How much is a hill of beans worth?

[Jeff the Green]

I was listening to a radio report about the Middle East yesterday and one of the guests said something to the effect that a Bill of Rights without rule of law "isn't worth a hill of beans."

Which of course made me wonder what a hill of beans would be worth.

Problem 1: What is a hill, anyway?

This one's relatively easy (http://www.howitworksdaily.com/environment/when-does-a-hill-become-a-mountain/), actually. At least according to America, a hill is anything less than 300 meters high. On the other hand, the OED defines it as anything less than 600 meters high. We'll use both.


Problem 2: How big is a hill of beans?

For this we need to know the angle of repose (http://en.wikipedia.org/wiki/Angle_of_repose) for beans. This is the angle at the base of a cone formed by granules. This is a nice picture explaining it.

http://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Angleofrepose.png/220px-Angleofrepose.png

Thankfully, I do not have to measure this, as Benedito C. Benedetti and José T. Jorge have done it for me (http://spiru.cgahr.ksu.edu/proj/iwcspp/pdf2/5/1777.pdf). Depending on moisture content, the angle is about 33.8°.

The equation for volume (v) of a cone is v = ⅓πr2h. We know h (300-600 m), but what about r? Time for some trigonometry.

...SOH-CAH-TOA (www.mathwords.com/s/sohcahtoa.htm). Right.

So h/r = tan(33.8°). Rearranged, r = h/tan(33.8°). Plug that into our volume equation and we get v = πh3/tan2(33.8°). When h=300, this is 63,069,448 m3, and when h=600 this is 504,555,580 m3.


Problem 3: How much does this hill weigh?

Mercifully, this part involves no trigonometry, just a quick conversion from volume to mass. So we need the density of beans. Again, I don't have to measure this because someone already did (http://www.tacwebdesign.com/clients/oe/materials.shtml): 45 lbs./ft., or (since I despise Imperial units) 720.83 kg/m3.

So 63,069,448 m3 of beans weighs 45,462,000,000 kg = 45,462,000 tonnes and 504,555,580 m3 weighs 363,700,000,000 kg = 363,700,000 tonnes

Looked at another way, this is a quarter to two million adult blue whales.


Problem 4: How much is this hill worth?

Another quick conversion. The cheapest bulk pinto beans (http://www.alibaba.com/trade/search?fsb=y&IndexArea=product_en&CatId=&SearchText=pinto+bean) I could find were $600/tonne and the most expensive were $1700/tonne. So our 300 m hill is worth $27,277,000,000 to $77,285,000,000 and our 600 m hill is worth $218,220,000,000 to $618,290,000,000.

This is in the range of GDP of countries ranging from Bolivia to Saudi Arabia. Fewer than fifty countries could buy our larger hill at the lowest price with their entire GDP for a year, and only nineteen could buy it at the highest.


Conclusion

This is a stupid metaphor.

[Spanish_Paladin]

I am impressed!!.. But if we have such a quantity of beans perhaps we´ll overflow the market lowering it´s price dangerously near to zero :smallwink:

.... But yes, it seems a stupid metaphor :smallbiggrin:

[Spuddles]

Hahaha, love the math.

Even if you go with wet beans, which I always assumed the beans in the metaphor were, you only lose by a factor of 2-4, which is still in the tens/hundreds of billions of dollars.

However, you use the upper bound of "hill"- 300m to 600m is pretty big, for a hill.

Here's what I think of when I hear the word "hill":
Sillbury Hill (http://en.wikipedia.org/wiki/Silbury_Hill), 30m high.
http://upload.wikimedia.org/wikipedia/commons/thumb/a/ac/SilburyHill_gobeirne.jpg/300px-SilburyHill_gobeirne.jpg

That only has a volume of 126,707 cubic meters. That still comes out to $54 million as a lower bound, and about 3x that as an upper bound.

Not quite $600 billion, but still a fairly ludicrous amount of wealth.

[Jeff the Green]

However, you use the upper bound of "hill"- 300m to 600m is pretty big, for a hill.

Perhaps.

