Daily "Check In" Thread For Us

[Kriegsspiel]

Google confirms.

[Libertarian666]

"[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".

Well if you perfectly understand i then you should easily understand the use of the Ramanujan Summation.

If these physics textbooks I'm looking at are wrong in using that result, then we ought to tell them.

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.

[Libertarian666]

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

[Libertarian666]

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

Ok, I get it now.
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/

[Smith1776]

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 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.

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.

[Libertarian666]

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 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.

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.

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.

That is true for some values of "=" and "sum".

And I'm a billionaire for some values of "billion".

[Smith1776]

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.

Now we're in Newtonian physics is incorrect territory.

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.

[Libertarian666]

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.

Now we're in Newtonian physics is incorrect territory.

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.

No problem. Good luck with your homework.

[stuper1]

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.

[CT-Scott]

Is this the right room for an argument?

[Maddy]

Beats me what this room is for.

[Xan]

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.

[Smith1776]

I've been eating breakfast for dinner every night this week because I can.

Argue with that.

[bedraggled]

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.

[Libertarian666]

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.

We saw that movie on an airplane. Very interesting!

[Libertarian666]

Beats me what this room is for.

https://www.youtube.com/watch?v=nFkazjodpeQ

[CT-Scott]

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.

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:
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

[Mountaineer]

Good morning fellow cats and dogs. I'm still here. Here is something to lighten us up a bit:

Personal Ad: Single man w/TP seeks single woman w/hand sanitizer.

How long is this social distancing supposed to last? My husband keeps trying to get into the house.

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…"

[dualstow]

...

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've seen that. It's so great. And his voice hasn't changed!

[Smith1776]

I finished my math assignment.

I think I've developed PTSD.

[stuper1]

I finished my math assignment.

I think I've developed PTSD.

I hope this doesn't sound snide, because I don't mean it that way at all, I'm just genuinely curious.

Why does someone who doesn't like math have a beautiful math equation as his signature line?

By the way, that math equation blows my mind every time I look at it. It's quite amazing to think 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.

Also, in one of your earlier posts you said that "infinite series suck". I could be wrong, but I'm pretty sure that there is no way to prove that beautiful math equation without using infinite series, so obviously they are quite useful.

[Mountaineer]

I finished my math assignment.

I think I've developed PTSD.

PTMA (post traumatic math assignment).

[Xan]

By 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.

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.

As Kronecker said, "God made the natural numbers; all else is the work of man."

[stuper1]

By 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.

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.

As Kronecker said, "God made the natural numbers; all else is the work of man."

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.

[Mountaineer]

By 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.

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.

As Kronecker said, "God made the natural numbers; all else is the work of man."

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.

pi - discovered

e - iffy (but not sure, probably discovered)

i - invented

mo - my opinion to the nth power where n = infinity