What-If 0011: "Droppings"

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Sourire
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Re: What-If 0011: Droppings

Postby Sourire » Wed Sep 12, 2012 5:55 am UTC

Surprised at his bit about unit conversions. Mostly because it's factually incorrect, and I tend to like him for being right on these things. :(

"miles per gallon" is lazy notation we accept in speech. If you want to use it in math, you need to recognize it's "miles traveled per gallon of gasoline". If you're tempted to eliminated units of length, you end up with something that looks like "traveled per meter squared of gasoline". In other words: It doesn't work.

That said, it's an amusing thought. :)
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Alsadius
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Re: What-If 0011: Droppings

Postby Alsadius » Wed Sep 12, 2012 6:13 am UTC

I don't think Randall is abusing equality - at least, not enough to be worth mentioning - but I do have a serious issue with his last formula being wrong. To see what I mean, 300 billion birds and 3 trillion miles means that a bird has to poop enough in a year to drive a car 10 miles. 0.5 oz/day*365 days/year/128 oz/gal ~= 1.4 gal/bird/year. 10 miles/1.4 gal ~= 7.14 MPG. His formula looks to be inverted somewhere along the line. Similarly, the fellow above who bragged about his monitor getting 20 million MPG has it backwards - a car that needed to dump a monitor-sized stream behind it would be horribly inefficient.

Also, my favourite example of unit cancellation being weird is the unit used for rocket/jet motor efficiency. The measure is thrust divided by weight flow of fuel, which has the unit of seconds.

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Re: What-If 0011: Droppings

Postby Ardee » Wed Sep 12, 2012 6:29 am UTC

A scientist at the LHC wrote a funny April Fools article last year riffing on the MPG in terms of collider efficiency:

http://www.quantumdiaries.org/2011/04/01/a-modest-proposal-for-new-fundamental-constants/

I was further amused to find that the unit of "inverse picobarn" wasn't part of the joke, and is real.

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Max™
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Re: What-If 0011: Droppings

Postby Max™ » Wed Sep 12, 2012 7:33 am UTC

A barn is approximately the size of a uraniumlarge nucleus, something large enough in nuclear processes that it was considered as easy to hit as "the broad side of a barn". *edited*

I think there's also an outhouse unit, but I can't remember the measurement it represents, though I assume it's smaller than a barn.

Got my history mixed up: http://www.physics.purdue.edu/about_us/ ... riod.shtml

The tradition of naming a unit after some great man closely associated with the field ran into difficulties since no such person could be brought to mind. Failing in this, the names Oppenheimer and Bethe were tried, since these men had suggested and made possible the work on the problem with which the Purdue project was concerned. The "Oppenheimer" was discarded because of its length, although in retrospect an "Oppy" or "Oppie" would seem to be short enough. The "Bethe" was thought to lend itself to confusion because of the widespread use of the Greek letter. Since John Manley was directing the work at Purdue, his name was tried, but the "Manley" was thought to be too long. The "John" was considered, but was discarded because of the use of the term for purposes other than as the name of a person. The rural background of one of the authors then led to the bridging of the gap between the "John" and the "barn". This immediately seemed good and further it was pointed out that a cross section of 10-24 cm2 for nuclear processes was really as big as a barn. Such was the birth of the "barn".
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Re: What-If 0011: Droppings

Postby Steve the Pocket » Wed Sep 12, 2012 1:52 pm UTC

I thought the thing about units was just useless pedantry until he got to the part about the tube. That was pretty neat. So basically, you could say that people with bulkier, less efficient vehicles need a fatter pipe.
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Re: What-If 0011: Droppings

Postby webgrunt » Wed Sep 12, 2012 2:21 pm UTC

This is all assuming that birds don't aim.

twcarlson
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Re: What-If 0011: Droppings

Postby twcarlson » Wed Sep 12, 2012 5:38 pm UTC

Sourire wrote:Surprised at his bit about unit conversions. Mostly because it's factually incorrect, and I tend to like him for being right on these things. :(

"miles per gallon" is lazy notation we accept in speech. If you want to use it in math, you need to recognize it's "miles traveled per gallon of gasoline". If you're tempted to eliminated units of length, you end up with something that looks like "traveled per meter squared of gasoline". In other words: It doesn't work.

