<p>(Don't vote on this; this is just my comment which is too long)</p>

<p>The Riemann-Zeta function, which is a general case for the Ramanujan sum, has many un-intuitive and baffling properties such as:</p>

<ul>
<li>having no closed-form solution</li>
<li>not being solvable with linear and stable methods</li>
</ul>

<p>The first roughly means that you need an infinite number of operations to expand out the actual Riemann-Zeta function. The second roughly means 0 is no longer an additive identity and/or associativity of addition breaks down. These things combined mean that you're gonna have weird issues treating infinite sums as if they were finite sums where you can do EZ-PZ operations with. It's almost as if you have to define the very concept of infinity as two separate, contradicting definitions.</p>

<p>Treating infinite sums as finite sums could be interesting in theoretical topics. But with my money? I don't think my accountant would appreciate me going in and saying that my finite sum of money can be treated as an infinite sum of money.</p>

CC BY-SA 3.0
2017-06-02T18:38:21.087Z
2017-06-02T18:38:21.087Z
Kitsune Cavalry
<p>In <a href="http://www.youtube.com/watch?v=w-I6XTVZXww" rel="nofollow noreferrer">this youtube video</a>  the speakers present a line of reasoning as to why
$$
 \sum_{n=1}^\infty  n =  -\frac{1}{12}
$$</p>

<p>in other words</p>

<p>$$1+2+3+\cdots=-\frac{1}{12}$$
and my brain still hurts.  It doesn't make any sense but it was also shown by other mathematicians like Euler.</p>

<p>They said that this answer shows itself in quantum physics in explaining the <a href="http://en.wikipedia.org/wiki/Casimir_effect" rel="nofollow noreferrer">Casimir effect</a> and it has a role in explaining why there are 26 dimensions in string theory.</p>

<p>But, I don't think we need to delve into quantum physics and string theory to find examples of phenomena where we get negative results for positive infinite sums.  The practically infinite sum of money, time, and effort to put a child through school and college, then the negative result of said child unable to obtain gainful employment. Economics immediately came to mind.  I did a google search on this but nothing relevant came up.</p>

<p>Can the Ramanujan sum be used to explain unexpected outcomes in macro-economics?
For example: 
return on investment for government spending</p>

<p>student debt for college education</p>

CC BY-SA 3.0
2017-06-02T13:48:25.730Z
You are way out of context here. This famous sum you talk about is intimately related to complex numbers and the Riemann zeta function. These topics are usually dealt with in complex analysis and bear hardly any economic relevance. Also, your question has nothing to do with government-debt or government-spending, so please don't include those tags.
Taufi
CC BY-SA 3.0
2017-06-02T14:00:21.847Z
If it is true and proven to be true then it must be relevant in all contexts.
0tyranny0poverty
CC BY-SA 3.0
2017-06-02T14:19:03.390Z
And why do you think that the return on investment of government spending is negative, to begin with?
Alecos Papadopoulos
CC BY-SA 3.0
2017-06-02T14:51:00.603Z
I think to argue that e.g. the mathematics of quantum mechanics are relevant in the social sciences on the basis of its being true is absurd. Again, the presented mathematical result is put out of context to elicit astonishment. I would recommend that you study the theorems behind that idea. I think you will quickly realize that there are hardly any applications in economics for this level of mathematics.
Taufi
CC BY-SA 3.0
2017-06-02T15:06:26.993Z
I'm voting to close this question as off-topic because it's not about economics. It's nonsense based on a misunderstanding
410 gone
CC BY-SA 3.0
2017-06-02T15:06:51.857Z
I'm voting to close this question as off-topic because it does not seem to have anything to do with economics beyond asking "does this have anything do with economics?"
Giskard
CC BY-SA 3.0
2017-06-02T15:27:25.623Z
@Alecos Papadopoulos  Obamacare? 'Defense' spending?
0tyranny0poverty
CC BY-SA 3.0
2017-06-02T15:38:39.797Z
Please check economy-wide statistics about loss of productivity due to health issues. Defense spending safeguards assets and also muscles economic expansion abroad. In general government spending creates positive externalities for the private sector, so returns can certainly be positive  in principle  (and this has nothing to do with who collects the returns - which is a distributional issue).
Alecos Papadopoulos
<mathematical-economics>
Can Ramanujan Sum : 1+2+3+4+5+... = -1/12 be used to explain some results in macro-economics?
0tyranny0poverty
# Can Ramanujan Sum : 1+2+3+4+5+... = -1/12 be used to explain some results in macro-economics?