For an example of a hill just about at the maximum American height (300 m), see Mount Davidson (http://en.wikipedia.org/wiki/Mount_Davidson_(California)) in San Francisco.

http://www.outsidelands.org/images/mt-davidson-1954.jpg

I'm from a fairly hilly area and an hour away from two mountain ranges, so my definitions may be skewed, but I'd definitely call Mount Davidson a hill, not a mountain. Thirty meters is about nine stories and slightly larger than a bump for around here, though it has the advantage of being a very well-defined conical shape while our hills are much more rolling and ill-defined.

[Spiryt]

Pretty crazy that a hill out of beans would cost so much...

There are mounds of wasted, thrown away food out there after all...

[Spuddles]

Perhaps.

For an example of a hill just about at the maximum American height (300 m), see Mount Davidson (http://en.wikipedia.org/wiki/Mount_Davidson_(California)) in San Francisco.

http://www.outsidelands.org/images/mt-davidson-1954.jpg

I'm from a fairly hilly area and an hour away from two mountain ranges, so my definitions may be skewed, but I'd definitely call Mount Davidson a hill, not a mountain. Thirty meters is about nine stories and slightly larger than a bump for around here, though it has the advantage of being a very well-defined conical shape while our hills are much more rolling and ill-defined.

Fair enough. I suppose I considered the "hill" in "hill of beans" to be more of a hillock of gnoll.

[Iruka]

NIce work. :smallbiggrin:

[Killer Angel]

You clearly won an internet. :smallbiggrin:



Here's what I think of when I hear the word "hill":


This (http://en.wikipedia.org/wiki/The_Englishman_Who_Went_Up_a_Hill_But_Came_Down_a_ Mountain) is what I think, everytime I hear talking 'bout hills' heights.

[warty goblin]

You are aware that a hill of beans is a group of perhaps 3 - 5 beans planted in close proximity, with the dirt mounded around them, right?

[Kneenibble]

You are aware that a hill of beans is a group of perhaps 3 - 5 beans planted in close proximity, with the dirt mounded around them, right?

Given the context, I hesitate to ask what that whooshing sound might have been.

[truemane]

We're dealing with an illogical, poetic idiom. It is (and was) common enough to say that such and such wasn't worth beans. Beans were cheap, poor-person food. That makes sense.

So, poetically (if not logically) a 'hill of beans' is a whole PILE of something cheap and worthless.

warty goblin: I've never heard that before, that a "hill of beans" specifically refers to a planted mound or two or three beans. That's interesting. My suspicion is that the two are unrelated. I can't find a reference one way or the other.

[Taet]

What a delightful study. Common sense wins.


Given the context, I hesitate to ask what that whooshing sound might have been.

:smalltongue:

That was the sound of the beans growing out of control and taking over the rest of the plot.

[Deepbluediver]

This reads kind of like the "What If?" section of XKCD.

Step 1) take something totally ludicrous
Step 2) treat it completely serious
Step 3) profit

[TheWolfe]

I like the different definitions of a hill. The Netherlands, where I live, are so flat, that our highest point is only about 500 meters (1500 feet) high, so we call everything higher than about 3 meters a hill and everything over about 15 meters is a mountain. Maybe the interviewee was from the Netherlands?

[Jeff the Green]

This reads kind of like the "What If?" section of XKCD.

Step 1) take something totally ludicrous
Step 2) treat it completely serious
Step 3) profit

High praise indeed. :smallbiggrin:


I like the different definitions of a hill. The Netherlands, where I live, are so flat, that our highest point is only about 500 meters (1500 feet) high, so we call everything higher than about 3 meters a hill and everything over about 15 meters is a mountain. Maybe the interviewee was from the Netherlands?

He was Indian, works at one of the more famous British universities (can't remember which), and has been spending a lot of time in the Middle East and Northern Africa. It's probably irrelevant, though, since it's a common, if old-fashioned, idiom in English. My grandpa uses it occasionally.

[Amidus Drexel]

This reads kind of like the "What If?" section of XKCD.

Step 1) take something totally ludicrous
Step 2) treat it completely serious
Step 3) profit

Agreed. This is some awesome stuff. :smallcool: