## What-If 0011: "Droppings"

What if there was a forum for discussing these?

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Quicksilver
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### What-If 0011: "Droppings"

MacFreek
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### Re: What-If 0011: Droppings

The last equation only considers the number of cars in the US, but the number of birds in all the world. As the rest of the world likes to exclaim:

Hey, use your own bird poop!

Aka: how much would the required fuel efficiency, err, required bird poop efficiency change if the number would be considered per continent? What is the ratio of birds over cars? And how would this equation change if we consider the general required poop efficiency instead of only the bird poop efficiency. A mammal has certainly different poop characteristics than a bird. Most interestingly, what would be the required human poop efficiency be if we where to support our own car fuel?

So many questions....

[edit: typo fixed]

Angelastic
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### Re: What-If 0011: Droppings

I wonder if he subtracted flightless birds from the total, or assumed they would walk over our faces.
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AvatarIII
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### Re: What-If 0011: Droppings

the stuff about unit cancellation has irked me,

Sure miles is a unit of distance and gallons is a unit of volume, but gallons per mile shouldn't cancel out and convert to square meters, because miles is a unit of distance travelled, and gallons is a unit of volume consumed.
it might make sense if the fuel was directly converted into distance, ie consumption of fuel actually means it is extruded and laid as a plane of fuel on your path, but it doesn't, it's vaporised and ignited which causes expansion against a piston (normally measured in litres or cc), which in turn is converted to rotary energy, which turns an axle which is connected to wheels which roll on the ground

so really it should be litres per litre per degree per meter. the litres cancel out so it should be degrees per meter. I think.

cstdenis
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### Re: What-If 0011: Droppings

The formulas are somewhat broken in Chrome.

PM 2Ring
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### Re: What-If 0011: Droppings

Curiously, it's almost exactly 3 years ago that I said this in the Science forum:
PM 2Ring wrote:1 picohectare is the area of a 0.1mm x 0.1mm square. I like the image of a vehicle consuming a fuel "stream" measured this way.

And gmalivuk & I were also discussing this topic a couple of months ago in this Linguistics forum thread.
PM 2Ring wrote:FWIW, (1 litre) / (100 km) = 10-12 hectares, so I like to quote fuel consumption in picohectares.

gmalivuk wrote:Yeah, that way it's the area of a stream of gasoline trailing behind your car, corresponding exactly to the amount of fuel you use.

ryzvonusef (1151717)
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### Re: What-If 0011: Droppings

I am from the Internet, here to let you know the formula magic doesn't work in Opera.

ycc1988
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### Re: What-If 0011: Droppings

I am now imagining a long, thin strand of bird poop trailing out of everyone's cars. Congratulations, Randall.

PM 2Ring
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### Re: What-If 0011: Droppings

ryzvonusef (1151717) wrote:I am from the Internet, here to let you know the formula magic doesn't work in Opera.

The formulas use MathJax, which should work in Opera 9.5 and later, as long as you have JavaScript enabled.

Feel free to post a sample of the non-working formula stuff, so we know exactly what you're seeing.

http://www.mathjax.org/help-v2/user/ wrote:MathJax User Help

MathJax is a JavaScript library that allows page authors to include mathematics in their web pages. It works in most browsers, on most operating system, and it does not require plugins, fonts, or other installations on the part of the user. When you view a page that includes MathJax, you should see beautifully typeset mathematics, though it may take a few moments to process (depending on your network and computer speeds). You should not need to do anything to make that happen — just make sure JavaScript is enabled in your browser.

Browsers: MathJax works with most modern browsers. See our browser compatibility chart for details.

Fonts: MathJax will use certain math fonts if they are installed on your computer; otherwise, it will use web-based fonts if your browser supports them, and image fonts if not. Although they are not required, having fonts installed locally will speed up MathJax’s typesetting. See the MathJax font help page for more details.

Math Menu: MathJax has a contextual menu that it applies to every equation that it typesets. You get the menu when you right-click (on Windows) or control-click (on MacOS) over a mathematical formula that MathJax has typeset. It allows you to view the formula’s source markup, and change settings that control various aspects of MathJax. See the MathJax Menu page for more information.

ryzvonusef (1151717)
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### Re: What-If 0011: Droppings

PM 2Ring wrote:
ryzvonusef (1151717) wrote:I am from the Internet, here to let you know the formula magic doesn't work in Opera.