(Asked by: username_0 on 2017-06-02)

In [this youtube video](http://www.youtube.com/watch?v=w-I6XTVZXww) the speakers present a line of reasoning as to why
$$
\sum\_{n=1}^\infty n = -\frac{1}{12}
$$

in other words

$$1+2+3+\cdots=-\frac{1}{12}$$
and my brain still hurts. It doesn't make any sense but it was also shown by other mathematicians like Euler.

They said that this answer shows itself in quantum physics in explaining the [Casimir effect](http://en.wikipedia.org/wiki/Casimir_effect) and it has a role in explaining why there are 26 dimensions in string theory.

But, I don't think we need to delve into quantum physics and string theory to find examples of phenomena where we get negative results for positive infinite sums. The practically infinite sum of money, time, and effort to put a child through school and college, then the negative result of said child unable to obtain gainful employment. Economics immediately came to mind. I did a google search on this but nothing relevant came up.

Can the Ramanujan sum be used to explain unexpected outcomes in macro-economics?
For example:
return on investment for government spending

student debt for college education

**Tags:** mathematical-economics

> **Comments:**
> **username_1**: You are way out of context here. This famous sum you talk about is intimately related to complex numbers and the Riemann zeta function. These topics are usually dealt with in complex analysis and bear hardly any economic relevance. Also, your question has nothing to do with government-debt or government-spending, so please don't include those tags.  
> **username_0**: If it is true and proven to be true then it must be relevant in all contexts.  
> **username_2**: And why do you think that the return on investment of government spending is negative, to begin with?  
> **username_1**: I think to argue that e.g. the mathematics of quantum mechanics are relevant in the social sciences on the basis of its being true is absurd. Again, the presented mathematical result is put out of context to elicit astonishment. I would recommend that you study the theorems behind that idea. I think you will quickly realize that there are hardly any applications in economics for this level of mathematics.  
> **username_3**: I'm voting to close this question as off-topic because it's not about economics. It's nonsense based on a misunderstanding  
> **username_4**: I'm voting to close this question as off-topic because it does not seem to have anything to do with economics beyond asking "does this have anything do with economics?"  
> **username_0**: @username_2  Obamacare? 'Defense' spending?  
> **username_2**: Please check economy-wide statistics about loss of productivity due to health issues. Defense spending safeguards assets and also muscles economic expansion abroad. In general government spending creates positive externalities for the private sector, so returns can certainly be positive  in principle  (and this has nothing to do with who collects the returns - which is a distributional issue).  

---

## 1 answers

### Answer by username_5 on 2017-06-02. Score: 1

(Don't vote on this; this is just my comment which is too long)

The Riemann-Zeta function, which is a general case for the Ramanujan sum, has many un-intuitive and baffling properties such as:

* having no closed-form solution
* not being solvable with linear and stable methods

The first roughly means that you need an infinite number of operations to expand out the actual Riemann-Zeta function. The second roughly means 0 is no longer an additive identity and/or associativity of addition breaks down. These things combined mean that you're gonna have weird issues treating infinite sums as if they were finite sums where you can do EZ-PZ operations with. It's almost as if you have to define the very concept of infinity as two separate, contradicting definitions.

Treating infinite sums as finite sums could be interesting in theoretical topics. But with my money? I don't think my accountant would appreciate me going in and saying that my finite sum of money can be treated as an infinite sum of money.


---