That said, it's an amusing thought. :)

Not so fast, there. Just because it's hard to conceive doesn't mean it's "factually incorrect". First, a quick correction: "miles" really is the unit; "traveled" is just explanatory. You can't cancel the word "miles" and leave "traveled" — they go together, so when you cancel it you end up with something like 1 / (meter squared of gasoline).

You're right that it is a bit hard to envision what length-2 means, but could there actually be a physical meaning? I propose that there is.

Consider a car with a fuel efficiency of 4 gallons per 100 miles. Its tube would be .094 mm2. The reciprocal of this measure is 25 mpg, which cancels to 10.6 mm-2. "Nonsense!" you say. "What kind of measurement is 10.6 mm-2?"

Well, what if you had a tube with an area of exactly 1 mm2 — how many cars would it take to consume that tube of fuel? You would need 10.6 cars (10.6 * .094 mm2 = 1 mm2).

10.6 cars for a 1 mm2 tube ... 10.6 cars / mm2. Since "cars" is unitless*, you end up with 10.6 mm-2. And the meaning is found.

*Another example of a unitless quantity is "cycles" in cycles per second = s-1 = Hz.
Last edited by twcarlson on Wed Sep 12, 2012 8:45 pm UTC, edited 1 time in total.

RantingRaven
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Re: What-If 0011: Droppings

Postby RantingRaven » Wed Sep 12, 2012 8:41 pm UTC

twcarlson wrote:
Sourire wrote:Surprised at his bit about unit conversions. Mostly because it's factually incorrect, and I tend to like him for being right on these things. :(

"miles per gallon" is lazy notation we accept in speech. If you want to use it in math, you need to recognize it's "miles traveled per gallon of gasoline". If you're tempted to eliminated units of length, you end up with something that looks like "traveled per meter squared of gasoline". In other words: It doesn't work.

That said, it's an amusing thought. :)

Not so fast, there. Just because it's hard to conceive doesn't mean it's "factually incorrect". First, a quick correction: "miles" really is the unit; "traveled" is just explanatory. You can't cancel the word "miles" and leave "traveled" — they go together, so when you cancel it you end up with something like 1 / (meter squared of gasoline).

You're right that it is a bit hard to envision what length-2 means, but could there actually be a physical meaning? I propose that there is.

Consider a car with a fuel efficiency of 4 gallons per 100 miles. Its tube would be .094 mm2. The reciprocal of this measure is 25 mpg, which cancels to 10.6 mm-2. Nonsense! What kind of measurement is 10.6 mm-2?

Well, what if you had a tube with an area of exactly 1 mm2 — how many cars would it take to consume that tube of fuel? You would need 10.6 cars (10.6 * .094 mm2 = 1 mm2).

10.6 cars per mm2. Cars is unitless*, so you end up with 10.6 mm-2.

*Another example of a unitless quantity is "cycles" in cycles per second = s-1 = Hz.


Not sure I agree. I think that if I bought a liter of urine instead of a liter of cola, I would have a pretty pissed-off argument over unit equivalence with whoever filled my order. Likewise, when calculating limiting reactants, the unit cancellation is [math]{some grams of Element A*{(moles of Element A/grams of element A)}*(moles of Element B/moles of Element A)*(grams of Element B/moles of Element B)}[/math]
Although the starting and ending units are in mass of something, that something matters. Likewise, you can't divide a mass of Element A by the molar mass of Element B and obtain anything useful (OK, this thread is full of describing odd units, so maybe there is some meaning; however, not the meaning that we're looking for.)

twcarlson
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Re: What-If 0011: Droppings

Postby twcarlson » Wed Sep 12, 2012 8:52 pm UTC

RantingRaven wrote:Although the starting and ending units are in mass of something, that something matters.

Perhaps you're right.

Do you agree, though, that there is meaning in the tube model of fuel efficiency? In the tube of fuel, miles traveled is the same thing as miles of gasoline, so canceling should be just fine.

And do you also agree that there is also meaning in the reciprocal explanation using mm-2 as the units?

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VectorZero
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Re: What-If 0011: Droppings

Postby VectorZero » Wed Sep 12, 2012 11:06 pm UTC

webgrunt wrote:This is all assuming that birds don't aim.
I am convinced they do.
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Showsni
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Re: What-If 0011: Droppings

Postby Showsni » Wed Sep 12, 2012 11:42 pm UTC

Of course, some species of birds actively aim for humans. Consider nesting gulls - if they perceive a human is too close to the nest, they'll first give off warning cries, and then switch to aimed dive bombing of faeces and vomit (before progressing to full on head scratching and pecking). And since an awful lot of these gulls now colonise UK towns and cities, "too close to the nest" could include walking down a city street...