The formulas use MathJax, which should work in Opera 9.5 and later, as long as you have JavaScript enabled.

Feel free to post a sample of the non-working formula stuff, so we know exactly what you're seeing.

Spoiler:

Then it proceeds to load, fail and give the same error for MathMenu.js and MathZoom.js

I am using opera 12.02.

Max™
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### Re: What-If 0011: Droppings

Is... that Windows 98?
mu

AvatarIII
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### Re: What-If 0011: Droppings

Max™ wrote:Is... that Windows 98?

lol, I think it might be XP with classic grey theme.
it's not 7, because I use 7 with classic grey theme and it doesn't look like that, but I doubt opera 12 would ruin on win 98

The_Alchemist
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### Re: What-If 0011: Droppings

First, I cry foul - no, now fowl. "it varies" isn't a great answer, or even a good answer. It feels like the whole thing was an excuse to just go off on unit cancellation, which if they whole thing were put into the webcomic, instead of 'What-if' might be funny (hrm, he got distracted from the 'what-if' answer, yesterday's comic was ADD....hrm.....? is it possible?).

Next, my thought about 'unit cancellation is weird' is that he didn't follow the unwritten (or is it?) rule of cancellation that the unit should convey useful, not just amusing, information. I even recall this from a physics class back eons ago. And by going to square meters for mileage he is breaking that rule. Frankly, it seems that is where the odd units of elephants or 747's came from - to make them more intuitive and in theory, more able to be understood (ok, and silly sometimes). And that one should not simplify a unit if it inhibits understanding of the information being presented....at least that's what my physics prof said, and he must be right

So, if this was 'linked' to yesterday's comic, ok, I'll concede subtle humor....but if not....well, that link is still interesting, but at the 'what-if's' expense.

algorerhythms
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### Re: What-If 0011: Droppings

Something doesn't smell right about that last formula. Suppose we double the number of miles driven, to 6 trillion a year. The amount of guano is constant, so one would expect that the efficiency needed in miles per gallon to increase, but if we put it into the formula, we find that it decreases.
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ryzvonusef (1151717)
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### Re: What-If 0011: Droppings

AvatarIII wrote:
Max™ wrote:Is... that Windows 98?

lol, I think it might be XP with classic grey theme.
it's not 7, because I use 7 with classic grey theme and it doesn't look like that, but I doubt opera 12 would ruin on win 98

Heavens, no! It's Windows 7 Home premium
Spoiler:

mathmannix
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### Re: What-If 0011: Droppings

I think his switch from fuel economy in terms of miles per gallon to its inverse is misleading... can you say "20 MPG equals 0.1 square millimeters" ??? You have to invert.

Anway, I wanted to run the calculations myself:

20 miles per gallon is 0.05 gallons per mile. A U.S. gallon is defined as 231 cubic inches, so 0.05 gallons per mile = 11.55 cubic inches per mile, or 11.55 / 63360 = 0.00018229167 square inches, or converting back into metric, 0.001176 square cm, or 0.1176 square millimeters. If my SUV gets 25 miles per gallon, then that's 0.04 gallons/mile, or 0.0941 square millimeters. Okay. So, the higher the gas mileage a car gets (a higher miles-per-gallon), the smaller the tube would need to be. Makes sense.

EDIT: I said "larger" instead of "smaller" in the original post. (and I caught it myself before twcarlson's comment.)
Last edited by mathmannix on Tue Sep 11, 2012 2:15 pm UTC, edited 3 times in total.
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twcarlson
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### Re: What-If 0011: Droppings

algorerhythms wrote:Something doesn't smell right about that last formula. Suppose we double the number of miles driven, to 6 trillion a year. The amount of guano is constant, so one would expect that the efficiency needed in miles per gallon to increase, but if we put it into the formula, we find that it decreases.

You're right; he starts with mm^2 (volume / distance) and then shows its corresponding mpg (distance / volume). The two are inversely proportional. He is abusing the equal sign. The last expression should say "= 1 / (13 mpg)".
Last edited by twcarlson on Tue Sep 11, 2012 2:12 pm UTC, edited 1 time in total.

philip1201
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### Re: What-If 0011: Droppings

ycc1988 wrote:I am now imagining a long, thin strand of bird poop trailing out of everyone's cars. Congratulations, Randall.

The poop goes into the car.

