecker said, "God made the natural numbers; all else is the work of man."
pi - discoveredstuper1 wrote: ↑Mon Mar 30, 2020 2:43 pmYou say the magic is really in i, but that's not so clear to me. We defined i as the square root of -1. We defined pi as the ratio of circumference to diameter. We defined e as the natural logarithm of 1. To me, it seems that we "invented" all of these things, or maybe a better word is "discovered". Then, the magic is that when they are combined in a certain way, which nobody had even thought of when the original definitions were made, instead of getting a nonsense irrational-number result like say 4.6239281394821..., we get an absolute whole number of -1.Xan wrote: ↑Mon Mar 30, 2020 11:57 amIt is a fascinating thing, but really the magic is in i. The square root of negative 1 is at least as much of an abstraction as an infinite series. We basically invented it and defined its behavior such that e^iπ = -1.stuper1 wrote: ↑Mon Mar 30, 2020 11:45 amBy the way, that math equation blows my mind every time I look at it. It's quite amazing to thing that two irrational numbers could do something like that. Written in longhand it is something like (2.71828...) to the power of i times (3.14159...) is equal to -1. It's quite trippy.
As Kronecker said, "God made the natural numbers; all else is the work of man."