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Re: What-If 0011: Droppings

Postby chewbakken » Thu Sep 13, 2012 2:23 am UTC

I know the gas mileage bit is pretty off-topic. But I know I've thought about the fact that's it's technically [m/m3], so I found it amusing.

A quick tidbit on that: if a car gets X mpg, its "fuel tube" would have a diameter of very nearly [imath]\sqrt{3/X}[/imath] mm.
Last edited by chewbakken on Sun Sep 16, 2012 7:34 pm UTC, edited 2 times in total.

elwood
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Re: What-If 0011: Droppings

Postby elwood » Thu Sep 13, 2012 11:09 am UTC

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.


Bonus points if you manage to shag his girlfriend after he's gone in the morning.

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Unclevertitle
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Re: What-If 0011: Droppings

Postby Unclevertitle » Thu Sep 13, 2012 2:15 pm UTC

Angelastic wrote:
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.

Thanks for correcting me. I thought it was too good to be even pseudo-true.

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Re: What-If 0011: Droppings

Postby Chicagojon » Thu Sep 13, 2012 3:00 pm UTC

As a bird owner I have a problem with the 1 poop/hour. A budgie poops every 12~15 minutes when awake/active and typically 40-50 times/day. I would suspect the same is true of similar small birds and a quick google search says a large bird like a macaw may poop ~20 times/day. I have no idea what the average bird size is, but surely it must be on the smaller end - maybe 6-8" at most. This has got to be a 30+/day poop average which throws that fraction off by 25%+.

The volume per poop per bird is a fascinating (if disgusting) thought. I'll admit that I've weighed my bird on a kitchen scale (29g FWIW) but now I need a more accurate scale so I can weigh her poop.

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Re: What-If 0011: Droppings

Postby bmonk » Thu Sep 13, 2012 5:31 pm UTC

Sourire wrote:Surprised at his bit about unit conversions. Mostly because it's factually incorrect, and I tend to like him for being right on these things. :(

"miles per gallon" is lazy notation we accept in speech. If you want to use it in math, you need to recognize it's "miles traveled per gallon of gasoline". If you're tempted to eliminated units of length, you end up with something that looks like "traveled per meter squared of gasoline". In other words: It doesn't work.

That said, it's an amusing thought. :)

I think that way too--but the math purists always say, "numbers don't come with attached units"--so even canceling units doesn't really make sense in their way of thinking.
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Re: What-If 0011: Droppings

Postby oblivimous » Fri Sep 14, 2012 1:44 am UTC

Once I was lying on my back on the lawn and a hummingbird peed/pood in my eye. It was flying by 15 or 20 feet above me and I clearly saw, and then felt, a small single drop of ick fall from it to me.

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Re: What-If 0011: Droppings

Postby rmsgrey » Fri Sep 14, 2012 10:18 am UTC

bmonk wrote:
Sourire wrote:Surprised at his bit about unit conversions. Mostly because it's factually incorrect, and I tend to like him for being right on these things. :(

"miles per gallon" is lazy notation we accept in speech. If you want to use it in math, you need to recognize it's "miles traveled per gallon of gasoline". If you're tempted to eliminated units of length, you end up with something that looks like "traveled per meter squared of gasoline". In other words: It doesn't work.

That said, it's an amusing thought. :)

I think that way too--but the math purists always say, "numbers don't come with attached units"--so even canceling units doesn't really make sense in their way of thinking.

Numbers don't come with attached units, but a vector in phase-space can be expressed as a scalar multiple of a unit vector.

If you ask a real mathematician about arithmetic in Rn with a non-orthonormal basis, you'll get told about something that sounds a lot like dimensional analysis...

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Re: What-If 0011: Droppings

Postby thevicente » Fri Sep 14, 2012 12:42 pm UTC

I've come from the past to say when I learned about BMI I and ended with kg/m²

It seems units are not considered at all by bio people, they... they just ignore it out. :shock:

( BMI = Body Mass Index , here's the Wikipedia article: http://en.wikipedia.org/wiki/Body_mass_index )

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Re: What-If 0011: Droppings

Postby J Thomas » Fri Sep 14, 2012 2:37 pm UTC

thevicente wrote:I've come from the past to say when I learned about BMI I and ended with kg/m²

It seems units are not considered at all by bio people, they... they just ignore it out. :shock:

( BMI = Body Mass Index , here's the Wikipedia article: http://en.wikipedia.org/wiki/Body_mass_index )


How fat are you? It's easy to measure height and weight. Weight isn't enough because tall people can carry more weight and still be skinny.