What comes out is, in the case of gasoline, (720 (kg/L)/1.98 (kg/L)^(2/3)*(32+12)u/12u*0.335 mm^2=62 mm^2 of CO2, neglecting the mass contribution of non-carbon atoms in petroleum, and assuming perfect combustion. So really more something like 60 mm^2 of CO2.

twcarlson
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### Re: What-If 0011: Droppings

philip1201 wrote:What comes out is, in the case of gasoline, (720 (kg/L)/1.98 (kg/L)^(2/3)*(32+12)u/12u*0.335 mm^2=62 mm^2 of CO2, neglecting the mass contribution of non-carbon atoms in petroleum, and assuming perfect combustion. So really more something like 60 mm^2 of CO2.

Imagining a tube of CO2 around a centimeter in diameter streaming out of our cars is a really good visual for how much they produce. It's not a big leap for me to place all those tubes next to each other on the highway and see how much CO2 we are leaving behind.

I'll leave it to the scientists to figure out how much is too much. (Emphasis on scientists.)

jtboofle
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### Re: What-If 0011: Droppings

Rather than the surface area of the earth, we should probably be using the surface area of the land mass. Various estimates exist, but for simplicity, let's use 150,000,000 km2. Using the rest of Randall's numbers, we come to 57 years.

If you lie on your back long enough, you will live to have a bird crap in it.

Randall also doesn't allow for nocturnal birds (or perhaps he assumes we close our mouths when we sleep). OWL POOP IS REAL POOP, my friend.

Moose Anus
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### Re: What-If 0011: Droppings

jtboofle wrote:Randall also doesn't allow for nocturnal birds (or perhaps he assumes we close our mouths when we sleep). OWL POOP IS REAL POOP, my friend.
He does not exclude nocturnal poop, only poop while birds are not awake. Owls sleep during the day, so their 16 hours of pooping would be during the night or something.

The thing is, if you really want a bird to crap in your mouth, you should just feed a bird a burrito and strap it to your face, centipede style.

Lyth
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### Re: What-If 0011: Droppings

An erratum: in order to really cancel out the units in the last formula, it should read '((0.5 fl oz / day) / bird)'
Last edited by Lyth on Wed Sep 12, 2012 1:23 pm UTC, edited 1 time in total.

rockachu2
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### Re: What-If 0011: Droppings

I can confirm this works with opera, windows 7 x64 dev version. HOWEVER it took 10 seconds and caused a system freeze before it changed from what was posted above. (Freeze may be due to running unstable opera).

This is on a modern machine. with 6 cores. at 3.2 ghz. with fast memory.

flicky1991
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### Re: What-If 0011: Droppings

I'm wondering the formulae are displaying weirdly for other people... I'm on Windows 7 with Chrome, and it takes less than a second to display correctly.

Edit:
cstdenis wrote:The formulas are somewhat broken in Chrome.

Not for everyone XD
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Unclevertitle
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### Re: What-If 0011: Droppings

So what I learned from this is that MPG is a hilarious unit of measurement when misapplied.

For example, if based on Randall's logic 20 MPG = 0.1 mm2 = 2 pixels. Then a single pixel is equivalent to 10 MPG.

Thus my 1920 x 1080 monitor (2073600 pixels total) manages to just exceed a whopping 20 million miles per gallon.

Now that's what I call "efficiency."

Max™
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### Re: What-If 0011: Droppings

AvatarIII wrote:
Max™ wrote:Is... that Windows 98?

lol, I think it might be XP with classic grey theme.
it's not 7, because I use 7 with classic grey theme and it doesn't look like that, but I doubt opera 12 would ruin on win 98

Ah, my last experience with 7 was an unfortunate encounter with 7 starter on a netbook (go go gadget Bodhi Linux!) and the XP I run in a VM for proctored tests (since the software has no linux or wine port yet), didn't mess with the different styles on XP.

I was like "wait, that looks familiar... how the hell is he running newer browsers on that?"
mu

keithl
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### Re: What-If 0011: Droppings

Years ago, I lived on the second floor of an apartment complex. A cyclist sans auto, "my" parking space went unused until a jerkwad from another building decided to park his car there. His reason? If he parked in his own space, the "be-boop" of his keyless entry system woke his girlfriend in the morning. When I protested that it woke ME in the morning, he smirked and said something like "sue me".

Lawyers are expensive. Instead I prepared a solution of Elmers glue, egg white, and green chalk, which looked like bird poop. Using an eyedropper, I splattered some on the eaves above my window, and a few splatters on the unoccupied parking spot below, as fair warning.

