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fun with math

#1 User is offline   y66 

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Posted 2018-September-06, 06:33

The clarity of the example of using the Monte Carlo method to estimate pi in the overview section of this wikipedia article blew my mind.
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#2 User is offline   The_Badger 

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Posted 2018-September-06, 09:33

View Posty66, on 2018-September-06, 06:33, said:

The clarity of the example of using the Monte Carlo method to estimate pi in the overview section of this wikipedia article blew my mind.


This is dangerous territory to me, given that I have been recently finally diagnosed with autistic and OCD tendencies. Thankfully as I get older I have become less curious about articles such as this: once upon a time I would want to know (on some level) what every bit of it meant.

But it does illustrate how brilliant mathematics is. Thanks for posting.
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#3 User is online   kenberg 

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Posted 2018-September-06, 09:47

View Posty66, on 2018-September-06, 06:33, said:

The clarity of the example of using the Monte Carlo method to estimate pi in the overview section of this wikipedia article blew my mind.


I am not sure if you are being serious here. I find it not well written at all. If a circle is inscribed in a square then the ratio of the area of the circle to the area of the square is pi/4. Why speak of a quadrant? Even if we understand that a quadrant is a quarter-circle (and surely there are other uses of the term), why bother? And then, to get pi/4, we need to divide the area of this quarter circle by the area of a quarter square, and I don't see them saying that. They say "the ratio of their areas". "their"?
And "uniformly scatter"? "uniformly" and "scatter" at least appear, at first glance, to be contradictory. I know what is meant, but I wouldn't call it clear.

But while we are on math:
I was watching PBS Newshour last night and there was a brief segement about the crash of the Rial. Judy Woodruff explained that the Rial had lost a quarter of its value since Saturday and then said that is down 140% since the US quit the Iran nuclear deal. Look at around minute 34 of https://www.google.c...ent=firefox-b-1

I am trying to think of what it could mean for a currency to be down 140%. It would seem to mean that if you paid in Rials then, after paying, you would still owe 40% more than you did before paying. Or something like that. Is there any financial sense in which a currency can lose 140% of its value? I would think that it would be completely worthless after losing 100% of its value. Where do we go after that? I guess "down 140%" maybe doesn't mean "lost 140% of its value". But then what does it mean?
Ken
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#4 User is online   kenberg 

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Posted 2018-September-06, 10:01

View PostThe_Badger, on 2018-September-06, 09:33, said:

This is dangerous territory to me, given that I have been recently finally diagnosed with autistic and OCD tendencies. Thankfully as I get older I have become less curious about articles such as this: once upon a time I would want to know (on some level) what every bit of it meant.

But it does illustrate how brilliant mathematics is. Thanks for posting.


Not that you have asked me, but some free advice that I feel strongly about. Don't let a diagnosis define you.

I am 79, and from time to time I must remind myself as well as doctors not to rely on this to explain things. Of course it matters, but still, one thing at a time. I have jumped my last jack, the knees object, and I walk instead of jog. And yes, I sometimes screw up the play of a hand. But I sometimes screwed up the play of a hand when I was 40. I expect myself to play it right.

Anyway, just a thought.

Ken
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#5 User is offline   y66 

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Posted 2018-September-06, 13:03

View Postkenberg, on 2018-September-06, 09:47, said:

I am not sure if you are being serious here. I find it not well written at all. If a circle is inscribed in a square then the ratio of the area of the circle to the area of the square is pi/4. Why speak of a quadrant? Even if we understand that a quadrant is a quarter-circle (and surely there are other uses of the term), why bother? And then, to get pi/4, we need to divide the area of this quarter circle by the area of a quarter square, and I don't see them saying that. They say "the ratio of their areas". "their"?
And "uniformly scatter"? "uniformly" and "scatter" at least appear, at first glance, to be contradictory. I know what is meant, but I wouldn't call it clear.

But while we are on math:
I was watching PBS Newshour last night and there was a brief segement about the crash of the Rial. Judy Woodruff explained that the Rial had lost a quarter of its value since Saturday and then said that is down 140% since the US quit the Iran nuclear deal. Look at around minute 34 of https://www.google.c...ent=firefox-b-1

I am trying to think of what it could mean for a currency to be down 140%. It would seem to mean that if you paid in Rials then, after paying, you would still owe 40% more than you did before paying. Or something like that. Is there any financial sense in which a currency can lose 140% of its value? I would think that it would be completely worthless after losing 100% of its value. Where do we go after that? I guess "down 140%" maybe doesn't mean "lost 140% of its value". But then what does it mean?

I'm serious. I think the author chose a quadrant (which was confusing to me, but he did link to an explanation that cleared it up immediately) because it simplifies the example: generated data points are either inside or outside the inscribed quarter circle if their distance from the origin is <= 1 or > 1. When I explained this example to my wife at the dinner table, she got it instantly -- the relationship between pi, the area of the quadrant and the area of the square, and the point of the example, which is to help readers understand what "Monte Carlo method" means.
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#6 User is offline   barmar 

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Posted 2018-September-06, 14:16

View Postkenberg, on 2018-September-06, 09:47, said:

But while we are on math:
I was watching PBS Newshour last night and there was a brief segement about the crash of the Rial. Judy Woodruff explained that the Rial had lost a quarter of its value since Saturday and then said that is down 140% since the US quit the Iran nuclear deal. Look at around minute 34 of https://www.google.c...ent=firefox-b-1

That link just goes to a Google search result, not a specific video. But many of the search results mention the same 140% drop.