So if we were to cut a slice out of your middle, some standard thickness, and weigh it, that would say something about how fat you are. It would be more accurate to cut a slice out of your middle and measure the diameter and circumference, but this is easier. kg/m^2.

It isn't a great measure, but it's easy.
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Re: What-If 0011: Droppings

Postby Kandralla » Fri Sep 14, 2012 4:28 pm UTC

twcarlson wrote:
RantingRaven wrote:Although the starting and ending units are in mass of something, that something matters.

Perhaps you're right.

Do you agree, though, that there is meaning in the tube model of fuel efficiency? In the tube of fuel, miles traveled is the same thing as miles of gasoline, so canceling should be just fine.

And do you also agree that there is also meaning in the reciprocal explanation using mm-2 as the units?


What the "Tube model" is essentially telling you is a characteristic area of the fuel system; it's basically telling you the smallest area conduit that can deliver enough fuel to an engine that averages 20 mile per gallon, assuming incompressible liquids, and that fuel is density isn't affected by temperature which are both reasonable assumptions in this case. It's essentially saying that milage is related to fuel flow rate.

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Re: What-If 0011: Droppings

Postby bmonk » Fri Sep 14, 2012 8:23 pm UTC

rmsgrey wrote:
bmonk wrote:
Sourire wrote:Surprised at his bit about unit conversions. Mostly because it's factually incorrect, and I tend to like him for being right on these things. :(

"miles per gallon" is lazy notation we accept in speech. If you want to use it in math, you need to recognize it's "miles traveled per gallon of gasoline". If you're tempted to eliminated units of length, you end up with something that looks like "traveled per meter squared of gasoline". In other words: It doesn't work.

That said, it's an amusing thought. :)

I think that way too--but the math purists always say, "numbers don't come with attached units"--so even canceling units doesn't really make sense in their way of thinking.

Numbers don't come with attached units, but a vector in phase-space can be expressed as a scalar multiple of a unit vector.

If you ask a real mathematician about arithmetic in Rn with a non-orthonormal basis, you'll get told about something that sounds a lot like dimensional analysis...


See? My point. On occasion, I encounter a number more or less by itself--but more often I don't see "three", but "three crows" or $25.30 in cash, or whatever. Three crows has certain commonalities with three pennies, or three dollar bills, or even three dollars in assorted cash--but it makes a difference which is which. If the clerk in the store asks for three dollars, I'd better not offer three pennies, or three pencils. I guess the way I see it is not that numbers have attached units, but rather that the units have attached numbers, which are a reference to the world in some particular way.
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Re: What-If 0011: Droppings

Postby CarlLaMagouille » Sat Sep 15, 2012 10:23 am UTC

Chrome user here, seems like MathJax can't load.

http://cdn.mathjax.org/mathjax/latest/MathJax.js fails to be resolved, at least from China, and not since long ago.

Maybe the tex/math transformation only works if you have that file cached somewhere...

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Re: What-If 0011: Droppings

Postby phlip » Sat Sep 15, 2012 1:12 pm UTC

CarlLaMagouille wrote:Chrome user here, seems like MathJax can't load.

http://cdn.mathjax.org/mathjax/latest/MathJax.js fails to be resolved, at least from China, and not since long ago.

Maybe the tex/math transformation only works if you have that file cached somewhere...

The script loads fine for me... I suspect it's something on your end.

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
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Re: What-If 0011: Droppings

Postby rmsgrey » Sun Sep 16, 2012 1:55 pm UTC

bmonk wrote:See? My point. On occasion, I encounter a number more or less by itself--but more often I don't see "three", but "three crows" or $25.30 in cash, or whatever. Three crows has certain commonalities with three pennies, or three dollar bills, or even three dollars in assorted cash--but it makes a difference which is which. If the clerk in the store asks for three dollars, I'd better not offer three pennies, or three pencils. I guess the way I see it is not that numbers have attached units, but rather that the units have attached numbers, which are a reference to the world in some particular way.


If the clerk asks for three dollars, you'd also better not give him two (unless you then proceed to give a third) - getting the right unit doesn't help unless you also get the right number.

