Gyroscopic Investing

vnatale wrote: ↑Sat Mar 28, 2020 11:56 am ...
I no longer wanted to be a part of in any way supporting an industry that has proven to be so destructive to the lives of so many individuals and their families.

dualstow wrote: ↑Sat Mar 28, 2020 1:15 pm

vnatale wrote: ↑Sat Mar 28, 2020 11:56 am ...
I no longer wanted to be a part of in any way supporting an industry that has proven to be so destructive to the lives of so many individuals and their families.

You could probably say the same about the sugar industry.

Smith1776 wrote: ↑Sun Mar 29, 2020 5:41 am I am 90% of my way through finishing the last math assignment I will ever have to do... for the rest of my life!

By the way, infinite sequences and series suck. Like... a lot. Did you know that the sum of all positive integers from 1 to infinity is -1/12? Okay, fine, that's actually pretty interesting. Still, they suck. A lot.

Libertarian666 wrote: ↑Sun Mar 29, 2020 8:41 am

Smith1776 wrote: ↑Sun Mar 29, 2020 5:41 am I am 90% of my way through finishing the last math assignment I will ever have to do... for the rest of my life!

By the way, infinite sequences and series suck. Like... a lot. Did you know that the sum of all positive integers from 1 to infinity is -1/12? Okay, fine, that's actually pretty interesting. Still, they suck. A lot.

I'm pretty sure that isn't right. I suspect that is an example of how not to sum infinite series.

But of course there really isn't any such thing as an infinite series. That is just an abstraction that can be useful sometimes and wildly off-target other times.

Smith1776 wrote: ↑Sun Mar 29, 2020 8:53 am

Libertarian666 wrote: ↑Sun Mar 29, 2020 8:41 am

Smith1776 wrote: ↑Sun Mar 29, 2020 5:41 am I am 90% of my way through finishing the last math assignment I will ever have to do... for the rest of my life!

By the way, infinite sequences and series suck. Like... a lot. Did you know that the sum of all positive integers from 1 to infinity is -1/12? Okay, fine, that's actually pretty interesting. Still, they suck. A lot.

I'm pretty sure that isn't right. I suspect that is an example of how not to sum infinite series.

But of course there really isn't any such thing as an infinite series. That is just an abstraction that can be useful sometimes and wildly off-target other times.

It is unbelievable but true. I've been studying this section for a good while and so much of it still doesn't make sense to me.

https://medium.com/cantors-paradise/the ... cc23dea793

https://youtu.be/w-I6XTVZXww

The mathematician in the youtube video literally does the proof, and I still don't have my mind quite wrapped around it.

MangoMan wrote: ↑Sun Mar 29, 2020 9:13 am The whole thing is based on believing that 1-1+1-1+1-1+1-1......infinity = 1/2. Does it? Taking an average because you don't know when it ends seems suspect.

Mountaineer wrote: ↑Sun Mar 29, 2020 10:14 am I'm more into Schrödinger's cat. Should I have posted this in the Kat thread?

shekels wrote: ↑Sun Mar 29, 2020 10:56 am

Mountaineer wrote: ↑Sun Mar 29, 2020 10:14 am I'm more into Schrödinger's cat. Should I have posted this in the Kat thread?

I will just believe you did..

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

Smith1776 wrote: ↑Sun Mar 29, 2020 5:41 am I am 90% of my way through finishing the last math assignment I will ever have to do... for the rest of my life!

By the way, infinite sequences and series suck. Like... a lot. Did you know that the sum of all positive integers from 1 to infinity is -1/12? Okay, fine, that's actually pretty interesting. Still, they suck. A lot.

WiseOne wrote: ↑Sun Mar 29, 2020 4:22 pm Oh come on Smith....Taylor series and the rabbit & turtle race analogy are both pretty cool!

Smith1776 wrote: ↑Sun Mar 29, 2020 4:10 pm

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 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.

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."

Smith1776 wrote: ↑Sun Mar 29, 2020 4:45 pm

WiseOne wrote: ↑Sun Mar 29, 2020 4:22 pm Oh come on Smith....Taylor series and the rabbit & turtle race analogy are both pretty cool!

It's all indeed actually very fascinating, but I'm kind of glad that any math going forward is going to be optional.

For posterity: in defense of Numberphile's video, yes it's true that in traditional maths, you can't say that the sum of all natural numbers equals -1/12. They actually explain why they pulled their slight of hand in a follow up video. They needed the video to be simple enough for general audiences. https://youtu.be/8hgeIDY7We4

It's not "true" in the traditional sense as 1 + 1 = 2, but it's a perfectly legitimate value to assign to the sum for theoretical maths and string theory.

Libertarian666 wrote: ↑Sun Mar 29, 2020 4:46 pm

Smith1776 wrote: ↑Sun Mar 29, 2020 4:10 pm

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 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.

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."

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...

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...

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.

Smith1776 wrote: ↑Sun Mar 29, 2020 4:51 pm

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...

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.

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.

Smith1776 wrote: ↑Sun Mar 29, 2020 4:52 pm

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.

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.

EDIT: and yes, my bad for the typo.

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".

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.

Smith1776 wrote: ↑Sun Mar 29, 2020 4:59 pm

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".

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.