Libertarian666 wrote: ↑Sun Mar 29, 2020 4:46 pmOk, then you pay me an amount of money equal to each positive integer from 1 to infinity, and I'll pay you -1/12th of a dollar, and we'll call it square.Smith1776 wrote: ↑Sun Mar 29, 2020 4:10 pmThe idea that the sum of all positive integers from 1 to infinity equaling -1/12 isn't just hocus pocus though. It has structure in the form of the Ramanujan Summation.Libertarian666 wrote: ↑Sun Mar 29, 2020 9:07 am
No it isn't true. It's an excellent example of why you can't treat "infinite series" like actual things.
Again, they are abstractions, not reality.
Here's a simpler example which is equally valid:
Assume that we have two variables a and b, and that: a = b
Multiply both sides by a to get: a2 = ab
Subtract b2 from both sides to get: a2 - b2 = ab - b2
This is the tricky part: Factor the left side (using FOIL from algebra) to get (a + b)(a - b) and factor out b from the right side to get b(a - b). If you're not sure how FOIL or factoring works, don't worry—you can check that this all works by multiplying everything out to see that it matches. The end result is that our equation has become: (a + b)(a - b) = b(a - b)
Since (a - b) appears on both sides, we can cancel it to get: a + b = b
Since a = b (that's the assumption we started with), we can substitute b in for a to get: b + b = b
Combining the two terms on the left gives us: 2b = b
Since b appears on both sides, we can divide through by b to get: 2 = 1
The Ramanujan Summation has practical applications and is used in real world physics calculations, particularly in string theory.
Given that it has legitimate real world use in physics calculations such as the Casimir Effect, it's fair to say it's an actual "thing."
Also note that "real world physics calculations" and "string theory" don't really belong in the same sentence without a negating qualifier...
Daily "Check In" Thread For Us
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Re: Daily "Check In" Thread For Us
DNA has its own language (code), and language requires intelligence. There is no known mechanism by which matter can give birth to information, let alone language. It is unreasonable to believe the world could have happened by chance.
Re: Daily "Check In" Thread For Us
Haha but I can't though! Since infinity is a process and not a number. Which of course is what the whole thing relies on.Libertarian666 wrote: ↑Sun Mar 29, 2020 4:46 pm
Ok, then you pay me an amount of money equal to each positive integer from 1 to infinity, and I'll pay you -1/12th of a dollar, and we'll call it square.
Also note that "real world physics calculations" and "string theory" don't really belong in the same sentence without a negating qualifier...
Joking aside, yes, as I posted just above, you can't assign -1/12 to the sum like 1 + 1 = 2. You're totally right in that regard. I am just pointing out it's a legitimate way to work with divergent series in a similar vein of how we work with imaginary numbers like the square root of -1.
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Re: Daily "Check In" Thread For Us
Well, it's a stretch to say they're deceiving the audience, it's just highly theoretical and too much to have in a video for the laymen.Libertarian666 wrote: ↑Sun Mar 29, 2020 4:48 pm
A. It's "sleight of hand".
B. If you have to use sleight of hand, that means you are deceiving the audience.
Q. E. D.
EDIT: and yes, my bad for the typo.
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Re: Daily "Check In" Thread For Us
"[L]egitimate" and "divergent series" also don't belong in the same sentence without a negating qualifier.Smith1776 wrote: ↑Sun Mar 29, 2020 4:51 pmHaha but I can't though! Since infinity is a process and not a number. Which of course is what the whole thing relies on.Libertarian666 wrote: ↑Sun Mar 29, 2020 4:46 pm
Ok, then you pay me an amount of money equal to each positive integer from 1 to infinity, and I'll pay you -1/12th of a dollar, and we'll call it square.
Also note that "real world physics calculations" and "string theory" don't really belong in the same sentence without a negating qualifier...
Joking aside, yes, as I posted just above, you can't assign -1/12 to the sum like 1 + 1 = 2. You're totally right in that regard. I am just pointing out it's a legitimate way to work with divergent series in a similar vein of how we work with imaginary numbers like the square root of -1.
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".
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Re: Daily "Check In" Thread For Us
Ok, but if you're claiming to explain something to laypersons, it's important to say if it is oversimplified and not really a complete and valid explanation.Smith1776 wrote: ↑Sun Mar 29, 2020 4:52 pmWell, it's a stretch to say they're deceiving the audience, it's just highly theoretical and too much to have in a video for the laymen.Libertarian666 wrote: ↑Sun Mar 29, 2020 4:48 pm
A. It's "sleight of hand".
B. If you have to use sleight of hand, that means you are deceiving the audience.
Q. E. D.
EDIT: and yes, my bad for the typo.
I always do that in those circumstances.
Re: Daily "Check In" Thread For Us
Well 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.
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Re: Daily "Check In" Thread For Us
Yes, that's why I pointed out that they did a follow-up video.Libertarian666 wrote: ↑Sun Mar 29, 2020 4:57 pm
Ok, but if you're claiming to explain something to laypersons, it's important to say if it is oversimplified and not really a complete and valid explanation.
I always do that in those circumstances.
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Re: Daily "Check In" Thread For Us
That's the dude Stellan Skarsgard talks about in Good Will Hunting, I presume?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.
You there, Ephialtes. May you live forever.
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Re: Daily "Check In" Thread For Us
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.
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.
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Re: Daily "Check In" Thread For Us
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
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Re: Daily "Check In" Thread For Us
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
Ramanujan made up a new definition for summation, or for =.
If you're allowed to make up new definitions for existing words or symbols, you can prove anything you want.
https://www.smithsonianmag.com/smart-ne ... 180949559/
Last edited by Libertarian666 on Sun Mar 29, 2020 5:17 pm, edited 1 time in total.
Re: Daily "Check In" Thread For Us
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.
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.
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Re: Daily "Check In" Thread For Us
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.
And I'm a billionaire for some values of "billion".
Re: Daily "Check In" Thread For Us
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.
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.
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Re: Daily "Check In" Thread For Us
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.
Re: Daily "Check In" Thread For Us
For all of you COVID-19 isolationists, Ramanujan's story was told in an excellent book called "The Man Who Knew Infinity". The 2014 movie of the same name is okay, but sensationalizes a few things, and the book of course is much better.
Re: Daily "Check In" Thread For Us
Is this the right room for an argument?
Re: Daily "Check In" Thread For Us
Beats me what this room is for.
Re: Daily "Check In" Thread For Us
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.
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.
Re: Daily "Check In" Thread For Us
I've been eating breakfast for dinner every night this week because I can.
Argue with that.
Argue with that.
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Re: Daily "Check In" Thread For Us
Must I subscribe to or disprove any, or maybe several, aspects of Newtonian physics to report that I am not ill sitting here in Florida- per the title of this thread?
An abundance of your input much appreciated.
An abundance of your input much appreciated.
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Re: Daily "Check In" Thread For Us
We saw that movie on an airplane. Very interesting!
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Re: Daily "Check In" Thread For Us
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.
http://www.montypython.net/scripts/argument.php
...and for anyone who doesn't know what an LP is:
https://en.wikipedia.org/wiki/LP_record