If you're doing arithmetic, which is about the properties of numbers, then it's natural to give the numbers priority over the units, though most counting systems include their own form of units - the standard decimal notation counts ones and tens and hundreds and thousands and millions and so on (and counts units bigger than a hundred in ones tens and hundreds) - even a simple tally-mark system groups the marks in units of 5-counts.

Units are only important to a calculation in that you need to know whether or not they match up - if they don't, then you can't do the arithmetic; if they do, you can. 2+2=4 whether you're talking about apples, oranges, or Olympic gold medals, but two apples plus two oranges doesn't equal four apples, nor four oranges, nor four Olympic gold medals (but it does make four pieces of fruit)

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Re: What-If 0011: Droppings

Postby IntegraR0064 » Mon Dec 10, 2012 11:08 pm UTC

Sourire wrote:Surprised at his bit about unit conversions. Mostly because it's factually incorrect, and I tend to like him for being right on these things. :(

"miles per gallon" is lazy notation we accept in speech. If you want to use it in math, you need to recognize it's "miles traveled per gallon of gasoline". If you're tempted to eliminated units of length, you end up with something that looks like "traveled per meter squared of gasoline". In other words: It doesn't work.

That said, it's an amusing thought. :)


Sorry to bring up an old thread, but I don't think this was ever properly addressed. I just was going through some of the what ifs I missed and this was one.

This post I quoted is very correct in that you can't just divide units by each other if they're measuring different things. They don't cancel out. The example of moles of a compound was a great example - you can't divide moles of hydrogen by moles of oxygen without converting and get a dimensionless number. This is another great example. Miles per gallon is miles (of distance traveled) per gallon (of fuel in the tank). So you cannot normally divide these out and get 1/distance^2 because distance traveled and a dimension of your fuel tank are not equivalent.

The part that no one talked about and the reason that this one actually DOES work even though it shouldn't is kind of a fun brain exercise.

So the reason it shouldn't work is the units are basically (miles traveled)/( (length of gas used)*(width of gas used)*(height of gas used) )

Nothing divides out there.

But, you can assume that the gas used will fill a tube that the length is exactly equal to the miles traveled. Then the miles traveled and length of the gas tank are equivalent and can be cancelled out! So:
(miles traveled)/( (miles traveled)*(width of gas used)*(height of gas used) )
=1/(width of gas tank*height of gas tank)

Thus, the dimensions of a square tube (or area of another shape tube) that follows the car along and fill with the gas that's utilized to propel that distance.

cutech
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Re: What-If 0011: Droppings

Postby cutech » Sun Aug 04, 2013 4:58 am UTC

I found an interesting corollary:

Nitroguanidine which according to Wikipedia can be used as a propellant.

So we can give an energy value to the poo.

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Re: What-If 0011: Droppings

Postby Plasma_Wolf » Sat Aug 16, 2014 6:54 pm UTC

And it just happened. A bird has dropped his feces in the mouth of football player Ashley Young, just as he was talking to someone else. This happened today on Old Trafford, the home stadium of Manchester United. You can find it on YouTube, just search for Man Utd Swansea Ashley Young Bird and you can find the footage (I refrained from watching).

Now my question is: to how many people have suffered from this in the meantime, between the release of the What-If about bird droppings and the moment Young had received a dropping in his mouth? Luckily, the formula at the start has a surface area factor in it, which we could multiply by 7 billion. This would reduce the period of one bird poop ending in someone's mouth by that factor. The period would then be (if I did the calculations correct, I think I did) to 0.87 seconds.

It, of course, assumes that everyone is lying on the ground with his or her mouth wide open. The question now is, for how long do people have their mouth open, while they are outside of their house. Is this for one thousandth of the total time spent outside? One millionth? Either way: if someone has accidentally eaten a bird poop at the time What-if 11 was released, the period for the next arbitrary person doing that is about 2 years, or one hundredth of the period that you get a bird poop by lying on the ground the whole time, with your mouth open.

Whichever the period is going to be, we can now measure it. We have the first victim, we just have to measure the time for the second one to appear. Time to keep tabs on the "weird" news bulletins.

seanbrockest
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Re: What-If 0011: Droppings

Postby seanbrockest » Sun Aug 17, 2014 4:10 am UTC

Damnit, you beat me here!

http://bleacherreport.com/articles/2165 ... ungs-mouth

I unfortunately have no data to add. My mouth has never been crapped in... by a bird... (the extra part at the end may or not have been unnecessary)


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