Mr. Jerkwad did not notice, and persisted in his evil ways. So I dropped a splatter on his parked car. A couple of days later, I dropped another. He finally decided there were too many pooping birds there, and moved on. I'm sure it damaged his paint. But he spent less fixing that than he would have on a lawyer.

Later, in an alternate universe, I went on to develop the car-alarm-seeking missile, for which I won the Nobel Peace Prize.

How long before you get bird poop in your mouth? Depends on whether there is a misanthrope in the apartment window above, and whether you make noises like a keyless entry system.

Angelastic
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### Re: What-If 0011: Droppings

Unclevertitle wrote:So what I learned from this is that MPG is a hilarious unit of measurement when misapplied.

For example, if based on Randall's logic 20 MPG = 0.1 mm2 = 2 pixels. Then a single pixel is equivalent to 10 MPG.

Thus my 1920 x 1080 monitor (2073600 pixels total) manages to just exceed a whopping 20 million miles per gallon.

Now that's what I call "efficiency."

No, it's the other way around… the area is from the gallons per mile, not miles per gallon. Miles per gallon only reduces to the reciprocal of an area. He just happened to convert it to miles per gallon because that's the unit more common in the US. The area of your monitor (assuming it has the same dpi as whatever Randall is comparing it with; Retina displays aren't magically less efficient in this crazy comparison) would be something like 0.000002MPG.
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dotancohen
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### Re: What-If 0011: Droppings

> If you took all the gas you burned on a trip and stretched it out into a thin tube along
> your route, 0.1 square millimeters would be the cross-sectional area of that tube.

It seems to me that is rather close to the cross section of the fuel line actually going from the tank to the engine. Anybody see anything more profound than coincidence there?

Red Hal
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### Re: What-If 0011: Droppings

It's probably around two orders higher than that. I'd suggest around 25 square mm.
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Max™
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### Re: What-If 0011: Droppings

keithl wrote:Years ago, I lived on the second floor of an apartment complex. A cyclist sans auto, "my" parking space went unused until a jerkwad from another building decided to park his car there. His reason? If he parked in his own space, the "be-boop" of his keyless entry system woke his girlfriend in the morning. When I protested that it woke ME in the morning, he smirked and said something like "sue me".

Lawyers are expensive. Instead I prepared a solution of Elmers glue, egg white, and green chalk, which looked like bird poop. Using an eyedropper, I splattered some on the eaves above my window, and a few splatters on the unoccupied parking spot below, as fair warning.

Mr. Jerkwad did not notice, and persisted in his evil ways. So I dropped a splatter on his parked car. A couple of days later, I dropped another. He finally decided there were too many pooping birds there, and moved on. I'm sure it damaged his paint. But he spent less fixing that than he would have on a lawyer.

Later, in an alternate universe, I went on to develop the car-alarm-seeking missile, for which I won the Nobel Peace Prize.

How long before you get bird poop in your mouth? Depends on whether there is a misanthrope in the apartment window above, and whether you make noises like a keyless entry system.

While this is amusing as hell and I approve, this is why they say not to eat packets of silica gel.
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twcarlson
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### Re: What-If 0011: Droppings

dotancohen wrote:> If you took all the gas you burned on a trip and stretched it out into a thin tube along
> your route, 0.1 square millimeters would be the cross-sectional area of that tube.

It seems to me that is rather close to the cross section of the fuel line actually going from the tank to the engine. Anybody see anything more profound than coincidence there?

If that's true, it means that the average speed of fuel flowing through the line equals the average speed of your car.

twcarlson
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### Re: What-If 0011: Droppings

I wanted to offer my take on the fuel economy units. The best form to use depends on what you're most interested; in other words, what is fixed and what is variable.

In the beginning, people were more concerned about distance. For a given fill-up, how much distance do I get? A car that could get 20 miles for every gallon was better than one that only drove you 15 miles. These days, we are more concerned about fuel. For a given commute, how much fuel am I using? Here it really makes more sense to put fuel in the numerator and compare based on a fixed distance.

If gas stations were scarce and we faced an inability to drive far enough to reach the beach, mpg would still be the best measurement ("more miles, please"). But we can fill up wherever we want, so "less fuel usage, please" is the better request, and gallons per 100 miles is the better unit.