Quote

I am trying to think of what it could mean for a currency to be down 140%. It would seem to mean that if you paid in Rials then, after paying, you would still owe 40% more than you did before paying. Or something like that. Is there any financial sense in which a currency can lose 140% of its value? I would think that it would be completely worthless after losing 100% of its value. Where do we go after that? I guess "down 140%" maybe doesn't mean "lost 140% of its value". But then what does it mean?

Percentages can be used in a number of different ways, and sometimes non-mathematicians get confused by them.

For instance, if something increased from 10 to 15, we can say that the new value is 150% of the previous value, or that it increased by 50%. However, if it drops from 15 to 10, the new value is 67% of the old, and the decrease was by 33%. Notice the asymmetry there -- the same difference of 5 is a different percentage depending on what you're measuring it from. But innumerate people might get these things confused, and call a drop by 5 a 150% drop because an increase by 5 from 10 would be 150% of the old value.

All that said, I can't figure out where this 140% number is coming from. https://www.xe.com/c...&to=IRR&view=1Y has a historical chart of the Rial-to-US$ conversion rate over the past year. On April 11 the Rial dropped precipitously, from 37874 Rial to the US$ to 42016; this was about an 11% drop in value. But that wasn't when we withdrew from the nuclear deal, that happened on May 8. The current exchange rate is about 44000, so it's now down 16% from April 11.

However, if we go back to when Trump was inaugurated, the Rial was about 32400 to the dollar. From then, the drop in value is about 36%, which isn't far from 40%. If someone translated "down by 40%" to "value is 140% lower", we would get that quoted number.

#7 User is online   kenberg 

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Posted 2018-September-06, 15:34

Sorry about the link. You can get to the broadcast by putting in PBS Newshour. It allows you to listen to the entire show, and you can drag through to get to minute 33, as with watching something on youtube.

My guess on how this 140% could come about: I'll make up an example. Suppose a shirt is on sale for 20% off the marked price and suppose you have a coupon that takes 10% off from the purchase price at checkout. It's not hard to imagine that someone thinks the price is now 30% off the original rather than the actual 28% off. [For anyone wondering, a $100 shirt is now marked down to $80 and the coupon gives you another $8 off at checkout, so you pay $72 for this $100 shirt.]

So, for the Rial, suppose someone looked up a chart and for each week it gives the drop in value of the Rial as a percentage of its value at the start of the week. You can imagine someone adding up the percentage drops and finding that they total 140%.

I don't rule out the possibility of the 140 being some legit number, but I cannot imagine what it would be.

Judy Woodruff, although not a mathematician (so I assume), strikes me as both smart and aware. I was a little surprised that after reading this figure she didn't do something like "Hey what? Joe, check this figure for me".

And so, inevitably, education arises. Imo we are doing a pretty good job of providing good students with good opportunity. AP calculus classes are in a great many high schools. But I am not so sure we are doing better, maybe we are doing worse, than in my childhood when it comes to helping those who are not particularly mathematically inclined to have a basic grasp. I would hope that a normal 8th grader would say "What? How can a currency decline in value by 140% ?" If this has some meaning, I would like to learn it.
Ken
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#8 User is online   hrothgar 

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Posted 2018-September-06, 16:46

If you like this example, I recommend googling Buffon's needle.

Much less intuitive, but equally cool...
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#9 User is online   johnu 

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Posted 2018-September-06, 19:07

View Postkenberg, on 2018-September-06, 15:34, said:

I would hope that a normal 8th grader would say "What? How can a currency decline in value by 140% ?" If this has some meaning, I would like to learn it.


Maybe it was a decline of 140% of the current value, not the original value?

or is currently 41.67% ( = 100/240) of the original value. Certainly an awkward way to describe the situation if that was the intent.
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#10 User is online   smerriman 

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Posted 2018-September-06, 20:01

I suspect the 140% might make more sense in the context of this tweet:

https://twitter.com/...6456071?lang=en

Namely, that the price of a US dollar has gone up by 140% over that time, vs a 140% decrease in value.
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#11 User is online   kenberg 

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Posted 2018-September-06, 20:08

View Postsmerriman, on 2018-September-06, 20:01, said:

I suspect the 140% might make more sense in the context of this tweet:

https://twitter.com/...6456071?lang=en

Namely, that the price of a US dollar has gone up by 140% over that time, vs a 140% decrease in value.



That does seem to be it. When the cost of something increases by 140% we don't, or at least I don't, say that the value of my money has decreased by 140%, but apparently that's what was intended.

This would mean that the value of the dollar compared to the rial is ow 2.4 times what it was a year ago, so the value of the rial compared to the dollar is 1/2.4, or about 0.42 the value that it had a year ago. Usually this is expressed as a drop of 58% of its value. For example if a stock that was once priced at $100 is now priced at $42, we say the stock has lost 58 of 100 dollars, or 58%.

We of course could say that previously it took 1 share of stock to equal $100, and now it would take 2.4 shares of stock to equal $100, and so the value of the stock has declined by 140% but certainly that is not standard and it seems odd.Usually, whether it is a house or a stock, we look at what the price was in dollars, we look at what the price is in dollars, we take the change in price and divide it by the original price. and use this to express percentage appreciation or depreciation. Of course we do not have to measure the value of a rial, or anything, in dollars, but as long as we decide to measure the value of a rial by comparing it with the dollar, it seems to me we should use the same approach as we do for a house or a stock.
Ken
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