You can draw an analogy to the power consumption of a desktop or laptop computer. For a desktop, you want to know how much energy is consumed for a fixed period of use (energy / time = power), so you'd use watts. For a laptop with a fixed amount of energy inside, you want to know how long you can use it before it dies (time / energy = 1 / power), so the best measure would be hours per charge.

RantingRaven
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### Re: What-If 0011: Droppings

I wrote a post but accidentally closed a page and don't have my steps.

Summary: poops, like mouths, have a diameter. If we assume a round poop of 1 sq cm and a round mouth, the target area increases; expected wait time is now 123 years.

Waiting for poop is a poisson process, and the wait time is exponentially distributed. Average person in world [cite]CIA world factbook[/cite] would have a 41.7% chance of having their mouth pooped in. Probability of eating s*** in any given timeframe is [imath]1-e^{t/123}[/imath]

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### Re: What-If 0011: Droppings

twcarlson wrote:I wanted to offer my take on the fuel economy units. The best form to use depends on what you're most interested; in other words, what is fixed and what is variable.

In the beginning, people were more concerned about distance. For a given fill-up, how much distance do I get? A car that could get 20 miles for every gallon was better than one that only drove you 15 miles. These days, we are more concerned about fuel. For a given commute, how much fuel am I using? Here it really makes more sense to put fuel in the numerator and compare based on a fixed distance.

If gas stations were scarce and we faced an inability to drive far enough to reach the beach, mpg would still be the best measurement ("more miles, please"). But we can fill up wherever we want, so "less fuel usage, please" is the better request, and gallons per 100 miles is the better unit.

You can draw an analogy to the power consumption of a desktop or laptop computer. For a desktop, you want to know how much energy is consumed for a fixed period of use (energy / time = power), so you'd use watts. For a laptop with a fixed amount of energy inside, you want to know how long you can use it before it dies (time / energy = 1 / power), so the best measure would be hours per charge.

Thank you SO MUCH for explaining it this way. I had been trying valiantly to wrap my mind around what Randall was trying to say about this in the article, and you explained it in a way that finally, FINALLY makes perfect sense to me. The desktop/laptop analogy was the icing on the cake. Thanks!

Djehutynakht
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### Re: What-If 0011: Droppings

This was a wierd 'un.

ChrisTilley
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### Re: What-If 0011: Droppings

I was picturing a city with a network of pipes containing enough gas for one days worth of car driving over that section of road. It would be interesting to see graphically as large "arterial" roads branch off into smaller and small streets. Out of curiosity I worked it out for the Golden Gate Bridge. With 110,000 cars crossing it daily and a very roughly estimated 20mpg the pipe across would have a 2 and 1/3 diameter or a 110 square cm cross section.

PM 2Ring
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### Re: What-If 0011: Droppings

For the people who can't see the formulae in this What-If, here they are as a PNG.

(Click on the image to see it full-size).

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### Re: What-If 0011: Droppings

The question clearly stipulates being on dry land, so can't we increase the odds by eliminating all the space taken up by water thus increasing this poor man's hopes of eating in-transit bird feces?

Even if we remove birds standing/flying over water, there still has to be close to 290 billion over 29.22% of the Earth's surface which is land....

290 billion / (.292 * 4pi Earth's radius^2) = 290,000,000,000 / 148 248 569.07 = 1956.17 hours?

I know i've not done that right, but I can't be bothered to write this out properly at the moment...

Arariel
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### Re: What-If 0011: Droppings

Well, we might get a better approximation if we just consider North America, which evidently has 10-15 billion birds in the spring and 20-30 billion in the fall, so maybe about 20 billion birds. Area is about 24,710,000 km², and so that's a density of about 809 birds/km² (Randall's was 587 birds/km²).

But since we're considering random dropping, shouldn't we be looking at this more probabilistically? In that case, we would have:

[imath]N_b ~ \text{(number of birds in a given area)}[/imath]
[imath]r_s ~ \text{(rate for an average bird)}[/imath]
[imath]A_L ~ \text{(given area containing birds)}[/imath]
[imath]A_m ~ \text{(area of mouth)}[/imath]
[imath]P = 1 - (\frac{A_m}{A_L})^{N_b ~ r_s ~ t}[/imath]
[imath]t = \frac{\log(1-P)}{\log(\frac{A_m}{A_L}) N_b ~ r_s}[/imath]

With my stats, the time for a probability of 50:50 will be in 98 years. Randall's assumptions give 63.3% probability in 195 years, while mine give 74.9% probability in the same period.